Slow diffusion underlies alternation of fast and slow growth periods of microtubule assembly

In vitro microtubule assembly exhibits a rhythmic phenomenon, that is, fast growth periods alternating with slow growth periods. Mechanism underlying this phenomenon is unknown. Here a simple diffusion mechanism coupled with small diffusion coefficients is proposed to underlie this phenomenon. Calculations based on previously published results demonstrate that such a mechanism can explain the differences in the average duration of the interval encompassing a fast growth period and a slow growth period in in vitro microtubule assembly experiments in different conditions. Because no parameter unique to the microtubule assembly process is involved in the analysis, the proposed mechanism is expected to be generally applicable to heterogeneous chemical reactions. Also because biological systems are characterized by heterogeneous chemical reactions, the diffusion-based rhythmic characteristic of heterogeneous reactions is postulated to be a fundamental element in generating rhythmic behaviors in biological systems.