Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems

Vascular tissue in plants provides a resource distribution network for water and nutrients that exhibits remarkable diversity in patterning among different species. In many succulent plants, the vascular network includes longitudinally-oriented supplemental vascular bundles (SVBs) in the central core of the succulent stems and roots in addition to the more typical zone of vascular tissue development (vascular cambium) in a cylinder at the periphery of the succulent organ. Plant SVBs evolved in over 38 plant families often in tandem with evolutionary increases in stem and root parenchyma storage tissue, so it is of interest to understand the evolutionary-developmental processes responsible for their recurrent evolution and patterning. Previous mathematical models have successfully recreated the two-dimensional vascular patterns in stem and root cross sections, but such models have yet to recreate three-dimensional vascular patterning. Here, a stochastic reaction-diffusion model of plant vascular bundle patterning is developed in an effort to highlight a potential mechanism of three dimensional patterning–Turing pattern formation coupled with longitudinal efflux of a regulatory molecule. A relatively simple model of four or five molecules recreated empirical SVB patterns and many other common vascular arrangements. SVBs failed to develop below a threshold width of parenchymatous tissues, suggesting a mechanism of evolutionary character loss due to changes in the spatial context in which development takes place. Altered diffusion rates of the modeled activator and substrate molecules affected the number and size of the simulated SVBs. This work provides a first mathematical model employing a stochastic Turing-type mechanism that recreates three dimensional vascular patterns seen in plant stems. The model offers predictions that can be tested using molecular-genetic approaches. Evolutionary-developmental ramifications concerning evolution of diffusion rates, organ size and geometry are discussed.