Optimal Experimental Design in the Modelling of Pattern Formation

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Gene regulation plays a major role in the control of developmental processes. Pattern formation, for example, is thought to be regulated by a limited number genes translated into transcription factors that control the differential expression of other genes in different cells in a given tissue. We focused on the Notch pathway during the formation of chess-like patterns along development. Simplified models exist of the patterning by lateral inhibition due to the Notch-Delta signalling cascade. We show here how parameters from the literature are able to explain the steady-state behavior of model tissues of several sizes, although they are not able to reproduce time series of experiments. In order to refine the parameters set for data from real experiments we propose a practical implementation of an optimal experimental design protocol that combines parameter estimation tools with sensitivity analysis, in order to minimize the number of additional experiments to perform.