Measuring and modeling forces generated by microtubules.

Tubulins are essential proteins, which are conserved across all eukaryotic species. They polymerize to form microtubules, cytoskeletal components of paramount importance for cellular mechanics. The microtubules combine an extraordinarily high flexural rigidity and a non-equilibrium behavior, manifested in their intermittent assembly and disassembly. These chemically fueled dynamics allow microtubules to generate significant pushing and pulling forces at their ends to reposition intracellular organelles, remodel membranes, bear compressive forces, and transport chromosomes during cell division. In this article, we review classical and recent studies, which have allowed the quantification of microtubule-generated forces. The measurements, to which we owe most of the quantitative information about microtubule forces, were carried out in biochemically reconstituted systems in vitro. We also discuss how mathematical and computational modeling has contributed to the interpretations of these results and shaped our understanding of the mechanisms of force production by tubulin polymerization and depolymerization.

VII Congress of Russian Biophysicists-2023, Krasnodar, Russia.

This special issue of Biophysical Reviews contains the materials presented at the VII Congress of Biophysicists of Russia, held from 17 to 23 April in Krasnodar. We believe that we have managed to prepare a selection of articles that well reflects the current state of biophysical science in Russia and its place in the world science. The VII Russian Congress on Biophysics was held in Krasnodar in April 2023, continuing the tradition of the series of biophysics conferences held every 4 years. The congress discussed physical principles and mechanisms of biological processes occurring at different life levels-from molecular to cellular and population levels. The results of fundamental and applied research in molecular biophysics, cell biophysics, and biophysics of complex systems were presented at plenary, sectional, and poster sessions. The works in the field of medical biophysics and neurobiology were especially widely presented. The structure and dynamics of biopolymers and fundamental mechanisms underlying the effects of physicochemical factors on biological systems, membrane, and transport processes were actively discussed. Much attention was paid to new experimental methods of biophysical research, methods of bioinformatics, computer, and mathematical modeling as necessary tools of the research at all levels of living systems. Along with fundamental problems of studying biophysical mechanisms of regulation of processes at the molecular, subcellular, and cellular levels, much attention was paid to applied research in the field of biotechnology and environmental monitoring. The Congress has formed the National Committee of Russian biophysicists.

Microtubule rescue control by drugs and MAPs examined with in vitro pedestal assay.

Microtubules are essential cytoskeletal polymers, which exhibit stochastic transitions between assembly and disassembly, known as catastrophes and rescues. Understanding of catastrophes, rescues, and their control by drugs and microtubule associated proteins (MAPs) has been informed by in vitro reconstitutions of microtubule dynamics. In such experiments microtubules are typically observed on a flat surface of the coverslip. In contrast, we have recently proposed a modified setup in which microtubules assemble from stabilized seeds, overhanging from microfabricated pedestals, so that their dynamic extensions are fully isolated from contact with the coverslip. This assay allows to eliminate potential artifacts, which may substantially affect the frequency of microtubule rescues in vitro. Here we use the pedestal assay to study the sensitivity of microtubules to paclitaxel, one of the best-known inhibitors of microtubule dynamics. By comparing observations in the conventional and the pedestal assays, we find that microtubule dynamics are substantially more sensitive to paclitaxel when the polymers can contact the coverslip. We interpret this as a consequence of the coverslip-induced microtubule assembly perturbation, leading to formation of lattice with defects, and thereby enhancing the efficiency of paclitaxel binding to microtubules in the conventional assay. To test this idea, we use vinblastine, another small-molecule inhibitor, which had been previously shown to cause microtubule growth perturbations. We find that in the pedestal assay vinblastine sensitizes microtubules to paclitaxel to the level, observed in the conventional assay. Interestingly, a minimal fragment of MAP called CLASP2, a previously characterized rescue factor, has a strong effect on microtubule rescues, regardless of the type of assay. Overall, our study underscores the role of microtubule damage in promoting rescues and highlights the utility of the in vitro pedestal assay to study microtubule dynamics modulation by tubulin inhibitors and MAPs.

Theory of tip structure-dependent microtubule catastrophes and damage-induced microtubule rescues.

Microtubules are essential cytoskeletal polymers that exhibit stochastic switches between tubulin assembly and disassembly. Here, we examine possible mechanisms for these switches, called catastrophes and rescues. We formulate a four-state Monte Carlo model, explicitly considering two biochemical and two conformational states of tubulin, based on a recently conceived view of microtubule assembly with flared ends. The model predicts that high activation energy barriers for lateral tubulin interactions can cause lagging of curled protofilaments, leading to a ragged appearance of the growing tip. Changes in the extent of tip raggedness explain some important but poorly understood features of microtubule catastrophe: weak dependence on tubulin concentration and an increase in its probability over time, known as aging. The model predicts a vanishingly rare frequency of spontaneous rescue unless patches of guanosine triphosphate tubulin are artificially embedded into microtubule lattice. To test our model, we used in vitro reconstitution, designed to minimize artifacts induced by microtubule interaction with nearby surfaces. Microtubules were assembled from seeds overhanging from microfabricated pedestals and thus well separated from the coverslip. This geometry reduced the rescue frequency and the incorporation of tubulins into the microtubule shaft compared with the conventional assay, producing data consistent with the model. Moreover, the rescue positions of microtubules nucleated from coverslip-immobilized seeds displayed a nonexponential distribution, confirming that coverslips can affect microtubule dynamics. Overall, our study establishes a unified theory accounting for microtubule assembly with flared ends, a tip structure-dependent catastrophe frequency, and a microtubule rescue frequency dependent on lattice damage and repair.

An open call for contributions to a special issue of Biophysical Reviews highlighting the research themes of VII Congress of Russian Biophysicists 2023.

We announce a call for contributions to a Special Issue of Biophysical Reviews associated with the VII Congress of Russian Biophysicists (to be held in Krasnodar, Russia, 17-23 April 2023). The Congress is the main biophysical meeting held within Russia and is organized every four years. The Congress will focus on both the physical principles and mechanisms of biological processes occurring at different levels of structural organization, from molecular to cellular to organism and to population levels. The Special Issue will accept reviews on topics from molecular biophysics, structure and dynamics of biopolymers, biophysics of the cell, energy transformation mechanisms, biophotonics, ecological biophysics, and medical biophysics, following the sections of the Congress. The VII Congress of Russian Biophysicists is supported by International Union of Pure and Applied Biophysics (IUPAB). Here we describe main topics and sections of the coming event, the paper types for the journal issue, and the key deadline dates.

Regulation of microtubule dynamics, mechanics and function through the growing tip.

Microtubule dynamics and their control are essential for the normal function and division of all eukaryotic cells. This plethora of functions is, in large part, supported by dynamic microtubule tips, which can bind to various intracellular targets, generate mechanical forces and couple with actin microfilaments. Here, we review progress in the understanding of microtubule assembly and dynamics, focusing on new information about the structure of microtubule tips. First, we discuss evidence for the widely accepted GTP cap model of microtubule dynamics. Next, we address microtubule dynamic instability in the context of structural information about assembly intermediates at microtubule tips. Three currently discussed models of microtubule assembly and dynamics are reviewed. These are considered in the context of established facts and recent data, which suggest that some long-held views must be re-evaluated. Finally, we review structural observations about the tips of microtubules in cells and describe their implications for understanding the mechanisms of microtubule regulation by associated proteins, by mechanical forces and by microtubule-targeting drugs, prominently including cancer chemotherapeutics.

Expanding Stereoelectronic Limits of endo-tet Cyclizations: Synthesis of Benz[b]azepines from Donor-Acceptor Cyclopropanes.

The importance of intramolecular constraints in cyclic transition-state geometries is especially pronounced in n-endo-tet cyclizations, where the usual backside approach of a nucleophile to the breaking bond is impossible for the rings containing less than eight atoms. Herein, we expand the limits of endo-tet cyclizations and show that donor-acceptor cyclopropanes can provide a seven-membered ring via a genuine 6-endo-tet process. Substrates containing a N-alkyl-N-arylcarbamoyl moiety as an acceptor group undergo Lewis acid-induced cyclization to form tetrahydrobenz[b]azepin-2-ones in high yields. The reaction proceeds with the inversion of the configuration at the electrophilic carbon. In this process, a formally six-membered transition state yields a seven-membered ring as the pre-existing cycle is merged into the forming ring. The stereochemistry of the products can be controlled by the reaction time and by the nature of Lewis acid, opening access to both diastereomers by tuning of the reaction conditions.

Correction: Brownian dynamics simulation of protofilament relaxation during rapid freezing.

[This corrects the article DOI: 10.1371/journal.pone.0247022.].

Brownian dynamics simulation of protofilament relaxation during rapid freezing.

Electron cryo-microscopy (Cryo-EM) is a powerful method for visualizing biological objects with up to near-angstrom resolution. Instead of chemical fixation, the method relies on very rapid freezing to immobilize the sample. Under these conditions, crystalline ice does not have time to form and distort structure. For many practical applications, the rate of cooling is fast enough to consider sample immobilization instantaneous, but in some cases, a more rigorous analysis of structure relaxation during freezing could be essential. This difficult yet important problem has been significantly under-reported in the literature, despite spectacular recent developments in Cryo-EM. Here we use Brownian dynamics modeling to examine theoretically the possible effects of cryo-immobilization on the apparent shapes of biological polymers. The main focus of our study is on tubulin protofilaments. These structures are integral parts of microtubules, which in turn are key elements of the cellular skeleton, essential for intracellular transport, maintenance of cell shape, cell division and migration. We theoretically examine the extent of protofilament relaxation within the freezing time as a function of the cooling rate, the filament's flexural rigidity, and the effect of cooling on water's viscosity. Our modeling suggests that practically achievable cooling rates are not rapid enough to capture tubulin protofilaments in conformations that are incompletely relaxed, suggesting that structures seen by cryo-EM are good approximations to physiological shapes. This prediction is confirmed by our analysis of curvatures of tubulin protofilaments, using samples, prepared and visualized with a variety of methods. We find, however, that cryofixation may capture incompletely relaxed shapes of more flexible polymers, and it may affect Cryo-EM-based measurements of their persistence lengths. This analysis will be valuable for understanding of structures of different types of biopolymers, observed with Cryo-EM.

Mechanisms of microtubule dynamics and force generation examined with computational modeling and electron cryotomography.

Microtubules are dynamic tubulin polymers responsible for many cellular processes, including the capture and segregation of chromosomes during mitosis. In contrast to textbook models of tubulin self-assembly, we have recently demonstrated that microtubules elongate by addition of bent guanosine triphosphate tubulin to the tips of curving protofilaments. Here we explore this mechanism of microtubule growth using Brownian dynamics modeling and electron cryotomography. The previously described flaring shapes of growing microtubule tips are remarkably consistent under various assembly conditions, including different tubulin concentrations, the presence or absence of a polymerization catalyst or tubulin-binding drugs. Simulations indicate that development of substantial forces during microtubule growth and shortening requires a high activation energy barrier in lateral tubulin-tubulin interactions. Modeling offers a mechanism to explain kinetochore coupling to growing microtubule tips under assisting force, and it predicts a load-dependent acceleration of microtubule assembly, providing a role for the flared morphology of growing microtubule ends.

Mechanical properties of tubulin intra- and inter-dimer interfaces and their implications for microtubule dynamic instability.

Thirteen tubulin protofilaments, made of αß-tubulin heterodimers, interact laterally to produce cytoskeletal microtubules. Microtubules exhibit the striking property of dynamic instability, manifested in their intermittent growth and shrinkage at both ends. This behavior is key to many cellular processes, such as cell division, migration, maintenance of cell shape, etc. Although assembly and disassembly of microtubules is known to be linked to hydrolysis of a guanosine triphosphate molecule in the pocket of ß-tubulin, detailed mechanistic understanding of corresponding conformational changes is still lacking. Here we take advantage of the recent generation of in-microtubule structures of tubulin to examine the properties of protofilaments, which serve as important microtubule assembly and disassembly intermediates. We find that initially straight tubulin protofilaments, relax to similar non-radially curved and slightly twisted conformations. Our analysis further suggests that guanosine triphosphate hydrolysis primarily affects the flexibility and conformation of the inter-dimer interface, without a strong impact on the shape or flexibility of αß-heterodimer. Inter-dimer interfaces are significantly more flexible compared to intra-dimer interfaces. We argue that such a difference in flexibility could be key for distinct stability of the plus and minus microtubule ends. The higher flexibility of the inter-dimer interface may have implications for development of pulling force by curving tubulin protofilaments during microtubule disassembly, a process of major importance for chromosome motions in mitosis.