Theoretical Analysis of Microtubule Dynamics at All Times

Abstract

Microtubules are biopolymers consisting of tubulin dimer subunits. As a major component of cytoskeleton they are essential for supporting most important cellular processes such as cell division, signaling, intracellular transport and cell locomotion. The hydrolysis of guanosine triphosphate (GTP) molecules attached to each tubulin subunit supports the nonequilibrium nature of microtubule dynamics. One of the most spectacular properties of microtubules is their dynamic instability when their growth from continuous attachment of tubulin dimers stochastically alternates with periods of shrinking. Despite the critical importance of this process to all cellular activities, its mechanism remains not fully understood. We investigated theoretically microtubule dynamics at all times by analyzing explicitly temporal evolution of various length clusters of unhydrolyzed subunits. It is found that the dynamic behavior of microtubules depends strongly on initial conditions. Our theoretical findings provide a microscopic explanation for recent experiments which found that the frequency of catastrophes increases with the lifetime of microtubules. It is argued that most growing microtubule configurations cannot transit in one step into a shrinking state, leading to a complex overall temporal behavior.Theoretical calculations combined with Monte Carlo computer simulations are also directly compared with experimental observations, and the good agreement is found.

Polymerization kinetics of tubulin from mung seedlings modeled as a competition between nucleation and GTP‐hydrolysis rates

“…While our focus was on GTP hydrolysis and GTP‐cap size maintenance to trigger catastrophes, more recent modeling has demonstrated the emergence of a “stochastic cap” arising from modeling unbinding events between protofilaments (Margolin et al, 2012). Additionally, modeling microscopic details has been shown to be useful for predicting the effect of MT aging on increased catastrophe rates (Li & Kolomeisky, 2014). Thus, despite the limitations of this study, primarily the low concentration of the isolated protein and the presence of even lower concentrations of copurified proteins, our ability to assemble MTs from an unusual plant source provides an opportunity to examine the diversity of available tubulins to further refine our models.…”

Behaviors of individual microtubules and microtubule populations relative to critical concentrations: dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis

“…We utilized both the simplified and detailed computational models because each has particular strengths for addressing problems related to MT dynamics. The simplified model has fewer kinetic parameters, all of which are directly comparable to parameters in typical analytical models (i.e., mathematical equations), and it is similar to single-protofilament models that have been used by other authors (e.g., Padinhateeri et al, 2012;Li and Kolomeisky, 2014;Aparna et al, 2017). Thus, the simplified model is useful for testing analytical model predictions relating biochemical properties to individual filament level and bulk population level behaviors.…”

Regulation of Microtubule Growth and Catastrophe: Unifying Theory and Experiment

“…Even for the apparently simple case of a single protofilament, solving these models is difficult and requires sophisticated mathematical techniques. Recently two important cases, the vectorial and random hydrolysis models, were solved analytically, meaning that mathematical expressions could be derived that give the growth speed and catastrophe frequency in terms of the molecular rate constants [65–69] ( see Box 1 for further details). The expressions can then be readily compared to experimental data.…”