Information Theory of Chemotactic Agents Using Both Spatial and Temporal Gradient Sensing
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Abstract
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 and 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 comparisons. We account for the physical limits of chemosensation: molecule counting noise at physiological concentrations and motility noise inevitable at the microscale. Our simulation data collapse onto an empirical power law that predicts an optimal weighting of information as a 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. Published by the American Physical Society 2024
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By employing Pontryagin's minimum principle on the probability density function space, the solution satisfying the optimality condition δJ/δu = 0 is given by Eq. (S4).
“By employing Pontryagin's minimum principle on the probability density function space [1-9], the solution that satisfies the optimality condition δ ˜ J/δ ˜ u = 0 is given by”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [7]
The Analytical theory section (pp. 16–19) describes a likelihood map and decision rules for chemotactic agents, but does not state a solution derived using Pontryagin’s minimum principle or the condition δJ/δu = 0. Searches for Pontryagin, the optimality condition, and Eq. (S4) found no passage establishing the attributed result. (LLM, conf=0.75)
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- Authors
- Rode, J., Novak, M., & Friedrich, B. M.
- Affiliations
- Center for Advancing Electronics Dresden (DE)
- University of Zagreb (HR)
- Corresponding author
- Friedrich, Benjamin M.
- Venue
- PRX Life
- Publisher
- American Physical Society (APS)
- Published
- 2024-06-18
- Volume
- 2
- Issue
- 2
- ISSN
- 2835-8279 (ISSN-L)
- OpenAlex
- W4399775729
- Cited by
- 26
- References
- 66
- Citations by year
- 2026: 10 · 2025: 9 · 2024: 6 · 2023: 1
- FWCI
- 3.41
- Type
- journal article
- Language
- en
- Update notices
- correction (2024-11-05)
- Open access
- diamond
- doi.org
- Licence
- Locations
- PRX Life (publishedVersion, cc-by)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- Funders
- Deutsche Forschungsgemeinschaft (391963627, EXC-2068-390729961, 421143374)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Micro and Nano Robotics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Keywords
- chemotaxis, gradient sensing, spatial comparison, temporal comparison, information theory, chemosensation, power law
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