# Complete integrability of information processing by biochemical reactions

Source: [Complete integrability of information processing by biochemical reactions](<https://www.sota2.com/research/paper/68fa3f191e209131ce8eacda>)

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

Data updated: 2025-10-27T04:09:14.353Z

Authors: Elena Agliari, Adriano Barra, Lorenzo Dello Schiavo, Antonio Moro

Published: 2016-05-05T15:25:52.000Z

## Abstract

Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions. Within such framework far-reaching analogies are established among (anti-) cooperative collective behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical mechanics and operational amplifiers/flip-flops in cybernetics. The underlying modeling -- based on spin systems -- has been proved to be accurate for a wide class of systems matching classical (e.g. Michaelis--Menten, Hill, Adair) scenarios in the infinite-size approximation. However, the current research in biochemical information processing has been focusing on systems involving a relatively small number of units, where this approximation is no longer valid. Here we show that the whole statistical mechanical description of reaction kinetics can be re-formulated via a mechanical analogy -- based on completely integrable hydrodynamic-type systems of PDEs -- which provides explicit finite-size solutions, matching recently investigated phenomena (e.g. noise-induced cooperativity, stochastic bi-stability, quorum sensing). The resulting picture, successfully tested against a broad spectrum of data, constitutes a neat rationale for a numerically effective and theoretically consistent description of collective behaviors in biochemical reactions.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1605.01624>)

[PDF](<https://arxiv.org/pdf/1605.01624.pdf>)