The Arrhenius law explains how a single enzymatic step speeds up with temperature, yet many multi-step complex biological processes still look roughly Arrhenius, until they don’t. Here we will address this question. 

We start with the biochemical cell-cycle oscillator driving early embryonic cleavages. Using new measurements and modeling across ectotherms, we find that cycle periods share similar apparent activation energies and are approximately Arrhenius over a broad range, but break down at cold and hot ends. These deviations are traced to concrete circuit features: biphasic temperature responses in key regulators and imbalances in activation energies across partially rate-determining steps, supported by Xenopus extract and in-vitro assays (Rombouts et al., Nature Comm. 2025).

We then generalize beyond oscillations: viewing biological durations as mean-first-passage times through reversible multi-step networks yields a robust curved middle regime (quadratic-exponential) produced by averaging across many steps, flanked by Arrhenius-like extremes where a few steps dominate. Simple network motifs also account for warm-edge slowdowns and apparent negative activation energies without invoking denaturation. This framework matches more than 100 datasets across species and developmental processes (Jacobs et al., BioRxiv 2025). We then test these rules in new systems and study how they help predict when biological timing will stay coordinated, drift, or fail as environments warm.

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