Optimality Theory of Stigmergic Collective Information Processing by Chemotactic Cells

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 in which chemotactic cells locate sparsely distributed targets by sharing information of them through active generation and modulation of endogenous chemical cues. While the optimality of sensing target-derived gradients has been studied extensively in the context of single-cell information processing, the optimality of collective information processing that self-organizes endogenous cue gradient towards the targets remains underexplored. In this study, we employ the reinforcement learning (RL) framework to formalize the collective exploration, in which a population adaptively optimize its navigation toward targets through active cue modulation. 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 relationship between self-organized gradient generation and sensing and demonstrates that the optimal cue-generation strategy changes qualitatively depending on whether cells sense gradients linearly or logarithmically. The underlying RL structure is leveraged to compare the derived collective dynamics with single-agent searching dynamics, showing that distributed information processing by the population enables a fraction of agents to reach the target robustly. Our formulation provides a foundation for understanding collective exploration mediated by active modulation and sensing of cues.