Modeling the Shoot Apical Meristem in A. thaliana : Parameter Estimation for Spatial Pattern Formation

Understanding the self-regulatory mechanisms controlling the spatial and temporal structure of multicellular organisms represents one of the major challenges in molecular biology. In the context of plants, shoot apical meristems (SAMs), which are populations of dividing, undifferentiated cells that generate organs at the tips of stems and branches throughout the life of a plant, are of particular interest and currently studied intensively. Here, one key goal is to identify the genetic regulatory network organizing the structure of a SAM and generating the corresponding spatial gene expression patterns. This paper addresses one step in the design of SAM models based on ordinary differential equations (ODEs): parameter estimation for spatial pattern formation. We assume that the topology of the genetic regulatory network is given, while the parameters of an ODE system need to be determined such that a particular stable pattern over the SAM cell population emerges. To this end, we propose an evolutionary algorithm-based approach and investigate different ways to improve the efficiency of the search process. Preliminary results are presented for the Brusselator, a well-known reaction-diffusion system.