Modeling Plant Tissue Growth and Cell Division

Morphogenesis is the creation of form, a complex process requiring the integration of genetics, mechanics, and geometry. Patterning processes driven by molecular regulatory and signaling networks interact with growth to create organ shape, often in unintuitive ways. Computer simulation modeling is becoming an increasingly important tool to aid our understanding of these complex interactions. In this chapter we introduce computational approaches for studying these processes on spatial, multicellular domains. For some problems, such as the exploration of many patterning processes, simulation can be done on static (non-growing) templates. These can range from abstract idealized cells, such as rectangular or hex grids, to more realistic shapes such as Voronoi regions, or even shapes extracted from bio-imaging data. More dynamic processes like phyllotaxis involve the interaction of growth and patterning, and require the simulation of growing domains. In the simplest case growth can be modeled descriptively, provided as an input to the model. Growth is specified globally, and must be designed carefully to avoid conflicts (growing cells must fit together). We present several methods for this that can be applied to shoots, roots, leaves, and other plant organs. However when shape is an emergent property of the model, different cells or areas of the tissue need to specify their growth locally, and physically-based methods (mechanics) are required to resolve conflicts. Among these are mass-spring, finite element, and Hamiltonian-based approaches