Physical limits on galvanotaxis depends on cell morphology and orientation

Galvanotaxis is believed to be driven by the redistribution of transmembrane proteins and other molecules, referred to as "sensors", through electrophoresis and electroosmosis. Here, we update our previous model of the limits of galvanotaxis due to stochasticity of sensor movements to account for cell shape and orientation. Computing the Fisher information, we find that cells in principle possess more information about the electric field direction when their long axis is parallel to the field, but that for weak fields maximum-likelihood estimators of the field direction may actually have lower variability when the cell's long axis is perpendicular to the field. In an alternate possibility, we find that if cells instead estimate the field direction by taking the average of all the sensor locations as its directional cue ("vector sum"), this introduces a bias towards the short axis, an effect not present for isotropic cells. We also explore the possibility that cell elongation arises downstream of sensor redistribution. We argue that if sensors migrate to the cell's rear, the cell will expand perpendicular the field - as is more commonly observed - but if sensors migrate to the front, the cell will elongate parallel to the field.