1. Bridging Time and Length Scales in Materials Science and Bio-Physics Workshop I: Multiscale Modelling in Soft Matter and Bio-Physics September 26-30, 2005

2. The Enigma of Biological Fusion A comparison of two routes With Kirill Katsov (MRL, UC Santa Barbara) Marcus Mueller (Institute fur Theoretische Physik, Gottingen)

3. Why is Fusion Important? Cell Trafficking Excocytosis/Endocytosis Viral Entry

4. Trafficking

5. Exocytosis

6. Viral Entry

7. 1.Stability: long-lived holes must be difficult to form 2.Fusion: long-lived holes must be easy to form Why is Fusion Difficult to Understand?

8. The Biologist’s View of Fusion

9. The Physicist’s View Kozlov and Markin 1983

10. SIMULATING FUSION

11. Stalk Formation

12. Stalk Formation and Expansion

13. Stalks increase rate of hole formation

14. Why does rate of hole formation go up? Presumably, due to reduced line tension

15. Why does rate of hole formation go up? Presumably, due to reduced line tension

18. The intermediate in this second scenario

19. Hole Formation and Fusion are Correlated

20. Consequence for Experiment: Leakage

21. An experiment to measure leakage V.A. Frolov et al. 2003

23. Analytic Approach to Fusion Self-Consistent Field Theory Investigate many possible configurations Calculate free energy barriers of each Change architecture easily Analogous to Hartree Theory Highly Non-Linear Set of Equations

24. Results for the Standard Mechanism

25. Formation of fusion pore

26. 1. Main Barrier in Old Mechanism is Expansion Two Consequences

27. 2. Regime of Successful Fusion is Limited

28. SCF Calculation of New Mechanism Line tension of extended stalk favors small R and 

29. SCF Calculation (cont) Reduced line tension of hole favors large  Membrane tension favors large R

30. Just before F 1 (R,  ) =  F IMI (R) +F S 

31. IMI and its free eneregy      

32. Just before F 1 (R,  ) =  F IMI (R) +F S  Just after F 2 (R,  ) =  F HI (R) +(1-  F H (R-  )+F d F 1 (R,  ) = F 2 (R,  ) defines a ridge  (R)

33. Free energy landscape in  and R

34. Free energy barriers in new and old mechanism newold barriers decrease with decreasing f and increasing 

35. Difference in free energy barriers of new and old mechanism

36. Prediction for  at barrier: leakage Circumference =2  R  

37. Resolving the enigma of fusion 1.Membranes are stable because line tension of holes is large

38. Resolving the enigma of fusion 1.Membranes are stable because line tension of holes is large 2.But if hole forms next to stalk, line tension is reduced

39. Line tension of holes far from, and near to, stalk

40. Dependence of free energy on line tension Energy of hole 2   R-  R 2 Energy of critical hole     Boltzmann factor P H = (A H /s 2 ) exp(-     kT)

41. Boltzmann factor P H =(A H /s 2 ) exp(-     kT) EXPONENTIAL DEPENDENCE ON SQUARE OF LINE TENSION: 1.ENSURES STABILITY OF NORMAL MEMBRANES

42. Boltzmann factor P H =(A H /s 2 ) exp(-     kT) EXPONENTIAL DEPENDENCE ON SQUARE OF LINE TENSION: 1.ENSURES STABILITY OF NORMAL MEMBRANES Example: In simulation  H 2 /  kT = 8.76, A H /s 2 =39 P H ~ 6x10 -3

43. Boltzmann factor P H =(A H /s 2 ) exp(-     kT) EXPONENTIAL DEPENDENCE ON SQUARE OF LINE TENSION: 1.ENSURES STABILITY OF NORMAL MEMBRANES 2.ENABLES FUSION TO OCCUR BY REDUCING THAT LINE TENSION

44. Reducing the line tension from H to dr =  sh +(1-  H P H -->P sh = (N s a s /s 2 ) exp(-   dr /  kT) so P sh /P H = (N s a s /A H ) exp(   H /  kT)(1-  dr /  bare ) = (N s a s /A H ) (A H /s 2 P H ) x x= (1-  dr /  bare ) Stability implies P H <<1 Therefore rate of hole formation near stalk P sh /P H >>1

45. P~ exp(-    kT) P H ~ 6x10 -3  dr = H /2, N s a s /A H ~0.3 P dressed /P bare ~ 14  EXAMPLE: IN SIMULATION

46. In Biological Membranes, Effect is Greater  H ~2.6x10 -6 erg/cm  20 erg/cm 2 P H ~1.7 x 10 -11 (A H /s 2 ) very stable 

47. In Biological Membranes, Effect is Greater  H ~2.6x10 -6 erg/cm  20 erg/cm 2 P H ~1.7 x 10 -11 (A H /s 2 ) very stable dr / H = 0.5, N s a s /A H ~0.3 P sh /P H =0.3(1/ 1.7 x 10 -11 ) 7/16 ~1x10 4 four orders of magnitude 

48. Conclusion: The Enigma’s Solution Because 1.fusion is thermally excited and 2.excitation energy proportional to 

49. Conclusion: The Enigma’s Solution Because 1.fusion is thermally excited and 2.excitation energy proportional to  Membranes can both be stable and undergo fusion

50. Furthermore  Any process which affects the line tension slightly affects the rate of fusion greatly i.e. exquisite control

51. To Do 1.Effect of mixture of lipids

52. To Do 1.Effect of mixture of lipids 2.Effect of different composition of leaves

53. To Do 1.Effect of mixture of lipids 2.Effect of different composition of leaves 3.Effect of fusion proteins

54. Effect of Fusion Proteins?

55. To Do 1.Effect of mixture of lipids 2.Effect of different composition of leaves 3.Effect of fusion proteins 4.Dynamics

56. Thanks to  isha Kozlov, Joshua Zimmerberg, Vadim Frolov, Leonid Chernomordik, David Siegel, Barry Lentz, Siewert Jan Marrink  ATIONAL SCIENCE FOUNDATION

57. AND