# Response and fluctuations of a two-state signaling module with feedback

Source: [Response and fluctuations of a two-state signaling module with feedback](<https://www.sota2.com/research/paper/68fa20eb7a2b558e293341c1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T23:39:32.647Z

Authors: Manoj Gopalakrishnan, Peter Borowski, Frank J\\"ulicher, Martin Zapotocky

Published: 2006-07-05T07:59:37.000Z

## Abstract

We study the stochastic kinetics of a signaling module consisting of a two-state stochastic point process with negative feedback. In the active state, a product is synthesized which increases the active-to-inactive transition rate of the process. We analyze this simple autoregulatory module using a path-integral technique based on the temporal statistics of state flips of the process. We develop a systematic framework to calculate averages, autocorrelations, and response functions by treating the feedback as a weak perturbation. Explicit analytical results are obtained to first order in the feedback strength. Monte Carlo simulations are performed to test the analytical results in the weak feedback limit and to investigate the strong feedback regime. We conclude by relating some of our results to experimental observations in the olfactory and visual sensory systems.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/q-bio/0607007>)

[PDF](<https://arxiv.org/pdf/q-bio/0607007.pdf>)