Abstract
A simple model for mass transport within a growing fungal
filament is proposed. Inspired by the role in fungal tip
growth of microtubule-transported vesicles, we embody the dynamics of mass
along a quasi-one-dimensional hypha with mutually excluding particles hopping on a growing one-dimensional
lattice. The model is a generalisation of the asymmetric exclusion process (ASEP) to a dynamically extending
lattice.
We discuss mean-field and improved mean-field equations and present a phase diagram of the model's steady state
behaviour
which generalises that of the ASEP.
In particular we identify a region in which a shock in the density
travels forward more slowly than the tip of the lattice and thus moves away from both boundaries.
We compare our results to experimental data in the context of
filamentous fungus, Neurospora crassa, and discuss possible mechniasms for
Spitzenkorper formation.
Reference
K. E. P. Sugden, M. R. Evans, W. C. K. Poon and N. D. Read
Phys. Rev. E vol. 75, 031909 (2007)
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