Short time extremal response to step stimulus for a single cell {\sl E. coli}

TL;DR

This paper investigates the immediate extremal response of E. coli cells to sudden environmental changes, deriving conditions for peak activity and predicting an optimal stimulus size for fastest response.

Contribution

It provides exact analytical conditions for extremal responses and predicts an optimal stimulus size for quickest extremal response in E. coli.

Findings

Exact conditions for extremal receptor activity and tumbling bias responses.

Prediction of an optimal step stimulus size for fastest extremal response.

Good agreement between analytical results and numerical simulations.

Abstract

After application of a step stimulus, in the form of a sudden change in attractant environment, the receptor activity and tumbling bias of an {\sl E. coli} cell change sharply to reach their extremal values before they gradually relax to their post-stimulus adapted levels in the long time limit. We perform numerical simulations and exact calculations to investigate the short time response of the cell. For both activity and tumbling bias, we exactly derive the condition for extremal response and find good agreement with simulations. We also make experimentally verifiable prediction that there is an optimum size of the step stimulus at which the extremal response is reached in the shortest possible time.