Transcript Peter Westh - Department of Physics

Thermodynamic approaches to
membranes and membrane interactions
Peter Westh
NSM, Research Unit for Biomolecules
Roskilde University
[email protected]
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 ?
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
For the (experimentally convenient) (P,T,ni) variable system
Equilibrium
state
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}
mi {ni}
Cp {T,T}
dCp/dT {T,T,T}
a {P,T}
Etc etc
k {P,P}
Koga (2007) Solution Thermodynamics: a
differential approach. Elsevier.
mi-j {ni, nj}
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):
-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, 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 Methd 50, 269.
Free energy of interaction
an example
Water-phospholipid interactions
(membrane hydration)
Direct measurements of the water
vapor pressure
30.0
23.5
18.4
Adsorption isotherm POPC 25C
14.5
Water adsorption @ 25 C
POPC
0.4
g water/g lipid
0.3
Temperature scanning, DMPC-water.
Pressure difference between moist lipid
and pure water.
0.2
0.1
0.0
0
20
40
60
80
100
Relative humidity
Andersen et al (2005) J Biochem Biophys Methd 50, 269.
Faster methods
Dynamic 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
(DHw)
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.)
 
G

T
 T


p

1
H
2
T
• 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)
DSC
ITC
Measures heat required to Measures heat of mixing
linearly increase T
(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
Binary membrane (two PCs)
Phase diagram
Schrader et al (2002) J.Phys.Chem. 106, 6581
Lever rule :
nF lG

nG l F
The ratio nF/nG quantifies the conversion of
gel to fluid phase and is hence reflected in
the callorimetric heat flow
Increasing water content
Phase diagram for DOPE at low
temperature and water content
Derived – and remarkably
complex – phase diagram
DSC data
Sharlev & Steponkus (1999) BBA 1419, 229.
Mixed membrane systems
Phase behavior of
phospholipid-cholesterol systems
19
25
30
Temperature
McMullen et al (1993) Biochem 32, 516.
DMPC/POPC + 28 % Cholesterol
Luis Bagatolli
http://scienceinyoureyes.memphys.sdu.dk
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
110
HII
KSCN
90
o
T ( C)
100
80
Sucrose
La
70
Lb'
60
0,0
0,5
1,0
1,5
2,0
2,5
3,0
[Solute] (mol L-1)
Koynova, et al. (1997) Europ. Biophys. J. 25, 261
Binding and Partitioning
ITC
”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:
DH  0
Basic idea!
+
→
Technical overview
Power compensated ITC (after ~1990)
The feed-back system sustains a
constant and very small DT between
cell and reference.
Net refcell heat flow
Electrical heater
Exothermic process is compensated out
by (fast) adjustment of the feed-back
heaters.
+++
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
ITC and partitioning:
data analysis
Partitioning scheme:
A(aq) ↔ A(mem)
DH  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
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.B 103; 4751
Interaction of ethanol and DMPC
Dependence 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.
Trandum et al (1999) BBA, 1420, 179
Cholesterol content
Trandum et al (1999) BBA 1420; 179
Trandum et al (2000) Biophys J 78; 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 resolution
Micelle formation and protein surfactant
interactions
CMC (T)
3000
25C
30C
35C
40C
45C
DH (J/mol)
DCp
2000
DH(45oC)
1000
0
2
4
6
8
SDS (mM)
De-micellization of SDS
CMC readily determined to within 10-50mM
Otzen et al In press
SDS-apo a-LA
Another asset of calorimetry is high resolution
Micelle formation and protein surfactant
interactions
Binding isotherms
Mb-SDS
MOPS pH 7.0
400
200
0
DH (cal/mol)
-200
-400
-600
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
-800
-1000
-1200
-1400
-1600
0
5
10
[SDS]
15
Andersen et al Langmuir in press
20
A new generation of DSC
Temperature 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
Thermal denaturation of two
globular proteins
Area equals the volume change,
DV, for the denaturation
Melting of egg sphingomyelin.
Conventional DSC and PPC. DH=30.5
kJ/mol, DV=21 ml/mol
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 ml
Thermostatted 0.001 K
F~300Hz
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 membranesolute systems
A typical sample consists of
97% water
2.9% Phospholipid
0.1% fatty acid
Measured specific volume V
Apparent v olume of non - aqueous phase (doped membrane)
App
Vmem
 solute 
V  wH 2OVH* 2O
wnon aqueous
Apparent v olume of solute in membrane
App
Vsolute

app
*
Vmem
 solute  wlipidVlipid
wsolute
Molecular packing of alcohols in
DMPC
DV=Vapp-V
(standard pure alcohol)
Volume of each component
Lipid
alcohol
water
Aagaard et al 2005
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.