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Living cells can leverage correlations in environmental fluctuations topredict the future environment and mount a response ahead of time. To this end,cells need to encode the past signal into the output of the intracellularnetwork from which the future input is predicted. Yet, storing information iscostly while not all features of the past signal are equally informative on thefuture input signal. Here, we show, for two classes of input signals, thatcellular networks can reach the fundamental bound on the predictive informationas set by the information extracted from the past signal: push-pull networkscan reach this information bound for Markovian signals, while networks thattake a temporal derivative can reach the bound for predicting the futurederivative of non-Markovian signals. However, the bits of past information thatare most informative about the future signal are also prohibitively costly. Asa result, the optimal system that maximizes the predictive information for agiven resource cost is, in general, not at the information bound. Applying ourtheory to the chemotaxis network of Escherichia coli reveals that its adaptivekernel is optimal for predicting future concentration changes over a broadrange of background concentrations, and that the system has been tailored topredicting these changes in shallow gradients.

Trade-offs between cost and information in cellular prediction