Mechanochemical modeling of dynamic microtubule growth involving sheet-to-tube transition

Microtubule dynamics is largely influenced by nucleotide hydrolysis and the resultant tubulin configuration changes. The GTP cap model has been proposed to interpret the stabilizing mechanism of microtubule growth from the view of hydrolysis effects. Besides, the microtubule growth involves the closure of a curved sheet at its growing end. The curvature conversion also helps to stabilize the successive growth, and the curved sheet is referred to as the conformational cap. However, there still lacks theoretical investigation on the mechanical-chemical coupling growth process of microtubules. In this paper, we study the growth mechanisms of microtubules by using a coarse-grained molecular method. Firstly, the closure process involving a sheet-to-tube transition is simulated. The results verify the stabilizing effect of the sheet structure, and the minimum conformational cap length that can stabilize the growth is demonstrated to be two dimers. Then, we show that the conformational cap can function independently of the GTP cap, signifying the pivotal role of mechanical factors. Furthermore, based on our theoretical results, we describe a Tetris-like growth style of microtubules: the stochastic tubulin assembly is regulated by energy and harmonized with the seam zipping such that the sheet keeps a practically constant length during growth.

💡 Research Summary

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This paper presents a novel coarse‑grained molecular model that simultaneously captures the chemical effects of GTP hydrolysis and the mechanical effects of the curved sheet at the growing end of a microtubule. The authors construct a “70‑interaction” potential framework in which each interaction is decomposed into elastic terms (stretch, shear, twist) and binding free‑energy terms (longitudinal, lateral, and inter‑protofilament bonds). Parameter values are expressed in units of kBT per dimer (e.g., G_long = ‑19 kBT/dimer, G_lat = ‑4 kBT/dimer, S = 11 kBT/dimer) and calibrated against both atomistic simulations and experimental measurements.

The simulation proceeds through three mechanochemical events: (1) stochastic addition of tubulin dimers to the tip, governed by Boltzmann‑weighted association rates; (2) formation of a curved sheet composed of newly added dimers, which incurs a substantial elastic penalty; and (3) sheet‑to‑tube transition, during which the curvature relaxes, releasing elastic energy and stabilizing the structure. By explicitly tracking the total potential energy, the authors identify a critical “conformational cap” length of two dimers (four tubulin subunits). When the sheet shortens below this threshold, the energy barrier for closure collapses, the sheet snaps shut, and the microtubule enters a shrinking phase.

A key finding is that the conformational cap can function independently of the GTP cap. Simulations in which all bound tubulins remain GTP‑loaded still exhibit stable growth as long as the sheet exceeds the two‑dimer minimum. Conversely, a GTP‑only cap without a sufficient sheet fails to prevent rapid depolymerization. This decouples the mechanical stabilization provided by the sheet from the chemical stabilization traditionally ascribed to the GTP cap.

Building on these observations, the authors propose a “Tetris‑like” growth mechanism. Random tubulin addition tends to increase sheet length, while simultaneous seam zipping (sheet closure) reduces it, resulting in a statistically constant sheet length during steady‑state growth. The balance is maintained by the interplay between binding free energy (which drives addition) and elastic energy (which drives closure). This dynamic equilibrium explains how microtubules can sustain high growth rates without sacrificing structural integrity.

Model validation is performed by comparing simulated sheet curvature, inter‑protofilament angles (≈5°–10°), and sheet‑length distributions with cryo‑EM data from previous studies (e.g., Nogales et al., 2009; Noga et al., 2010). The agreement supports the physical realism of the coarse‑grained approach. Moreover, the authors decompose the total energy into chemical and mechanical components for each event, demonstrating that the mechanical contribution dominates the barrier to sheet closure, while GTP hydrolysis primarily modulates the longitudinal bond strength.

In summary, this work introduces a quantitative mechanochemical framework that unifies the GTP‑cap and conformational‑cap concepts, identifies a minimal sheet length required for stability, and elucidates a self‑regulating “Tetris” growth mode. The model offers a powerful tool for exploring microtubule dynamics in vivo, for designing drugs that target specific mechanical or chemical steps, and for guiding the engineering of synthetic tubulin‑based nanostructures.