Physical Limits on Galvanotaxis

Eukaryotic cells of many types can polarize and migrate in response to electric fields via “galvano-

taxis”; this ability helps skin cells heal wounds. Recent experimental evidence suggests galvanotaxis

occurs because membrane proteins redistribute via electrophoresis, though the sensing species has

not yet been conclusively identified. We use a physical model to show that stochasticity due to

the finite number of sensing proteins limits the accuracy of galvanotaxis via electrophoresis. Using

maximum likelihood estimation, we show how cells can best interpret this noisy signal, and how

their accuracy should depend on the cell size and electric field strength. Our model can be fit well

to data measuring galvanotaxis of keratocytes, neural crest cells, and granulocytes. Our results

show that eukaryotic cells can likely achieve experimentally observed directionalities with either a

relatively small number (around 100) of highly-polarized proteins, or a large number (∼ 10000) of

proteins with a relatively small change in concentration across the cell (∼ 7% change from cathode

to anode). This may explain why identifying the sensor species has been difficult, as candidates

need not be strongly polarized even in large electric fields. A second prediction of the model is that

the accuracy of cells in predicting the electric field direction only weakly depends on their size.