We propose a theoretical mechanism that enables the elaboration of veins to supply distant cells during leaf development. In contrast to the more standard view that a signal (e.g., auxin) is produced at isolated sites to stimulate growth, we determine the consequences of the hypothesis that auxin is produced at a constant rate in every cell. High concentration sites for auxin emerge naturally in a reaction-diffusion model, together with global information about leaf shape and existing venation. Because the global information is encoded as auxin concentration and its gradient, those signals provide individual cells with sufficient information to determine their own fate. Unlike other models, a single substance suffices for the reaction-diffusion at early, but not initial, stages of development. Neither complex interactions nor predetermination are necessary. We predict angiosperm areolation patterns in simulation, and our model further implies the Sachs Canalization Hypothesis and resolves a dilemma regarding the role of auxin in cell growth.canalization hypothesis ͉ emergent behavior ͉ reaction-diffusion I solated sites of high auxin concentration have been observed in developing leaves (1), and it has been assumed that auxin production is dominant there. However, evidence (1, 2) is emerging that production may be present at other sites. We demonstrate that discrete regulated sites of synthesis need not exist to develop a spatial pattern of discrete responses. Formally, our ''constant production hypothesis'' holds that auxin is produced in all cells at the same constant rate. Mathematical analysis of a schematic reaction diffusion model indicates that high concentration sites emerge, which agrees with observations (1) but also shows that distributions carry rich information about the geometry of the leaf and its venation. This information can be interpreted locally as a signal at the cell level, thereby providing global cues. The concentration together with the gradient of concentration have substantial predictive power about vein formation (Fig. 1). Signals for initiating differentiation are readily available locally, removing the need for complex intercellular communication.Our model differs from others that focus on local phenomena (4-6). We seek to articulate those global pattern features that emerge from purely local phenomena. Such structural questions on a larger scale have, to our knowledge, only been considered in the work of Meinhardt and Gierer (7,8) and, more recently, in the empirical models by Mündermann et al. (9) and Feugier et al. (10). We show, contrary to Meinhardt (8) and certain current opinion (11,12), that a single substance traveling purely by diffusion [or its equivalent (13)] is theoretically sufficient as a basis for a mechanistic model of venation patterning when it is uniformly and constantly produced (cf. ref. 10).
Motivation and AssumptionsWe demonstrate how simple local behaviors, occurring simultaneously and independently at the cell level, can give rise to complex global pattern...
