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The Mechanics of (Poro-)Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton
Published on: March 10, 2023
A viscous two-phase model for contractile actomyosin bundles.
1Johann Radon Institute for Computational and Applied Mathematics (RICAM), Mathematical Methods in Molecular and Systems Biology-Group, Apostelgasse 23, 1030, Vienna, Austria, dietmar.oelz@oeaw.ac.at.
Journal of Mathematical Biology
|May 15, 2013
Summary
This study introduces a mathematical model for actomyosin bundles, explaining how myosin forces and protein interactions drive F-actin flows and bundle contraction. The model quantifies these forces, revealing how disordered filaments can effectively contract the bundle tips.
Area of Science:
- Biophysics
- Mathematical Biology
- Cellular Mechanics
Background:
- Actomyosin bundles are crucial for cellular processes.
- Understanding their mechanics, especially non-sarcomeric types, is complex.
- F-actin and myosin interactions drive bundle contractility.
Purpose of the Study:
- To introduce a one-dimensional mathematical model for non-sarcomeric actomyosin bundles.
- To relate F-actin flows to protein cross-linking, myosin forces, and external forces.
- To quantitatively describe the contractile forces and anti-parallel F-actin flows.
Main Methods:
- Coarse-graining approach from a microscopic model.
- Modeling chemical bonds as elastic springs and including myosin filament forces.
- Analyzing the asymptotic regime with short filament lengths and lowest order contributions.
Main Results:
- Myosin filaments generate forces partially counteracted by cross-linking protein drag.
- Bundling proteins' viscosity propagates local contractile forces to bundle tips.
- The model explains how disordered actomyosin bundles contract effectively.
Conclusions:
- The mathematical model provides a quantitative description of actomyosin bundle contraction.
- It elucidates the roles of myosin, cross-linking, and bundling proteins in force generation and propagation.
- An asymptotic model yields an explicit solution for the upper bound of contractile force.
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