gel-like behavior in amorphous protein dense phases: …

GEL-LIKE BEHAVIOR IN AMORPHOUS PROTEIN DENSE PHASES

PHASE BEHAVIOR NEUTRON SCATTERING

AND RHEOLOGY

by

Sai Prasad Ganesh

A thesis submitted to the Faculty of the University of Delaware in partial

fulfillment of the requirements for the degree of Master of Chemical Engineering

Summer 2019

copy 2019 Sai Prasad Ganesh

All Rights Reserved



AND RHEOLOGY

by

Sai Prasad Ganesh

Approved __________________________________________________________

Abraham M Lenhoff PhD

Professor in charge of thesis on behalf of the Advisory Committee

Approved __________________________________________________________

Norman J Wagner PhD


Approved __________________________________________________________

Eric M Furst PhD

Chair of the Department of Chemical and Biomolecular Engineering

Approved __________________________________________________________

Levi T Thompson PhD

Dean of the College of Engineering

Approved __________________________________________________________

Douglas J Doren PhD

Interim Vice Provost for Graduate and Professional Education and Dean

of the Graduate College

iv

ACKNOWLEDGMENTS

The lsquobehind the scenesrsquo when performing scientific research is often left out I

was able to work in the labs of two pioneers in their respective fields my advisors

professor Abraham Lenhoff and professor Norman Wagner They made me challenge

the way I think and helping me raise my own self-expectations I am still astounded by

their boundless knowledge and ability to correctly interpret experiments despite not

being there physically to perform them Furthermore I am thankful to the Department

of Chemical and Biomolecular Engineering for giving me the opportunity to pursue my

post-graduate education

On a professional note there are several people I want to thank for helping me

develop this thesis Firstly the members of the Wagner group and Lenhoff group for

helping me go through the nitty-gritty experimental plans and details I would like to

thank Julie Hipp for helping me collect the USANS data at ORNL as well as always

being available to answer any doubts I have I also owe gratitude to Dr Stijn Koshari

Yu Fan Lee and Ohnmar Khanal for helping me collect my SANS data I also would

like to thank Dr Daniel Greene I never got the chance to meet him in person but he

was extremely helpful during our phone conversations and email correspondence Dr

Ryan Murphy was also very helpful in helping me identify how to capture gelation

behavior of my system Professor Eric Furst and professor Christopher Roberts were

also helpful in giving me their insights on my project direction I would also like to

thank the national laboratories the NIST Center for Neutron Research (NCNR) and the

Oak Ridge National Lab (ORNL) for allowing our group to utilize their crucial

v

instrumentation for these experiments I would also like to thank Dr Yun Liu and Dr

Ken Littrell for helping me work on the neutron beams at NCNR and ORNL

respectively Their help was crucial in obtaining data presented in this thesis The

National Science Foundation and the NCNR have my eternal gratitude for funding my

attendance at the CHRNS Neutron Summer School which was useful in teaching me

how to operate the beams and interpret scattering data

On a personal note I have had the privilege of meeting some of the smartest yet

kindest individuals many of whom I have made friends with The lsquofamily packrsquo Brian

Esther Max Phillip and Zach have been a great group for me to confide in and have

fun with Vijesh Jordan Mukund Yi Praneet Arnav Arjita and Eric were people who

I made great friends with Gerald is truly a great friend and an even better human being

I was moved when he brought lunch from main street restaurants and spent time with

me when I was on crutches and bed-ridden while recovering from surgery There are

several more people Irsquod like to acknowledge but doing so would prevent me from ever

reaching the introduction of the thesis But they know who they are and they have my

eternal gratitude and friendship

Finally (and most importantly) I would like to acknowledge my family

consisting of my parents and my brother They are truly what matters to me in this world

above all else I had the misfortune of requiring two complicated knee surgeries which

left me learning how to walk again on two separate occasions I am thankful to my

advisors who were patient and very understanding of the situation I am deeply indebted

to my surgeon Dr Handling for doing his very best to fix what was described as an

lsquoextremely involved and complicatedrsquo injury Mike and Jared from UD physical therapy

were two awesome guys who truly cared about my recovery and gave me pointers on

vi

how to keep fit despite me being resigned to crutches for 5 months Finally I am most

thankful to my mother who was with me for months during my complicated recovery

She helped keep me on track and on a positive note she enjoyed her first snow

A portion of this research used resources at the Spallation Neutron Source a

DOE Office of Science User Facility operated by the Oak Ridge National Laboratory

This was done through the BL-1A USANS located at the SNS Oak Ridge National

Laboratory Oak Ridge TN We acknowledge the support of the National Institute of

Standards and Technology US Department of Commerce in providing the neutron

research facilities used in this work

vii

TABLE OF CONTENTS

LIST OF TABLES x LIST OF FIGURES xi NOMENCLATURE xvi ABSTRACT xix

Chapter

1 INTRODUCTION AND BACKGROUND 1

11 Protein-Protein Interactions 3 12 Salting-Out of Proteins 4

13 Protein Phase Diagram 8 14 Gelled Protein Phases 11

15 Neutron Scattering 17 16 Gelation Rheology 20 17 Thesis Objectives and Outline 22

2 PHASE BEHAVIOR AND RHEOLOGY OF SALTED-OUT

RIBONUCLEASE A PROTEIN GELS 24

21 Introduction and Background 24

211 Oscillatory frequency sweep 27 212 Oscillation time tests 30

22 Materials and Methods 31

221 Chemicals and protein solutions 31 222 Measurement of phase diagram 32 223 Rheology data acquisition 32

23 Results and Discussion 33

231 Phase behavior of salted-out ribonuclease A 33

232 Oscillation time test 36 233 Frequency sweep 39 234 Qualifying gel behavior 43

235 Yielding behavior of ribonuclease A gel 44

24 Summary and Concluding Remarks 45

viii

3 STRUCTURE OF SALTED-OUT RIBONUCLEASE A GELS

NEUTRON SCATTERING AND MICROSCOPY 47


311 Selected empirical structural models 49

3111 Guinierrsquos law and Guinier-Porod model (GP model) 49 3112 Correlation length model 51

3113 Mass fractal flocs - power law 51

312 Microscopy and USAXS of ribonuclease A in ammonium

sulfate at pH 70 53


3211 Optical microscopy of ribonuclease A gel 57 3212 TR-SANS and static SANS 57

3213 USANS 58


331 Microscopy of ribonuclease A samples 58

332 TR-SANS of ribonuclease A gels 59

3321 Initial data set 62

3322 Behavior at longer times 65 3323 Relating mechanical properties to structural

properties 72 3324 Limitations of the TR-SANS experiment 73

333 SANS-USANS of ribonuclease A gel 76


4 CONCLUSIONS AND FUTURE WORK 82

41 Conclusions 82 42 Future Directions 83

421 Microrheology experiments 83 422 Cavitational rheology 85

423 DLS 86 424 Alternative precipitants 88 425 Change in protein-protein interactions due to gelation 88

ix

BIBLIOGRAPHY 90

Appendix

A REPRINT PERMISSION LETTERS 103

x

LIST OF TABLES

Table 120784 120783 Rheological parameters used to calculate parameters for the low-torque

limit (equation 25) and instrument inertial limit (equation 28) 41

Table 120785 120783 Times for SANS measurements along with the order of SDD The time

at the end of the run corresponds to the cumulative time at which the

scattering for the measurement ended and the new measurement began

62

Table 120785 120784 Fits of the TR-SANS data to the GP model in the low-Q region

showing the scale Rg s and m values 68

Table 120785 120785 Fits of the TR-SANS data to the GP model in the mid-Q region


xi

LIST OF FIGURES

Figure 120783 120783 Protein phase diagram for general protein and precipitant adapted from

calculations based on a short-ranged attractive Yukawa potential [51]

F S correspond to fluid and solids respectively G L correspond to gas

and liquid respectively The solid lines correspond to the F S and G L

phase separations The dashed line is the spinodal and solid circles are

the gelation line computed from mode-coupling theory [51] Reprinted

with permission from [16] 10

Figure 120783 120784 Growth of ovalbumin gel beads at 187 mgmL 22 M ammonium

sulfate 5 mM ammonium phosphate at pH 7 23 degC The gel beads grow

larger with time and correspond to a protein-rich phase while the

supernatant is protein-poor Reprinted with permission from [16] 13

Figure 120783 120785 Image showing GIPEG hydrogel formed with 86 mgml GI and 7

(wv) PEG1500 The authors contend the gel phase occurs due to an

isotropic depletion attraction Gel behavior was verified by dynamic

light scattering (DLS) Adapted from Van Driessche et al and reprinted


Figure 120783 120786 GIPEG1000 phase diagram with microscopy images on the right The

dotted lines follow the same color code as the single points indicating

the phase boundaries in PEG1500 Ceavg indicates the solubility line

PEG1000 6wv contains only 1222 crystals that are on the order of 1

mm while 7 wv contains tiny rods of P21212 crystals that are

dispersed in a gel phase Furthermore 8 wv PEG1000 yields the

presence of a kinetically-arrested gel phase Reprinted with permission

from [59] 16

Figure 120783 120787 TR-SANS of ovalbumin gel beads (40 mgmL) in 22 M ammonium

sulfate pD 70 in D2O Inset and high-Q region shows the development

of a nanocrystalline peak Reprinted with permission from [15] 19

Figure 120783 120788 Log-log plot of G(ω) and G(ω) versus angular frequency ω for a

139 (ww) solution of polystyrene in di-(2-ethylhexyl) phthalate

Measurements were made on a Rheometrics RMS 800 instrument at

25degC using a parallel plate geometry Reprinted with permission from

[42] 21

xii

Figure 120784 120783 Low-torque and instrument inertia limits shown for oscillatory

frequency sweep of hagfish gel based on data obtained from Ewoldt et

al The low-torque limit and instrument inertia effects are calculated

from equations 25 and 28 respectively Reprinted with permission

from [79] 28

Figure 120784 120784 Protein phase diagram for ribonuclease A and ammonium sulfate in

D2O and 5 mM phosphate buffer pD 70 A gel-like phase exists

beyond the first aggregation boundary The salt concentration axis is

inverted in order to represent a measure of dimensionless temperature

[16 51] 35

Figure 120784 120785 (A) Clear viscous liquid corresponding to liquid phase (B) Red arrow

points to the gel-like phase that adheres to walls of the Eppendorf tube

upon inversion 36

Figure 120784 120786 Oscillation time test for ribonuclease A gel captures the aging of the

gel which becomes more rigid over time Tan(δ) was calculated using

equation 26 The plateau G(ω) increases to ~ 1200 Pa after 3 hours

37

Figure 120784 120787 G(ω) and G(ω) of 20 mgmL fibrin gels with active factor XIII and

inactive factor XIII during the gelation process The plateau modulus is

reached after roughly 2000 seconds in fibril gels with inactive factor

XIII which is faster than ribonuclease A gelation Reprinted with

permission from [89] 38

Figure 120784 120788 At long times G ~ t04 this result is in agreement with aging behavior

seen in colloidal silica gels [6 90] 39

Figure 120784 120789 Frequency sweep of gel formed from 40 mgmL ribonuclease A and 22

M ammonium sulfate The low-torque limit was calculated from

equation 25 while the instrument inertial limit was calculated from

equation 28 The sample inertial limit is not plotted due to its negligible

value The grey area shows data susceptible to instrumentation error or

low torque limits of the rheometer Tan(δ) is not affected by instrument

limits 40

Figure 120784 120790 Frequency sweep of a 3 mgmL fibrin gel obtained from Weigandt and

Pozzo [8] The frequency sweep data appear qualitatively similar to

Figure 27 but the plateau moduli appear to be an order of magnitude

lower than for the ribonuclease A gel Reprinted with permission from

[8] 42

xiii

Figure 120784 120791 Forward and backward frequency sweep of ribonuclease A gel shows

minimal hysteresis The lsquo1rsquo denotes frequency in the forward direction

from 001 rads to 10 rads while lsquo2rsquo denotes the sweep applied in the

reverse direction 43

Figure 120785 120783 Phase behavior of ribonuclease A as a function of protein concentration

in 16 M ammonium sulfate in 5 mM phosphate buffer at pH 70 after

1 day Reprinted with permission from [16] 53

Figure 120785 120784 TEM images of ribonuclease A at 20 mgmL salted-out in 22 M

ammonium sulfate in 5 mM phosphate buffer at pH 70 from Greene

The images show the presence of largely amorphous structures on the

micron scale Reprinted with permission from [15] 55

Figure 120785 120785 USAXS data for 40 mgmL ribonuclease A salted-out in 20 M 21 M

and 22 M ammonium sulfate in pH 70 The data were fitted to the

correlation length model (equation 38) (solid lines) Reprinted with


Figure 120785 120786 Optical microscopy of ribonuclease A gel at 40 mgmL and 22 M

ammonium sulfate which shows the presence of micron-sized

aggregates 59

Figure 120785 120787 TR-SANS data for sample with 40 mgmL ribonuclease A in 22 M

ammonium sulfate at pD 70 The data show distinct patterns of

evolution with time in the low-Q (red box) and mid-Q (blue box)

regions Inset shows a magnified image of the mid-Q region 61

Figure 120785 120788 TR-SANS data of initial data set for sample with 40 mgmL

ribonuclease A in 22 M ammonium sulfate at pD 70 Power-law fits

show two distinct regimes with the low-Q region showing a slope of

21 (black) and the mid-Q region showing a slope of 14 (blue) 64

Figure 120785 120789 TR-SANS data of initial data set with 40 mgmL ribonuclease A in 22

M ammonium sulfate at pD 70 GP model fits are shown for the low-

Q (red) and mid-Q regions (blue) 65

Figure 120785 120790 TR-SANS data from scans 2-4 for sample prepared from 40 mgmL

ribonuclease A in 22 M ammonium sulfate Profiles have been shifted

vertically by a factor of 10 with the time and are referred by the time at

the end of the scan The dashed lines are fits to the data using the GP

model The vertical dashed black line indicates the different ranges of

the independent GP models used to fit the data 66

xiv

Figure 120785 120791 TR-SANS data for scans 5-7 for sample prepared from 40 mgmL


vertically by a factor of 10 and are referred by the time at the end of the

scan The dashed lines are fits to the data using the GP model The

vertical dashed black line indicates the different ranges of the

independent GP models used to fit the data 67

Figure 120785 120783120782Oscillation time test of ribonuclease A gel (figure 24) overlaid with Rg

from the low-Q and mid-Q regions Throughout experimentation the

Rg of the mid-Q region is close to a value of 15 Å which is close to the

hydrodynamic radius of ribonuclease A (14 Å) The Rg of the low-Q

region decreases from 88 Å to 75 Å (grey box) and then remains

constant throughout the rest of the data aquisition This reduction of Rg

is seen by the development of the broad peak which is indicative of gel

hardening 70

Figure 120785 120783120783Oscillation time test of ribonuclease A gel (figure 24) overlaid with

dimensionality parameter s and Porod exponent m fitted from the low-

Q and mid-Q regions 72

Figure 120785 120783120784Oscillation time test data for the ribonuclease A gelation with TR-

SANS end-of-run times overlaid for the first three scans The 13-m

SDD (low-Q region) scan times for the first three data sets (green red

and blue rectangles respectively) are overlaid The width of each

rectangle is ~300 seconds The sharp lines signify the end points of the

individual scans 75

Figure 120785 120783120785USANS data of 40 mgmL ribonuclease A in 18 M ammonium sulfate

in 5 mM sodium phosphate at pD 70 The GP model was used to fit

SANS spectra data and parameters were used to extrapolate the

predicted intensity into the USANS regime (grey box) Both the

predicted and the actual USANS data show the absence of scattering

above background 77

Figure 120785 120783120786USANS data of sample prepared from 40 mgmL ribonuclease A in 22

M ammonium sulfate The dashed line is a fit to the data using the GP

model 78

xv

Figure 120785 120783120787SANS data for sample prepared from 40 mgmL ribonuclease A in 22

M ammonium sulfate The model fits are indicated by the dashed lines

The correlation length model is used to fit data from 0001 Å -1 to 003

Å -1 while the GP model is used to fit data from 003 Å -1 to 008 Å -1

The grey box highlights the Q-range not accessible by TR-SANS due

to the use of 13 m SDD instead of 153 m with lens The blue box

highlights the sharp uptick in I(Q) which correspond to scattering from

clusters captured by the correlation length model 80

xvi

NOMENCLATURE

Cryo-TEM Cryogenic transmission electron microscopy

DLCA Diffusion limited cluster aggregation

DWS Diffusion wave spectroscopy

DLS Dynamic Light Scattering

df Fractal dimension

119863 Gap height (microm) or diffusion coefficient

EQ-SANS Extended Q-range small-angle neutron scattering

11986411198881198981 Extinction coefficient

E Youngrsquos modulus

F Fluid

119865120574 Strain constant

119865120591 Stress constant (119875119886

119873119898)

G Complex modulus (Pa)

1198922(120591) Electric field correlation function

119866 Gas

GSER Generalized Stokes Einstein relation

GI Glucose Isomerase

GP Guinier-Porod

1198921(120591) Intensity correlation function

G (ω) Loss modulus (Pa)

119866119898119894119899 Minimum modulus measurable by configuration (Pa)

G (ω) Storage modulus (Pa)

119868 Geometry inertia (Nms2)

xvii

kB Boltzmann constant (m2 kg s-2 K-1)

119871 Liquid

LLPS Liquid-Liquid Phase Separation

m Porod exponent

MPT Multiple particle tracking

Pc Critical pressure

P Fitting parameter

pI Isoelectric point

PEG Polyethylene Glycol

Q Scattering wave vector (Åminus1)

r Inner radius of needle (m)

119877119892 Radius of gyration (Å)

RLCA Rate limited cluster aggregation

s Dimensionality parameter

SDD Sample-to-detector distance (m)

SAOS Small amplitude oscillatory shear

SANS Small-angle neutron scattering

SAXS Small-Angle X-ray Scattering

119878 Solid

T Dimensionless temperature

119879119894119899119890119903119905119894119886 Inertial torque (Nm)

119879119898119886119905119890119903119894119886119897 Material torque (Nm)

119879119898119894119899 Minimum torque (Nm)

t Time (seconds)

xviii

TR-SANS Time-resolved small-angle neutron scattering

T Torque (Nm) or Temperature (K)

USALS Ultra-small-angle light scattering

USANS Ultra-small-angle neutron scattering

VSFS Vibrational sum frequency spectroscopy

1205740 Amplitude

ω Angular frequency (second-1)

ε Characteristic length (m)

ξel Characteristic length of elastic bob (m)

120585 Correlation length (Å)

Γ Decay rate

120588119890119897 Density of solution (

119896119892

1198983)

1205790 Displacement (rad)

120588 Density of solution (119892

1198981198713)

∆1199032 (120591) Mean-squared displacement (units)

δ Phase angle

γ Surface tension

Φ Volume fraction

β Zero decay function value

xix

ABSTRACT

Protein dense phases are ubiquitous in pharmaceutical downstream processing

and crystallization screens Identifying the various dense phases that exist for different

proteins and precipitants is of significant interest with several theoretical and

experimental papers published that study the various aggregation boundaries and phase

behavior mechanisms that exist due to competition between various equilibrium and

non-equilibrium driving forces A protein phase diagram with dense phases such as

dense liquids gels crystals and precipitates can be obtained upon the addition of a

precipitant or due to temperature or pH changes for a suitable set of samples Of the

dense phases discussed the primary interest lies in gels which are materials that are

composed primarily of liquids but exhibit solid-like mechanical properties due to the

individual proteins interacting and aggregating to form an interconnected structure

The goal of this project is to prepare gels of globular protein that arise from

dense phases salted-out at ambient conditions (room temperature (~23ordmC) and pH 70)

and measure their structural and mechanical properties To our knowledge there have

been studies that show gelation due to low temperature quenches in lysozyme as well

as gelation of proteins due to heating However there are very limited studies of the

physical and structural properties of salted-out protein gel phases Additionally not all

combinations of proteins and precipitants lead to the formation of a gel phase To

address these challenges we conducted a screening test involving a phase behavior

study to identify the protein the precipitant and the associated concentrations that lead

to an apparent gel phase For a combination of ribonuclease A and ammonium sulfate

in 5 mM phosphate buffer in D2O at pD 70 two distinct types of behavior are seen (1)

a clear liquid corresponding to a single-phase viscous liquid that does not show gel-like

xx

behavior (2) an opaque gel-phase that appears near the aggregation boundary of

ribonuclease A that is attributed to spinodal decomposition and that adheres to the tube

wall upon inversion

Following this different small-amplitude oscillatory shear (SAOS) bulk-

rheology experiments utilizing a cone-and-plate geometry were performed on the gel-

phase (1) an oscillation time test for 104 seconds allowing for gel formation (2) a

frequency sweep that showed a predominant storage modulus (G(ω) gt G(ω)) that

confirms the presence of a gel phase

Obtaining the structural properties of the gel is a challenge due to the opacity

Thus a combination of small-angle neutron scattering (SANS) and ultra-small-angle

neutron scattering (USANS) was used to study and characterize this system Firstly TR-

SANS (time-resolved small-angle neutron scattering) was performed for a duration of

104 seconds corresponding to the time scale used for the oscillation time test TR-SANS

show two distinct regions of structural evolution a low-Q region and a mid-Q region

that show broad-peak evolution and monomer-monomer level interactions respectively

SANS and USANS data for the gel formulation are fit utilizing shape independent

structural models that show the presence of gel network USANS data show the absence

of any structure for the single-phase liquid indicating that the gelation behavior

evidenced in rheological studies for the lsquogel phasersquo are characteristic of higher-order

structures that give rise to a system spanning gel

To conclude a combination of phase behavior studies neutron scattering and

bulk-rheology can provide an adequate framework for identifying a gel phase that exists

for salted-out proteins and obtaining its structural and mechanical properties

Implications from this study could provide insight on discovering and characterizing

xxi

more such protein-salt combinations that display a gel phase for which further research

is necessary

1

INTRODUCTION AND BACKGROUND

Nijenhuis famously commented ldquoA gel is a gel as long as one cannot prove that

it is not a gelrdquo [1] Nishinhari [2] agreed that this statement while not to be taken in a

literal sense encapsulates the struggle to accurately capture the definition of what a gel

is The literature includes numerous journal articles that review the material properties

that characterize a lsquogelrsquo [2ndash4] Almdal et al proposed that gels should behave solid-like

to humans ie a relaxation time on the order of seconds and the gel should exhibit no

flow under its own weight The authors arrived at a conclusion that a gel should satisfy

two conditions

1 A gel is a soft solid or solid-like material of two or more components of

which liquid is predominant

2 Solid-like gels are characterized by the absence of an equilibrium modulus

by a storage modulus G(ω) that exhibits a pronounced plateau extending to

times at least of the order of seconds and by a loss modulus G(ω) that is

considerably smaller than G(ω) in the plateau region [3]

The authors conceded that the upper limits of the moduli magnitudes may be unspecified

due to the variety of materials that exist in different scientific fields For example weak

biopolymers might not behave as a lsquogelrsquo to materials scientists who work with cement

2

While gel phases exist in a variety of interesting soft matter from polymers [5]

to nanoparticle systems [6] they are also exhibited in various biological molecules in

the form of protein gels where the solid component is protein and the liquid component

is an aqueous solution [4] Protein gels in vivo exist in the form of biological gels that

are hydrated and porous to allow transport of enzymes and small molecules involved in

biological processes For example blood clots which have a high water content are

made of a system-spanning protein fiber network of fibrinogen [7] Protein gels are

typically formed because of environmental triggers associated with the presence of

enzymes as well as salt pH or temperature changes which cause individual proteins to

interact and aggregate to form an interconnected structure Protein gels have inspired

scientists to create biopolymers that mimic their physiological properties for various

medical applications such as contact lenses cell and drug delivery systems and tissue

engineering [7ndash9] In addition to purely biological systems gelation is used in the food

industry among several others [10] to manufacture commonly-consumed items such

as comminuted meat fruit jellies and bread doughs [11]

Protein gelation mechanisms are often classified based on their mechanism of

self-assembly depending on protein-protein interactions chemical gelation occurs due

to the formation of permanent networks of covalent bonds while physical gelation is

driven predominantly by van der Waalsrsquo forces hydrogen bonding or hydrophobic

interactions The thermal gelation of egg-white is due to the expo sure of hydrophobic

residues which triggers physical gelation A well-known process used to gel proteins in

food systems at ambient temperature is the cold-gelation process which involves

heating and denaturing the protein [12] Hydrogels have the propensity to form

interconnected gel networks as they are formed by natural or synthetic hydrophilic

3

polymers [13] Previous research has shown that for typical globular proteins gelation

is an occurrence due to denaturation either through temperature changes [14] or through

the addition of a denaturing solvent such as n-propyl alcohol at a very high concentration

(~50) This denatures individual protein molecules and causes the production of long-

chain molecules which associate to form a system-spanning gel network [4] On the

other hand an admixture of salts such as ammonium sulfate can lead to the formation

of protein dense phases [15] without protein denaturation Dumetz et al demonstrated

that salting-out of high-density protein solutions can cause a metastable liquid-liquid

phase separation (LLPS) to a solid-fluid equilibrium because of the screening of long-

ranged electrostatic protein interactions Additionally kinetically-trapped phases such

as arrested glasses and gels may form within this liquid-liquid co-existence region [16]

The goal of this project is to discover gels of globular protein that arise from dense

phases salted-out at ambient conditions (room temperature (~23ordmC) and pH 70) and

measure their structural and mechanical properties Previous studies show gelation due

to low temperature quenches in lysozyme [17] as well as gelation of proteins due to

heating [12] However to our knowledge studies of the mechanical and structural

properties of salted-out protein gel phases at ambient conditions have been very limited

We aim to do this utilizing a combination of phase behavior studies to understand the

conditions that lead to a gelled phase neutron scattering to probe the structure of the

sample microscopy to provide a microscale structural understanding of the protein and

rheology to obtain mechanical properties and prove gelation

11 Protein-Protein Interactions

Proteins are polyampholytes meaning they can be thought of as charged

polymers containing both acidic and basic functional groups with concentration- and

4

pH-dependent conformations [18] Protein interactions comprise several different

contributions such as van der Waals interactions salt bridges electrostatic forces

hydration effects hydrogen binding hydrodynamic forces and ion binding [19 20] The

size of protein monomers lies near the lower limit of the colloidal particle size range

generally considered to be on the order of microm to nm [21] However due to their complex

nature protein molecules behave differently from simple spherical colloidal particles in

solution due to their anisotropy which is a consequence of their non-spherical shape

rough local topography and heterogeneous surface functionality [22] Furthermore it

is found that protein-protein interactions can be altered depending on the pH [23] and

the ionic strength of the solution[24] among other factors At high ionic strengths the

solubility of many globular proteins is reduced and solutions become insoluble in a

phenomenon called lsquosalting-outrsquo [25]

12 Salting-Out of Proteins

Salting-out of proteins lead to the presence of dense phases such as arrested gels

glasses precipitates and LLPSs [19] Specifically it was found that the anions and

cations that form the salt were able to induce this effect uniquely [26] and the dense

phases and salting-out ability exhibited by a protein could potentially differ based on

the salt-added [24] The salting-out ability of anions was determined by Hofmeister in

1888 [27] by conducting precipitation measurements on ovalbumin an acidic protein

(pI ~46) The order of this series is 11987811987442minus gt 1198671198751198744

2minus gt 119874119860119888minus gt 119888119894119905minus gt 119874119867minus gt 119862119897minus gt 119861119903minus

gt 1198621198971198743minus gt 1198611198654

minus gt 119878119862119873minus gt 1198751198656minus while for cations the salting-out ability varies as 119873(1198621198673)

4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

Several hypotheses have been postulated for the specific ion effects that give

rise to the Hofmeister series including water structuring [28] dispersion forces between

ions [29] and the impact of dissolved gases [30] Hofmeister initially proposed that the

effect was due to the ions that had water-withdrawing abilities [31] and these ions were

initially classified based on their ability to disrupt water structuring (chaotropes) or

promote it (kosmotropes) Kosmotropes are ions that have high charge density which

results in structuring of water around themselves and they are seen experimentally to

be stronger salting-out agents [32] Chaotropes are ions that have low charge density

and disrupt the hydrogen-bonding structure of water and they are found to be weak

salting-out agents Collins [33] considered that the differences in the behavior of

kosmotropes and chaotropes is due to their differences in charge density and ion size

Ions are treated as spheres with the charge concentrated at the center and kosmotropes

bind strongly to water due to their smaller size Salting-out appears to result from

interfacial effects of strongly-hydrated anions near the protein surface Strongly-

hydrated cations on the other hand are thought to increase protein solubility by

interacting with polar surface groups of the protein Strongly-hydrated anions such as

sulfates compete for water molecules in the second hydration layer of the protein This

makes water unable to effectively reach the first hydration layer to solvate the protein

surface rendering the bulk solution a weaker solvent [33] On average 57 of the

surface of a soluble globular protein is non-polar [34] and for these regions the nearby

strongly-hydrated anions raise the surface tension of the solvent [33] This in turn

encourages minimization of these non-polar surface regions and therefore reduces the

accessible surface area causing a screening effect whereby protein-protein attractions

are favored and formed resulting in potential aggregation

6

Despite numerous studies that support the individual ionrsquos abilities to act as

kosmotropes and chaotropes the mechanistic basis for the Hofmeister series is still

debated [35 36] Zhang and Cremer [35] cast doubt on whether water structure-making

and -breaking are the basis for the Hofmeister series and the series is due to direct ion-

protein interactions They cited evidence from dynamic measurements of water

molecules using mid-infrared pump-probe spectroscopy which showed that the

rotational dynamics of water molecules outside the first hydration shell of the ion is not

influenced by both kosmotropic and chaotropic ions and that the presence of these ions

does not disrupt the hydrogen-bond network in bulk water [37] Furthermore they cited

a study on the thermodynamic analysis of water structure in the presence of 17 protein

stabilizers and denaturants that suggested that a solutersquos impact on water structure had

no effect on protein stability [38] The third source of evidence they use was a study

that applied vibrational sum frequency spectroscopy (VSFS) on the airwater interface

of an octadecylamine monolayer spread on various sodium salt solutions VSFS is

sensitive to alkyl chain conformation of the monolayer and the technique captures the

propensity of a given anionrsquos ability to induce gauche effects onto the monolayer at

constant temperature and pressure The authors collected VSFS data at the monolayers

spread on D2O subphases and found that the anionrsquos ability to disorder the alkyl chain

followed the Hofmeister series However when they collected interfacial water data on

the airmonolayerwater interface they found a significant deviation from the

Hofmeister series in the way the anions affected water structure This discrepancy the

authors inferred argues against the idea that the Hofmeister effect is due to the ionrsquos

ability to lsquomakersquo or lsquobreakrsquo water structure [35 39] These papers led the authors to

7

discount the effect of ions on bulk water properties in a counter to Collinss argument

and to state that ion-protein interactions are the main cause for the order of the series

The original Hofmeister series measurements were conducted on ovalbumin (pI

~46) an acidic protein For proteins with isoelectric point (pI) greater than the pH

tested the inverse Hofmeister series is followed [40] Small angle x-ray scattering

(SAXS) studies by Finet et al on lysozyme α-crystallin γ-crystallin and ATCase and

brome mosaic virus revealed

1 The addition of salt screens electrostatic interactions between protein

molecules while inducing a short-ranged attractive potential that becomes

stronger with decreasing temperature

2 Macromolecules studied at pH lower than the pI follow the reverse

Hofmeister series while studies at pH values higher than the pI follow the

Hofmeister series

3 Individual ion effects are much less pronounced and sometimes disappears

at pH values near the pI

4 Salting-out ability is affected by the ion valency at 50 mM MgCl2 had the

same effect as NaCl at 10 times the concentration (500 mM)

5 Larger proteins exhibited weaker monovalent salt induced attractions [41]

Furthermore the characteristics of dense phases formed by salting-out proteins

depend strongly on solution conditions In the work of Greene et al nanocrystalline

regions of ovalbumin monomers precipitated with ammonium sulfate were seen only

for salt concentrations between 24 M and 28 M [42] Nanocrystallinity was also

captured using SAXS for ribonuclease A precipitated with ammonium sulfate at pH 40

However such crystallinity was not seen at pH 70 for otherwise the same solution

8

conditions [15] reflecting the customary susceptibility of protein solution properties to

changes in pH [43]

With these findings it is apparent that the molecular understanding of salting-

out of proteins is still under debate Additionally it is important to understand that

salting-out involves a complex interplay among several factors that affect solution

conditions solution pH protein type precipitant type pI of protein All these need to

be considered in the context of arriving at a dense protein phase Moreover the dense-

phase behavior exhibited in salting-out are specific to each solution condition and not

necessary reproducible among different combinations of proteins precipitants and salts

[15 16]

Salting-out does not severely affect the properties of RNA DNA and proteins

which has resulted in the technique being used routinely for isolation of proteins [44]

and in industries such as the pharmaceutical industry [45] Salting-out of proteins leads

to insolubilization [25] and has been used for low-value product purification due to its

cost-efficiency [46] Furthermore the high salt concentrations that lead to

insolubilization occur during hydrophobic interaction chromatography (HIC) or

lsquosalting-outrsquo chromatography [47 48] HIC is typically used for purifying antibodies

recombinant proteins and plasmid DNA Given the widespread use of the principle of

salting-out of proteins finding a gel-phase and understanding both the structural and the

mechanical properties would be of interest from both a fundamental research point of

view as well as from an industrial perspective

13 Protein Phase Diagram

The protein phase diagram provides one perspective on the effect of a precipitant on a

protein solution The structure of the phase diagram for proteins can be interpreted

9

within the framework of the theoretical phase diagram for colloids interacting via short-

ranged attraction Numerous studies have treated proteins as spheres within an implicit

solvent with these spheres interacting through an isotropic pair potential [22] with

potentials such as the square-well [49] modified Lennard-Jones [50] Yukawa [51]

adhesive hard sphere [52] and DLVO [53] being used However given the anisotropy

of individual protein molecules these models are a simplistic representation of actual

interactions Phase boundaries are experimentally broader than described by isotropic

models [54] Thus more elaborate models such as those with highly-attractive patches

on the spheres have been proposed to seek a more accurate depiction of protein phase

diagrams [22 54ndash56] Nevertheless within the context of this thesis we explain the

phase diagram of proteins using an isotropic Yukawa potential (Figure 11) [16 51]

The phase behavior exhibited by proteins depends on solution conditions Phase

separation is typically induced by adding a precipitant or by inducing a temperature or

a pH change which in turn alters the strength of protein-protein attractions Here the

dimensionless temperature T = kbTε and Φ is the volume fraction Since a decrease in

temperature gives rise to increased colloidal attraction in the theoretical model a

decrease in T is treated as corresponding to an increase in salt concentration for the

case of salting-out The gelation line computed using mode coupling theory (MCT) [51]

represents a dynamically-arrested state The intersection of the binodal and the gelation

line yields a gas-liquid phase separation (protein-poor supernatant and protein-rich

aggregates) The region of the gelation line above the binodal corresponds to a phase-

separated liquid that yields a liquid-liquid phase separation (LLPS) into protein-rich and

protein-poor phases At T values below the binodal LLPS does not occur and thus the

10

gel can be viewed as a frustrated liquid with the dense-phase concentration being the

gelation line intersection with the supernatant-gel line [16]

Figure 120783 120783

Protein phase diagram for general protein and precipitant adapted

from calculations based on a short-ranged attractive Yukawa

potential [51] F S correspond to fluid and solids respectively G

L correspond to gas and liquid respectively The solid lines

correspond to the F S and G L phase separations The dashed line

is the spinodal and solid circles are the gelation line computed

from mode-coupling theory [51] Reprinted with permission from

[16]

11

The work of Dumetz et al [16 23 57] mapped out phase boundaries as a function

of temperature and pH and utilized several different precipitants The phase boundaries

qualitatively resembled each other and an increase in salt concentration was found to be

equivalent to the effect of a temperature drop for a given protein concentrations This

shows that the origin of physical attraction does not determine the form of the phase

diagram and that protein solutions follow the general qualitative trend of the colloidal

phase diagram Likewise the co-existence curve for protein salting-out follows a similar

trend with lower salt concentrations required at higher protein concentration to arrive

at the phase transition [19]

14 Gelled Protein Phases

The protein phase diagram for a globular protein modeled as a simple attractive

colloid (hard sphere with an isotropic attractive interaction) displays the presence of an

attractive spinodal gel (Figure 12) [56] Schurtenberger et al [17 58] explored the

phase behavior of concentrated lysozyme solutions as a function of volume fraction and

quench temperature Quenching to 15degC on the phase diagram revealed that this

temperature corresponded to an arrested tie line and solutions quenched to this final

temperature displayed a classic spinodal decomposition including the formation of a

transient bicontinuous network with protein-rich and protein-poor regions Utilizing

ultra-small-angle light scattering (USALS) that covered a Q-range of 01 μm-1 to 2 μm-

1 coupled with video microscopy performed in phase-contrast mode the authors were

able to obtain a characteristic length ε based on the intensity of the USALS peak They

found that ε scaled with time t as t13 [17 58] For temperatures below 15 ordmC an

lsquoarrested spinodal gelrsquo was formed where the characteristic length is independent of

12

time Frequency sweep confirmed the gel-identity for a protein solution with volume

fraction Φ = 015 [17] The sample was pre-heated to exceed the liquid-liquid

coexistence temperature in order to form a single-phase solution Subsequently

temperature quenching gave rise to spinodal decomposition leading to a quasi-

equilibrium when two distinct phases were formed with only the lower protein-dense

phase used for rheological experiments [17]

Although the results above provide examples of how protein gels are formed and

can be characterized there is not a definitive way to identify solution conditions that

will yield a protein gel The anisotropy of protein molecular shape and interactions

coupled with the sensitivity of solution behavior to different buffer and salt

formulations makes finding the gelation curve challenging In the context of salting-

out the phase behavior and location of the gelation line have been measured in some

cases [15 16] It was also suggested in this work that the trend in protein concentration

in the dense phase as a function of salt concentration can aid differentiation between

LLPS and gelation For the former the protein concentration in the dense phase is

expected to increase with increasing salt concentration while it is expected to decrease

along the gelation line Dumetz et al [16] reported a gel phase for lysozyme between

08 M and 16 M sodium chloride at pH 70 but did not report the macroscopic

appearance of the protein solution For ovalbumin gelation was seen as gel beads that

grew with time (Figure 12) [16]

Therefore while the protein phase diagram can help point to a gel phase it is an

idealized representation of protein solution behavior and primarily qualitative

information is readily obtained from it in the absence of extensive phase behavior

measurements Indeed it is not possible to conclude in the absence of such

13

measurements whether a gelled phase can be formed at all from a given protein and

precipitant Furthermore the goal of this thesis is to find a system-spanning gelled

phase where the entire solution behaves like a gel as opposed to a phase-separated gel

such as the ovalbumin gel beads shown in Figure 12


sulfate 5 mM ammonium phosphate at pH 7 23 degC The gel beads

grow larger with time and correspond to a protein-rich phase while

the supernatant is protein-poor Reprinted with permission from

[16]

14

Van Driessche et al [59] obtained a gel from formulations glucose isomerase

(GI) with PEG1000 at ambient conditions (Figure 14) PEG is non-denaturating [60]

and has a wider crystallization range than salts [19 61] Crystals formed within the gel

in different space groups depending on the concentration of the protein and precipitant

(Figure 15) The crystals that formed were found to be linked to the gradual dissolution

of the gel phase At higher concentrations of PEG1000 (8 wv) and for protein

concentrations of 20 mgmL to 70 mgmL only gel phases were seen without crystals

which the authors attributed to an isotropic depletion attraction that yields a dynamically

arrested gel phase which was verified by dynamic light scattering (DLS) [59]

15


(wv) PEG1500 The authors contend the gel phase occurs due to

an isotropic depletion attraction Gel behavior was verified by

dynamic light scattering (DLS) Adapted from Van Driessche et al

and reprinted with permission from [59]

16

Figure 120783 120786 GIPEG1000 phase diagram with microscopy images on the right

The dotted lines follow the same color code as the single points

indicating the phase boundaries in PEG1500 Ceavg indicates the

solubility line PEG1000 6wv contains only 1222 crystals that

are on the order of 1 mm while 7 wv contains tiny rods of P21212

crystals that are dispersed in a gel phase Furthermore 8 wv

PEG1000 yields the presence of a kinetically-arrested gel phase

Reprinted with permission from [59]

17

15 Neutron Scattering

Small-angle neutron scattering is a powerful technique that can non-invasively

probe the internal structure of a salted-out protein sample at ambient conditions to yield

structural information [42] The use of a combination of small angle neutron scattering

(SANS) and ultra-small-angle neutron scattering (USANS) by Greene et al showed a

novel and unexpected result whereby presumed amorphous protein dense of ovalbumin

are found to be hierarchically structured with a regular nanocrystal building block that

self-assembles into a structured gel that is microscopically amorphous [42]

Additionally the work of Weigandt et al studied fibrin hydrogel networks in D2O at

concentrations mirroring blood clots in vivo by utilizing a combination of SANS

USANS and bulk rheology For a given sample the complementary length scales

probed by the techniques allowed the authors to obtain information of the internal

structures and the radial dimensions of fibers using SANS They also characterized

larger features such as the fractal dimension of the network (df) and the correlation

length (ξ) over which the fractal structure persists [13] Furthermore studies on heat-set

gelation of proteins using SAXS [62] and SANS [63] have yielded structural features

such as df ξ and lsquobuilding blockrsquo sizes of the gels [64]

Time-resolved small-angle neutron scattering (TR-SANS) is a useful technique

to study kinetic pathways and structural changes in salted-out proteins [15] Dumetz et

al showed the existence of ovalbumin gel-beads (Figure 12) that grew with time [16]

The existence of this gel bead was seen between the first and second aggregation

boundaries of ovalbumin in D2O [42] Greene conducted TR-SANS on ovalbumin gel

beads which showed the formation of nanocrystals that appeared ~30 minutes after

18

experimentation (Figure 15) [15] Interestingly nucleation of ovalbumin gel beads

(Figure 12) is seen at 20 minutes with the appearance of tiny lsquospecklesrsquo that go on to

form gel beads with time Thus a combination of SANS USANS and TR-SANS can

provide meaningful structural information on the nanoscale

19


sulfate pD 70 in D2O Inset and high-Q region shows the

development of a nanocrystalline peak Reprinted with permission

from [15]

20

16 Gelation Rheology

Complex fluids that exhibit yield flow behavior can be divided into two types

viscoelastic solids and gels Below the yield stress these fluids deform elastically while

above the yield stress liquid flow is seen The difference therein lies in the flow above

the yield stress gels behave like viscoelastic liquids while viscoelastic solids behave

like viscous fluids Ideally gels exhibit a predominant plateau in the frequency sweep

regime with G(ω) exceeds G(ω) while viscoelastic liquids appear to yield in the

frequency range where G(ω) exceeds G(ω) and display an apparent yield stress or

critical stress [65] Almdal et al contended that a 139 (ww) solution of polystyrene

in di(2-ethylhexyl) phthalate behaves like a gel (Figure 16) since (1) the dispersed

phase is solid while the solvent is liquid (2) G(ω) exhibits a plateau extending to

frequencies lower than 1 rads which corresponds to times longer than 1 second and

G(ω) is larger than G(ω) in this region and therefore behaves solid-like in lsquoreal timersquo

[3]

21



Measurements were made on a Rheometrics RMS 800 instrument

at 25degC using a parallel plate geometry Reprinted with permission

from [42]

Bulk rheological studies are time-intensive and require a large amount of material

in order to conduct tests [66] Due to the limitations of using expensive globular

proteins a screening test that involves placing protein solutions upside down in a test

tube [67] in order to screen protein samples can be used However the inversion test

does not confirm gel behavior but can indicate solid-like behavior in the solution and

22

can be implemented as an easy and reliable screening test prior to bulk rheological

experiments

17 Thesis Objectives and Outline

The rheological study of a system spanning salted-out gelled protein phase at

ambient conditions has to the knowledge of the author not been investigated before

This thesis shows the formation of an opaque gel-like material that corresponds to the

aggregation boundary of ribonuclease A precipitated by using ammonium sulfate in a

deuterated buffer As such this study shows rheological evidence of the gelation along

with SANSTR-SANSUSANS data that captures the kinetics and structure of the

system spanning gel

Small amplitude oscillatory shear (SAOS) rheology is used to characterize the

mechanical properties of the protein gel Given that globular proteins do not have the

propensity to naturally aggregate to form a system spanning gel the gelled sample

obtained behaves like a weak physical gel that irreversibly ages This feature occurs in

certain colloidal gel systems and has been seen for laponite suspensions with salt (NaCl)

[68] The evolving or aging of the gel was captured using an oscillation time sweep at a

strain that was within the linear viscoelastic region of the gel A frequency sweep is then

performed to then capture the gelation of the system

The sample preparation the phase behavior methodology and the rheological

protocol are presented in chapter 2 This is necessary to screen for the protein gel phase

and prove gel behavior of the sample and obtain associated mechanical properties In

Chapter 3 the structural properties of the ribonuclease A protein gel are analyzed

Optical microscopy images of the gel sample are complemented with SANS and

USANS measurements of the gelled protein system Additionally time-resolved small-

23

angle neutron scattering (TR-SANS) data was collected for freshly prepared

ribonuclease A gel phase and shows corresponding structural development on the

nanoscale Finally conclusions and future directions are included in chapter 4

24

PHASE BEHAVIOR AND RHEOLOGY OF SALTED-OUT RIBONUCLEASE

A PROTEIN GELS

21 Introduction and Background

Gelation causes solid-like behavior to occur for a variety of complex fluids and

typically arises when particles aggregate to form mesoscopic clusters and networks

often as a result of irreversible aggregation that is a result of the formation of physical

andor chemical bonds [10] Several mechanisms and models have been postulated for

gelation such as diffusion-limited cluster aggregation (DLCA) [69] kinetic arrest

jamming [70] arrested spinodal decomposition [58] and percolation [71] Lu et al

showed that gelation of a colloidal system composed of polymethylmethacrylate

spheres of radius 560 nm occurs due to an equilibrium phase separation [10] Spinodal

decomposition is a non-equilibrium de-mixing process in which a homogeneous fluid

instantaneously de-mixes when quenched into a thermodynamically-unstable

coexistence region This can result in a bi-continuous structure with domains that grow

with time [72] However in systems in which the kinetics of formation of one or both

phases are quenched the spinodal decomposition can be arrested with vitrification of

the bi-continuous structure over observable time frames [72 73] A similar mechanism

was seen in the work of Schurtenberger et al on temperature-quenched lysozyme gels

where an initial spinodal decomposition of lysozyme gels is arrested once the dense

phase enters an attractive glassy state [17 58]

A possible explanation for different gelation mechanisms could be the nature of

the attraction which could dictate specific pathways For example adhesive hard

spheres gel before phase transitions occur [74] while in depletion systems gelation

arises due to arrested spinodal decompositions [10 58 59]

25

While these mechanisms can help identify gel formation mechanisms we are

primarily interested in identifying a protein-precipitant combination that demonstrates

system-spanning gel behavior As previously mentioned gel-like behavior is screened

by using an lsquoinversion-testrsquo If a salted-out protein solution displays strong adhesion to

an Eppendorf tube upon inversion it is selected for bulk-rheological experimentation to

confirm gelation and obtain mechanical properties

To identify gelation SAOS rheology was performed during the phase transition

and aging In SAOS rheology the gel retains its rigid network structure and oscillates

with small structural fluctuations leading to the elastic stress showing a linear

viscoelastic response [75] This means that the gel maintains its structure without

appreciable structural changes and the observed linear behavior is a consequence of the

rigid network structure [75]

In a strain-controlled rheometer the sample is subjected to applied sinusoidal

strain

120574 = 1205740 119904119894119899 120596119905 (2 1)

with the strain represented as a function of the amplitude 1205740 angular frequency 120596 and

time t The linear response of the material to the applied strain takes the form of a

sinusoidal shear stress that also varies with time but lags the applied strain by δ and is

represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26

where 120575 is the phase angle The stress response based on the applied strain can quantify

material behavior and this response can be decomposed into strain and stress

amplitudes namely the loss modulus G(ω) and the storage modulus G(ω) which

also vary sinusoidally G(ω) corresponds to viscous dissipation while G(ω) is the

elastic response to deformation The stress response can be decomposed into

contributions from G(ω) and G(ω) [76] in the form of

120590 = 119866prime(120596) 119904119894119899 120596119905 + 119866primeprime(120596) 119888119900119904 120596119905 (2 3)

For stress-controlled SAOS rheology which is used in this thesis the sample is

loaded onto a Peltier plate and the upper plate oscillates back and forth at a given stress

amplitude and frequency Thus an oscillating torque is applied via the upper plate from

which the angular displacement is measured and resulting strain can be calculated The

ratio of the applied stress to the measured strain gives the complex modulus (G) which

is a measure of material stiffness or deformation resistance For a purely elastic material

the maximum stress occurs at the maximum strain thus the applied stress and measured

strain are in phase For a purely viscous material the maximum stress and strain are out

of phase by 120587

2 radians The phase angle of a viscoelastic medium is between 0 and

120587

2 [77]

with 120587

4 representing a characteristic boundary between a solid-like and a liquid-like

material which could signify a sol-gel transition or network formationbreakdown

Since the solid contribution arises when the stress and strain are in-phase and the liquid

contribution arises when they are out-of-phase the moduli may be represented with the

viscous dissipation 119866primeprime(120596) = 119866lowast 119904119894119899 120575 and the solid-like response 119866prime(120596) = 119866lowast cos δ

We can then arrive at a relation relationship among δ G G(ω) and G(ω)

27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)

where tan(δ) is the loss tangent If tan(δ) is greater than 1 liquid behavior dominates

and if tan(δ) is less than one the material behaves more like a solid [77] Tan(δ) is an

important parameter that reflects bond relaxation in gels and has been used to

characterize complex gels [78]

211 Oscillatory frequency sweep

An oscillatory frequency sweep is a necessary test to confirm that a material has

the properties of a gel [23] In SAOS rheology the time dependence can be evaluated

by varying the frequency of the applied stress (or strain) Higher frequencies correspond

to shorter time scales while longer time scales are probed by lower frequencies For a

gel-like material G(ω) gt G(ω) and the moduli are parallel or close to parallel as a

function of frequency which results in a value of δ that is close to constant with a value

between 0deg and 45deg [77] While a frequency sweep can confirm the gel behavior on a

variety of colloidal gels [6] biomaterials are softer and instrumentational errors can

significantly affect data collected The plateau value of G(ω) can vary from 01 Pa for

hagfish gels [79] to G(ω) ~ 100 Pa for 3 mgmL fibrin gels [8] and rennet-induced milk

gelation [78] to G(ω) ~ 104 Pa for fibrin gels that have cofactor factor XIII activity [8]

Given that biomaterials can be weak rheological experiments need to be carefully

implemented and interpreted to rule out non-material effects Typically good

rheological measurements show data along with corresponding experimental and

instrumentational limits For frequency sweeps the limitations are (1) low-torque

28

effects (2) instrument inertia effects (3) sample inertia effects and when these

calculations (Figure 21) are overlaid it validates the rheological data and can flag

deceptive features that could be falsely attributed to the sample tested [80]


frequency sweep of hagfish gel based on data obtained from Ewoldt

et al The low-torque limit and instrument inertia effects are

calculated from equations 25 and 28 respectively Reprinted with

permission from [79]

For a frequency sweep experiment the low-torque limit can be calculated based

on the minimum measurable viscoelastic moduli

119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29

where Gmin refers to either G(ω) or G(ω) 119865120591 is the stress constant 1205740 is the amplitude

used for the frequency sweep and Tmin is the minimum torque an instrument can

measure as specified by the manufacturer In this thesis we utilize a cone-and-plate

geometry and thus 119865120591 = 3(2πR3) where R is the cone radius

For oscillatory shear the material torque Tmaterial should exceed the instrument-

inertia torque which is a function of ω displacement 1205790 and instrument inertia I

119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)

By substituting in their dependent variables

1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740

1205790 is the strain constant 119865120574 By substituting this into equation 27 we can arrive

at a relation for the minimum measurable moduli for which no inertial effects exist

119866 gt 119868119865120591

1198651205741205962

(2 8)

These effects are seen in higher-frequency measurements given the quadratic relation

between 120596 and Gmin [80]

30

212 Oscillation time tests

Samples undergoing rheological tests may undergo micro- or macro-structural

changes with time An oscillatory time sweep can provide information on changes in

mechanical properties during structural evolution or aging By selecting an amplitude

within the linear viscoelastic region along with a corresponding frequency at a

temperature of interest mechanical properties of the sample can be recorded as a

function of time [81] Given that gelation may arise as a result of phase equilibrium or

arrested spinodal decompositions where bicontinuous networks are formed samples

may display gelation due to aging This has been seen in different complex fluids such

as laponite gels [68] and thermoreversible organogels [82] Weigandt and Pozzo [8]

showed that fibrin gels display time-dependent gelation owing to activation by the

trigger enzyme thrombin In milk gelation can occur due to several factors such as

acidification heating or addition of the enzyme rennet [78] Oscillation time tests have

been used to show the dynamic nature of milk gelation upon the addition of rennet [78]

Heat-induced β-lactoglobulin gels also display aging behavior including as a function

of pH temperature and concentration despite different stiffness values shown by gels

as functions of these variables the aging process proceeded very similarly after 20

minutes with G increasing constantly [83] Therefore the incorporation of an

oscillation time test and a frequency sweep is necessary to capture aging of salted-out

proteins and proving gelation respectively

31

22 Materials and Methods

221 Chemicals and protein solutions

Chromatographically-purified lyophilized ribonuclease A from bovine

pancreas (LS003433) was purchased from Worthington Biochemical Corporation

Lakewood NJ) Ribonuclease A is a single-domain protein that catalyzes the cleavage

of single-stranded RNA It contains 124 amino acid residues and has a molecular weight

(MW) of 137 kDa It is used as a model protein for protein folding due its small size

stability and native structure [84] Ribonuclease A has a pI of 96 and a charge of +4e

at pH 70 At pH values between 65 and 80 it shows attractive interactions at low ionic

strength and repulsive interactions at high ionic strength [40]

Monobasic sodium phosphate (S 369-500) sodium hydroxide (SS410-4) and

ammonium sulfate (A702-3) were purchased from Fisher Scientific (Pittsburgh PA)

Deuterium oxide (DLM-6-PK) was purchased from Cambridge Isotope Laboratories

Inc (Tewksbury MA)

Solutions were prepared by dissolving ribonuclease A in 5 mM sodium

phosphate buffer at pD 70 and concentrated using a 3 kDa MWCO Amicon

ultracentrifugal filter from Millipore Concentrated samples were diluted with buffer

and re-concentrated three times before filtration using a 022 microm filter Solution

concentrations were determined using UV absorbance (Thermo Scientific Nanodrop

2000) at 280 nm based on an extinction coefficient 11986411198881198981 = 714 [15 16 85] Ten microL of

protein solution were diluted by a factor of 10 using the buffer for concentration

measurements in a vial The final protein solution concentrations were calculated to be

in the range of 180-225 mgml

32

A concentrated stock solution of ammonium sulfate at 315 M was prepared and

adjusted to pD 70 in 5 mM sodium phosphate buffer before filtration through a 022

microm filter and lyophilized once prior to experimentation The hydrogen-deuterium

exchange was calculated to be 40

222 Measurement of phase diagram

The phase diagram for ribonuclease A in D2O was determined by means of

visual inspection and microscopy Samples of volume 60 microL were prepared in an

Eppendorf tube by mixing concentrated salt solution buffer and concentrated

ribonuclease A solution in order Solutions were then handled carefully to prevent

bubble formation and were mixed to ensure uniform solution concentration Samples

were left at room temperature and visually inspected over the course of 24 hours to

determine if they displayed gel-like behavior Gel-like behavior was noted by strong

adhesion to the Eppendorf tube upon inversion

223 Rheology data acquisition

Rheological data were obtained using a stress-controlled DHR-3 rheometer (TA

Instruments) controlled by TRIOS software using a cone-and-plate tool (diameter 40

mm 0035 rad) with a gap height of 56 microm

The sample was prepared in a glass vial by adding in order calculated amounts

of salt solution buffer and protein totaling 1 ml of solution Each solution was mixed

carefully to prevent localized salt or protein gradients and a vortex mixer was used at

very low shear rates for 5 seconds to ensure good mixing The solution was poured

directly onto the Peltier plate before it gelled To avoid sample drying a low-viscosity

mineral oil was applied using a pipette on the air-liquid interface in order to isolate the

33

sample following the protocol of Vaynberg et al [86] The sample was surrounded by

the oil in the form of a pool which was then pipetted and cleaned away using Kimberly-

Clark Kimtech Science wipes leaving a thin layer of oil on the interface Care was taken

not to allow oil onto the cone-and-plate geometry itself which may affect inertial

rotation calculations A solvent trap was applied to prevent further evaporation Prior

inversion tests revealed that the solution becomes more rigid over time The samples

were subjected to 01 strain oscillations at a frequency of 628 rads for a calculated

amount of time in order to ensure that gel formation had reached completion Following

this the linear moduli of the solution (G(ω) and G(ω)) were measured from a

frequency sweep (001 rads to 10 rads) at a fixed strain of 01

23 Results and Discussion

231 Phase behavior of salted-out ribonuclease A

The phase diagram for ribonuclease A in 5 mM sodium phosphate pD 70 and

deuterated ammonium sulfate in D2O is shown in Figure 22 The aggregation boundary

appears qualitatively similar to that previously reported [15 16] with the salt

concentration decreasing with increasing protein concentration The error bars are

calculated from differences in protein concentration from the absorbance

measurements The protein concentration of the final formulation was varied between

20 mgmL and 100 mgmL with the goal of finding a gel-like material which was

assessed by an inversion test (Figure 23) Stronger gel-like behavior was noted at salt

concentrations slightly above the aggregation boundary

Gel-like behavior was also correlated with the appearance of a white opaque

solution that was interpreted as a possible spinodal decomposition by Dumetz et al in a

34

similar ribonuclease A preparation in H2O containing ammonium sulfate in 5 mM

sodium phosphate buffer at pH 70 [16] At low volume fraction Φ increasing the

interparticle attraction (equivalent to increasing salt concentrations) can lead to floc

formation When the solution components are not density matched flocs can either

sediment or cream leading to gel formation at low particle concentrations [21] that

exhibit delayed settling and are shear sensitive [87] This form of gelation which arises

from phase separation has been previously seen for colloid-polymer mixtures and is

termed as lsquodynamic percolationrsquo [21 88]

Despite gel-like behavior over a range of solution compositions in Figure 22

for bulk rheological characterization only gels prepared at 40 mgmL and 22 M

ammonium sulfate were selected since such gels displayed stronger gel-like behavior

than 20 mgmL and were readily prepared at a relatively low protein concentration

35



beyond the first aggregation boundary The salt concentration axis

is inverted in order to represent a measure of dimensionless

temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)

Protein concentration (mgmL)

36

Figure 120784 120785 (A) Clear viscous liquid corresponding to liquid phase (B) Red

arrow points to the gel-like phase that adheres to walls of the

Eppendorf tube upon inversion

232 Oscillation time test

Initial tests of the ribonuclease A gel-like phase revealed that the gel properties

developed gradually and not instantaneously Rheological measurements showed that

any pre-shear or conditioning irreversibly broke down the gel A stress-controlled

rheometer with a 40 mm cone-and-plate geometry (2deg cone angle) was used to apply

small amplitude oscillations of 01 strain at a frequency of 1 Hz (628 rads) Thus

aging behavior was captured by an oscillation time test (Figure 24) which showed the

emergence of a plateau where G(ω) gt G(ω) Initially tan(δ) decreases from 070 to

020 after an hour before attaining a value of 016 corresponding to the plateau G(ω)

after 3 hours (104 seconds) Ribonuclease A gelation is slower than that of fibrin gels

which display a G(ω) modulus within 2000 seconds (Figure 35) [8] but faster than

rennet-induced milk gels which take ~2x104 seconds [78]

The oscillation time test data show that the behavior is qualitatively similar to

that of fibrin gels (Figure 25) seen by Weigandt and Pozzo [89] The plateau G(ω) for

B A

37

both gels (ribonuclease A and 20 mgmL fibrin with inactive factor XIII) is roughly the

same [8] Ribonuclease A gel is stiffer than other biomaterials such as low-concentration

fibrin and β-lactoglobulin heat-set gels [83] On the other hand the plateau G(ω) is

roughly an order of magnitude lower than that of temperature-quenched lysozyme gels

formulated at Φ = 015 [17] and that of fibrin gels with active factor XIII [89]

Figure 120784 120786 Oscillation time test for ribonuclease A gel captures the aging of

the gel which becomes more rigid over time Tan(δ) was calculated

using equation 26 The plateau G(ω) increases to ~ 1200 Pa after

3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Oscillation time test of ribonuclease A

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38

At long time behavior we find that G ~ t04 (Figure 26) a characteristic of

colloidal silica gel aging which shows this scaling behavior independent of Φ [6 90]

However given that rheological parameters are only obtained for one sample in the

protein phase diagram we are unable to confirm if this relationship is independent of Φ

for the ribonuclease A gel

Figure 120784 120787 G(ω) and G(ω) of 20 mgmL fibrin gels with active factor XIII

and inactive factor XIII during the gelation process The plateau

modulus is reached after roughly 2000 seconds in fibril gels with

inactive factor XIII which is faster than ribonuclease A gelation


39

233 Frequency sweep

Following the oscillation time test a frequency sweep was conducted for the

ribonuclease A gel from 001 rads to 10 rads (Figure 27) For the given amplitude

strain (01) the frequency range was chosen to avoid inertial effects at higher

frequencies Sample inertial effects were calculated but deemed negligible for the

sample tested and is not shown in the figure

05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))

log10(t) (log10(seconds))

04

Figure 120784 120788 At long times G ~ t04 this result is in agreement with aging

behavior seen in colloidal silica gels [6 90]

40

Figure 120784 120789 Frequency sweep of gel formed from 40 mgmL ribonuclease A and

22 M ammonium sulfate The low-torque limit was calculated from


equation 28 The sample inertial limit is not plotted due to its

negligible value The grey area shows data susceptible to

instrumentation error or low torque limits of the rheometer Tan(δ)

is not affected by instrument limits

10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa

Instrument Inertia Limit

G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)

Angular frequency (w) (rads)

g = 01

Frequency sweep of ribonuclease A

41

Correspondingly equations 25 and 28 were used to calculate the low-torque

limit modul and the instrument inertial limit respectively using the parameter values

that are provided in table 21 119865120591 119865120574 I and D were obtained using Trios software [91]

for the particular geometry used 1205740 was determined from the experimental amplitude

to perform the frequency measurement while Tmin was based on the manufacturerrsquos

specifications

Weigandt and Pozzo showed that fibrin forms gels in dilute conditions spanning

2ndash40 mgmL [8] However these kinds of proteins have the propensity to form gel

networks unlike gels formed from globular proteins The frequency sweep (Figure 28)

Parameter Notation Value Units

Geometry inertia I 256E-06 Nms2

Stress constant 119865120591 597E+04 119875119886

119873119898

Strain constant 119865120574 290E+01 1

119903119886119889

Amplitude 1205740 100E-03 None

Minimum torque 119879119898119894119899 500E-10 Nm

Minimum

modulus limit 119866119898119894119899 298E-02 Pa

Gap height D 56E+01 microm

Table 120784 120783 Rheological parameters used to calculate parameters for the low-

torque limit (equation 25) and instrument inertial limit (equation

28)

42

of 3 mgmL fibrin appears qualitatively similar to the frequency sweep of salted-out

ribonuclease A (Figure 24) Furthermore frequency sweeps in both directions (forward

and backward) for the ribonuclease A gel (Figure 29) show minimal hysteresis over the

range of frequencies tested showing reproducibility of data

Figure 120784 120790 Frequency sweep of a 3 mgmL fibrin gel obtained from Weigandt

and Pozzo [8] The frequency sweep data appear qualitatively

similar to Figure 27 but the plateau moduli appear to be an order

of magnitude lower than for the ribonuclease A gel Reprinted with

permission from [8]

43

234 Qualifying gel behavior

For the oscillation time test the phase angle initially starts at 60ordm and reduces to

9deg at the end of the test while for the frequency sweep the value decreases from 16deg at

001 rads to 9ordm at 10 rads Since the phase angle lt 90⁰ we can further conclude that

there are no instrument inertial effects that could potentially disqualify the data For the

oscillation time test (Figure 24) tan(δ) initially attains a value of 070 before decreasing

10-3 10-2 10-1 100 101 102100

1000

g = 01 Forward and backward frequency sweep of ribonuclease A

G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)

Figure 120784 120791 Forward and backward frequency sweep of ribonuclease A gel

shows minimal hysteresis The lsquo1rsquo denotes frequency in the forward

direction from 001 rads to 10 rads while lsquo2rsquo denotes the sweep

applied in the reverse direction

44

to 016 at the end of the test while for the frequency sweep tan(δ) is 016 at 10 rads and

increases to 03 at 001 rads This suggests largely solid-like behavior throughout

experimentation Since tan(δ) is lt 1 the sample does not show a sol-gel transition as

seen for other colloidal solutions [67 92] The gelation criteria of Almdal et al [3]

require

(1) A predominantly liquid solvent with a solid dispersed in it This condition is

met since the protein solution is predominantly phosphate buffer in D2O and the

dispersed solute is the protein at a volume fraction Φ ~ 0035 [19]

(2) Solid-like gels are characterized by the absence of an equilibrium modulus

and G(ω) gt G(ω) extending to times at least of the order of seconds This criterion is

satisfied by the frequency sweep as the frequencies tested extend to the order of seconds

and the material exhibits a predominantly solid characteristic Almdal et alrsquos criteria

for gelation are met for ribonuclease A

Nishinari [2] argues from a rheological perspective a gel would show 120575 lt 01

for a frequency range of 10-3 rads to 102

rads which this sample does not satisfy [2]

However Ahmdal et alrsquos definition might be better suited to characterize a lsquogelrsquo since

the second criteria argues that a gel is a solution that is solid-like to humans ie shows

solid-like characteristics on the order of seconds

235 Yielding behavior of ribonuclease A gel

Yield stress experiments were attempted in the form of creep tests where a stress

was applied and a strain was measured Stresses were applied for 30 seconds with no

preconditioning steps at very low values up to 025 Pa The measured strain values were

less than 005 after 30 seconds for 025 Pa However this measured strain did not

reach a plateau value at this time point which suggests that further tests are required to

45

measure the yield stress An additional challenge posed by this system is that the gel

structure showed no recovery after the application of a pre-shear followed by a

conditioning step This suggests that the gel is irreversibly destroyed meaning that a

fresh sample must be loaded into the rheometer for further tests

24 Summary and Concluding Remarks


deuterated ammonium sulfate in D2O was mapped and the aggregation boundary

revealed a qualitatively similar behavior to other protein phase diagrams Gel-like

phases which were screened via an inversion test by utilizing an Eppendorf tube are

determined to correspond to a spinodal decomposition of ribonuclease A solution Due

to the limited amount of protein solution only one formulation (40 mgmL ribonuclease

A and 22 M ammonium sulfate) from the phase diagram was used for bulk rheological

experimentation The sample displayed aging behavior captured with an oscillation test

and consequent frequency sweeps performed showed minimal hysteresis and

successfully met the gelation criteria of Almdal et al [3] It is also seen that the

ribonuclease A gel exhibits time-independent aging behavior which scales G ~ t04 at

long time scales similar to what is seen for colloidal silica gels [6 90] Nevertheless

the origin and the mechanism of the gelation characteristics are not known Furthermore

since only one formulation is used for bulk rheology associated relationships from

varying two variables namely the protein- and the salt-concentrations along the

aggregation boundary are not known Therefore we are unable to comment on how the

two concentration variables affect the mechanical properties of ribonuclease A gels

For systems that display curved aggregation boundaries in the phase diagram

structure property relationships have been derived as a function of the quench depths of

46

the attractive force (salt concentration) [15 58] Consequently future experiments can

be performed by using the same rheological protocol performed in this thesis on

different gel formulations as a function of the protein concentration and the relative

quench depth in the aggregation boundary Of interest would be the relationship

displayed between G and t for data obtained from the oscillation time test and whether

the protein gels would display the same aging behavior at long times regardless of

protein and salt concentrations For the frequency sweep the plateau G(ω) can be

plotted as a function of either the quench depth or the protein concentration These

experiments while highly time- and protein- intensive may provide additional insight

into this interesting soft matter

47

STRUCTURE OF SALTED-OUT RIBONUCLEASE A GELS NEUTRON

SCATTERING AND MICROSCOPY


SANS and USANS are well-established experimental tools that together can

reveal the microstructure on length scales in the range of 1 nm to 1 microm They can provide

valuable information such as the shape the size the structure and the interactions

within a system [93] Importantly it is a tool that allows probing of heterogeneities as

well as the static and the dynamic structural features of a system [94] Neutrons can

penetrate most materials and are unlike X-rays which due to their strong electric field

can ionize atoms All these mean that these methods can be used to probe samples with

minimal disruption [95] which is necessary for sensitive systems such as salted-out

proteins A combination of SANS USANS and TR-SANS on salted-out ovalbumin

complemented cryo-TEM measurements and provided information on structural

features at accurate length scales [42]

The protein phase that corresponds to a gel phase of ribonuclease A is optically

opaque therefore laser-dependent techniques such as DLS and static light scattering

(SLS) are unable to provide structural information due to scattering or absorption of

light [96] Furthermore the oscillation time test (Figure 24) shows irreversible aging

dynamics of the ribonuclease A protein gel Therefore we utilize TR-SANS to better

understand the structural changes that occur at the nanoscale and mesoscale which could

provide insight on gel formation kinetics To capture the static structure of ribonuclease

A gel we utilize a combination of SANS and USANS These together yield the static

and dynamic structural information at the length scales lt 1 microm This is complemented

48

by optical microscopy of the ribonuclease A gel which provides images on a length

scale larger than SANSUSANS regime

In SANS the intensity of neutrons is collected as a function of their deflections

from the incident beam with the deflection angle defined as 2θ Typically SANS data

are reported as a function of the momentum transfer vector or scattering vector Q

119876 = 4120587

120582119904119894119899 120579 (3 1)

where 120582 is the wavelength of the neutrons Q has dimensions of inverse length and is

typically represented in units of nm-1 or Åminus1 [42] Based on the Bragg law relation this

is directly related to the real length scale L by

119871 = 2120587

119876 (3 2)

The measured intensity I(Q) (count s-1) is the count rate of neutrons at a certain

Q or deflection I(Q) provides information on the sample structure at a given length

scale and models that capture structural properties are fit to this variable Complex

fluids typically display SANS data that are featureless and are a challenge to

morphologists [97 98] due to structural parameters that can often vary in the mesoscale

Heuristics dictate that these data sets can be empirically fit to shape independent models

that capture gross structural features

49

311 Selected empirical structural models

3111 Guinierrsquos law and Guinier-Porod model (GP model)

The Guinier regime probes long range order that dominates the low-Q region

Guinierrsquos law has been used to quantify the fiber cross-section sizes in fibrin gels [13]

the long range orders in peptide gels [99] and the pore size distributions in

chromatographic resins in solution [100] Additionally it has been used to characterize

structural features of the aggregation boundary of ribonuclease A protein dense phase

[15] Guinierrsquos law [98] can be generalized as

119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)

where G is the scaling factor A dimensionality parameter s has the values 0 for 3-

dimensional globular objects 1 for rods and 2 for lamellae In addition to the Guinier

regime systems typically show several structural features for a given SANS spectra

[97] The Porod regime in the high-Q region captures scattering from sharp interfaces

and mass fractals [93] By combining the Guinier and Porod regimes we attain the

generalized (Gunier-Porod) GP model which is given as [98 100]

119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)

This model is generalized since it accounts for non-spherical scattering objects such as

roads or lamellae In the GP model m is the Porod exponent while D and G are the

Porod and Guinier scale factors respectively The fractal dimensions of the

microstructure on short and long real-space length scales are captured by s and m

respectively Rg is attained from the Q-value of the inflection point Q1 which lies

between the two fractal regions Therefore s and m capture the fractal dimension at real

length scales greater than and smaller than Rg respectively The GP model has been

used for analyzing aggregates of acidified silk proteins of varying turbidity [101] and

capturing the formation of larger order aggregates upon thermally-inducing

conformational changes in bovine serum albumin solutions [102] Koshari et al used a

GP model fit for neat cellulosic S HyperCel (Pall Corporation) particles which gave

one characteristic Rg of 35 Å [100] This corresponds very well with pore sizes observed

for the same particles determined via inverse size-exclusion chromatography by Angelo

et al who reported a mean pore radius of 44 Å while the Ogston model [103] yielded

a mean pore radius of 36 plusmn 4 Å [104] However while salted-out protein does not

resemble a chromatographic resin these findings show that SANS and GP model can

be used in a variety of complex fluids and can characterize the microstructure at length

scales agreeable with alternative techniques

51

3112 Correlation length model

Phase behavior experimentation for ribonuclease A yielded a gel phase which

arises as a result of phase separation One such model that accounts for aggregates in a

phase separated solution is the correlation length model that was developed to quantify

clusters formed in water- poly(ethylene oxide) systems [105]

119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)

The first term describes Porod scattering from polymer clusters that are typically

larger in scale while the second term is a Lorentzian function that describes scattering

from polymer chains A and B are scaling factors while 120585 is the correlation length and

n and m are power-law exponents Typically these models are used when SANS data

exhibits broad peaks The breadth of the peaks is due to instrument effects and

characteristic length scales of structural features [15]

3113 Mass fractal flocs - power law

Gelation can occur due to percolation of flocs in a system with strongly attractive

forces The aggregates that form these flocs can be modeled as fractals which are self-

similar structures on a length scale that can vary from a few molecules to the size of a

floc [21] In real space the density distribution within the cluster is derived as

120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)

where r is the distance in real space In reciprocal space upon taking the Fourier

transform equation 39 scales as Q-df which produces a straight line of slope -df on a

52

logarithmic plot Typically df attains a value between 1 to 3 where 1 corresponds to

rod-like structures while 3 corresponds to a very compact dense phase

There are two well-known regimes [106] which differ based on the aggregation

mechanism of constituent particles When every collision successfully yields the

formation of a permanent bond diffusion-limited cluster aggregation (DLCA) occurs

(df ~ 21) The other limiting regime is reaction-limited colloidal aggregation (RLCA)

(df ~ 18) when not every collision successfully forms a permanent bond [21]

The power law regime is a characteristic of several complex fluids [10 88 106]

For salted out proteins prior to Greene [15] most studies of the microstructures of

salted-out proteins were limited to lysozyme [15 107] The presence of power law

regimes has been seen in salted-out protein solutions Georgalis et al utilized a

combination of DLS and SLS to measure the flocculation rate of lysozyme due to the

addition of two salts sodium chloride and ammonium sulfate [107] The value of df of

salted-out flocs was found to be 18 when sodium chloride was added characteristic of

DLCA When ammonium sulfate was added df varied depending on the salt

concentration Initially it was 18 at 0125 M before decreasing to 15 at 05 M For a

concentration of 14 M df increased to 22 which lies above the RLCA regime The

authors attributed the initial decrease to clusters becoming larger but more tenuous as

collisions started to occur at the floc periphery The later increase in df was attributed to

cluster percolation a characteristic of RLCA and the onset of a gelation transition

[24107] At pH 40 a protein-precipitant system of ribonuclease A and ammonium

sulfate shows the presence of nanocrystalline spherulites with df = 24 plusmn 01 and a

characteristic peak at Q = 008 Å-1 [15]

53

312 Microscopy and USAXS of ribonuclease A in ammonium sulfate at pH 70

Studies by Dumetz et al [16] observed phase behavior by optical microscopy of

ribonuclease A with a 16 M ammonium sulfate solution for a range of protein

concentrations Images collected 1 day after preparation are shown in Figure 31 for

nine samples in order of increasing protein concentration The authors interpreted the

6th and 7th wells as corresponding to fractal-like aggregates while the 8th and 9th wells

showed the presence of a second-aggregation boundary (Figure 31) [16]

Figure 120785 120783 Phase behavior of ribonuclease A as a function of protein

concentration in 16 M ammonium sulfate in 5 mM phosphate

buffer at pH 70 after 1 day Reprinted with permission from [16]

54

Greene performed cryo-TEM and USAXS on the same system [15] At pH 70

the phase observed beyond the aggregation boundary has a different microstructure

Largely amorphous precipitates are seen in the cryo-TEM images (Figure 32) and the

USAXS spectra showed the emergence of a broad peak at the low-Q region Correlation

lengths from USAXS and cryo-TEM were determined and excellent agreement was

seen independent of the instrument used For 20 mgmL of ribonuclease A a GP model

was fitted to the low-Q region yielding parameter values Rg = 278 plusmn 20 nm and the

dimensionality parameter s of 8 times 10-7 plusmn 02 suggesting a globular characteristic for the

object The authors contend a lack of a fractal-like network due to the absence of a

power-law decay with the presence of a large broad peak in the mid-Q region For 40

mgmL ribonuclease A a correlation length model fit (Figure 33) was performed and

since no characteristic fractal dimension could be extracted Greene argued that the

aggregates were not fractal in nature as suggested in the work of Dumetz et al [16]

55

Figure 120785 120784 TEM images of ribonuclease A at 20 mgmL salted-out in 22

M ammonium sulfate in 5 mM phosphate buffer at pH 70 from

Greene The images show the presence of largely amorphous

structures on the micron scale Reprinted with permission from

[15]

56

Figure 120785 120785 USAXS data for 40 mgmL ribonuclease A salted-out in 20 M

21 M and 22 M ammonium sulfate in pH 70 The data were

fitted to the correlation length model (equation 38) (solid

lines) Reprinted with permission from [15]

57


3211 Optical microscopy of ribonuclease A gel

Microscopy of the gelled phase was documented using a Leitz Laborlux S

microscope equipped with a universal digital coupler (Mel Sobel Microscopes

Hicksville NY) and a Nikon Coolpix 8700 Digital camera (Nikon Tokyo Japan) Ten

microL of the protein solution was transferred onto a glass slide on which a coverslip was

placed This was loaded into the microscope for observation

3212 TR-SANS and static SANS

Measurements were carried out on the NGB30 SANS instrument [108] at the

National Center for Neutron Research (NCNR) National Institute for Standards and

Technology (NIST) Gaithersburg MD For static SANS the sample was prepared 3

hours prior to experimentation All SANS samples were loaded into demountable

titanium cells with a thickness (path length) of 1 mm and performed in a 10-cell sample

holder at 25 C

Three different sample-to-detector distances (SDDs) were used and the amount

of time for each configuration was based on achieving adequate neutron counts

bull high-119876 1 m SDD with 6 Aring neutrons for 106 counts

bull intermediate-119876 4 m SDD with 6 Aring neutrons for 3x105 s counts

bull low-119876 13 m SDD with 6 Aring neutrons or 153 m SDD with lenses with 8 Aring

neutrons for 105 counts

These measurements together yield a Q-range of 0001 Aring-1 lt Q lt 06 Aring-1 with a

wavelength spread Δλλ of 015

For the TR-SANS study the low-Q the mid-Q and the high-Q SDDs were 13

m 4 m and 1 m respectively For the first and the second-last scan (6th scan) the

58

transmission files for 13 m and 4 m were calculated for a period of 3 minutes For

scattering the count time was 5 minutes for 4 m and 1 m SDD and 10 minutes for 13 m

SSD

Standard data reduction procedures were followed using IGOR Pro to obtain

corrected and radially-averaged SANS macroscopic scattering cross-sections [109] The

radially averaged data were fit using the SasView software package [110]

3213 USANS

USANS data were collected at the Oak Ridge National Laboratoryrsquos Spallation

Neutron Source (SNS) to provide access to length scales on the order of 100 nm to 1

microm Samples were loaded into banjo cells with a path length of 2 mm The samples were

prepared and then loaded into the banjo cells using a syringe 3 hours prior to

experimetnation The time taken to collect one spectrum was roughly 8 hours The raw

data were reduced using the Mantid framework to compute I(Q) For the samples run a

background run was taken using an unloaded banjo cell The analytical solutions were

calculated using the SasView software package [110]


331 Microscopy of ribonuclease A samples

Optical microscopy of ribonuclease A at 40 mgmL and 22 M ammonium

sulfate in D2O at pD 70 showed the presence of amorphous aggregates on the micron

scale (Figure 34) similar to phase behavior data studied by Greene[15] However the

protocol utilized a pipette to transfer the sample to a glass slide on which a cover slip

was placed which could have sheared the gel and affected the structure observed While

59

utilizing a well-plate with paraffin oil may have been a better option to preserve the gel

structure the magnification would have been lower than what was possible utilizing a

glass slide and coverslip This would prevent subtle features from being observed due

to the lower resolution

332 TR-SANS of ribonuclease A gels

TR-SANS was performed to develop an understanding of the ribonuclease A

gelation kinetics at the nanoscale and mesoscale The data span a period of 3 hours

(~104 seconds) which corresponds to the time scale of ribonuclease A gel hardening

observed by rheological measurements (Figure 24) The protein solution was

formulated transferred immediately into the titanium cell and used for measurements

in the configurations discussed in section 3222 During this time 7 total scans that



aggregates

100 microm

60

capture the nanoscale structural evolution were obtained (Figure 35) The time at the

end of each data set acquisition along with the order of the SDD are given (Table 31)

The development of a broad peak is seen in the low-Q and mid-Q regions which

corresponds to USAXS results seen for this combination of protein and precipitant at

this solution condition in H2O [15] For Q gt 008 Å-1 the spectra showed no discernable

changes The data sets were fitted to independent GP models for the low-Q (0004ndash003

Å-1) and mid-Q regions (003ndash008 Å-1) [110]

61




regions Inset shows a magnified image of the mid-Q region

62

3321 Initial data set

The first scan could be fit using the power-law (Figure 36) and the GP model

(Figure 37) However the GP model fits are much better at capturing the emergence of

a broad peak in the low-Q and mid-Q region In the low-Q region the power-law fit

yields a slope of 21 which is consistent with RLCA kinetics which could reflect the

formation of compact clusters [88 107] which percolate to form a gel structure The

mid-Q region yields a slope of 14 which is lower than the value expected for DLCA

(df ~18) The low fractal dimension indicates a more open network which means larger

Scan SDD 1 (m) SDD 2 (m) SDD 3 (m) Time at the end of

scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620

Table 120785 120783 Times for SANS measurements along with the order of SDD The

time at the end of the run corresponds to the cumulative time at

which the scattering for the measurement ended and the new

measurement began

63

floc sizes for a given mass However a closer comparison of the residuals (not shown)

reveals that the GP model provides a better fit due to the lower χ2 Rg values of 88 and

13 were obtained from fitting for the low-Q and mid-Q regions respectively The

mid-Q Rg is similar to the hydrodynamic radius of ribonuclease A (14 Å) [111] which

suggests that this broad peak captures the protein monomer

The power law and GP model are different interpretations of the mesoscale

structural evolution of the ribonuclease A gel Based on literature observing an RLCA

in the low-Q region is an indication of gel percolation as seen in lysozyme floc [107]

However the low-Q region develops a broad peak in further timescales If the initial

scan were fit to the GP model the peak observed is weakly protruding as opposed to

later time scales indicative of initial broad peak formation

64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA


ribonuclease A in 22 M ammonium sulfate at pD 70 Power-law

fits show two distinct regimes with the low-Q region showing a

slope of 21 (black) and the mid-Q region showing a slope of 14

(blue)

65

3322 Behavior at longer times

GP model fits were performed for the six additional data sets (Figure 38 and

Figure 39) For the low-Q region Rg was found to be close to 75 Å (Table 32) for all

scans while for the mid-Q region (Table 33) Rg remains close to the hydrodynamic

radius of ribonuclease A for all scans and therefore little changed from the value for

the initial data set (Figure 38 and Figure 39)

10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)

Figure 120785 120789 TR-SANS data of initial data set with 40 mgmL ribonuclease A in

22 M ammonium sulfate at pD 70 GP model fits are shown for

the low-Q (red) and mid-Q regions (blue)

66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)


ribonuclease A in 22 M ammonium sulfate Profiles have been

shifted vertically by a factor of 10 with the time and are referred by

the time at the end of the scan The dashed lines are fits to the data

using the GP model The vertical dashed black line indicates the

different ranges of the independent GP models used to fit the data

67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)



vertically by a factor of 10 and are referred by the time at the end of

the scan The dashed lines are fits to the data using the GP model The


independent GP models used to fit the data

68

Time

(seconds)

Scale Rg (Å) Dimensionality

parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268


showing the scale Rg s and m values

69

The difference between the low-Q Rg values for the initial data (88 Å) and the

rest of the data (75 Å) is relatively small but statistically significant This difference

(Figure 310) reflects the emergence of a broad peak in the low-Q region which may

indicate a structural evolution that corresponds to gel hardening Furthermore when

overlaid with the gel evolution data (Figure 24) the difference in Rg seen in the low-Q

region between the first and second data sets corresponds with the development of the

plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)

Figure 120785 120783120782 Oscillation time test of ribonuclease A gel (figure 24) overlaid with

Rg from the low-Q and mid-Q regions Throughout experimentation

the Rg of the mid-Q region is close to a value of 15 Å which is close

to the hydrodynamic radius of ribonuclease A (14 Å) The Rg of the

low-Q region decreases from 88 Å to 75 Å (grey box) and then

remains constant throughout the rest of the data aquisition This

reduction of Rg is seen by the development of the broad peak which

is indicative of gel hardening

71

The dimensional parameter s and the Porod exponent m evolve with time

(Figure 311) A reduction in s is seen initially before a constant value of 12 is seen for

both regions (low-Q and mid-Q) indicating that the aggregates at both length scales are

becoming more compact For both regions m has a value between 2 and 3 which is

indicative of a gel network [93] Furthermore gel hardening is also associated with an

increase in m (226 to 268 for low-Q 197 to 220 for mid-Q) suggesting the evolution

of the gel network

72

3323 Relating mechanical properties to structural properties

Tsuji et al [112] correlated the characteristic size of an elastically effective

single elastic blob of PEG with the storage modulus as

119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Dimensionality parameter s

Low-Q Porod exponent m

Mid-Q Dimensionality parameter s

Mid-Q Porod exponent m

Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t


dimensionality parameter s and Porod exponent m fitted from the

low-Q and mid-Q regions

73

is the characteristic size of the blob 120588el is the density of the solution kB is the Boltzmann

constant and T is the absolute temperature Using the measured value of about 1200 Pa

for the plateau 119866prime(120596) of the ribonuclease A gel yields ξel ~ 150 Å This is double the

value of Rg estimated from the low-Q region of TR-SANS However Tsuji et alrsquos

model is based on covalently crosslinked system of PEG while salting-out of

ribonuclease A yields a gel composed of a physically gelled percolating floc so some

discrepancy is to be expected

3324 Limitations of the TR-SANS experiment

The TR-SANS data are limited by the relatively low neutron flux of the

instrument used While the 153 m SDD would have made a lower Q-range accessible

it was not possible to use this configuration due to time constraints Furthermore when

the 13 m SDD (low-Q) runs are overlaid with the oscillation time test data (Figure 312)

certain time points of the structural evolution are missed For the initial data set the 13-

m SDD captures the structural evolution while G(ω) and G(ω) are on the order of 101

Pa However the subsequent two sets capture the low-Q region only when the gel has

evolved to have G(ω) ~103 Pa so characteristic features of gel vitrification may not be

captured due to the absence of low-Q data between these run times

Specific kinetic pathways affect the phase behavior of crystals gels and

aggregates from protein-precipitant interactions TR-SANS and time-resolved small-

angle X-ray scattering (TR-SAXS) can be used to model the mesoscale and nanoscale

structural evolution that takes place For TR-SANS EQ-SANS (extended Q-range

small-angle neutron scattering) at the Spallation Neutron Source (SNS) at ORNL can

traverse the Q-range of traditional SANS in approximately 15 minutes due to the high

74

neutron flux [113] which would allow more efficient data acquisition than on the NGB-

30 line However TR-SAXS can provide data in the same Q-range (00054 Aring-1 lt Q lt

059 Aring-1) as traditional SANS has data acquisition times on the order of seconds and

requires smaller sample volumes than SANS [113 114] Thus TR-SAXS data would

be useful to observe kinetics of protein solutions that display rapid gelation such as

ribonuclease A protein gels Another advantage of TR-SAXS is the low sample volume

which makes possible accommodation of multiple samples and a larger sample space

Despite these advantages care must be taken to ensure that the protein gel is not

damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1

Figure 120785 120783120784 Oscillation time test data for the ribonuclease A gelation with TR-

SANS end-of-run times overlaid for the first three scans The 13-

m SDD (low-Q region) scan times for the first three data sets

(green red and blue rectangles respectively) are overlaid The

width of each rectangle is ~300 seconds The sharp lines signify

the end points of the individual scans

76

333 SANS-USANS of ribonuclease A gel

The single-phase solution of ribonuclease A (Figure 23) appears and behaves

like a clear viscous liquid For 40 mgmL and 18 M ammonium sulfate in 5 mM sodium

phosphate at pD 70 a GP model was fit for the SANS regime (Q = 0007ndash009 Å-1) and

yields Rg = 2165 Å indicative of higher order aggregates or oligomers of ribonuclease

A and s = 00122 showing that they are globular shaped (Figure 313) Interestingly

USANS data collected on the same formulation shows the lack of a structure factor for

this protein solution at the length scales probed by USANS (~ 01 - 7 microm) We can

predict the USANS scattering intensity by substituting the Rg and the s obtained from

the SANS spectra into equation 34 and plotting the resultant I(Q) for the USANS Q-

range The predicted intensity shows a flat scattering profile customary of the absence

of scattering above the background and the lack of a structure factor in the USANS

regime

77

Slit-smeared USANS data for the gel formulation (Figure 314) were fit to the

GP model in order to approximate features and extract the Rg value and the

dimensionality parameter s in the USANS regime The best-fit value of Rg is 3830 plusmn

180 Å and the best-fit dimension parameter s = 166 plusmn 003 In comparison for 20

10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring

Figure 120785 120783120785 USANS data of 40 mgmL ribonuclease A in 18 M ammonium

sulfate in 5 mM sodium phosphate at pD 70 The GP model was

used to fit SANS spectra data and parameters were used to

extrapolate the predicted intensity into the USANS regime (grey

box) Both the predicted and the actual USANS data show the

absence of scattering above background

78

mgmL of ribonuclease A in ammonium sulfate Greene reported Rg = 2780 plusmn 200 Å

and s = 8 times 10-7 plusmn 02 from USAXS data The differences in the Rg and s values could

be due to the different solvent used (D2O vs H2O) and the effect of concentration (20

mgmL vs 40 mgmL) The parameters suggest that the aggregates are elongated as

opposed to globular in nature as seen in Greene Furthermore the value of Rg extracted

from the USANS regime is on the order of 100 times the size of an individual

ribonuclease A monomer which indicates the presence of large aggregates that form a

system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)

Figure 120785 120783120786 USANS data of sample prepared from 40 mgmL ribonuclease A

in 22 M ammonium sulfate The dashed line is a fit to the data

using the GP model

79

For the SANS data the 153 m SDD setting was used for low-Q data acquisition

as opposed to the 13 m SDD used for the TR-SANS data The mid-Q data were fit using

the GP model capturing the monomer peak The low-Q data were fit using the

correlation length model (equation 38) to capture the sharp increase in the intensity and

yielded a correlation length of 123plusmn2 Å which is about the size of 4 ribonuclease A

monomers (Figure 315) The correlation length model was better at capturing the uptick

in low-Q A characteristic feature of this spectra is the presence of a broad peak close

to Q = 001 Å-1 similar to the broad peak emergence in the TR-SANS spectra The

Porod exponent in this case attains a value of 255 plusmn 0045 suggesting scattering from

a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)

Correlation length model

GP-model

Figure 120785 120783120787 SANS data for sample prepared from 40 mgmL ribonuclease A in

22 M ammonium sulfate The model fits are indicated by the dashed

lines The correlation length model is used to fit data from 0001 Å-

1 to 003 Å -1 while the GP model is used to fit data from 003 Å -1 to

008 Å -1 The grey box highlights the Q-range not accessible by TR-

SANS due to the use of 13 m SDD instead of 153 m with lens The

blue box highlights the sharp uptick in I(Q) which correspond to

scattering from clusters captured by the correlation length model

81


The opacity of the ribonuclease A gel precluded structural characterization by

optical methods A combination of SANS and USANS was therefore used to study and

characterize this system First TR-SANS was performed for a duration of 104 seconds

corresponding to the time scale used for the oscillation time test These measurements

showed two distinct regions (1) a low-Q region that initially showed an Rg value of 88

Å with a subsequent decrease to 75 Å which coincided with the development of a broad

peak (2) a mid-Q region that had Rg ~ 15 Å corresponding to the hydrodynamic radius

of ribonuclease A Interestingly from mechanical properties obtained from rheology a

mesh size of Rg of 75 Å is predicted from Tsuji et alrsquos model [112] which shows there

is some agreement between the mechanical properties and the structural properties

However since the model is based on covalently-crosslinked PEG and not a physical

gel the agreement may not be fundamentally correct

For static SANS the low-Q data were fit using a correlation length model to

capture the sharp increase in the intensity and yielded a correlation length of 123 plusmn 2 Å

which is on the order of 4 ribonuclease A monomers Slit-smeared USANS had a best-

fit Rg = 3830 plusmn 180 Å and a dimensional parameter s = 166 plusmn 003 The extracted Rg is

on the order of 100 times the size of an individual ribonuclease A monomer which

indicates the presence of large aggregates that are implicated in forming a system-

spanning gel USANS data also show the absence of any structure for the single-phase

liquid indicating that the gelation behavior evidenced in rheological studies for the gel

phase are due to higher-order structures that give rise to a system-spanning gel

82

CONCLUSIONS AND FUTURE WORK

41 Conclusions

This thesis describes a study of the structural and mechanical properties of a

salted-out protein gel formulated from ammonium sulfate and ribonuclease A in a

deuterated phosphate buffer for which a combination of gel-inversion testing bulk

rheology and neutron scattering was used SAOS rheology was conducted using a cone-

and-plate geometry and gelation was confirmed using measurements of two kinds (1)

an oscillation time test for 104 seconds allowing for gel formation (2) a frequency sweep

that showed a predominant storage modulus (G(ω) gt G(ω)) and plateau G(ω) of 1200

Pa Additionally during the oscillation time test scaling behavior of G ~ t04 was seen

at long time scales similar to what is seen for colloidal silica gels

Obtaining the structural properties of the gel proved to be a challenge due to the

opacity of the gel A combination of SANS and USANS was therefore used to study

and characterize this system Firstly TR-SANS was performed for a duration of 104

seconds corresponding to the time scale used for the oscillation time test These

measurements showed two distinct regions (1) a low-Q region that initially showed an

Rg value of 88 Å with a subsequent decrease to 75 Å which coincided with the evolution

of a broad peak (2) a mid-Q region that had a Rg ~ 15 Å corresponding to the

hydrodynamic radius of ribonuclease A The low-Q data were fit using a correlation

length model to capture the sharp increase in the intensity and yielded a correlation

length of 123 plusmn 2 Å which is in the order of 10 ribonuclease A monomers Slit-smeared

USANS had a best-fit of 3830 plusmn 180 Å and a dimensional parameter s of 166 plusmn 003

The extracted is on the order of 100 times the size of an individual ribonuclease A

83

monomer which indicates the presence of large aggregates that are implicated in

forming a system-spanning gel USANS data also show the absence of any structure for

the single-phase liquid indicating that the gelation behavior evidenced in rheological

studies for the lsquogel-phasersquo are characteristic of higher-order structures that give rise to

a system-spanning gel

Indeed this thesis shows the existence of a protein gel phase by utilizing a

protein phase diagram For the sample that behaved like a gel structural and mechanical

properties were measured However these measurements were made on a single gel-

like sample in the phase diagram Additionally this is one combination of protein and

precipitant that displays a gel phase Therefore further investigation into the properties

shown by different points within the protein phase diagram for different protein-

precipitant concentrations is warranted Furthermore a better understanding is required

to explain how the structural properties at the mesoscale relate to the mechanical

properties for the ribonuclease A gel This means that many future directions to continue

discovering and analyzing the protein gels not only those that arise from this protein

and precipitant combination exist

42 Future Directions

421 Microrheology experiments

There is a high cost associated with purifying and isolating proteins so

performing bulk rheological experiments on a comprehensive scale may be unfeasible

This is compounded by the fact that gelation is observed mainly at higher protein

concentrations (gt~40 mgml) Alternative rheological characterization methods include

techniques that use minimal protein volumes and fall in the field of microrheology A

84

good candidate to conduct high-throughput studies that can confirm gelation is passive

microrheology via multiple particle tracking (MPT) MPT allows for small sample

volumes (10ndash20 microL) and quick data acquisition (order of minutes) [92] However a

drawback of MPT is the potential for probe aggregation which would complicate data

analysis in giving rise to a heterogeneous distribution of probe sizes in the generalized

Stokes-Einstein relation (GSER) Josephson et al showed that this probe stability is

protein- and protein concentration-dependent and used a surfactant if necessary to

prevent probe aggregation [116] Probe stability is also diminished in solutions with

high ionic strengths To counter this Kim et al used toluene as a solvent to adsorb

Pluronic F-108 on the surface of polystyrene probe particles as a means to prevent

probe aggregation [117] However a typical salt concentration for which these

Pluronics are effective is 02 M NaCl which is an order of magnitude lower than where

we observed the aggregation boundary for ribonuclease A gels

Time sweeps performed in this work on ribonuclease A gel phases showed the

evolution of the mechanical properties with G(ω) ~ 103 Pa after 3 hours Based on the

operating regime for microrheology ribonuclease A gels appear too stiff to conduct

MPT and their moduli lie within a regime more suitable for diffusive wave spectroscopy

(DWS) which can allow calculation of viscoelastic moduli and demonstrate gelation of

protein solutions [118] However microscopy and USANS data show that the

microstructure of the ribonuclease A gel include features that are larger than probe sizes

that would be necessary to probe a sample that has the strength of the ribonuclease A

gel which would violate the assumptions of the GSER In addition the sample volume

requirement for DWS (01ndash1 ml) is around the same as the minimum requirements for

85

cone-and-plate rheometry (05ndash1 ml) [118] Thus conventional bulk rheology is a better

technique to obtain mechanical properties and capture gelation for ribonuclease A

422 Cavitational rheology

Cavitation rheology is performed by measuring the pressure dynamics of a

growing bubble within a solution When this bubble or cavity is created within the

material the critical pressure of mechanical instability can be quantified and is directly

related to the modulus of the material Given that the modulus is local to the cavitation

site heterogeneities can be measured with this technique [66] which would be ideal for

a system of salted-out proteins given the non-uniformity of aggregate sizes

The Youngrsquos modulus measured by cavitation rheology is consistent with bulk

rheological measurements if it can be assumed that stress is distributed isotropically

when the instability due to cavitation occurs The cavitation pressure or critical pressure

(Pc) to induce the instability for an isotropically-distributed stress is related to the

Youngrsquos modulus and the surface tension as well as the sample medium via

119875119888 = 5119864

6+

2120574

119903 (41)

where E is the Youngrsquos modulus γ is the surface tension between the sample and the

medium and r is the inner radius of the needle attached to the syringe The critical

pressure plotted for various needle radii provides information on the mechanical

properties and the surface tension which are independent of the orientation of the

surroundings Cui et al measured the mechanical properties of bovine eye lenses and

reported the Youngrsquos moduli of the cortex and nucleus to be 08 kPa and 118 kPa

respectively [119]

86

Given the opacity of the ribonuclease A gel accurate cavitation rheological

measurements would be challenging to perform However this technique may be

suitable to apply to PEG-precipitated protein gels Ribonuclease A gelation kinetics

displays irreversible aging and requires a few hours to display predominantly elastic

characteristics Furthermore the high salt content causes evaporation and drying of the

solution when exposed to the air To counter this paraffin oil could be applied on top

of the gels where it forms a layer and prevents evaporation

423 DLS

DLS is a powerful tool for characterizing colloidal suspensions In addition to

enabling measurement of the hydrodynamic radii of particles in solution it can also be

used to determine MWs of and interactions among polymers [120] For colloidal gels

of high-volume fraction an arrested decay would be observed in the correlation

function as opposed to complete decay at lower volume fractions Moreover gel moduli

can be extracted from DLS [121] Van Driessche et al utilized DLS to characterize an

arrested gel phase formed at ambient conditions upon precipitation of GI with PEG1000

and PEG1500 [59]For DLS the intensity autocorrelation function 1198922(120591) minus 1 where τ is

the delay time is related to the electric-field correlation function 1198921(120591) minus 1 via the

Siegert relation [59 121]

1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)

where B is the baseline of the correlation function at infinite delay and β is the function

value at zero delay For PEG-GI gels a double-exponential function was used to fit

1198921(120591) [59] before kinetic arrest and was modeled as

87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)

where Γ = DQ2 is the decay rate defined by the diffusion coefficient D of the particles

and by the scattering vector Q at the given angle and time t The first term of equation

43 captures the fast-diffusing populations comprised of monomers while a slowly-

diffusing population corresponding to clusters that grow as a function of time is captured

by the second term Post-gelation a stretched exponential can used to reproduce[121]

the auto-correlation function as

1198921(120591) = 119890minus119875120548119905 (4 4)

where P is a fitting parameter Stretched-exponentials are a characteristic of gels and

kinetically-arrested gel phases and equation 44 was fit for PEG-GI gels [59] Therefore

DLS can act as a screening tool for protein gel phases

DLS measures single scattering event meaning that each detected photon has

only been scattered once by the sample [123] For a strongly-scattering sample like a

ribonuclease A gel multiple scattering events occur One option may be to reduce the

path length to prevent multiple scattering A light-scattering microscope has also been

shown to be capable of measuring Q for turbid samples [124] However these

alternative techniques require small sample sizes that are very susceptible to drying and

could prove difficult to handle Additionally dilution of samples would not work since

ribonuclease A gels are concentration-dependent as seen in the phase diagram (Figure

22) and the observed turbidity is a sign of gelation In conclusion while DLS is a

88

powerful tool it may not be effective for ribonuclease A protein gels but may be better

suited for alternative systems such as PEG-based protein gels

424 Alternative precipitants

As previously mentioned not all precipitants and protein concentrations lead to

the formation of a system-spanning gel network Apart from salt-based precipitants the

phase diagram of glucose isomerase in the presence of PEG1000 and PEG1500 has been

explored (Figure 15) and has been shown to include a system-spanning macroscopic

gel at ambient conditions (pH 70 and room temperature) [59] Similar studies to those

performed here could be performed on phases formed in the presence of PEG or other

non-denaturing precipitants used to manipulate protein interactions

425 Change in protein-protein interactions due to gelation

Protein pharmaceutical products are typically comprised of folded monomers

with monoclonal antibodies forming the bulk of the drug pipelines [125] On the other

hand for biologically active drug molecules the proteins must remain folded to

function As previously stated protein-protein interactions are a complex interplay

between many forces both attractive and repulsive in nature Drug dosages for these

biomolecules are often on the order of 102 mgmL At these large concentrations

proteins can form aggregated states in addition to the folded monomer state [126]

Proteins can form reversible aggregates where monomers reversibly form stable

complexes of oligomers and small dimers [127] These typically can be reversed by

either dilution or shifting solution conditions such as pH or salt-concentration A major

issue to avoid is are irreversible aggregates which are non-dissociable unless exposed

to extremes of temperature pH or chemical denaturants When proteins irreversibly

89

aggregate they lose their native secondary and tertiary structure to make way for strong

contacts formed from hydrophobic interactions or hydrogen bonds that arise when these

individual monomers misfold and form intertwined irreversible aggregates [126] From

a drug formulation perspective it is imperative that these products remain stable at high

concentrations for intramuscular or subcutaneous delivery More importantly there are

concerns that if these proteins are irreversibly folded and persist in the bloodstream

during delivery they could even cause an autoimmune disorder such as antibody-

mediated pure red phase aphasia [128] Additionally the presence of aggregates that are

visible from a marketing perspective would not bode well for the product itself [129]

While the presence of a gel-phase material for salted-out ribonuclease A in ambient

conditions has been shown in this thesis the structural changes occurring with how

individual proteins interact with each other and fold are still unknown

Size Exclusion Chromatography (SEC) is a technique that can quantify the

presence of oligomers monomers and sub-monomer aggregates [129 130] One

experiment might be to formulate a protein gel dilute the solution and perform SEC

Dilution would yield a clear solution below the aggregation boundary and reversible

aggregates maybe reduced However SEC maybe able to quantify how gelation affects

protein-protein interactions by showing the presence of larger irreversible aggregates or

low-MW fragments that are formed This would provide a unique understanding of how

being in a gel-phase affects the protein at the monomer and sub-monomer level

90

BIBLIOGRAPHY

[1] Nijenhuis K te (1997) Advances in Polymer Science Thermoreversible Networks

1301ndash12

[2] Nishinhari K (2009) Progress in Colloid and Polymer Science Some Thoughts

on The Definition of a Gel 13687ndash94 httpsdoiorg1010072882

[3] Almdal K Dyre J Hvidt S Kramer O (1993) Polymer Gels and Networks

Towards a phenomenological definition of the term ldquogelrdquo 15ndash17 (1)

httpsdoiorg1010160966-7822(93)90020-I

[4] Ferry JD (1948) Advances in Protein Chemistry Protein Gels 41ndash78

httpsdoiorg101016B978-0-08-100722-800020-6

[5] Kavanagh GM Ross-Murphy SB (1998) Progress in Polymer Science

Rheological characterisation of polymer gels 23533ndash562 (3)

httpsdoiorg101016S0079-6700(97)00047-6

[6] Gordon MB Kloxin CJ Wagner NJ (2016) Journal of Rheology The rheology

and microstructure of an aging thermoreversible colloidal gel 6123ndash34 (1)

httpsdoiorg10112214966039

[7] Linnes MP Ratner BD Giachelli CM (2007) Biomaterials A fibrinogen-based

precision microporous scaffold for tissue engineering 285298ndash5306

httpsdoiorg101016jbiomaterials200708020

[8] Weigandt K Pozzo D (2013) Proteins in Solution and at Interfaces Methods and

Applications in Biotechnology and Materials Science Protein Gel Rheology

437ndash448 httpsdoiorg1010029781118523063ch22

[9] Caloacute E Khutoryanskiy V V (2015) Biomedical applications of hydrogels A

review of patents and commercial products

httpsdoiorg101016jeurpolymj201411024

[10] Lu PJ Zaccarelli E Ciulla F Schofield AB Sciortino F Weitz DA (2008)

Nature Gelation of particles with short-range attraction 453499ndash503 (7194)

httpsdoiorg101038nature06931

[11] Zayas JF (1997) Functionality of Proteins in Food Gelling Properties of Proteins

310ndash366 httpsdoiorg101007978-3-642-59116-7_7

91

[12] Alting AC Weijers M Hoog EHA De Pijpekamp AM Van De Cohen Stuart

MA Hamer RJ Kruif CG De Visschers RW (2004) Journal of Agricultural and

Food Chemistry Acid-Induced Cold Gelation of Globular Proteins Effects of

Protein Aggregate Characteristics and Disulfide Bonding on Rheological

Properties 52623ndash631 (3) httpsdoiorg101021jf034753r

[13] Weigandt KM Pozzo DC Porcar L (2009) Soft Matter Structure of high density

fibrin networks probed with neutron scattering and rheology 54321 (21)

httpsdoiorg101039b906256d

[14] Corrigan AM Donald AM (2009) Langmuir Passive microrheology of solvent-

induced fibrillar protein networks 258599ndash8605 (15)

httpsdoiorg101021la804208q

[15] Greene DG (2016) Dissertation The Formation and Structure of Precipitated

Protein Phases

[16] Dumetz AC Chockla AM Kaler EW Lenhoff AM (2008) Biophysical Journal

Protein phase behavior in aqueous solutions Crystallization liquid-liquid phase

separation gels and aggregates 94570ndash583 (2)

httpsdoiorg101529biophysj107116152

[17] Cardinaux F Gibaud T Stradner A Schurtenberger P (2007) Physical Review

Letters Interplay between spinodal decomposition and glass formation in

proteins exhibiting short-range attractions 991ndash4 (11)

httpsdoiorg101103PhysRevLett99118301

[18] Sarangapani PS Hudson SD Jones RL Douglas JF Pathak JA (2015)

Biophysical Journal Critical Examination of the Colloidal Particle Model of

Globular Proteins 108724ndash737 (3) httpsdoiorg101016jbpj2014113483

[19] Dumetz AC (2007) Dissertation Protein Interactions and Phase Behavior in

Aqueous Solutions Effects of Salt Polymer and Organic Additives

[20] Dill KA (1990) Biochemistry Dominant forces in protein folding 297133ndash7155

(31) httpsdoiorg101021bi00483a001

[21] Wagner NJ Mewis J (2011) Colloidal Suspension Rheology

httpsdoiorghttpsdoiorg101017CBO9780511977978

[22] Quang LJ Sandler SI Lenho AM (2014) Anisotropic Contributions to Protein minus

Protein Interactions

92

[23] Dumetz AC Chockla AM Kaler EW Lenhoff AM (2008) Biochimica et

Biophysica Acta (BBA) - Proteins and Proteomics Effects of pH on proteinndash

protein interactions and implications for protein phase behavior 1784600ndash610

(4) httpsdoiorg101016jbbapap200712016

[24] Dumetz AC Snellinger-OrsquoBrien AM Kaler EW Lenhoff AM (2007) Protein

Science Patterns of protein ndash protein interactions in salt solutions and

implications for protein crystallization 161867ndash1877

httpsdoiorg101110ps072957907Ultimately

[25] Oss CJ van Good R J Chaudhury MK (1986) Journal of Protein Chemistry

Solubility of Proteins 5385ndash405 (6)

[26] Kunz W (2010) Current Opinion in Colloid and Interface Science Specific ion

effects in colloidal and biological systems 1534ndash39 (1ndash2)

httpsdoiorg101016jcocis200911008

[27] Hofmeister F (1888) Arch Exp Pathol Pharmakol Zur Lehre yon der W irkung

tier Salze 251ndash30 httpsdoiorg101007BF01838161

[28] Marrink SJ Marčelja S (2001) Langmuir Potential of mean force computations

of ions approaching a surface 177929ndash7934 (25)

httpsdoiorg101021la015526r

[29] Ninham BW Yaminsky V (2002) Langmuir Ion Binding and Ion

Specificity The Hofmeister Effect and Onsager and Lifshitz Theories 132097ndash

2108 (7) httpsdoiorg101021la960974y

[30] Alfridsson M Ninham B Wall S (2000) Langmuir Role of Co-ion specificity

and dissolved atmospheric gas in colloid interaction 1610087ndash10091 (26)

httpsdoiorg101021la000841j

[31] Zavitsas AA (2016) Current Opinion in Colloid and Interface Science Some

opinions of an innocent bystander regarding the Hofmeister series 2372ndash81


[32] Curtis RA Lue L (2006) Chemical Engineering Science A molecular approach

to bioseparations Protein-protein and protein-salt interactions 61907ndash923 (3)

httpsdoiorg101016jces200504007

[33] Collins KD (2004) Methods Ions from the Hofmeister series and osmolytes

Effects on proteins in solution and in the crystallization process 34300ndash311 (3)

httpsdoiorg101016jymeth200403021

93

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subunit interfaces and interior of oligomeric proteins 204155ndash164 (1)

httpsdoiorg1010160022-2836(88)90606-7

[35] Zhang Y Cremer PS (2006) Current Opinion in Chemical Biology Interactions

between macromolecules and ions the Hofmeister series 10658ndash663 (6)

httpsdoiorg101016jcbpa200609020

[36] Xie WJ Gao YQ (2013) Journal of Physical Chemistry Letters A simple theory

for the hofmeister series 44247ndash4252 (24) httpsdoiorg101021jz402072g

[37] Omta AW Kropman MF Woutersen S Bakker HJ (2003) Science Negligible

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(5631) httpsdoiorg101126science1084801

[38] Batchelor JD Olteanu A Tripathy A Pielak GJ (2004) Supporting Information

for  Impact of Protein Denaturants and Stabilizers on Water Structure 1ndash10

(25)

[39] Gurau MC Lim SM Castellana ET Albertorio F Kataoka S Cremer PS (2004)

Journal of the American Chemical Society On the mechanism of the Hofmeister

effect 12610522ndash10523 (34) httpsdoiorg101021ja047715c

[40] Tessier PM Johnson HR Pazhianur R Berger BW Prentice JL Bahnson BJ

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Predictive crystallization of ribonuclease A via rapid screening of osmotic second

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[41] Finet S Skouri-Panet F Casselyn M Bonneteacute F Tardieu A (2004) Current

Opinion in Colloid and Interface Science The Hofmeister effect as seen by

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[42] Greene DG Modla S Wagner NJ Sandler SI Lenhoff AM (2015) Biophysical

Journal Local Crystalline Structure in an Amorphous Protein Dense Phase

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[43] Piazza R (2004) Current Opinion in Colloid and Interface Science Protein

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[45] Grover PK Ryall RL (2005) Chemical Reviews Critical Appraisal of Salting-Out

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[46] Martinez M Spitali M Norrant EL Bracewell DG (2018) Trends in

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[47] To BCS Lenhoff AM (2007) Journal of Chromatography A Hydrophobic

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[48] Shepard CC Tiselius A (1949) Discussions of the Faraday Society The

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with short-ranged attractive interactions Application to protein crystallization

651ndash17 httpsdoiorg101103PhysRevE65031407

[52] Miller MA Frenkel D (2004) Journal of Chemical Physics Phase diagram of the

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[53] Pellicane G Costa D Caccamo C (2003) JOURNAL OF PHYSICS

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protein solutions 15375ndash384

95

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[56] McManus JJ Charbonneau P Zaccarelli E Asherie N (2016) Current Opinion in

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[57] Dumetz AC Chockla AM Kaler EW Lenhoff AM (2009) Crystal Growth amp

Design Comparative Effects of Salt Organic and Polymer Precipitants on

Protein Phase Behavior and Implications for Vapor Diffusion 9682ndash691 (2)

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[58] Gibaud T Schurtenberger P (2009) Journal of Physics Condensed Matter A

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[59] Driessche AES Van Gerven N Van Bomans PHH Joosten RRM Friedrich H

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[63] Lefebvre J Renard D Sanchez-Gimeno AC (1998) Rheologica Acta Structure

and rheology of heat-set gels of globular proteins I Bovine serum albumin gels

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[64] Chodankar S Aswal VK Hassan PA Wagh AG (2010) Journal of

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Macromolecular Science Part B Physics Effect of pH and protein concentration

on rheological and structural behavior of temperature-induced bovine serum

albumin gels 49658ndash668 (4) httpsdoiorg10108000222341003591500

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[67] Chung YM Simmons KL Gutowska A Jeong B (2002) Biomacromolecules

Sol-Gel transition temperature of PLGA-g-PEG aqueous solutions 3511ndash516

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[68] Shahin A Joshi YM (2010) Langmuir Irreversible aging dynamics and generic

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[69] Zaccarelli E (2007) Journal of Physics Condensed Matter Colloidal gels

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[70] Trappe V Prasad V Cipelletti L Segre PN Weitz DA (2001) Nature Jamming

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coarsening during spinodal decomposition in thermoreversible colloidal gels

116360ndash6370 (32) httpsdoiorg101039c5sm00851d

[73] H T (2000) Journal of Physics Condensed Matter Viscoelastic phase

separation 12R207ndashR264 (15)

[74] Eberle APR Castantildeeda-Priego R Kim JM Wagner NJ (2012) Langmuir

Dynamical arrest percolation gelation and glass formation in model

nanoparticle dispersions with thermoreversible adhesive interactions 281866ndash

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97

[75] Park JD Ahn KH Lee SJ (2015) Soft Matter Structural change and dynamics of

colloidal gels under oscillatory shear flow 119262ndash9272 (48)

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[76] Deshpande AP (2018) PhysicsIitmAcin Techniques in oscillatory shear

rheology 1ndash23 httpwwwphysicsiitmacin~compfluLect-notesabhijitpdf

[77] Malvern Intruments Limited (2016) Whitepaper - A Basic Introduction to

Rheology 9ndash19

[78] Lucey JA (2002) Journal of Dairy Science Formation and Physical Properties of

Milk Protein Gels 85281ndash294 (2) httpsdoiorg103168jdss0022-

0302(02)74078-2

[79] Ewoldt RH Winegard TM Fudge DS (2011) International Journal of Non-

Linear Mechanics Non-linear viscoelasticity of hagfish slime 46627ndash636 (4)

httpsdoiorg101016jijnonlinmec201010003

[80] Ewoldt RH Johnston MT Caretta LM (2014) Experimental Challenges of Shear

Rheology How to Avoid Bad Data httpsdoiorg101007978-1-4939-2065-

5_6

[81] Mazzeo FA (2008) TA Instruments Importance of Oscillatory Time Sweeps in

Rheology 1ndash4 httpwwwtainstrumentscompdfliteratureRH081pdf

[82] Lescanne M Grondin P DrsquoAleacuteo A Fages F Pozzo J-L Monval OM Reinheimer

P Colin A (2004) Langmuir Thixotropic Organogels Based on a Simple N -

Hydroxyalkyl Amide Rheological and Aging Properties 203032ndash3041 (8)

httpsdoiorg101021la035219g

[83] Paulsson M Dejmek P Vliet T Van (1990) Journal of Dairy Science

Rheological Properties of Heat-Induced β-Lactoglobulin Gels 7345ndash53 (1)

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[84] Zhang J Peng X Jonas A Jonas J (1995) Biochemistry NMR Study of the Cold

Heat and Pressure Unfolding of Ribonuclease A 348631ndash8641 (27)

httpsdoiorg101021bi00027a012

[85] Keller PJ Cohen E Neurath H (1958) J Biol Chem The Proteins of Bovine

Pancreatic Juice 233344ndash349 (2)

[86] Vaynberg KA Wagner NJ (2001) Journal of Rheology Rheology of

polyampholyte (gelatin)-stabilized colloidal dispersions The tertiary

98

electroviscous effect 45451ndash466 (2) httpsdoiorg10112211339247

[87] Firth BA (1976) Journal of Colloid And Interface Science Flow properties of

coagulated colloidal suspensions II Experimental properties of the flow curve

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[88] Poon WCK Haw MD (1997) Advances in Colloid and Interface Science

Mesoscopic structure formation in colloidal aggregation and gelation 7371ndash126

httpsdoiorg101016S0001-8686(97)90003-8

[89] Weigandt K Pozzo D (2013) Proteins in Solution and at Interfaces Protein Gel

Rheology 437ndash448 httpsdoiorg1010029781118523063ch22

[90] Manley S Davidovitch B Davies NR Cipelletti L Bailey AE Christianson RJ

Gasser U Prasad V Segre PN Doherty MP Sankaran S Jankovsky AL Shiley

B Bowen J Eggers J Kurta C Lorik T Weitz DA (2005) Physical Review

Letters Time-dependent strength of colloidal gels 951ndash4 (4)


[91] Instruments TA TRIOS Software

[92] Schultz KM Furst EM (2012) Soft Matter Microrheology of biomaterial

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[93] Hammouda B (2008) National Institute of Standards and Technology Center for

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[94] Krueger S Andrews AP Nossal R (1994) Biophysical Chemistry Small angle

neutron scattering studies of structural characteristics of agarose gels 5385ndash94

(1ndash2) httpsdoiorg1010160301-4622(94)00079-4

[95] Windsor CG (1988) Journal of Applied Crystallography An introduction to

small-angle neutron scattering 21582ndash588 (6)

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[96] Toh HS Compton RG (2015) ChemistryOpen ldquoNano-impactsrdquo An

Electrochemical Technique for Nanoparticle Sizing in Optically Opaque

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[97] Beaucage G Schaefer DW (1994) Journal of Non-Crystalline Solids Structural

studies of complex systems using small-angle scattering a unified

Guinierpower-law approach 172ndash174797ndash805 (PART 2)

99

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[98] Hammouda B (2010) Journal of Applied Crystallography A new Guinier-Porod

model 43716ndash719 (4) httpsdoiorg101107S0021889810015773

[99] Guilbaud JB Saiani A (2011) Chemical Society Reviews Using small angle

scattering (SAS) to structurally characterise peptide and protein self-assembled

materials 401200ndash1210 (3) httpsdoiorg101039c0cs00105h

[100] Koshari SHS Wagner NJ Lenhoff AM (2015) Journal of Chromatography A

Characterization of lysozyme adsorption in cellulosic chromatographic materials

using small-angle neutron scattering 139945ndash52


[101] Tabatabai AP Weigandt KM Blair DL (2017) Physical Review E Acid-induced

assembly of a reconstituted silk protein system 961ndash7 (2)

httpsdoiorg101103PhysRevE96022405

[102] Molodenskiy D Shirshin E Tikhonova T Gruzinov A Peters G Spinozzi F

(2017) Physical Chemistry Chemical Physics Thermally induced conformational

changes and protein-protein interactions of bovine serum albumin in aqueous

solution under different pH and ionic strengths as revealed by SAXS

measurements 1917143ndash17155 (26) httpsdoiorg101039c6cp08809k

[103] Ogston AG (1958) Transactions of the Faraday Society The Spaces in a

Uniform Random Suspension of Fibres 541754ndash1757

httpsdoiorg101039tf9585401754

[104] Angelo JM Cvetkovic A Gantier R Lenhoff AM (2013) Journal of

Chromatography A Characterization of cross-linked cellulosic ion-exchange

adsorbents 1 Structural properties 131946ndash56


[105] Hammouda B Ho DL Kline S (2004) Macromolecules Insight into clustering

in poly(ethylene oxide) solutions 376932ndash6937 (18)

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[106] Tang S Preece JM McFarlane CM Zhang Z (2000) Journal of Colloid and

Interface Science Fractal morphology and breakage of DLCA and RLCA

aggregates 221114ndash123 (1) httpsdoiorg101006jcis19996565

[107] Georgalis Y Umbach P Raptis J Saenger W (1997) Acta Crystallographica

Section D Biological Crystallography Lysozyme aggregation studied by light

scattering I Influence of concentration and nature of electrolytes 53691ndash702

100

(6) httpsdoiorg101107S0907444997006847

[108] Glinka CJ Barker JG Hammouda B Krueger S Moyer JJ Orts WJ (1998)

Journal of Applied Crystallography The 30 m Small-Angle Neutron Scattering

Instruments at the National Institute of Standards and Technology 31430ndash445

(3) httpsdoiorg101107S0021889897017020

[109] Kline SR (2006) Journal of Applied Crystallography Reduction and analysis of

SANS and USANS data using IGOR Pro

httpsdoiorg101107s0021889806035059

[110] The Sasview Project httpwwwsasvieworg

[111] Garciacutea De La Torre J Huertas ML Carrasco B (2000) Biophysical Journal

Calculation of hydrodynamic properties of globular proteins from their atomic-

level structure 78719ndash730 (2) httpsdoiorg101016S0006-3495(00)76630-6

[112] Tsuji Y Li X Shibayama M (2018) Gels Evaluation of Mesh Size in Model

Polymer Networks Consisting of Tetra-Arm and Linear Poly(ethylene glycol)s

450 (2) httpsdoiorg103390gels4020050

[113] Zhao JK Gao CY Liu D (2010) Journal of Applied Crystallography The

extended Q -range small-angle neutron scattering diffractometer at the SNS

431068ndash1077 (5) httpsdoiorg101107s002188981002217x

[114] Jensen MH Toft KN David G Havelund S Peacuterez J Vestergaard B (2010)

Journal of Synchrotron Radiation Time-resolved SAXS measurements

facilitated by online HPLC buffer exchange 17769ndash773 (6)

httpsdoiorg101107S0909049510030372

[115] Meisburger SP Warkentin M Chen H Hopkins JB Gillilan RE Pollack L

Thorne RE (2013) Biophysical Journal Breaking the radiation damage limit with

cryo-SAXS 104227ndash236 (1) httpsdoiorg101016jbpj2012113817

[116] Josephson LL Furst EM Galush WJ (2016) Journal of Rheology Particle

tracking microrheology of protein solutions 60531ndash540 (4)


[117] Kim AJ Manoharan VN Crocker JC (2005) Journal of the American Chemical

Society Swelling-based method for preparing stable functionalized polymer

colloids 1271592ndash1593 (6) httpsdoiorg101021ja0450051

[118] Furst EM Squires TM (2018) Microrheology Microrheology

101

httpsdoiorg101093oso97801996552050010001

[119] Cui J Lee CH Delbos A McManus JJ Crosby AJ (2011) Soft Matter

Cavitation rheology of the eye lens 77827ndash7831 (17)

httpsdoiorg101039c1sm05340j

[120] Rochas C Geissler E (2014) Macromolecules Measurement of dynamic light

scattering intensity in gels 478012ndash8017 (22)


[121] Krall AH Weitz DA (1998) Physical Review Letters Internal Dynamics and

Elasticity of Fractal Colloidal Gels 80778ndash781 (4)

httpprlapsorgpdfPRLv80i4p778_15Cnpapers4b986d00-906f-493f-

a74b-71e29d82b719Paperp27562

[122] Berne BJ Robert P (1976) Dynamic Light Scattering With Applications to

Chemistry Biology and Physics

[123] Block ID Scheffold F (2010) Review of Scientific Instruments Modulated 3D

cross-correlation light scattering Improving turbid sample characterization

81(12) httpsdoiorg10106313518961

[124] Kaplan PD Trappe V Weitz DA (1999) Applied Optics Light-scattering

microscope 384151ndash4157 (19)

[125] Shukla AA Hubbard B Tressel T Guhan S Low D (2007) Journal of

Chromatography B Analytical Technologies in the Biomedical and Life

Sciences Downstream processing of monoclonal antibodies-Application of

platform approaches 84828ndash39 (1)

httpsdoiorg101016jjchromb200609026

[126] Roberts CJ (2014) Current Opinion in Biotechnology Protein aggregation and

its impact on product quality 30211ndash217

httpsdoiorg101016jcopbio201408001

[127] Mahler HC Friess W Grauschopf U Kiese S (2009) Journal of Pharmaceutical

Sciences Protein aggregation Pathways induction factors and analysis

982909ndash2934 (9) httpsdoiorg101002jps21566

[128] Macdougall IC (2005) Nephrology Dialysis Transplantation Antibody-

mediated pure red cell aplasia (PRCA) Epidemiology immunogenicity and risks

209ndash15 (SUPPL 4) httpsdoiorg101093ndtgfh1087

102

[129] Weiss IV WF Young TM Roberts CJ (2007) Journal of Pharmaceutical

Sciences Principles Approaches and Challenges for Predicting Protein

Aggregation Rates and Shelf Life 981246ndash1277 (4) httpsdoiorg101002jps

[130] Hong P Koza S Bouvier ESP (2012) Journal of Liquid Chromatography and

Related Technologies A review size-exclusion chromatography for the analysis

of protein biotherapeutics and their aggregates 352923ndash2950 (20)

httpsdoiorg101080108260762012743724

[131] Kuumlkrer B Filipe V Duijn E Van Kasper PT Vreeken RJ Heck AJR Jiskoot W

(2010) Pharmaceutical Research Mass spectrometric analysis of intact human

monoclonal antibody aggregates fractionated by size-exclusion chromatography

272197ndash2204 (10) httpsdoiorg101007s11095-010-0224-5

103

Appendix

REPRINT PERMISSION LETTERS

The following pages contain permission letters for 12 reprinted figures in the

thesis These figures are Figure 11 Figure 12 and Figure 31 from Dumetz et al [16]

Figure 13 and Figure 14 from Van Driessche et al [59] Figure 15 Figure 42 and

Figure 33 from Greene [15] Figure 16 from Almdal et al [3] Figure 31 by Ewoldt et

al [80] and Figure 25 and Figure 28 from Weigandt et al [8]

722019 RightsLink Printable License

httpss100copyrightcomCustomerAdminPLFjspref=22272d39-3a94-46d5-8b29-66e7438cfd1a 16

ELSEVIER LICENSETERMS AND CONDITIONS

Jul 02 2019

This Agreement between University of Delaware -- Sai Prasad Ganesh (You) and Elsevier(Elsevier) consists of your license details and the terms and conditions provided byElsevier and Copyright Clearance Center

License Number 4620430761059

License date Jul 01 2019

Licensed Content Publisher Elsevier

Licensed Content Publication Biophysical Journal

Licensed Content Title Protein Phase Behavior in Aqueous Solutions Crystallization Liquid-Liquid Phase Separation Gels and Aggregates

Licensed Content Author Andreacute C DumetzAaron M ChocklaEric W KalerAbraham MLenhoff

Licensed Content Date Jan 15 2008

Licensed Content Volume 94

Licensed Content Issue 2

Licensed Content Pages 14

Start Page 570

End Page 583

Type of Use reuse in a thesisdissertation

Portion figurestablesillustrations

Number offigurestablesillustrations

3

Format both print and electronic

Are you the author of thisElsevier article

No

Will you be translating No

Original figure numbers Figure 1 Figure 4 Figure 7

Title of yourthesisdissertation

GEL-LIKE BEHAVIOR IN AN AMORPHOUS PROTEIN DENSE PHASEPHASE BEHAVIOR NEUTRON SCATTERING AND RHEOLOGY

Expected completion date Aug 2019

Estimated size (number ofpages)

100

Requestor Location University of Delaware155 Colburn Lab150 Academy St

NEWARK DE 19716United StatesAttn Sai Prasad Ganesh

Publisher Tax ID 98-0397604

Total 000 USD

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v110 Last updated September 2015Questions customercarecopyrightcom or +1-855-239-3415 (toll free in the US) or+1-978-646-2777



AND RHEOLOGY

by

Sai Prasad Ganesh

Approved __________________________________________________________

Abraham M Lenhoff PhD


Approved __________________________________________________________

Norman J Wagner PhD


Approved __________________________________________________________

Eric M Furst PhD

Chair of the Department of Chemical and Biomolecular Engineering

Approved __________________________________________________________

Levi T Thompson PhD


Approved __________________________________________________________

Douglas J Doren PhD



iv

ACKNOWLEDGMENTS






















v

























vi










vii

TABLE OF CONTENTS


Chapter
















viii








sulfate at pH 70 53



3213 USANS 58













ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



httpsdoiorg101016S0079-6700(97)00047-6


















91













Protein Phases




















92


































93



httpsdoiorg1010160022-2836(88)90606-7











(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










Jul 02 2019












Start Page 570

End Page 583




3



No







100




Total 000 USD





























Jul 02 2019
















2





no









Total 000 USD




1 Grant of License




2 Scope of Licence














4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




1



No










Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































Approved __________________________________________________________

Levi T Thompson PhD


Approved __________________________________________________________

Douglas J Doren PhD



iv

ACKNOWLEDGMENTS






















v

























vi










vii

TABLE OF CONTENTS


Chapter
















viii








sulfate at pH 70 53



3213 USANS 58













ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



httpsdoiorg101016S0079-6700(97)00047-6


















91













Protein Phases




















92


































93



httpsdoiorg1010160022-2836(88)90606-7











(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










Jul 02 2019












Start Page 570

End Page 583




3



No







100




Total 000 USD





























Jul 02 2019
















2





no









Total 000 USD




1 Grant of License




2 Scope of Licence














4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




1



No










Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































iv

ACKNOWLEDGMENTS






















v

























vi










vii

TABLE OF CONTENTS


Chapter
















viii








sulfate at pH 70 53



3213 USANS 58













ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



httpsdoiorg101016S0079-6700(97)00047-6


















91













Protein Phases




















92


































93



httpsdoiorg1010160022-2836(88)90606-7











(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










Jul 02 2019












Start Page 570

End Page 583




3



No







100




Total 000 USD





























Jul 02 2019
















2





no









Total 000 USD




1 Grant of License




2 Scope of Licence














4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




1



No










Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































v

























vi










vii

TABLE OF CONTENTS


Chapter
















viii








sulfate at pH 70 53



3213 USANS 58













ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



httpsdoiorg101016S0079-6700(97)00047-6


















91













Protein Phases




















92


































93



httpsdoiorg1010160022-2836(88)90606-7











(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










Jul 02 2019












Start 70

End Page 583




3



No







100




Total 000 USD





























Jul 02 2019
















2





no









Total 000 USD




1 Grant of License




2 Scope of Licence














4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




1



No










Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































vi










vii

TABLE OF CONTENTS


Chapter
















viii








sulfate at pH 70 53



3213 USANS 58













ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



httpsdoiorg101016S0079-6700(97)00047-6


















91













Protein Phases




















92


































93



httpsdoiorg1010160022-2836(88)90606-7











(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










Jul 02 2019












Start Page 570

End Page 583




3



No







100




Total 000 USD





























Jul 02 2019
















2





no









Total 000 USD




1 Grant of License




2 Scope of Licence














4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




1



No










Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































vii

TABLE OF CONTENTS


Chapter
















viii








sulfate at pH 70 53



3213 USANS 58













ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



httpsdoiorg101016S0079-6700(97)00047-6


















91













Protein Phases




















92


































93



httpsdoiorg1010160022-2836(88)90606-7











(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










Jul 02 2019












Start Page 570

End Page 583




3



No







100




Total 000 USD





























Jul 02 2019
















2





no









Total 000 USD




1 Grant of License




2 Scope of Licence














4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




1



No










Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































viii








sulfate at pH 70 53



3213 USANS 58













ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



httpsdoiorg101016S0079-6700(97)00047-6


















91













Protein Phases




















92


































93



httpsdoiorg1010160022-2836(88)90606-7











(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










Jul 02 2019












Start Page 570

End Page 583




3



No







100




Total 000 USD





























Jul 02 2019
















2





no









Total 000 USD




1 Grant of License




2 Scope of Licence














4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




1



No










Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































ix

BIBLIOGRAPHY 90

Appendix


x

LIST OF TABLES






62





xi

LIST OF FIGURES
























from [59] 16








[42] 21

xii





from [79] 28





[16 51] 35



upon inversion 36




37














limits 40





[8] 42

xiii


















aggregates 59


















xiv














hardening 70









individual scans 75






above background 77



model 78

xv









xvi

NOMENCLATURE










F Fluid


119865120591 Stress constant (119875119886

119873119898)



119866 Gas



GP Guinier-Porod






xvii


119871 Liquid


m Porod exponent



P Fitting parameter












119878 Solid





t Time (seconds)

xviii






1205740 Amplitude





Γ Decay rate


119896119892

1198983)



1198981198713)


δ Phase angle

γ Surface tension

Φ Volume fraction


xix

ABSTRACT
























xx



wall upon inversion






















xxi


is necessary

1









two conditions










2

























3

























4






















gt 1198621198971198743minus gt 1198611198654


4+ gt 1198731198674

+ gt 119862119904+ gt 119877119887+ gt 119870+ gt 119873119886+ gt 119871119894+ gt 1198721198922+ gt 1198621198862+[26]

5

























6
























7













Hofmeister series












8


changes in pH [43]








[15 16]















9
























10



Figure 120783 120783








[16]

11
























12

























13









[16]

14










15






16









17
























18





19




from [15]

20














[3]

21





from [42]






22


experiments








system spanning gel















23




24


A PROTEIN GELS























25














strain

120574 = 1205740 119904119894119899 120596119905 (2 1)




represented as

120590 = 120590119900 119904119894119899(120596119905 + 120575) (2 2)

26
















of phase by 120587


120587

2 [77]

with 120587







27

119905119886119899(120575) =119866primeprime(120596)

119866prime(120596) (2 4)





















28











119866119898119894119899 =119865120591119879119898119894119899

1205740 (25)

29







119879119898119886119905119890119903119894119886119897 gt 119879119894119899119890119903119905119894119886 (2 6)


1198661205740

119865120591gt 11986812057901205962 (2 7)

where 1205740



119866 gt 119868119865120591

1198651205741205962

(2 8)



30





















31














Inc (Tewksbury MA)










32
























33
























34













35





temperature [16 51]

20 40 60 80 100 12030

25

20

15

10 Gel-like phase

Single phase

Salt c

oncentr

ation (

M)


36


















B A

37









3 hours

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104


G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

Tan(d)

g = 01 w = 628 rads

38











39

233 Frequency sweep






05 10 15 20 25 30 35 40 45

05

10

15

20

25

30

35

log

10G

(w

) (log

10(P

a))


04



40








10-3 10-2 10-1 100 101 10210-4

10-3

10-2

10-1

100

101

102

103

104

Low Torque Limit

G ~ 003 Pa


G(w)

G(w)

Tan(d)

G(

w)

G(

w)

(Pa)


g = 01


41






specifications







119873119898


119903119886119889



Minimum





28)

42









permission from [8]

43







10-3 10-2 10-1 100 101 102100

1000


G(

w)

G(

w)

(Pa)


G1(w)

G1(w)

G2(w)

G2(w)





44





require





















45

























46











47
























48






119876 = 4120587

120582119904119894119899 120579 (3 1)




119871 = 2120587

119876 (3 2)








49









119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) (3 3)







119868(119876) =119866

119876119904 119890119909119901 (

minus11987621198771198922

3 minus 119904) 119891119900119903 119876 le 1198761 (3 4)

119868(119876) =119863

119876119898119891119900119903 119876 gt 1198761 (3 5)

where

1198761 =1

119877119892(

(119898 minus 119904)(3 minus 119904)

2)

12

(3 6)

50

and

119863 = 119866119890119909119901 (minus1198761119877119892

2

3) 1198761

119889 = 119866119890119909119901 (minus1198762119877119892

2

3 minus 119904) 1198761

119889minus119904 (3 7)



















51






119868(119876) =119860

119876119898+

119861

1 + (119876120585)119899 (3 8)












120588(119903)~ 119898(119903)

119903119889= 119903119889119891minus119889 (3 9)



52
























53











54














55





[15]

56





57














holder at 25 C











58



SSD




3213 USANS
















59














aggregates

100 microm

60








61





62










scan (seconds)

1 13 4 1 1920

2 1 4 13 3300

3 13 4 1 4680

4 1 4 13 6060

5 13 4 1 7440

6 1 4 13 9240

7 13 4 1 10620




measurement began

63












64

10-3 10-2 10-110-1

100

101

102

103

Q-14

I(Q

) (c

m-1

)

Q(Aring-1)

Q-21 ~RCLA





(blue)

65







10-3 10-2 10-110-2

10-1

100

101

102

Rg ~ 12 Aring

Rg ~ 88 Aring

I(Q

) (c

m-1

)

Q (Aring-1)




66

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

1920 seconds

3300 seconds

4680 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







67

10-2 10-110-1

100

101

102

103

104

mid-Q GP model

low-Q GP model

7440 seconds

9240 seconds

10620 seconds

I(Q

) (c

m-1

)

Q(Aring-1)







68

Time

(seconds)


parameter s

Porod exponent m

1920 0064 879 plusmn 30 138 226

3300 0142 758 plusmn 13 124 244

4680 0160 774 plusmn 13 121 246

6060 0185 759 plusmn 11 119 255

7440 0198 766 plusmn 11 118 257

9240 0217 754 plusmn 10 117 268

10620 0201 730 plusmn 09 118 268



69







plateau G(ω)

Time

(seconds)


parameter s

Porod exponent m

1920 002 121plusmn08 133 197

3300 002 126plusmn06 135 210

4680 002 151plusmn06 120 220

6060 003 144plusmn05 124 214

7440 005 167plusmn14 109 220

9240 002 150plusmn11 118 224

10620 002 150plusmn12 118 220



70

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G

Low-Q Rg

Mid-Q Rg

Time (seconds)

G(

w)

G(

w)

(Pa

)

0

20

40

60

80

100

120

140

160

180

200

Rg (

Aring)









71







of the gel network

72




119866prime(120596) = 120588119890119897119896119861119879 (3 10)

where

ξel = 120588119890119897minus

13 (3 11)

0 2000 4000 6000 8000 10000 12000

10-1

100

101

102

103

104 G

G





Time (seconds)

G(

w)

G(

w)

(Pa

)

10

15

20

25

30

35

40

45

50

Dim

en

sio

nal p

ara

me

ter

or

Po

rod

exp

onen

t




73
























74









damaged by X-rays

75

0 2000 4000 6000 8000 10000 1200010-1

100

101

102

103

104

Scan 3

Scan 2

G(

w)

G(

w)

(Pa)

Time (s)

G(w)

G(w)

g = 01 w = 628 rads

Scan 1







76













regime

77





10-5 10-4 10-3 10-2 10-110-3

10-2

10-1

100

101

102

103

USANS Regime

GP model

Predicted I(Q)

I(Q

) (c

m-1

)

Q(Aring-1)

Rg ~ 21 Aring







78








system-spanning gel

10-4 10-3100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)



using the GP model

79










a gel network [93]

80

10-3 10-2 10-110-2

10-1

100

101

102

103

104

I(Q

) (c

m-1

)

Q(Aring-1)


GP-model









81























82


41 Conclusions






















83
























84
























85















119875119888 = 5119864

6+

2120574

119903 (41)







respectively [119]

86








423 DLS











1198922(120591) = 119861(1 + 120573|1198921(120591)|2) (4 2)




87

1198921(120591) = 1198601119890minus1205481119905 + 1198602119890minus1205482119905 (4 3)







1198921(120591) = 119890minus119875120548119905 (4 4)













88
























89





















90

BIBLIOGRAPHY


1301ndash12





httpsdoiorg1010160966-7822(93)90020-I


httpsdoiorg101016B978-0-08-100722-800020-6



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91













Protein Phases




















92


































93



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(25)



















94


323 (4) httpsdoiorg101002bit260480404
































95
















httpsdoiorg1010880953-89842132322201













30111980tb02595x





96


















89841932323101






2614 (4)









1878 (3) httpsdoiorg101021la2035054

97







Rheology 9ndash19



0302(02)74078-2






5_6

















98







httpsdoiorg101016S0001-8686(97)90003-8



















httpsdoiorg101107S0021889888008404







99

httpsdoiorg1010160022-3093(94)90581-9


































100

(6) httpsdoiorg101107S0907444997006847




(3) httpsdoiorg101107S0021889897017020



httpsdoiorg101107s0021889806035059














httpsdoiorg101107S0909049510030372











101

httpsdoiorg101093oso97801996552050010001










a74b-71e29d82b719Paperp27562





81(12) httpsdoiorg10106313518961

















102







httpsdoiorg101080108260762012743724





103

Appendix










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4 Acknowledgement








7 Warranty


8 Limitations
















Other Conditions

Version 12








Masterrsquos Thesis

Content title



G Greene

Portion




Type of use

Reuse in a thesis

Format


Title of the thesis



Signed

Daniel G Greene PhD




Jul 03 2019












Start Page 5

End Page 17




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Total 000 USD


INTRODUCTION




























Jul 02 2019














1




no




Portions figure 6



Total 000 USD






1 Grant of License




2 Scope of Licence













4 Acknowledgement








7 Warranty


8 Limitations















Other Conditions

Version 12





Jul 02 2019













Portion Figuretable






Languages English





100




Total 000 USD



































gel-like behavior in amorphous protein dense phases: …

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