A Mathematical Model of Mechanotransduction

This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between intracellular and extracellular displacements drive mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two dimensions. In several cases the equations are solved analytically, illustrating how displacements divide into two parts: monodomain displacements are identical in both spaces and therefore do not contribute to mechanotransduction, whereas bidomain displacements cause mechanotransduction. A new length constant depends on the intracellular and extracellular shear moduli and the integrin spring constant, and bidomain effects often occur within a few length constants of the tissue edge. Numerical methods for solving the model equations are being developed. Precursors to the model and potential applications are discussed. The bidomain model may be applicable to cardiac remodeling, blood vessel regulation, tissue engineering, stem cell differentiation, cancer biology, and development.

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