Plant morphogenesis requires differential and often asymmetric growth. A key role in controlling anisotropic expansion of individual cells is played by the cortical microtubule array. Although highly organized, the array can nevertheless rapidly change in response to internal and external cues. Experiments have identified the microtubule-severing enzyme katanin as a central player in controlling the organizational state of the array. Katanin action is required both for normal alignment and the adaptation of array orientation to mechanical, environmental, and developmental stimuli. How katanin fulfills its controlling role, however, remains poorly understood. On the one hand, from a theoretical perspective, array ordering depends on the "weeding out" of discordant microtubules through frequent catastrophe-inducing collisions among microtubules. Severing would reduce average microtubule length and lifetime, and consequently weaken the driving force for alignment. On the other hand, it has been suggested that selective severing at microtubule crossovers could facilitate the removal of discordant microtubules. Here we show that this apparent conflict can be resolved by systematically dissecting the role of all of the relevant interactions in silico. This procedure allows the identification of the sufficient and necessary conditions for katanin to promote array alignment, stresses the critical importance of the experimentally observed selective severing of the "crossing" microtubule at crossovers, and reveals a hitherto not appreciated role for microtubule bundling. We show how understanding the underlying mechanism can aid with interpreting experimental results and designing future experiments.@en

The dynamics of the plant microtubule cytoskeleton is a paradigmatic example of the complex spatiotemporal processes characterizing 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-organization through collisional interactions of these particles. To elucidate the behavior 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 behavior 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 behavior 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 ~103 microtubules on a time scale ~103 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.

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The ordered arrangement of cortical microtubules in growing plant cells is essential for anisotropic cell expansion and, hence, for plant morphogenesis. These arrays are dismantled when the microtubule cytoskeleton is rearranged during mitosis and reassembled following completion of cytokinesis. The reassembly of the cortical array has often been considered as initiating from a state of randomness, from which order arises at least partly through self-organizing mechanisms. However, some studies have shown evidence for ordering at early stages of array assembly. To investigate how cortical arrays are initiated in higher plant cells, we performed live-cell imaging studies of cortical array assembly in tobacco (Nicotiana tabacum) Bright Yellow-2 cells after cytokinesis and drug-induced disassembly. We found that cortical arrays in both cases did not initiate randomly but with a significant overrepresentation of microtubules at diagonal angles with respect to the cell axis, which coincides with the predominant orientation of the microtubules before their disappearance from the cell cortex in preprophase. In Arabidopsis (Arabidopsis thaliana) root cells, recovery from drug-induced disassembly was also nonrandom and correlated with the organization of the previous array, although no diagonal bias was observed in these cells. Surprisingly, during initiation, only about one-half of the new microtubules were nucleated from locations marked by green fluorescent protein-g-tubulin complex protein2-tagged g-nucleation complexes (g-tubulin ring complex), therefore indicating that a large proportion of early polymers was initiated by a noncanonical mechanism not involving g-tubulin ring complex. Simulation studies indicate that the high rate of noncanonical initiation of new microtubules has the potential to accelerate the rate of array repopulation.

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Despite their pivotal role in plant development, control mechanisms for oriented cell divisions have remained elusive. Here, we describe how a precisely regulated cell division orientation switch in an Arabidopsis stem cell is controlled by upstream patterning factors. We show that the stem cell regulatory PLETHORA transcription factors induce division plane reorientation by local activation of auxin signaling, culminating in enhanced expression of the microtubule-associated MAP65 proteins. MAP65 upregulation is sufficient to reorient the cortical microtubular array through a CLASP microtubule-cell cortex interaction mediator-dependent mechanism. CLASP differentially localizes to cell faces in a microtubule- and MAP65-dependent manner. Computational simulations clarify how precise 90° switches in cell division planes can follow self-organizing properties of the microtubule array in combination with biases in CLASP localization. Our work demonstrates how transcription factor-mediated processes regulate the cellular machinery to control orientation of formative cell divisions in plants. PaperFlick:@en

The highly aligned cortical microtubule array of interphase plant cells is a key regulator of anisotropic cell expansion. Recent computational and analytical work has shown that the non-equilibrium self-organization of this structure can be understood on the basis of experimentally observed collisional interactions between dynamic microtubules attached to the plasma membrane. Most of these approaches assumed that new microtubules are homogeneously and isotropically nucleated on the cortical surface. Experimental evidence, however, shows that nucleation mostly occurs from other microtubules and under specific relative angles. Here, we investigate the impact of directed microtubule-bound nucleations on the alignment process using computer simulations. The results show that microtubule-bound nucleations can increase the degree of alignment achieved, decrease the timescale of the ordering process and widen the regime of dynamic parameters for which the system can self-organize. We establish that the major determinant of this effect is the degree of co-alignment of the nucleations with the parent microtubule. The specific role of sideways branching nucleations appears to allow stronger alignment while maintaining a measure of overall spatial homogeneity. Finally, we investigate the suggestion that observed persistent rotation of microtubule domains can be explained through a handedness bias in microtubule-bound nucleations, showing that this is possible only for an extreme bias and over a limited range of parameters.@en