The Conundrum of Biological Fusion

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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 FusionA 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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Why is Fusion Difficult to Understand?

• Stability long-lived holes must be difficult to
  form
• Fusion long-lived holes must be easy to form

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The Biologists View of Fusion
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The Physicists 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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Two Consequences
1. Main Barrier in Old Mechanism is Expansion
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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
a
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SCF Calculation (cont)
Reduced line tension of hole favors large
a Membrane tension favors large R
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IMI
Just before F1(R,a) aFIMI(R) FS
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IMI and its free eneregy
g/g00.0
g/g00.4
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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)
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Free energy landscape in a and R
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Free energy barriers in new and old mechanism
new
old
barriers decrease with decreasing f and
increasing g
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Difference in free energy barriers of new and old
mechanism
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Prediction for a at barrier leakageCircumference
2pRa

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Resolving the enigma of fusion

• Membranes are stable because line tension of
  holes is large

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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

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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 2plHR-gpR2 Energy of critical
hole plH2/g Boltzmann factor PH (AH /s2) exp(-
plH2/gkT)
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• Boltzmann factor PH(AH/s2) exp(- plH2/gkT)
• EXPONENTIAL DEPENDENCE ON SQUARE OF
• LINE TENSION
• ENSURES STABILITY OF NORMAL MEMBRANES

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• 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/s239 PH 6x10-3
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• 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

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Reducing the line tension from lH to ldr
alsh(1-a) lH
PH--gtPsh (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
PHltlt1 Therefore rate of hole formation near stalk
Psh/PHgtgt1
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EXAMPLE IN SIMULATION
ldrlH/2, Nsas/AH0.3 Pdressed/Pbare 14

• P exp(-pl2/gkT)
• PH 6x10-3

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In Biological Membranes, Effect is Greater
lH2.6x10-6 erg/cm g 20 erg/cm2 PH1.7 x
10-11(AH/s2) very stable
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In Biological Membranes, Effect is Greater
lH2.6x10-6 erg/cm g 20 erg/cm2 PH1.7 x
10-11(AH/s2) very stable ldr/ lH 0.5,
Nsas/AH0.3 Psh/PH0.3(1/ 1.7 x 10-11)7/16
1x104 four orders of magnitude
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Conclusion The Enigmas Solution

• Because
• fusion is thermally excited and
• excitation energy proportional to l2

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Conclusion The Enigmas Solution

• Because
• fusion is thermally excited and
• excitation energy proportional to l2

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

• Effect of mixture of lipids

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To Do

• Effect of mixture of lipids
• Effect of different composition of leaves

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To Do

• Effect of mixture of lipids
• Effect of different composition of leaves
• Effect of fusion proteins

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Effect of Fusion Proteins?
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To Do

• Effect of mixture of lipids
• Effect of different composition of leaves
• Effect of fusion proteins
• Dynamics

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Thanks to
Misha Kozlov, Joshua Zimmerberg, Vadim Frolov,
Leonid Chernomordik, David Siegel, Barry Lentz,
Siewert Jan Marrink NATIONAL SCIENCE FOUNDATION
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AND