The growth and development of some recent plant models: A viewpoint

A nontechnical introduction to selected recent models of plant development and growth is presented. Problems of creating predictive, quantitative models for (1) regulatory networks and (2) the use of space by developing tissues are outlined. These problems can be addressed using suitable mathematical frameworks to represent the substantial variety of relevant biological mechanisms, including gene regulation, protein modification, and cell-cell signaling by ligand/receptor pairs and by polarized auxin transport; also relevant are cell growth and division, the changing topology of signaling relationships between cells, and mechanical interactions between cells. Modeling frameworks are briefly described for gene regulation networks, including signaling; for more general biochemical reaction networks; for mechanical interactions (using a weak spring model) and signaling mediated by a changing topology of neighbor relations among growing and dividing cells; and for approximating such models at the tissue level using spatially continuous descriptions with changing shape. Finally, a "dynamical grammar" framework allows naturally for integrative and multiscale models because it can, in principle, combine any or all of the foregoing mechanisms. With mathematical and computational tools such as these, and with the current rapid progress in instrumentation and imagery, the future looks bright for scientifically effective modeling of plant development.