# Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics

Source: [Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics](<https://www.sota2.com/research/paper/68fa29cf1e209131ce837999>)

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

Data updated: 2025-10-24T13:08:50.298Z

Authors: N. A. Sinitsyn, I. Nemenman

Published: 2010-01-24T00:13:16.000Z

## Abstract

We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the nonperiodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualitatively changes the outcome of the reaction kinetics.

## 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/1001.4212>)

[PDF](<https://arxiv.org/pdf/1001.4212.pdf>)