Theoretical Framework for Quantifying Single-Cell Chemotactic Efficiency

A new theoretical study posted to arXiv examines the chemotactic index, a measure of how effectively a single cell can sense and move along a spatial chemical gradient. Building on prior work that characterized this efficiency through a single dimensionless signal-to-noise parameter, the authors demonstrate that the relevant statistical cumulants in the model can be computed exactly, providing explicit results up to third order using diffusive current density and Gaunt coefficients. A key contribution is the identification of a new dimensionless group, lambda, defined as a ratio of concentrations, which quantifies the importance of non-Gaussian corrections to the chemotactic index via an Edgeworth expansion. The authors connect their framework to the classical Berg-Purcell limits on concentration gradient sensing uncertainty. By analyzing published experimental data on slime mold chemotaxis, they show that the original Gaussian approximation succeeded largely because those experiments involved shallow gradients where the non-Gaussian parameter lambda was much smaller than the signal-to-noise parameter. The results suggest that in steeper gradient regimes, the non-Gaussian corrections captured by lambda could become significant and should not be neglected.