hydrophobic effect: thermodynamics of cationic & anionic surfactant

Vilnius universityFaculty of natural sciences

IVth year student of Biophysics BSc

Povilas Norvaišas

Bachelor thesis

Hydrophobic effect: Thermodynamics of cationic &

anionic surfactant interaction and laws of additivity in

the structure-based drug design

Reviewed by: Supervisors:

Dr. Vytautas Smirnovas Dr. Daumantas Matulis

Dr. Visvaldas Kairys

Vilnius, 2012

Vilniaus universitetasGamtos mokslų fakultetas

Biofizikos studijų programos IV kurso studentas

Povilas Norvaišas

Bakalauro darbas

Hidrofobinis efektas: katijoninių ir anijoninių

detergentų sąveikos termodinamika bei adityvumo

dėsniai struktūra paremtame vaistų kūrime

Recenzavo: Darbo vadovai:

Dr. Vytautas Smirnovas Dr. Daumantas Matulis

Dr. Visvaldas Kairys

Vilnius, 2012

Bakalauro darbas


detergentų sąveikos termodinamika bei

adityvumo dėsniai struktūra paremtame vaistų

kūrime

Vilniaus Universitetas Biotechnologijos institutas

Biotermodinamikos ir vaistų tyrimo skyrius

Įvertinimas:

Darbo vadovai:

Dr. Daumantas Matulis

Dr. Visvadas Kairys

Studentas:

Povilas Norvaišas

Vilnius, 2012

Vilnius University

Faculty of Natural Sciences

Department of Biochemistry and Biophysics

IVth year student of Biophysics BScPovilas Norvaišas

Bachelor thesis

Hydrophobic effect: Thermodynamics of cationic &

anionic surfactant interaction and laws of additivity

in the structure-based drug design

Summary

Hydrophobic interactions are ubiquitous in the biological systems. They are involved in

protein folding, membrane formation, protein to ligand binding and many other processes. Even

though these interactions are crucial, it is yet impossible to comprehend them in a direct way – we

need simplifications. This thesis describes two different, but interrelated approaches of employing

such simplifications. In the first study, thermodynamics of hydrophobic effect were investigated

by employing a simple model system of oppositely charged surfactants. The results gathered

with isothermal titration calorimetry indicate that the hydrophobic aggregation in such systems

is driven primarily by the huge negative enthalpy and not positive entropy change – contrary

to the common theory. In the second study different computational modelling approaches and

simplified solvent effect representations were compared for their accuracy in predicting binding

energy of inhibitors to the human carbonic anhydrase II. The results suggested that solvent

representation needed not to depend on the binding event and that the simple docking method

might also be the best one.

Vilnius, 2012

Vilniaus universitetas

Gamtos mokslų fakultetas

Biochemijos ir biofizikos katedra

Biofizikos studijų programos IV kurso studentasPovilas Norvaišas

Bakalauro darbas


detergentų sąveikos termodinamika bei adityvumo

dėsniai struktūra paremtame vaistų kūrime

Santrauka

Hidrofobinė sąveika biologinėse sistemose yra esminė. Jos įnašas svarbus daugybėje

reakcijų: baltymų susivyniojime, membranų susidaryme, baltymų ir ligandų jungimesi ir t.t.

Nepaisant šios sąveikos svarbos, mes dar nesugabame tirti tokių sudėtingų biologinių procesų

tiosiogiai – mums būtini supaprastinti modeliai. Šiame bakalauro darbe pristatomi du skirtingi,

tačiau susiję tyrimai, kuriuose buvo panaudoti tokie modeliai. Pirmajame, izoterminio titrav-

imo kalorimetrijos metodu buvo tirta hidrofobinio efekto termodinamika, kaip modelinę sistemą

naudojant priešingą krūvį turinčius detergentus. Rezultatai parodė, kad hidrofobinė agregacija

tokiose sistemose yra nulemta didelio neigiamo entalpijos, o ne entropijos, įnašo – priešingai

negu teigia klasikinė hidrofobinio efekto teorija. Antrajame tyrime buvo lyginami įvairūs kompi-

uterinio modeliavimo metodai ir tirpiklio reprezentacijos juose, siekiant nustatyti optimaliausią

metodą vertinant slopiklių sąveiką su žmogaus karbonanhidraze II. Analizė atskleidė, kad pa-

prasčiausi modeliavimo metodai gali būti ir geriausi, o tirpiklio įtaka gali būti reprezentuota ne

vien jungimosi reakcijos sąvybėmis.

Vilnius, 2012

Povilas Norvaišas CONTENTS

Contents

1 Introduction 6

1.1 Thermodynamics of cationic & anionic surfactant interaction . . . . . . . . . . . . 6

1.2 Laws of additivity in the structure-based drug design . . . . . . . . . . . . . . . . . 6

2 Literature overview 8

2.1 The Hydrophobic effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 Historic overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.2 ”Classical” hydrophobic effect . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.3 ”Non-classical” hydrophobic effect? . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.4 The fingerprint of the hydrophobic effect . . . . . . . . . . . . . . . . . . . . 11

2.2 Surfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Mixtures of cationic and anionic surfactants . . . . . . . . . . . . . . . . . . 13

2.2.2 Interaction of cationic and anionic surfactants . . . . . . . . . . . . . . . . . 14

2.3 Isothermal Titration Calorimetry (ITC) . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Adiabatic and heat flux ITC . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.2 Planning of the ITC experiment . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4 Additivity – the 4th law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Carbonic anhydrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5.1 Structural properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5.2 Drug design for CAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5.3 Inhibitors of CAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.6 Computational structure-based drug design . . . . . . . . . . . . . . . . . . . . . . 23

2.7 Docking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.7.1 Posing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.7.2 Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7.3 Poisson-Boltzman surface area method . . . . . . . . . . . . . . . . . . . . . 25

3 Thermodynamics of Cationic and Anionic Surfactant Interaction 27

3.1 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.2 Isothermal Titration Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1.4 Statistical analysis of the data . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2 The mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3.1 Dependence on the order of titration . . . . . . . . . . . . . . . . . . . . . . 33

1

3.3.2 Dependence on the surfactant concentration . . . . . . . . . . . . . . . . . . 34

3.3.3 Dependence on the aliphatic chain length . . . . . . . . . . . . . . . . . . . 36

3.3.4 Dependence on the ionic force of the solvent . . . . . . . . . . . . . . . . . . 38

3.3.5 Dependence on the experimental temperature . . . . . . . . . . . . . . . . . 39

3.3.6 Structure of the aggregate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4 Laws of additivity in the structure-based drug design 44

4.1 Materials & methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.1 Protein and its structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.2 Inhibitors and their structures . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.3 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.4 Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.5 Docking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.6 PBSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 Docking with Vdock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.2 PBSA potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.3 Expressions of total modelled binding energy . . . . . . . . . . . . . . . . . 48

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5 Conclusion 53

6 Acknowledgements 54

References 63

7 Supplementary material 64

2

Nomenclature

[cell] Concentration of a surfactant in the cell of the calorimeter

[M ]0 Concentration of the compounds in the reaction cell with respect to the dilution effect.

Used in ITC data analysis

[X]0 Concentration of the ligand from the syringe in the reaction cell. Used in ITC data analysis

∆∆Gpre Change in the Gibbs free energy upon addition of methylene group

∆Cp Heat capacity change at constant pressure

∆Cliquidp Heat capacity for a liquid aggregate.

∆Csolidp Heat capacity for a solid aggregate.

∆G Gibbs free energy change for reaction

∆Gagg Entropy change for aggregation multiplied by absolute temperature

∆Gagg Gibbs free energy change for aggregation

∆Gexp Gibbs free energy change determined in TSA experiment.

∆Gmod Gibbs free energy change determined by docking

∆H Enthalpy change for reaction

δH Partial enthalpy change for one injection.

∆Hagg Enthalpy change for aggregation

∆Hexp Enthalpy change of a reaction, determined by direct integration of the dosing curve.

∆Hfit Enthalpy change of a reaction, determined by a fitting the dosing curve

∆Hfus Enthalpy of fusion.

∆Hpre Enthalpy change fro precipitation

∆Hstr Enthalpy of structural rearrangements prior to fusion.

∆SASA Solvent accessible surface area change upon binding

∆T∆Sobs Observed entropy change upon addition of one methylene group

∆∆G Change in the Gibbs free energy upon addition of one methylene group

∆∆Gobs Observed Gibbs free energy change upon addition of one methylene group

∆∆Hexp Enthalpy change upon addition of one methylene group

3


∆aggHalk Empirical enthalpy change for linear alkanes.

∆aggHalm Modelled enthalpy change for the surfactants system.

c Coefficient, used to evaluate ITC’s capability of determining Kb at the given experimental

concentration

cmc Critical micelle concentration

cmcmix Critical micelle concentration for a particular mixture of surfactants

cmt Critical micelle temperature. Analogoud to TK

Kb Binding constant

Kfitb Binding constant determined by fitting the dosing curve

Koff Disassociation constant, term used in the SPR studies.

Kon Association constant, term used in the SPR studies. Analogous to Kb.

m Total aliphatic chain length for the system of surfactants

N Stoichiometry of the reaction

n Aliphatic chain length for a single surfactant

Nfit Stoichiometry determined by fitting the dosing curve.

SAvdw Van der Waals surface area.

SASAHyd Hydrophobic solvent accessible surface area

T∆S Entropy change for reaction multiplied by temperature

TK Krafft temperature. Analogous to cmt.

V Colintr Coulomb electrostatic potential for the protein-ligand interaction

V Colint Coulomb electrostatic potential for ligand

V Dih Dihedral potential for ligand

V P B Poisson-Boltzmann electrostatic potential

V vdwattr Van der Waals attraction potential for protein-ligand interaction

V vdwint Van der Waals potential for ligand

V vdwrep Van der Waals repulsion potential for protein-ligand interaction

CPC Cetylpyridinium chloride C21H33CN ·H2O.

DPCl Decylpyridinium chloride C15H26C1N ·H2O

4


FFT Fast Fourier Transformation

MCS Micro Calorimetry System

SDS Sodium dodecyl sulfate, C12H25OSO3Na)

SPR Surface plasmon resonance

TSA Thermal shift assay (ThermoFluor)

5

1 Introduction

Biological systems are believed to have emerged in the aqueous medium and even now,

billions of years past, both most primitive and sophisticated forms of life are fully dependent on

it. A significant role is played here by the hydrophobic effect. The biochemical machinery has

developed in such a way that it employs hydrophobicity for its own needs in the interactions

between molecules or formation of biological compartments. Even though these processes are as

ubiquitous as life is, we can not yet comprehend them by direct approach – we need simplifications.

This is is the main theme of my bachelor thesis – simplifications for complex phenomenon regarding

hydrophobic effect and the contribution of solvent in general. It is further divided into two research

projects which tackle the same main idea from completely different perspectives.

1.1 Thermodynamics of cationic & anionic surfactant interaction

The main goal behind this research project was to investigate thermodynamics of hy-

drophobic effect for highly hydrophobic compounds by employing a simplistic system of cationic

and anionic surfactants. This could only be accomplished by investigating a number of proper-

ties regarding the thermodynamics of cationic and anionic surfactant complex formation with the

technique of isothermal titration calorimetry:

• dependence on the surfactant concentration

• dependence on the aliphatic chain length of the surfactants

• dependence on the ionic strength of the solvent

• dependence on the temperature

• structure of the oppositely charged surfactant complex.

1.2 Laws of additivity in the structure-based drug design

Overall different approach was taken in this study - testing of different computational

methods and representations of the possible solvent effect to find the best one to evaluate ligand

to protein binding energies in silico for human carbonic anhydrase II and inhibitors synthesised

in the Department of Biothermodynamics and Drug Design of Vilnius University Institute of

Biotechnology. In order to accomplish this goal several computational modelling methods had

to be taken:

• docking of inhibitors with VDock

• estimation of solvent effect according to Poisson-Boltzmann surface area (PBSA) method

6

Povilas Norvaišas Introduction

• development and evaluation of total modelled energy expressions with different representa-

tions of possible solvent effect.

7

2 Literature overview

2.1 The Hydrophobic effect

If water is considered to be the reason behind life on earth, so must be the hydrophobic

effect (Chaplin 2012). Formation of membranes, cellular compartments and the folding of polypep-

tides into native proteins is believed to be driven largely by hydrophobic interactions (Tanford 1978;

1997). Due to them the whole set of amphiphilic compounds as lipids or polypeptides are capable

of establishing sophisticated, self-assembled structures at the molecular scale and the only thing

required is aqueous media. Therefore, the hydrophobic effect can be regarded as an ”organiser” of

the biological world at the molecular scale. Besides all of this, it is hard to find any interactions

between biological compounds which would not be influenced by hydrophobicity. It might be a

ligand binding to a protein, protein folding, assembly of the protein complex, signal transduction

and many more, plenty of which have enormous biological significance. Therefore, the fundamental

processes behind hydrophobic effect are profoundly interesting and research on them might as well

help us better understand many biological/biochemical phenomena at the molecular scale.

2.1.1 Historic overview

The structural reason behind solubility and insolubility of various compounds was first

identified in 1891 by german scientist Isidor Traube (Tanford 1997). During his studies of thin

layers of amphiphilic compounds, he discovered that such molecules orient their hydrophobic parts

out of the aqueous solution. Further research done by Irvin Langmuir extended the ideas of Traube

and resulted into the series of publications, because of which Langmuir is considered the ”father”

of the science of surfactants (Tanford 1997). At the beginning of XXth century both chemistry and

physics underwent a revolution which expanded the toolkit of scientists and enabled observation of

phenomena in atomistic scale. In 1919 Moore together with Winmill hypothesised hydrogen bonds

(Moore and Winmill 1912). It was not long before 1920 when it was understood that there should

be an extensive network of such bonding in water (Latimer and Rodebush 1920) that might be

responsible for the extraordinary features of this solvent (Chaplin 2012; Bernal and Fowler 1933).

In 1945 Frank and Evans suggested that it was not an attractive force behind the aggregation of hy-

drophobic compounds in aqueous medium, but structure of the solvent itself (Mizutani 2011). Soon

it became clear that such theory would have wide implications when applied to biological systems.

The research led by Charles Tanford and Walter Kauzmann revealed significance of hydrophobic

effect in the formation of micelles, membranes and folding of the proteins (Tanford 1978; 1997;

1980; Kauzmann 1959). The main thermodynamic quantities of the dissolution reactions were

determined and the basis for the research on hydrophobic effect in biological systems established

8

Povilas Norvaišas Literature overview

during the period between 50s and 70s. These ideas were later widely applied in many fields of life

sciences – drug design, computational modelling of protein-ligand interaction and protein folding,

etc.

2.1.2 ”Classical” hydrophobic effect

The main contribution of Frank & Evans to the research on hydrophobic effect was that

they hypothesised an extensive network of hydrogen bonds in the liquid water which is responsible

for the strong cohesion of solvent molecules and repulsion of non-hydrated molecules (Frank and

Evans 1945). It is now known that water molecules form 3.6 hydrogen bonds on average with

one another. This property is unique to water, as there are no compounds of similar molecular

mass, which would form such tight bonding in between themselves (Chaplin 2012). As a result of

such network of bonds, any substance incapable of incorporating and forming sufficient number of

hydrogen bonds with the solvent will be forced to aggregate with similar non-polar compounds –

the hydrophobic effect will happen (Tanford 1978). According to the classical theory this process

is primarily driven by the positive entropy change due to a gain of motional freedom of water

molecules upon loss of contact with the hydrophobic compound. The bulk water molecules are

capable of freely rotating due to brownian motion, because in every direction there will be another

water molecule capable of forming favorable hydrogen bond. However, in the vicinity of hydropho-

bic compound, water molecules will be constrained forming hydrogen bonds only in the direction of

bulk water and therefore their motional freedom will be restricted and entropy of motion decreased.

The only way of avoiding this unfavorable interaction for water molecules is to decrease contact

with non-polar compound. It is accomplished by aggregating hydrophobic molecules together and

thus reducing their overall interface with the solvent. The aggregation is accomplished by brownian

motion of the solute and solvent – once hydrophobic molecules are aggregated, it is unfavorable

for them to be dissolved again. This theory was formulated by Frank & Evans and named the

”Iceberg theory” after the hypothetical layer of constrained ice-like water molecules surrounding

the hydrophobic molecule (Frank and Evans 1945). However, there was and still is a discussion

going whether the surface area of the hydrophobic solute is the best measure of hydrophobic effect.

The theory of protein folding due to the need of concealing hydrophobic residues from the aque-

ous medium formulated by Kauzmann was based on the idea of reduction of hydrophobic surface

(Kauzmann 1959) as well as the research done by Tanford (Tanford 1980; 1979; 1978). But there

are several alternatives like the molar volume of the hydrophobic compound (Hildebrand 1979) or

the number of hydrogen bonds in the first layer of hydration (Madan and Sharp 1997).

9


2.1.3 ”Non-classical” hydrophobic effect?

Even though positive entropy change was and still is considered the main driving force

behind hydrophobic effect, several research groups have presented contradicting results. As early

as 1969 Jencks separated two classes of hydrophobic effect: the ”classical” one, driven by the

positive entropy change (∆S > 0) and the ”non-classical” – driven by negative enthalpy change

(∆H < 0). Some experiments done in 60s and 70s gave results in favour of the notion of ”non-

classical” hydrophobic effect (Mizutani 2011; Fernández-Vidal et al. 2010). However, in many cases

the reason behind the negative enthalpy change was not clear and therefore it was attributed to

different processes than hydrophobic effect, as it was done in the research which can be called

a direct predecessor to our study (Papenmeier and Campagnoli 1969). Now it is clear that the

whole notion of separating hydrophobic effect into two different processes was misleading. Most

of the initial research concerning thermodynamics of hydrophobic effect done by Tanford (Nozaki

and Tanford 1971; Tanford 1979) concentrated on small hydrophobic compounds like glycine pep-

tides and separate amino acids. The results were obtained in so-called ”fractioning” experiments,

when solubility of hydrophobic compound was measured in the ethanol-water mixtures at various

concentrations of ethanol. The solubility in pure water, which could not be determined directly,

was calculated by making an extrapolation from the collected data. Indeed, dissolution reactions

of these compounds were driven by positive entropy change, however the limitations of methodol-

ogy prevented from testing much larger and more hydrophobic compounds, not mentioning that

solubility and in result the free energy of dissolution were obtained by extrapolation and not by

a direct measurement. At that time if was determined that the thermodynamics of dissolution

depend linearly on the number of aliphatic atoms (CH2 group) of the compounds (Mizutani 2011),

but once again it was tested only for small molecules. Only much later research done by Matulis

has shown that the situation for long chained (12-14 CH2 groups) largely hydrophobic aliphatic

amines is quite different (Matulis and Bloomfield 2001a;b). The dissolution and aggregation of

such compounds is driven by large negative enthalpy change (∆H << 0) and therefore should

be regarded as an example of ”non-classical” hydrophobic effect. However, further studies and

dissection of the thermodynamic parameters for the dissolution of alkanes, alcohols and amines

(Matulis 2001) stated that the Gibbs free energy of precipitation retains the same proportional-

ity per one methylene group: ∆∆G = −3.58 kJ/mol. Therefore, it is the same process, which

exhibits different contributions from enthalpy and entropy for compounds with different levels of

hydrophobicity. Besides, thermodynamics of aggregation depend significantly on the temperature

and concentration of the compounds. If the hydrophobic molecules aggregate into a liquid phase,

their dissolution reaction is primarily driven by the positive entropy change, as the gain in motional

freedom of water molecules is high compared to the restrain of liquid aggregate. However, when the

aggregate forms a solid state, molecules experience much more constrain and their loss of motional

freedom outweighs the positive entropy gain of water – process is dominated by enthalpy driven

10


interactions in a tightly packed aggregate (Matulis 2001; Norvaisas et al. 2012). Even though

the contribution of enthalpy and entropy might differ significantly, the overall value of ∆∆G per

one CH2 group is the same. This phenomenon is called ”Enthalpy-entropy compensation” and is

observed in various systems (Cornish-Bowden 2002; Chen et al. 1998; Tanford 1997). However,

there is a discussion happening for some time, whether it is a true fact of a physical world or just

an artefact of experimental limitations. Main thermodynamic parameters – enthalpy, entropy and

Gibbs free energy are related to another by equation 2. The problem is, that only enthalpy and

Gibbs free energy (through the binding constant Kb (Eq.1) or any other measure of difference in

chemical potentials) can be measured experimentally.

∆G = −RTln(Kb) (1)

No method for direct evaluation of binding entropy has been found yet. Therefore, ∆S is always

obtained by using the equation 2 and the ”compensation” is unavoidable, as one parameter is

dependant on the values of the other two (Cornish-Bowden 2002). Even though the relationship

stated in Eq.2 might be perfectly right, the values of ∆S have an error of both enthalpy and

entropy and should not be treated as certain.

∆G = ∆H − T∆S (2)

2.1.4 The fingerprint of the hydrophobic effect

In respect to the dither concerning the nature of hydrophobic effect and its true fin-

gerprint, one another property was considered – the change in the heat capacity of hydrophobic

reactions ∆Cp. It was discovered that this change is highly negative for the reactions of dissolution

and conversely – positive for the hydration (Matulis 2001; Matulis and Bloomfield 2001b; Baldwin

1986; Sturtevant 1977). The main reason behind it is the same ”iceberg” of highly structured

water molecules surrounding hydrophobic compound in the solvent. Upon hydration it increases

the heat capacity of the solution of hydrophobic compounds because additional energy will be

spent in breaking the constrained hydrogen bonding as if the ice would melt. And vice versa for

dissolution – decrease in the number of structured water molecules leads to the decrease of heat

capacity. This change is now considered the main fingerprint of hydrophobic effect as other pa-

rameters might change significantly and sometimes in rather unpredictable fashion (Shimizu and

Chan 2000).

2.2 Surfactants

Alkyl sulfates, alkane sulfonates and alkyl amines (Tab.1) are so called detergents – de-

terge agents. Together with most lipids and molecules of a comparable structure they belong to

11


Surfactants General formula

Alkyl sulfates CnH2n+2OSO–3

Alkane sulfonates CnH2n+2SO–3

Alkyl amines CnH2n+2NH+3

Table 1: General formulas of surfactants used in this study.

a much bigger class of compounds called surfactants – surface active agents. The main structural

elements of surfactants are the polar head-group which is hydrophilic and non-polar tail with hy-

drophobic properties. Such bivalent structure is responsible for the properties of these amphiphilic

compounds. Hydrophilic head makes detergents soluble in polar solvents, whereas hydrophobic

tail is responsible for their tendency to form a plentitude of complex colloidal phases, prononced

lyotrophic & thermotrophic properties, and solubility in non-polar solvents which depends on the

ratio of the size of hydrophobic and hydrophilic parts (Nagarajan 1991). Surfactants have been

given such name because of their non-linear influence on the physical properties of the solution.

Upon increase in the concentration of surfactants, surface tension and the conductivity of a so-

lution changes in an abrupt steps (Aniansson et al. 1976; Somasundaran et al. 1964). In order

to explain such anomalous behaviour, micelle theory was created (Hoerr et al. 1943), which was

largely based on the ideas of Irvin Langmuir and then recently established theory of the hydropho-

bic effect (Tanford 1997). According to the ”classical” theory once certain concentration of the

surfactant is reached it becomes more favourable to form micelles thus concealing hydrophobic

tails than orienting these tails out of the aqueous medium. In such a process, surfactants lose their

motional freedom, but it is recovered by an increase in the entropy of water upon reduction of

hydrophobic interface. The balance between two opposing forces is reached when the concentration

of the surfactant equals cmc – critical micelle concentration. Analogous parameter is the cmt –

critical micelle or Krafft (TK) temperature. If the temperature is higher than the cmt – micelles

will not form, and the surfactants will remain as fully dissolved monomers. The formation of mi-

celles is the first step towards various phase changes that the surfactants can undergo. However,

micellar phase itself can not be considered a ”true phase” on its own. For a phase transition like

melting of ice or evaporation change in the Gibbs free energy equals zero (∆G = 0). Even though

micelles have properties of a separate phase, it is not really correct to consider them so, because

micellisation is usually accompanied by non-zero change in the Gibbs free energy. Therefore, they

should be treated as a pseudophase (Stellner et al. 1988). In solution, formation of the micelles

is followed by disassemble and the equilibrium is expressed through the half-lifes of two states

(Kume et al. 2007). Alternatively to the micellisation and other colloidal states, where surfactans

are still at least partly dissolved in the solution, they may precipitate out of the solution upon loss

of the charge in the polar group. This can be caused by change in pH (Matulis and Bloomfield

2001a), neutralisation with acid/base (Matulis and Bloomfield 2001b) or any other substance of

12


opposite charge. Purely aliphatic compounds with similar hydrophobic tail length like alkanes are

almost completely insoluble (McAuliffe 1969). Therefore, such precipitation (aggregation) is highly

favourable and is accompanied by huge negative change in the Gibbs free energy (Matulis 2001;

Matulis and Bloomfield 2001b).

2.2.1 Mixtures of cationic and anionic surfactants

In the beginning of the XXth century, it was already much known about the physi-

cal properties and thermodynamics of homogeneous surfactant solutions (Saito 1982; Tartar and

Wright 1939; Hoerr and Ralston 1942a; Hoerr et al. 1943; Hoerr and Ralston 1943; 1942b; Ralston

et al. 1941; 1942). Because of their resemblance to lipids, surfactants can be used as a simple

model system to investigate general properties of membrane formation and other biochemical phe-

nomena. However, for the most part research on the surfactants was initiated not as an approach

to model biologically relevant systems with simpler compounds, but because of industry’s inter-

est. As it was mentioned, upon aggregation with oppositively charged compounds, surfactants

precipitate out of aqueous medium and become inactive. This property is especially important in

making multicomponent cleaners, where both cationic and anionic surfactants are mixed (Holland

and Rubingh 1992). Therefore, it became necessary to investigate systems of mixed surfactants

and at least determine their cmcmix values. Detailed research on the system of sodium dodecyl

sulfate (SDS, C12H25OSO3Na) and decylpyridinium chloride (DPCl, C15H26C1N ·H2O) revealed

that such systems form several colloidal phases in the solution (Fig.1) and may precipitate in a

wide range of concentrations (Stellner et al. 1988). Here is the description of the main phases of

the system:

• The concentration of both surfactants is sufficiently low and they remain as fully dissolved

monomers (Fig.1: [SDS] ≈ [DPCL] → 0).

• Concentration ratio is highly imbalanced – homogeneous micelles of only one surfactant form

(Fig.1: [SDS]/[DPCL] » 1 or [SDS]/[DPCL] « 1, if cmc is reached).

• Concentration ratio is more balanced and close to one – mixed micelles form (Fig.1: [SDS]/[DPCL]

> 1 or [SDS]/[DPCL] < 1, if cmcmix is reached)

• Concentration ratio is close or equal to one – surfactants precipitate (Fig.1: [SDS]/[DPCL]

→ 1, when [SDS] and [DPCL] >> 0 (solid aggregate in Tab.2 and Matulis (2001); Norvaisas

et al. (2012))

• With certain ratio of concentrations and proper temperature – coacervate may form which

resembles liquid hydrophobic droplets in an aqueous medium.

13


Figure 1: Phase diagram for the mixture of SDS and DPCL. Taken from Stellner et al. (1988)

2.2.2 Interaction of cationic and anionic surfactants

In the 1969 for the first time it was tried to speculate how such compounds interact and

what structural components are responsible for the corresponding thermodynamics (Papenmeier

and Campagnoli 1969). Group led by Campagnoli investigated reactions in various concentrations

of SDS and cetylpyridinium chloride (CPC, C21H33CN ·H2O). The main goal of this research

was to determine thermodynamic parameters of the micelle formation and possible precipitation

of the surfactants. The results suggested that the interaction is highly favoured by enthalpy –

∆H = −75.3 kJ/mol . At that time it was established that the hydrophobic reactions should

be primarily driven by positive entropy change (∆S > 0). Sadly, the idea of enthalpy driven

hydrophobic effect hasn’t been formulated back then and therefore, it was not speculated what

process or structural units responsible for such thermodynamics (Papenmeier and Campagnoli

1969). The study also determined Gibbs free energy change for the system. However, due to

technological limitations, the values of ∆G relied heavily on the model used to describe kinetics of

the reaction. ∆G equaled−62.76 kJ/mol if hypothetical micelles were assumed to be a pseudophase

and −37.6 kJ/mol if the micellar phase was neglected. In equimolar mixtures of the detergents,

micelles were really ”hypothetical”, because the researchers were instead observing the formation

of precipitate. This effect was especially pronounced at higher concentrations of both detergents,

as the precipitate forms gradually with increased concentration. Due to this effect, enthalpy of

the reaction is dependent on the concentration of the detergents, until no micelles are formed at

all and equilibrium fully shifts towards the formation of precipitate (see Fig.1 here and Table II

in Papenmeier and Campagnoli (1969)). What Campagnioli and colleagues also didn’t knew, was

14


that the critical micelle concentration for the mixture of cationic and anionic surfactants (cmcmix)

is always significantly lower than the one of pure surfactants (Stellner et al. 1988). Therefore, in

the experiments they observed micelle formation at the lower concentration than initially expected

and precipitate formation where the formation of micelles was assumed. All in all, even with some

invalid assumptions, research presented some interesting results. However, no speculations have

been made on the nature of such thermodynamics of binding.

Further research on the interaction of cationic and anionic surfactants have revealed some

other interesting properties (Amante 1991). Study focused on the interaction between DPCl and

alkyl sulfates of various aliphatic chain length (n = 8 − 12). With the increasing aliphatic chain

length, boundary between monomer and precipitate shifts towards lower concentrations, primarily,

because of smaller cmc values. If only one of the detergents is changed, then the whole phase

diagram shifts in the direction of decreased cmc (Fig.5 in Amante (1991)). Also, it was observed

that the change in the Gibbs free energy upon addition of one methylene group to the aliphatic

chain (∆∆G) is larger for the formation of the precipitate (∆∆Gpre = −4.14 kJ/mol ) than that

of micelles (∆∆Gpre = −2.96 kJ/mol ). Therefore, surfactants in the mixture are more likelly

to be found in precipitate than in micelles. Values of ∆Hpre were determined with then widely

used but prone to error method of Van’t Hoff analysis (Tellinghuisen 2006; Liu and Sturtevant

1997b; Chaires 1997; Liu and Sturtevant 1997a), when enthalpy values are estimated from the ∆G

dependence on the temperature. It was also suggested that with sufficiently small n, aggregation

might not happen at all, however it was not extensively tested. Only much later it was shown

that the short chained surfactants indeed can not aggregate or require concentration above the

experimental capabilities (Matulis and Bloomfield 2001b).

Influence of electrolytes on the hydrophobic effect has been acknowledged for some time

(Ben-Naim and Yaacobi 1974) and it was suggested that the salts act according to the Hoffmeister

series (Fernandes et al. 2010). However it is not clear whether salt changes structure of the water

(Nucci and Vanderkooi 2008) or directly interfere with the interaction between molecules (Zhang

and Cremer 2006). In the case of mixed surfactant solutions it has been observed that increase

in the salt concentration interferes with the hydrophobic effect and increases cmc values for the

surfactants. Therefore, precipitation would happen at higher concentration (Kume et al. 2007;

Amante 1991).

Even though research was done on many popular surfactant systems, it mostly concen-

trated on determining characteristics of the specific compounds and not the fundamental processes

behind. There is no unified theory explaining the thermodynamics of protein denaturation with

surfactants (Otzen 2011) or membrane partitioning – processes, that both exhibit ”non-classical”

hydrophobic effect. Some questions have been partly answered (Matulis and Bloomfield 2001a;b;

Matulis 2001), but the research needs to be extended to even more hydrophobic, partly polar

15


compounds which resemble biologically relevant molecules.

2.3 Isothermal Titration Calorimetry (ITC)

The name of this methodology itself explains main principle behind - measurement of a

heat flow created by reaction, while titrating at constant temperature. First commercially avail-

able isothermal titration calorimeters appeared in 1988 (Olofsson and Loh 2009; Wiseman et al.

1989). Quickly, it became one of the most widely used laboratory methodologies in various sorts

of research. Calorimetry has been in various forms for quite some time, like the differential scan-

ning calorimetry (DSC) in the research done by Papenmeier (Papenmeier and Campagnoli 1969).

However, only during the last decade of XXth century it became very popular and it’s not surpris-

ing why. ITC doesn’t require any additional preparation of the reagents, experiments are short

and easy to perform (Jelesarov and Bosshard 1999). It enables a direct measurement of reaction

enthalpy and binding constant Kb (by fitting the data according to the mathematical model of

reaction kinetics), thus instantly providing 2 out of 3 parameters of the reaction thermodynamics.

Newest ITC calorimeters are extremely sensitive and can measure binding energies of the com-

pounds in nanomolar concentration. The main competitors of the ITC have both advantages and

drawback of their own. Surface plasmon resonance (SPR) technique enables more detailed insight

into the binding constant, as it can measure both the constant of association Kon and dissociation

Koff in the same experiment. The main disadvantage of this method is the requirement to immo-

bilise one of the reagents onto the experimental surface. Thermal shift assay (TSA) in its regard

has much greater throughput, because of the use of the 96 well plates, which enables measurement

of the affinity for various ligands or same ligands with different pH, buffers or proteins during the

same experiment. However, it cannot measure the ∆H in a direct way, as ITC does(Matulis 2008).

ITC is widely employed in the research on protein-ligand interactions in the structure-

based drug design and measurements of various other kinds of interactions like protein-protein;

protein and metal, nucleic acid, polysacharids, polymers; nucleic acids and small molecule, deter-

mination of enzyme kinetics and many other (Velázquez Campoy and Freire 2005; Heerklotz and

Seelig 2000; Otzen 2011; Falconer et al. 2010).

2.3.1 Adiabatic and heat flux ITC

There are two types of ITC calorimeters currently available: heat flux and adiabatic ones.

The reaction cell of heat flux calorimeters is surrounded by a heat-sink. Between the heat sink

and the cell there is a layer of thermopile, which registers heat flux in or out of the cell. The main

advantage of such calorimeters is wide scale of sensitivity – from 10 µW to 10 mW. However, one

experiment with the heat flux calorimeter can last up to several hours, because thermal equilibrium

16


is reached slowly after the injection, even with high thermal conductivity. These calorimeters are

capable of measuring intensive heat flow from huge samples (Olofsson and Loh 2009).

Adiabatic calorimeters are made for a completely different purpose. They are fast and

sensitive enough to work with nanomolar amounts of substances. These calorimeters are in fact very

precise thermometers, measuring the temperature difference between reaction and experimental

cell. Cooling system surrounding the cells acts as a heat sink and the whole apparatus is covered

with adiabatic shielding. During the reaction, heat released or absorbed by the experimental cell

is measured by comparing the power needed to keep both experimental and reference cells at the

constant temperature. Because of such system, adiabatic calorimeters can measure heat flow of less

than 1 µcal/s. The most popular calorimeters are made by USA established company MicroCal®,

they have a reaction vessel of 1 mL (MCS ITC®, VP-ITC®), but the more sensitive ones have a

cell of 250 µL (ITC200®). Adiabatic calorimeter has been also used during this study, therefore the

planing of the experiment will concern this type of ITC.

2.3.2 Planning of the ITC experiment

One of the most important parameters which must be decided or at least guessed before

the actual experiment is the concentration of the reagents used (Doyle 1997). If the concentration

is too high, excess heat from the cell won’t be registered, if too low – heat flux will not be sufficient

to accurately determine reaction enthalpy. Same applies to the binding constant Kb. High con-

centration will increase the steepness of the binding curve, so that the titration is finished in one

injection. Low concentration, however, will cause the gradual ending of the reaction, which might

also be too flat for fitting model (Doyle 1997; Olofsson and Loh 2009; Jelesarov and Bosshard

1999). As it can be seen, planning requires finding a golden ratio between accuracy and techno-

logical limitations. Such golden ratio is called ”c” coefficient, which determines relation between

concentration of the substance in the calorimeter cell and the binding constant Kb:

c = [cell]×Kb. (3)

The range of ”good” c values is not consistent among different researchers. Most popular range

is 1 − 1000 (Wiseman et al. 1989), but the other authors suggest that the limitations are more

stringent and c ∈ 10 − 100 (Jelesarov and Bosshard 1999). However, it was proven that with

c < 0.1 it is still possible to determine binding constant Kb with sufficient level of confidence and

it becomes less dependent on the error in stoichiometry (Tellinghuisen 2008).

One of the technological experts of the ITC methodology, Joel Tellinghuisen have deter-

mined rules for the most effective ITC experiment (Tellinghuisen 2006):

1. titration should be carried out in 10 injections

17


2. concentration of the substances in the syringe and the cell (c) selected in such a way, that

after the last injection ratio of the titrant [X]0 and titrand [M ]0 concentrations in the cell is

determined by the relationship in Eq.4:

[X]0[M ]0

≡ Rm = 6.4c0.2 + 13

c, with Rm > 1.1 (4)

3. titration must be started with highest possible concentration, but c < 1000

When all of the mentioned rules are satisfied, the error in ∆H and Kb, which depends on

the technological limitations of the method is considered to be 1% (Tellinghuisen 2006). Even then

there is a possibility that the calorimeter has a systematic error. To check it, every calorimeter has

built in heat pulse generator which enables calibration of the instrument. However, even then there

might be some inconsistencies, which can only be ruled out by testing calorimeter with standard

reactions of high and accurately determined enthalpy. The examples of such reactions could be

the NaCl dilution into water (Tellinghuisen 2007a), neutralisation reaction HNO3 + TrisBase or

interaction of two salts NaI + AgNO3 (Baranauskiene et al. 2009).

2.4 Additivity – the 4th law of thermodynamics

The additivity of contribution made by chemical groups in terms of their physical, chem-

ical properties and thermodynamics is one of the most widely used principles in biochemistry and

other physical sciences. It is indeed so popular, that might be called the unofficial, 4th law of

thermodynamics (Dill 1997). Almost everything has been tried to be summed up: contribution to

the overall Gibbs free energy, entropy and enthalpy of the reaction, solubility, hydrophobic surface

area and the energy of chemical bonds. However, in many cases the assumptions are too stringent

to be true. Parameters of chemical groups should be independent of one another and each group

should experience more or less similar environment (Dill 1997). Besides, usually the additivity

models have a significant level of redundancy – for example Gibbs free energy can be calculated

in terms of the number of polar and non polar groups, types and energetics of the interactions

formed, primary and secondary structural components, etc. The only systems, which seem to obey

this 4th law are polymers, like alkanes, which are made of similar chemical groups (Dill 1997).

Good linear dependence of the parameters on the structure of such compounds is most likely to

be a consequence of similar bonding and environment that each atom experiences. The properties

of heterooligomeric structures with only a small number of differing monomers can also be calcu-

lated with a degree of certainty (Plyasunov et al. 2004; 2006; Plyasunov 2000a; Plyasunova et al.

2005; Plyasunov et al. 2000; Plyasunov 2000b; Plyasunov and Shock 2001; Matulis and Bloomfield

2001a;b; Matulis 2001). A good example of additivity concerning the hydrophobic effect are the

thermodynamics of aggregation for various classes of compounds (Tab.2).

18


∆Gagg, kJ/mol ∆Hagg, kJ/mol T∆Sagg, kJ/molA

ggre

gatio

n

Into

liqui

d Alkanes (m = 5− 17) −3.58m− 0.69 −1.25m + 9.25 2.33m + 9.94

Alcohols (m = 1− 12) −3.58m + 14.33 −1.25m + 12.70 2.33m− 1.63

Alkylamines (m = 3− 11) −3.58m + 19.30 −1.25m + 27.70 2.33m + 8.40

Into

solid Alkanes (m = 18− 20) −3.58m− 0.69 −5.20m + 18.41 −1.62m + 3.76

Alcohols (m = 13− 20) −3.58m + 14.33 −5.67m + 25.08 −2.06m− 5.09

Alkylamines (m = 12− 20) −3.58m + 19.30 −5.25m + 45.71 −1.67m + 11.00

Table 2: Dependency of the thermodynamic parameters of aggregation on aliphatic chain length

n for alkanes, alcohols and alkylamines at 25℃. Taken from Matulis (2001).

The attempts to calculate analogous dependencies for a much more complex biological

systems like protein-ligand complexes are complicated. In heterogeneous environment contribution

of various chemical groups is governed not only by additivity, but also by cooperativity – groups

influence one another. Polar groups could have a significant contribution to the change in the

entropy of the system and hydrophobic interactions might constitute a large part of the enthalpy

potential (Baum et al. 2010). Therefore, it becomes hard to dissect contributions of individual

groups, especially when it is only possible to observe the overall result of the pleiad of interac-

tions. Three main thermodynamic parameters (∆G, ∆H and T∆S) represent the final result of

a reaction. With such a level of abstractiveness a significant part of the information concerning

the system is lost and can only be recovered by the supplementary methods (X-ray crystallogra-

phy, FRET microscopy, etc.). The extent of ”non-additivity” becomes apparent in analyzing large

databases of protein-ligand interaction thermodynamics (Ladbury 2010; SCORPIO 2012). When

the thermodynamics are resolved according to structural units of the ligands, no correlation can

be found between, for example, hydrophobic surface area of the ligand and the entropy change of

the reaction (according the material of lecture by John E Ladbury). The conclusion regarding the

4th law of thermodynamics is clear – it is viable only in very simple and homogeneous systems.

These are the ones that can really help in understanding some basic processes behind more complex

phenomenon.

2.5 Carbonic anhydrases

Carbonic anhydrases (CAs) are ancient enzymes present in virtually every tissues, cell

types, subcellular organelles, and in organisms ranging from unicellular cyanobacteria to mammals

(Imtaiyaz Hassan et al. 2012). The reason behind such ubiquity is their role in the process of

respiration. CAs catalyse reaction of carbon dioxide (CO2) conversion to bicarbonate (HCO–3) and

19


vice versa

CO2 + H2O←−→ HCO−3 + H+. (5)

Bicarbonate is insoluble in lipid membranes and needs to be transported, while carbon dioxide is

more soluble, therefore it diffuses freely in and out of the cell (Imtaiyaz Hassan et al. 2012).

There are five evolutionarily unrelated gene families of CAs: the α-, β -, γ -, δ -, and

ζ -CAs. The α, β and δ-CAs contain a Zn2+ ion at the active site, the γ-CAs are probably

Fe2+ enzymes (but they are active also with bound Zn2+ or Fe2+ ions), while the metal ion is

usually replaced by Cd2+ in the ζ -CAs (Alterio et al. 2012). These enzymes are found in all

the kingdoms of life and are involved in respiration, photosynthesis in eukaryotes and cyanate

degradation in prokaryotes. In plant cells, they are related with the photosynthetic fixation of

CO2 in the presence of chloroplasts (Imtaiyaz Hassan et al. 2012). Behind such wide spectrum of

functions and occurrence, however, the main mechanism of activity is the same. Three histidine

residues (His94, His96 and His119) which coordinate the metal ion are conserved thorough all

families. In the case of a zinc-bound enzymes, catalitic reaction can be divided into two steps

(Alterio et al. 2012). In a direction of hydration, Zn2+ bound hydroxide makes a nucleophilic

attack on CO2, with consequent formation of bicarbonate HCO–3 and release of the proton H+.

The second step is rate limiting and involves regeneration of the catalytically active hydroxide.

During this step a protein is transferred from a water molecule bound to the Zn2+ to the bulk

solvent. It is accomplished by a network of structured water molecules which reside in the binding

pocket (Imtaiyaz Hassan et al. 2012; Alterio et al. 2012).

All human carbonic anhydrases belong to the α family. Up to now there are 15 iso-

forms identified, which differ significantly by molecular features, oligomeric arrangement, cellular

localization, distribution in organs and tissues, expression levels, kinetic properties and response

to diffierent classes of inhibitors. Twelve isoforms (CAs I−IV, VA −VB, VI −VII, IX, and XII−

XIV) show a variable degree of enzymatic activity, whereas three isoforms (VIII, X, and XI), the

so-called CA-related proteins (CARP’s) are devoid of catalitic activity (Alterio et al. 2012). It is

predicted that CAIV and CAVI has been the oldest mammalian isozymes, while CAI, CAII and

CAIII deviated in recent times (Imtaiyaz Hassan et al. 2012). Isoforms of CAs are involved in di-

verse physiological functions including pH regulation, ion transport, bone resorption and secretion

of gastric, cerebrospinal fluid and pancreatic juices (Alterio et al. 2012). In result of such wide range

of functions CAs differ for subcellular localizaton: CA I, II, III, VII and XIII exist in cytosol, CA

IV, IX, XII, and XIV are membrane associated, CA VA and VB reside in mitochondria, whereas

CA VI is secreted in saliva and milk (Alterio et al. 2012). CAs can be regarded as the central

enzymes for both transport and metabolic processes at the cellular level (Imtaiyaz Hassan et al.

2012). For example in the metabolically active tissue of a muscle, CA facilitates the CO2 transport

and in other cases it works as a key protective enzyme in elevated CO2 concentration (Imtaiyaz

Hassan et al. 2012; Alterio et al. 2012). Membrane associated CA is important in acidifying the

20


outer boundary layer through the catalyzed hydration of excreted CO2.

2.5.1 Structural properties

X-ray crystal structures are already available for the majority of the twelve catalytically

active members of the human CA family. All isoforms are highly homologous by their sequence

similarity and even with differing sequences preserve more or less similar structure (Imtaiyaz Hassan

et al. 2012). The active site of the enzyme is located in a large, conical cavity, approximately 12

Å wide and 13 Å deep, which spans from the protein surface to the center of the molecule. The

catalytic zinc ion is located at the bottom of this cavity, exhibiting a tetrahedral coordination

with three conserved His residues and a water molecule/hydroxide ion as ligands. On the basis

of hydrophobic and hydrophilic nature, the active site cavity is characteristically divided into two

halves. Hydrophobic part contains Ala121 and 135, Val 207, Phe91, Leu131, 138, 146, 109, and

Pro201, 202 while the hydrophilic part of the cavity consists of His64, 67, 200, Asn69, Gln92,

Thr199, Tyr7 and Val62 (Imtaiyaz Hassan et al. 2012). Such bipartite environment is required

for the carbon dioxide to bicarbonate conversion reaction catalysed by CAs. Hydrophobic part

is responsible for CO2 capture and orientation in the right direction, whereas hydrophilic side

arranges water molecules for the proton transfer from zinc-bound water molecule to the bulk

solvent. During the first step of the mentioned hydration, tetrahedrally coordinated hydroxide is

involved in a network of hydrogen bonds which helps to enhance its nucleophilicity. In particular,

it is hydrogen bonded with the hydroxyl moiety of a conserved Thr residue (Thr199) and with

two water molecules, located on two opposite sides: the first one, also called the “deep water”, is

located in a hydrophobic cavity (Alterio et al. 2012). The molecular dynamics studies, however,

suggest that up to six water molecules might be involved in the whole process (Tripp et al. 2001).

2.5.2 Drug design for CAs

Besides the the variety of roles, CAs assume at a normal tissue, they have also been

reported to be involved in various disease mechanisms. Therefore, extensive drug design studies

have been taken to find the potential inhibitors and stimulators of CAs (Alterio et al. 2012). In

the cases where memory and learning is impaired, like Alzheimer’s and other neurodegenerative

diseases – activators are sought for (Alterio et al. 2012). However, majority of potential CA

targeting drugs act as the inhibitors, like diuretics, antiglaucoma agents, antiepileptics, and in the

management of altitude sickness. The more novel generation compounds are undergoing clinical

investigation as antiobesity, and antitumor drugs/diagnostic tools and even as anti-malaria drugs

(Alterio et al. 2012). In the case of tumours, CAs have quite a special role as enzymes at least partly

responsible for the survival of cancerous cells in an hypoxic environment and the acidification of

the extracellular space (Pastorekova et al. 2008). There is now a solid evidence that CAs actively

21


contribute to adaptive responses of tumour cells to physiological stresses (Pastorekova et al. 2008).

Indeed, cancerous cells are remodelling expression of CA genes to gain new phenotypic properties

to become capable of rebuilding their metabolism and increase migration and invasion. This

adaptation to physiological stresses in microenvironment is an essential aspect of tumor progression

that significantly contributes to metastasis and resistance to anticancer therapy (Pastorekova et al.

2008).

Even though there is a handful of crystallised hCA structures, most of the reported

complexes with inhibitors regards just isozyme II, the most thoroughly characterized CA isoform

(Imtaiyaz Hassan et al. 2012; Alterio et al. 2012). Cytosolic CAII shows the highest distribution,

it covers almost every tissue and organ, including osteoclasts in bone, choroid plexus epithelia,

retinal muller cells, hepatocytes, kidney, oligodendrocytes in brain, salivary glands, erythrocytes

and platelets (Imtaiyaz Hassan et al. 2012). The major role of CAII is in the contribution of H+

production and acid–base homeostasis, pH balance, metabolic acidosis. It also triggers the CO2

exchange in the erythrocytes and lungs (Imtaiyaz Hassan et al. 2012). As a side-effect of such

properties, hCAII also participates in the mechanisms of glaucoma, edema, epilepsy and altitude

sickness (Alterio et al. 2012).

2.5.3 Inhibitors of CAs

The inhibitors of CAs can be classified into two major categories: those that are bound

to the active site but do not interact directly with the metal ion, and those that bind to the enzyme

active site by anchoring themselves to the catalytic zinc ion. The first class includes phenols (some

of which are natural compounds), polyamines, coumarins, and antiepileptic drug lacosamide. The

second class is more established and includes the ureates/hydroxamates, the mercaptophenols, the

metal-complexing anions (cyanide, azide, hydrogen sulfide and trithiocarbonate) and the sulfon-

amides and their bioisosteres, such as sulfamates and sulfamides. The majority of the clinically

used inhibitors of CAs are sulfonamides – R−SO2−NH2. The inhibitory properties of these com-

pounds are based on the coordination of the deprotonated sulfonamide nitrogen to the catalytic

Zn2+ ion, with consequent substitution of the zinc-bound water molecule. Thus, amine of the

sulfonamide group occupies the place of the hydroxide ion and prohibits nucleophilic attack of the

CO2.

Even though there is a handful of CA related drugs which already are in the clinical

trials (Alterio et al. 2012), none of the currently clinically used CA inhibitors shows selectivity for

a specific isozyme. This is especially important, because, for e.g., CA IX and XII in tumors should

be inhibited by compounds, which do not affect the activity of CA I, II, VA, and VB (Alterio et al.

2012). As CAs are ubiquitous and responsible for many vital functions, collective inhibition might

lead to the undesired side effects and even more extensive damage than that done by the initial

22


disease (Alterio et al. 2012).

2.6 Computational structure-based drug design

Structure-based drug design and computational drug design are interconnected method-

ologies in the process of new drug discovery or optimization (Kitchen et al. 2004). The basic idea

behind structure-based drug design is, that molecular structures of the target and the drug give

sufficient information to determine and predict the energetics of their interaction. This approach

is largely influenced by the biochemical laws of additivity and therefore it assumes, that the overall

energetics of the target-drug complex formation can be approximated by the sum of contribution

of the individual chemical groups (Dill 1997). Computational methods in their regard, provide

tools to investigate this affinity in silico by the use of the structural data. Nowadays, these meth-

ods have become a crucial component of many drug discovery programmes from hit identification

to lead optimization and beyond. When only the structure of a target and its active or binding

site is available, high-throughput docking is primarily used as a hit-identification tool. However,

similar calculations are often also used later on during lead optimization, when modifications to

known active structures can quickly be tested in computer models before the actual synthesis of

the compound. This, at least partly, is an effect of the improvements in techniques for structure

determination, such as high-throughput X-ray crystallography. The increase in the number of crys-

tallised protein structures allows the identification of new target and testing of prospective drugs

in silico. There are now a number of drugs, like inhibitors for HIV protease, whose development

was heavily influenced and, in some cases, based on the screening strategies or other computational

techniques (Kitchen et al. 2004).

2.7 Docking

One of the key methodologies in the computational structure-based drug design — dock-

ing of small molecules to protein binding sites was pioneered during the early 1980s (Kitchen et al.

2004). The term ”docking” is used for the computational modelling techniques, which ”dock” the

ligand into the rigid or semi-rigid protein and ”score” their potential complementarity to the bind-

ing site. The first step – prediction of ligand conformation and orientation is called posing. This in

itself is challenging, as even relatively simple organic molecules can contain many conformational

degrees of freedom. Sampling these degrees of freedom must be performed with sufficient accuracy

to identify the conformation that best matches the receptor structure, and must be fast enough to

permit the evaluation of thousands of compounds in relatively short time. These algorithms are

complemented by the scoring functions that are designed to predict the biological activity through

the evaluation of interactions between compounds and potential targets. In general, there are two

23


aims of docking studies: accurate structural modelling and correct prediction of activity (Kitchen

et al. 2004; Taylor et al. 2002).

Relatively simple scoring functions continue to be heavily used, at least during the initial

stages of drug discovery and docking simulations (Kitchen et al. 2004). From one side, they let the

very fast approximation of the binding energy, which is required for screening the huge number of

compounds. From the other side, they also include a number of assumptions which significantly

decrease their predictive value. A number of factors is not included, like inherent flexibility,

induced fit or other conformational changes that occur on binding, and the participation of water

molecules in protein–ligand interactions. Docking, by its nature can not evaluate the entropic term

of the interaction and bias the enthalpic one (Kitchen et al. 2004). These imperfections of scoring

functions continue to be a major limiting factor.

Because of all the mentioned weaknesses of the docking algorithms, re-selected conformers

are often further evaluated using more complex scoring schemes with more detailed treatment of

electrostatic and van der Waals interactions, and inclusion of at least some solvation or entropic

effects (Taylor et al. 2002).

2.7.1 Posing

Finding the right posing for the selected ligands is not an easy task. Most biological

molecules have a number of rotatable bonds and if we consider the rotational freedom in the ligand,

we deal with the problem called ”conformational explosion”. The number of possible conformations

Nconformations =N∏

i=1

ninc∏j=1

360θi,j

. (6)

increses exponentialy with the number of rotatable bonds N (ninc – number of incremental rota-

tional angles, θi,j – incremental rotational angle). Docking algorithms must somehow sample the

immense number of conformations and find the valid ones. Possible treatments of the problem can

be divided into three main categories (Kitchen et al. 2004):

• Systematic methods (incremental construction, conformational search, databases) – which

try to explore all the degrees of freedom and ultimately face the combinatorial explosion.

Ligands can be incrementally ”grown” into the binding site or be separated into rigid and

flexible parts.

• Stochastic methods (Monte Carlo, genetic algorithms, tabu search) – which operate by mak-

ing random changes to a conformation of a ligand or a number of ligands. It is done by

the ”random-walk” of a Markov chain or ”mutations” to the previous pose in the genetic

algorithm.

24


• Simulation methods (molecular dynamics, energy minimization) – which employ the molec-

ular dynamics simulation of the ligand.

2.7.2 Scoring

The generation of the right ligand conformation is not enough by itself, because it must

be identified and selected out of all other conformations. This is accomplished by the scoring

functions. Generally, there are three unique types of scoring functions available and one as a

complement.

• Force-field based scoring – use of molecular mechanics forcefields to quantify the binding

energy by the sum of two energies: protein-ligand interaction and internal energy (usually

only for the ligand). Interaction between the protein and the ligand is most often described

in terms of electrostatic Coulomb and steric Van de Waals potentials:

V col(r) =NA∑i=1

NB∑j=1

qiqj

4πϵrij(7)

where A and B are two atoms and rij – distance between them, and

V vdw(r) =NA∑i=1

NB∑j=1

4ϵ

[(σij

rij

)12

−(

σij

rij

)6]

(8)

where ϵ – well depth of the potential, σij – collision diameter for the respective atoms A

and B, and rij – distance between them. This method neglects the effect of the solvent or

approximates it in terms of the distance dependent dielectric (Kitchen et al. 2004).

• Empirical scoring – fit to reproduce experimental data, such as binding energies and/or con-

formations, as a sum of several parameterized functions. The design of empirical scoring

functions is based on the idea that binding energies can be approximated by a sum of indi-

vidual uncorrelated terms. Takes solvation into account, but depends heavily on the quality

of the empirical data (Kitchen et al. 2004).

• Knowledge based scoring – designed to reproduce experimental structures rather than binding

energies. May include solvent-accessibility corrections, but also depend on the number of high

quality protein-ligand complex structures (Kitchen et al. 2004).

• Consensus – combines information from different scores to balance errors in single scores and

improve the probability of identifying ”true” ligands (Kitchen et al. 2004).

2.7.3 Poisson-Boltzman surface area method

Poisson-Boltzman surface area method, or PBSA is one of the most popular methods

to calculate electrostatic potential in a salty solvent without explicitly modelling water molecules

25


(implicit solvation). Because of such capability it is also called the electrostatic continuum solvation

model (Kitchen et al. 2004). Due to a high computational cost it is mostly used as supplement to

the traditional methods (Kitchen et al. 2004) and applied after the initial pose detection by docking

or the molecular dynamics simulations (Massova 2000; Kollman et al. 2000; Fogolari et al. 2002).

PBSA acts as a scoring function and does not change the given pose of the ligand. It operates

by performing two separate tasks: calculation of the electrostatic potential by numerically solving

Poisson-Boltzman differential equation (Eq.9) and estimation of the change in the solvent accessible

surface area upon ligand binding to the protein (Fogolari et al. 2003).

∇⃗[ϵ(r⃗)∇⃗Ψ(r⃗)

]= −ρf (r⃗)−

∑i

c∞i ziqλ(r⃗) exp

[−ziqΨ(r⃗)

kBT

](9)

26

3 Thermodynamics of Cationic and Anionic Surfactant In-

teraction

3.1 Materials & Methods

3.1.1 Materials

Linear surfactants with differently charged polar head-groups and various aliphatic chain

length were used in this study to dissect the thermodynamic parameters of their aggregation.

Alkylsulfates and alkylsulfonates were chosen as negatively charged surfactants and alkylamines –

as the positively charged ones. The main reason behind such choice was the simple, non-branching

structure of these compounds, which is necessary in order to apply the laws of additivity (Dill 1997).

Moreover, all of the selected compounds have appropriate physicochemical properties which are

relevant to this study. First of all, given surfactants did not form micelles at any experimental

concentration (concentration of the surfactant in the cell and syringe was always lower than the

cmc) (Lide et al. 2009). At the lowest experimental temperature of 25℃ all surfactants were in a

solid crystalline form and only at greater temperatures they underwent a phase change (Lide et al.

2009). However, there also were several parameters, which were specific to a particular mixture of

oppositely charged surfactants and therefore could not be evaluated in advance. These were cmcmix

and Krafft temperature TK (Amante 1991; Stellner et al. 1988). It was not known whether all

systems of surfactants will form aggregates at the given conditions, but this was easily determined

from the thermodynamics of the reactions. In the case of no aggregation happening, ∆Hexp was

very small and represented only the ionic pairing of the headgroups (concentration of surfactants

was smaller than cmcmix and experimental temperature greater than TK). Theoretically, it should

be possible to observe aggregation reactions in all systems of surfactants with greater concentrations

and lower temperatures, but this was not extensively tested in this study.

The surfactants were bought from several sources. Acros Organics (New Jersey, USA:

1-800-ACROS-01; Geel, Belgium: +32 14 57 52 11) provided undecylamine (98%), dodecylamine

hidrochloride (99%) and tridecylamine (98%). Sigma Chemical Co. (P.O. Box 14508, St. Louis,

MO 63178 USA 314-771-5750): 1-decanesulfonic acid, sodium salt (98%), dodecylsulfate, sodium

salt (99%). Aldrich Chem. Co. (P.O. Box 355, Milw. WI 53201, 414-273-3850): 1-dodecanesulfonic

acid, sodium salt (99%). Pfaltz Bauer Inc. (375 Fairfield Ave., Stamford, Conn. 06902): 1-

nonanesulfonic acid, sodium salt (98%). Nonylamine (≥ 97%) was obtained from Fluka, Sigma-

Aldrich (CH-9471 Buchs, 081/75525 11). At room temperature surfactants were in a form of white

crystalline powder and only short-chained compounds as nonylamine appeared as a near-molten

wax. All surfactants were kept in the original packaging and used without further purification.

27

Povilas Norvaišas Thermodynamics of Cationic and Anionic Surfactant Interaction

Aqueous solutions were prepared using distilled milli-Q grade water, which was also boiled to

remove dissolved CO2. Solutions of alkylamines were kept in tightly sealed containers to minimize

chances of reaction with atmospheric CO2, which might lead to a decreased concentration of an

active surfactant.

3.1.2 Isothermal Titration Calorimetry

All experiments were performed with Microcal (Northampton, MA) Micro Calorime-

try System (MCS) calorimeter in temperature range 25 −− 65℃. Circulating cooling bath was

attached to calorimeter in order to perform experiments bellow or near room temperature (Olof-

sson and Loh 2009). The temperature of the refrigerant was constantly kept at 17℃. The ITC

unit was calibrated using its built-in electronic heat pulse generator and validated by reaction

NaI+AgNO3 −−→ AgI ↓ . The enthalpy change determined in five experiments ∆H = (−109.4±1.8)

kJ/mol was very close to that found in the literature: ∆H = −110.9 kJ/mol (Baranauskiene et al.

2009), thus confirming the accuracy of the device. Prior to every experiment the cell was washed

multiple times with water and once in every month treated with 20% ”Contrad 70” cleaning agent,

followed by rinsing with 0.1 M CH3COOH and 0.1 M NaOH at the temperature of 65℃. Similarly,

injection syringes were cleaned by pumping 100 mL of water through their volume and then leaving

them to passively dry out. The cell was always prerinsed with a portion of the same surfactant

solution before the actual filling to minimize dilution of reagents due to small water droplet which

might have not dried out. Reactant solutions were cooled at least 5℃ below experimental tem-

perature just before filling to assure quick equilibration of the calorimeter. The cell (1,3438 mL)

and the syringe were loaded with solutions of oppositely charged surfactants – 0.33 mM and 5

mM respectively. Titration was performed in 40 injections of 6,25 µL at intervals of 180 s, with a

250 µL injection syringe. During the period of equilibration syringe was set to spin in short bursts

at the maximum speed of 1200 rpm to buoy any microscopic air bubbles attached to the cell walls.

Afterwards, the syringe rotation was set to a constant speed of 400 rpm. At least 180 s of data was

collected prior to the first injection to check the stability of the baseline. The ”Refference offset”

parameter of calorimeter was changed according to every system of surfactants to keep baseline

level well above the 0 µJ/s as in the figure 2a. This setting assured that the calorimeter registered

all the heat flow in or out of the cell and it was not dissipated by the cooling system.

There were cases when the baseline did not return to the preinjection level after the

injection (as in Fig.2a). This effect became more pronounced for the systems of greater aliphatic

chain length. Yet the exact cause is not known, it can be speculated that after the injection

aggregate underwent slow structural rearrangements because of a change in the ratio of charges.

This can be understood by inspecting figure 1 in this text. As the titration happens, we are diluting

one surfactant and increasing concentration of the other one in the cell. Because of this, system

28


goes through different phases, which are determined by the charge and concentration ratio of the

surfactants (Stellner et al. 1988). These processes stopped when stoichiometry reached unity and

surfactants formed insoluble aggregate. It was tried to avoid this effect by increasing the intervals

between injections to the maximum of 380 s (Fig.3), however it did not affect the integral enthalpies

of interaction (∆Hexp) and therefore, periods of 180 s were used to reduce the overall length of the

experiments.

3.1.3 Data Analysis

Pow

er (μ

J/s)

50

60

70

80

90

100

110

Time (min)0 20 40 60 80 100 120

(a)

δH (k

J/mol

)

−80

−60

−40

−20

0

Molar ratio0 1 2 3

Parameters:ΔHexp = -64.98 kJ/mol ΔHfit = -70.69 kJ/mol Kb

fit = 1.47x105 N = 1.03

(b)

Figure 2: ITC data of dodecylammonium binding to decane sulfonate at 25℃. (a) Raw data,

straight line represents the baseline. (b) Dosing curve, line represent the fit according to the one

site binding model.

Raw binding curves obtained from the ITC experiments were analysed with Origin 5.0

software package, which has Microcal plug-in. In addition to usual functionality of the Origin, this

plug-in enabled fitting of the data according to the models of ”one-on-one” or ”two-site” binding,

thus providing the possibility to extract valuable information about the reaction kinetics. Most

of the experiments could be treated as an ”one-on-one” binding reactions despite the aggregation

that followed and negligible baseline drift due to structural rearrangement (as in Fig.2). Such data

didn’t require any sophisticated approach as the analysis was straightforward:

1. Conversion of units from calories (cal) to joules (J)

2. Automated fitting of the baseline and it’s straightening with FFT (Fast Fourier Transforma-

tion) filter, which removes ”high-frequency” fluctuations in the baseline without changing its

overall shape OR approximation of the baseline as a straight line if the power supplied to the

cell does not differ significantly before and after experiment (baseline drift ≤1 − 2 µJ/s).

3. Integration of the raw data curve (Power, µJ/s over time, s) and automatic conversion to the

dosing curve (δH, kJ/mol over Molar ratio)

29


4. Subtraction of the dilution energy, which is determined by the last injections of constant

partial enthalpy change (δH)

5. Integration of the dosing curve, thus acquiring ∆Hexp

6. Fitting curve with ”one-on-one” binding model, thus acquiring binding constant (Kfitb , M−1),

enthalpy change of the reaction (∆Hfit, kJ/mol), stoichiometry (N) and entropy change (∆S,

J/(mol K)), which was calculated using the equation 2

In some cases baseline drift was greater than 1 − 2 µJ/s and therefore straight baseline

was preferred over the automatically determined one in order to keep consistency in the data

analysis. Such a difference in heat-flux supplied to the calorimeter cell before and after experiment

was primarily caused by periodical temperature change in the room during the course of the day.

These fluctuations were described in the manual of MCS and are natural for such a temperature

sensitive instrument as calorimeter is.

The dilution enthalpy of a higher concentration surfactant solution being injected into one

of lower concentration was determined to be comparably small (overall ≈ 2 kJ/mol) and constant

during the course of titration. Therefore it was decided to simplify the process of data analysis

and subtract the dilution enthalpy acquired in the last injections of each titration experiment if

two conditions were satisfied: dilutions’ partial enthalpy (δH) was smaller than 2 kJ/mol and it

remained constant after the end of the aggregation.

Not all experiments could be analysed with the mentioned straight-forward approach,

especially ones for a longer overall aliphatic chain length m . These reactions exhibited greater

influence of aggregation process after the ionic pairing. Thus, the second part of the reaction

became more apparently expressed and the usual ”one-in-one” reaction scheme could not be applied

(Fig.3). There is no appropriate model devised to evaluate kinetics of such a two part – ionic pairing

and aggregation/dissolution reaction. However, it was possible to acquire rough estimates with a

”two binding site” or ”alosteric/cooperative” binding model. This model was devised for a case,

when protein has two active sites which alosterically regulate one another. During the course of

reaction, binding of a ligand to one of the active sites increases its affinity to the other. In our

case ionic pairing represented kinetics of the first binding site and aggregation – of the second

binding site. Thermodynamic parameters Kfitb and ∆Hfit, determined via such binding model

were considered less reliable. In many cases it was not possible to obtain reasonable values of

∆Hfit due to sharp increase in δH near the point of stoichiometric unity (Fig.3b). The accuracy

of ∆Hexp, however, didn’t suffer from these problems as it was obtained by direct integration of

the dosing curve. Therefore ∆Hexp and not ∆Hfit was used as a measure of reaction enthalpy

change in this study.

30


Pow

er (μ

J/s)

10

20

30

40

50

60

70

Time (min)0 50 100 150 200

(a)

δH (k

J/mol

)

−200

−150

−100

−50

0

Molar ratio0 1 2 3

Parameters:ΔHexp = -95.07 kJ/molΔHfit = - - kJ/molKb

fit = 5.5x106

N = 1.01

(b)

Figure 3: ITC data of dodecylammonium binding to dodecane sulfate at 25℃. (a) Raw data,

straight line represent the baseline. (b) Dosing curve, line represent the fit according to the II site

binding model.

3.1.4 Statistical analysis of the data

Most reactions have been carried out more than once, therefore it was possible to perform

statistical analysis of the data. First of all it was determined whether data sets were normally

distributed by employing Shapiro-Wilk W test from Statistica 8.0 software package. If such an

assumption could not be ruled out – mean value and confidence intervals of 95% were calculated.

Values of Kfitb have not been analysed directly, but instead were transformed to more informative

form of ∆G (q.1). Such transformation was viable, because Kfitb would have been nevertheless

transformed with the ln Kb to increase the normality of distribution. Confidence intervals of entropy

change T∆S were fully dependent on the ones of ∆G and ∆Hexp, therefore equation 10 has been

used to calculate them. The results for every use of error bars in the figures can be found in the

section of supplementary material (Sec.7).

Err.T ∆S =√

Err.2∆G + Err.2∆H (10)

3.2 The mathematical model

In order to explain the thermodynamics of cationic and anionic surfactant interaction, Dr.

Daumantas Matulis has devised a mathematical model which describes main processes happening

upon formation of the precipitate (Norvaisas et al. 2012). As it was already mentioned, the process

can be divided into two arbitrary stages – ionic pairing and hydrophobic aggregation. The first

part can be expressed via reaction 11:

R1NH+3 + R2SO−

3 ←−→ R1NH+3 · · ·R2SO−

3 , (11)

31


where R1 and R2 denote aliphatic chains of both surfactants. The parameter describing overall

chain length of the conjugate – m = R1 +R2 has been used extensively in this study. In the second

stage (reaction 12), following a loss of charge of the surfactants, aggregate of indefinite size ν is

formed which precipitates out of aqueous solution:

ν(R1NH+3 · · ·R2SO−

3 )←−→ (R1NH+3 · · ·R2SO−

3 )ν ↓ . (12)

These two processes are then approximated as independent reactions – ion pair formation in am-

monium sulfate aqueous solution and precipitation of m length alkane. By using such approach it

is then possible to calculate Gibbs free energy of the alkylammonium interaction with alkane sul-

fonate by summing up individual contributions of ionic pairing (∆AGion) and alkane precipitation

(∆AGalk):

∆AG = ∆AGion + ∆AGalk. (13)

The Gibbs free energy of ammonium sulfate aggregation at 1 M reference state is equal to

∆AGion = −RT ln(Aion) = RT ln(Sion), (14)

where Sion is the solubility Aion = 1/Sion – aggregation parameter of ammonium sulfate. For

concentrations different than the 1 M reference state, concentration parameter C was introduced:

∆aggGion = −RT ln(AionC). (15)

The Gibbs free energy of alkane aggregation can be obtained from the following equation (Matulis

2001; Matulis and Bloomfield 2001a):

∆aggGalk = −RT ln(AalkC) = −RT (m ln(∆w) + ln(w0) + ln(C)), (16)

where ∆w is an increase in aggregation upon addition of one methylene (CH2) group and is equal

to 4.241 (Matulis 2001). The parameter w0 is an empirical coefficient and is equal to 1.32 for

n-alkanes (Matulis 2001).

The given model is already sufficient to calculate Gibbs free energy of the surfactant

precipitation. Lets consider a reaction between decane sulfonate and dodecylammonium (see Fig.2

in the section 3.1.3 Data analysis). Required parameters are: C = 0.33 mM, Sion = 4.1 M at

T = 25℃ (Dawson et al. 1986), Aion = 0.244 M−1 and m = 22. Ionic contribution according to

equation (15) is then estimated to be ∆aggGion = 23.4 kJ/mol and alkane precipitation according

(16) – ∆AGalk = −59.6 kJ/mol. Upon summation, the overall expected Gibbs free energy of the

reaction is ∆aggG = −36.2 kJ/mol. The observed Gibbs free energy of the mentioned system

was measured with ITC and equals −30.6 kJ/mol. Given at hand the assumptions made, such

a discrepancy is surprisingly small, but larger than the expected error of the calorimeter of 1

kJ/mol . After the further investigation it was discovered that the experimentally observed ∆Gfit

was always smaller by ≈ 5 kJ/mol . Therefore correction by empirical coefficient B = 4.03× 10−5

was introduced.

32


The final expression of modelled association constant Kmodb could then be derived. First

of all, association constants for the reactions of ionic pairing (11)

Aion = [R1NH+3 · · ·R2SO−

3 ][R1NH+

3 ][R2SO−3 ]

(17)

and aggregation (12)

Aalk = [R1NH+3 · · ·R2SO−

3 ↓ ][R1NH+

3 · · ·R2SO−3 ]

(18)

were determined. Then, the factors of concentration C and empirical correction coefficient B were

introduced, thus giving the final expression of

Kmodb = [R1NH+

3 · · ·R2SO−3 ↓ ]

[R1NH+3 ][R2SO−

3 ]BC = AionBAalkC. (19)

The modelled Gibbs free energy can then be calculated with

∆aggGmod = −RT ln(Kmodb ). (20)

The enthalpy of alkane aggregation into a solid phase at 25℃ can be estimated by an

empirical equation (Matulis and Bloomfield 2001b)

∆aggHalk = −5.2m + 18.41, (21)

where m is the number of aliphatic atoms. In the case of alkylammonium interaction with the

alkyl sulfate or alkane sulfonate, rough approximation of the enthalpy can be derived by adding

the enthalpy of ammonium sulfate crystallization (−6.62 kJ/mol, (Dean 1999)) to the equation 21,

which then becomes

∆aggHsurf = −5.2m + 11.79. (22)

3.3 Results

3.3.1 Dependence on the order of titration

First of all it was necessary to determine whether the reaction thermodynamics were

dependent only on the state of the system and not on the route to it. This was done by performing

titration reactions where the contents of the cell and syringe were swapped. If we analyse phase

diagram of the mixed surfactant system (Fig.1), it can be seen that the precipitation occurs on

the diagonal line. During titration, surfactant in the cell is slightly diluted and concentration of

the surfactant from the syringe increases steadily until and after the equimolar ratio is reached.

If we switch the contents of the syringe and the cell – same state will be approached by going

through different pseudophases in the phase diagram (Fig.1) (Amante 1991; Stellner et al. 1988).

This was tested in several systems of the surfactants and as it can be seen in the example of

dodecylammonium/decyl sulfate (Fig.4 and Tab.3) – no significant difference was observed.

33


δH (k

J/mol

)

−80

−60

−40

−20

0

Molar ratio0 0.5 1 1.5 2

cell - decane sulfonatesyringe - dodecylammonium

syringe - decane sulfonatecell - dodecylammonium

Figure 4: Dodecylammonium titrated to decane sulfonate and vice versa at 25℃, with [cell] = 0.33

mM, [syringe] = 5 mM.

Cell Syringe ∆Hexp Kfitb Nfit

C10H21SO–3 (0.33 mM ) C12H25NH+

3 (5 mM) −70.69 1.47× 105 1.03

C12H25NH+3 (0.33 mM ) C10H21SO–

3 (5 mM) −70.93 1.96× 105 1.05

Table 3: Dodecylammonium titrated to decane sulfonate at 25℃: dependence on the order of

titration.

3.3.2 Dependence on the surfactant concentration

The association constant of an usual reaction does not depend on the experimental

concentration. However, if the reaction is followed by an aggregation as in the case of the positively

and negatively charged surfactants, linear dependency in the apparent binding constant Kfitb can

be observed. This was determined with the system of dodecylammonium/decyl sulfonate at various

concentrations. Upon the proportional increase in the concentration of surfactant in the cell and

syringe (and thus concentration of the final aggregate), Kfitb increased (Fig.5,6) so that the ratio

of the concentrations is approximately proportional to the ratio of Kfitb (Fig.6). Therefore, 2-

fold increase in concentration leads to the 2-fold increase in the Kfitb . The enthalpy, however,

was constant for all concentrations within the experimental error, thus we could be sure that the

precipitation is full for m = 22. These results agree with the predictions of the mathematical

model (see supplementary material, tables 6,2,7).

34


δH (k

J/mol

)

−80

−60

−40

−20

0

Molar ratio0 0.5 1 1.5 2 2.5

[cell] (mM) 0.66 0.33 0.165

Figure 5: Dodecylammonium binding to decane sulfonate at 25℃: Dosing curves of 0.66 (open

triangles), 0.33 (solid circles), and 0.165 (open squares) decane sulfonate concentrations in the cell.

Dodecylammonium concentrations in the syringe were 10 mM, 5mM and 2.5 mM, respectively.

K bfit

(M-1

)

0

105

2×105

3×105

4×105

[cell] (mM)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 6: Dodecylammonium binding to decane sulfonate at 25℃: the observed binding constant

dependence on decane sulfonate concentration in the cell. For the statistical analysis data see

supplementary material, table 7).

35


δH (k

J/mol

)

−100

−80

−60

−40

−20

0

Molar ratio0 0.5 1 1.5 2

m22 23 24

Figure 7: Dodecylammonium binding to alkane sulfonate of varying aliphatic chain length. Filled

circle – decane sulfonate, open square – undecane sulfonate and filled diamond – dodecane sulfonate.

3.3.3 Dependence on the aliphatic chain length

For the systems of cationic and anionic surfactants all three thermodynamic parameters

exhibited clear dependence on the total aliphatic chain length m. This was anticipated from the

results of previous studies (Matulis and Bloomfield 2001b) and the predictions of the mathematical

model (comparison in the supplementary material, Tab.6). The experiments have been carried

out for surfactants with m = 18 − 25 at the experimental temperature of 25℃ and surfactant

concentration in the cell 0.33 mM. For each chain length m there were at least two different

surfactant systems tested. Surfactants with the total chain length of m = 18 − 21 did not fully

precipitate (see supplementary material Fig.2). However, it was hypothesized that this might

be due to the low experimental concentration, which is not sufficient for the full aggregation.

Indeed, it was determined that the enthalpy for the systems with m = 21 is dependent on the

concentration and reaches plateau with the double concentration of 0.66 mM, whereas m = 22

showed no significant difference in enthalpy for various concentrations (see supplementary material

Fig.2 and Tab.7). Therefore data of m = 21 at the 0.66 mM experimental concentration was used

in the final analysis.

In this study oxygen atom between aliphatic tail and the headgroup of alkyl sulfates

was approximated as an additional methylene group. With such approach, the energetics of the

reactions have added up precisely. However, the enthalpies of alkyl sulfate reaction with alky-

lammoniums were systematically less exothermic when compared with alkane sulfonate reactions

with alkylammoniums. These differences might be attributed to the distinct phase and solubility

36


(kJ/m

ol)

−120

−100

−80

−60

−40

−20

0

m, aliphatic chain length20 21 22 23 24 25 26 27

ΔGobs

TΔSobs

ΔHexp

Figure 8: Dependence of the thermodynamic parameters on the alyphatic chain length m with

linear fits. For statistical analysis data see supplementary material tables in 7,7 and 6.

behaviour of both species (Chen et al. 2004) and possibly, less ordered packaging in the aggregate.

Enthalpy: As it can be seen in figure 8, experimentally observed values of enthalpy

follow a linear trend and becomes more negative for longer aliphatic chains. The linear regression

of the data gave a result of

∆Hexp = −8.38×m + 112.33 (kJ/mol), (23)

with correlation coefficient r = 0.976 and the significance p = 0.004. The contribution of methylene

group to the ratio of the concentrations approximately ∆∆Hexp = −8.38 kJ/mol per CH2.

Gibbs free energy: Gibbs free energies were increasingly more negative upon increasing

aliphatic chain length of the surfactant in all tested series of surfactants (Fig.8). However, due

to the use of ”two binding site” fitting model and steep binding curve, values of Kb seemed to

be underestimated. Besides, according to the Kfitb values with the mathematical model (see

supplementary material table 7), with m = 24 − 25 at the concentration of 0.33 mM, limits of

the calorimeter sensitivity were reached (c ≈ 1000)(Tellinghuisen 2007b). Linear regression gave a

result of

∆Gfit = −1.87×m + 12, 267 (kJ/mol), (24)

with correlation coefficient r = 0.74 and the significance p = 0.15. The contribution of methylene

group to the association process: ∆∆Gfit = −1.87 kJ/mol per CH2.

Entropy: The entropy values were determined by using equation 2 and therefore they

were completely dependent on enthalpy and Gibbs free energy. This thermodynamic parameter

should be considered the least reliable one. It was only possible to give a qualitative conclusion

37


δH (k

J/mol

)

−80

−60

−40

−20

0

Molar ratio0 0.5 1 1.5 2 2.5

[NaCl] (M) 0 0.5 1.0

Figure 9: Dosing curves of the dodecylammonium binding to decane sulfonate at 25℃ with surfac-

tant concentration in the cell 0.33 mM: dependence of the partial enthalpy on the concentration

of NaCl

that the aggregation of long chained cationic and anionic surfactants was primarily driven by the

huge negative enthalpy change and opposed by unfavorable entropy (Fig.8). T∆Sobs data has been

approximated with the linear fit of

T∆Sobs = −7.28×m + 119, 33 kJ/mole, (25)

with correlation coefficient r = 0.9784 and the significance p = 0.004. The contribution of methy-

lene group to the association process: T∆∆Sobs = −7.28 kJ/mole per CH2 at 25℃.

3.3.4 Dependence on the ionic force of the solvent

The series of titration experiments were carried out with dodecylammonium/decane sul-

fonate and different concentrations of salt in both cell and syringe to dissect the role of the elec-

trostatics in the reaction. If the association is primarily driven by the ionic interaction of the

headgroups, then the saline solution with heightened ionic force would inhibit it. However, the

results suggested that the ionic interaction is not so important as it was suggested (Bai et al. 2001),

(Fig.9). The effect of salt only appeared when 0.2 − 0.5 M of NaCl was added – concentration

600− 1500 times higher than that of a surfactant in the cell (0.33 mM). In the extreme case with

the 1 M of NaCl (3000 higher than [cell]), reaction enthalpy determined according to the model

(∆Hfit) significantly decreased and stoichiometry shifted to the higher values (Fig.9). However,

change in the ∆Hexp which is determined by integrating the dosing curve was not so pronounced.

38


Shift in the stoichiometry means, that more surfactant from the syringe was need for the precipi-

tate to form. It seems that the salt ions (Na+, Cl–) were competitively inhibiting the association

of the headgroups of surfactants (R1NH+3 , R2SO–

3). Therefore, a higher concentration of differ-

ently charged surfactant was needed to shift the equilibrium back to the formation of complex

R1NH+3 · · ·R2SO–

3.

3.3.5 Dependence on the experimental temperature

The series of experiments with dodecylammonium/decane sulfonate were performed at

various temperatures to determine the heat capacity ∆Cp, temperature of melting Tm and enthalpy

of fusion ∆Hfus for this system. It was observed that the aggregate undergoes a phase transition

into a liquid state at the Tm ≈46−51℃ (Fig.10a). From the slope of the enthalpy dependency on

the temperature, heat capacity for solid and liquid state of the aggregate was determined to be

∆Csolidp = −1.56 kJ/(mol K) and ∆Cliquid

p = −0.23 kJ/(mol K) respectively.

It was interesting to compare physical properties of surfactant aggregate with those of a

pure alkane of similar aliphatic chain length m = 22 (Fig.10b). Surprisingly enough, these both

compounds melt at nearly the same temperature and with the same enthalpy of fusion (∆Hfus ≈

−75 kJ/mol ).

3.3.6 Structure of the aggregate

We found no studies concerning the structure of our investigated surfactant systems,

apart from chemical composition (Stellner et al. 1988). Therefore, a schematic model of surfactant

packing was developed using crystallographic data kindly provided by Dr. Musti J. Swamy, of

the most smilar conjugate available O-lauroylethanolamine-dodecylsulfate (Tarafdar et al. 2010).

O-lauroylethanolamine was modified to dodecylammonium and the resulting structure optimized

using the semiempirical quantum chemistry algorithm MOPAC (Stewart 2008) in the open source

program Gabedit QC (Allouche 2011). During the optimization, decylsulfate molecules as well as

dodecylammonium headgroups were frozen assuming no qualitative difference in hydrogen bonding.

11 shows the modeled structure of dodecylamine bound to dodecyl sulfate. The oppositely charged

ionic headgroups bind to each other stoichiometrically as determined by ITC. Aliphatic tails form

well-packed layer of parallel hydrophobic tails.

3.4 Discussion

This research investigated the thermodynamics of oppositely charged surfactant hy-

drophobic aggregation for a series of surfactant systems with varying aliphatic chain length. By

39


ΔH

(kJ

/mo

l)

−100

−80

−60

−40

−20

0

(b)

(a)

C22H46

ΔH

(kJ

/mo

l)

−100

−80

−60

−40

−20

0

T (oC)20 30 40 50 60 70

ΔHfus

ΔHfus+ΔHstr

C18H

38

C19H

40

C20H

42

C21H

44

C22H

46

C23H

48

C24H

50

C25H

52

C26H

54

Figure 10: (a) Enthalpy dependence on temperature for decane sulfonate reaction with dodecy-

lammonium. For statistical analysis data see supplementary material table 7 (b) Enthalpies of

phase transitions of alkanes containing various number of carbon atoms (from 18 to 26) (Lide

et al. 2009): narrow grey bars represent the enthalpy changes of solid-to-liquid phase transition

(∆Hfus), while black bars represent the sum of enthalpy changes ∆Hfus + ∆Hstr, where ∆Hstr

is related to structural rearrangements of molecules in solid phase. The grey patterned column

marks temperature interval at which both the structural and solid-to-liquid phase transitions in

C22H46 occurs. (Temperature and enthalpy data taken from (Dirand et al. 2002)).

40


Figure 11: Packing diagrams of dodecylamine complex with dodecyl sulfate: (a) crystalline lat-

tice unit cell, (b) and (c) – orthogonal enlarged views of the hydrogen bonding network with

the distances between ionic headgroups. The model was build according to the structure of O-

Lauroylethanolamine complex with dodecylsulfate provided by Tarafdar et al. (2010).

41


changing the experimental conditions in respect to the temperature, surfactant and salt concentra-

tion it was possible to dissect thermodynamic additivity rules for the chemical groups (Dill 1997;

Matulis 2001) and several interesting properties of such systems were determined for the first time.

Thermodynamics of reactions between the cationic and anionic surfactants were shown

to depend on concentration in terms of the association constant Kb. This effect is unusual and pri-

marily arises due to the aggregation reaction which follows the ion pair formation of the surfactant

headgroups. However, this was anticipated from the results of the mathematical model describing

the process.All thermodynamic parameters of the reactions showed linear dependence on the total

aliphatic chain length m of the surfactant systems. The linear regression of data suggests that

there are deviations from the expected values determined by model. However, in the case of Gibbs

free energy it could be explained by a limiting factor of calorimeters capability of determining

association constants with high values – Kb > 107 − 108, at the given experimental concentration.

And also the influence of the fitting model, which, in this case, was not completely appropriate. In

the case of ∆Hexp, mathematical model approximated the contribution of one methylene group for

the aggregation of surfactants as that of a pure alkane (see Tab.2, Eq.22 section 3.2 and Matulis

and Bloomfield (2001b)). When this assumption is taken into account, the discrepancy actually

appears to be surprisingly small.

The ionic contributions to the overall process seems to be non-critical. Only very high

concentration of salt could inhibit the association of the headgroups. This is mainly caused by

the overall unfavourable energetics of ammonium sulfate formation as both headgroups are highly

soluble. Therefore, the process was primarily driven by the association of the hydrophobic tails

and the effect of saline environment was dampened. This is rather unexpected result, because in

other studies on hydrophobic effect, much of the energetics of hydrophobic reactions have been

attributed to the ionic pair formation (Bai et al. 2001).

The association reactions between cationic and anionic surfactants were driven by huge

negative enthalpy change and the contribution of entropy was unfavourable. Analogous reactions

of polymer-polymer or polymer-surfactant association (Courtois and Berret 2010) are favored by

entropy. However, according to the crystallographic data (Tarafdar et al. 2010) (Fig.11), such high

enthalpy in the association of the oppositely charger surfactants could be attributed to the tight

packaging of aliphatic tails in the aggregate. These observations expand the conventional under-

standing of the hydrophobic effect, which states that the entropy drives hydrophobic interactions.

Instead, here we confirm our earlier findings with alkylamines (Matulis 2001), that long aliphatic

chain association in water is an enthalpy-driven and entropy-opposed process.

ITC experiments of dodecylammonium binding to decane sulfonate carried at various

temperatures revealed physical properties of the aggregate. Negative heat capacity change ∆Cp

indicated that indeed, the observed reactions were driven by the hydrophobic effect (Baldwin 1986).

42


Properties of the liquid aggregate at temperature higher than ≈ 50℃ were significantly different

from those of a solid one. Enthalpy contribution was measured to be only ≈ −30 kJ/mol instead

of nearly -100 kJ/mol. Therefore, it may be concluded that if aliphatic chains are unable to form

a solid phase, the enthalpic contribution will be much smaller than if the solid phase is formed.

This was the first research to extensively investigate thermodynamics of long chained

aliphatic compound aggregation. Result might not have a huge relevance from the practical point

of view, however, the selected model system of surfactants can help us better understand the

fundamental processes behind formation of biological membranes and surfactant induced protein

denaturation. The additivity values for chemical groups which were derived in this study can be

used in approximation of the thermodynamics for hydrophobic effect induced aggregation.

The results were published as: Norvaišas, P., Petrauskas, V., & Matulis, D. (2012).

Thermodynamics of Cationic and Anionic Surfactant Interaction. The Journal of Physical Chem-

istry B, 116(7), 2138-44. doi:10.1021/jp2095888

43

doi:10.1021/jp2095888

4 Laws of additivity in the structure-based drug design

4.1 Materials & methods

Figure 12: Schematic depiction of the modelling process.

4.1.1 Protein and its structure

The crystallographic structure of human carbonic anhydrase II was obtained from the

”RSCB PDB” protein data bank (Berman 2000). The priorities in selecting the particular data

were high resolution and non-ambiguously resolved position of dynamic amino acid residues. The

requirements were satisfied by the structure PDB ID: 3M96, resolved in 1.4 Å (Čapkauskaitė

et al. 2010). The protein was further prepared by removing ligand and water molecules, then

adding charges and explicit hydrogens. Upon addition of the hydrogens it was selected that the

δ1 nitrogens of histidine residues were protonated, except the case of His119, whose δ1 nitrogen

forms a bond with Zn2+ and therefore ϵ1 nitrogen is protonated.

4.1.2 Inhibitors and their structures

The inhibitors of hCAII were synthesised by Dr. Virginija Dudulienė (Labanauskas et al.

2009; Baranauskienė et al. 2010; Dudutiene et al. 2007) and Edita Čapkauskaitė (Čapkauskaitė

et al. 2010; Capkauskaitė et al. 2012). They were named according to the initials of the chemist

and therefore will be referred to as VD-compounds and E-compounds. All of these inhibitors

were benzensulfonamide derivatives, however, their structural properties differ significantly and

therefore analysis was performed on two separate sets of data.

Initially, data of inhibitor structures was collected and imported to the Instant JChem

database, to check whether there are no duplicates. After standardising the structures, adding

the explicit hydrogens and performing initial optimisation, they were exported in the MDL .mol

44

Povilas Norvaišas Laws of additivity in the structure-based drug design

Figure 13: An example of the structures of the inhibitors. (a) E-compound, (b) VD-compound.

formate. Each structure was then optimized with OBabel (O’Boyle et al. 2011) by using MMFF94

forcefield (Halgren 1996) and selecting conformer with the lowest energy out of 20 candidates.

4.1.3 Software

Various software packages were required to perform this study. First of all, programs

which are capable of visualizing protein and ligand structures, like Accelrys Discovery Studio 3.0

(Accelrys Software 2012), UCSF Chimera 1.5.3. (Pettersen et al. 2004) and Avogadro (Avogadro

2012). Then – command line tools to automate various transformations and adjustments made to

the number of structures. The mostly used one was OBabel (O’Boyle et al. 2011) – management and

conversion tool for all popular chemistry file formats. Where possible, processes were automated

with scripts written in Bash and Perl.

4.1.4 Database

During the process of this study it became clear that the management of such a huge

amount of data concerning structures of the inhibitors, their physical, structural, chemical proper-

ties and the results of their experimentally determined and modelled binding affinities can not be

accomplished without a proper tool. Therefore, an academic license for the ChemAxons’ JChem

cheminformatics software package (ChemAxon 2012) was acquired and the database established.

All the data collected in the study was managed and analysed with this software.

4.1.5 Docking

For the docking VDock program was used (Kairys and Gilson 2002), which implements

Mining minima algorithm (David et al. 2001). In this program ligand posing is performed by the

genetic algorithm and scoring is force-field based. Initially other tools like Autodock (Morris et al.

1998) or Autodock Vina (Trott and Olson 2010) were tested. However they lacked the proper

45


Interaction energy Internal energy

• Van der Waals attraction (V vdwattr )

• Van der Waals repulsion (V vdwrep )

• Coulomb electrostatics (V Colintr)

• Van der Waals (V vdwint )

• Coulomb electrostatics (V Colint )

• Dihedral (V Dih)

Table 4: Potentials of protein-inhibitor interaction, determined by docking with Vdock.

parametrisation of the Zn2+ ion in the binding pocket of CA’s and were incapable to restrain

certain parts of the ligand – options, both of which were implemented in the VDock.

After import to the program each ligand’s translational center was placed on a sulfon-

amide amino group and freely rotating bonds were automatically detected. Dreiding force field

(Mayo and Olafson 1990) with the VeraChem’s (Gilson et al. 2003) partial atomic charges were

used for the ligands. In the case of a protein, binding box with the 5Å sides was placed in the

vicinity of the Zn2+ ion. The binding box was oriented in such a way that the Zn2+ was included at

the one corner and diagonal line of the box went into the direction out of the binding pocket. Dur-

ing the docking simulation, translational center of the ligand is always kept in the box, therefore

assuring interaction of the amino group of the ligand with the zinc and prohibiting the generation

of ligand poses where such interaction is not present. The NB buffer – extension of the binding

box where interaction potentials were also calculated, was set to incorporate a whole side of the

protein with the binding pocket. For the protein, CHARMM22 forcefield (Mackerell 2004) was

used. Most of the parameters were set to their default values. However, 20 000 trial conformations

were tested for each ligand before selecting 20 of the highest binding energy instead of the default

value of 3 000 trials per 10 conformation. This let the more extensive testing of ligands with huge

number of rotatable bonds and did not significantly increase the computation time. The effect

of the solvent was modelled with the distance-dependent dielectric approach with ϵij = 4ij . As a

result, VDock has determined various potentials concerning the interaction between protein and

the inhibitor (Tab.4). The total modelled binding energy ∆Gmod is simply expressed as a sum of

these potentials

∆Gmod = V vdwattr + V vdw

rep + V Colintr + V vdw

int + V Colint + V Dih. (26)

Data from the VDock output files was extracted and summarized by using Bash scripts.

4.1.6 PBSA

Poisson-Boltzman surface area method was employed to investigate the effect of solvent

in more detailed way. For each ligand, 5 poses with highest energy were selected and underwent

calculation of solvent accessible surface area change upon binding (∆SASA) by program SIMS

(Vorobjev and Hermans 1997). Afterwards, APBS (Baker et al. 2001) was used to calculate PB

46


VD-compounds E-coumpoundsPB

SAV

Doc

k

ΔG

mod

(kJ/

mo

l)

0

−10

−20

−30

−40

−50

−60

ΔG

mod

(kJ/

mo

l)

0

−20

−40

−60

−80

−100

ΔGexp (kJ/mol)0 −10 −20 −30 −40 −50 −60

ΔGexp (kJ/mol)0 −10 −20 −30 −40 −50 −60

Figure 14: Binding energies obtained by docking with VDock and PBSA method against the

experimental results for both VD- and E-compounds. Lines mark linear regression of the data.

potential (V P B). The overall modelling binding energy could then be determined:

∆Gmod = V P B + γ∆SASA. (27)

The coefficient γ describes the non-polar contribution to the desolvation. In this study, the value

of 6 cal/mol/Å2 (0.025 kJ/mol/Å2) was used (Luo and Sharp 2002).

4.2 Results

The results were gathered and analysed at three stages during the whole modelling pro-

cess: after the initial docking with VDock, PBSA evaluation and the use of fitting models. Accord-

ing to the ranking of VDock, 5 best poses were selected their binding energies compared against the

experimental results collected exclusively in thermal shift assay (TSA) studies made at the depart-

ment (Capkauskaitė et al. 2012; Baranauskienė et al. 2010; Čapkauskaitė et al. 2010). All in all,

47


152 ligand underwent complete modelling cycle and results of 132 of them were compared against

the experimental data. Unfavourable binding energies (∆Gmod > 0) determined with VDock, were

mostly caused by steric clashes of huge ligands in a constrained binding pocket. Results of these

ligands were not included in the final figures and linear regression.

4.2.1 Docking with Vdock

The initial docking with VDock already showed promising results, especially with VD-

compounds, however performed poorly with the E-coumpounds. As it can be seen in the figure

14, VDock has managed to differentiate ligands and distributed them more or less according to

their real binding energies but also made significant errors. The linear approximation of the data

suggested the overall trend to be ∆Gmod ≈ 0.83×∆Gexp +7.72 (r = 0.55, p = 0.00). These results

indicate that there is a significant amount of information about possible ligand binding affinities

in the potentials determined by VDock.

In the case of the E-compounds situation was quite different (Fig.14). VDock didn’t

managed to differentiate good and bad binders and there was no correlation between modelled and

experimental results (∆Gmod ≈ 0.13×∆Gexp − 39.96, r = 0.14, p = 0.03).

4.2.2 PBSA potential

The PBSA analysis returned results more or less similar to those of VDock. Again, VD-

compounds seemed to be better differentiated than E-compounds (Fig.14). However, results for the

VD series were more scattered than in the case of VDock ranking – ∆Gmod ≈ 0.4×∆Gexp−37.68,

r = 0.23, p = 0.00.

E-compounds, again, could not be properly ranked and results were even worse than in

the case of VDock analysis – ∆Gmod ≈ 0.02×∆Gexp − 34.70, r = 0.02, p = 0.79.

4.2.3 Expressions of total modelled binding energy

After the initial analysis of the VDock and PBSA results, three different expressions of

the total modelled binding energy ∆Gmod for different representations of the effect of the solvent

were tested. One already used by Dr. Visvaldas Kairys (Capkauskaitė et al. 2012) and two as

modifications to it. Expression of Dr. Kairys, represented effect of the solvent in terms of the

solvent accessible surface area change upon binding ∆SASA, whereas two models of mine used

hydrophobic solvent accessible surface area of the ligand (SASAHyd) and the Van der Waals

surface area of the ligand (SAvdw). They were named according to the differing approach to the

solvent – ∆SASA-model, SASAHyd-model and the SAvdw-model accordingly. All three expression

48


VD-compounds E-compounds

SA

SA

vd

wS

AH

yd

∆S

AS

A

ΔG

mod

(kJ/

mo

l)

0

−20

−40

−60

−80

ΔG

mod

(kJ/

mo

l)

0

−10

−20

−30

−40

−50

−60

ΔG

mod

(kJ/

mo

l)

0

−10

−20

−30

−40

−50

−60

ΔGexp (kJ/mol)0 −10 −20 −30 −40 −50 −60

ΔGexp (kJ/mol)0 −10 −20 −30 −40 −50 −60

Figure 15: Modelled binding energies obtained by fitting models to the experimental data. Lines

mark linear regression of the data.

49


incorporated coefficients α, β, γ and δ for different potentials involved in the binding process (more

information in Tab.5). They represented the weights for different potentials used in the expressions.

Values of these coefficients were determined by equating the expression to the experimental data

∆Gexp and finding the best fit with the least squares method.

Contribution Coefficient Representation

Electrostatic α V Colintr + V P B

Van der Waals β V vdwattr + V vdw

rep

Solvent effect γ ∆SASA, SASAhyd or SAvdw

Linear error δ –

Table 5: Potentials and their coefficients used in the expressions of total modelled binding energy

∆Gmod.

The ∆SASA-model:

α(V Colintr + V P B) + β(V vdw

attr + V vdwrep ) + γ∆SASA + δ = ∆Gexp (28)

Results obtained by using the ∆SASA-model were somewhere intermediate between those purely of

VDock and PBSA. Once again VD-compounds were less scattered and exhibited greater correlation

with the experimental results (Fig.15): ∆Gmod ≈ 0.24×∆Gexp − 33.95, r = 0.50, p = 0.00.

Fitted binding energies of E-compounds once again did not show any significant correla-

tion with the experimental data (Fig.15): ∆Gmod ≈ 0.11×∆Gexp − 36.97, r = 0.22, p = 0.00.

The SASAHyd-model:


attr + V vdwrep ) + γSASAhyd + δ = ∆Gexp (29)

The approach of SASAHyd-model was to include property, which depends only on the ligand and

not on the binding event like ∆SASA does. Quite surprisingly, results for VD-compounds were

just as good as with the ∆SASA-model (Fig.15): ∆Gmod ≈ 0.50 × ∆Gexp − 34.22, r = 0.51,

p = 0.00.

For the E-compounds, however, it was the worst case, with even negative correlation

coefficient (Fig.15): ∆Gmod ≈ −0.02×∆Gexp − 60.76, r = −0.01, p = 0.92.

The SAvdw-model:


attr + V vdwrep ) + γSAvdw + δ = ∆Gexp (30)

Much like the SASAHyd-model, this approach included property dependent on the ligand alone –

its Van der Waals surface area (SAvdw). However, neither VD-compounds (∆Gmod ≈ −43.15 +

0.09×∆Gexp, r = 0.36, p = 0.00.) nor E-compounds (∆Gmod ≈ +0.01×∆Gexp− 40.73, r = 0.05,

p = 0.41.) were ranked correctly with this model.

50


4.3 Discussion

The approach of modelling taken in this study can be regarded as somewhat a mixture

of screening (Grüneberg et al. 2002) and the ”precise” docking techniques (Capkauskaitė et al.

2012). As in the screening studies, multiple ligands were ranked without paying attention to their

correlation to the crystallographic data. But, 152 ligands used in this study is nothing near to the

thousands or hundreds of thousands compounds used in the screening approaches. Similarly to the

usual ”precise” docking studies, more sophisticated methods of solvent approximation and data

analysis were employed. But, none of the ligand poses were analysed in very detail or compared

to the crystallographic data. Besides, the ligands weren’t grouped according to the details of their

structures (Capkauskaitė et al. 2012) and only according their main scaffold.

The initial binding energies obtained with VDock, exhibited good correlation with the

experimental data for VD-compounds. However, the method was not capable of distinguishing

good binders in the set of E-compounds. Overall, if the E-compounds are neglected, VDock gave

the best experimental and modelled energies correlation with the least effort.

The systematically lower correlation for the modelled energies of E-coumpounds rep-

resents quite different structural properties of these inhibitors. VD-compounds are comparably

bigger and because of that, Van der Waals interactions dominates their binding mode. Whereas,

E-compounds are smaller and more influenced by the the electrostatic potential. However, the ef-

fect might also been caused by high structural variability of the E-compounds. This concludes, that

the method used in this study cannot be employed to rank structurally very distinct compounds

when they are the same set.

Comparison of the four methods used to evaluate the effect of solvation provided interest-

ing results. Firstly, it approved the ∆SASA-model used by Dr. Kairys (Capkauskaitė et al. 2012),

which overly gave quite satisfactory result for the VD-compounds (Fig.15). Secondly, SASAHyd

method, which approximated the solvation effect by using hydrophobic solvent accessible surface

area of each ligand, gave comparable results with those of ∆SASA model. This indicates that

SASAHyd might carry relevant information concerning the possible binding energy of each ligand

without having any concerning the particular binding event. Van der Waals surface area of each

ligand (SAvdw), in its regard did not carry such information at all and PBSA method performed

surprisingly poorly.

The results obtained with such an approach also appear intermediate between the two

mentioned major techniques. With the respect of the screening studies, the observed tendencies

have a comparable level of correlation between the experimental and modelling results (Grüneberg

et al. 2002), especially in the case of VDock and ∆SASA-model output for VD-compounds. How-

ever, these tendencies are only very approximate when compared to the usual, ”precise” docking

51


(Capkauskaitė et al. 2012), primarily because of the use of large number of structurally distinct

compounds.

There is also a huge practical aspect of this research project. For the first time such

number of ligands developed in the Department of Biothermodynamics and Drug Design were

analysed in one study. The workbench has been created, primarily in terms of the database and

the scripts written. The database enables more general observation of various tendencies within the

data and better management of it. Hopefully, it will be further developed for all the proteins and

ligands investigated in the department. The scripts will allow the similar study to be performed

more easily in an automated way.

52

5 Conclusion

In this thesis two different approaches in investigating the biologically relevant systems

in respect to the solvation and hydrophobic effect were described. The first research project con-

cerned the quantification of an already approved simple linear model of chemical groups additivity

in dissecting the thermodynamics of oppositely charged surfactants interaction. Whereas, in the

second study it was tried to identify the best method and simplistic representation of the solvent

in the protein-ligand interaction modelling. Both ”wet” laboratory experimentation methods like

isothermal titration calorimetry and computational methods like docking were employed respec-

tively. The results can be concluded as follows:

Thermodynamics of cationic and anionic surfactant reaction

• The association constant Kb depends on the concentration of surfactants when the aggrega-

tion reaction is taking place

• Ionic interaction of the surfactant heads seems to be not crucial and generally unfavourable

for the process of aggregation

• Thermodynamic parameters depend linearly on the overall aliphatic chain length of the

surfactant conjugate

• The aggregation of oppositely charged surfactants is driven by the huge negative enthalpy

contribution, whereas entropy change is unfavourable

• If the liquid aggregate is formed, the enthalpy contribution is significantly smaller .

Laws of additivity in the structure-based drug design

• VDock program was the most accurate – it provided the best results with the least effort

• Expression of modelled binding energy, which incorporated properties of the ligand alone

(SASAHyd) performed just as good as one that used properties regarding the binding event

(∆SASA)

• It was not possible to rank multitude of significantly different inhibitors with the same method

• The workbench for computational and structure-activity relation studies has been established

in the department and, hopefully, it will be developed further.

53

6 Acknowledgements

I would like to thank both of my supervisors Dr. Daumantas Matulis and Dr. Visvaldas

Kairys for their friendly and sincere attitude towards me and other students. It was a pleasure

both learning and working with them. One another colleague which was not mentioned as my

supervisor, but definitely should have been so is Dr. Vytautas Petrauskas. From him I have

gained invaluable experience, which helped me in various projects that I have been involved in. I

would also thank Lithuanian Science Council for the financial support given during my work in

both projects – Student Summer Research Practice and Student Scientific Research scholarships.

Special thanks also go to the Dr. Vytautas Smirnovas, whose review and insights helped me to

improve this thesis.

54

Povilas Norvaišas REFERENCES

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Alterio, V., Fiore, A. D., Ambrosio, K. D., Supuran, C. T., and Simone, G. D. (2012). Multiple

Binding Modes of Inhibitors to Carbonic Anhydrases: How to Design Specific Drugs Targeting

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7 Supplementary material

Kb

[cell], mM W p

0.66 0.97 0.88

0.33 0.91 0.52

0.165 0.78 0.09

Table 2: Dodecylammonium binding to the decane sulfonate. The normality of Kb for different

concentrations of the surfactant in the cell (decane sulfonate), according to Shapiro-Wilk (W) test.

ΔHex

p (kJ

/mol

)

−120

−100

−80

−60

−40

−20

0

m, aliphatic chain length17 18 19 20 21 22 23 24 25 26

ΔHexp(0.33mM)ΔHexp(0.66mM) ΔH=-8.4m+112

Figure 2: ∆Hexp dependence on the aliphatic chain length m at 25℃ with linear regression data.

64

Povilas Norvaišas Supplementary material

[cel

l],

mM

∆H

ex

p,

kJ/m

ol

Erro

r,

±kJ

/mol

∆H

fit

,

kJ/m

ol

Erro

r,

±kJ

/mol

Nf

itEr

ror,

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,

M−

1

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r,95

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1

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,

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mol

∆a

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,kJ/

mol

CH

2

T∆

ag

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obs,

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olK

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lcco

nc

alk c

on

cfit

calc

alk

0.66

-68.

902.

08-7

0.85

3.74

1.01

0.03

3.49

E+05

3.98

E+04

5.45

E+05

-31.

64-3

2.75

-61.

33-7

0.85

-102

.61

-95.

9912

-39.

20

0.59

4-6

9.51

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2.53

-0.

99-

3.04

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91E+

05-3

1.30

-32.

48-6

1.07

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53-1

02.6

1-9

5.99

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1.23

0.52

8-7

1.00

--7

1.65

-1.

02-

3.25

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-4.

36E+

05-3

1.46

-32.

19-6

0.78

-71.

65-1

02.6

1-9

5.99

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0.19

0.46

2-6

8.83

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0.89

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01-

3.11

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82E+

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1.35

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86-6

0.45

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89-1

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9.54

0.39

6-6

6.68

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8.22

-1.

03-

2.72

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-3.

27E+

05-3

1.02

-31.

48-6

0.06

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22-1

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7.20

0.36

3-6

6.65

--6

9.33

-1.

00-

2.17

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00E+

05-3

0.46

-31.

26-5

9.85

-69.

33-1

02.6

1-9

5.99

12-3

8.87

0.33

-65.

254.

19-7

0.48

5.16

0.98

0.05

1.86

E+05

4.31

E+04

2.73

E+05

-30.

08-3

1.03

-59.

61-7

0.48

-102

.61

-95.

9912

-40.

40

0.29

7-5

4.40

--6

8.26

-0.

96-

1.72

E+05

-2.

45E+

05-2

9.89

-30.

77-5

9.35

-68.

26-1

02.6

1-9

5.99

12-3

8.36

0.26

4-6

6.91

--7

2.83

-0.

98-

1.38

E+05

-2.

18E+

05-2

9.34

-30.

47-5

9.06

-72.

83-1

02.6

1-9

5.99

13-4

3.48

0.23

1-6

3.45

--7

2.28

-0.

96-

1.34

E+05

-1.

91E+

05-2

9.27

-30.

14-5

8.73

-72.

28-1

02.6

1-9

5.99

13-4

3.00

0.19

8-5

9.08

--6

8.50

-0.

98-

1.30

E+05

-1.

64E+

05-2

9.18

-29.

76-5

8.34

-68.

50-1

02.6

1-9

5.99

12-3

9.31

0.16

5-5

5.52

19.6

4-7

2.69

15.9

10.

990.

031.

05E+

052.

63E+

041.

36E+

05-2

8.66

-29.

31-5

7.89

-72.

69-1

02.6

1-9

5.99

13-4

4.03

Tabl

e3:

Dod

ecyl

amm

oniu

mtit

ratio

nto

deca

nesu

lfona

teat

25◦ C

:de

pend

ence

ofth

erm

odyn

amic

para

met

ers

onsu

rfact

ant

conc

entr

atio

n

65


m∆

He

xp,

kJ/m

ol

Erro

r,

±kJ

/mol

∆H

fit

,

kJ/m

ol

Erro

r,

±kJ

/mol

Nf

itEr

ror,

±K

fit

,

M−

1

Aa

lkC

Aio

nB

,

M−

1

∆a

ggG

,kJ/

mol

∆a

ggH

,kJ/

mol

CH

2

T∆

ag

gS

obs,

kJ/m

ol

Erro

r,

±kJ

/mol

fitEr

r.ca

lc0.

33m

Mal

k 0.3

3mM

fitca

lcal

k

18-2

.92

–-3

.54

–0.

88–

2.35

E+05

8.43

E+02

-30.

65–

-16.

70-4

5.28

-2.9

2-8

1.81

-75.

192

27.2

6–

19-5

.67

––

––

––

3.58

E+03

––

-20.

28-4

8.87

-5.6

7-8

7.01

-80.

392

––

20-1

.91

3.77

-18.

79–

0.57

–5.

85E+

041.

52E+

04-2

7.21

–-2

3.86

-52.

45-1

.91

-92.

21-8

5.59

224

.88

–

21-5

4.10

4.49

-83.

2648

.50

0.97

0.09

2.76

E+04

6.43

E+04

-25.

353.

25-2

7.45

-56.

03-5

4.10

-97.

41-9

0.79

11-2

8.27

5.54

22-6

7.45

3.20

-71.

273.

221.

050.

131.

81E+

052.

73E+

05-3

0.01

0.12

-31.

03-5

9.61

-67.

45-1

02.6

1-9

5.99

13-3

6.81

3.20

23-8

1.92

10.1

6-8

4.89

14.8

00.

840.

082.

61E+

051.

16E+

06-3

0.92

0.61

-34.

61-6

3.19

-81.

92-1

07.8

1-1

01.1

916

-50.

1410

.17

24-9

1.14

7.31

-151

.79

140.

041.

230.

121.

29E+

064.

90E+

06-3

4.88

1.35

-38.

19-6

6.77

-91.

14-1

13.0

1-1

06.3

918

-55.

317.

43

25-9

5.81

7.29

-418

.58

656.

501.

060.

204.

47E+

052.

08E+

07-3

2.25

1.91

-41.

77-7

0.36

-95.

81-1

18.2

1-1

11.5

919

-62.

507.

54

Tabl

e4:

Vario

ussu

rfact

ant

syst

ems

at25

℃,c

once

ntra

tion

ofth

esu

rfact

ant

inth

ece

ll-0

.33

mM

:dep

ende

nce

ofth

erm

odyn

amic

para

met

ers

onal

ipha

tic

chai

nle

ngth

m.

m∆

He

xp,

kJ/m

ol

Erro

r,

±kJ

/mol

∆H

fit

,

kJ/m

ol

Erro

r,

±kJ

/mol

Nf

itEr

ror,

±K

fit

,

M−

1

Aa

lkC

Aio

nB

,

M−

1

∆a

ggG

,kJ/

mol

∆a

ggH

,kJ/

mol

CH

2

T∆

ag

gS

obs,

kJ/m

ol

Erro

r,

±kJ

/mol

fitEr

r.ca

lcco

nc

alk c

on

cfit

calc

alk

20-1

1.43

91.4

0-3

7.78

–1.

02–

6.80

E+04

3.03

E+04

-27.

58–

-25.

58-5

4.17

-11.

43-9

2.21

-85.

593

15.8

8264

–

21-6

5.76

2.14

-64.

7115

.09

1.32

–1.

65E+

051.

29E+

05-2

9.79

4.43

-29.

16-5

7.75

-65.

76-9

7.41

-90.

7913

-35.

365

4.91

5427

22-6

8.90

2.08

-70.

853.

741.

01–

3.48

E+05

5.45

E+05

-31.

630.

28-3

2.75

-61.

33-6

8.90

-102

.61

-95.

9914

-36.

6448

2.09

518

Tabl

e5:

Vario

ussu

rfact

ant

syst

ems

at25

℃,c

once

ntra

tion

ofth

esu

rfact

ant

inth

ece

ll-0

.66

mM

:dep

ende

nce

ofth

erm

odyn

amic

para

met

ers

onal

ipha

tic

chai

nle

ngth

m.

66


m

∆Hexp ∆Gfit

0.33 mM 0.66 mM 0.33 mM 0.66 mM

W p W p W p W p

18 – – – –

19 – – – –

20 0.96 0.81 – – – – – –

21 0.85 0.15 0.98 0.95 0.77 0.04 0.77 0.04

22 0.88 0.27 0.78 0.08 0.93 0.56 0.93 0.56

23 0.78 0.05 0.85 0.22

24 0.82 0.06 0.90 0.33

25 0.93 0.55 0.83 0.11

Table 6: The normality of thermodynamic parameters for different lengths of aliphatic chain m,

according to Shapiro-Wilk (W) test

t, ℃ No. of exp. Avg. ∆Hexp, kJ/mol Error, ± kJ/mol

25 4 -65.25 4.19

37 5 -83.02 2.88

52 2 -26.82 1.75

69 2 -32.66 2.24

Table 7: Analysis of enthalpies of dodecylammonium binding to decane sulfonate at various tem-

peratures.

67

hydrophobic effect: thermodynamics of cationic & anionic surfactant

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