Catastrophic depolymerization of microtubules driven by subunit shape change

Building blocks of non-Euclidean ribbons: size-controlled self-assembly via discrete frustrated particles

Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current challenge is to understand the connection between microscopic physical properties of misfitting "building blocks" and emergent assembly behavior at the mesoscale. We present and analyze a particle-based description of what is arguably the best studied example for frustrated soft matter assembly, negative-curvature ribbon assembly, observed in both assemblies of chiral surfactants and shape-frustrated nanoparticles. Based on our particle model, known as saddle wedge monomers, we numerically test the connection between microscopic shape and interactions of the misfitting subunits and the emergent behavior at the supra-particle scale, specifically focussing on the propagation and relaxation of inter-particle strains, the emergent role of extrinsic shape on frustrated ribbons and the equilibrium regime of finite width selection. Beyond the intuitive role of shape misfit, we show that self-limitation is critically dependent on the finite range of cohesive interactions, with larger size finite assemblies requiring increasing short-range interparticle forces. Additionally, we demonstrate that non-linearities arising from discrete particle interactions alter self-limiting behavior due to both strain-softening in shape-flattened assembly and partial yielding of highly strained bonds, which in turn may give rise to states of hierarchical, multidomain assembly. Tracing the regimes of frustration-limited assembly to the specific microscopic features of misfitting particle shapes and interactions provides necessary guidance for translating the theory of size-programmable assembly into design of intentionally-frustrated colloidal particles.

Polymorphic self-assembly of helical tubules is kinetically controlled

In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger than the size scale of the individual monomers. In many such cases, the finite dimension is selected by a preferred curvature of the monomers, which leads to self-closure of the assembly. In this article, we study an example class of self-closing assemblies: cylindrical tubules that assemble from triangular monomers. By combining kinetic Monte Carlo simulations, free energy calculations, and simple theoretical models, we show that a range of programmable size scales can be targeted by controlling the intricate balance between the preferred curvature of the monomers and their interaction strengths. However, their assembly is kinetically controlled-the tubule morphology is essentially fixed shortly after closure, resulting in a distribution of tubule widths that is significantly broader than the equilibrium distribution. We develop a simple kinetic model based on this observation and the underlying free-energy landscape of assembling tubules that quantitatively describes the distributions. Our results are consistent with recent experimental observations of tubule assembly from triangular DNA origami monomers. The modeling framework elucidates design principles for assembling self-limited structures from synthetic components, such as artificial microtubules that have a desired width and chirality.

XMAP215 promotes microtubule catastrophe by disrupting the growing microtubule end

The GTP-tubulin cap is widely accepted to protect microtubules against catastrophe. The GTP-cap size is thought to increase with the microtubule growth rate, presumably endowing fast-growing microtubules with enhanced stability. It is unknown what GTP-cap properties permit frequent microtubule catastrophe despite fast growth. Here, we investigate microtubules growing in the presence and absence of the polymerase XMAP215. Using EB1 as a GTP-cap marker, we find that GTP-cap size increases regardless of whether growth acceleration is achieved by increasing tubulin concentration or by XMAP215. Despite increased mean GTP-cap size, microtubules grown with XMAP215 display increased catastrophe frequency, in contrast to microtubules grown with more tubulin, for which catastrophe is abolished. However, microtubules polymerized with XMAP215 have large fluctuations in growth rate; display tapered and curled ends; and undergo catastrophe at faster growth rates and with higher EB1 end-localization. Our results suggest that structural perturbations induced by XMAP215 override the protective effects of the GTP-cap, ultimately driving microtubule catastrophe.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

Tubulin islands containing slowly hydrolyzable GTP analogs regulate the mechanism and kinetics of microtubule depolymerization

Dynamic instability of microtubules is characterized by stochastically alternating phases of growth and shrinkage and is hypothesized to be controlled by the conformation and nucleotide state of tubulin dimers within the microtubule lattice. Specifically, conformation changes (compression) in the tubulin dimer following the hydrolysis of GTP have been suggested to generate stress and drive depolymerization. In the present study, molecular dynamics simulations were used in tandem with in vitro experiments to investigate changes in depolymerization based on the presence of islands of uncompressed (GMPCPP) dimers in the microtubule lattice. Both methods revealed an exponential decay in the kinetic rate of depolymerization corresponding to the relative level of uncompressed (GMPCPP) dimers, beginning at approximately 20% incorporation. This slowdown was accompanied by a distinct morphological change from unpeeling "ram's horns" to blunt-ended dissociation at the microtubule end. Collectively these data demonstrated that islands of uncompressed dimers can alter the mechanism and kinetics of depolymerization in a manner consistent with promoting rescue events.

Diverse balances of tubulin interactions and shape change drive and interrupt microtubule depolymerization

Microtubules are stiff biopolymers that self-assemble via the addition of GTP-tubulin (αβ-dimer bound to GTP), but hydrolysis of GTP- to GDP-tubulin within the tubules destabilizes them toward catastrophically-fast depolymerization. The molecular mechanisms and features of the individual tubulin proteins that drive such behavior are still not well-understood. Using molecular dynamics simulations of whole microtubules built from a coarse-grained model of tubulin, we demonstrate how conformational shape changes (i.e., deformations) in subunits that frustrate tubulin-tubulin binding within microtubules drive depolymerization of stiff tubules via unpeeling "ram's horns" consistent with experiments. We calculate the sensitivity of these behaviors to the length scales and strengths of binding attractions and varying degrees of binding frustration driven by subunit shape change, and demonstrate that the dynamic instability and mechanical properties of microtubules can be produced based on either balanced or imbalanced strengths of lateral and vertical binding attractions. Finally, we show how catastrophic depolymerization can be interrupted by small regions of the microtubule containing undeformed dimers, corresponding to incomplete lattice hydrolysis. The results demonstrate a mechanism by which microtubule rescue can occur.

Inhibition of Microtubule Depolymerization by Osmolytes

Microtubule dynamics play a critical role in the normal physiology of eukaryotic cells as well as a number of cancers and neurodegenerative disorders. The polymerization/depolymerization of microtubules is regulated by a variety of stabilizing and destabilizing factors, including microtubule-associated proteins and therapeutic agents (e.g., paclitaxel, nocodazole). Here we describe the ability of the osmolytes polyethylene glycol (PEG) and trimethylamine- N-oxide (TMAO) to inhibit the depolymerization of individual microtubule filaments for extended periods of time (up to 30 days). We further show that PEG stabilizes microtubules against both temperature- and calcium-induced depolymerization. Our results collectively suggest that the observed inhibition may be related to combination of the kosmotropic behavior and excluded volume/osmotic pressure effects associated with PEG and TMAO. Taken together with prior studies, our data suggest that the physiochemical properties of the local environment can regulate microtubule depolymerization and may potentially play an important role in in vivo microtubule dynamics.