Current models used in our laboratory to assess the migration and traction of a population of cells within biopolymer gels are extended to investigate temporal changes in these parameters during compaction of mechanically constrained gels. The random cell migration coefficient, μ(t) is calculated using a windowing technique by regressing the mean-squared displacement of cells tracked at high magnification in three dimensions with a generalized least squares algorithm for a subset of experimental time intervals, and then shifting the window interval-by-interval until all time points are analyzed. The cell traction parameter, τ0(t), is determined by optimizing the solution of our anisotropic biphasic theory to tissue equivalent compaction. The windowing technique captured simulated sinusoidal and step changes in cell migration superposed on a persistent random walk in simulated cell movement. The optimization software captured simulated time dependence of compaction on cell spreading. Employment of these techniques on experimental data using rat dermal fibroblasts (RDFs) and human foreskin fibroblasts (HFFs) demonstrated that these cells exhibit different migration-traction relationships. Rat dermal fibroblast migration was negatively correlated to traction, suggesting migration was not the driving force for compaction with these cells, whereas human foreskin fibroblast migration was positively correlated to traction.
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