Dynamic Instability from Non-equilibrium Structural Transitions on the Energy Landscape of Microtubule

Modulating the Curvature of Protein Self-Assembled Spiral Nanotubules

Structural transformations from ribbons to twisted ribbons to helical ribbons are often observed across supramolecular assemblies and macroscopic structures and can be described under a consistent theoretical framework. Conical molecular self-assembled structures, however, are rarely observed, may require more than one subunit, their dimensions are hard to control, and are poorly understood. Cytoskeleton microtubule (MT) is a dynamic protein-polymer that self-assembles from αβ-tubulin heterodimer, providing mechanical support to Eukaryotic cells. Colchicine is a drug known to bind the exchangeable nucleotide site on the β-tubulin subunit and suppress MT assembly. The tetravalent polyamine spermine promotes MT assembly and tubulin spiral structures, including conical tubulin spirals, tubules of conical spirals, and inverted helical tubules. Here we show how colchicine as a single agent suppressed MT and tubulin single ring assembly already at substoichiometric concentrations, whereas in the presence of spermine, the tubulin-colchicine stoichiometry controlled the dimensions and curvature of tubulin spiral assemblies. At a fixed spermine concentration, the concentration of colchicine modulated the radii of the nanotubular structures. The radii of the inverted helical nanotubules and conical spiral nanotubules monotonically decreased with colchicine concentration. We attribute our observation to the increased curvature of the tubulin dimer subunit induced by colchicine.

Reaction Coordinates Are Optimal Channels of Energy Flow

Reaction coordinates (RCs) are the few essential coordinates of a protein that control its functional processes, such as allostery, enzymatic reaction, and conformational change. They are critical for understanding protein function and provide optimal enhanced sampling of protein conformational changes and states. Since the pioneering work in the late 1990s, identifying the correct and objectively provable RCs has been a central topic in molecular biophysics and chemical physics. This review summarizes the major advances in identifying RCs over the past 25 years, focusing on methods aimed at finding RCs that meet the rigorous committor criterion, widely accepted as the true RCs. Notably, the newly developed physics-based energy flow theory and generalized work functional method provide a general and rigorous approach for identifying true RCs, revealing their physical nature as the optimal channels of energy flow in biomolecules.

The alterations of repetitive transcranial magnetic stimulation on the energy landscape of resting-state networks differ across the human cortex

Repetitive transcranial magnetic stimulation (rTMS) is a promising intervention tool for the noninvasive modulation of brain activity and behavior in neuroscience research and clinical settings. However, the resting-state dynamic evolution of large-scale functional brain networks following rTMS has rarely been investigated. Here, using resting-state fMRI images collected from 23 healthy individuals before (baseline) and after 1 Hz rTMS of the left frontal (FRO) and occipital (OCC) lobes, we examined the different effects of rTMS on brain dynamics across the human cortex. By fitting a pairwise maximum entropy model (pMEM), we constructed an energy landscape for the baseline and poststimulus conditions by fitting a pMEM. We defined dominant brain states (local minima) in the energy landscape with synergistic activation and deactivation patterns of large-scale functional networks. We calculated state dynamics including appearance probability, transitions and duration. The results showed that 1 Hz rTMS induced increased and decreased state probability, transitions and duration when delivered to the FRO and OCC targets, respectively. Most importantly, the shortest path and minimum cost between dominant brain states were altered after stimulation. The absolute sum of the costs from the source states to the destinations was lower after OCC stimulation than after FRO stimulation. In conclusion, our study characterized the dynamic trajectory of state transitions in the energy landscape and suggested that local rTMS can induce significant dynamic perturbation involving stimulated and distant functional networks, which aligns with the modern view of the dynamic and complex brain. Our results suggest low-dimensional mapping of rTMS-induced brain adaption, which will contribute to a broader and more effective application of rTMS in clinical settings.

Interface-acting nucleotide controls polymerization dynamics at microtubule plus- and minus-ends

GTP-tubulin is preferentially incorporated at growing microtubule ends, but the biochemical mechanism by which the bound nucleotide regulates the strength of tubulin:tubulin interactions is debated. The 'self-acting' (cis) model posits that the nucleotide (GTP or GDP) bound to a particular tubulin dictates how strongly that tubulin interacts, whereas the 'interface-acting' (trans) model posits that the nucleotide at the interface of two tubulin dimers is the determinant. We identified a testable difference between these mechanisms using mixed nucleotide simulations of microtubule elongation: with a self-acting nucleotide, plus- and minus-end growth rates decreased in the same proportion to the amount of GDP-tubulin, whereas with interface-acting nucleotide, plus-end growth rates decreased disproportionately. We then experimentally measured plus- and minus-end elongation rates in mixed nucleotides and observed a disproportionate effect of GDP-tubulin on plus-end growth rates. Simulations of microtubule growth were consistent with GDP-tubulin binding at and 'poisoning' plus-ends but not at minus-ends. Quantitative agreement between simulations and experiments required nucleotide exchange at terminal plus-end subunits to mitigate the poisoning effect of GDP-tubulin there. Our results indicate that the interfacial nucleotide determines tubulin:tubulin interaction strength, thereby settling a longstanding debate over the effect of nucleotide state on microtubule dynamics.

Interface-acting nucleotide controls polymerization dynamics at microtubule plus- and minus-ends

GTP-tubulin is preferentially incorporated at growing microtubule ends, but the biochemical mechanism by which the bound nucleotide regulates the strength of tubulin:tubulin interactions is debated. The 'self-acting' (cis) model posits that the nucleotide (GTP or GDP) bound to a particular tubulin dictates how strongly that tubulin interacts, whereas the 'interface-acting' (trans) model posits that the nucleotide at the interface of two tubulin dimers is the determinant. We identified a testable difference between these mechanisms using mixed nucleotide simulations of microtubule elongation: with self-acting nucleotide, plus- and minus-end growth rates decreased in the same proportion to the amount of GDP-tubulin, whereas with interface-acting nucleotide, plus-end growth rates decreased disproportionately. We then experimentally measured plus- and minus-end elongation rates in mixed nucleotides and observed a disproportionate effect of GDP-tubulin on plus-end growth rates. Simulations of microtubule growth were consistent with GDP-tubulin binding at and 'poisoning' plus-ends but not at minus-ends. Quantitative agreement between simulations and experiments required nucleotide exchange at terminal plus-end subunits to mitigate the poisoning effect of GDP-tubulin there. Our results indicate that the interfacial nucleotide determines tubulin:tubulin interaction strength, thereby settling a longstanding debate over the effect of nucleotide state on microtubule dynamics.

Diverse cytomotive actins and tubulins share a polymerization switch mechanism conferring robust dynamics

Protein filaments are used in myriads of ways to organize other molecules within cells. Some filament-forming proteins couple the hydrolysis of nucleotides to their polymerization cycle, thus powering the movement of other molecules. These filaments are termed cytomotive. Only members of the actin and tubulin protein superfamilies are known to form cytomotive filaments. We examined the basis of cytomotivity via structural studies of the polymerization cycles of actin and tubulin homologs from across the tree of life. We analyzed published data and performed structural experiments designed to disentangle functional components of these complex filament systems. Our analysis demonstrates the existence of shared subunit polymerization switches among both cytomotive actins and tubulins, i.e., the conformation of subunits switches upon assembly into filaments. These cytomotive switches can explain filament robustness, by enabling the coupling of kinetic and structural polarities required for cytomotive behaviors and by ensuring that single cytomotive filaments do not fall apart.

Effect of tubulin self-association on GTP hydrolysis and nucleotide exchange reactions

We investigated how the self-association of isolated tubulin dimers affects the rate of GTP hydrolysis and the equilibrium of nucleotide exchange. Both reactions are relevant for microtubule (MT) dynamics. We used HPLC to determine the concentrations of GDP and GTP and thereby the GTPase activity of SEC-eluted tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates. When GTP hydrolysis was negligible, the nucleotide exchange mechanism was studied by determining the concentrations of tubulin-free and tubulin-bound GTP and GDP. We observed no GTP hydrolysis below the critical conditions for MT assembly (either below the critical tubulin concentration and/or at low temperature), despite the assembly of tubulin 1D curved oligomers and single-rings, showing that their assembly did not involve GTP hydrolysis. Under conditions enabling spontaneous slow MT assembly, a slow pseudo-first-order GTP hydrolysis kinetics was detected, limited by the rate of MT assembly. Cryo-TEM images showed that GTP-tubulin 1D oligomers were curved also at 36 °C. Nucleotide exchange depended on the total tubulin concentration and the molar ratio between tubulin-free GDP and GTP. We used a thermodynamic model of isodesmic tubulin self-association, terminated by the formation of tubulin single-rings to determine the molar fractions of dimers with exposed and buried nucleotide exchangeable sites (E-sites). Our analysis shows that the GDP to GTP exchange reaction equilibrium constant was an order-of-magnitude larger for tubulin dimers with exposed E-sites than for assembled dimers with buried E-sites. This conclusion may have implications on the dynamics at the tip of the MT plus end.

The longitudinal neural dynamics changes of whole brain connectome during natural recovery from poststroke aphasia

Poststroke aphasia is one of the most dramatic functional deficits that results from direct damage of focal brain regions and dysfunction of large-scale brain networks. The reconstruction of language function depends on the hierarchical whole-brain dynamic reorganization. However, investigations into the longitudinal neural changes of large-scale brain networks for poststroke aphasia remain scarce. Here we characterize large-scale brain dynamics in left-frontal-stroke aphasia through energy landscape analysis. Using fMRI during an auditory comprehension task, we find that aphasia patients suffer serious whole-brain dynamics perturbation in the acute and subacute stages after stroke, in which the brains were restricted into two major activity patterns. Following spontaneous recovery process, the brain flexibility improved in the chronic stage. Critically, we demonstrated that the abnormal neural dynamics are correlated with the aberrant brain network coordination. Taken together, the energy landscape analysis exhibited that the acute poststroke aphasia has a constrained, low dimensional brain dynamics, which were replaced by less constrained and high dimensional dynamics at chronic aphasia. Our study provides a new perspective to profoundly understand the pathological mechanisms of poststroke aphasia.

Out-of-Equilibrium Biophysical Chemistry: The Case for Multidimensional, Integrated Single-Molecule Approaches

Out-of-equilibrium processes are ubiquitous across living organisms and all structural hierarchies of life. At the molecular scale, out-of-equilibrium processes (for example, enzyme catalysis, gene regulation, and motor protein functions) cause biological macromolecules to sample an ensemble of conformations over a wide range of time scales. Quantifying and conceptualizing the structure–dynamics to function relationship is challenging because continuously evolving multidimensional energy landscapes are necessary to describe nonequilibrium biological processes in biological macromolecules. In this perspective, we explore the challenges associated with state-of-the-art experimental techniques to understanding biological macromolecular function. We argue that it is time to revisit how we probe and model functional out-of-equilibrium biomolecular dynamics. We suggest that developing integrated single-molecule multiparametric force–fluorescence instruments and using advanced molecular dynamics simulations to study out-of-equilibrium biomolecules will provide a path towards understanding the principles of and mechanisms behind the structure–dynamics to function paradigm in biological macromolecules.

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.