The physical principles

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The physical principles of viral budding
Markus Deserno, MPI-P
Scientific Symposium on the occasion of the 20th
anniversary of the Max-Planck-Institut für
Polymerforschung Polymer Research problems,
progress, pathways MPI-P, June 10-11, 2004
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The phospholipid bilayer
Phospholipid bilayer membranes in all living
cells accomplish two diametrical tasks
Partitioning
Transport
Transport mechanisms span many orders of
magnitude in particle size, and are actively
controlled by the cell.
However
Sometimes generic mechanisms alone do the job!
Example Budding of animal viruses
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A typical viral life cycle
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Viral budding
Viral budding is the process by which most animal
viruses leave their host cell
Review H. Garoff, R. Hewson, D.-J. E. Opstelten,
Microbiol. Mol. Biol. Rev. 62, 1171 (1998)
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Aim for the following
Study the physical principles governing this event
Elasticity of the membrane
Entropy of spike proteins
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Aim for the following
Study the physical principles governing this event
Elasticity of the membrane
Entropy of spike proteins
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Idealized wrapping scenario
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Shape of the free membrane
Energy of membrane is functional of its shape
? Solve corresponding Euler-Lagrange-equations .
. .
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Shapes in equilibrium
Movie by Timo Schürg
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Structural phase diagram
Envelopment transition is discontinuous !
M. Deserno and T. Bickel, Europhys. Lett. 62, 767
(2003)
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Hysteresis
M. Deserno, Phys. Rev. E 69, 031903 (2004)
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Scaled envelopment boundary
Remember
For small tension we had the asymptotic form
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Scaled envelopment boundary
Remember
For small tension we had the asymptotic form
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Scaled envelopment boundary
Bending and tension are often inseparable !
M. Deserno, Phys. Rev. E 69, 031903 (2004)
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Contact with biology
It is meaningful to talk about moving within the
structural phase diagram
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Contact with biology
It is meaningful to talk about moving within the
structural phase diagram
Adhesion energy

• Chemistry
• Density of adhesion proteins

Tension

• Cell can change membrane tension
• Switch between membranes

But where does viral wrapping happen in biology?
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Contact with biology
Wrapping and unwrapping is basically spontaneous
? System should be close to envelopment boundary
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Contact with biology
Problem
Too large to be overcome by thermal fluctuations!
Speculation Will multi-componentness help?
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Aim for the following
Study the physical principles governing this event
Elasticity of the membrane
Entropy of spike proteins
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Spike mediated budding
Problem involves Langmuir adsorption, phase
separation of spikes and buds, competition
between buds, maximum virus production rate. . .
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Simplest possible theory
Lattice-gas of spikes, dissolved in membrane,
able to bind to capsids, additional curvature
energy.
adhesion energy
bending energy
line tension
entropy of buds
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Coexistence lines
Equating chemical potential and pressure of
spikes ? equilibrium densities in bud- and planar
phase.
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Coexistence lines
Spike density for a rather floppy membrane
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Coexistence lines
Moral Real viruses in nature are completely
covered with spikes, because the cell membrane is
stiff compared to thermal energy!
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Acknowledgements

• Thomas Bickel (UCLA, now Univ. Bordeaux)
• Bill Gelbart (UCLA)
• Shelly Tzlil (HU, Jerusalem)
• Avinoam Ben-Shaul (HU, Jerusalem)
• Theory group at MPI-P
• German Science Foundation
• (Emmy Noether research group)

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Helfrich in nuce
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Helfrich in nuce
At every point a surface has two extremal radii
of curva-ture. Their inverses are called
principal curvatures, and they are eigenvalues of
the curvature tensor (second fundamental form).