Temperature compensation and scaling in vertebrate segmentation*

Development requires a precise coordination of patterning, growth and morphogenesis. Experimental perturbations such as temperature variation allow us to probe the feedbacks between these components. In this work, we study temperature scaling and developmental compensation in the context of vertebrate segmentation. During segmentation, patterning is controlled by phase waves of a genetic oscillator, the segmentation clock, and is happening simultaneously with axis elongation. As we subject Medaka fish embryos to a range of constant temperatures and temperature cycles, we find the rates of these processes increase with temperature, yet the morphology is unperturbed. We then use singular value decomposition to reduce the dynamics to two principal modes: spatial and temporal. We extract the associated parameters describing the waves, segmentation front, and axis growth, and quantify the temperature scaling and response time. From our analysis, we establish two scaling laws. Firstly, the segmentation frequency and the patterning front speed are compensated, producing a constant size pattern. Next, the system’s secondary time scale, the rate of oscillator’s slowing down, scales precisely with the oscillation frequency. Conversely, the growth component is in partial compensation and follows temperature with a time delay. From these results and modeling, we predict that short temperature cycles induce a perturbation in the wave pattern, which is further confirmed by experiment.