Membrane Bioinformatics SoSe 2009 Helms/Böckmann

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Membrane Bioinformatics SoSe 2009

Helms/Böckmann

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Thermodynamics of Membranes

Why important?Membrane-protein-interaction

Drug transport in liposomes

Protein function

O. Mouritsen Life – as a Matter of Fat Springer (2005)

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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

Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)

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Th. Mehnert PhD Thesis TU München (2004)

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Temperature dependent phases:

Lα: fluid phase

P‘β: ripple phase, solid & fluid (periodic structure)

Lβ: crystalline, chains tilted

Lc: crystalline

S. Pisch-Heberle PhD Thesis Uni Stuttgart (2000)

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All-trans / gauge isomerisation:

Th. Heimburg NBI Copenhagen

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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Ripple phase Pβ‘ observed for a DPPC bilayer in experiments:

D.Czajkowsky et al. Biochemistry 34 (1995) 12501-12505

Two different domains with different thickness (X-ray)High degree of tail stretching (FTI, NMR)Organisation of lipids unknown

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Ripple phase Pβ‘ observed for a DPPC bilayer in experiments:

O. Mouritsen Life – as a Matter of Fat Springer (2005)

AFM picture ripple phase of a DPPC bilayer in water

(600nm x 600nm)

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A.H. de Vries et al. PNAS 102 (2005) 5392-5396


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


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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Transition temperature increases with increasing chain length

Tm(PE) > Tm(PC)

transition temperature increases with increasing packing density: area(PE)<area(PC)

Tran

sitio

n te

mpe

ratu

re


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Transition temperature increases with increasing chain length:

Tran

sitio

n te

mpe

ratu

re MK/J 212

nS

M/kJ 5.05.4n

H

2

2

CH

CH

t

tt

tttt

SHT

0STHG

For Dialkyl-Phosphatidylethanolamine:

Free enthalpy at transition (t) point:

PE/PC lipids show similar increments for ΔHt and ΔSt:

Pβ‘ → Lα mainly determined by cohesion of the hydrocarbon chains!


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Tran

sitio

n te

mpe

ratu

re

Variation of chain melting temperatures of 18:1 lipid bilayers with position of

double bond within the chain:

Influence of Carbon Saturation on Phase Transition:

Largest decrease in melting temperature observed for double bond in the center of the chains


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occur at defined temperatures

Depend on:

Chain lengthDegree of saturationLipid chargeHeadgroup size (transition temperature increases with increasing packing density)

Phase transitions:

Transition temperatures depend on:

Cholesterol contentPresence of proteinsPresence of anesthetics (chloroform, alcohol, ..)

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Some general considerations

(1) Probability of state i with energy Ei:

k

kT/E

kT/E

k

i

eeip

(2) Entropy: .constplnpkSi

ii

sum over all states i (also degenerated states)

(3) Partition function: i

kT/EieZ

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(4) Density of states Ω(E):

Energy distribution: EeZ1E E

c

canonical partition funcion

E

E E

Ee Average energy:

EEEdE

EmaxE:N

Large number of particles N:

Eln

dEd

EE

0EEEE

dEd0

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Duhem-Gibbs relation:

.constN,V,ElnkN,V,ESS

N,V,ElnE

kkT1

ES

dVTpdN

TdE

T1dS

V,N

Thus the entropy is proportional to ln(density of states)!

Re-write the partition function:

k

kTF

k

kTTSE

kT/E

kk

i

kT/E

kkk

ki

ee

e EeZ

sum over states with different energies

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Lipid states:

Simplified lipid carbon chain

: rotation by 120o: change from trans to gauche conformation

-120o

gauche–+120o

gauche+0o

trans

E(Ф)

Ф

Ф

Probability of excited state 1 (gauche) and ground state 0 (trans):

K11p

K1K

eeep

0

kT/H1

kT/H0

kT/H1

1 10

1

With kTG

kTSTH

kT/H

0

1 eeeK

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Ground state = all-trans (all angles Ф=0):

constant) some( 01lnkplnpkSk

kko

General case (probability γ of finding CH2–CH2 bond in excited gauche state)

1ln1k

2ln

22kplnpkS

kkkCH2

Equal distribution between all states at high temperature (T→∞): 32

€

dΔSCH2dCH2

= k ln3 = 9.134kJ /mol /K

Entropy of unordered state proportional to the chain length n (two chains per phospholipid):

2

CHo dCH

Sd2n2SS 2

Enthalpy of unordered/excited state:

2

CHo dCH

Hd2n2HH 2

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Typical values: phosphatidylcholines (2 chains):

€

H0 = −51.78kJmol

ΔS0 = −134.38J

mol ⋅KδΔSCH2δCH2

= 9.05 Jmol ⋅K

δΔHCH2δCH2

= 3.20 kJmol

Assumption: only two possible states, all-trans and all-gauche

The melting temperature is then given by:

SHT0STH1TK

TPTP

mmmm0

m1

The transition temperature of lipids is in the physiological range of -20oC to +60oK!

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Cooperativity:

The equilibrium constant K is temperature dependent:

HdT

TKlndRT

HRT

1dT

TKlndRS

RTHTKlneK

2

2

kT/G

: van‘t Hoff law

Average enthalpy change/mol:K1

KHH

probability of excited stateHeat capacity:

2

2

2RT/G

RT/G

pp RT

H

e1

edT

Hc

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Cooperativity:

Heat capacity:

2

2

2RT/G

RT/G

pp RT

H

e1

edT

Hc

With mol/kJ35H : width of transition curve cp(T) approx. 60oC!

But: Experiment: width of transition curve cp(T) <1oC!

→Many lipids melt in a cooperative transition!

Membrane Bioinformatics SoSe 2009 Helms/Böckmann

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