Prolonging assembly through dissociation: A self-assembly paradigm in microtubules

Sumedha, Michael F. Hagan, and Bulbul Chakraborty

Phys. Rev. E 83, 051904 – Published 3 May 2011

Abstract

We study a one-dimensional model of microtubule assembly and disassembly in which GTP bound to tubulins within the microtubule undergoes stochastic hydrolysis. In contrast to models that consider only a cap of GTP-bound tubulin, stochastic hydrolysis allows GTP-bound tubulin remnants to exist within the microtubule. We find that these buried GTP remnants enable an alternative mechanism of recovery from shrinkage and enhances fluctuations of filament lengths. Under conditions for which this alternative mechanism dominates, an increasing depolymerization rate leads to a decrease in dissociation rate and thus a net increase in assembly.

Received 19 August 2009

DOI:https://doi.org/10.1103/PhysRevE.83.051904

Authors & Affiliations

Sumedha, Michael F. Hagan, and Bulbul Chakraborty

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454,USA

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Vol. 83, Iss. 5 — May 2011

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Images

Figure 1
Schematic of microtubule dynamics. We assume that all the activity occurs at the right end (denoted by $>$ ) of the MT.Reuse & Permissions
Figure 2
(a) The average time at which the number of GTP-bound subunits goes to zero ( $< t_{N} >$ ) as a function of $\ln μ$ . The inset shows a scaling collapse of the plots, with $y$ axis scaled by $e^{λ} / λ$ and the $x$ axis displaced by $λ$ , for $λ = 8$ , 10, 12. (b) The average growth velocity $(v = < L (t_{N}) > / < t_{N} >)$ for indicated values of $λ$ as a function of $\ln μ$ . In the inset we have scaled $v$ for $λ = 3$ , 5, 8, 10, 12, and $μ > 1$ , by $(λ - 1)$ to illustrate the scaling collapse implied by Eq. (6) for different values of $λ$ . We find the scaled values lie on the $μ / (1 + μ)$ curve. The scaling holds for $λ ⩾ 8$ , with data for $λ = 5$ , showing deviations at small values of $μ$ .Reuse & Permissions
Figure 3
Average probability distribution of size of disassembly events for $λ = 5$ on a semilog plot. Average is calculated by looking at all the disassembly events except the final complete disassembly. Inset shows the same distribution for $λ = 5$ and $μ = 5$ when the average is done over time $t = 0.08 t_{N} (+)$ , $0.2 t_{N} (\times)$ , $0.4 t_{N} (*)$ , and $t_{N} (□)$ .Reuse & Permissions
Figure 4
(a)–(c) The distributions of times at which the amount of GTP in the MT goes to zero $(t_{N})$ . The distribution shifts to the right with increasing $μ$ until it saturates. (d) The distribution of maximum lengths for $λ = 5$ . The distributions of maximum lengths and $t_{N}$ have similar dependencies on $μ$ .Reuse & Permissions
Figure 5
(a) Comparison of excursions ( $δ l$ ) predicted by the GTP remnants model ( $⊡$ ) with $λ = 12 p = 0, μ = 0.1$ , and experimental measurements ( $+$ ) [6] ( $δ l$ is measured in nm in the experiment). (b) The distribution of excursions with $λ = 12$ ; $p = 0$ for $μ = 0.1, 0.5$ , and $1$ . While growth excursions have the distribution $\exp (- δ l / λ) / λ$ , the distribution of shortening excursions changes from being exponential to nonexponential and broader distributions with increasing $μ$ .Reuse & Permissions
Figure 6
MT length $L (t)$ (solid lines) as a function of time for $λ = 5, μ = 4$ , and $p = 0$ (a), $p = 0.01$ (b). The dotted lines show the total amount of GTP(T(t)) as a function of time for the same runs. Arrows in the second plot indicate the $-$ attachment events due to $p > 0$ . The inset shows MT length $L (t)$ for $λ = 12$ , $μ = 0.1$ , and $p = 0.0007$ . This trajectory looks qualitatively similar to the ones observed experimentally, and these growth-phase fluctuations are different from the rapid shrinkage and slow growth observed in catastrophes and rescues [6].Reuse & Permissions

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