Abstract
Pattern formation during development is a highly dynamic process. In spite of this, few experimental and modelling approaches take into account the explicit time-dependence of the rules governing regulatory systems. We address this problem by studying dynamic morphogen interpretation by the gap gene network in Drosophila melanogaster. Gap genes are involved in segment determination during early embryogenesis. They are activated by maternal morphogen gradients encoded by bicoid (bcd) and caudal (cad). These gradients decay at the same time-scale as the establishment of the antero-posterior gap gene pattern. We use a reverse-engineering approach, based on data-driven regulatory models called gene circuits, to isolate and characterise the explicitly time-dependent effects of changing morphogen concentrations on gap gene regulation. To achieve this, we simulate the system in the presence and absence of dynamic gradient decay. Comparison between these simulations reveals that maternal morphogen decay controls the timing and limits the rate of gap gene expression. In the anterior of the embyro, it affects peak expression and leads to the establishment of smooth spatial boundaries between gap domains. In the posterior of the embryo, it causes a progressive slow-down in the rate of gap domain shifts, which is necessary to correctly position domain boundaries and to stabilise the spatial gap gene expression pattern. We use a newly developed method for the analysis of transient dynamics in non-autonomous (time-variable) systems to understand the regulatory causes of these effects. By providing a rigorous mechanistic explanation for the role of maternal gradient decay in gap gene regulation, our study demonstrates that such analyses are feasible and reveal important aspects of dynamic gene regulation which would have been missed by a traditional steady-state approach. More generally, it highlights the importance of transient dynamics for understanding complex regulatory processes in development.