Browse Theses

In this dissertation we consider the plant cell as a computational unit and demonstrate how simple programs can give rise to some of the complex patterns observed in nature. We focus on vein pattern formation and propose a novel class of reaction-diffusion models in three successive refinements. Each iteration uncovers a new uniformity principle that improves the scope and quality of our predictions. Surprisingly, these principles also explain root patterning phenomena.

First, we propose that each non-vascular cell produces a hormone at the same constant rate: the constant production hypothesis (CPH). Assuming that vascular cells deplete hormone concentration and diffusion is the sole transport mechanism, we prove that the equilibrium distribution (the solution of a Poisson equation) of this hormone carries rich information about the geometry of the leaf and its venation. If cells become vascular when they measure a sufficiently large difference in concentration, then familiar vein patterns emerge.

Second, we propose that the CPH applies to all cells, and that the hormone is destroyed by all cells in equal proportion to its concentration—the Proportional Destruction Hypothesis (PDH). A Helmholtz equation ensues. Noting the consistent variation of cell sizes, we demonstrate that our previous patterning result holds unchanged in young leaves. In mature tissues, we predict that this same mechanism can repair wounded veins.

Third, we propose that the difference of auxin concentration through interfaces (membrane and cell wall) is maintained low and constant wherever auxin carriers exist—the Constant Gradient Hypothesis (CGH). Formulating a non-linear transport model, we demonstrate how these three principles predict the location, directionality and intensity of the hormone carriers. Our predictions mimic experimental observations and have, on one occasion, preceded them.

Finally, our three principles enable us to predict a longer distance phenomenon: the synchronization of shoot and root growth rates. We show that the auxin carrier intensity, rather than the hormone itself, can effectively encode the required information. As a result, we propose a novel mechanism for positional information that is outside the scope of reaction-diffusion systems.