Diffusion Approximation of the Stochastic Process of Microtubule Assembly

Abstract

Microtubules are protein polymers that guide intracellular motility. Stochastic switching of a microtubule between states of elongation, shortening, and pause is described in detail by the dynamic instability (DI) model. Recently we have described the dynamics of microtubules phenomenologically as generalized diffusion of their ends. Genesis of the diffusion dynamics and accuracy of diffusion model are studied in this work. It is shown that wandering of the end of a microtubule undergoing DI asymptotically approaches the Wiener diffusion process. Accuracy of the diffusion approximation is evaluated by comparing its predictions with results of simulation of DI. Stationary distributions of microtubule length and life-time that are predicted by both models differ qualitatively between two cell types considered. However, predictions of the diffusion model are in each case practically identical to predictions of the DI model being also consistent with experimental data. The peculiar stochastic process of microtubule assembly thus converges at cell scale to a kind of widespread-in-nature diffusion process. This result is considered an example of qualitative change in dynamical properties in transition from the molecular to cellular level of biological organization. Additionally, it suggests employment of diffusion process theory in studying functions of microtubules in the cell.

Insights into cytoskeletal behavior from computational modeling of dynamic microtubules in a cell-like environment

“…The observation that catastrophe frequency displays position dependence in vivo has been addressed previously: Komarova et al and Maly et al have suggested that the cell edge induces catastrophe in persistently growing MTs, causing the catastrophe asymmetry and resulting in the MT length distribution observed in vivo (Komarova et al, 2002b;Maly, 2002). Induction of catastrophe by physical boundaries has been observed experimentally (Janson et al, 2003).…”

“…leads to an alternative hypothesis for the origin of the persistent growth: (1) the cell boundary induces catastrophe prematurely (Komarova et al, 2002b;Maly, 2002); (2) Fig. 3A (Johnson and Borisy, 1977;Oosawa and Asakura, 1975;Oosawa and Kasai, 1962), see also Howard for a more recent discussion (Howard, 2001).…”

Regulation of microtubule dynamics in 3T3 fibroblasts by Rho family GTPases

“…However, to evaluate quantitatively the difference between MTs plus end behavior in the control cells and after inhibition of Cdc42 or Rac1 dynamic instability approach appeared to be inadequate. Thus, to quantify this effect we further used random walk approach [Vorobjev et al, 1997, which describes dynamic instability in the steady state conditions [Maly, 2002].…”

Comparative Autoregressive Moving Average Analysis of Kinetochore Microtubule Dynamics in Yeast

“…This conclusion does not purport that dynamic instability is an inappropriate model of S. cerevisiae kMT dynamics-it simply means that, within the context of dynamic instability models, the average and distributions of growth and shrinkage speeds and rescue and catastrophe frequencies are not sufficient, and additional parameters are needed to obtain a complete characterization of kMT dynamics. An alternative approach for the analysis of MT dynamics that requires the estimation of only a small number of parameters is diffusion analysis (9), or diffusion-with-drift analysis (32,33). In this model, an MT end is assumed to undergo a one-dimensional, possibly confined, random walk with drift.…”

“…However, diffusion-with-drift models are only asymptotically equivalent to dynamic instability models (32). They do not capture the details of MT behavior at a short timescale (32), which is precisely the scale at which changes in kMT dynamics due to kinetochore and MT-associated protein mutations occur (9). Therefore, diffusion analysis is inappropriate for our task.…”