Polymerization of Actin and Actin-like Systems: Evaluation of the Time Course of Polymerization in Relation to the Mechanism

The time course of protein polymerization of the nucleation-elongation type is examined by using a general computer-simulation solution. For a simple nucleation-elongation scheme, it is shown that the half-time of polymerization is not necessarily a good measure of the nucleus size as has been previously suggested [Oosawa, F., & Kasai, M. (1962) J. Mol. Biol. 4, 10–21] since, depending on the mechanism, the apparent nucleus size, measured by a ratio of half-times at two actin concentrations, may be either larger or smaller than the real size. Steady-state equations developed by Wegner and Engel [Wegner, A., & Engel, J. (1975) Biophys. Chem. 3, 215–225] present a good description of the time course of polymerization although they are somewhat inflexible with regard to allowing for different mechanisms. Some of the assumptions implicit in the development of these equations are discussed in terms of the effect of changing individual rate constants or dissociation constants on the time course of polymerization. In addition, these steady-state equations have been expanded to include the consequences of a reversible first-order conformational change prior to polymerization. It is shown that a conformational change as a prerequisite to polymerization lengthens the lag time of polymerization and, depending on the conditions, may slow the rate of polymerization. The question of fragmentation and of reannealling is examined, and it is noted that simple relationships to describe these processes may not be possible. It is also shown that studies of the mechanism of polymerization require that a wide range of protein concentrations be used since data over a 2-fold concentration range can easily be fit by at least two different mechanisms. Experimental data for the polymerization of actin which demonstrate some of these points are given.