Evaluating the Arrhenius equation for developmental processes

Joseph Crapse, Nishant Pappireddi, Meera Gupta, Stanislav Y. Shvartsman, Eric Wieschaus, Martin Wühr

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


The famous Arrhenius equation is well suited to describing the temperature dependence of chemical reactions but has also been used for complicated biological processes. Here, we evaluate how well the simple Arrhenius equation predicts complex multi-step biological processes, using frog and fruit fly embryogenesis as two canonical models. We find that the Arrhenius equation provides a good approximation for the temperature dependence of embryogenesis, even though individual developmental intervals scale differently with temperature. At low and high temperatures, however, we observed significant departures from idealized Arrhenius Law behavior. When we model multi-step reactions of idealized chemical networks, we are unable to generate comparable deviations from linearity. In contrast, we find the two enzymes GAPDH and β-galactosidase show non-linearity in the Arrhenius plot similar to our observations of embryonic development. Thus, we find that complex embryonic development can be well approximated by the simple Arrhenius equation regardless of non-uniform developmental scaling and propose that the observed departure from this law likely results more from non-idealized individual steps rather than from the complexity of the system.

Original languageEnglish (US)
Article numbere9895
JournalMolecular Systems Biology
Issue number8
StatePublished - Aug 2021

All Science Journal Classification (ASJC) codes

  • Information Systems
  • General Immunology and Microbiology
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


  • Arrhenius equation
  • Drosophila melanogaster
  • Xenopus laevis
  • embryonic development
  • temperature dependence


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