Abstract
Timing of embryonic development is precisely controlled, but the mechanisms underlying biological timers are still unclear. Here, a validated model for timing under control of Sonic Hedgehog is revisited and generalized to an arbitrary number of genes. The developmental dynamics where a temporal sequence of gene expression recapitulates a steady-state spatial pattern can be realized through a simple network close to criticality, controlled by the duration of exposure to a morphogen. Criticality simultaneously accounts for many observed biological properties, such as timing, multistability, and canalization of genetic expression. This process can be parsimoniously generalized in many dimensions with a minimum number of genes, all repressing each other with asymmetrical strengths, which also explains sequential activation of different fates. Separation of timescales allows for a simple analytical interpretation. Finally, it is shown that even in the presence of noise, coupling between cells preserves criticality and robust patterning. The model offers a simple theoretical framework for the study of emergent developmental timers.