# Results from a field-theoretic approach to membrane fusion Michael Schick Department of Physics University of Washington.

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Results from a field-theoretic approach to membrane fusion Michael Schick Department of Physics University of Washington

à mon cher maître

Maurice Ravel

Synaptic Vesicles They are small R~15-25 nm cf bilayer thickness t~4nm They dock: nothing happens They are triggered: fuse rapidly Fusion on demand

Synaptic vesicles in C. Elegans J.L. Bessereau: www.biologie.ens.fr

Questions Why does fusion occur and how? What are free energy barriers to fusion? What factors promote fusion?

Theoretical Procedure Consider fusion of vesicles of block copolymer: universality

Theoretical Procedure Consider fusion of vesicles of block copolymer: universality Polymers->Random walk->Diffusion Eq.-> Quantum Mech.

Theoretical Procedure Consider fusion of vesicles of block copolymer: universality Polymers->Random walk->Diffusion Eq.-> Quantum Mech. SCFT of interacting polymers-> Hartree Theory Advantages: microscopic model->architecture calculation of free energies

Bringing bilayers together removes water-> free energy per area increases-> bilayers are under tension WHY DOES FUSION OCCUR?

Bringing bilayers together removes water-> free energy per area increases-> bilayers are under tension Fusion eliminates area -> reduces the free energy Fusion is one possible response to induced tension Lysis (rupture) is another WHY DOES FUSION OCCUR?

HOW DOES FUSION OCCUR? one commonly accepted mechanism

Kozlov and Markin 1983 Profiles obtained by the theory

WHAT ARE THE FREE ENERGY BARRIERS TO FUSION?

Consider the fusion of two bilayers One component only A lamellar former

Kozlov and Markin 1983 Profiles obtained by the theory

One component, f = 0.4 (DOPC),  /  0 = 0.2, equilibrium H, stalk 1 bilayer =4.3 R g

One component, f = 0.4,  /  0 = 0.2, equilibrium H, stalk

One component, f = 0.4,  /  0 = 0.2, equilibrium H, pore

One component, f = 0.4,  /  0 = 0.2, equilibrium H, stalk & pore

In lipids, barrier would be 50 kT !

WHAT FACTORS AFFECT FUSION?

Effect of Tension

Effect of Two Components and Asymmetry in Leaves SMALL HEADS, LARGE TAILS FAVORED HERE IN PROXIMAL LEAF

Effect of Two Components and Asymmetry in Leaves Average concentration of hex-former is 0.35 0.35 in cis 0.40 in cis 0.43 in cis F/k b T f=0.4 (DOPC) and f=0.294 (DOPE)

Effect of Two Components and Asymmetry in Leaves Average concentration of hex-former is 0.35 0.35 in cis 0.40 in cis 0.43 in cis F/k b T Note that stalk becomes metastable. Its formation is now largest barrier

Effect of curvature Fusion of Bilayer and Vesicle: 1 bilayer =4.3 R g 60:40 mixture J Y Lee & M.S. BJ 2008

What should we expect the effect of curvature to be?

As vesicle radius decreases, effective tension increases, which decreases barrier

Fusion of two identical vesicles 60:40 mixture

H = 2.2 R_g, zero tension, 60:40 mixture Control Fusion by Controlling the Interbilayer Spacing

H = 2.2, 2.7 R_g, zero tension

H = 2.2, 2.7, 3.2 R_g, zero tension

H = 2.2, 2.7, 3.2, 3.7 R_g, zero tension

H = 2.2, 2.7, 3.2, 3.7, 4.0 R_g, zero tension

Conclusions Two barriers to fusion

Conclusions Two barriers to fusion Barrier to stalk formation linear in distance ->easy to prevent fusion

Conclusions Two barriers to fusion Barrier to stalk formation linear in distance ->easy to prevent fusion Second barrier reduced by composition and curvature

Conclusions Two barriers to fusion Barrier to stalk formation linear in distance ->easy to prevent fusion Second barrier reduced by composition and curvature Consequently, when brought close, stalk barrier is small, ~13kT, and fusion is quick Fusion on demand!

Acknowledgements Marcus Mueller Kirill Katsov Jae-Youn Lee NSF Grant DMR 0503752

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