Efficient event-driven simulations shed new light on microtubule organization in the plant cortical array

摘要

The dynamics of the plant microtubule cytoskeleton is a paradigmatic example of the complex spatiotemporal processes characterising 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-organisation through collisional interactions of these particles. To elucidate the behaviour 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 behaviour 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 behaviour 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 $sim 10^3$ microtubules on a time scale $sim 10^{3}$ 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.