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.