A minimal physical model of adhesion-dependent protrusion explains confined haptotaxis and oscillatory cell migration

Haptotaxis is the directed migration of cells along gradients of substrate adhesion, and is an important guidance mechanism in biology. Recent experiments on fibronectin patterned tracks show that cells typically migrate toward higher adhesion, then oscillate around the adhesion maximum, with substantial variability in speed and cell length. To explain these cellular shape and migration dynamics we present a minimal model for confined haptotaxis, built around one key physical ingredient: local adhesion strength directly enhances the recruitment of protrusive actin polymerization activity at the cell edge. This coupling creates a front rear difference in protrusive activity, biasing the cell towards polarization in the direction of the higher adhesion. Quantitative comparison with experiment shows strong agreement at multiple levels: cell population level directionality statistics and position-dependent changes in cell length and velocity. At the single cell level, the model reproduces the full diversity of experimentally observed trajectories, including haptotactic bias and its dependence on adhesion-gradient strength, initial position, length and speed variations, myosin II inhibition, and migration on inverted adhesion gradients. Variability in experimental trajectories and migration speed is explained by differences in intrinsic actin polymerization activity and stochastic fluctuations, accounting for the full spectrum of observed migration patterns. Together, our results identify adhesion-dependent amplification of protrusive activity as a minimal and sufficient physical mechanism for understanding haptotaxis.