Optimal Distributions of Receptors on Arbitrarily Shaped Cell Surfaces

Efficient absorption of molecules through receptors on cell surfaces is crucial for various biological processes. While ubiquitous patterns of receptor distributions, including polar localization in rod-shaped cells, have been widely observed, the underlying evolutionary advantage of these patterns is unclear. In this Letter, we investigate how the spatial distribution of receptors on the cell surface affects the total flux entering the cell. We develop a numerical method that allows for the calculation of fluxes through all receptors using linear equations. Our calculations show that the flux through each receptor is spatially dependent for uniformly distributed receptors: the fluxes are highest near the poles in rod-shaped cells and near the invagination in defective spherical cells. Surprisingly, we show that the optimal receptor distribution on an arbitrarily shaped cell, which maximizes the total flux, is precisely the charge density distribution on an ideal conductor of the same shape, in agreement with numerical simulations. Our Letter unveils the evolutionary origin of receptor localizations.