Optimal Experimental Design in the Modelling of Pattern Formation Adri´ an L´ opez Garc´ ıa de Lomana, ` Alex G´ omez-Garrido, David Sportouch, and Jordi Vill` a-Freixa Grup de Recerca en Inform`atica Biom` edica, IMIM-Universitat Pompeu Fabra, C/Doctor Aiguader, 88, 08003 Barcelona, Catalunya, Spain {adrianlopezgarciadelomana,david.sportouch}@gmail.com {agomez,jvilla}@imim.es http://cbbl.imim.es Abstract. Gene regulation plays a major role in the control of develop- mental processes. Pattern formation, for example, is thought to be reg- ulated 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 pat- terning 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 im- plementation 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. Key words: lateral inhibition, GRN, optimal experimental design, mul- ticellular system 1 Introduction One of the most breathtaking processes in biology is the development of a com- plex creature. In a matter of just a day (a fly maggot), a few weeks (a mouse) or several months (ourselves), an egg grows into millions, billions, or, in the case of humans, 10 trillion cells formed into organs, tissues and parts of the body. So, the main question in developmental biology is to understand how do cells arising from division of a single cell become different from each other. The com- plexity of the process of pattern formation in developmental biology has been dealt with by a number of researchers in the last decades (for reviews see [1]), both topologically, studying the different genes involved in the process and their relationships, and dynamically, measuring and modeling the temporal behav- ior of those genes and their products. Different simulation methods have been applied to dynamical models of patterning, involving both ordinary (ODE) [2]