Latent information about optimal behaviour forces evolution of noisy signal transduction

Abstract

An open problem in biology is to understand when particular adaptation strategies of microorganisms are selected during evolution. They range from random, bet-hedging strategies to deterministic, responsive strategies, relying on signalling circuits. We present an evolutionary model that integrates basic statistical physics of molecular circuits with fitness maximisation and information theory. This model provides an explanation for a puzzling observation on responsive strategies: the accuracy with which signalling networks track external signals seems remarkably low. Single cells often distinguish only between 2 to 4 concentration ranges, corresponding to 1 or 2 bits of mutual information between signal and response. Why did evolution lead to such low-fidelity signalling systems? Our theory offers an explanation by taking a novel perspective. It considers the fitness benefit of all signals, including those that are not sensed. We introduce a new concept, latent information, which captures the mutual information between all non-sensed signals and the optimal response. The theory predicts that it is often evolutionarily optimal to transduce sensed signals noisily when latent information is present. It indicates that fitness can indeed be maximal when the mutual information extracted from sensed signals is not maximal, but rather has a low value of about 1 or 2 bits. Cells likely do not sense all signals because of the fitness cost of expressing idle signalling systems that consume limited biosynthetic resources. Our theory illustrates that as the total available information about the optimal behaviour decreases, the cell should trust the available information less, and gamble more. Significance StatementSurprisingly, microorganisms appear to sense only very few environmental signals (such as nutrients and stresses) compared to the number of conditions they can encounter. Even worse, the signals they do sense are transduced at low fidelity. We study the accuracy of sensing in the situation where multiple signals determine the optimal response, but only few signals are actually sensed. We show that it is in fact to be expected that sensing in the presence of latent information should be imprecise, and that signalling circuits should underperform.