Modeling the dynamic development of vascular bundles in plants: radial patterns in stems and roots

Spontaneous spatial pattern formation as a result of dynamic interactions is common in nature at all scales. In plant development and morphogenesis, several regular patterns have been widely studied such as the establishment of the main axes, organ shapes and venation. The radial arrangement of plant vascular bundles and other tissues, i.e. the stele, varies between species and organs. The topic has been analyzed in morphological, physiological and genetic studies and discussed in terms of evolutionary perspectives. In the last decades, simulation models have proven to be useful tools for hypotheses testing on complex systems. Several studies have been carried out using computer simulation in plant development. Two main mechanisms have been proposed for the generation of venation in plants, the canalization hypothesis by Sachs et al. (1969) and the pre-pattern theory by local activation and long-range inhibition formulated by Meinhardt (1976, 1998). Both approaches have been applied to several developmental problems like axes establishment, phyllotaxis, SAM and RAM functioning and leaf venation. So far, no modeling effort has been done yet on the formation of primary structures observed in different plant taxa. In this study we propose a new 2D cellular automaton model based on the spatial dynamics (reaction-diffusion) of hypothetical autocatalytic substrate-depleting morphogens, which promote the differentiation of procambium, phloem and xylem. The model defines a set of logical and functional rules to simulate activation of procambial and vascular cell differentiation in stem and root radial sections. Simulation results show that our model is capable of qualitatively reproduce most stelar structures, simulating the dynamic development of different radial spatial patterns of vascular bundles.