Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis.

During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a "staircase" pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.

Physical limits on galvanotaxis.

Eukaryotic cells can polarize and migrate in response to electric fields via "galvanotaxis," which aids wound healing. Experimental evidence suggests cells sense electric fields via molecules on the cell's surface redistributing via electrophoresis and electroosmosis, though the sensing species has not yet been conclusively identified. We develop a model that links sensor redistribution and galvanotaxis using maximum likelihood estimation. Our model predicts a single universal curve for how galvanotactic directionality depends on field strength. We can collapse measurements of galvanotaxis in keratocytes, neural crest cells, and granulocytes to this curve, suggesting that stochasticity due to the finite number of sensors may limit galvanotactic accuracy. We find cells can achieve experimentally observed directionalities with either a few (∼100) highly polarized sensors or many (∼10^{4}) sensors with an ∼6-10% change in concentration across the cell. We also identify additional signatures of galvanotaxis via sensor redistribution, including the presence of a tradeoff between accuracy and variance in cells being controlled by rapidly switching fields. Our approach shows how the physics of noise at the molecular scale can limit cell-scale galvanotaxis, providing important constraints on sensor properties and allowing for new tests to determine the specific molecules underlying galvanotaxis.