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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.
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