Single-molecule analysis of osmolyte-mediated nanomechanical unfolding behavior of a protein domain

The small organic molecules, known as osmolytes being ubiquitously present in different cell types, affect protein folding, stability and aggregation. However, it is unknown how the osmolytes affect the nanomechanical unfolding behavior of protein domain. Here, we show the osmolyte-dependent mechanical unfolding properties of protein titin immunoglobulin-27 (I27) domain using an atomic force microscopy (AFM)-based single-molecule force spectroscopy. We found that amines and methylamines improved the mechanical stability of I27 domain, whereas polyols had no effect. Interestingly, glycine betaine (GB) or trimethylamine-N-oxide (TMAO) increased the average unfolding force of the protein domain. The kinetic parameters analyzed at single-molecule level reveal that stabilizing effect of osmolytes is due to a decrease in the unfolding rate constant of I27, which was confirmed by molecular dynamics simulations. Our study reveals different effects that diverse osmolytes have on the mechanical properties of the protein, and suggests the potential use of osmolytes in modulating the mechanical stability of proteins required for various nano-biotechnological applications.

Study of the interfacial viscoelasticity of human serum albumin microcapsules using a viscoelasto-electrohydrodynamic technique

Crosslinked proteins are widely used as the encapsulating membranes in microcapsules for many biomedical and food industries. The interfacial rheological properties of these capsules are due to the complex microstructure of cross-linked globular proteins owing to structural changes at quaternary, tertiary and secondary levels. These changes in structure can be induced by high protein concentration, hydrophobic-hydrophillic interfaces, and pH. In this work, the interfacial viscoelastic rheological properties of human serum albumin (HSA) microcapsules are estimated using a novel electrodeformation technique exhibiting creep and oscillatory responses. Insights into the microstructure-rheology relationship are obtained using FTIR and SEM studies. The results show a complex dependence of the interfacial properties on the size, concentration and pH of the capsules. An interplay of inter-molecular interactions, adsorption and multilayer formation, accessibility to reactive functional groups, and dependence on the relative content of alpha helix, beta sheet and beta turn is observed. The interfacial rheological properties are estimated using the Burger model and creep is found to sensitively affect the rheological properties due to irreversible changes in microstructure. Furthermore, the electrodeformation technique allows analysis of interfacial rheology at high frequencies, 10 Hz to 1 kHz, which is otherwise not easily possible with conventional rheometers.

Stretching the story of titin and muscle function

The discovery of the giant protein titin, also known as connectin, dates almost half a century back. In this review, I recapitulate major advances in the discovery of the titin filaments and the recognition of their properties and function until today. I briefly discuss how our understanding of the layout and interactions of titin in muscle sarcomeres has evolved and review key facts about the titin sequence at the gene (TTN) and protein levels. I also touch upon properties of titin important for the stability of the contractile units and the assembly and maintenance of sarcomeric proteins. The greater part of my discussion centers around the mechanical function of titin in skeletal muscle. I cover milestones of research on titin's role in stretch-dependent passive tension development, recollect the reasons behind the enormous elastic diversity of titin, and provide an update on the molecular mechanisms of titin elasticity, details of which are emerging even now. I reflect on current knowledge of how muscle fibers behave mechanically if titin stiffness is removed and how titin stiffness can be dynamically regulated, such as by posttranslational modifications or calcium binding. Finally, I highlight novel and exciting, but still controversially discussed, insight into the role titin plays in active tension development, such as length-dependent activation and contraction from longer muscle lengths.

The N-terminus of obscurin is flexible in solution

The N-terminal half of the giant cytoskeletal protein obscurin is comprised of more than 50 Ig-like domains, arranged in tandem. Domains 18-51 are connected to each other through short 5-residue linkers, and this arrangement has been previously shown to form a semi-flexible rod in solution. Domains 1-18 generally have slightly longer ~7 residue interdomain linkers, and the multidomain structure and motion conferred by this kind of linker is understudied. Here, we use NMR, SAXS, and MD to show that these longer linkers are associated with significantly more domain/domain flexibility, with the resulting multidomain structure being moderately compact. Further examination of the relationship between interdomain flexibility and linker length shows there is a 5 residue "sweet spot" linker length that results in dual-domain systems being extended, and conversely that both longer or shorter linkers result in a less extended structure. This detailed knowledge of the obscurin N terminus structure and flexibility allowed for mathematical modeling of domains 1-18, which suggests that this region likely forms tangles if left alone in solution. Given how infrequently protein tangles occur in nature, and given the pathological outcomes that occur when tangles do arise, our data suggest that obscurin is likely either significantly scaffolded or else externally extended in the cell.

Myofilament-associated proteins with intrinsic disorder (MAPIDs) and their resolution by computational modeling

The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.

CHARMM-GUI Enhanced Sampler for various collective variables and enhanced sampling methods

Enhanced sampling methodologies modifying underlying Hamiltonians can be used for the systems with a rugged potential energy surface that makes it hard to observe convergence using conventional unbiased molecular dynamics (MD) simulations. We present CHARMM-GUI Enhanced Sampler, a web-based tool to prepare various enhanced sampling simulations inputs with user-selected collective variables (CVs). Enhanced Sampler provides inputs for the following nine methods: accelerated MD, Gaussian accelerated MD, conformational flooding, metadynamics, adaptive biasing force, steered MD, temperature replica exchange MD, replica exchange solute tempering 2, and replica exchange umbrella sampling for the method-implemented MD packages including AMBER, CHARMM, GENESIS, GROMACS, NAMD, and OpenMM. Users only need to select a group of atoms via intuitive web-implementation in order to define commonly used nine CVs of interest: center of mass based distance, angle, dihedral, root-mean-square-distance, radius of gyration, distance projected on axis, two types of angles projected on axis, and coordination numbers. The enhanced sampling methods are tested with several biological systems to illustrate their efficiency over conventional MD. Enhanced Sampler with carefully optimized system-dependent parameters will help users to get meaningful results from their enhanced sampling simulations.

Challenges in describing the conformation and dynamics of proteins with ambiguous behavior

Traditionally, our understanding of how proteins operate and how evolution shapes them is based on two main data sources: the overall protein fold and the protein amino acid sequence. However, a significant part of the proteome shows highly dynamic and/or structurally ambiguous behavior, which cannot be correctly represented by the traditional fixed set of static coordinates. Representing such protein behaviors remains challenging and necessarily involves a complex interpretation of conformational states, including probabilistic descriptions. Relating protein dynamics and multiple conformations to their function as well as their physiological context (e.g., post-translational modifications and subcellular localization), therefore, remains elusive for much of the proteome, with studies to investigate the effect of protein dynamics relying heavily on computational models. We here investigate the possibility of delineating three classes of protein conformational behavior: order, disorder, and ambiguity. These definitions are explored based on three different datasets, using interpretable machine learning from a set of features, from AlphaFold2 to sequence-based predictions, to understand the overlap and differences between these datasets. This forms the basis for a discussion on the current limitations in describing the behavior of dynamic and ambiguous proteins.

Elastic versus brittle mechanical responses predicted for dimeric cadherin complexes

Cadherins are a superfamily of adhesion proteins involved in a variety of biological processes that include the formation of intercellular contacts, the maintenance of tissue integrity, and the development of neuronal circuits. These transmembrane proteins are characterized by ectodomains composed of a variable number of extracellular cadherin (EC) repeats that are similar but not identical in sequence and fold. E-cadherin, along with desmoglein and desmocollin proteins, are three classical-type cadherins that have slightly curved ectodomains and engage in homophilic and heterophilic interactions through an exchange of conserved tryptophan residues in their N-terminal EC1 repeat. In contrast, clustered protocadherins are straighter than classical cadherins and interact through an antiparallel homophilic binding interface that involves overlapped EC1 to EC4 repeats. Here we present molecular dynamics simulations that model the adhesive domains of these cadherins using available crystal structures, with systems encompassing up to 2.8 million atoms. Simulations of complete classical cadherin ectodomain dimers predict a two-phased elastic response to force in which these complexes first softly unbend and then stiffen to unbind without unfolding. Simulated α, β, and γ clustered protocadherin homodimers lack a two-phased elastic response, are brittle and stiffer than classical cadherins and exhibit complex unbinding pathways that in some cases involve transient intermediates. We propose that these distinct mechanical responses are important for function, with classical cadherin ectodomains acting as molecular shock absorbers and with stiffer clustered protocadherin ectodomains facilitating overlap that favors binding specificity over mechanical resilience. Overall, our simulations provide insights into the molecular mechanics of single cadherin dimers relevant in the formation of cellular junctions essential for tissue function.

Collective mechanical responses of cadherin-based adhesive junctions as predicted by simulations

Cadherin-based adherens junctions and desmosomes help stabilize cell-cell contacts with additional function in mechano-signaling, while clustered protocadherin junctions are responsible for directing neuronal circuits assembly. Structural models for adherens junctions formed by epithelial cadherin (CDH1) proteins indicate that their long, curved ectodomains arrange to form a periodic, two-dimensional lattice stabilized by tip-to-tip trans interactions (across junction) and lateral cis contacts. Less is known about the exact architecture of desmosomes, but desmoglein (DSG) and desmocollin (DSC) cadherin proteins are also thought to form ordered junctions. In contrast, clustered protocadherin (PCDH)-based cell-cell contacts in neuronal tissues are thought to be responsible for self-recognition and avoidance, and structural models for clustered PCDH junctions show a linear arrangement in which their long and straight ectodomains form antiparallel overlapped trans complexes. Here, we report all-atom molecular dynamics simulations testing the mechanics of minimalistic adhesive junctions formed by CDH1, DSG2 coupled to DSC1, and PCDHγB4, with systems encompassing up to 3.7 million atoms. Simulations generally predict a favored shearing pathway for the adherens junction model and a two-phased elastic response to tensile forces for the adhesive adherens junction and the desmosome models. Complexes within these junctions first unbend at low tensile force and then become stiff to unbind without unfolding. However, cis interactions in both the CDH1 and DSG2-DSC1 systems dictate varied mechanical responses of individual dimers within the junctions. Conversely, the clustered protocadherin PCDHγB4 junction lacks a distinct two-phased elastic response. Instead, applied tensile force strains trans interactions directly, as there is little unbending of monomers within the junction. Transient intermediates, influenced by new cis interactions, are observed after the main rupture event. We suggest that these collective, complex mechanical responses mediated by cis contacts facilitate distinct functions in robust cell-cell adhesion for classical cadherins and in self-avoidance signaling for clustered PCDHs.

Nanosurgical Manipulation of Titin and Its M-Complex

Titin is a multifunctional filamentous protein anchored in the M-band, a hexagonally organized supramolecular lattice in the middle of the muscle sarcomere. Functionally, the M-band is a framework that cross-links myosin thick filaments, organizes associated proteins, and maintains sarcomeric symmetry via its structural and putative mechanical properties. Part of the M-band appears at the C-terminal end of isolated titin molecules in the form of a globular head, named here the “M-complex”, which also serves as the point of head-to-head attachment of titin. We used high-resolution atomic force microscopy and nanosurgical manipulation to investigate the topographical and internal structure and local mechanical properties of the M-complex and its associated titin molecules. We find that the M-complex is a stable structure that corresponds to the transverse unit of the M-band organized around the myosin thick filament. M-complexes may be interlinked into an M-complex array that reflects the local structural and mechanical status of the transversal M-band lattice. Local segments of titin and the M-complex could be nanosurgically manipulated to achieve extension and domain unfolding. Long threads could be pulled out of the M-complex, suggesting that it is a compact supramolecular reservoir of extensible filaments. Nanosurgery evoked an unexpected volume increment in the M-complex, which may be related to its function as a mechanical spacer. The M-complex thus displays both elastic and plastic properties which support the idea that the M-band may be involved in mechanical functions within the muscle sarcomere.

Microbial production of megadalton titin yields fibers with advantageous mechanical properties

Manmade high-performance polymers are typically non-biodegradable and derived from petroleum feedstock through energy intensive processes involving toxic solvents and byproducts. While engineered microbes have been used for renewable production of many small molecules, direct microbial synthesis of high-performance polymeric materials remains a major challenge. Here we engineer microbial production of megadalton muscle titin polymers yielding high-performance fibers that not only recapture highly desirable properties of natural titin (i.e., high damping capacity and mechanical recovery) but also exhibit high strength, toughness, and damping energy - outperforming many synthetic and natural polymers. Structural analyses and molecular modeling suggest these properties derive from unique inter-chain crystallization of folded immunoglobulin-like domains that resists inter-chain slippage while permitting intra-chain unfolding. These fibers have potential applications in areas from biomedicine to textiles, and the developed approach, coupled with the structure-function insights, promises to accelerate further innovation in microbial production of high-performance materials.

Metadynamics-Based Approaches for Modeling the Hypoxia-Inducible Factor 2α Ligand Binding Process

Several methods based on enhanced-sampling molecular dynamics have been proposed for studying ligand binding processes. Here, we developed a protocol that combines the advantages of steered molecular dynamics (SMD) and metadynamics. While SMD is proposed for investigating possible unbinding pathways of the ligand and identifying the preferred one, metadynamics, with the path collective variable (PCV) formalism, is suggested to explore the binding processes along the pathway defined on the basis of SMD, by using only two CVs. We applied our approach to the study of binding of two known ligands to the hypoxia-inducible factor 2α, where the buried binding cavity makes simulation of the process a challenging task. Our approach allowed identification of the preferred entrance pathway for each ligand, highlighted the features of the bound and intermediate states in the free-energy surface, and provided a binding affinity scale in agreement with experimental data. Therefore, it seems to be a suitable tool for elucidating ligand binding processes of similar complex systems.

Design of intrinsically disordered proteins that undergo phase transitions with lower critical solution temperatures

Many naturally occurring elastomers are intrinsically disordered proteins (IDPs) built up of repeating units and they can demonstrate two types of thermoresponsive phase behavior. Systems characterized by lower critical solution temperatures (LCST) undergo phase separation above the LCST whereas systems characterized by upper critical solution temperatures (UCST) undergo phase separation below the UCST. There is congruence between thermoresponsive coil-globule transitions and phase behavior whereby the theta temperatures above or below which the IDPs transition from coils to globules serve as useful proxies for the LCST / UCST values. This implies that one can design sequences with desired values for the theta temperature with either increasing or decreasing radii of gyration above the theta temperature. Here, we show that the Monte Carlo simulations performed in the so-called intrinsic solvation (IS) limit version of the temperature-dependent the ABSINTH (self-Assembly of Biomolecules Studied by an Implicit, Novel, Tunable Hamiltonian) implicit solvation model, yields a useful heuristic for discriminating between sequences with known LCST versus UCST phase behavior. Accordingly, we use this heuristic in a supervised approach, integrate it with a genetic algorithm, combine this with IS limit simulations, and demonstrate that novel sequences can be designed with LCST phase behavior. These calculations are aided by direct estimates of temperature dependent free energies of solvation for model compounds that are derived using the polarizable AMOEBA (atomic multipole optimized energetics for biomolecular applications) forcefield. To demonstrate the validity of our designs, we calculate coil-globule transition profiles using the full ABSINTH model and combine these with Gaussian Cluster Theory calculations to establish the LCST phase behavior of designed IDPs.

The hierarchical emergence of worm-like chain behaviour from globular domain polymer chains

Biological organisms make use of hierarchically organised structures to modulate mechanical behaviour across multiple lengthscales, allowing microscopic objects to generate macroscopic effects. Within these structural hierarchies, the resultant physical behaviour of the entire system is determined not only by the intrinsic mechanical properties of constituent subunits, but also by their organisation in three-dimensional space. When these subunits are polyproteins, colloidal chains or other globular domain polymers, the Kratky-Porod model is often assumed for the individual subunits. Hence, it is implicitly asserted that the polymeric object has an intrinsic parameter, the persistence length, that defines its flexibility. However, the persistence lengths extracted from experiment vary, and are often relatively small. Through a series of simulations on polymer chains formed of globular subunits, we show that the persistence length itself is a hierarchical structural property, related not only to the intrinsic mechanical properties of the underlying monomeric subunits, but emerging due to the organisation of inhomogenous geometry along the polymer contour.

Effects of S-glutathionylation on the passive force-length relationship in skeletal muscle fibres of rats and humans

This study investigated the effect of S-glutathionylation on passive force in skeletal muscle fibres, to determine whether activity-related redox reactions could modulate the passive force properties of muscle. Mechanically-skinned fibres were freshly obtained from human and rat muscle, setting sarcomere length (SL) by laser diffraction. Larger stretches were required to produce passive force in human fibres compared to rat fibres, but there were no fibre-type differences in either species. When fibres were exposed to glutathione disulfide (GSSG; 20 mM, 15 min) whilst stretched (at a SL where passive force reached ~ 20% of maximal Ca²⁺-activated force, denoted as SL_{20 % max}), passive force was subsequently decreased at all SLs in both type I and type II fibres of rat and human (e.g., passive force at SL_{20 % max} decreased by 12 to 25%). This decrease was fully reversed by subsequent reducing treatment with dithiothreitol (DTT; 10 mM for 10 min). If freshly skinned fibres were initially treated with DTT, there was an increase in passive force in type II fibres (by 10 ± 3% and 9 ± 2% in rat and human fibres, respectively), but not in type I fibres. These results indicate that (i) S-glutathionylation, presumably in titin, causes a decrease in passive force in skeletal muscle fibres, but the reduction is relatively smaller than that reported in cardiac muscle, (ii) in rested muscle in vivo, there appears to be some level of reversible oxidative modification, probably involving S-glutathionylation of titin, in type II fibres, but not in type I fibres.

Obscurin is a semi-flexible molecule in solution

Obscurin, a giant modular cytoskeletal protein, is comprised mostly of tandem immunoglobulin-like (Ig-like) domains. This architecture allows obscurin to connect distal targets within the cell. The linkers connecting the Ig domains are usually short (3-4 residues). The physical effect arising from these short linkers is not known; such linkers may lead to a stiff elongated molecule or, conversely, may lead to a more compact and dynamic structure. In an effort to better understand how linkers affect obscurin flexibility, and to better understand the physical underpinnings of this flexibility, here we study the structure and dynamics of four representative sets of dual obscurin Ig domains using experimental and computational techniques. We find in all cases tested that tandem obscurin Ig domains interact at the poles of each domain and tend to stay relatively extended in solution. NMR, SAXS, and MD simulations reveal that while tandem domains are elongated, they also bend and flex significantly. By applying this behavior to a simplified model, it becomes apparent obscurin can link targets more than 200 nm away. However, as targets get further apart, obscurin begins acting as a spring and requires progressively more energy to further elongate.

The Assembling and Contraction Mechanisms of Striated Muscles

A novel approach to the description of the assembly mechanism of functional biological structures is presented. The approach is based on the identification of fundamental self-assembling processes to which an additional structurization "engineered" by Nature to optimize functions is superimposed. Application of the approach to the structure and contraction of the striated muscle evidences a key role of the residual liquid crystallinity of a constrained structure and the alteration of the compatibility between the thin and thick filaments driven by ionic interactions. ATP hydrolysis boosts the relaxation process. A strong protein scaffold, engineered during the evolutionary process and based on the selective anchoring of coordinated filaments, directs a demixing tendency of the two filaments toward a sliding motion along the fiber axis. The Huxley-Hanson sliding filament hypothesis aimed to explain the contraction-relaxation function of the striated muscle, but does not offer any clue on the overall assembling mechanism of the myofibril.

Micromechanical model for protein materials: From macromolecules to macroscopic fibers

We propose a model for the mechanical behavior of protein materials. Based on a limited number of experimental macromolecular parameters (persistence and contour length) we obtain the macroscopic behavior of keratin fibers (human, cow, and rabbit hair), taking into account the damage and residual stretches effects that are fundamental in many functions of life. We also show the capability of our approach to describe the main dissipation and permanent strain effects observed in the more complex spider silk fibers. The comparison between our results and the data obtained experimentally from cyclic tests demonstrates that our model is robust and is able to reproduce with a remarkable accuracy the experimental behavior of all protein materials we tested.

Nanomechanics of multidomain neuronal cell adhesion protein contactin revealed by single molecule AFM and SMD

Contactin-4 (CNTN4) is a complex cell adhesion molecule (CAM) localized at neuronal membranes, playing a key role in maintaining the mechanical integrity and signaling properties of the synapse. CNTN4 consists of six immunoglobulin C2 type (IgC2) domains and four fibronectin type III (FnIII) domains that are shared with many other CAMs. Mutations in CNTN4 gene have been linked to various psychiatric disorders. Toward elucidating the response of this modular protein to mechanical stress, we studied its force-induced unfolding using single molecule atomic force microscopy (smAFM) and steered molecular dynamics (SMD) simulations. Extensive smAFM and SMD data both indicate the distinctive mechanical behavior of the two types of modules distinguished by unique force-extension signatures. The data also reveal the heterogeneity of the response of the individual FNIII and IgC2 modules, which presumably plays a role in the adaptability of CNTN4 to maintaining cell-cell communication and adhesion properties under different conditions. Results show that extensive sampling of force spectra, facilitated by robot-enhanced AFM, can help reveal the existence of weak stabilizing interactions between the domains of multidomain proteins, and provide insights into the nanomechanics of such multidomain or heteromeric proteins.

A map of the phosphoproteomic alterations that occur after a bout of maximal-intensity contractions

KEY POINTS

Mechanical signals play a critical role in the regulation of muscle mass, but the molecules that sense mechanical signals and convert this stimulus into the biochemical events that regulate muscle mass remain ill-defined. Here we report a mass spectrometry-based workflow to study the changes in protein phosphorylation that occur in mouse skeletal muscle 1 h after a bout of electrically evoked maximal-intensity contractions (MICs). Our dataset provides the first comprehensive map of the MIC-regulated phosphoproteome. Using unbiased bioinformatics approaches, we demonstrate that our dataset leads to the identification of many well-known MIC-regulated signalling pathways, as well as to a plethora of novel MIC-regulated events. We expect that our dataset will serve as a fundamentally important resource for muscle biologists, and help to lay the foundation for entirely new hypotheses in the field.

ABSTRACT

The maintenance of skeletal muscle mass is essential for health and quality of life. It is well recognized that maximal-intensity contractions, such as those which occur during resistance exercise, promote an increase in muscle mass. Yet, the molecules that sense the mechanical information and convert it into the signalling events (e.g. phosphorylation) that drive the increase in muscle mass remain undefined. Here we describe a phosphoproteomics workflow to examine the effects of electrically evoked maximal-intensity contractions (MICs) on protein phosphorylation in mouse skeletal muscle. While a preliminary phosphoproteomics experiment successfully identified a number of MIC-regulated phosphorylation events, a large proportion of these identifications were present on highly abundant myofibrillar proteins. We subsequently incorporated a centrifugation-based fractionation step to deplete the highly abundant myofibrillar proteins and performed a second phosphoproteomics experiment. In total, we identified 5983 unique phosphorylation sites of which 663 were found to be regulated by MIC. GO term enrichment, phosphorylation motif analyses, and kinase-substrate predictions indicated that the MIC-regulated phosphorylation sites were chiefly modified by mTOR, as well as multiple isoforms of the MAPKs and CAMKs. Moreover, a high proportion of the regulated phosphorylation sites were found on proteins that are associated with the Z-disc, with over 74% of the Z-disc proteins experiencing robust changes in phosphorylation. Finally, our analyses revealed that the phosphorylation state of two Z-disc kinases (striated muscle-specific serine/threonine protein kinase and obscurin) was dramatically altered by MIC, and we propose ways these kinases could play a fundamental role in skeletal muscle mechanotransduction.

Structural advances on titin: towards an atomic understanding of multi-domain functions in myofilament mechanics and scaffolding

Titin is a gigantic filamentous protein of the muscle sarcomere that plays roles in myofibril mechanics and homoeostasis. 3D-structures of multi-domain fragments of titin are now available that start revealing the molecular mechanisms governing its mechanical and scaffolding functions. This knowledge is now being translated into the fabrication of self-assembling biopolymers. Here we review the structural advances on titin, the novel concepts derived from these and the emerging translational avenues.

Mechanics of Vascular Smooth Muscle

Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress-development, sustained stress-maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip-catch bond, and a regulated two-step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress-strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure-function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM.

Role of the central cations in the mechanical unfolding of DNA and RNA G-quadruplexes

Cations are known to mediate diverse interactions in nucleic acids duplexes but they are critical in the arrangement of four-stranded structures. Here, we use all-atom molecular dynamics simulations with explicit solvent to analyse the mechanical unfolding of representative intramolecular G-quadruplex structures: a parallel, a hybrid and an antiparallel DNA and a parallel RNA, in the presence of stabilising cations. We confirm the stability of these conformations in the presence of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\rm {K}^+$\end{document} central ions and observe distortions from the tetrad topology in their absence. Force-induced unfolding dynamics is then investigated. We show that the unfolding events in the force-extension curves are concomitant to the loss of coordination between the central ions and the guanines of the G-quadruplex. We found lower ruptures forces for the parallel configuration with respect to the antiparallel one, while the behaviour of the force pattern of the parallel RNA appears similar to the parallel DNA. We anticipate that our results will be essential to interpret the fine structure rupture profiles in stretching assays at high resolution and will shed light on the mechanochemical activity of G-quadruplex-binding machinery.

Mechanical dissociation of the M-band titin/obscurin complex is directionally dependent

Titin and obscurin, two giant muscle proteins, bind to each other in an antiparallel Ig-Ig fashion at the M-band. This interaction must be able to withstand the mechanical strain that the M-band typically experiences and remain intact. The mechanical force on these domains is likely exerted along one of two axes: a longitudinal axis, resulting in a 'shearing' force, or a lateral axis, resulting in a 'peeling' force. Here we present molecular dynamics data suggesting that these forces result in distinct unraveling pathways of the titin/obscurin complex and that peeling the domains apart requires less work and force.

Molecular basis of the mechanical hierarchy in myomesin dimers for sarcomere integrity

Myomesin is one of the most important structural molecules constructing the M-band in the force-generating unit of striated muscle, and a critical structural maintainer of the sarcomere. Using molecular dynamics simulations, we here dissect the mechanical properties of the structurally known building blocks of myomesin, namely α-helices, immunoglobulin (Ig) domains, and the dimer interface at myomesin's 13th Ig domain, covering the mechanically important C-terminal part of the molecule. We find the interdomain α-helices to be stabilized by the hydrophobic interface formed between the N-terminal half of these helices and adjacent Ig domains, and, interestingly, to show a rapid unfolding and refolding equilibrium especially under low axial forces up to ∼ 15 pN. These results support and yield atomic details for the notion of recent atomic-force microscopy experiments, namely, that the unique helices inserted between Ig domains in myomesin function as elastomers and force buffers. Our results also explain how the C-terminal dimer of two myomesin molecules is mechanically outperforming the helices and Ig domains in myomesin and elsewhere, explaining former experimental findings. This study provides a fresh view onto how myomesin integrates elastic helices, rigid immunoglobulin domains, and an extraordinarily resistant dimer into a molecular structure, to feature a mechanical hierarchy that represents a firm and yet extensible molecular anchor to guard the stability of the sarcomere.

The role of binding site on the mechanical unfolding mechanism of ubiquitin

We apply novel atomistic simulations based on potential energy surface exploration to investigate the constant force-induced unfolding of ubiquitin. At the experimentally-studied force clamping level of 100 pN, we find a new unfolding mechanism starting with the detachment between β₅ and β₃ involving the binding site of ubiquitin, the Ile44 residue. This new unfolding pathway leads to the discovery of new intermediate configurations, which correspond to the end-to-end extensions previously seen experimentally. More importantly, it demonstrates the novel finding that the binding site of ubiquitin can be responsible not only for its biological functions, but also its unfolding dynamics. We also report in contrast to previous single molecule constant force experiments that when the clamping force becomes smaller than about 300 pN, the number of intermediate configurations increases dramatically, where almost all unfolding events at 100 pN involve an intermediate configuration. By directly calculating the life times of the intermediate configurations from the height of the barriers that were crossed on the potential energy surface, we demonstrate that these intermediate states were likely not observed experimentally due to their lifetimes typically being about two orders of magnitude smaller than the experimental temporal resolution.

Peroxinectin catalyzed dityrosine crosslinking in the adhesive underwater silk of a casemaker caddisfly larvae, Hysperophylax occidentalis

Aquatic caddisfly larvae use sticky silk fibers as an adhesive tape to construct protective composite structures under water. Three new silk fiber components were identified by transcriptome and proteome analysis of the silk gland: a heme-peroxidase in the peroxinectin (Pxt) sub-family, a superoxide dismutase 3 (SOD3) that generates the H2O2 substrate of the silk fiber Pxt from environmental reactive oxygen species (eROS), and a novel structural component with sequence similarity to the elastic PEVK region of the muscle protein, titin. All three proteins are co-drawn with fibroins to form silk fibers. The Pxt and SOD3 enzymes retain activity in drawn fibers. In native fibers, Pxt activity and dityrosine crosslinks are co-localized at the boundary of a peripheral layer and the silk fiber core. To our knowledge, dityrosine crosslinks, heme peroxidase, and SOD3 activities have not been previously reported in an insect silk. The PEVK-like protein is homogeneously distributed throughout the fiber core. The results are consolidated into a model in which caddisfly silk Pxt-catalyzed dityrosine crosslinking occurs post-draw using H2O2 generated within the silk fibers by SOD3. The ROS substrate of caddisfly silk SOD3 occurs naturally in aquatic environments, from biotic and abiotic sources. The radially inhomogeneous dityrosine crosslinking and a potential titin-like PEVK protein network have important implications for the mechanical properties of caddifly silk fibers.

Cavity approach for modeling and fitting polymer stretching

The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly studied force-elongation relation is typically hard. Here we draw from techniques developed in the context of disordered systems to solve models for single and double-stranded DNA stretching in the limit of a long polymeric chain. Since we directly derive the marginals for the molecule local orientation, our approach allows us to readily calculate the experimental elongation as well as other observables at wish. As an example, we evaluate the correlation length as a function of the stretching force. Furthermore, we are able to fit successfully our solution to real experimental data. Although the model is admittedly phenomenological, our findings are very sound. For single-stranded DNA our solution yields the correct (monomer) scale and yet, more importantly, the right persistence length of the molecule. In the double-stranded case, our model reproduces the well-known overstretching transition and correctly captures the ratio between native DNA and overstretched DNA. Also in this case the model yields a persistence length in good agreement with consensus, and it gives interesting insights into the bending stiffness of the native and overstretched molecule, respectively.

Gigantic business: titin properties and function through thick and thin

The giant protein titin forms a unique filament network in cardiomyocytes, which engages in both mechanical and signaling functions of the heart. TTN, which encodes titin, is also a major human disease gene. In this review, we cover the roles of cardiac titin in normal and failing hearts, with a special emphasis on the contribution of titin to diastolic stiffness. We provide an update on disease-associated titin mutations in cardiac and skeletal muscles and summarize what is known about the impact of protein-protein interactions on titin properties and functions. We discuss the importance of titin-isoform shifts and titin phosphorylation, as well as titin modifications related to oxidative stress, in adjusting the diastolic stiffness of the healthy and the failing heart. Along the way we distinguish among titin alterations in systolic and in diastolic heart failure and ponder the evidence for titin stiffness as a potential target for pharmacological intervention in heart disease.

Nanomechanics of β-rich proteins related to neuronal disorders studied by AFM, all-atom and coarse-grained MD methods

Computer simulations of protein unfolding substantially help to interpret force-extension curves measured in single-molecule atomic force microscope (AFM) experiments. Standard all-atom (AA) molecular dynamics simulations (MD) give a good qualitative mechanical unfolding picture but predict values too large for the maximum AFM forces with the common pulling speeds adopted here. Fine tuned coarse-grain MD computations (CG MD) offer quantitative agreement with experimental forces. In this paper we address an important methodological aspect of MD modeling, namely the impact of numerical noise generated by random assignments of bead velocities on maximum forces (F_max) calculated within the CG MD approach. Distributions of CG forces from 2000 MD runs for several model proteins rich in β structures and having folds with increasing complexity are presented. It is shown that F_max have nearly Gaussian distributions and that values of F_max for each of those β-structures may vary from 93.2 ± 28.9 pN (neurexin) to 198.3 ± 25.2 pN (fibronectin). The CG unfolding spectra are compared with AA steered MD data and with results of our AFM experiments for modules present in contactin, fibronectin and neurexin. The stability of these proteins is critical for the proper functioning of neuronal synaptic clefts. Our results confirm that CG modeling of a single molecule unfolding is a good auxiliary tool in nanomechanics but large sets of data have to be collected before reliable comparisons of protein mechanical stabilities are made.

Figure

Catch bond-like kinetics of helix cracking: network analysis by molecular dynamics and milestoning

The first events of unfolding of secondary structure under load are considered with Molecular Dynamics simulations and Milestoning analysis of a long helix (126 amino acids). The Mean First Passage Time is a non-monotonic function of the applied load with a maximum of 3.6 ns at about 20 pN. Network analysis of the reaction space illustrates the opening and closing of an off-pathway trap that slows unfolding at intermediate load levels. It is illustrated that the nature of the reaction networks changes as a function of load, demonstrating that the process is far from one-dimensional.

An energetic model for macromolecules unfolding in stretching experiments

We propose a simple approach, based on the minimization of the total (entropic plus unfolding) energy of a two-state system, to describe the unfolding of multi-domain macromolecules (proteins, silks, polysaccharides, nanopolymers). The model is fully analytical and enlightens the role of the different energetic components regulating the unfolding evolution. As an explicit example, we compare the analytical results with a titin atomic force microscopy stretch-induced unfolding experiment showing the ability of the model to quantitatively reproduce the experimental behaviour. In the thermodynamic limit, the sawtooth force-elongation unfolding curve degenerates to a constant force unfolding plateau.

Elasticity, structure, and relaxation of extended proteins under force

Force spectroscopies have emerged as a powerful and unprecedented tool to study and manipulate biomolecules directly at a molecular level. Usually, protein and DNA behavior under force is described within the framework of the worm-like chain (WLC) model for polymer elasticity. Although it has been surprisingly successful for the interpretation of experimental data, especially at high forces, the WLC model lacks structural and dynamical molecular details associated with protein relaxation under force that are key to the understanding of how force affects protein flexibility and reactivity. We use molecular dynamics simulations of ubiquitin to provide a deeper understanding of protein relaxation under force. We find that the WLC model successfully describes the simulations of ubiquitin, especially at higher forces, and we show how protein flexibility and persistence length, probed in the force regime of the experiments, are related to how specific classes of backbone dihedral angles respond to applied force. Although the WLC model is an average, backbone model, we show how the protein side chains affect the persistence length. Finally, we find that the diffusion coefficient of the protein's end-to-end distance is on the order of 10(8) nm(2)/s, is position and side-chain dependent, but is independent of the length and independent of the applied force, in contrast with other descriptions.

GFP's mechanical intermediate states

Green fluorescent protein (GFP) mutants have become the most widely used fluorescence markers in the life sciences, and although they are becoming increasingly popular as mechanical force or strain probes, there is little direct information on how their fluorescence changes when mechanically stretched. Here we derive high-resolution structural models of the mechanical intermediate states of stretched GFP using steered molecular dynamics (SMD) simulations. These structures were used to produce mutants of EGFP and EYFP that mimic GFP's different mechanical intermediates. A spectroscopic analysis revealed that a population of EGFP molecules with a missing N-terminal α-helix was significantly dimmed, while the fluorescence lifetime characteristic of the anionic chromophore state remained unaffected. This suggests a mechanism how N-terminal deletions can switch the protonation state of the chromophore, and how the fluorescence of GFP molecules in response to mechanical disturbance might be turned off.

Gauging the flexibility of the active site in soybean lipoxygenase-1 (SLO-1) through an atom-centered density matrix propagation (ADMP) treatment that facilitates the sampling of rare events

We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical toward maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

GPU/CPU Algorithm for Generalized Born/Solvent-Accessible Surface Area Implicit Solvent Calculations

Molecular dynamics methodologies comprise a vital research tool for structural biology. Molecular dynamics has benefited from technological advances in computing, such as multi-core CPUs and graphics processing units (GPUs), but harnessing the full power of hybrid GPU/CPU computers remains difficult. The generalized Born/solvent-accessible surface area implicit solvent model (GB/SA) stands to benefit from hybrid GPU/CPU computers, employing the GPU for the GB calculation and the CPU for the SA calculation. Here, we explore the computational challenges facing GB/SA calculations on hybrid GPU/CPU computers and demonstrate how NAMD, a parallel molecular dynamics program, is able to efficiently utilize GPUs and CPUs simultaneously for fast GB/SA simulations. The hybrid computation principles demonstrated here are generally applicable to parallel applications employing hybrid GPU/CPU calculations.

Engineering proteins with enhanced mechanical stability by force-specific sequence motifs

Use of atomic force microscopy (AFM) has recently led to a better understanding of the molecular mechanisms of the unfolding process by mechanical forces; however, the rational design of novel proteins with specific mechanical strength remains challenging. We have approached this problem from a new perspective that generates linear physical-chemical properties (PCP) motifs from a limited AFM data set. Guided by our linear sequence analysis, we designed and analyzed four new mutants of the titin I1 domain with the goal of increasing the domain's mechanical strength. All four mutants could be cloned and expressed as soluble proteins. AFM data indicate that at least two of the mutants have increased molecular mechanical strength. This observation suggests that the PCP method is useful to graft sequences specific for high mechanical stability to weak proteins to increase their mechanical stability, and represents an additional tool in the design of novel proteins besides steered molecular dynamics calculations, coarse grained simulations, and ϕ-value analysis of the transition state.

Two immunoglobulin tandem proteins with a linking β-strand reveal unexpected differences in cooperativity and folding pathways

The study of the folding of single domains, in the context of their multidomain environment, is important because more than 70% of eukaryotic proteins are composed of multiple domains. The structures of the tandem immunoglobulin (Ig) domain pairs A164–A165 and A168–A169, from the A-band of the giant muscle protein titin, reveal that they form tightly associated domain arrangements, connected by a continuous β-strand. We investigate the thermodynamic and kinetic properties of these tandem domain pairs. While A164–A165 apparently behaves as a single cooperative unit at equilibrium, unfolding without the accumulation of a large population of intermediates, domains in A168–A169 behave independently. Although A169 appears to be stabilized in the tandem protein, we show that this is due to nonspecific stabilization by extension. We elucidate the folding and unfolding pathways of both tandem pairs and show that cooperativity in A164–A165 is a manifestation of the relative refolding and unfolding rate constants of each individual domain. We infer that the differences between the two tandem pairs result from a different pattern of interactions at the domain/domain interface.

Extension of a three-helix bundle domain of myosin VI and key role of calmodulins

The molecular motor protein myosin VI moves toward the minus-end of actin filaments with a step size of 30-36 nm. Such large step size either drastically limits the degree of complex formation between dimer subunits to leave enough length for the lever arms, or requires an extension of the lever arms' crystallographically observed structure. Recent experimental work proposed that myosin VI dimerization triggers the unfolding of the protein's proximal tail domain which could drive the needed lever-arm extension. Here, we demonstrate through steered molecular dynamics simulation the feasibility of sufficient extension arising from turning a three-helix bundle into a long α-helix. A key role is played by the known calmodulin binding that facilitates the extension by altering the strain path in myosin VI. Sequence analysis of the proximal tail domain suggests that further calmodulin binding sites open up when the domain's three-helix bundle is unfolded and that subsequent calmodulin binding stabilizes the extended lever arms.

Atoms-to-microns model for small solute transport through sticky nanochannels

Modeling the transport of solutes through fluidic systems that have adsorbing surfaces is challenging due to the range of length and time scales involved. The components of such systems typically have dimensions from hundreds of nanometres to microns, whereas adsorption of solutes is sensitive to the atomic-scale structure of the solutes and surfaces. Here, we describe an atomic-resolution Brownian dynamics method for modeling the transport of solutes through sticky nanofluidic channels. Our method can fully recreate the results of all-atom molecular dynamics simulations at a fraction of the computational cost of the latter, which makes simulations of micron-size channels at a millisecond time scale possible without losing information about the atomic-scale features of the system. We demonstrate the capability of our method by simulating the rise and fall of solute concentration in sub-micron-long sticky nanochannels, showing that the atomic-scale features of the channels' surfaces have a dramatic effect on the kinetics of solute transport in and out of the channels. We expect our method to find applications in design and optimization of micro and nanofluidic systems for solute-specific transport and to complement existing approaches to modeling lab-on-a-chip devices by providing atomic scale information at a low computational cost.

Understanding the molecular mechanism of enzyme dynamics of ribonuclease A through protonation/deprotonation of HIS48

Molecular dynamics simulation is carried out to investigate the enzyme dynamics of RNase A with the HIS48 in three different states (HIP48 (protonated), HID48 (deprotonated), and H48A mutant). Insights derived from the current theoretical study, combined with the available experimental observations, enabled us to provide a microscopic picture for the efficient enzyme dynamics. Specifically, in the "closed" state or HIP48, the N-terminal hinge loop is intact and the enzyme remains in a relatively stable conformation which is preferred for catalytic reaction. Deprotonation of HIS48 induces the denaturing of this hinge-loop into a 3(10)-helix, causing it to break the original interaction network around the loop-1 and drive the partial unfolding of the N-terminal. The enhanced dynamic motion of the N-terminal helix facilitates the release of the catalytic product (the rate limiting step) and speeds up the overall catalytic process. The current study established that HIS49 acts as a modulator for the transformation of conformational states through the perturbing of hydrogen bond networks across loop-1, the N-terminal helix, and other residues nearby. Our study suggests that HIS48 may also serve to transport loop-1's kinetic energy to the reaction center.

Improved resolution of tertiary structure elasticity in muscle protein

Rearrangement of tertiary structure in response to mechanical force (termed tertiary structure elasticity) in the tandem Ig chain is the first mode of elastic response for muscle protein titin. Tertiary structure elasticity occurs at low stretching forces (few tens of pN), and was described at atomic resolution in a recent molecular dynamics study, in which an originally crescent-shaped six-Ig chain was stretched into a linear chain. However, the force-extension profile that resulted from this explicit solvent simulation was dominated by the hydrodynamic drag force, and effects of tertiary structure elasticity only manifested for stretching forces above 20 pN. Here we report a slow pulling 100-ns simulation (along with other auxiliary simulations), in which hydrodynamic drag force is seen to reduce to near 0 pN, such that tertiary structure elasticity could be characterized over a 0-200 pN range. Statistical mechanical analysis showed that the stretching velocity was sufficiently low such that the protein remained significantly relaxed during the major part of its extension.