A New Theoretical Approach to Analyze Complex Processes in Cytoskeleton Proteins

Association-dissociation process with aging subunits: Recursive solution

The coupling of stochastic growth and shrinkage of one-dimensional structures to random aging of the constituting subunits defines the simple association-dissociation-aging process which captures the essential features of the nonequilibrium assembly of cytoskeletal filaments. Because of correlations, previously employed mean-field methods fail to correctly describe filament growth. We study an alternative formulation of the full master equation of the stochastic process. An ansatz for the steady-state solution leads to a recursion relation which allows for the calculation of all emergent quantities with increasing accuracy and in excellent agreement with stochastic simulations.

Theoretical analysis of microtubule dynamics at all times

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 good agreement is found.