Bridging Time and Length Scales in MaterialsScience 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 leakageV.A. Frolov et al. 2003

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

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 F1(R,) = FIMI(R) +FS

IMI and its free eneregy

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)

Free energy landscape in and R

Free energy barriers in new and old mechanism

new old

barriers decrease with decreasing f and increasing

Difference in free energy barriers of new and old mechanism

Prediction for at barrier: leakageCircumference =2R

Resolving the enigma of fusion1. Membranes are stable because line tension of holes is large

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

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

Dependence of free energy on line tension

Energy of hole 2R-R2

Energy of critical hole

Boltzmann factorPH= (AH /s2) exp(-

kT)

Boltzmann factor PH=(AH/s2) exp(- kT)

EXPONENTIAL DEPENDENCE ON SQUARE OF

LINE TENSION:

1. ENSURES STABILITY OF NORMAL MEMBRANES

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

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

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

P~ exp(-kT)

PH~ 6x10-3

dr=H/2, Nsas/AH~0.3 Pdressed/Pbare~ 14

EXAMPLE: IN SIMULATION

In Biological Membranes, Effect is GreaterH~2.6x10-6 erg/cm

20 erg/cm2

PH~1.7 x 10-11(AH/s2) very stable

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

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

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