The vertebrate segmentation clock is a gene expression oscillator controlling rhythmic segmentation of the vertebral column during embryonic development. The period of oscillations becomes longer as cells are displaced along the posterior to anterior axis, which results in traveling waves of clock gene expression sweeping in the unsegmented tissue. Although various hypotheses necessitating the inclusion of additional regulatory genes into the core clock network at different spatial locations have been proposed, the mechanism underlying traveling waves has remained elusive. Here, we combined molecularlevel computational modeling and quantitative experimentation to solve this puzzle. Our model predicts the existence of an increasing gradient of gene expression time delays along the posterior to anterior direction to recapitulate spatiotemporal profiles of the traveling segmentation clock waves in different genetic backgrounds in zebrafish. We validated this prediction by measuring an increased time delay of oscillatory Her1 protein production along the unsegmented tissue. Our results refuted the need for spatial expansion of the core feedback loop to explain the occurrence of traveling waves. Spatial regulation of gene expression time delays is a novel way of creating dynamic patterns; this is the first report demonstrating such a control mechanism in any tissue and future investigations will explore the presence of analogous examples in other biological systems.

SUMMARYOscillations are prevalent in natural systems. A gene expression oscillator, called the segmentation clock, controls segmentation of precursors of the vertebral column. Genes belonging to the Hes/her family encode the only conserved oscillating genes in all analyzed vertebrate species. Hes/Her proteins form dimers and negatively autoregulate their own transcription. Here, we developed a stochastic two-dimensional multicellular computational model to elucidate how the dynamics, i.e. period, amplitude and synchronization, of the segmentation clock are regulated. We performed parameter searches to demonstrate that autoregulatory negative-feedback loops of the redundant repressor Her dimers can generate synchronized gene expression oscillations in wild-type embryos and reproduce the dynamics of the segmentation oscillator in different mutant conditions. Our model also predicts that synchronized oscillations can be robustly generated as long as the half-lives of the repressor dimers are shorter than 6 minutes. We validated this prediction by measuring, for the first time, the half-life of Her7 protein as 3.5 minutes. These results demonstrate the importance of building biologically realistic stochastic models to test biological models more stringently and make predictions for future experimental studies.