MICROTUBULE DYNAMICS .2. KINETICS OF SELF-ASSEMBLY

Inverse scattering theory describes the conditions necessary and suffi cient to determine an unknown potential from known scattering data. No similar theory exists for when and how one may deduce the kinetics of an unknown chemical reaction from quantitative information about its final state and its dependence on initial conditions-except it is know n to be impossible for equilibrium reactions. This article presents a case study of a far-from-equilibrium reaction: it presents a systemati c phenomenological analysis of experimental time series for the amount of final product, a biopolymer, formed from various initial concentra tions of monomers. Distinct mathematical properties of the kinetics of the unknown reaction pathway are found. These properties are shown to restrict the kinetics to a single model that generalizes Oosawa's cla ssical nucleation-polymerization model. The methods used here to analy ze the self-assembly of microtubules from tubulin are general, and man y other reactions and processes may be studied as inverse problems wit h these methods when enough experimental data are available.