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Bridging Time and Length Scales in Materials Science and Bio-Physics

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. The Enigma of Biological Fusion A comparison of two routes. With Kirill Katsov (MRL, UC Santa Barbara)

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Bridging Time and Length Scales in Materials Science and Bio-Physics

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

  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

  16. The intermediate in this second scenario

  17. Hole Formation and Fusion are Correlated

  18. Consequence for Experiment: Leakage

  19. An experiment to measure leakageV.A. Frolov et al. 2003

  20. Analytic Approach to FusionSelf-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

  21. Results for the Standard Mechanism

  22. Formationof fusion pore

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

  24. 2. Regime of Successful Fusion is Limited

  25. SCF Calculation of New Mechanism Line tension of extended stalk favors small R and a

  26. SCF Calculation (cont) Reduced line tension of hole favors large a Membrane tension favors large R

  27. IMI Just before F1(R,a) = aFIMI(R) +FS

  28. IMI and its free eneregy g/g0=0.0 g/g0=0.4

  29. IMI Just before F1(R,a) = aFIMI(R) +FS Just after F2(R,a) = aFHI(R) +(1-a)FH(R-d)+Fd F1(R,a) = F2(R,a) defines a ridge a(R)

  30. Free energy landscape in a and R

  31. Free energy barriers in new and old mechanism new old barriers decrease with decreasing f and increasing g

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

  33. Prediction for a at barrier: leakageCircumference =2pRa

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

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

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

  37. Dependence of free energy on line tension Energy of hole 2plHR-gpR2 Energy of critical hole plH2/g Boltzmann factor PH= (AH /s2)exp(- plH2/gkT)

  38. Boltzmann factor PH=(AH/s2) exp(- plH2/gkT) EXPONENTIAL DEPENDENCE ON SQUARE OF LINE TENSION: ENSURES STABILITY OF NORMAL MEMBRANES

  39. Boltzmann factor PH=(AH/s2) exp(- plH2/gkT) EXPONENTIAL DEPENDENCE ON SQUARE OF LINE TENSION: ENSURES STABILITY OF NORMAL MEMBRANES Example: In simulation p lH2/gkT = 8.76, AH/s2=39 PH~ 6x10-3

  40. Boltzmann factor PH=(AH/s2) exp(- plH2/gkT) EXPONENTIAL DEPENDENCE ON SQUARE OF LINE TENSION: ENSURES STABILITY OF NORMAL MEMBRANES ENABLES FUSION TO OCCUR BY REDUCING THAT LINE TENSION

  41. Reducing the line tension from lH to ldr = alsh+(1-a) lH PH-->Psh = (Nsas/s2) exp(-pl2dr/gkT) so Psh/PH = (Nsas/AH) exp(pl2H/gkT)(1-l2dr/l2bare) = (Nsas/AH) (AH/s2 PH)x x= (1-l2dr/l2bare) Stability implies PH<<1 Therefore rate of hole formation near stalk Psh/PH>>1

  42. EXAMPLE: IN SIMULATION ldr=lH/2, Nsas/AH~0.3 Pdressed/Pbare~ 14 P~ exp(-pl2/gkT) PH~ 6x10-3

  43. In Biological Membranes, Effect is Greater lH~2.6x10-6 erg/cm g ~ 20 erg/cm2 PH~1.7 x 10-11(AH/s2) very stable

  44. In Biological Membranes, Effect is Greater lH~2.6x10-6 erg/cm g ~ 20 erg/cm2 PH~1.7 x 10-11(AH/s2) very stable ldr/ lH= 0.5, Nsas/AH~0.3 Psh/PH=0.3(1/ 1.7 x 10-11)7/16 ~1x104 four orders of magnitude

  45. Conclusion: The Enigma’s Solution Because fusion is thermally excited and excitation energy proportional to l2

  46. Conclusion: The Enigma’s Solution Because fusion is thermally excited and excitation energy proportional to l2 Membranes can both be stable and undergo fusion

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

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