Optimal concentration and gradient sensing by perfect monitors
Abstract
Cells often estimate chemical concentrations from only a few diffusing molecules, whose stochastic motion limits sensing precision. We consider a perfect monitoring instrument that records the instantaneous molecular density throughout a finite region without perturbing the concentration field or distinguishing molecular identities. The standard Berg-Purcell estimator weights all positions uniformly. Here we derive the optimal spatial weighting within a large class of unbiased estimators for both concentration and gradient sensing. Variance minimization maps to an electrostatic problem. Surprisingly, although the instrument monitors the entire volume, the optimal estimator assigns all weight to its boundary, reducing the uncertainty in both concentration and gradient sensing. We extend the results to arbitrary geometries and spatial dimensions.
Related
- Concentration gradient of plastic debris larger than 500 μm detected across the Southwest Indian ocean
- Toward Digital-Twin-Enabled Bioprocess Monitoring: Fault-Inclusive Soft Sensing of Penicillin Concentration Under Process Deviations
- A phase field model with stochastic input simulates cellular gradient sensing, morphodynamics, and fidelity of haptotaxis
- A helper NLR monitors catalytic perturbation of a vesicle trafficking regulator targeted by pathogen effectors
- No practice and still perfect: Different routes for promoting offline gains in perceptual learning
BibTeX
@misc{jafarpour2026optimal,
title = {{Optimal concentration and gradient sensing by perfect monitors}},
author = {Farshid Jafarpour},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.08816},
eprint = {2608.08816},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08816},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal concentration and gradient sensing by perfect monitors
AU - Farshid Jafarpour
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2608.08816
UR - https://arxiv.org/abs/2608.08816
AB - Cells often estimate chemical concentrations from only a few diffusing molecules, whose stochastic motion limits sensing precision. We consider a perfect monitoring instrument that records the instantaneous molecular density throughout a finite region without perturbing the concentration field or distinguishing molecular identities. The standard Berg-Purcell estimator weights all positions uniformly. Here we derive the optimal spatial weighting within a large class of unbiased estimators for both concentration and gradient sensing. Variance minimization maps to an electrostatic problem. Surprisingly, although the instrument monitors the entire volume, the optimal estimator assigns all weight to its boundary, reducing the uncertainty in both concentration and gradient sensing. We extend the results to arbitrary geometries and spatial dimensions.
ER -