Understanding phase behavior of plant cell cortex microtubule organization

Abstract

Plant microtubules are found to be strongly associated with the cell cortex and to experience polymerization/depolymerization processes that are responsible for the organization of microtubule cortical array. Here we propose a minimal model that incorporates the basic assembly dynamics and intermicrotubule interaction to understand the unexplored phase behavior of such a system. Through kinetic Monte Carlo simulations and theoretical calculations, we show that the self-organized patterns of plant cell cortical microtubules can be regulated by controlling single microtubule assembly dynamics. Biologically, this means that the structural reorganization can be regulated by microtubule-associated proteins via changing microtubule dynamic instability parameters, such as the microtubule plus-end growing rate, GTP-tubulin hydrolysis rate, etc. Such regulation is indirectly confirmed by various in vivo experiments. For the physical aspects, we not only construct the phase diagram that determines under what parameters ordered microtubule arrays form, but also predict that the essentially different ordered structures may appear through continuous and discontinuous transitions. The present study will play a central role in our understanding of the basic mechanism of plant cell noncentrosomal microtubule arrays.cortical microtubule array | cytoskeleton | nematic phase | treadmilling | steric interaction U nderstanding the structural organization of the microtubule (MT) cytoskeleton is a central problem in cell biology (1-4). In plant cell, MTs are confined to a thin layer of the interior side of the plasma membrane and may organize into the so-called cortical MT array-a highly ordered structure just beneath the plasma membrane. In contrast to equilibrium ordered structures, such a MT cortical array, which is unique in the plant cell, constantly changes its appearance and even may disappear and reform during different phases of cell cycle (5-7). One open question is how the plant cell regulates the formation of cortical arrays and what dictates the self-organized patterns of MTs. From a physical point of view, it is also interesting to understand these phenomena by asking how the ordered structures are achieved through the noncentrosomal MT cortical organization and whether there are any basic mechanisms governing such dynamic order transitions.Recent in vivo experimental studies have made great progress in revealing the possible formation of plant cell cortical arrays (5,8). Unlike animal cells, the nucleation of new MTs is found to be widely dispersed on plasma membrane (9-11), because of the lack of centrioles in plant cells. MTs are found stably attached to the membrane, and therefore lateral and rotational diffusions of MTs are suppressed. Instead, treadmilling behavior of MTs, which is achieved by plus-end polymerization and minusend depolymerization, was observed on the plasma membrane (9, 10), and consequent intermicrotubule collisions may frequently occur between a polymerizing MT and a preexisting one (9, 12). If t...

Computer simulation and mathematical models of the noncentrosomal plant cortical microtubule cytoskeleton

“…However, their model is limited in the sense that only growth-prone dynamics can be studied due to exclusion of dynamic instability. Shi and Ma [2010] simulated CMT organization using a similar CMT interaction mechanism with stalling-that they called steric interactions-with dynamic instability modeled at both ends according to a GTP-cap model [Margolin et al, 2006]. They particularly focused on the effect of dynamicity parameters on self-organization, by scanning a wide range of parameters to locate points of transition between ordered and disordered CMT array states [Shi and Ma, 2010].…”

“…In a subsequent study, the authors show that the predictions of this mathematical model agree well with their simulations, although the performance deteriorates for simulations that include bundling . Similarly, Shi and Ma [2010] combined n 148…”

“…They also introduce an alternative version of this metric where the contribution of each CMT is weighted by its length. Shi and Ma [2010] employ a method that is based on computation of eigenvalues of a standard nematic order matrix [Chaikin and Lubensky, 1995]. Hawkins et al [2010] and Tindemans et al [2010] employ another nematic liquid crystal order parameter based on the orientation and length densities of CMTs.…”

“…Allard et al [2010b] uses a modified version of the cost function in Baulin et al [2007], that represents the difference between projected polymer length in the dominant direction and its perpendicular direction. Despite the diversity of methodologies used to measure CMT organization, it is worth noting that Allard [2010] found that the metrics used by Shi and Ma. [2010], Tindemans et al [2010], Allard et al [2010b], and Baulin et al [2007] are equivalent.…”

TONNEAU2/FASS Regulates the Geometry of Microtubule Nucleation and Cortical Array Organization in Interphase Arabidopsis Cells

“…Experimental and theoretical studies suggest that organization of plant cortical microtubules into ordered arrays depends on intrinsic microtubule behaviors, such as polymer treadmilling, encounters between microtubules with angle-dependent outcomes, microtubule-dependent microtubule nucleation, and alteration of essential properties, such as plus-end stability in specific cell domains (Shaw et al, 2003;Dixit and Cyr, 2004;Baulin et al, 2007;Kawamura and Wasteneys, 2008;Allard et al, 2010;Eren et al, 2010;Hawkins et al, 2010;Nakamura et al, 2010;Shi and Ma, 2010;Tindemans et al, 2010;Ambrose et al, 2011;Deinum et al, 2011). While clues to how arrays might attain parallel organization are arising from these studies, outstanding questions are how particular array orientations are obtained, how arrays are dynamically reorganized by developmental and environmental cues, and what microtubule properties and behaviors are important for array reorganization.…”