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Bridging Time and Length Scales in MaterialsScience 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 leakageV.A. Frolov et al. 2003
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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
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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 F1(R,) = FIMI(R) +FS
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IMI and its free eneregy
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Just before F1(R,) = FIMI(R) +FS
Just after F2(R,) = FHI(R) +(1-FH(R-)+Fd
F1(R,) = F2(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
new old
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: leakageCircumference =2R
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Resolving the enigma of fusion1. Membranes are stable because line tension of holes is large
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Resolving the enigma of fusion1. 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 2R-R2
Energy of critical hole
Boltzmann factorPH= (AH /s2) exp(-
kT)
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Boltzmann factor PH=(AH/s2) exp(- kT)
EXPONENTIAL DEPENDENCE ON SQUARE OF
LINE TENSION:
1. ENSURES STABILITY OF NORMAL MEMBRANES
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Boltzmann factor PH=(AH/s2) exp(- kT)
EXPONENTIAL DEPENDENCE ON SQUARE OF
LINE TENSION:
1. ENSURES STABILITY OF NORMAL MEMBRANES
Example: In simulation
H2/kT = 8.76, AH/s2=39
PH~ 6x10-3
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Boltzmann factor PH=(AH/s2) 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
PH-->Psh = (Nsas/s2) exp(-dr/kT)
so
Psh/PH = (Nsas/AH) exp(H/kT)(1-
dr/bare)
= (Nsas/AH) (AH/s2 PH)x
x= (1-dr/
bare)
Stability implies PH<<1
Therefore rate of hole formation near stalk
Psh/PH>>1
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P~ exp(-kT)
PH~ 6x10-3
dr=H/2, Nsas/AH~0.3 Pdressed/Pbare~ 14
EXAMPLE: IN SIMULATION
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In Biological Membranes, Effect is GreaterH~2.6x10-6 erg/cm
20 erg/cm2
PH~1.7 x 10-11(AH/s2) very stable
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In Biological Membranes, Effect is GreaterH~2.6x10-6 erg/cm
20 erg/cm2
PH~1.7 x 10-11(AH/s2) very stable
dr/ H= 0.5, Nsas/AH~0.3
Psh/PH=0.3(1/ 1.7 x 10-11)7/16
~1x104
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