On the Nature and Shape of Tubulin Trails: Implications on Microtubule Self-Organization

Abstract

Microtubules, major elements of the cell skeleton are, most of the time, well organized in vivo, but they can also show self-organizing behaviors in time and/or space in purified solutions in vitro. Theoretical studies and models based on the concepts of collective dynamics in complex systems, reaction-diffusion processes and emergent phenomena were proposed to explain some of these behaviors. In the particular case of microtubule spatial self-organization, it has been advanced that microtubules could behave like ants, self-organizing by 'talking to each other' by way of hypothetic (because never observed) concentrated chemical trails of tubulin that are expected to be released by their disassembling ends. Deterministic models based on this idea yielded indeed like-looking spatio-temporal self-organizing behaviors. Nevertheless the question remains of whether microscopic tubulin trails produced by individual or bundles of several microtubules are intense enough to allow microtubule self-organization at a macroscopic level. In the present work, by simulating the diffusion of tubulin in microtubule solutions at the microscopic scale, we measure the shape and intensity of tubulin trails and discuss about the assumption of microtubule self-organization due to the production of chemical trails by disassembling microtubules. We show that the tubulin trails produced by individual microtubules or small microtubule arrays are very weak and not elongated even at very high reactive rates. Although the variations of concentration due to such trails are not significant compared to natural fluctuations of the concentration of tubuline in the chemical environment, the study shows that heterogeneities of biochemical composition can form due to microtubule disassembly. They could become significant when produced by numerous microtubule ends located in the same place. Their possible formation could play a role in certain conditions of reaction. In particular, it gives a mesoscopic basis to explain the collective dynamics observed in excitable microtubule solutions showing the propagation of concentration waves of microtubules at the millimeter scale, although we doubt that individual microtubules or bundles can behave like molecular ants.

Microtubule nucleation complex behavior is critical for cortical array homogeneity and xylem wall patterning

“…Most importantly, the tubulin concentration also influences the nucleation rate (48,49). However, GTP-tubulin profiles (52) are so flat for realistic tubulin diffusion coefficients that we do not expect a large impact from including such aspects. Furthermore, cytoplasmic streaming is likely to result in a greater effective diffusion coefficient for tubulin in plants compared to the available measurements from animal cells (58), making it even less likely that local tubulin depletion can effectively ensure homogeneity.…”

“…Therefore, our first hypothesis is that local tubulin depletion could serve only as a homogenizing factor if the GDP–tubulin state is sufficiently long lived. The question remains whether this effect would be strong enough as simulations on small numbers of microtubules suggest that tubulin diffusion is so fast that local depletion has a very limited effect on concentration ( 52 ).…”