Folding-unfolding transitions in single titin molecules characterized with laser tweezers

Conformational manipulation of scale-up prepared single-chain polymeric nanogels for multiscale regulation of cells

Folded single chain polymeric nano-objects are the molecular level soft material with ultra-small size. Here, we report an easy and scalable method for preparing single-chain nanogels (SCNGs) with improved efficiency. We further investigate the impact of the dynamic molecular conformational change of SCNGs on cellular interactions from molecular to bulk scale. First, the supramolecular unfoldable SCNGs efficiently deliver siRNAs into stem cells as a molecular drug carrier in a conformation-dependent manner. Furthermore, the conformation changes of SCNGs enable dynamic and precise manipulation of ligand tether structure on 2D biomaterial interfaces to regulate the ligand-receptor ligation and mechanosensing of cells. Lastly, the dynamic SCNGs as the building blocks provide effective energy dissipation to bulk biomaterials such as hydrogels, thereby protecting the encapsulated stem cells from deleterious mechanical shocks in 3D matrix. Such a bottom-up molecular tailoring strategy will inspire further applications of single-chain nano-objects in the biomedical area.

Label-free Imaging and Bending Analysis of Microtubules by ROCS Microscopy and Optical Trapping

Mechanical manipulation of single cytoskeleton filaments and their monitoring over long times is difficult because of fluorescence bleaching or phototoxic protein degradation. The integration of label-free microscopy techniques, capable of imaging freely diffusing, weak scatterers such as microtubules (MTs) in real-time, and independent of their orientation, with optical trapping and tracking systems, would allow many new applications. Here, we show that rotating-coherent-scattering microscopy (ROCS) in dark-field mode can also provide strong contrast for structures far from the coverslip such as arrangements of isolated MTs and networks. We could acquire thousands of images over up to 30 min without loss in image contrast or visible photodamage. We further demonstrate the combination of ROCS imaging with fast and nanometer-precise 3D interferometric back-focal-plane tracking of multiple beads in time-shared optical traps using acoustooptic deflectors to specifically construct and microrheologically probe small microtubule networks with well-defined geometries. Thereby, we explore the frequency-dependent elastic response of single microtubule filaments between 0.5 Hz and 5 kHz, which allows for investigating their viscoelastic response up to the fourth-order bending mode. Our spectral analysis reveals constant filament stiffness at low frequencies and frequency-dependent stiffening following a power law ∼ω^p with a length-dependent exponent p(L). We find further evidence for the dependence of the MT persistence length on the contour length L, which is still controversially debated. We could also demonstrate slower stiffening at high frequencies for longer filaments, which we believe is determined by the molecular architecture of the MT. Our results shed new light on the nanomechanics of this essential, multifunctional cytoskeletal element and pose new questions about the adaptability of the cytoskeleton.

Tensile Loads on Tethered Actin Filaments Induce Accumulation of Cell Adhesion-Associated Proteins in Vitro

Focal adhesions (FAs) and adherens junctions (AJs), which serve as a mechanical interface of cell-matrix and cell-cell interactions, respectively, experience tensile force either originating from the deformation of the surrounding tissues or generated by the actomyosin machinery in the cell. These mechanical inputs cause enlargement of FAs and AJs, while the detailed mechanism for the force-dependent development of FAs and AJs remain unclear. Both FAs and AJs provide sites for tethering of actin filaments and actin polymerization. Here, we develop a cell-free system, in which actin filaments are tethered to glass surfaces, and show that application of tensile force to the tethered filaments in the cell extract induces accumulation of several FA and AJ proteins, associated with further accumulation of actin filaments via de novo actin polymerization. Decline in the tensile force results in a decrease in the amount of the accumulated proteins. These results suggest that the tensile force acting on the tethered actin filaments plays a crucial role in the accumulation of FA and AJ proteins.

Passive force enhancement in striated muscle

Passive force enhancement is defined as the increase in passive, steady-state, isometric force of an actively stretched muscle compared with the same muscle stretched passively to that same length. Passive force enhancement is long lasting, increases with increasing muscle length and increasing stretch magnitudes, contributes to the residual force enhancement in skeletal and cardiac muscle, and is typically only observed at muscle lengths at which passive forces occur naturally. Passive force enhancement is typically equal to or smaller than the total residual force enhancement, it persists when a muscle is deactivated and reactivated, but can be abolished instantaneously when a muscle is shortened quickly from its stretched length. There is strong evidence that the passive force enhancement is caused by the filamentous sarcomeric protein titin, although the detailed molecular mechanisms underlying passive force enhancement remain unknown. Here I propose a tentative mechanism based on experimental evidence that associates passive force enhancement with the shortening of titin's free spring length in the I-band region of sarcomeres. I suggest that this shortening is accomplished by titin binding to actin and that the trigger for titin-actin interactions is associated with the formation of strongly bound cross bridges between actin and myosin that exposes actin attachment sites for titin through movement of the regulatory proteins troponin and tropomyosin.

An Overview of Molecular Modeling for Drug Discovery with Specific Illustrative Examples of Applications

In this paper we review the current status of high-performance computing applications in the general area of drug discovery. We provide an introduction to the methodologies applied at atomic and molecular scales, followed by three specific examples of implementation of these tools. The first example describes in silico modeling of the adsorption of small molecules to organic and inorganic surfaces, which may be applied to drug delivery issues. The second example involves DNA translocation through nanopores with major significance to DNA sequencing efforts. The final example offers an overview of computer-aided drug design, with some illustrative examples of its usefulness.

Posttranslational modifications of titin from cardiac muscle: how, where, and what for?

Titin is a giant elastic protein expressed in the contractile units of striated muscle cells, including the sarcomeres of cardiomyocytes. The last decade has seen enormous progress in our understanding of how titin molecular elasticity is modulated in a dynamic manner to help cardiac sarcomeres adjust to the varying hemodynamic demands on the heart. Crucial events mediating the rapid modulation of cardiac titin stiffness are post‐translational modifications (PTMs) of titin. In this review, we first recollect what is known from earlier and recent work on the molecular mechanisms of titin extensibility and force generation. The main goal then is to provide a comprehensive overview of current insight into the relationship between titin PTMs and cardiomyocyte stiffness, notably the effect of oxidation and phosphorylation of titin spring segments on titin stiffness. A synopsis is given of which type of oxidative titin modification can cause which effect on titin stiffness. A large part of the review then covers the mechanically relevant phosphorylation sites in titin, their location along the elastic segment, and the protein kinases and phosphatases known to target these sites. We also include a detailed coverage of the complex changes in phosphorylation at specific titin residues, which have been reported in both animal models of heart disease and in human heart failure, and their correlation with titin‐based stiffness alterations. Knowledge of the relationship between titin PTMs and titin elasticity can be exploited in the search for therapeutic approaches aimed at softening the pathologically stiffened myocardium in heart failure patients.

Gaussian Process-Integrated State Space Model for Continuous Joint Angle Prediction from EMG and Interactive Force in a Human-Exoskeleton System

As one of the most direct indicators of the transparency between a human and an exoskeleton, interactive force has rarely been fused with electromyography (EMG) in the control of human-exoskeleton systems, the performances of which are largely determined by the accuracy of the continuous joint angle prediction. To achieve intuitive and naturalistic human intent learning, a state space model (SSM) for continuous angle prediction of knee joint is developed. When the influence of the interactive force is often ignored in the existing models of human-exoskeleton systems, interactive force is applied as the measurement model output of the proposed SSM, and the EMG signal is used as the state model input signal to indicate muscle activation. The forward dynamics of joint motion and the human-machine interaction mechanism, i.e., the biomechanical interpretations of the interactive force generation mechanism, are derived as the bases for the state model and measurement model based on Hill’s muscle model and semiphenomenological (SP) muscular model, respectively. Gaussian process (GP)-based nonlinear autoregressive with the exogenous inputs (NARX) model and back-propagation neural network (BPNN) are applied to provide better adaptivity for the SSM in practical applications. Corresponding experimental results demonstrate the validity and superiority of the method.

Generalization of the elastic network model for the study of large conformational changes in biomolecules

The elastic network (EN) is a prime model that describes the long-time dynamics of biomolecules. However, the use of harmonic potentials renders this model insufficient for studying large conformational changes of proteins (e.g. stretching of proteins, folding and thermal unfolding). Here, we extend the capabilities of the EN model by using a harmonic approximation described by Lennard-Jones (LJ) interactions for far contacts and native contacts obtained from the standard overlap criterion as in the case of Gō-like models. While our model is validated against the EN model by reproducing the equilibrium properties for a number of proteins, we also show that the model is suitable for the study of large conformation changes by providing various examples. In particular, this is illustrated on the basis of pulling simulations that predict with high accuracy the experimental data on the rupture force of the studied proteins. Furthermore, in the case of DDFLN4 protein, our pulling simulations highlight the advantages of our model with respect to Gō-like approaches, where the latter fail to reproduce previous results obtained by all-atom simulations that predict an additional characteristic peak for this protein. In addition, folding simulations of small peptides yield different folding times for α-helix and β-hairpin, in agreement with experiment, in this way providing further opportunities for the application of our model in studying large conformational changes of proteins. In contrast to the EN model, our model is suitable for both normal mode analysis and molecular dynamics simulation. We anticipate that the proposed model will find applications in a broad range of problems in biology, including, among others, protein folding and thermal unfolding.

3D Conformations of Thick Synthetic Polymer Chains Observed by Cryogenic Electron Microscopy

The backbone conformations of individual, unperturbed synthetic macromolecules have so far not been observed directly in spite of their fundamental importance to polymer physics. Here we report the dilute solution conformations of two types of linear dendronized polymers, obtained by cryogenic transmission electron stereography and tomography. The three-dimensional trajectories show that the wormlike chain model fails to adequately describe the scaling of these thick macromolecules already beyond a few nanometers in chain length, in spite of large apparent persistence lengths and long before a signature of self-avoidance appears. This insight is essential for understanding the limitations of polymer physical models, and it motivated us to discuss the advantages and disadvantages of this approach in comparison to the commonly applied scattering techniques.

A dual role in regulation and toxicity for the disordered N-terminus of the toxin GraT

Bacterial toxin-antitoxin (TA) modules are tightly regulated to maintain growth in favorable conditions or growth arrest during stress. A typical regulatory strategy involves the antitoxin binding and repressing its own promoter while the toxin often acts as a co-repressor. Here we show that Pseudomonas putida graTA-encoded antitoxin GraA and toxin GraT differ from other TA proteins in the sense that not the antitoxin but the toxin possesses a flexible region. GraA auto-represses the graTA promoter: two GraA dimers bind cooperatively at opposite sides of the operator sequence. Contrary to other TA modules, GraT is a de-repressor of the graTA promoter as its N-terminal disordered segment prevents the binding of the GraT₂A₂ complex to the operator. Removal of this region restores operator binding and abrogates Gr aT toxicity. GraTA represents a TA module where a flexible region in the toxin rather than in the antitoxin controls operon expression and toxin activity.

The Pseudomonas putida toxin GraT and antitoxin GraA form a type II toxin-antoxin module. Here the authors present the crystal structures of the GraA dimer, GraTA and GraA-DNA complexes and show that GraT contains a functionally important N-terminal intrinsic disordered region that prevents the binding of the GraTA complex to the operator.

Uncertainty quantification for Markov state models of biomolecules constructed using rare event acceleration techniques

Markov state models (MSMs) of biomolecular systems are often constructed using the molecular dynamics (MD) technique. Despite having very long MD trajectories, some states and pathways can be missing in the MD data, which may make the MSMs incomplete. Consequently, uncertainty quantification for the resulting MSM becomes important. Using deca-alanine as a prototype system, we demonstrate that rare-event acceleration techniques can be employed to greatly lower the MSM uncertainty with a high computational efficiency with the assumption that the rare-event acceleration technique is able to determine most pathways that are relevant to the dynamics. In particular, we explore applications of steered MD to construct MSMs. Upper and lower bounds for uncertainty in the resulting MSM are derived. Safeguards are built into our approach to handle scenarios where the rare-event acceleration technique is unable to discover some important pathways.

Multiple stochastic pathways in forced peptide-lipid membrane detachment

We have used high resolution AFM based dynamic force spectroscopy to investigate peptide-lipid membrane interactions by measuring the detachment (last-rupture) force distribution, P(F), and the corresponding force dependent rupture rate, k(F), for two different peptides and lipid bilayers. The measured quantities, which differed considerably for different peptides, lipid-membranes, AFM tips (prepared under identical conditions), and retraction speeds of the AFM cantilever, could not be described in terms of the standard theory, according to which detachment occurs along a single pathway, corresponding to a diffusive escape process across a free energy barrier. In particular, the prominent retraction speed dependence of k(F) was a clear indication that peptide-lipid membrane dissociation occurs stochastically along several detachment pathways. Thereby, we have formulated a general theoretical approach for describing P(F) and k(F), by assuming that peptide detachment from lipid membranes occurs, with certain probability, along a few dominant diffusive pathways. This new method was validated through a consistent interpretation of the experimental data. Furthermore, we have found that for moderate retraction speeds at intermediate force values, k(F) exhibits catch-bond behavior (i.e. decreasing detachment rate with increasing force). According to the proposed model this behavior is due to the stochastic mixing of individual detachment pathways which do not convert or cross during rupture. To our knowledge, such catch-bond mechanism has not been proposed and demonstrated before for a peptide-lipid interaction.

Stable Substructures in Proteins and How to Find Them Using Single-Molecule Force Spectroscopy

Three-dimensional structures of proteins are a source of fascination for scientists, due to the beauty of their sequence-encoded architectures and their highly diverse range of functions. These functions include acting as powerful catalysts, signal receptors, and versatile molecular motors as well as being building blocks for macroscopic structures, thus defining the shape of multicellular organisms. How protein structure is organized and assembled at the sub-nanometer scale is of great current interest. Specifically, the discovery of stable substructures and supersecondary structures has inspired research into their potential use in rationally engineered proteins with tailor-made properties. Here, we show how the search for stable substructures in large proteins can benefit from recent advances in single-molecule force spectroscopy using highly sensitive dual-beam optical tweezers. Our chapter provides a step-by-step description of the experimental workflow for (1) preparing proteins for mechanical interrogation, (2) interpreting the data, and (3) avoiding the most commonly occurring mistakes.

Tailoring biomimetic polymer networks towards an unprecedented combination of versatile mechanical characteristics

Biomimetic polymeric materials, adopting the basic molecular design principles of biological materials, have been extensively studied in recent years but it is still challenging to combine assorted mechanical characteristics in a single material. Here, we present a simple and effective strategy to prepare mechanically robust yet resilient biomimetic polymer networks by utilizing dual noncovalent and covalent cross-linkings. Tailoring the dual cross-links consisting of thiourea noncovalent interactions and epoxy–amine covalent linkages in the biomimetic polymer networks enables a rare combination of excellent elastic modulus (1.1 GPa), yield stress (39 MPa), extensibility (320%), as well as complete strain and performance recovery after deformation at room temperature. The biomimetic polymer networks also exhibit highly adaptive mechanical properties in response to multiple-stimuli including strain rate, temperature, light, and solvent.

A simple and effective strategy to prepare biomimetic polymer networks with stiff, strong, tough, resilient, and adaptive mechanical properties, through controlling thiourea noncovalent and epoxy–amine covalent cross-linkings, is presented.

A cyclic cinnamate dimer mechanophore for multimodal stress responsive and mechanically adaptable polymeric materials

A methanone tethered cinnamate dimer manifests both multimodal stress-responsiveness and mechanical adaptability by light.

Manipulating the mechanical properties of biomimetic hydrogels with multivalent host–guest interactions

Biomimetic hydrogels with multivalent host–guest interactions as reversible crosslinks provide not only energy storage capacity, but also energy dissipation capacity to the dually crosslinked networks.

Downsizing the molecular spring of the giant protein titin reveals that skeletal muscle titin determines passive stiffness and drives longitudinal hypertrophy

Titin, the largest protein known, forms an elastic myofilament in the striated muscle sarcomere. To establish titin’s contribution to skeletal muscle passive stiffness, relative to that of the extracellular matrix, a mouse model was created in which titin’s molecular spring region was shortened by deleting 47 exons, the Ttn^Δ112-158 model. RNA sequencing and super-resolution microscopy predicts a much stiffer titin molecule. Mechanical studies with this novel mouse model support that titin is the main determinant of skeletal muscle passive stiffness. Unexpectedly, the in vivo sarcomere length working range was shifted to shorter lengths in Ttn^Δ112-158 mice, due to a ~ 30% increase in the number of sarcomeres in series (longitudinal hypertrophy). The expected effect of this shift on active force generation was minimized through a shortening of thin filaments that was discovered in Ttn^Δ112-158 mice. Thus, skeletal muscle titin is the dominant determinant of physiological passive stiffness and drives longitudinal hypertrophy.

Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Redox regulation of protein nanomechanics in health and disease: Lessons from titin

The nanomechanics of sarcomeric proteins is a key contributor to the mechanical output of muscle. Among them, titin emerges as a main target for the regulation of the stiffness of striated muscle. In the last years, single-molecule experiments by Atomic Force Microscopy (AFM) have demonstrated that redox posttranslational modifications are strong modulators of the mechanical function of titin. Here, we provide an overview of the recent development of the redox mechanobiology of titin, and suggest avenues of research to better understand how the stiffness of molecules, cells and tissues are modulated by redox signaling in health and disease.

Titin as a force-generating muscle protein under regulatory control

Titin has long been recognized as a mechanical protein in muscle cells that has a main function as a molecular spring in the contractile units, the sarcomeres. Recent work suggests that the titin spring contributes to muscle contraction in a more active manner than previously thought. In this review, we highlight this property, specifically the ability of the immunoglobulin-like (Ig) domains of titin to undergo unfolding-refolding transitions when isolated titin molecules or skeletal myofibrils are held at physiological force levels. Folding of titin Ig domains under force is a hitherto unappreciated, putative source of work production in muscle cells, which could work in synergy with the actomyosin system to maximize the energy delivered by a stretched, actively contracting muscle. This review also focuses on the mechanisms shown to modulate titin-based viscoelastic forces in skeletal muscle cells, including chaperone binding, titin oxidation, phosphorylation, Ca²⁺ binding, and interaction with actin filaments. Along the way, we discuss which of these modulatory mechanisms might contribute to the phenomenon of residual force enhancement relevant for eccentric muscle contractions. Finally, a brief perspective is added on the potential for the alterations in titin-based force to dynamically alter mechano-chemical signaling pathways in the muscle cell. We conclude that titin from skeletal muscle is a determinant of both passive and active tension and a bona fide mechanosensor, whose stiffness is tuned by various independent mechanisms.

What makes skeletal muscle striated? Discoveries in the endosarcomeric and exosarcomeric cytoskeleton

One of the most iconic images in biology is the cross-striated appearance of a skeletal muscle fiber. The repeating band pattern shows that all of the sarcomeres are the same length. All of the A bands are the same length and are located in the middle of the sarcomeres. Furthermore, all of the myofibrils are transversely aligned across the muscle fiber. It has been known for 300 yr that skeletal muscle is striated, but only in the last 40 yr has a molecular understanding of the striations emerged. In the 1950s it was discovered that the extraction of myosin from myofibrils abolished the A bands, and the myofibrils were no longer striated. With the further extraction of actin, only the Z disks remained. Strangely, the sarcomere length did not change, and these "ghost" myofibrils still exhibited elastic behavior. The breakthrough came in the 1970s with the discovery of the gigantic protein titin. Titin, an elastic protein ~1 µm in length, runs from the Z disk to the middle of the A band and ensures that each sarcomere is the same length. Titin anchors the A band in the middle of the sarcomere and may determine thick-filament length and thus A-band length. In the 1970s it was proposed that the intermediate filament desmin, which surrounds the Z disks, connects adjacent myofibrils, resulting in the striated appearance of a skeletal muscle fiber.

Preface: Special Topic on Single-Molecule Biophysics

Single-molecule measurements are now almost routinely used to study biological systems and processes. The scope of this special topic emphasizes the physics side of single-molecule observations, with the goal of highlighting new developments in physical techniques as well as conceptual insights that single-molecule measurements bring to biophysics. This issue also comprises recent advances in theoretical physical models of single-molecule phenomena, interpretation of single-molecule signals, and fundamental areas of statistical mechanics that are related to single-molecule observations. A particular goal is to illustrate the increasing synergy between theory, simulation, and experiment in single-molecule biophysics.

Conformational entropy of a single peptide controlled under force governs protease recognition and catalysis

An immense repertoire of protein chemical modifications catalyzed by enzymes is available as proteomics data. Quantifying the impact of the conformational dynamics of the modified peptide remains challenging to understand the decisive kinetics and amino acid sequence specificity of these enzymatic reactions in vivo, because the target peptide must be disordered to accommodate the specific enzyme-binding site. Here, we were able to control the conformation of a single-molecule peptide chain by applying mechanical force to activate and monitor its specific cleavage by a model protease. We found that the conformational entropy impacts the reaction in two distinct ways. First, the flexibility and accessibility of the substrate peptide greatly increase upon mechanical unfolding. Second, the conformational sampling of the disordered peptide drives the specific recognition, revealing force-dependent reaction kinetics. These results support a mechanism of peptide recognition based on conformational selection from an ensemble that we were able to quantify with a torsional free-energy model. Our approach can be used to predict how entropy affects site-specific modifications of proteins and prompts conformational and mechanical selectivity.

Accelerated Construction of Kinetic Network Model of Biomolecules Using Steered Molecular Dynamics

A new class of rare event acceleration techniques based on steered molecular dynamics (SMD) simulations is introduced. A stretching force applied on a biomolecule causes it to access large end-to-end distances. Under these conditions the biomolecule undergoes rapid conformational changes that are rare at zero-force conditions. A theory describing kinetics of a biomolecule at various stretching forces is presented. Using the theory, a master-Markov state model (master-MSM) is constructed from rates frequently accessed over a small range of force conditions. The master-MSM is shown to be applicable over a wide range of force conditions. We demonstrate application of the theory to three different biomolecular systems, namely, deca-alanine, TBA (thrombin binding aptamer), and a RNA hairpin. The master-MSM is used to estimate the kinetics at zero-force conditions, i.e., on the unbiased free-energy landscape, resulting inasmuch as 2-6 orders-of-magnitude speed-up over standard molecular dynamics.

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.

A myosin II nanomachine mimicking the striated muscle

The contraction of striated muscle (skeletal and cardiac muscle) is generated by ATP-dependent interactions between the molecular motor myosin II and the actin filament. The myosin motors are mechanically coupled along the thick filament in a geometry not achievable by single-molecule experiments. Here we show that a synthetic one-dimensional nanomachine, comprising fewer than ten myosin II dimers purified from rabbit psoas, performs isometric and isotonic contractions at 2 mM ATP, delivering a maximum power of 5 aW. The results are explained with a kinetic model fitted to the performance of mammalian skeletal muscle, showing that the condition for the motor coordination that maximises the efficiency in striated muscle is a minimum of 32 myosin heads sharing a common mechanical ground. The nanomachine offers a powerful tool for investigating muscle contractile-protein physiology, pathology and pharmacology without the potentially disturbing effects of the cytoskeletal-and regulatory-protein environment.

FEATHER: Automated Analysis of Force Spectroscopy Unbinding and Unfolding Data via a Bayesian Algorithm

Single-molecule force spectroscopy (SMFS) provides a powerful tool to explore the dynamics and energetics of individual proteins, protein-ligand interactions, and nucleic acid structures. In the canonical assay, a force probe is retracted at constant velocity to induce a mechanical unfolding/unbinding event. Next, two energy landscape parameters, the zero-force dissociation rate constant (k_o) and the distance to the transition state (Δx^‡), are deduced by analyzing the most probable rupture force as a function of the loading rate, the rate of change in force. Analyzing the shape of the rupture force distribution reveals additional biophysical information, such as the height of the energy barrier (ΔG^‡). Accurately quantifying such distributions requires high-precision characterization of the unfolding events and significantly larger data sets. Yet, identifying events in SMFS data is often done in a manual or semiautomated manner and is obscured by the presence of noise. Here, we introduce, to our knowledge, a new algorithm, FEATHER (force extension analysis using a testable hypothesis for event recognition), to automatically identify the locations of unfolding/unbinding events in SMFS records and thereby deduce the corresponding rupture force and loading rate. FEATHER requires no knowledge of the system under study, does not bias data interpretation toward the dominant behavior of the data, and has two easy-to-interpret, user-defined parameters. Moreover, it is a linear algorithm, so it scales well for large data sets. When analyzing a data set from a polyprotein containing both mechanically labile and robust domains, FEATHER featured a 30-fold improvement in event location precision, an eightfold improvement in a measure of the accuracy of the loading rate and rupture force distributions, and a threefold reduction of false positives in comparison to two representative reference algorithms. We anticipate FEATHER being leveraged in more complex analysis schemes, such as the segmentation of complex force-extension curves for fitting to worm-like chain models and extended in future work to data sets containing both unfolding and refolding transitions.

The multiple roles of titin in muscle contraction and force production

Titin is a filamentous protein spanning the half-sarcomere, with spring-like properties in the I-band region. Various structural, signaling, and mechanical functions have been associated with titin, but not all of these are fully elucidated and accepted in the scientific community. Here, I discuss the primary mechanical functions of titin, including its accepted role in passive force production, stabilization of half-sarcomeres and sarcomeres, and its controversial contribution to residual force enhancement, passive force enhancement, energetics, and work production in shortening muscle. Finally, I provide evidence that titin is a molecular spring whose stiffness changes with muscle activation and actin-myosin-based force production, suggesting a novel model of force production that, aside from actin and myosin, includes titin as a "third contractile" filament. Using this three-filament model of sarcomeres, the stability of (half-) sarcomeres, passive force enhancement, residual force enhancement, and the decrease in metabolic energy during and following eccentric contractions can be explained readily.

Influence of residual force enhancement and elongation of attached cross-bridges on stretch-shortening cycle in skinned muscle fibers

Increased muscle force during stretch‐shortening cycles (SSCs) has been widely examined. However, the mechanisms causing increased muscle force in SSCs remain unknown. The purpose of this study was to determine the influence of residual force enhancement and elongation of attached cross‐bridges on the work enhancement in SSCs. For the Control condition, skinned rabbit soleus fibers were elongated passively from an average sarcomere length of 2.4 to 3.0 μm, activated and then actively shortened to 2.4 μm. For the Transition condition, fibers were elongated actively from an average sarcomere length of 2.4 to 3.0 μm. Two seconds after the end of active lengthening, fibers were actively shortened to 2.4 μm. In the SSC condition, fibers were lengthened actively from an average sarcomere length of 2.4 to 3.0 μm, and then immediately shortened actively to 2.4 μm. Increased muscle force in the SSCs was quantified by the increase in mechanical work during active shortening compared to the mechanical work measured during the purely active shortening contractions. Work enhancement was significantly greater in the SSC compared to the Transition conditions. This difference was associated with the pause given between the active lengthening and shortening phase in the Transition test, which likely resulted in a reduction of the average elongation of the attached cross‐bridges caused by active stretching. Since some work enhancement was still observed in the Transition condition, another factor, for example the stretch‐induced residual force enhancement, must also have contributed to the work enhancement in SSCs.

Do Actomyosin Single-Molecule Mechanics Data Predict Mechanics of Contracting Muscle?

In muscle, but not in single-molecule mechanics studies, actin, myosin and accessory proteins are incorporated into a highly ordered myofilament lattice. In view of this difference we compare results from single-molecule studies and muscle mechanics and analyze to what degree data from the two types of studies agree with each other. There is reasonable correspondence in estimates of the cross-bridge power-stroke distance (7–13 nm), cross-bridge stiffness (~2 pN/nm) and average isometric force per cross-bridge (6–9 pN). Furthermore, models defined on the basis of single-molecule mechanics and solution biochemistry give good fits to experimental data from muscle. This suggests that the ordered myofilament lattice, accessory proteins and emergent effects of the sarcomere organization have only minor modulatory roles. However, such factors may be of greater importance under e.g., disease conditions. We also identify areas where single-molecule and muscle data are conflicting: (1) whether force generation is an Eyring or Kramers process with just one major power-stroke or several sub-strokes; (2) whether the myofilaments and the cross-bridges have Hookean or non-linear elasticity; (3) if individual myosin heads slip between actin sites under certain conditions, e.g., in lengthening; or (4) if the two heads of myosin cooperate.

Viscoelastic properties of vimentin originate from nonequilibrium conformational changes

Structure and dynamics of living matter rely on design principles fundamentally different from concepts of traditional material science. Specialized intracellular filaments in the cytoskeleton permit living systems to divide, migrate, and grow with a high degree of variability and durability. Among the three filament systems, microfilaments, microtubules, and intermediate filaments (IFs), the physical properties of IFs and their role in cellular mechanics are the least well understood. We use optical trapping of individual vimentin filaments to investigate energy dissipation, strain history dependence, and creep behavior of stretched filaments. By stochastic and numerical modeling, we link our experimental observations to the peculiar molecular architecture of IFs. We find that individual vimentin filaments display tensile memory and are able to dissipate more than 70% of the input energy. We attribute these phenomena to distinct nonequilibrium folding and unfolding of α helices in the vimentin monomers constituting the filaments.

Topology of interaction between titin and myosin thick filaments

Titin is a giant protein spanning between the Z- and M-lines of the sarcomere. In the A-band titin is associated with the myosin thick filament. It has been speculated that titin may serve as a blueprint for thick-filament formation due to the super-repeat structure of its A-band domains. Accordingly, titin might provide a template that determines the length and structural periodicity of the thick filament. Here we tested the titin ruler hypothesis by mixing titin and myosin at in situ stoichiometric ratios (300 myosins per 12 titins) in buffers of different ionic strength (KCl concentration range 100-300 mM). The topology of the filamentous complexes was investigated with atomic force microscopy. We found that the samples contained distinct, segregated populations of titin molecules and myosin thick filaments. We were unable to identify complexes in which myosin molecules were regularly associated to either mono- or oligomeric titin in either relaxed or stretched states of the titin filaments. Thus, the electrostatically driven self-association is stronger in both myosin and titin than their binding to each other, and it is unlikely that titin functions as a geometrical template for thick-filament formation. However, when allowed to equilibrate configurationally, long myosin thick filaments appeared with titin oligomers attached to their surface. The titin meshwork formed on the thick-filament surface may play a role in controlling thick-filament length by regulating the structural dynamics of myosin molecules and placing a mechanical limit on the filament length.

The Role of Glycans in Bacterial Adhesion to Mucosal Surfaces: How Can Single-Molecule Techniques Advance Our Understanding?

Bacterial adhesion is currently the subject of increased interest from the research community, leading to fast progress in our understanding of this complex phenomenon. Resent research within this field has documented the important roles played by glycans for bacterial surface adhesion, either through interaction with lectins or with other glycans. In parallel with this increased interest for and understanding of bacterial adhesion, there has been a growth in the sophistication and use of sensitive force probes for single-molecule and single cell studies. In this review, we highlight how the sensitive force probes atomic force microscopy (AFM) and optical tweezers (OT) have contributed to clarifying the mechanisms underlying bacterial adhesion to glycosylated surfaces in general and mucosal surfaces in particular. We also describe research areas where these techniques have not yet been applied, but where their capabilities appear appropriate to advance our understanding.

"Patterning with loops" to dynamically reconfigure polymer gels

The structural and mechanical properties of gels can be controlled by promoting the unfolding (and refolding) of loops (stored lengths) embedded within the networks. As a loop unfolds, the released chain length can increase the extensibility and reconfigurability of the gel. Here, we develop a theoretical model that couples the elasticity of the gel to the dynamic transitions occurring in loops that lie between the crosslinks. Using this model, we show that a thermally-induced swelling of the gel generates an internal strain, which unfolds the loops and thereby further increases the degree of gel swelling. We exploit this cooperative behavior to reconfigure the gel by patterning the location of the loops within the sample. Through this approach, we convert flat, two-dimensional layers into three-dimensional forms and introduce architectural features into uniform 3D slabs. At a fixed temperature, an applied force produces analogous structural transformations. The shape-changes are reversible: the systems return to their original structure when the temperature is reset or the force is removed. The findings provide guidelines for creating materials that interconvert thermal, chemical and mechanical energy to perform work. Such systems could be useful for designing soft robotic materials that convert environmental stimuli into useful functionality.

Structure Versus Stochasticity-The Role of Molecular Crowding and Intrinsic Disorder in Membrane Fission

Cellular membranes must undergo remodeling to facilitate critical functions including membrane trafficking, organelle biogenesis, and cell division. An essential step in membrane remodeling is membrane fission, in which an initially continuous membrane surface is divided into multiple, separate compartments. The established view has been that membrane fission requires proteins with conserved structural features such as helical scaffolds, hydrophobic insertions, and polymerized assemblies. In this review, we discuss these structure-based fission mechanisms and highlight recent findings from several groups that support an alternative, structure-independent mechanism of membrane fission. This mechanism relies on lateral collisions among crowded, membrane-bound proteins to generate sufficient steric pressure to drive membrane vesiculation. As a stochastic process, this mechanism contrasts with the paradigm that deterministic protein structures are required to drive fission, raising the prospect that many more proteins may participate in fission than previously thought. Paradoxically, our recent work suggests that intrinsically disordered domains may be among the most potent drivers of membrane fission, owing to their large hydrodynamic radii and substantial chain entropy. This stochastic view of fission also suggests new roles for the structure-based fission proteins. Specifically, we hypothesize that in addition to driving fission directly, the canonical fission machines may facilitate the enrichment and organization of bulky disordered protein domains in order to promote membrane fission by locally amplifying protein crowding.

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density for the transverse fluctuations of the free end of a cantilevered polymer as fingerprint of its semiflexibility. In contrast to clamped polymers, free polymers display a circularly symmetric probability density and their distributions are identical for compression and stretching forces.

Mechanical transduction via a single soft polymer

Molecular machines from biology and nanotechnology often depend on soft structures to perform mechanical functions, but the underlying mechanisms and advantages or disadvantages over rigid structures are not fully understood. We report here a rigorous study of mechanical transduction along a single soft polymer based on exact solutions to the realistic three-dimensional wormlike-chain model and augmented with analytical relations derived from simpler polymer models. The results reveal surprisingly that a soft polymer with vanishingly small persistence length below a single chemical bond still transduces biased displacement and mechanical work up to practically significant amounts. This "soft" approach possesses unique advantages over the conventional wisdom of rigidity-based transduction, and potentially leads to a unified mechanism for effective allosterylike transduction and relay of mechanical actions, information, control, and molecules from one position to another in molecular devices and motors. This study also identifies an entropy limit unique to the soft transduction, and thereby suggests a possibility of detecting higher efficiency for kinesin motor and mutants in future experiments.

Improved free-energy landscape reconstruction of bacteriorhodopsin highlights local variations in unfolding energy

Precisely quantifying the energetics that drive the folding of membrane proteins into a lipid bilayer remains challenging. More than 15 years ago, atomic force microscopy (AFM) emerged as a powerful tool to mechanically extract individual membrane proteins from a lipid bilayer. Concurrently, fluctuation theorems, such as the Jarzynski equality, were applied to deduce equilibrium free energies (ΔG0) from non-equilibrium single-molecule force spectroscopy records. The combination of these two advances in single-molecule studies deduced the free-energy of the model membrane protein bacteriorhodopsin in its native lipid bilayer. To elucidate this free-energy landscape at a higher resolution, we applied two recent developments. First, as an input to the reconstruction, we used force-extension curves acquired with a 100-fold higher time resolution and 10-fold higher force precision than traditional AFM studies of membrane proteins. Next, by using an inverse Weierstrass transform and the Jarzynski equality, we removed the free energy associated with the force probe and determined the molecular free-energy landscape of the molecule under study, bacteriorhodopsin. The resulting landscape yielded an average unfolding free energy per amino acid (aa) of 1.0 ± 0.1 kcal/mol, in agreement with past single-molecule studies. Moreover, on a smaller spatial scale, this high-resolution landscape also agreed with an equilibrium measurement of a particular three-aa transition in bacteriorhodopsin that yielded 2.7 kcal/mol/aa, an unexpectedly high value. Hence, while average unfolding ΔG0 per aa is a useful metric, the derived high-resolution landscape details significant local variation from the mean. More generally, we demonstrated that, as anticipated, the inverse Weierstrass transform is an efficient means to reconstruct free-energy landscapes from AFM data.

Compressive Force Spectroscopy: From Living Cells to Single Proteins

One of the most successful applications of atomic force microscopy (AFM) in biology involves monitoring the effect of force on single biological molecules, often referred to as force spectroscopy. Such studies generally entail the application of pulling forces of different magnitudes and velocities upon individual molecules to resolve individualistic unfolding/separation pathways and the quantification of the force-dependent rate constants. However, a less recognized variation of this method, the application of compressive force, actually pre-dates many of these "tensile" force spectroscopic studies. Further, beyond being limited to the study of single molecules, these compressive force spectroscopic investigations have spanned samples as large as living cells to smaller, multi-molecular complexes such as viruses down to single protein molecules. Correspondingly, these studies have enabled the detailed characterization of individual cell states, subtle differences between seemingly identical viral structures, as well as the quantification of rate constants of functionally important, structural transitions in single proteins. Here, we briefly review some of the recent achievements that have been obtained with compressive force spectroscopy using AFM and highlight exciting areas of its future development.

Amyloid Properties of Titin

This review considers data on structural and functional features of titin, on the role of this protein in determination of mechanical properties of sarcomeres, and on specific features of regulation of the stiffness and elasticity of its molecules, amyloid aggregation of this protein in vitro, and possibilities of formation of intramolecular amyloid structure in vivo. Molecular mechanisms are described of protection of titin against aggregation in muscle cells. Based on the data analysis, it is supposed that titin and the formed by it elastic filaments have features of amyloid.

RBM20, a potential target for treatment of cardiomyopathy via titin isoform switching

Cardiomyopathy, also known as heart muscle disease, is an unfavorable condition leading to alterations in myocardial contraction and/or impaired ability of ventricular filling. The onset and development of cardiomyopathy have not currently been well defined. Titin is a giant multifunctional sarcomeric filament protein that provides passive stiffness to cardiomyocytes and has been implicated to play an important role in the origin and development of cardiomyopathy and heart failure. Titin-based passive stiffness can be mainly adjusted by isoform switching and post-translational modifications in the spring regions. Recently, genetic mutations of TTN have been identified that can also contribute to variable passive stiffness, though the detailed mechanisms remain unclear. In this review, we will discuss titin isoform switching as it relates to alternative splicing during development stages and differences between species and muscle types. We provide an update on the regulatory mechanisms of TTN splicing controlled by RBM20 and cover the roles of TTN splicing in adjusting the diastolic stiffness and systolic compliance of the healthy and the failing heart. Finally, this review attempts to provide future directions for RBM20 as a potential target for pharmacological intervention in cardiomyopathy and heart failure.

The Role of Nanomechanics in Healthcare

Nanomechanics has played a vital role in pushing our capability to detect, probe, and manipulate the biological species, such as proteins, cells, and tissues, paving way to a deeper knowledge and superior strategies for healthcare. Nanomechanical characterization techniques, such as atomic force microscopy, nanoindentation, nanotribology, optical tweezers, and other hybrid techniques have been utilized to understand the mechanics and kinetics of biospecies. Investigation of the mechanics of cells and tissues has provided critical information about mechanical characteristics of host body environments. This information has been utilized for developing biomimetic materials and structures for tissue engineering and artificial implants. This review summarizes nanomechanical characterization techniques and their potential applications in healthcare research. The principles and examples of label-free detection of cancers and myocardial infarction by nanomechanical cantilevers are discussed. The vital importance of nanomechanics in regenerative medicine is highlighted from the perspective of material selection and design for developing biocompatible scaffolds. This review interconnects the advancements made in fundamental materials science research and biomedical technology, and therefore provides scientific insight that is of common interest to the researchers working in different disciplines of healthcare science and technology.

Single-molecule techniques in biophysics: a review of the progress in methods and applications

Single-molecule biophysics has transformed our understanding of biology, but also of the physics of life. More exotic than simple soft matter, biomatter lives far from thermal equilibrium, covering multiple lengths from the nanoscale of single molecules to up to several orders of magnitude higher in cells, tissues and organisms. Biomolecules are often characterized by underlying instability: multiple metastable free energy states exist, separated by levels of just a few multiples of the thermal energy scale k _B T, where k _B is the Boltzmann constant and T absolute temperature, implying complex inter-conversion kinetics in the relatively hot, wet environment of active biological matter. A key benefit of single-molecule biophysics techniques is their ability to probe heterogeneity of free energy states across a molecular population, too challenging in general for conventional ensemble average approaches. Parallel developments in experimental and computational techniques have catalysed the birth of multiplexed, correlative techniques to tackle previously intractable biological questions. Experimentally, progress has been driven by improvements in sensitivity and speed of detectors, and the stability and efficiency of light sources, probes and microfluidics. We discuss the motivation and requirements for these recent experiments, including the underpinning mathematics. These methods are broadly divided into tools which detect molecules and those which manipulate them. For the former we discuss the progress of super-resolution microscopy, transformative for addressing many longstanding questions in the life sciences, and for the latter we include progress in 'force spectroscopy' techniques that mechanically perturb molecules. We also consider in silico progress of single-molecule computational physics, and how simulation and experimentation may be drawn together to give a more complete understanding. Increasingly, combinatorial techniques are now used, including correlative atomic force microscopy and fluorescence imaging, to probe questions closer to native physiological behaviour. We identify the trade-offs, limitations and applications of these techniques, and discuss exciting new directions.

Introduction to Optical Tweezers: Background, System Designs, and Commercial Solutions

Optical tweezers are a means to manipulate objects with light. With the technique, microscopically small objects can be held and steered, while forces on the trapped objects can be accurately measured and exerted. Optical tweezers can typically obtain a nanometer spatial resolution, a picoNewton force resolution, and a millisecond time resolution, which makes them excellently suited to study biological processes from the single-cell down to the single-molecule level. In this chapter, we will provide an introduction on the use of optical tweezers in single-molecule approaches. We will introduce the basic principles and methodology involved in optical trapping, force calibration, and force measurements. Next we describe the components of an optical tweezers setup and their experimental relevance in single-molecule approaches. Finally, we provide a concise overview of commercial optical tweezers systems. Commercial systems are becoming increasingly available and provide access to single-molecule optical tweezers experiments without the need for a thorough background in physics.