Membrane Bioinformatics SoSe 2009 Helms/Böckmann

1. Membrane BioinformaticsSoSe 2009Helms/Böckmann

2. Membrane-protein-interaction Protein function Drug transport in liposomes Thermodynamics of Membranes Why important? 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: 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)

6. 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! Th. Heimburg NBI Copenhagen

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

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

9. Thermodynamics of Membranes Ripple phase Pβ‘ observed for a DPPC bilayer in molecular dynamics simulations: A.H. de Vries et al. PNAS 102 (2005) 5392-5396

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

11. Thermodynamics of Membranes • Transition temperature increases with increasing chain length • Tm(PE) > Tm(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: Free enthalpy at transition (t) point: Transition temperature For Dialkyl-Phosphatidylethanolamine: PE/PC lipids show similar increments for ΔHt and ΔSt: Pβ‘ → Lαmainly determined by cohesion of the hydrocarbon chains! Lipowski & Sackmann Structure and Dynamics of Membranes Elsevier (1995)

13. Thermodynamics of Membranes Influence of Carbon Saturation on Phase Transition: Variation of chain melting temperatures of 18:1 lipid bilayers with position of double bond within the chain: Transition temperature 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 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, ..)

15. Thermodynamics of Membranes Some general considerations (1) Probability of state i with energy Ei: (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. Ф E(Ф) Ф -120o gauche– +120o gauche+ 0o trans Thermodynamics of Membranes : rotation by 120o: change from trans to gauche conformation Lipid states: Probability of excited state 1 (gauche) and ground state 0 (trans): Simplified lipid carbon chain With

19. Thermodynamics of Membranes Ground state = all-trans (all angles Ф=0): General case (probability γ of finding CH2–CH2 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 -20oC to +60oK!

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: : width of transition curve cp(T) approx. 60oC! With But: Experiment: width of transition curve cp(T) <1oC! →Many lipids melt in a cooperative transition!