Information theory of chemotactic agents using both spatial and temporal gradient-sensing

Biological cells and small organisms navigate in concentration fields of signaling molecules using two fundamental gradient-sensing strategies: spatial comparison of concentrations measured at different positions on their surface, or temporal comparison of concentrations measured at different locations visited along their motion path. It is believed that size and speed dictate which gradient-sensing strategy cells choose, yet this has never been formally proven. Using information theory, we investigate the optimal gradient-sensing mechanism for an ideal chemotactic agent that combines spatial and temporal comparison. We account for physical limits of chemo-sensation: molecule counting noise at physiological concentrations, and motility noise inevitable at the micro-scale. Our simulation data collapses onto an empirical power-law that predicts an optimal weighting of information as function of motility and sensing noise, demonstrating how spatial comparison becomes more beneficial for agents that are large, slow and less persistent. This refines and quantifies the previous heuristic notion. Our idealized model assuming unlimited information processing capabilities serves as a benchmark for the chemotaxis of biological cells.