STABLE LENGTH DISTRIBUTIONS IN COLOCALIZED POLYMERIZING AND DEPOLYMERIZING PROTEIN FILAMENTS

A model for the dynamics of the length distribution in colocalized groups of polar polymer filaments is presented. It considers nucleation, polymerization at plus-ends, and depolymerization at minus-ends and is derived as a continuous macroscopic limit from a discrete description. Its main feature i...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2012-01, Vol.72 (5), p.1428-1448
Main Authors: FREISTÜHLER, HEINRICH, SCHMEISER, CHRISTIAN, SFAKIANAKIS, NIKOLAOS
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary conditions
Boundary value problems
Conservation laws
Depolymerization
Entropy
Mathematical models
Microfilaments
Molecules
Nucleation
Polymerization
Proteins
Uniqueness
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Summary:A model for the dynamics of the length distribution in colocalized groups of polar polymer filaments is presented. It considers nucleation, polymerization at plus-ends, and depolymerization at minus-ends and is derived as a continuous macroscopic limit from a discrete description. Its main feature is a nonlinear coupling due to competition of the depolymerizing ends for the limited supply of a depolymerization agent. The model takes the form of an initial-boundary value problem for a one-dimensional nonlinear hyperbolic conservation law, subject to a nonlinear, nonlocal boundary condition. Besides existence and uniqueness of entropy solutions, convergence to a steady state is proven. Technical difficulties are caused by the fact that the prescribed boundary data are not always assumed by entropy solutions.
ISSN:0036-1399
1095-712X
DOI:10.1137/100815773