Simulations of tubulin sheet polymers as possible structural intermediates in microtubule assembly

Modulating the Self-Assembly of a Camptothecin Prodrug with Paclitaxel for Anticancer Combination Therapy: A Molecular Dynamics Approach

Camptothecin (CPT) and paclitaxel (PTX), derived from natural products, are recognized for their significant efficacy in clinical cancer treatments. Despite its therapeutic advantages, CPT is challenged by issues of toxicity and solubility, necessitating its use in conjugation with other compounds for enhanced compatibility. This study delves into the coassembly mechanism of Evans blue-conjugated camptothecin (EB-CPT) with PTX, aiming to elucidate their synergistic potential in combination therapy applications, employing all-atom molecular dynamics simulations. The EB-CPT prodrug is reported to form a self-aggregated cluster. Our findings suggest that increasing the PTX concentration induces a dispersion of EB-CPT clusters, thereby disrupting their inherent self-assembly. This disruption is explained to be facilitated by the coassembly of EB-CPT and PTX. With increasing concentration of PTX, a lengthening of the coassembled structures is observed, supporting the experimental findings of tube-like coassembled structures at higher weight ratios of PTX. Hydrophobic interactions and π-π stacking are the primary forces responsible for the formation of both self- and coassembled structures. Interestingly, the structural analysis reveals that the CPT moiety of EB-CPT is less involved in assemblies due to steric hindrances. Instead, the interaction and coassembly processes are predominantly mediated by the EB derivative component of the prodrug. This research underscores the critical role of the solubilizing agent, EB derivative, in mediating the flexibility and interaction of CPT in combination therapy strategies, particularly with PTX, thus emphasizing the importance of conjugates for therapeutic developments. Furthermore, the molecular insights into the interaction sites and mechanisms facilitating coassembly between EB-CPT and PTX contribute valuable knowledge to the field, highlighting the potential of these nanomedicine combinations in advancing cancer treatment modalities.

Brain Microtubule Electrical Oscillations-Empirical Mode Decomposition Analysis

Microtubules (MTs) are essential cytoskeletal polymers of eukaryote cells implicated in various cell functions, including cell division, cargo transfer, and cell signaling. MTs also are highly charged polymers that generate electrical oscillations that may underlie their ability to act as nonlinear transmission lines. However, the oscillatory composition and time-frequency differences of the MT electrical oscillations have not been identified. Here, we applied the Empirical Mode Decomposition (EMD) to bovine brain MT sheet recordings to determine the number and fundamental frequencies of the Intrinsic Modes Functions (IMF) and evaluate their energetic contribution to the electrical signal. As previously reported, raw signals were obtained from cow brain MTs (Cantero et al. Sci Rep 6:27143, 2016), sampled, filtered, and subjected to signal decomposition from representative experiments. Filtered signals (200 Hz) allowed us to identify either six or seven IMFs. The reconstructed tracings faithfully resembled the original signals, with identifiable frequency peaks. To extend the analysis to obtain time-frequency information and the energy implicated in each IMF, we applied the Hilbert-Huang Transform (HHT) and the Continuous Wavelet Transform (CWT) to the same samples. The analyses disclosed the presence of more fundamental frequency peaks than initially reported and evidenced the advantages and disadvantages of each transform. The study indicates that the EMD is a robust approach to quantifying signal decomposition of brain MT oscillations and suggests novel similarities with human brain wave electroencephalogram (EEG) recordings. The evidence points to the potentially fundamental role of MT oscillations in brain electrical activity.

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

Microtubules are the backbone of the cytoskeleton and vital to numerous cellular processes. The central dogma of microtubules is that all their functions are driven by dynamic instability, but its mechanism has remained unresolved for over 30 years because of conceptual difficulties inherent in the dominant GTP-cap framework. We present a physically rigorous structural mechanochemical model: dynamic instability is driven by non-equilibrium transitions between the bent (B), straight (S), and curved (C) forms of tubulin monomers and longitudinal interfaces in the two-dimensional lattice of microtubule. All the different phenomena (growth, shortening, catastrophe, rescue, and pausing) are controlled by the kinetic pathways for B↔S↔C transitions and corresponding energy landscapes. Different kinetics at minus end are due to different B↔S↔C pathways imposed by the polarity of microtubule lattice. This model enables us to reproduce all the observed phenomena of dynamic instability of purified tubulins in kinetic simulations.

Mechanics and kinetics of dynamic instability

During dynamic instability, self-assembling microtubules (MTs) stochastically alternate between phases of growth and shrinkage. This process is driven by the presence of two distinct states of MT subunits, GTP- and GDP-bound tubulin dimers, that have different structural properties. Here, we use a combination of analysis and computer simulations to study the mechanical and kinetic regulation of dynamic instability in three-dimensional (3D) self-assembling MTs. Our model quantifies how the 3D structure and kinetics of the distinct states of tubulin dimers determine the mechanical stability of MTs. We further show that dynamic instability is influenced by the presence of quenched disorder in the state of the tubulin subunit as reflected in the fraction of non-hydrolysed tubulin. Our results connect the 3D geometry, kinetics and statistical mechanics of these tubular assemblies within a single framework, and may be applicable to other self-assembled systems where these same processes are at play.

Mimicking Sub-Structures Self-Organization in Microtubules

Microtubules (MTs) are highly dynamic polymers distributed in the cytoplasm of a biological cell. Alpha and beta globular proteins constituting the heterodimer building blocks combine to form these tubules through polymerization, controlled by the concentration of Guanosine-triphosphate (GTPs) and other Microtubule Associated Proteins (MAPs). MTs play a crucial role in many intracellular processes, predominantly in mitosis, organelle transport and cell locomotion. Current research in this area is focused on understanding the exclusive behaviors of self-organization and their association with different MAPs through organized laboratory experiments. However, the intriguing intelligence behind these tiny machines resulting in complex self-organizing structures is mostly unexplored. In this study, we propose a novel swarm engineering framework in modeling rules for these systems, by combining the principles of design with swarm intelligence. The proposed framework was simulated on a game engine and these simulations demonstrated self-organization of rings and protofilaments in MTs. Analytics from these simulations assisted in understanding the influence of GTPs on protofilament formation. Also, results showed that the population density of GTPs rather than their bonding probabilities played a crucial role in polymerization in forming microtubule substructures.

Lattice defects induce microtubule self-renewal

Microtubules are dynamic polymers, which grow and shrink by addition and removal of tubulin dimers at their extremities. Within the microtubule shaft, dimers adopt a densely packed and highly ordered crystal-like lattice structure, which is generally not considered to be dynamic. Here we report that thermal forces are sufficient to remodel the microtubule shaft, despite its apparent stability. Our combined experimental data and numerical simulations on lattice dynamics and structure suggest that dimers can spontaneously leave and be incorporated into the lattice at structural defects. We propose a model mechanism, where the lattice dynamics is initiated via a passive breathing mechanism at dislocations, which are frequent in rapidly growing microtubules. These results show that we may need to extend the concept of dissipative dynamics, previously established for microtubule extremities, to the entire shaft, instead of considering it as a passive material.

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.

Kinetic stability analysis of protein assembly on the center manifold around the critical point

Background

Non-linear kinetic analysis is a useful method for illustration of the dynamic behavior of cellular biological systems. To date, center manifold theory (CMT) has not been sufficiently applied for stability analysis of biological systems. The aim of this study is to demonstrate the application of CMT to kinetic analysis of protein assembly and disassembly, and to propose a novel framework for nonlinear multi-parametric analysis. We propose a protein assembly model with nonlinear kinetics provided by the fluctuation in monomer concentrations during their diffusion.

Results

When the diffusion process of a monomer is self-limited to give kinetics non-linearity, numerical simulations suggest the probability that the assembly and disassembly oscillate near the critical point. We applied CMT to kinetic analysis of the center manifold around the critical point in detail, and successfully demonstrated bifurcation around the critical point, which explained the observed oscillation.

Conclusions

The stability kinetics of the present model based on CMT illustrates a unique feature of protein assembly, namely non-linear behavior. Our findings are expected to provide methodology for analysis of biological systems.

Electrical Oscillations in Two-Dimensional Microtubular Structures

Microtubules (MTs) are unique components of the cytoskeleton formed by hollow cylindrical structures of αβ tubulin dimeric units. The structural wall of the MT is interspersed by nanopores formed by the lateral arrangement of its subunits. MTs are also highly charged polar polyelectrolytes, capable of amplifying electrical signals. The actual nature of these electrodynamic capabilities remains largely unknown. Herein we applied the patch clamp technique to two-dimensional MT sheets, to characterize their electrical properties. Voltage-clamped MT sheets generated cation-selective oscillatory electrical currents whose magnitude depended on both the holding potential, and ionic strength and composition. The oscillations progressed through various modes including single and double periodic regimes and more complex behaviours, being prominent a fundamental frequency at 29 Hz. In physiological K(+) (140 mM), oscillations represented in average a 640% change in conductance that was also affected by the prevalent anion. Current injection induced voltage oscillations, thus showing excitability akin with action potentials. The electrical oscillations were entirely blocked by taxol, with pseudo Michaelis-Menten kinetics and a KD of ~1.29 μM. The findings suggest a functional role of the nanopores in the MT wall on the genesis of electrical oscillations that offer new insights into the nonlinear behaviour of the cytoskeleton.

Relating nucleotide-dependent conformational changes in free tubulin dimers to tubulin assembly

The complex dynamic behavior of microtubules (MTs) is believed to be primarily due to the αβ-tubulin dimer architecture and its intrinsic GTPase activity. Hence, a detailed knowledge of the conformational variations of isolated α-GTP-β-GTP- and α-GTP-β-GDP-tubulin dimers in solution and their implications to interdimer interactions and stability is directly relevant to understand the MT dynamics. An attempt has been made here by combining molecular dynamics (MD) simulations and protein-protein docking studies that unravels key structural features of tubulin dimer in different nucleotide states and correlates their association to tubulin assembly. Results from simulations suggest that tubulin dimers and oligomers attain curved conformations in both GTP and GDP states. Results also indicate that the tubulin C-terminal domain and the nucleotide state are closely linked. Protein-protein docking in combination with MD simulations suggest that the GTP-tubulin dimers engage in relatively stronger interdimer interactions even though the interdimer interfaces are bent in both GTP and GDP tubulin complexes, providing valuable insights on in vitro finding that GTP-tubulin is a better assembly candidate than GDP-tubulin during the MT nucleation and elongation processes.

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm²) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies.

Conformational changes in tubulin in GMPCPP and GDP-taxol microtubules observed by cryoelectron microscopy

Microtubules are dynamic polymers that stochastically switch between growing and shrinking phases. Microtubule dynamics are regulated by guanosine triphosphate (GTP) hydrolysis by β-tubulin, but the mechanism of this regulation remains elusive because high-resolution microtubule structures have only been revealed for the guanosine diphosphate (GDP) state. In this paper, we solved the cryoelectron microscopy (cryo-EM) structure of microtubule stabilized with a GTP analogue, guanylyl 5'-α,β-methylenediphosphonate (GMPCPP), at 8.8-Å resolution by developing a novel cryo-EM image reconstruction algorithm. In contrast to the crystal structures of GTP-bound tubulin relatives such as γ-tubulin and bacterial tubulins, significant changes were detected between GMPCPP and GDP-taxol microtubules at the contacts between tubulins both along the protofilament and between neighboring protofilaments, contributing to the stability of the microtubule. These findings are consistent with the structural plasticity or lattice model and suggest the structural basis not only for the regulatory mechanism of microtubule dynamics but also for the recognition of the nucleotide state of the microtubule by several microtubule-binding proteins, such as EB1 or kinesin.

Comparative studies of microtubule mechanics with two competing models suggest functional roles of alternative tubulin lateral interactions

The dynamic assembly and disassembly of microtubules and the mechanical properties of these polymers are essential for many key cellular processes. Mathematical and computational modeling, especially coupled mechanochemical modeling, has contributed significantly to our understanding of microtubule dynamics. However, critical discrepancies exist between experimental observations and modeling results that need to be resolved before further progress toward a complete model can be made. Open sheet structures ranging in length from several hundred nanometers to one micron have often been observed at the growing ends of microtubules in in vitro studies. Existing modeling studies predict these sheet structures to be short and rare intermediates of microtubule disassembly rather than important components of the assembly process. Atomic force microscopy (AFM) studies also reveal interesting step-like gaps of the force-indentation curve that cannot yet be explained by existing theoretical models. We have carried out computational studies to compare the mechanical properties of two alternative models: a more conventional model where tubulin dimers are added directly into a microtubule lattice, and one that considers an additional type of tubulin lateral interaction proposed to exist in intermediate sheet structures during the microtubule assembly process. The first model involves a single type of lateral interactions between tubulin subunits, whereas the latter considers a second type that can convert to the canonical lateral contact during microtubule closure into a cylinder. Our analysis shows that only the second model can reproduce the AFM results over a broad parameter range. We propose additional studies using different sizes of AFM tips that would allow to unambiguously distinguish the relative validity of the two models.

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 mechanisms of microtubule growth from the view of hydrolysis effects. Besides, the growth of a microtubule involves the closure of a curved sheet at its growing end. The curvature conversion from the longitudinal direction to the circumferential direction 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. First, the closure process involving a sheet-to-tube transition is simulated. The results verify the stabilizing effect of the sheet structure and predict that the minimum conformational cap length that can stabilize the growth is two dimers. Then, we show that the conformational cap and the GTP cap can function independently and harmoniously, 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.

Modulation of microtubule interprotofilament interactions by modified taxanes

Microtubules assembled with paclitaxel and docetaxel differ in their numbers of protofilaments, reflecting modification of the lateral association between αβ-tubulin molecules in the microtubule wall. These modifications of microtubule structure, through a not-yet-characterized mechanism, are most likely related to the changes in tubulin-tubulin interactions responsible for microtubule stabilization by these antitumor compounds. We have used a set of modified taxanes to study the structural mechanism of microtubule stabilization by these ligands. Using small-angle x-ray scattering, we have determined how modifications in the shape and size of the taxane substituents result in changes in the interprotofilament angles and in their number. The observed effects have been explained using NMR-aided docking and molecular dynamic simulations of taxane binding at the microtubule pore and luminal sites. Modeling results indicate that modification of the size of substituents at positions C7 and C10 of the taxane core influence the conformation of three key elements in microtubule lateral interactions (the M-loop, the S3 β-strand, and the H3 helix) that modulate the contacts between adjacent protofilaments. In addition, modifications of the substituents at position C2 slightly rearrange the ligand in the binding site, modifying the interaction of the C7 substituent with the M-loop.

GDP-tubulin incorporation into growing microtubules modulates polymer stability

Microtubule growth proceeds through the endwise addition of nucleotide-bound tubulin dimers. The microtubule wall is composed of GDP-tubulin subunits, which are thought to come exclusively from the incorporation of GTP-tubulin complexes at microtubule ends followed by GTP hydrolysis within the polymer. The possibility of a direct GDP-tubulin incorporation into growing polymers is regarded as hardly compatible with recent structural data. Here, we have examined GTP-tubulin and GDP-tubulin incorporation into polymerizing microtubules using a minimal assembly system comprised of nucleotide-bound tubulin dimers, in the absence of free nucleotide. We find that GDP-tubulin complexes can efficiently co-polymerize with GTP-tubulin complexes during microtubule assembly. GDP-tubulin incorporation into microtubules occurs with similar efficiency during bulk microtubule assembly as during microtubule growth from seeds or centrosomes. Microtubules formed from GTP-tubulin/GDP-tubulin mixtures display altered microtubule dynamics, in particular a decreased shrinkage rate, apparently due to intrinsic modifications of the polymer disassembly properties. Thus, although microtubules polymerized from GTP-tubulin/GDP-tubulin mixtures or from homogeneous GTP-tubulin solutions are both composed of GDP-tubulin subunits, they have different dynamic properties, and this may reveal a novel form of microtubule "structural plasticity."