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Dynamics of the Goodwin-Trainor mechanochemical model

Dynamics of the Goodwin-Trainor mechanochemical model The dynamics of calcium in the cortical cytoplasm of plant cells has been modeled by Goodwin & Trainor (1985) using a mechanochemical field theory based on the interaction between calcium ions and the cytoskeleton. The resulting mathematical model is a system of two non-linear partial differential equations which rule the evolution of the free calcium concentration and of the cytogel strain field in the cytoplasm. According to the values of parameters such as: calcium diffusion coefficient, strength of the calcium-strain coupling, gel elasticity or total calcium concentration, this system may be stable or unstable around an homogeneous equilibrium state. With the aid of numerical simulations, various kinds of solutions have been observed. When inertial forces ar neglected or for low values of the gel density, most of the solutions are asymptotically stable and are reached after a more or less complex transient. But for higher values of the volumetric density more complex solutions may exist, periodic in time and space or eventually chaotic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Dynamics of the Goodwin-Trainor mechanochemical model

Brière, Christian
Acta Biotheoretica , Volume 42 (3) – Nov 13, 2004
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References (7)

Publisher
Springer Journals
Copyright
Copyright
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/BF00709486
Publisher site
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Abstract

The dynamics of calcium in the cortical cytoplasm of plant cells has been modeled by Goodwin & Trainor (1985) using a mechanochemical field theory based on the interaction between calcium ions and the cytoskeleton. The resulting mathematical model is a system of two non-linear partial differential equations which rule the evolution of the free calcium concentration and of the cytogel strain field in the cytoplasm. According to the values of parameters such as: calcium diffusion coefficient, strength of the calcium-strain coupling, gel elasticity or total calcium concentration, this system may be stable or unstable around an homogeneous equilibrium state. With the aid of numerical simulations, various kinds of solutions have been observed. When inertial forces ar neglected or for low values of the gel density, most of the solutions are asymptotically stable and are reached after a more or less complex transient. But for higher values of the volumetric density more complex solutions may exist, periodic in time and space or eventually chaotic.

Journal

Acta Biotheoretica – Springer Journals

Published: Nov 13, 2004

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