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Thermodynamic approaches to membranes and membrane interactions. Peter Westh NSM, Research Unit for Biomolecules Roskilde University Thermodynamic approaches to membranes and membrane interactions. thermodynamics ?. Thermodynamics.

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Thermodynamic approaches to membranes and membrane interactions

Peter Westh

NSM, Research Unit for Biomolecules

Roskilde University

Thermodynamic approaches to membranes and membrane interactions

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

Macroscopic – gross properties – heat and mechanical energy – statistics - phenomenological

Relevance to molecular biology and biochemistry ?

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)


Is a wonderful structure with no contents

Aharon Katchalsky

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

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

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

Thermodynamic studies of membranes – a practical approach

  • Free energy of interaction

  • Calorimetry (energy of interaction):



    -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, DG°)

    Any technique (e.g. spectral, hydrodynamic, thermal) which quantifies the concentration of a species in a proposed reaction. For example protein folding

    UN ,K=[N]/[U] and DG=-RTlnK

    Or membrane partitioning

    Peptide (aq)  peptide (membrane)

Andersen et al (2005) J Biochem Biophys Methd50, 269.

Free energy of interactionan example

Water-phospholipid interactions (membrane hydration)

Direct measurements of the water vapor pressure




Adsorption isotherm POPC 25C


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

Andersen et al (2005) J Biochem Biophys Methd50, 269.

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 25C DMPC 27 C

Sorption isotherm

(net water affinity)

Heat of sorption


Markova et al. (2000) J Phys Chem B104, 8052

Lyotropic phase transitions



Markova et al. (2000) J Phys Chem B104, 8052


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

  • 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 ~0.002mCal/sec or about 10nW.

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

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)

Classic use of DSC phase diagrams

Blume (1983) Biochem. 22; 5436.

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

Böckman et al (2003) Biophys J.85, 1647

DSC and the lever rule

Binary membrane (two PCs) Phase diagram

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

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

Derived – and remarkably complex – phase diagram

Increasing water content

DSC data

Sharlev & Steponkus (1999) BBA1419, 229.

Mixed membrane systemsPhase behavior of phospholipid-cholesterol systems





McMullen et al (1993) Biochem32, 516.

DMPC/POPC + 28 % Cholesterol

Luis Bagatolli

Alcohols depress the main (Pb – La) 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

Complex solute effects in Phosphatidyl enthanoamine



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

DH  0


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!

Technical overviewPower compensated ITC (after ~1990)

The feed-back system sustains a constant and very small DT between cell and reference.

Net refcell heat flow

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

Electrical heater

  • +++

  • Fast responce, high sensitivity

  • - - -

  • Narrow applicability,

Feed-Back Control

Simple approach

Ligand 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

OcOH depletion

Rowe et al (1998) Biochem. 37, 2430

DH  0


ITC and partitioning:data analysis

Partitioning scheme: A(aq) ↔ A(mem)

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

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.

Trandum et al (1999) J.Phys.Chem.B103; 4751

Interaction of ethanol and DMPCDependence of phase and cholesterol

Phase behavior

Interaction enthalpy

And partitioning coefficient

DMPC+10% Ganglioside Kp=87

DMPC+10% Sphingomyelin Kp=85

DMPC, Kp=28

DMPC+30% Cholesterol Kp=12

Partitioning of small alcohols scales with the membrane surface density

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

Cholesterol content

Trandum et al (1999) BBA, 1420, 179

Trandum et al (1999) BBA1420; 179

Trandum et al (2000) Biophys J78; 2486

Heat (and thus calorimetry) is the universal detector.Specialized methods show great versatility

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

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

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

Another asset of calorimetry is high resolutionMicelle formation and protein surfactant interactions

De-micellization of SDS

CMC readily determined to within 10-50mM

Otzen et al In press

Another asset of calorimetry is high resolutionMicelle formation and protein surfactant interactions

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


Heat Flow

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

Pressure perturbation DSC



Which is tantamount to


PPC – two examples from biophysics

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

Thermal denaturation of two globular proteins

Area equals the volume change, DV, for the denaturation

Heerklotz (2004) J. Phys Condens Matter16, 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 ml

Thermostatted 0.001 K

Hook’s law

Period measured to 1nsec

Calibrate against air and water


For liqiuds (and gasses):

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

Vibrating tube densitometry

Volume (density) of pure membranes

  • DMPC @ 30C V~0.978 cm3/g (d~1.022 g/cm3)

  • DV @ Tm 4%

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

  • Polyunsaturated PC (like di-linolenoyl PC i.e. 18:3/18:3-cis-D9,12,15) have volumes similar to saturated PC

Volume (density) of mixtures

  • Illustrates how the different species pack

  • May benchmark MD simulations

Nagle & Wilkinson (1978) Biophys J 23, 159

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

Molecular packing:Experiment vs. simulation

Voronoi assignments of molecular volumes

DVhexanol (exp)= 4.2 ml/mol

DVhexanol (exp)= 3.9 ml/mol

Densitometry on membrane of membrane-solute systems

A typical sample consists of

97% water

2.9% Phospholipid

0.1% fatty acid

Measured specific volume V

Molecular packing of alcohols in DMPC


(standard pure alcohol)

Volume of each component




Aagaard et al 2005


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.

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