We use a 3D computer simulation model that is based on experimental data to understand how the noncentrosomal plant cortical microtubules self-organize into specific ordered patterns in both wild-type and mutant plants.

There is rising interest in modeling the noncentrosomal cortical microtubule cytoskeleton of plant cells, particularly its organization into ordered arrays and the mechanisms that facilitate this organization. In this review, we discuss quantitative models of this highly complex and dynamic structure both at a cellular and molecular level. We report differences in methodologies and assumptions of different models as well as their controversial results. Our review provides insights for future studies to resolve these controversies, in addition to underlining the common results between various models. We also highlight the need to compare the results from simulation and mathematical models with quantitative data from biological experiments in order to test the validity of the models and to further improve them. It is our hope that this review will serve to provide guidelines for how to combine quantitative and experimental techniques to develop higher-level models of the plant cytoskeleton in the future. V C 2012Wiley Periodicals, Inc

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.

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