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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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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creator FREISTÜHLER, HEINRICH
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description 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.
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subjects Applied mathematics
Boundary conditions
Boundary value problems
Conservation laws
Depolymerization
Entropy
Mathematical models
Microfilaments
Molecules
Nucleation
Polymerization
Proteins
Uniqueness
title STABLE LENGTH DISTRIBUTIONS IN COLOCALIZED POLYMERIZING AND DEPOLYMERIZING PROTEIN FILAMENTS
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