Theoretical Analysis of Microtubules Dynamics Using a Physical–Chemical Description of Hydrolysis

2015

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Microtubules and actin filaments are biopolymer molecules that are major components of cytoskeleton networks in biological cells. They play important roles in supporting fundamental cellular processes such as cell division, signaling, locomotion, and intracellular transport. In cells, cytoskeleton proteins function under nonequilibrium conditions that are powered by hydrolysis of adenosine triphosphate (ATP) or guanosine triphosphate (GTP) molecules attached to them. Although these biopolymers are critically important for all cellular processes, the mechanisms that govern their complex dynamics and force generation remain not well explained. One of the most difficult fundamental issues is to understand how different components of cytoskeleton proteins interact together. We develop an approximate theoretical approach for analyzing complex processes in cytoskeleton proteins that takes into account the multifilament structure, lateral interactions between parallel protofilaments, and the most relevant biochemical transitions during the biopolymer growth. It allows us to fully evaluate collective dynamic properties of cytoskeleton filaments as well as the effect of external forces on them. It is found that for the case of strong lateral interactions the stall force of the multifilament protein is a linear function of the number of protofilaments. However, for weak lateral interactions, deviations from the linearity are observed. We also show that stall forces, mean velocities, and dispersions are increasing functions of the lateral interactions. Physical−chemical explanations of these phenomena are presented. Our theoretical predictions are supported by extensive Monte Carlo computer simulations.

Section: ■ Introductionmentioning

confidence: 99%

The Role of Multifilament Structures and Lateral Interactions in Dynamics of Cytoskeleton Proteins and Assemblies

2015

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“…1. 15,21 The hydrolysis mechanism for the cytoskeleton filament is still under discussion, [21][22][23][24][25][26][27][28][29][30] and we assume here that all T-subunits on microtubules can be hydrolyzed with the same rate r as indicated in Fig.1. The hydrolyzed D-subunits can detach from the "plus" end of the microtubules with a rate W D (see Fig.…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…2,3,8,11,12 Another issue is that even more detailed theoretical investigations concentrate mostly on stationarystate behavior of the system. [13][14][15][16] In other words, dynamic properties of microtubules are assumed to be stationary and independent of the time. However, these theoretical views have been challenged recently by high-resolution measurements of filament length and lifetime distributions.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of Microtubule Dynamics at All Times

2014

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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.

“…14,15 However, our understanding of underlying mechanisms of these processes is still limited. In recent years, several theoretical approaches have been proposed and applied to explain these fascinating phenomena, 13,16−21 but none of them is able to fully describe them.…”

Section: ■ Introductionmentioning

confidence: 99%

“…13,17,20 It gives a reasonable description of many features in actin filaments and microtubules, especially at high concentrations of free actin and tubulin monomers in the solution. However, current methods do not work well at biologically relevant conditions which correspond to small and intermediate concentrations near the critical concentration.…”

Section: ■ Introductionmentioning

confidence: 99%

A New Theoretical Approach to Analyze Complex Processes in Cytoskeleton Proteins

2014

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Cytoskeleton proteins are filament structures that support a large number of important biological processes. These dynamic biopolymers exist in nonequilibrium conditions stimulated by hydrolysis chemical reactions in their monomers. Current theoretical methods provide a comprehensive picture of biochemical and biophysical processes in cytoskeleton proteins. However, the description is only qualitative under biologically relevant conditions because utilized theoretical mean-field models neglect correlations. We develop a new theoretical method to describe dynamic processes in cytoskeleton proteins that takes into account spatial correlations in the chemical composition of these biopolymers. Our approach is based on analysis of probabilities of different clusters of subunits. It allows us to obtain exact analytical expressions for a variety of dynamic properties of cytoskeleton filaments. By comparing theoretical predictions with Monte Carlo computer simulations, it is shown that our method provides a fully quantitative description of complex dynamic phenomena in cytoskeleton proteins under all conditions.