Thermodynamic approaches to membranes and membrane interactions

Peter WesthNSM, Research Unit for Biomolecules

Roskilde University

pwesth@ruc.dk

Thermodynamic approaches to membranes and membrane interactions

thermodynamics ?

Thermodynamics

The science that deals with the relationship of heat and mechanical energy and the conversion of one into the other

Webster’s New Universal Dictionary 1979

A branch of physics that studies …… systems at the macroscopic scale by analyzing the collective motion of their particles using statistics

Wikipedia Jan. 2008

A macroscopic phenomenological discipline concerned with a description of the gross properties of systems

Kirkwood & Oppenheim: Chemical Thermodynamics, 1961

Relevance to molecular biology and biochemistry ?

Macrosc

opic – g

ross properti

es – heat a

nd mech

anical

energy – sta

tistic

s - phenomenologica

l

Thermodynamics and (bio)molecules

• Department of molecular thermodynamics…..• Hydrogen bond thermodynamics. Calculation of local and molecular

physicochemical descriptors ”HYBOT-PLUS”• Thermodynamics of protein folding (Cooper 1999)• Thermodynamics of membrane receptors and channels (MB Jacson 1993)

How is that possible for an approach which is: ”phenomenological” “macroscopic” and describes “gross properties” ?

Thermodynamics is your x-ray glasses which enables you to screen the models and mechanisms which are suggested to rationalize the exploding amount of empirical biochemical knowledge (functional and structural)

Thermodynamics

Is a wonderful structure with no contents

Aharon Katchalsky

Equilibriumstate

1st derivatives 2nd derivatives(response functions)

3rd derivatives

G S {T} (H {S} ) Hi {T,ni} Hi-j {T,ni,nj}

V {P} Vi {P,ni} Vi-j {P,ni,nj}

i {ni} Cp {T,T} dCp/dT {T,T,T}

{P,T} Etc etc

{P,P}

i-j {ni, nj}

For the (experimentally convenient) (P,T,ni) variable system

For membranous (colloidal) systems perhaps a fourth variable: Area (dG/dA=)

Koga (2007) Solution Thermodynamics: a differential approach. Elsevier.

Thermodynamic studies of membranes – a practical approach

• Free energy of interaction • Calorimetry (energy of interaction):

-scanning-titration-pressure perturbation-temperature modulated

• Volumetric properties

Measuring free energy (chemical potential) changes of interactions

Two experimental approaches:

• Direct (model free)Measures the equilibrium distribution. For example dialysis

equilibrium, freezing point depression, membrane osmometry, liquid-liquid partitioning, vapor pressure (ion selective electrode)

• Indirect (model based, G°)Any technique (e.g. spectral, hydrodynamic, thermal) which

quantifies the concentration of a species in a proposed reaction. For example protein folding

UN , K=[N]/[U] and G=-RTlnKOr membrane partitioning

Peptide (aq) peptide (membrane)

Andersen et al (2005) J Biochem Biophys Methd 50, 269.

Free energy of interactionan example

Water-phospholipid interactions (membrane hydration)

Direct measurements of the water vapor pressure

Water adsorption @ 25 CPOPC

Relative humidity

0 20 40 60 80 100

g w

ater

/g li

pid

0.0

0.1

0.2

0.3

0.4

Andersen et al (2005) J Biochem Biophys Methd 50, 269.

Adsorption isotherm POPC 25C

Temperature scanning, DMPC-water. Pressure difference between moist lipid and pure water.

14.5

18.423.5

30.0

Faster methodsDynamic Vapor Sorption (DVS)

Sorption calorimetry

Heat (enthalpy) of adsorption is measured directly – the amount adsorbed is calculated from the evaporation enthalpy

Bagger et al (2006) Eu. Biophys. J. 35, 367.

Sorption calorimetry

DLPC 25C DMPC 27 C

Sorption isotherm

(net water affinity)

Heat of sorption

(Hw)

Markova et al. (2000) J Phys Chem B 104, 8052

Lyotropic phase transitions

DLPC

DMPC

Markova et al. (2000) J Phys Chem B 104, 8052

Calorimetry

• We measure the temperature dependence of the free energy (Gibbs Helmholtz eq.)

H

TTT

G

p

2

1

• Most often, this is not explicitly used – we quantify the course of a process through the heat it produces

Membrane calorimetry

• One of the oldest analytical principles still in use – Lavoisier had rather precise calorimeters by 1780.

• Readily measured thermodynamic function. • Heat cannot be measured – temperature

can.• Heat is NOT at state function – enthalpy

and internal energy are.

Modern instruments (ITC200)No water bath Noise level ~0.002Cal/sec

or about 10nW.

The heat capacity is about 3 J/K – detection level ~0.1J

Hence the the thermal noise is about 1x10-

7/3~3x10-8K !

Two types of calorimeters have revolutionized biochemical

applications• Differential Scanning Calorimetry (DSC)• Isothermal Titration Calorimetry (ITC)

DSC ITCMeasures heat required to linearly increase T

Measures heat of mixing (titrand into titrate)

Constant composition – temperature perturbed

Constant T – composition perturbed

Thermal breakdown, denaturation, phase transitions

Ligand binding, receptor studies, adsorption, kinetics

Classic use of DSC phase diagrams

Blume (1983) Biochem. 22; 5436.

Böckman et al (2003) Biophys J. 85, 1647 Schrader et al (2002) J.Phys.Chem. 106, 6581

DSC and the lever rule

Schrader et al (2002) J.Phys.Chem. 106, 6581

Binary membrane (two PCs) Phase diagram

F

G

G

F

l

l

n

n :ruleLever The ratio nF/nG quantifies the conversion of

gel to fluid phase and is hence reflected in the callorimetric heat flow

Phase diagram for DOPE at low temperature and water content

Incr

easi

ng w

ate

r co

nte

nt

DSC data

Derived – and remarkably complex – phase diagram

Sharlev & Steponkus (1999) BBA 1419, 229.

Mixed membrane systemsPhase behavior of

phospholipid-cholesterol systems

DMPC/POPC + 28 % Cholesterol

Luis Bagatolli http://scienceinyoureyes.memphys.sdu.dk

Temperature

19 25 30

McMullen et al (1993) Biochem 32, 516.

Alcohols depress the main (P – L) phase transition temperature

Pressure Increases Tm – Le chateliers principle!

Alcohol and interdigitated phases

Rowe & Cutera (1990) Biochem. 29, 10398

Other compounds increase the main transition temperature

[Solute] (mol L-1)

0,0 0,5 1,0 1,5 2,0 2,5 3,0

T (

o C)

60

70

80

90

100

110

HII

L

L'

Sucrose

KSCN

Complex solute effects in Phosphatidyl enthanoamine

Koynova, et al. (1997) Europ. Biophys. J. 25, 261

Binding and PartitioningITC

”Foreign molecules” bind or partitioning into membranes

We already saw the DSC approach to this – change in phase behavior reflects partitioning !

ITC approach – directly measure interaction:

Basic idea!

+ →

H 0

Technical overviewPower compensated ITC (after ~1990)

Electrical heater

Feed-Back Control

The feed-back system sustains a constant and very small T between cell and reference. Net refcell heat flow

Exothermic process is compensated out by (fast) adjustment of the feed-back heaters.

+++Fast responce, high sensitivity-- - - Narrow applicability,

Simple approachLigand in cell – titrate with membrane (NB the other way

around won’t work since there is no saturation – it is partitioning between two phases)

Lipid membrane; 47.4mM

Octanol 0.61mM 1-octanol

Rowe et al (1998) Biochem. 37, 2430

OcOH depletion

ITC and partitioning:data analysis

Partitioning scheme: A(aq) ↔ A(mem)

+ →

H 0

Law of mass action: Kp=[Amem]/[Aaq]

Mass conservation: [A]tot=[Amem]+[Aaq]

Rowe et al. (1998) Biochem. 37; 2430.

Weaker interaction requires more complex procedures

Trandum et al (1999) J.Phys.Chem.B 103; 4751

Excess enthalpy, HE, of DMPC in 1-propanol

HE is the enthalpic contribution of DMPC towards the total enthalpy of the system

Hence, the slope HE/Calcohol is a measure of the enthalpy of DMPC-alcohol interactions

Note that HE vs Calcohol is not linear.

Interaction of ethanol and DMPCDependence of phase and cholesterol

Trandum et al (1999) BBA 1420; 179Trandum et al (2000) Biophys J 78; 2486

Interaction enthalpyAnd partitioning coefficient

DMPC, Kp=28

DMPC+30% Cholesterol Kp=12

DMPC+10% Sphingomyelin Kp=85

DMPC+10% Ganglioside Kp=87

Phase behavior

Cholesterol content

Partitioning of small alcohols scales with the membrane surface density

DeYoung & Dill (1988) Biochem. 27, 5281.

Trandum et al (1999) BBA, 1420, 179

Heat (and thus calorimetry) is the universal detector.

Specialized methods show great versatility

A ”release protocol” for the determination of membrane permeation rates

Heerklotz & Selig (2000) Biophys. J. 81, 184.

10mM POPC vesicles injected into 150M C10EO7 (upper) and 1mM C10EO7+10mM POPC (lower)

Another asset of calorimetry is high resolutionMicelle formation and protein surfactant

interactions

De-micellization of SDS

CMC readily determined to within 10-50M

Otzen et al In press

Another asset of calorimetry is high resolutionMicelle formation and protein surfactant

interactionsBinding isotherms

Mb-SDSMOPS pH 7.0

[SDS]0 5 10 15 20

H

(ca

l/mo

l)

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

200

400

24 uM vs Col 2 49 uM vs Col 5 74 uM vs Col 8 98 uM vs Col 11 124 uM vs Col 14 150 uM vs Col 17 182 uM vs Col 20 204 uM vs Col 23 241 uM vs Col 26

Andersen et al Langmuir in press

A new generation of DSCTemperature Modulated DSC

A linear gradient in T with a sine wave or zigzag superimposed

Temperature

Heat Flow

In-phase and out-of-phase heat capacity single out different response/relaxation processes

Pressure perturbation DSC

Measures

HEAT OF COMPRESSION

Which is tantamount to

THERMAL EXPANSIVITY

PPC – two examples from biophysics

Area equals the volume change, V, for the denaturation

Melting of egg sphingomyelin. Conventional DSC and PPC. H=30.5 kJ/mol, V=21 ml/mol

Thermal denaturation of two globular proteins

Heerklotz (2004) J. Phys Condens Matter 16, R441

Volumetric properties

• V=dG/dp

• Readily measured by vibrating tube densitometry.

• ”Structural interpretation” and relationship to physical dimensions

Vibrating tube densitometry

Hollow quartz U-tube. Volume 1 mlThermostatted 0.001 K

Hook’s lawPeriod measured to 1nsecCalibrate against air and water

For liqiuds (and gasses):

Specific volume (density) measured to within 10-6 to 10-5 cm3g-1 (g cm-3)

F~300Hz

Vibrating tube densitometry

Volume (density) of pure membranes

• DMPC @ 30C V~0.978 cm3/g (d~1.022 g/cm3) V @ Tm 4%

• Monounsaturated PC membranes (e.g. both cis and trans DOPC) have higher volumes (~1.020 to 1.050 cm3/g @ 30C.

• Polyunsaturated PC (like di-linolenoyl PC i.e. 18:3/18:3-cis-9,12,15) have volumes similar to saturated PC

Nagle & Wilkinson (1978) Biophys J 23, 159

Trandum & Westh (2000) J Phys Chem B 104, 11334

Volume (density) of mixtures

•Illustrates how the different species pack

•May benchmark MD simulations

Molecular packing:Experiment vs. simulation

Vhexanol (exp)= 4.2 ml/mol

Vhexanol (exp)= 3.9 ml/mol

Voronoi assignments of molecular volumes

Densitometry on membrane of membrane-solute systems

A typical sample consists of 97% water2.9% Phospholipid0.1% fatty acid

Measured specific volume V

solute

lipidlipidapp

solutememAppsolute

aqueousnon

OHOHAppsolutemem

w

VwVV

w

VwVV

*

*

membranein solute of olumeApparent v

membrane) (doped phase aqueous-non of olumeApparent v

22

Molecular packing of alcohols in DMPC

V=Vapp-V

(standard pure alcohol)

Aagaard et al 2005

Volume of each component

alcohol

Lipid

water

Closing

Although thermodynamic functions reflects ”macroscopic properties” they effectly elucidate molecular aspects of membranes and membrane interactions.

Calorimetry is the most precise and versatile experimental approach.