The mechanisms by which biological processes are effected by gravity are not understood. Theoreticians have proposed that gravitational effects could come about from the bifurcation properties of certain types of non-linear chemical reactions that self-organise by reaction and diffusion. We have found that in-vitro preparations of microtubules, an important element of the cellular skeleton, show this type of behaviour. They self-organise by reaction and diffusion and the morphology that arises depend upon the presence of gravity, at a critical moment or bifurcation time, early in the process. At a molecular level this behaviour results from an interaction of gravity with macroscopic concentration and density fluctuations created by microtubule contraction and elongation. Numerical simulations predict macroscopic self-organisation in qualitative agreement with experiment. It is plausible that microtubule organisation by these processes occurs in-vivo.