Microtubule organization and cell geometry.

Abstract

A characteristic feature of nondividing animal cells is the radial organization of microtubules (MTs), emanating from a single microtubule organizing center (MTOC). As generically these cells are not spherically symmetric, this raises the question of the influence of cell geometry on the orientational distribution of microtubules. We present a systematic study of this question in a simplified setting where MTs are nucleated from a single fixed MTOC in the center of an elliptical cell geometry. Within this context we introduce four models of increasing complexity, each one introducing additional mechanisms that govern the interaction of the MTs with the cell boundary. In order, we consider the cases: MTs that can bind to the boundary with a fixed mean residence time (M0), force-producing MTs that can slide on the boundary towards the cell poles (MS), MTs that interact with a generic polarity factor that is transported and deposited at the boundary, and which in turn stabilizes the MTs at the boundary (MP), and a final model in which both sliding and stabilization by polarity factors is taken into account (MSP). In the baseline model (M0), the exponential length distribution of MTs causes most of the interactions at the cell boundary to occur along the shorter transverse direction in the cell, leading to transverse biaxial order. MT sliding (MS) is able to reorient the main axis of this biaxial order along the longitudinal axis. The polarization mechanism introduced in MP and MSP overrules the geometric bias towards bipolar order observed in M0 and MS, and allows the establishment of unipolar order either along the short (MP) or the long cell axis (MSP). The behavior of the latter two models can be qualitatively reproduced by a very simple toy model with discrete MT orientations.