Analytic study of three-dimensional single cell migration with and without proteolytic enzymes.

Cell motility is a fundamental physiological process that regulates cellular fate in healthy and diseased systems. Cells cultured in 3D environments often exhibit biphasic dependence of migration speed with cell adhesion. Much is not understood about this very common behavior. A phenomenological model for 3D single-cell migration that exhibits biphasic behavior and highlights the important role of steric hindrance is developed and studied analytically. Changes in the biphasic behavior in the presence of proteolytic enzymes are investigated. Our methods produce a framework to determine analytic formulae for the mean cell speed, allowing general statements in terms of parameters to be explored, which will be useful when interpreting future experimental results. Our formula for mean cell speed as a function of ligand concentration generalizes and extends previous computational models that have shown good agreement with in vitro experiments.