Transcript Membrane Bioinformatics - uni

Membrane Bioinformatics
SoSe 2009
Helms/Böckmann
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Thermodynamics of Membranes
Membrane-protein-interaction
Why important?
Protein function
Drug transport in liposomes
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O. Mouritsen Life – as a Matter of Fat Springer (2005)
Thermodynamics of Membranes
Lipid membranes have the ability to adopt different phases.
Measurement: Microcalorimetry
-measurement of the excess heat to increase the temperature of the material
from T to T+ΔT
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Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)
Thermodynamics of Membranes
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Th. Mehnert PhD Thesis TU München (2004)
Thermodynamics of
Membranes
Temperature dependent phases:
Lα: fluid phase
P‘β: ripple phase, solid & fluid
(periodic structure)
Lβ: crystalline, chains tilted
Lc: crystalline
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S. Pisch-Heberle PhD Thesis Uni Stuttgart (2000)
Thermodynamics of
Membranes
All-trans / gauge isomerisation:
Different conformations of lipid chains by rotation around the C-C bonds (trans-gauche
isomerisation):
Lowest energy: all-trans conformation (zigzag)
Gauche-isomer: larger enthalpic energy but also larger entropy!
Lipid conformation is temperature dependent!
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Th. Heimburg NBI Copenhagen
Thermodynamics of Membranes
Ripple phase Pβ‘ observed for a DPPC bilayer
in experiments:
Two different domains with different thickness (X-ray)
High degree of tail stretching (FTI, NMR)
Organisation of lipids unknown
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D.Czajkowsky et al. Biochemistry 34 (1995) 12501-12505
Thermodynamics of Membranes
Ripple phase Pβ‘ observed for a DPPC bilayer
in experiments:
AFM picture ripple phase of a DPPC
bilayer in water
(600nm x 600nm)
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O. Mouritsen Life – as a Matter of Fat Springer (2005)
Thermodynamics of Membranes
Ripple phase Pβ‘ observed for a DPPC bilayer
in molecular dynamics simulations:
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A.H. de Vries et al. PNAS 102 (2005) 5392-5396
Thermodynamics of Membranes
Ripple phase Pβ‘ observed for a DPPC bilayer
in molecular dynamics simulations:
Ripple phase consists of
two domains of different
length and orientation,
connected by a kink
First domain: like splayed
gel
Second domain: fully
interdigitated, gel-like lipids
Lipids disordered in the
concave part of the kinks
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A.H. de Vries et al. PNAS 102 (2005) 5392-5396
Transition temperature increases
with increasing chain length
Tm(PE) > Tm(PC)
transition temperature increases with
increasing packing density:
area(PE)<area(PC)
Transition temperature
Thermodynamics of Membranes
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Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)
Thermodynamics of Membranes
Free enthalpy at transition (t) point:
Gt  Ht  Tt St  0

Tt 
Ht
St
For Dialkyl-Phosphatidylethanolamine:
H
 4.5  0.5 kJ / M
nCH 2
Transition temperature
Transition temperature increases with
increasing chain length:
S
 12  2 J / K  M
nCH 2
PE/PC lipids show similar increments for ΔHt and ΔSt:
Pβ‘ → Lα mainly determined by cohesion of the hydrocarbon chains!
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Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)
Thermodynamics of Membranes
Variation of chain melting temperatures
of 18:1 lipid bilayers with position of
double bond within the chain:
Largest decrease in melting
temperature observed for double
bond in the center of the chains
Transition temperature
Influence of Carbon Saturation on
Phase Transition:
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Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)
Thermodynamics of Membranes
Phase transitions:
occur at defined temperatures
Depend on:
Chain length
Degree of saturation
Lipid charge
Headgroup size (transition temperature increases with
increasing packing density)
Transition temperatures depend on:
Cholesterol content
Presence of proteins
Presence of anesthetics (chloroform, alcohol, ..)
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Thermodynamics of Membranes
Some general considerations
(1) Probability of state i with energy Ei:
e Ei / kT
pi 
E / kT
e k
k
(2) Entropy:
S  k  pi lnpi   const.
i
sum over all states i (also degenerated states)
(3) Partition function:
Z   eEi / kT
i
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Thermodynamics of Membranes
Some general considerations
(4) Density of states Ω(E):
Energy distribution:
E  
1 E
e E 
Zc
canonical partition funcion
e  E
Average energy:
E 
E   dEEE
E
Large number of particles N:
N:
E
E  max E
d
E 
0
 E   E 
0
dE
E 
E  d


ln E 
E  dE
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Thermodynamics of Membranes
Some general considerations
1

p
dE  dN  dV
T
T
T
1

 S 


k


k
ln E, V,N
 
E
 E N,V T
dS 
Duhem-Gibbs relation:
 S  SE, V,N  k ln E, V,N  const.
Thus the entropy is proportional to ln(density of states)!
Re-write the partition function:
Z   eEi / kT   Ek  eEk / kT
i

k
k
E TS k
 k
e kT

F
 k
e kT
sum over states with different energies
k
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Thermodynamics of Membranes
: rotation by 120o: change from trans to
gauche conformation
E(Ф)
Lipid states:
Ф
Ф
-120o
gauche–
+120o
gauche+
0o
trans
Probability of excited state 1 (gauche) and ground state 0 (trans):
1eH1 / kT
K
p1 

0eH0 / kT  1eH1 / kT 1  K
p0 
Simplified lipid
carbon chain
With
1
1 K


K  1 eH / kT  e
0
HTS
kT
e

G
kT
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Thermodynamics of Membranes
Ground state = all-trans (all angles Ф=0):
So  k  pk lnpk  k ln 1  0 ( some constant)
k
General case (probability γ of finding CH2–CH2 bond in excited gauche state)
 
SCH2  k  pk lnpk    k  2   ln   k 1   ln1   
k
2 2
Equal distribution between all states at high temperature (T→∞):
dSCH 2
dCH2

2
3
 k ln 3  9.134kJ /m ol/K
Entropy of unordered state proportional to the chain length n (two chains per phospholipid):
dSCH2
S  So  2n  2
dCH2

Enthalpy of unordered/excited state:
H  Ho  2n  2
dHCH2
dCH2
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Thermodynamics of Membranes
Typical values: phosphatidylcholines (2 chains):
kJ
m ol
J
S0  134.38
m ol K
SCH 2
J
 9.05
CH 2
m ol K
HCH 2
kJ
 3.20
CH 2
m ol
H 0  51.78
Assumption: only two possible states, all-trans and all-gauche
The melting temperature is then
given by:
P1Tm 
H
 K Tm   1  H  TmS  0  Tm 
P0 Tm 
S
The transition temperature of lipids is in the physiological range of -20oC to +60oK!
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Thermodynamics of Membranes
Cooperativity:
The equilibrium constant K is temperature dependent:
K  e  G / kT  ln K T   
d ln K T 
1

H
2
dT
RT
d ln K T 
 RT 2
 H
dT
H S

RT R

Average enthalpy change/mol:
: van‘t Hoff law
 H  H 
K
1 K
probability of excited state
Heat capacity:
eG / RT
 H 
cp  
 
 dT p 1  eG / RT

H2
2
RT 2

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Thermodynamics of Membranes
Cooperativity:
Heat capacity:
eG / RT
 H 
cp  
 
 dT p 1  eG / RT

With
H  35kJ / mol
H2
2
RT 2

: width of transition curve cp(T) approx. 60oC!
But: Experiment: width of transition curve cp(T) <1oC!
→Many lipids melt in a cooperative transition!
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