A hyperbolic cell cycle law for early embryonic developmental timing
Across metazoans, early embryos exhibit a strikingly conserved slowing down of their cell duplication speed, despite widely varying developmental paces and underlying molecular mechanisms. Here we show that this common behavior arises because early development unfolds along a biochemical rather than a chronological timescale, resulting from the coupling of finite maternal resource consumption to the Michaelis-Menten-like kinetics governing the rates of the biochemical reactions involved in cell duplication. This leads to a hyperbolic growth of the Cell Cycle Length (CCL), approaching a mathematical singularity, which would correspond to developmental arrest. Data from a wide range of organisms -- cnidarians, nematodes, arthropods, molluscs, echinoderms, tunicates, amphibians, and fish -- collapse on a single curve, quantitatively capturing not only a universal CCL dynamical behaviour, but also key hallmarks of early metazoan development, including cell-number temporal evolution, the dependency of CCL on cell size, and, remarkably, gastrulation timing at the predicted singularity. Crucially, experimental modulation of resource availability and consumption rates validate the model and further demonstrate that a source of heterochrony in early development is an altered biochemical timescale of resource depletion. Overall, this work reveals resource consumption rates as a fundamental mechanism driving developmental timing in early embryogenesis across species.