Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for...
-
Upload
piers-hawkins -
Category
Documents
-
view
217 -
download
0
Transcript of Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for...
![Page 1: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/1.jpg)
Thermodynamic approaches to membranes and membrane interactions
Peter WesthNSM, Research Unit for Biomolecules
Roskilde University
![Page 2: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/2.jpg)
Thermodynamic approaches to membranes and membrane interactions
thermodynamics ?
![Page 3: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/3.jpg)
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
![Page 4: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/4.jpg)
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)
![Page 5: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/5.jpg)
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.
![Page 6: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/6.jpg)
Thermodynamic studies of membranes – a practical approach
• Free energy of interaction • Calorimetry (energy of interaction):
-scanning-titration-pressure perturbation-temperature modulated
• Volumetric properties
![Page 7: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/7.jpg)
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.
![Page 8: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/8.jpg)
Free energy of interactionan example
Water-phospholipid interactions (membrane hydration)
![Page 9: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/9.jpg)
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
![Page 10: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/10.jpg)
Faster methodsDynamic Vapor Sorption (DVS)
![Page 11: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/11.jpg)
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.
![Page 12: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/12.jpg)
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
![Page 13: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/13.jpg)
Lyotropic phase transitions
DLPC
DMPC
Markova et al. (2000) J Phys Chem B 104, 8052
![Page 14: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/14.jpg)
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
![Page 15: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/15.jpg)
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.
![Page 16: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/16.jpg)
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 !
![Page 17: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/17.jpg)
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
![Page 18: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/18.jpg)
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
![Page 19: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/19.jpg)
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
![Page 20: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/20.jpg)
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.
![Page 21: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/21.jpg)
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.
![Page 22: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/22.jpg)
Alcohols depress the main (P – L) phase transition temperature
Pressure Increases Tm – Le chateliers principle!
![Page 23: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/23.jpg)
Alcohol and interdigitated phases
Rowe & Cutera (1990) Biochem. 29, 10398
![Page 24: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/24.jpg)
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
![Page 25: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/25.jpg)
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
![Page 26: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/26.jpg)
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,
![Page 27: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/27.jpg)
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
![Page 28: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/28.jpg)
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.
![Page 29: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/29.jpg)
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.
![Page 30: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/30.jpg)
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
![Page 31: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/31.jpg)
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)
![Page 32: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/32.jpg)
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
![Page 33: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/33.jpg)
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
![Page 34: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/34.jpg)
A new generation of DSCTemperature Modulated DSC
![Page 35: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/35.jpg)
A linear gradient in T with a sine wave or zigzag superimposed
Temperature
Heat Flow
![Page 36: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/36.jpg)
In-phase and out-of-phase heat capacity single out different response/relaxation processes
![Page 37: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/37.jpg)
Pressure perturbation DSC
Measures
HEAT OF COMPRESSION
Which is tantamount to
THERMAL EXPANSIVITY
![Page 38: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/38.jpg)
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
![Page 39: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/39.jpg)
Volumetric properties
• V=dG/dp
• Readily measured by vibrating tube densitometry.
• ”Structural interpretation” and relationship to physical dimensions
![Page 40: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/40.jpg)
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
![Page 41: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/41.jpg)
Vibrating tube densitometry
![Page 42: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/42.jpg)
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
![Page 43: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/43.jpg)
Molecular packing:Experiment vs. simulation
Vhexanol (exp)= 4.2 ml/mol
Vhexanol (exp)= 3.9 ml/mol
Voronoi assignments of molecular volumes
![Page 44: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/44.jpg)
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
![Page 45: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/45.jpg)
Molecular packing of alcohols in DMPC
V=Vapp-V
(standard pure alcohol)
Aagaard et al 2005
Volume of each component
alcohol
Lipid
water
![Page 46: Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk.](https://reader035.fdocuments.us/reader035/viewer/2022062409/56649ed15503460f94be0709/html5/thumbnails/46.jpg)
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.