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) Marcus Mueller (Institute fur Theoretische Physik, Gottingen)

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

Trafficking

Exocytosis

Viral Entry

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?

The Biologist’s View of Fusion

The Physicist’s View Kozlov and Markin 1983

SIMULATING FUSION

Stalk Formation

Stalk Formation and Expansion

Stalks increase rate of hole formation

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

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

The intermediate in this second scenario

Hole Formation and Fusion are Correlated

Consequence for Experiment: Leakage

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

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

Results for the Standard Mechanism

Formation of fusion pore

1. Main Barrier in Old Mechanism is Expansion Two Consequences

2. Regime of Successful Fusion is Limited

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

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

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

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

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)

Free energy landscape in  and R

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

Difference in free energy barriers of new and old mechanism

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

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

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

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

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)

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

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

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

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

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

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

In Biological Membranes, Effect is Greater  H ~2.6x10 -6 erg/cm  20 erg/cm 2 P H ~1.7 x (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 ) 7/16 ~1x10 4 four orders of magnitude 

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

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

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

To Do 1.Effect of mixture of lipids

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

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

Effect of Fusion Proteins?

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

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

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