1 Membrane Bioinformatics SoSe 2009 Helms/Böckmann

2 Thermodynamics of Membranes Why important? Membrane-protein-interaction Drug transport in liposomes Protein function O. Mouritsen Life – as a Matter of Fat Springer (2005)

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

4 Thermodynamics of Membranes Th. Mehnert PhD Thesis TU München (2004)

5 Thermodynamics of Membranes Temperature dependent phases: L α : fluid phase P‘ β : ripple phase, solid & fluid (periodic structure) L β : crystalline, chains tilted L c : crystalline S. Pisch-Heberle PhD Thesis Uni Stuttgart (2000)

6 Thermodynamics of Membranes 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!

7 Thermodynamics of Membranes Ripple phase P β‘ observed for a DPPC bilayer in experiments: D.Czajkowsky et al. Biochemistry 34 (1995)  Two different domains with different thickness (X-ray)  High degree of tail stretching (FTI, NMR)  Organisation of lipids unknown

8 Thermodynamics of Membranes Ripple phase P β‘ 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)

9 A.H. de Vries et al. PNAS 102 (2005) Thermodynamics of Membranes Ripple phase P β‘ observed for a DPPC bilayer in molecular dynamics simulations:

10 A.H. de Vries et al. PNAS 102 (2005) Thermodynamics of Membranes Ripple phase P β‘ 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

11 Thermodynamics of Membranes  Transition temperature increases with increasing chain length  T m (PE) > T m (PC)  transition temperature increases with increasing packing density: area(PE)<area(PC) Transition temperature Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)

12 Thermodynamics of Membranes Transition temperature increases with increasing chain length: Transition temperature For Dialkyl-Phosphatidylethanolamine: Free enthalpy at transition (t) point: PE/PC lipids show similar increments for ΔH t and ΔS t : P β‘ → L α mainly determined by cohesion of the hydrocarbon chains! Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)

13 Thermodynamics of Membranes Transition temperature 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 Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)

14 Thermodynamics of Membranes  occur at defined temperatures Depend on:  Chain length  Degree of saturation  Lipid charge  Headgroup size (transition temperature increases with increasing packing density) Phase transitions: Transition temperatures depend on:  Cholesterol content  Presence of proteins  Presence of anesthetics (chloroform, alcohol,..)

15 Thermodynamics of Membranes Some general considerations (1) Probability of state i with energy E i : (2) Entropy: sum over all states i (also degenerated states) (3) Partition function:

16 Thermodynamics of Membranes Some general considerations (4) Density of states Ω(E): Energy distribution: canonical partition funcion Average energy: Large number of particles N:

17 Thermodynamics of Membranes Some general considerations Duhem-Gibbs relation:  Thus the entropy is proportional to ln(density of states)! Re-write the partition function: sum over states with different energies

18 Thermodynamics of Membranes Lipid states: Simplified lipid carbon chain : rotation by 120 o : change from trans to gauche conformation -120 o gauche – +120 o gauche + 0 o trans E(Ф) Ф Ф Probability of excited state 1 (gauche) and ground state 0 (trans): With

19 Thermodynamics of Membranes Ground state = all-trans (all angles Ф=0): General case (probability γ of finding CH 2 –CH 2 bond in excited gauche state) Equal distribution between all states at high temperature (T→∞): Entropy of unordered state proportional to the chain length n (two chains per phospholipid): Enthalpy of unordered/excited state:

20 Thermodynamics of Membranes Typical values: phosphatidylcholines (2 chains): Assumption: only two possible states, all-trans and all-gauche The melting temperature is then given by:  The transition temperature of lipids is in the physiological range of -20 o C to +60 o K!

21 Thermodynamics of Membranes Cooperativity: The equilibrium constant K is temperature dependent: : van‘t Hoff law Average enthalpy change/mol: probability of excited state Heat capacity:

22 Thermodynamics of Membranes Cooperativity: Heat capacity: With : width of transition curve c p (T) approx. 60 o C! But: Experiment: width of transition curve cp(T) <1 o C! →Many lipids melt in a cooperative transition!