Weber's Law in Autocatalytic Reaction Networks

TL;DR

This paper demonstrates that simple autocatalytic reaction networks can exhibit Weber's law, where responses depend only on fold changes, through slow synthesis or oscillatory adaptive processes, suggesting a common biological mechanism.

Contribution

It introduces a mechanism showing how autocatalytic reactions can naturally obey Weber's law in biological systems.

Findings

Autocatalytic reactions show Weber's law with slow synthesis.

Series or parallel autocatalytic reactions exhibit oscillatory adaptive responses.

The proposed mechanism is likely common in biological reactions.

Abstract

Biological responses often obey Weber's law, according to which the magnitude of the response depends only on the fold change in the external input. In this study, we demonstrate that a system involving a simple autocatalytic reaction shows such response when a chemical is slowly synthesized by the reaction from a faster influx process. We also show that an autocatalytic reaction process occurring in series or in parallel can obey Weber's law with an oscillatory adaptive response. Considering the simplicity and ubiquity of the autocatalytic process, our proposed mechanism is thought to be commonly observed in biological reactions.