Protein diffusion controls how single cells respond to electric fields

Cells sense and respond to electric fields, using these fields as a guidance cue in wound healing and development. This sensing is done by redistribution of charged membrane proteins on the cell's surface ("sensors") via electrophoresis and electroosmotic flow. If membrane proteins have to physically rearrange on the cell's surface, how quickly can a cell respond to an applied signal? What limits the cell's ability to respond? Are galvanotaxing cells, like chemotaxing cells, limited by stochasticity from the finite number of molecules? Here, we develop a model for the response dynamics of galvanotaxing cells and show that, for weak enough field strengths, two relevant timescales emerge: the time for the cell's sensors to rearrange, which depends on their diffusion across the cell, and the time for the cell's orientation to respond to an applied field, which may be very different. We fit this model to experimental measurements on the recently-identified sensor galvanin (TMEM154) in neutrophil-like HL-60 cells, finding that given the dynamics of a cell responding to an applied field, we can predict the dynamics of the cell after the field is turned off. This fit constrains the noise of the galvanotaxis process, demonstrating that HL-60 is not limited by the stochasticity of finite sensor number. Our model also allows us to explain the effect of media viscosity on cell dynamics, and predict how cells respond to pulsed DC fields. These results place constraints on the ability to guide cells with pulsed fields, predicting that a field on half of the time is no better than a field that is always on with half the magnitude.