Trade-offs between cost and information in cellular prediction

Experiments have revealed that E. coli is able to predict changes in its environment, and that this capacity yields a growth benefit. Yet, how accurately it can predict future environmental changes remains unknown. Fundamentally, the ability of any system to predict the future is limited by the information it has collected from the past. This constitutes a universal upper bound on prediction accuracy. Using existing experimental data, we show that E. coli cells are far below this upper bound for signals typically encountered during chemotaxis. To understand this surprising result, we investigate two questions: what is the predictive power of the collected information? And what does the information cost in terms of physical resources like proteins and energy? We find that the most recent information is not only the most predictive information, but also the costliest. To maximize prediction accuracy under a resource constraint, it can therefore be beneficial to collect information that is less predictive but cheaper to obtain. Indeed, this is the strategy E. coli employs, and it maximizes the prediction accuracy in shallow concentration gradients. This shows that the price of information plays an important role for simple bacteria such as E. coli, especially in noisy environments.