Biological Self-Organization by Way of Microtubule Reaction−Diffusion Processes

Abstract

This article addresses the physical chemical processes underlying biological self-organization by which a homogeneous solution of reacting chemicals spontaneously self-organizes. Theoreticians have predicted that self-organization 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 behavior. Preparations spontaneously self-organize by reaction−diffusion, and the morphology that develops depends on the presence of gravity at a critical bifurcation time early in the process. Numerical simulations of a population of microtubules involving only reactive and diffusive terms reproduce this behavior. Microtubules can grow from one end while shrinking from the other. The shrinking end leaves behind itself a chemical trail of high tubulin concentration. Neighboring microtubules preferentially grow into these regions, while avoiding regions of low concentration. The chemical trails produced by individual microtubules thus activate and inhibit the formation of their neighbors, and this progressively leads to self-organization. Gravity acts by way of its directional interaction with the macroscopic density fluctuations present in the solution arising from microtubule disassembly. Evidence is presented that similar processes might occur both during the cell cycle and the early stages of Drosophila fruit fly embryogenesis.