Navigation driven by bidirectional information transmission between sensing and actuation

Abstract

A wide variety of biological functions are driven by feedback between sensing and actuation. A paradigmatic example is cellular navigation. During navigation, the sensory system maps the environmental input signal onto a sensory output, which then drives an actuation response, thereby changing the future sensory input. How the accuracy of this bidirectional information transmission controls navigation is not currently understood. Here, we study how information controls navigation by analytically solving two generic models that describe two major classes of biological navigators: spatial- and temporal-sensing cells. We find that, in the linear-response regime of shallow gradients, navigation performance is fully determined by bidirectional information transmission alone, as quantified by feedforward and feedback transfer entropies. Elementary system parameters affect navigation performance only through their effect on these information flows. We call these relations Behavioral Equations of State (BESTs): equalities that map information to function in a system-independent way. BESTs predict an experimentally testable data collapse for the performance of navigators with different sensing and actuation parameters. We test the validity of our theory by performing stochastic simulations of chemotaxis of the bacterium Escherichia coli, computing the relevant transfer entropies exactly with the TE-PWS algorithm. The observed performance obeys the BEST without any fitting or scaling parameters. Thus, our theory identifies bidirectional information transmission between sensing and actuation as an organizing principle for navigation.