Regensburg 2010 – scientific programme
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BP: Fachverband Biologische Physik
BP 4: Statistical Physics of Biological Systems II (joint BP, DY)
BP 4.7: Talk
Monday, March 22, 2010, 16:00–16:15, H45
A growth model for bacterial flagella — •Maximilian Schmitt, Reinhard Vogel, and Holger Stark — Institut für Theoretische Physik, TU Berlin
Bacterial flagella of e.g. E.coli consist of up to 30000 flagellin molecules
which are arranged in a hollow tube with outer and inner diameters
of 20nm and 3nm, respectively,
and a length of up to 20µ m. When the flagellum grows, flagellin
molecules are transported through the hollow core of the filament and
attached at its tip.
As a model for this growth process, we extend one model system of
non-equilibrium statistical mechanics, the ASEP (Asymmetric Simple
Exclusion Process), to an exclusion process on a growing lattice. In this
one-dimensional model, particles enter the lattice with rate α,
travel forward with jump rate q and backward with rate p. At the tip
particles can transform into a new lattice site with rate γ.
Monte Carlo simulations and mean-field approximations both give the same
phase diagram in (α,γ) phase space
with distinct low density, high density and maximal current phases. In
case of symmetric dynamics (q=p) both low density and high density phase
vanish, which is in agreement with the SSEP (Symmetric Simple Exclusion
Process). Special attention is put on the tip velocity with which the
length L of the flagellum grows. It shows an
unstable fixed point at q=p. For q>p the model is ballistic with
⟨ L2⟩∼ t2, for q=p diffusive with
⟨ L2⟩∼ t, and for q<p sub-diffusive with a tip velocity
slower than single-file diffusion: ⟨ L2⟩∼ t1/6.