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State- versus Reaction-Based Information Processing in Biochemical Networks

Anne-Lena Moor1,2,*, Age Tjalma3, Manuel Reinhardt3, Pieter Rein ten Wolde3,†, and Christoph Zechner4,1,2,‡

  • *Contact author: annemoor96@gmail.com
  • †Contact author: tenwolde@amolf.nl
  • ‡Contact author: czechner@sissa.it
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Phys. Rev. Lett. 136, 248401 – Published 17 June, 2026

DOI: https://doi.org/10.1103/nfk6-8x5s

Abstract

Trajectory mutual information is frequently used to quantify information transfer in biochemical systems. Tractable solutions of the trajectory mutual information can be obtained via the widely used linear-noise approximation (LNA) using Gaussian channel theory. This approach is expected to be accurate for sufficiently large systems. However, recent observations show that there are cases, where the mutual information obtained this way differs qualitatively from results derived using an exact Markov jump process formalism, and that the differences remain even in the large copy number regime. In this Letter, we show that these differences can be explained by introducing the notion of reaction- versus state-based descriptions of trajectories. In chemical systems, the information is encoded in the sequence of reaction events, and the reaction-based trajectories of Markov jump processes capture this information. We show that within the Gaussian formalism, trajectories can be defined either based on individual reaction channels, or on a state-based level, where different reaction channels are summarized into a single noise term. While both definitions agree in terms of copy number fluctuations, state-based trajectories contain in general less information than reaction-based trajectories. The commonly used Gaussian mutual information via the linear-noise approximation is consistent with a state-based trajectory notion, which causes a systematic loss of information independent of system size. We show that an alternative, reaction-based variant of the Gaussian mutual information prevents this loss of information. We illustrate the consequences of different trajectory descriptions for two common cellular reaction motifs and discuss their connection with Berg-Purcell and maximum-likelihood sensing.

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Phys. Rev. Lett. 136, 248401– Published 17 June, 2026
  • Received 22 May 2025
  • Accepted 25 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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