Transcript maws1 5990

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
Why is Fusion Difficult to
Understand?
1. Stability: long-lived holes must be difficult to
form
2. Fusion: long-lived holes must be easy to form
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
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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
Two Consequences
1. Main Barrier in Old Mechanism is Expansion
2. Regime of Successful Fusion is Limited
SCF Calculation of New Mechanism
Line tension of extended stalk favors small R and a
SCF Calculation (cont)
Reduced line tension of hole favors large a
Membrane tension favors large R
IMI
Just before
F1(R,a) = aFIMI(R) +FS
IMI and its free eneregy
g/g0=0.0
g/g0=0.4
IMI
Just before
Just after
F1(R,a) = aFIMI(R) +FS
F2(R,a) = aFHI(R) +(1-a)FH(R-d)+Fd
F1(R,a) = F2(R,a) defines a ridge a(R)
Free energy landscape in a and R
Free energy barriers in new and old mechanism
new
old
barriers decrease with decreasing f and increasing g
Difference in free energy barriers
of new and old mechanism
Prediction for a at barrier: leakage
Circumference =2pRa
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 2plHR-gpR2
Energy of critical hole plH2/g
Boltzmann factor
PH= (AH /s2) exp(- plH2/gkT)
Boltzmann factor PH=(AH/s2) exp(- plH2/gkT)
EXPONENTIAL DEPENDENCE ON SQUARE OF
LINE TENSION:
1. ENSURES STABILITY OF NORMAL
MEMBRANES
Boltzmann factor PH=(AH/s2) exp(- plH2/gkT)
EXPONENTIAL DEPENDENCE ON SQUARE OF
LINE TENSION:
1. ENSURES STABILITY OF NORMAL
MEMBRANES
Example: In simulation
p lH2/gkT = 8.76, AH/s2=39
PH~ 6x10-3
Boltzmann factor PH=(AH/s2) exp(- plH2/gkT)
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
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
EXAMPLE: IN SIMULATION
P~ exp(-pl2/gkT) l =l /2, N a /A ~0.3
dr
H
s s
H
Pdressed/Pbare~ 14
PH~ 6x10-3
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
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
Conclusion: The Enigma’s Solution
Because
1. fusion is thermally excited and
2. excitation energy proportional to l2
Conclusion: The Enigma’s Solution
Because
1. fusion is thermally excited and
2. excitation energy proportional to l2
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
Misha Kozlov, Joshua Zimmerberg,
Vadim Frolov, Leonid Chernomordik, David
Siegel, Barry Lentz, Siewert Jan Marrink
NATIONAL SCIENCE FOUNDATION
AND