# Reconstructing the gradient source position from steady-state fluxes to small receptors

## TL;DR

This paper investigates how a biological cell can determine the position of a diffusing source using steady-state fluxes through small receptors, providing a computational method for gradient source localization.

## Contribution

It introduces a novel approach using Narrow Escape Time theory to reconstruct source position from fluxes, requiring at least three receptors within a certain distance.

## Key findings

- Source position can be recovered with at least 3 receptors within 10 cell radii
- The method applies in two-dimensional domains and narrow strips
- Provides a basis for gradient sensing at the single-cell level

## Abstract

Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape Time approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in two dimensions. {We find that the location of a source can be recovered when there are at least 3 receptors and the source is positioned no further than 10 cell radii away}, but this condition is not necessary in a narrow strip. The present approach provides a computational basis for the first step of direction sensing of a gradient at a single cell level.