Nicolas Glade

Microtubule self-organisation and its gravity dependence.

The molecular processes by which gravity affects biological systems are poorly, if at all, understood. Under equilibrium conditions, chemical and biochemical reactions do not depend upon gravity. It has been proposed that biological systems might depend on gravity by way of the bifurcation properties of certain types of non-linear chemical reactions that are far-from-equilibrium. In such reactions, the initially homogenous solution spontaneously self-organises by way of a combination of reaction and diffusion. Theoreticians have predicted that the presence or absence of an external field, such as gravity, at a critical moment early in the self-organising process may determine the morphology that subsequently develops. We have found that the formation in vitro of microtubules, a major element of the cellular skeleton, shows this type of behaviour. The microtubule preparations spontaneously self-organise by way of reaction and diffusion, and the morphology of the state that forms depends upon gravity at a critical bifurcation time early in the process. Experiments carried out under low gravity conditions show that the presence of gravity at the bifurcation time actually triggers the self-organising process. This is an experimental demonstration of how a very simple biochemical system, containing only two molecules, can be gravity sensitive. At a microscopic level the behaviour results from an interaction of gravity with the concentration and density fluctuations that arise from processes of microtubule shortening and elongation. We have developed a numerical reaction-diffusion scheme, based on the chemical dynamics of a population of microtubules, that simulate self-organisation. These simulations provide insight into how self-organisation occurs at a microscopic level and how gravity triggers this process. Recent experiments on cell lines cultured in space suggest that microtubule organisation may not occur properly under low gravity conditions. As microtubule organisation is essential to cellular function, it is quite plausible that the type of processes described in this article provide an underlying explanation for the gravity dependence of living systems at a cellular level.

Numerical Simulations of Microtubule Self-Organisation by Reaction and Diffusion

This article addresses the physical chemical processes underlying biological self-organisation by which a homogenous solution of reacting chemicals spontaneously self-organises. Theoreticians have predicted that self-organisation can arise from a coupling of reactive processes with molecular diffusion. In addition, the presence of an external field, such as gravity, at a critical moment early in the process may determine the morphology that subsequently develops. The formation, in-vitro, of microtubules, a constituent of the cellular skeleton, shows this type of behaviour. The preparations spontaneously self-organise by reaction-diffusion and the morphology that develops depends upon the presence of gravity at a critical bifurcation time early in the process. Here, we present numerical simulations of a population of microtubules that reproduce this behaviour. Microtubules can grow from one end whilst shrinking from the other. The shrinking end leaves behind a chemical trail of high tubulin concentration. Neighbouring microtubules preferentially grow into these regions, whilst avoiding regions of low tubulin concentration. The chemical trails produced by individual microtubules thus activate and inhibit the formation of neighbouring microtubules and this progressively leads to self-organisation. Gravity acts by way of its directional interaction with the macroscopic density fluctuations present in the solution arising from microtubule disassembly.

Comparison of reaction–diffusion simulations with experiment in self-organised microtubule solutions

This article deals with the physical chemical processes underlying biological self-organization by which an initially homogenous solution of reacting chemicals spontaneously self-organizes so as to give rise to a preparation of macroscopic order and form. Theoreticians have predicted that self-organization can arise from a coupling of reactive processes with molecular diffusion. In addition, the presence or absence of an external field, such as gravity, at a critical moment early in the self-organizing process may determine the morphology that subsequently develops. We have found that the formation in vitro of microtubules, a major element of the cellular skeleton, show this type of behaviour. The microtubule preparations spontaneously self-organise by way of reaction and diffusion, and the morphology of the state that forms depends on the presence of gravity at a critical moment early in the process. We have developed a numerical reaction-diffusion scheme, based on the chemical dynamics of a population of microtubules, which simulates the experimental self-organisation. In this article we outline the main features of these simulations and discuss the manner by which a permanent dialogue with experiment has helped develop a microscopic understanding of the collective behaviour.