Molecular investigations into the mechanics of actin in different nucleotide states

Advances in coarse-grained modeling of macromolecular complexes

Recent progress in coarse-grained (CG) molecular modeling and simulation has facilitated an influx of computational studies on biological macromolecules and their complexes. Given the large separation of length-scales and time-scales that dictate macromolecular biophysics, CG modeling and simulation are well-suited to bridge the microscopic and mesoscopic or macroscopic details observed from all-atom molecular simulations and experiments, respectively. In this review, we first summarize recent innovations in the development of CG models, which broadly include structure-based, knowledge-based, and dynamics-based approaches. We then discuss recent applications of different classes of CG models to explore various macromolecular complexes. Finally, we conclude with an outlook for the future in this ever-growing field of biomolecular modeling.

Data-driven reduced-order model of microtubule mechanics

A beam element is constructed for microtubules based upon data reduction of the results from atomistic simulation of the carbon backbone chain of αβ-tubulin dimers. The database of mechanical responses to various types of loads from atomistic simulation is reduced to dominant modes. The dominant modes are subsequently used to construct the stiffness matrix of a beam element that captures the anisotropic behavior and deformation mode coupling that arises from a microtubule's spiral structure. In contrast to standard Euler-Bernoulli or Timoshenko beam elements, the link between forces and node displacements results not from hypothesized deformation behavior, but directly from the data obtained by molecular scale simulation. Differences between the resulting microtubule data-driven beam model (MTDDBM) and standard beam elements are presented, with a focus on coupling of bending, stretch, shear deformations. The MTDDBM is just as economical to use as a standard beam element, and allows accurate reconstruction of the mechanical behavior of structures within a cell as exemplified in a simple model of a component element of the mitotic spindle.

SOP-GPU: influence of solvent-induced hydrodynamic interactions on dynamic structural transitions in protein assemblies

Hydrodynamic interactions (HI) are incorporated into Langevin dynamics of the Cα -based protein model using the Truncated Expansion approximation (TEA) to the Rotne-Prager-Yamakawa diffusion tensor. Computational performance of the obtained GPU realization demonstrates the model's capability for describing protein systems of varying complexity (10(2) -10(5) residues), including biological particles (filaments, virus shells). Comparison of numerical accuracy of the TEA versus exact description of HI reveals similar results for the kinetics and thermodynamics of protein unfolding. The HI speed up and couple biomolecular transitions through cross-communication among protein domains, which result in more collective displacements of structure elements governed by more deterministic (less variable) dynamics. The force-extension/deformation spectra from nanomanipulations in silico exhibit sharper force signals that match well the experimental profiles. Hence, biomolecular simulations without HI overestimate the role of tension/stress fluctuations. Our findings establish the importance of incorporating implicit water-mediated many-body effects into theoretical modeling of dynamic processes involving biomolecules. © 2016 Wiley Periodicals, Inc.

Nucleotides regulate the mechanical hierarchy between subdomains of the nucleotide binding domain of the Hsp70 chaperone DnaK

The regulation of protein function through ligand-induced conformational changes is crucial for many signal transduction processes. The binding of a ligand alters the delicate energy balance within the protein structure, eventually leading to such conformational changes. In this study, we elucidate the energetic and mechanical changes within the subdomains of the nucleotide binding domain (NBD) of the heat shock protein of 70 kDa (Hsp70) chaperone DnaK upon nucleotide binding. In an integrated approach using single molecule optical tweezer experiments, loop insertions, and steered coarse-grained molecular simulations, we find that the C-terminal helix of the NBD is the major determinant of mechanical stability, acting as a glue between the two lobes. After helix unraveling, the relative stability of the two separated lobes is regulated by ATP/ADP binding. We find that the nucleotide stays strongly bound to lobe II, thus reversing the mechanical hierarchy between the two lobes. Our results offer general insights into the nucleotide-induced signal transduction within members of the actin/sugar kinase superfamily.

Mechanics of severing for large microtubule complexes revealed by coarse-grained simulations

We investigate the mechanical behavior of microtubule (MT) protofilaments under the action of bending forces, ramped up linearly in time, to provide insight into the severing of MTs by microtubule associated proteins (MAPs). We used the self-organized polymer model which employs a coarse-grained description of the protein chain and ran Brownian dynamics simulations accelerated on graphics processing units that allow us to follow the dynamics of a MT system on experimental timescales. Our study focused on the role played in the MT depolymerization dynamics by the inter-tubulin contacts a protofilament experiences when embedded in the MT lattice, and the number of binding sites of MAPs on MTs. We found that proteins inducing breaking of MTs must have at least three attachment points on any tubulin dimer from an isolated protofilament. In contrast, two points of contact would suffice when dimers are located in an intact MT lattice, in accord with experimental findings on MT severing proteins. Our results show that confinement of a protofilament in the MT lattice leads to a drastic reduction in the energy required for the removal of tubulin dimers, due to the drastic reduction in entropy. We further showed that there are differences in the energetic requirements based on the location of the dimer to be removed by severing. Comparing the energy of tubulin dimers removal revealed by our simulations with the amount of energy resulting from one ATP hydrolysis, which is the source of energy for all MAPs, we provided strong evidence for the experimental finding that severing proteins do not bind uniformly along the MT wall.

Daam1 is a regulator of filopodia formation and phagocytic uptake of Borrelia burgdorferi by primary human macrophages

Borrelia burgdorferi is the causative agent of Lyme disease, an infectious disease that primarily affects the skin, nervous system, and joints. Uptake of borreliae by immune cells is decisive for the course of the infection, and remodelling of the host actin cytoskeleton is crucial in this process. In this study, we showed that the actin-regulatory formin Daam1 is important in Borrelia phagocytosis by primary human macrophages. Uptake of borreliae proceeds preferentially through capture by filopodia and formation of coiling pseudopods that enwrap the spirochetes. Using immunofluorescence, we localized endogenous and overexpressed Daam1 to filopodia and to F-actin-rich uptake structures. Live-cell imaging further showed that Daam1 is enriched at coiling pseudopods that arise from the macrophage surface. This filopodia-independent step was corroborated by control experiments of phagocytic cup formation with latex beads. Moreover, siRNA-mediated knockdown of Daam1 led to a 65% reduction of borreliae-induced filopodia, and, as shown by the outside-inside staining technique, to a 50% decrease in phagocytic uptake of borreliae, as well as a 37% reduction in coiling pseudopod formation. Collectively, we showed that Daam1 plays a dual role in the phagocytic uptake of borreliae: first, as a regulator of filopodia, which are used for capturing spirochetes, and second, in the formation of the coiling pseudopod that enwraps the bacterial cell. These data identify Daam1 as a novel regulator of B. burgdorferi phagocytosis. At the same time, this is the first demonstration of a role for Daam1 in phagocytic processes in general.-Hoffmann, A.-K., Naj, X., Linder, S. Daam1 is a regulator of filopodia formation and phagocytic uptake of Borrelia burgdorferi by primary human macrophages.

A mechanochemical model of actin filaments

In eukaryotic cells, actin filaments are involved in important processes such as motility, division, cell shape regulation, contractility, and mechanosensation. Actin filaments are polymerized chains of monomers, which themselves undergo a range of chemical events such as ATP hydrolysis, polymerization, and depolymerization. When forces are applied to F-actin, in addition to filament mechanical deformations, the applied force must also influence chemical events in the filament. We develop an intermediate-scale model of actin filaments that combines actin chemistry with filament-level deformations. The model is able to compute mechanical responses of F-actin during bending and stretching. The model also describes the interplay between ATP hydrolysis and filament deformations, including possible force-induced chemical state changes of actin monomers in the filament. The model can also be used to model the action of several actin-associated proteins, and for large-scale simulation of F-actin networks. All together, our model shows that mechanics and chemistry must be considered together to understand cytoskeletal dynamics in living cells.

Multiscale modeling of the nanomechanics of microtubule protofilaments

Large-size biomolecular systems that spontaneously assemble, disassemble, and self-repair by controlled inputs play fundamental roles in biology. Microtubules (MTs), which play important roles in cell adhesion and cell division, are a prime example. MTs serve as ″tracks″ for molecular motors, and their biomechanical functions depend on dynamic instability-a stochastic switching between periods of rapid growing and shrinking. This process is controlled by many cellular factors so that growth and shrinkage periods are correlated with the life cycle of a cell. Resolving the molecular basis for the action of these factors is of paramount importance for understanding the diverse functions of MTs. We employed a multiscale modeling approach to study the force-induced MT depolymerization by analyzing the mechanical response of a MT protofilament to external forces. We carried out self-organized polymer (SOP) model based simulations accelerated on Graphics Processing Units (GPUs). This approach enabled us to follow the mechanical behavior of the molecule on experimental time scales using experimental force loads. We resolved the structural details and determined the physical parameters that characterize the stretching and bending modes of motion of a MT protofilament. The central result is that the severing action of proteins, such as katanin and kinesin, can be understood in terms of their mechanical coupling to a protofilament. For example, the extraction of tubulin dimers from MT caps by katanin can be achieved by pushing the protofilament toward the axis of the MT cylinder, while the removal of large protofilaments curved into ″ram's horn″ structures by kinesin is the result of the outward bending of the protofilament. We showed that, at the molecular level, these types of deformations are due to the anisotropic, but homogeneous, micromechanical properties of MT protofilaments.

Exploring the role of topological frustration in actin refolding with molecular simulations

Actin plays crucial roles in the life of the cell while being notorious for its inability to reach a functional conformation without the help of assistant proteins. In eukaryotes, for example, the cytosolic chaperonin containing TCP-1 (CCT) and prefoldin (PFD) are required for actin folding assistance and prevention of protein aggregation in the crowded cellular environment. The folding of non-native actin is known to occur in a number of steps, but the reasons underlying its folding difficulty are unknown. Because a full, atomistic-level, investigation of the kinetics and thermodynamics of folding of such a large molecule is beyond computational reach, we focused our investigation on the role of topological frustration on the folding of actin. Namely, we studied the (re)folding of actin using simulations of a variant self-organized polymer model (SOP-DH) starting from a stretched state, leading to results that correlate well with experimentally driven conclusions and allowing us to make a number of testable predictions. Primarily, our simulations reveal that the successful refolding of the C-terminus end of actin occurs through a zipping process in which the α-helices wind up turn by turn upon formation of their native tertiary contacts. In turn, an early formation of the helical structure in this region of the chain has deleterious effects for actin's refolding fitness. Moreover, the C-terminus refolding is a very rare event in our simulations, in agreement with the large activation barrier predicted on the basis of experimental studies of actin unfolding in EDTA. We also discovered that subdomain 4 has a low refolding probability, which can help explain why many of the non-native actin target binding sites for CCT and PFD are located within this subdomain.