Chemotaxis in uncertain environments: hedging bets with multiple receptors

Eukaryotic cells are able to sense chemical gradients over a wide range of different environments. We show that, if a cell is exposed to a widely variable environment, cells may gain additional chemotactic accuracy by expressing multiple types of receptors with varying affinities for the same signal. As the uncertainty of the environment is increased, there is a transition between cells preferring to express a single receptor type and a mixture of types - hedging their bets against the possibility of an unfavorable environment. We use this to predict the optimal receptor dissociation constants given a particular environment. In sensing this signal, cells may also integrate their measurement over time. Surprisingly, time-integration with multiple receptor types is qualitatively different from gradient sensing by a single receptor type - it is possible for cells to extract orders of magnitude more information out of a signal by using a maximum likelihood estimate than naive time integration.