Computational Study of Microtubule Networks for Cell Division

Abstract

The dynamics of the meiotic spindle, the microtubule-based macromolecular machine responsible for the segregation of chromosomes and equal partitioning of genetic information during cellular division, are immensely complex and not quantitatively understood. This study involves building computational models of what we consider the most fundamental components for the formation and stability of the meiotic spindle. All calculations were done using over-damped Langevin dynamics and kinetic Monte Carlo methods with the open source code Cytosim. We modelled microtubules as flexible, soft-core filaments that can regulate their length through dynamic instability. Microtubules are introduced into the system by nucleators that are spatially regulated in a decaying gradient, mimicking the RanGTP pathway in cells. Plus-end directed extensile motors (kinesins) and minusend directed contractile motors (dynein) then organize these microtubules into the desired steady-state structure. Using these components, we aimed to build a two-dimensional bipolar spindle starting from nothing. This would help us quantitatively rationalize how the spindle self-assembles and the cell cycle transitions from prophase up to metaphase. To this end, we systematically varied (i) the microtubule nucleation profile and (ii) the concentration and relative amounts of the two motor proteins and observed how that affected the resultant microtubule networks. We quantified and compared different networks by calculating nematic order parameters and motor to microtubule ratios, both as functions of time and space. From our simulations, which serve as a simplification of a complex process, we were able to infer some of the necessary physical rules and conditions that must be met in order to assemble and maintain a functional bipolar spindle. We discuss where our conclusions might be particularly important in the context of recent theoretical and experimental studies of the spindle.