Microtubule organization and cell geometry.

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.

A microtubule-based minimal model for spontaneous and persistent spherical cell polarity.

We propose a minimal model for the spontaneous and persistent generation of polarity in a spherical cell based on dynamic microtubules and a single mobile molecular component. This component, dubbed the polarity factor, binds to microtubules nucleated from a centrosome located in the center of the cell, is subsequently delivered to the cell membrane, where it diffuses until it unbinds. The only feedback mechanism we impose is that the residence time of the microtubules at the membrane increases with the local density of the polarity factor. We show analytically that this system supports a stable unipolar symmetry-broken state for a wide range of parameters. We validate the predictions of the model by 2D particle-based simulations. Our model provides a route towards the creation of polarity in a minimal cell-like environment using a biochemical reconstitution approach.

The effect of anisotropic microtubule-bound nucleations on ordering in the plant cortical array.

The highly orientationally ordered cortical microtubule array in plant cells is a key component for cell growth and development. Recent experimental and computational work has shown that the anisotropic nucleation of new microtubules from pre-existing microtubules has a major effect on the alignment process. We formulate a theoretical model to investigate the role of the microtubule-bound nucleation on the self-organization of the dynamical cortical microtubules. A bifurcation analysis of the stability of the disordered phase of the model reveals that the effective degree of co-aligned nucleation is the main determinant of the location of the transition. Increased co-aligned nucleation creates a positive feedback effect on the ordering process that can significantly widen the ordered region. We validate these predictions by comparing to the results of particle-based simulations.