Modeling the effects of lattice defects on microtubule breaking and healing

Microtubule Severing Enzymes Oligomerization and Allostery: A Tale of Two Domains

Severing proteins are nanomachines from the AAA+ (ATPases associated with various cellular activities) superfamily whose function is to remodel the largest cellular filaments, microtubules. The standard AAA+ machines adopt hexameric ring structures for functional reasons, while being primarily monomeric in the absence of the nucleotide. Both major severing proteins, katanin and spastin, are believed to follow this trend. However, studies proposed that they populate lower-order oligomers in the presence of cofactors, which are functionally relevant. Our simulations show that the preferred oligomeric assembly is dependent on the binding partners and on the type of severing protein. Essential dynamics analysis predicts that the stability of an oligomer is dependent on the strength of the interface between the helical bundle domain (HBD) of a monomer and the convex face of the nucleotide binding domain (NBD) of a neighboring monomer. Hot spots analysis found that the region consisting of the HBD tip and the C-terminal (CT) helix is the only common element between the allosteric networks responding to nucleotide, substrate, and intermonomer binding. Clustering analysis indicates the existence of multiple pathways for the transition between the secondary structure of the HBD tip in monomers and the structure(s) it adopts in oligomers.

The rate of microtubule breaking increases exponentially with curvature

Microtubules, cylindrical assemblies of tubulin proteins with a 25 nm diameter and micrometer lengths, are a central part of the cytoskeleton and also serve as building blocks for nanobiodevices. Microtubule breaking can result from the activity of severing enzymes and mechanical stress. Breaking can lead to a loss of structural integrity, or an increase in the numbers of microtubules. We observed breaking of taxol-stabilized microtubules in a gliding motility assay where microtubules are propelled by surface-adhered kinesin-1 motor proteins. We find that over 95% of all breaking events are associated with the strong bending following pinning events (where the leading tip of the microtubule becomes stuck). Furthermore, the breaking rate increased exponentially with increasing curvature. These observations are explained by a model accounting for the complex mechanochemistry of a microtubule. The presence of severing enzymes is not required to observe breaking at rates comparable to those measured previously in cells.

Exploring the Effect of Mechanical Anisotropy of Protein Structures in the Unfoldase Mechanism of AAA+ Molecular Machines

Essential cellular processes of microtubule disassembly and protein degradation, which span lengths from tens of μm to nm, are mediated by specialized molecular machines with similar hexameric structure and function. Our molecular simulations at atomistic and coarse-grained scales show that both the microtubule-severing protein spastin and the caseinolytic protease ClpY, accomplish spectacular unfolding of their diverse substrates, a microtubule lattice and dihydrofolate reductase (DHFR), by taking advantage of mechanical anisotropy in these proteins. Unfolding of wild-type DHFR requires disruption of mechanically strong β-sheet interfaces near each terminal, which yields branched pathways associated with unzipping along soft directions and shearing along strong directions. By contrast, unfolding of circular permutant DHFR variants involves single pathways due to softer mechanical interfaces near terminals, but translocation hindrance can arise from mechanical resistance of partially unfolded intermediates stabilized by β-sheets. For spastin, optimal severing action initiated by pulling on a tubulin subunit is achieved through specific orientation of the machine versus the substrate (microtubule lattice). Moreover, changes in the strength of the interactions between spastin and a microtubule filament, which can be driven by the tubulin code, lead to drastically different outcomes for the integrity of the hexameric structure of the machine.

Cargo Transport by Microtubule-Associated Motor Protein Along Mechanically Deformed Microtubules

Mechanical forces play pivotal roles in regulating various cellular functions. Biomolecular motor protein-driven intracellular transportation is one example which is affected by mechanical forces, although the mechanism at molecular level is unknown. In this chapter, we describe deformation of microtubules under compressive stress and we show that such deformation of microtubules affects the kinetics of dynein-driven cargo transportation along the microtubules. The extent of alteration in the kinetics of dynein-driven transportation is found strongly dependent on the extent of deformation of microtubules under compressive stress.

Modeling the Mechanical Response of Microtubule Lattices to Pressure

Microtubules, the largest and stiffest filaments of the cytoskeleton, have to be well adapted to the high levels of crowdedness in cells to perform their multitude of functions. Furthermore, fundamental processes that involve microtubules, such as the maintenance of the cellular shape and cellular motion, are known to be highly dependent on external pressure. In light of the importance of pressure for the functioning of microtubules, numerous studies interrogated the response of these cytoskeletal filaments to osmotic pressure, resulting from crowding by osmolytes, such as poly(ethylene glycol)/poly(ethylene oxide) (PEG/PEO) molecules, or to direct applied pressure. The interpretation of experiments is usually based on the assumptions that PEG molecules have unfavorable interactions with the microtubule lattices and that the behavior of microtubules under pressure can be described by using continuous models. We probed directly these two assumptions. First, we characterized the interaction between the main interfaces in a microtubule filament and PEG molecules of various sizes using a combination of docking and molecular dynamics simulations. Second, we studied the response of a microtubule filament to compression using a coarse-grained model that allows for the breaking of lattice interfaces. Our results show that medium length PEG molecules do not alter the energetics of the lateral interfaces in microtubules but rather target and can penetrate into the voids between tubulin monomers at these interfaces, which can lead to a rapid loss of lateral interfaces under pressure. Compression of a microtubule under conditions corresponding to high osmotic pressure results in the formation of the deformed phase found in experiments. Our simulations show that the breaking of lateral interfaces, rather than the buckling of the filament inferred from the continuous models, accounts for the deformation.

Biological cells and coupled electro-mechanical effects: The role of organelles, microtubules, and nonlocal contributions

Biological cells are exposed to a variety of mechanical loads throughout their life cycles that eventually play an important role in a wide range of cellular processes. The understanding of cell mechanics under the application of external stimuli is important for capturing the nuances of physiological and pathological events. Such critical knowledge will play an increasingly vital role in modern medical therapies such as tissue engineering and regenerative medicine, as well as in the development of new remedial treatments. At present, it is well known that the biological molecules exhibit piezoelectric properties that are of great interest for medical applications ranging from sensing to surgery. In the current study, a coupled electro-mechanical model of a biological cell has been developed to better understand the complex behaviour of biological cells subjected to piezoelectric and flexoelectric properties of their constituent organelles under the application of external forces. Importantly, a more accurate modelling paradigm has been presented to capture the nonlocal flexoelectric effect in addition to the linear piezoelectric effect based on the finite element method. Major cellular organelles considered in the developed computational model of the biological cell are the nucleus, mitochondria, microtubules, cell membrane and cytoplasm. The effects of variations in the applied forces on the intrinsic piezoelectric and flexoelectric contributions to the electro-elastic response have been systematically investigated along with accounting for the variation in the coupling coefficients. In addition, the effect of mechanical degradation of the cytoskeleton on the electro-elastic response has also been quantified. The present studies suggest that flexoelectricity could be a dominant electro-elastic coupling phenomenon, exhibiting electric fields that are four orders of magnitude higher than those generated by piezoelectric effects alone. Further, the output of the coupled electro-mechanical model is significantly dependent on the variation of flexoelectric coefficients. We have found that the mechanical degradation of the cytoskeleton results in the enhancement of both the piezo and flexoelectric responses associated with electro-mechanical coupling. In general, our study provides a framework for more accurate quantification of the mechanical/electrical transduction within the biological cells that can be critical for capturing the complex mechanisms at cellular length scales.

Mechanics of the Microtubule Seam Interface Probed by Molecular Simulations and in Vitro Severing Experiments

Microtubules (MTs) are structural components essential for cell morphology and organization. It has recently been shown that defects in the filament's lattice structure can be healed to create stronger filaments in a local area and ultimately cause global changes in MT organization and cell mobility. The ability to break, causing a defect, and heal appears to be a physiologically relevant and important feature of the MT structure. Defects can be created by MT severing enzymes and are target sites for complete severing or for healing by newly incorporated dimers. One particular lattice defect, the MT lattice ''seam" interface, is a location often speculated to be a weak site, a site of disassembly, or a target site for MT binding proteins. Despite seams existing in many MT structures, very little is known about the seam's role in MT function and dynamics. In this study, we probed the mechanical stability of the seam interface by applying coarse-grained indenting molecular dynamics. We found that the seam interface is as structurally robust as the typical lattice structure of MTs. Our results suggest that, unlike prior results that claim the seam is a weak site, it is just as strong as any other location on the MT, corroborating recent mechanical measurements.

Katanin catalyzes microtubule depolymerization independently of tubulin C-terminal tails

Microtubule network remodeling is an essential process for cell development, maintenance, cell division, and motility. Microtubule‐severing enzymes are key players in the remodeling of the microtubule network; however, there are still open questions about their fundamental biochemical and biophysical mechanisms. Here, we explored the ability of the microtubule‐severing enzyme katanin to depolymerize stabilized microtubules. Interestingly, we found that the tubulin C‐terminal tail (CTT), which is required for severing, is not required for katanin‐catalyzed depolymerization. We also found that the depolymerization of microtubules lacking the CTT does not require ATP or katanin's ATPase activity, although the ATP turnover enhanced depolymerization. We also observed that the depolymerization rate depended on the katanin concentration and was best described by a hyperbolic function. Finally, we demonstrate that katanin can bind to filaments that lack the CTT, contrary to previous reports. The results of our work indicate that microtubule depolymerization likely involves a mechanism in which binding, but not enzymatic activity, is required for tubulin dimer removal from the filament ends.

Microtubule self-healing and defect creation investigated by in-line force measurements during high-speed atomic force microscopy imaging

Microtubules are biopolymers composed of tubulin and play diverse roles in a wide variety of biological processes such as cell division, migration and intracellular transport in eukaryotic cells. To perform their functions, microtubules are mechanically stressed and, thereby, susceptible to structural defects. Local variations in mechanical properties caused by these defects modulate their biological functions, including binding and transportation of microtubule-associated proteins. Therefore, assessing the local mechanical properties of microtubules and analyzing their dynamic response to mechanical stimuli provide insight into fundamental processes. It is, however, not trivial to control defect formation, gather mechanical information at the same time, and subsequently image the result at a high temporal resolution at the molecular level with minimal delay. In this work, we describe the so-called in-line force curve mode based on high-speed atomic force microscopy. This method is directly applied to create defects in microtubules at the level of tubulin dimers and monitor the following dynamic processes around the defects. Furthermore, force curves obtained during defect formation provide quantitative mechanical information to estimate the bonding energy between tubulin dimers.

Damage and Failure of Axonal Microtubule under Extreme High Strain Rate: An In-Silico Molecular Dynamics Study

As a major cytoskeleton element of the axon, the breaking of microtubules (MTs) has been considered as a major cause of the axon degeneration. High strain rate loading is considered as one of the key factors in microtubule breaking. Due to the small size of microtubule, the real-time behavior of microtubule breaking is hard to capture. This study employs fully-atomistic molecular dynamics (MD) simulation to determine the failure modes of microtubule under different loadings conditions such as, unidirectional stretching, bending and hydrostatic expansion. For each loading conditions, MT is subjected to extreme high strain rate (108-109 s-1) loading. We argue that such level of high strain rate may be realized during cavitation bubble implosion. For each loading type, we have determined the critical energy for MT rupture. The associated rupture mechanisms are also discussed. We observed that the stretching has the lowest energy barrier to break the MT at the nanosecond time scale. Moreover, the breakage between the dimers starts at ~16% of total strain when stretched, which is much smaller compared to the reported strain-at-failure (50%) for lower strain rate loading. It suggests that MT fails at a significantly smaller strain states when loaded at higher strain rates.

Microtubules soften due to cross-sectional flattening

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.

Dynamics of microtubules: highlights of recent computational and experimental investigations

Microtubules are found in most eukaryotic cells, with homologs in eubacteria and archea, and they have functional roles in mitosis, cell motility, intracellular transport, and the maintenance of cell shape. Numerous efforts have been expended over the last two decades to characterize the interactions between microtubules and the wide variety of microtubule associated proteins that control their dynamic behavior in cells resulting in microtubules being assembled and disassembled where and when they are required by the cell. We present the main findings regarding microtubule polymerization and depolymerization and review recent work about the molecular motors that modulate microtubule dynamics by inducing either microtubule depolymerization or severing. We also discuss the main experimental and computational approaches used to quantify the thermodynamics and mechanics of microtubule filaments.

Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots

Biological systems have evolved to harness non-equilibrium processes from the molecular to the macro scale. It is currently a grand challenge of chemistry, materials science, and engineering to understand and mimic biological systems that have the ability to autonomously sense stimuli, process these inputs, and respond by performing mechanical work. New chemical systems are responding to the challenge and form the basis for future responsive, adaptive, and active materials. In this article, we describe a particular biochemical-biomechanical network based on the microtubule cytoskeletal filament - itself a non-equilibrium chemical system. We trace the non-equilibrium aspects of the system from molecules to networks and describe how the cell uses this system to perform active work in essential processes. Finally, we discuss how microtubule-based engineered systems can serve as testbeds for autonomous chemical robots composed of biological and synthetic components.