Trade-offs between cost and information in cellular prediction

TL;DR

This paper investigates the trade-offs in cellular prediction, showing how different network types reach information bounds for predicting environmental signals, but optimal prediction often involves costly information storage, with applications to E. coli chemotaxis.

Contribution

It introduces a theoretical framework for understanding cost-information trade-offs in cellular prediction and demonstrates how specific network architectures optimize predictive information.

Findings

Push-pull networks reach the information bound for Markovian signals.

Derivative networks reach the bound for non-Markovian signals.

E. coli chemotaxis network is optimized for predicting concentration changes.

Abstract

Living cells can leverage correlations in environmental fluctuations to predict 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 intracellular network from which the future input is predicted. Yet, storing information is costly while not all features of the past signal are equally informative on the future input signal. Here, we show, for two classes of input signals, that cellular networks can reach the fundamental bound on the predictive information as set by the information extracted from the past signal: push-pull networks can reach this information bound for Markovian signals, while networks that take a temporal derivative can reach the bound for predicting the future derivative of non-Markovian signals. However, the bits of past information that are most informative about the future signal are also prohibitively costly. As a result, the optimal system that maximizes the predictive information for a given resource cost is, in general, not at the information bound. Applying our theory to the chemotaxis network of Escherichia coli reveals that its adaptive kernel is optimal for predicting future concentration changes over a broad range of background concentrations, and that the system has been tailored to predicting these changes in shallow gradients.