A cell migration model is developed based on the mechanical and physicochemical properties of the cell and its extracellular environment. The model includes four adjustable parameters; average number of cell receptors, average distance of receptors from the cell mass center, average linear elastic modulus of the cell, and average strength of receptor adhesion to substrate. It is assumed that available levels of nutrient(s), oxygen, and growth factor(s) are sufficient for cell migration but not for proliferation.

A cell's movement is broken into two steps, stretching and retraction. A cell stretches to create new bounded receptors (stored elastic energy). In the next step, the stored elastic energy is minimized by reducing the number of bounded receptors. Changes in the positions of bounded receptors are used to determine cell movement (migration). The speed of this movement, fluctuations in movement length, fluctuations in stored elastic energy, and total migration length are variables that are functions of input and adjustable parameters. These variables are studied for various elastic properties of a cell (constant linear elasticity, static non-linear elasticity, and dynamic non-linear elasticity) and physical and mechanical properties of the substrate (ideal cross-linked network, entangled cross-linked network, entangled cross-linked network with static dangling ends, and entangled cross-linked network with dynamic dangling ends).

Comparison of migration speed and total migration length for different cases and to experimental results indicates a strong correlation between the elastic properties of a cell and number of bounded receptors and therefore migration speed and length.