An introduction to modeling the initiation of the floral primordium

This chapter presents models of the processes involved in floral initiation and development. It begins by briefy presenting models of hormonal transport. The focus is on two key aspects of floral development, namely floral initiation, due to the periodic local accumulation of auxin (a plant hormone) near the plant apex, and the genetic regulation of floral development. The main assumptions about auxin transport that have been proposed and tested in the literature are described, and it is shown how the use of models makes it possible to test assumptions expressed in terms of local cell-cell interaction rules and to check if they lead to patterning in the growing tissue that is consistent with observation. The gene regulatory networks (GRNs) that control the initial steps of floral development and differentiation are investigated. In a simplified form, this network contains dozens of components that interact with each other in space and time. The understanding of such a complex system also requires a modeling approach in order to quantify these interactions and analyze their properties. There are two main formalisms that are used to model GRN: the Boolean and the ODE formalisms. Both these are illustrated on a submodule of the floral GRN and their main advantages and drawbacks are discussed. It is shown how manipulations of the network models can be used to make predictions corresponding to possible biological manipulations of the GRN (e.g., loss-of-function mutants). Throughout, specific mathematical topics of particular interest for the development of these ideas are detailed in separate boxes which can be read relatively independently of the main text.