Efficient event-driven approach to simulating microtubule dynamics in the plant cortical array

The dynamics of the plant microtubule cytoskeleton is a paradigmatic example of the complex spatiotemporal processes characterizing life at the cellular scale. This system is composed of large numbers of spatially extended particles, each endowed with its own intrinsic stochastic dynamics, and is capable of non-equilibrium self-organization through collisional interactions of these particles. To elucidate the behavior of such a complex system requires not only conceptual advances, but also the development of appropriate computational tools to simulate it. As the number of parameters involved is large and the behavior is stochastic, it is essential that these simulations be fast enough to allow for an exploration of the phase space and the gathering of sufficient statistics to accurately pin down the average behavior as well as the magnitude of fluctuations around it. Here we describe a simulation approach that meets this requirement by adopting an event-driven methodology that encompasses both the spontaneous stochastic changes in microtubule state as well as the deterministic collisions. In contrast with finite time step simulations this technique is intrinsically exact, as well as several orders of magnitude faster, which enables ordinary PC hardware to simulate systems of ~103 microtubules on a time scale ~103 faster than real time. In addition we present new tools for the analysis of microtubule trajectories on curved surfaces. We illustrate the use of these methods by addressing a number of outstanding issues regarding the importance of various parameters on the transition from an isotropic to an aligned and oriented state.