Elastic deformation

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Elastic deformation of a fluid membrane upon
colloid binding
Markus Deserno
Max-Planck-Institut für Polymerforschung, Ackerman
nweg 10, 55128 Mainz, Germany
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Motivation Viral budding
Phospholipid bilayers in all cells accomplish two
diametrical tasks partitioning and 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 Viral budding
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Viral budding
Viral budding is the process by which many 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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Outline for what follows
The aim is to theoretically understand the local
elastic deformations of a membrane after it binds
to a spherical colloidal particle.
Basic tool Elasticity theory (Helfrich
Hamiltonian)
. . . but in varying details

• Full nonlinear shape equations (? numerical)
• Small gradient approximation (? analytical)
• Scaling (? analytical guess
• numerical verification)

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Helfrich in nuce
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Helfrich in nuce
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Introduction of the main players
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Variational shape determination
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Variational shape determination
? Solve corresponding Euler-Lagrange-equations .
. .
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and thus you get the 3d shape!
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Wrapping sequence
Reduced tension
, scan detachment angle
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How to get the phase diagram
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How to get the phase diagram
2.738
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How to get the phase diagram
2.738
4
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How to get the phase diagram
2.738
4
6
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How to get the phase diagram
2.738
4
6
6.142
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How to get the phase diagram
2.738
4
6
6.142
7.464
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How to get the phase diagram
2.738
4
6
6.142
7.464
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Structural phase diagram
Envelopment transition is discontinuous !
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Hysteresis
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Rescaled envelopment boundary
Remember
For small tension we had the asymptotic form
for the envelopment boundary. In other words
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Rescaled envelopment boundary
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Enough numerics!
Is there anything analytical we can do?
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? Small gradient expansion
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? Scaling relation for high tension
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Predictions from the scaling ansatz
The scaling ansatz quantifies the way in which
the high tension regime of various observables is
reached
All scaling forms are validated by comparison
with the numerical results. Even better An
asymptotic fit always yields the same value for
the prefactor A !
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Contact with biology
For typical biological systems
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Extension of the model Spikes
Binding mediated by spike proteins
Classical example SFV
Problem involves Langmuir adsorption, phase
separation of spikes and buds, competition
between buds, maximum virus production rate. . .
Work in progress !
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Example spike distribution
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Unwrapping scenario
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That was all for today!
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Acknowledgements

• Thomas Bickel
• Bill Gelbart
• Shelly Tzlil
• Avinoam Ben-Shaul
• German Science Foundation
• (Emmy Noether research group)