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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

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

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

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Trafficking

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Exocytosis

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Viral Entry

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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?

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The Biologist’s View of Fusion

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The Physicist’s View Kozlov and Markin 1983

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SIMULATING FUSION

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Stalk Formation

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Stalk Formation and Expansion

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Stalks increase rate of hole formation

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

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

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The intermediate in this second scenario

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Hole Formation and Fusion are Correlated

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Consequence for Experiment: Leakage

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

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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

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Results for the Standard Mechanism

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Formation of fusion pore

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1. Main Barrier in Old Mechanism is Expansion Two Consequences

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2. Regime of Successful Fusion is Limited

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

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

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Just before F 1 (R, ) = F IMI (R) +F S

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IMI and its free eneregy

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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)

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Free energy landscape in and R

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

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Difference in free energy barriers of new and old mechanism

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Prediction for at barrier: leakage Circumference =2 R

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

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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

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

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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)

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

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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

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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

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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

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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

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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

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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

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

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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

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

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To Do 1.Effect of mixture of lipids

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

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

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Effect of Fusion Proteins?

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

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

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AND

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