Bayesian gradient sensing in the presence of rotational diffusion

Abstract

Biological cells estimate concentration gradients of signaling molecules with a precision that is limited not only by sensing noise, but additionally by the cell's own stochastic motion. We ask for the theoretical limits of gradient estimation in the presence of both motility and sensing noise. We introduce a minimal model of a stationary chemotactic agent in the plane subject to rotational diffusion, which uses Bayesian estimation to optimally infer a gradient direction from noisy concentration measurements. Contrary to the known case of gradient sensing by temporal comparison, we show that for spatial comparison, the ultimate precision of gradient sensing scales not with the rotational diffusion time, but with its square-root. To achieve this precision, an individual agent needs to know its own rotational diffusion coefficient. This agent can accurately estimate the expected variability within an ensemble of agents. If an agent, however, does not account for its own motility noise, Bayesian estimation fails in a characteristic manner.

arXiv comment11 pages + 5 pages appendix, 2 color figures

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Cited by in corpus (6)

• Research Notes: Gradient sensing in Bayesian chemotaxis
• Gradient sensing limit of a cell when controlling the elongating direction
• Tradeoffs in concentration sensing in dynamic environments
• Theory for Optimal Estimation and Control under Resource Limitations and Its Applications to Biological Information Processing and Decision-Making
• Resource Limitations induce Phase Transitions in Biological Information Processing
• Learning stochastic filtering