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  .
Eukaryotic cells are able to sense chemical gradients in a wide range of environments. We show that, if a cell is exposed to a highly variable environment, it may gain chemotactic accuracy by expressing multiple receptor types with varying affinities for the same signal , as found commonly in chemotaxing cells like Dictyostelium. As environment uncertainty is increased, there is a transition between cells preferring a single receptor type and a mixture of types - hedging their bets against the possibility of an unfavorable environment. We predict the optimal receptor affinities given a particular environment. In chemotaxing , cells may also integrate their measurement over time. Surprisingly, time-integration with multiple receptor types is qualitatively different from gradient sensing by a single type -- cells may extract orders of magnitude more chemotactic information than expected by naive time integration . Our results show when cells should express multiple receptor types to chemotax, and how cells can efficiently interpret the data from these receptors .
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