Evaluating the Simple Arrhenius Equation for the Temperature Dependence of Complex Developmental Processes

The famous Arrhenius equation is well motivated to describe 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 multistep biological processes, using frog and fruit fly embryogenesis as two canonical models. We find the Arrhenius equation provides a good approximation for the temperature dependence of embryogenesis, even though individual developmental stages scale differently with temperature. At low and high temperatures, however, we observed significant departures from idealized Arrhenius Law behavior. When we model multistep reactions of idealized chemical networks we are unable to generate comparable deviations from linearity. In contrast, we find the single enzyme GAPDH shows 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 Law and propose that the observed departure from this law results primarily from non-idealized individual steps rather than the complexity of the system.