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  • Open Access

Generic Temperature Response of Large Biochemical Networks

Julian B. Voits1 and Ulrich S. Schwarz1,2,*

  • *Contact author: schwarz@thphys.uni-heidelberg.de
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PRX Life 3, 043011 – Published 13 November, 2025

DOI: https://doi.org/10.1103/nyr3-5my3

Abstract

Biological systems are remarkably susceptible to relatively small temperature changes. The most obvious example is fever, when a modest rise in body temperature of only few Kelvin has strong effects on our immune system and how it fights pathogens. Another very important example is climate change, when even smaller temperature changes lead to dramatic shifts in ecosystems. Although it is generally accepted that the main effect of an increase in temperature is the acceleration of biochemical reactions according to the Arrhenius equation, it is not clear how it affects large biochemical networks with complicated architectures. For developmental systems such as fly and frog, it has been shown that the system response to temperature deviates in a characteristic manner from the linear Arrhenius plot of single reactions, but a rigorous explanation has not been given yet. Here we use a graph-theoretical interpretation of the mean first-passage times of a biochemical master equation to give a statistical description. We find that in the limit of large system size and if the network has a bias towards a target state, then the Arrhenius plot is generically quadratic, in excellent agreement with numerical simulations for large networks as well as with experimental data for developmental times in fly. We also discuss under which conditions this generic response can be violated, for example for linear chains, which have only one spanning tree.

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PRX Life 3, 043011– Published 13 November, 2025
  • Received 25 March 2024
  • Accepted 9 October 2025
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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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