Optimality theory of stigmergic collective information processing by chemotactic cells

Abstract: Collective information processing is fundamental in various biological systems, where the cooperation of multiple cells results in complex functions beyond individual capabilities. A distinctive example is collective exploration where chemotactic cells not only sense the gradient of guiding exogeneous cues originating from targets but also generate and modulate endogenous cues to coordinate their collective behaviors. While the optimality of gradient sensing has been studied extensively in the context of single-cell information processing, the optimality of collective information processing that includes both gradient sensing and gradient generation remains underexplored. In this study, we formulate the collective exploration problem as a reinforcement learning (RL) by a population. Based on RL theory, we derive the optimal exploration dynamics of agents and identify their structural correspondence with the Keller-Segel model, the established phenomenological model of collective cellular dynamics. Our theory identifies an optimal coupling relation between gradient sensing and gradient generation and demonstrates that the optimal way to generate a gradient qualitatively differs depending on whether the gradient sensing is logarithmic or linear. The underlying RL structure is leveraged to compare the derived collective dynamics with single-agent searching dynamics, showing that distributed information processing by population enables a fraction of agents to reach the target robustly. Our formulation provides a foundation for understanding the collective information processing mediated by dynamic sensing and modulation of cues.