Stochastic models for plant microtubule self-organization and structure.

One of the key enablers of shape and growth in plant cells is the cortical microtubule (CMT) system, which is a polymer array that forms an appropriately-structured scaffolding in each cell. Plant biologists have shown that stochastic dynamics and simple rules of interactions between CMTs can lead to a coaligned CMT array structure. However, the mechanisms and conditions that cause CMT arrays to become organized are not well understood. It is prohibitively time-consuming to use actual plants to study the effect of various genetic mutations and environmental conditions on CMT self-organization. In fact, even computer simulations with multiple replications are not fast enough due to the spatio-temporal complexity of the system. To redress this shortcoming, we develop analytical models and methods for expeditiously computing CMT system metrics that are related to self-organization and array structure. In particular, we formulate a mean-field model to derive sufficient conditions for the organization to occur. We show that growth-prone dynamics itself is sufficient to lead to organization in presence of interactions in the system. In addition, for such systems, we develop predictive methods for estimation of system metrics such as expected average length and number of CMTs over time, using a stochastic fluid-flow model, transient analysis, and approximation algorithms tailored to our problem. We illustrate the effectiveness of our approach through numerical test instances and discuss biological insights.