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

Impact of lengthening velocity on the generation of eccentric force by slow-twitch muscle fibers in long stretches

After an initial increase, isovelocity elongation of a muscle fiber can lead to diminishing (referred to as Give in the literature) and subsequently increasing force. How the stretch velocity affects this behavior in slow-twitch fibers remains largely unexplored. Here, we stretched fully activated individual rat soleus muscle fibers from 0.85 to 1.3 optimal fiber length at stretch velocities of 0.01, 0.1, and 1 maximum shortening velocity, vmax, and compared the results with those of rat EDL fast-twitch fibers obtained in similar experimental conditions. In soleus muscle fibers, Give was 7%, 18%, and 44% of maximum isometric force for 0.01, 0.1, and 1 vmax, respectively. As in EDL fibers, the force increased nearly linearly in the second half of the stretch, although the number of crossbridges decreased, and its slope increased with stretch velocity. Our findings are consistent with the concept of a forceful detachment and subsequent crossbridge reattachment in the stretch's first phase and a strong viscoelastic titin contribution to fiber force in the second phase of the stretch. Interestingly, we found interaction effects of stretch velocity and fiber type on force parameters in both stretch phases, hinting at fiber type-specific differences in crossbridge and titin contributions to eccentric force. Whether fiber type-specific combined XB and non-XB models can explain these effects or if they hint at some not fully understood properties of muscle contraction remains to be shown. These results may stimulate new optimization perspectives in sports training and provide a better understanding of structure-function relations of muscle proteins.

Four phases of a force transient emerge from a binary mechanical system

Accurate models of muscle contraction are important for understanding both muscle performance and the therapeutics that enhance physiological function. However, models are only accurate and meaningful if they are consistent with physical laws. A single muscle fiber contains billions of randomly fluctuating atoms that on the spatial scale of a muscle fiber generate unidirectional force and power output. This thermal system is formally constrained by the laws of thermodynamics, and a recently developed thermodynamic model of muscle force generation provides qualitative descriptions of the muscle force-velocity relationship, muscle force generation, muscle force transients, and the thermodynamic work loop of muscle with a thermodynamic (not molecular) power stroke mechanism. To demonstrate the accuracy of this model requires that its outputs be quantitatively compared with experimentally observed muscle function. Here I show that a two-state thermodynamic model accurately describes the experimentally observed four-phase force transient response to both mechanical and chemical perturbations. This is the simplest possible model of one of the most complex characteristic signatures of muscle mechanics.

Titin: roles in cardiac function and diseases

The giant protein titin is an essential component of muscle sarcomeres. A single titin molecule spans half a sarcomere and mediates diverse functions along its length by virtue of its unique domains. The A-band of titin functions as a molecular blueprint that defines the length of the thick filaments, the I-band constitutes a molecular spring that determines cell-based passive stiffness, and various domains, including the Z-disk, I-band, and M-line, serve as scaffolds for stretch-sensing signaling pathways that mediate mechanotransduction. This review aims to discuss recent insights into titin's functional roles and their relationship to cardiac function. The role of titin in heart diseases, such as dilated cardiomyopathy and heart failure with preserved ejection fraction, as well as its potential as a therapeutic target, is also discussed.

A low-cost 2-D sarcomere model to demonstrate titin-related mechanisms for force production

Given the recently proposed three-filament theory of muscle contraction, we present a low-cost physical sarcomere model aimed at illustrating the role of titin in the production of active force in skeletal muscle. With inexpensive materials, it is possible to illustrate actin-myosin cross-bridge interactions between the thick and thin filaments and demonstrate the two different mechanisms by which titin is thought to contribute to active and passive muscle force. Specifically, the model illustrates how titin, a molecule with springlike properties, may increase its stiffness by binding free calcium upon muscle activation and reducing its extensible length by attaching itself to actin, resulting in the greater force-generating capacity after an active than a passive elongation that has been observed experimentally. The model is simple to build and manipulate, and demonstration to high school students was shown to result in positive perception and improved understanding of the otherwise complex titin-related mechanisms of force production in skeletal and cardiac muscles.NEW & NOTEWORTHY Our physical sarcomere model illustrates not only the classic view of muscle contraction, the sliding filament and cross-bridge theories, but also the newly discovered role of titin in force regulation, called the three-filament theory. The model allows for easy visualization of the role of titin in muscle contraction and aids in explaining complex muscle properties that are not captured by the traditional cross-bridge theory.

Life under tension: the relevance of force on biological polymers

Optical tweezers have elucidated numerous biological processes, particularly by enabling the precise manipulation and measurement of tension. One question concerns the biological relevance of these experiments and the generalizability of these experiments to wider biological systems. Here, we categorize the applicability of the information garnered from optical tweezers in two distinct categories: the direct relevance of tension in biological systems, and what experiments under tension can tell us about biological systems, while these systems do not reach the same tension as the experiment, still, these artificial experimental systems reveal insights into the operations of biological machines and life processes.

Construction and operation of high-resolution magnetic tape head tweezers for measuring single-protein dynamics under force

Mechanical forces are critical to protein function across many biological contexts-from bacterial adhesion to muscle mechanics and mechanotransduction processes. Hence, understanding how mechanical forces govern protein activity has developed into a central scientific question. In this context, single-molecule magnetic tweezers has recently emerged as a valuable experimental tool, offering the capability to measure single proteins over physiologically relevant forces and timescales. In this chapter, we present a detailed protocol for the assembly and operation of our magnetic tape head tweezers instrument, specifically tailored to investigate protein dynamics. Our instrument boasts a simplified microscope design and incorporates a magnetic tape head as the force-generating apparatus, facilitating precise force control and enhancing its temporal stability, enabling the study of single protein mechanics over extended timescales spanning several hours or even days. Moreover, its straightforward and cost-effective design ensures its accessibility to the wider scientific community. We anticipate that this technique will attract widespread interest within the growing field of mechanobiology and expect that this chapter will provide facilitated accessibility to this technology.

Magnetic tweezers in cell mechanics

The chapter provides an overview of the applications of magnetic tweezers in living cells. It discusses the advantages and disadvantages of magnetic tweezers technology with a focus on individual magnetic tweezers configurations, such as electromagnetic tweezers. Solutions to the disadvantages identified are also outlined. The specific role of magnetic tweezers in the field of mechanobiology, such as mechanosensitivity, mechano-allostery and mechanotransduction are also emphasized. The specific usage of magnetic tweezers in mechanically probing cells via specific cell surface receptors, such as mechanosensitive channels is discussed and why mechanical probing has revealed the opening and closing of the channels. Finally, the future direction of magnetic tweezers is presented.

Exploring the free energy landscape of proteins using magnetic tweezers

Proteins fold to their native states by searching through the free energy landscapes. As single-domain proteins are the basic building block of multiple-domain proteins or protein complexes composed of subunits, the free energy landscapes of single-domain proteins are of critical importance to understand the folding and unfolding processes of proteins. To explore the free energy landscapes of proteins over large conformational space, the stability of native structure is perturbed by biochemical or mechanical means, and the conformational transition process is measured. In single molecular manipulation experiments, stretching force is applied to proteins, and the folding and unfolding transitions are recorded by the extension time course. Due to the broad force range and long-time stability of magnetic tweezers, the free energy landscape over large conformational space can be obtained. In this article, we describe the magnetic tweezers instrument design, protein construct design and preparation, fluid chamber preparation, common-used measuring protocols including force-ramp and force-jump measurements, and data analysis methods to construct the free energy landscape. Single-domain cold shock protein is introduced as an example to build its free energy landscape by magnetic tweezers measurements.

Introduction to Optical Tweezers: Background, System Designs, and Applications

Optical tweezers are a means to manipulate objects with light. With the technique, microscopically small objects can be held and steered, allowing for accurate measurement of the forces applied to these objects. Optical tweezers can typically obtain a nanometer spatial resolution, a picoNewton force resolution, and a millisecond time resolution, which makes the technique well suited for the study of biological processes from the single-cell down to the single-molecule level. In this chapter, we aim to provide an introduction to the use of optical tweezers for single-molecule analyses. We start from 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. Finally, we will provide an overview of the broad applications in context of biological research, with the emphasis on the measurement modes, experimental assays, and possible combinations with fluorescence microscopy techniques.

Behavioral Motor Performance

The human sensorimotor control system has exceptional abilities to perform skillful actions. We easily switch between strenuous tasks that involve brute force, such as lifting a heavy sewing machine, and delicate movements such as threading a needle in the same machine. Using a structure with different control architectures, the motor system is capable of updating its ability to perform through our daily interaction with the fluctuating environment. However, there are issues that make this a difficult computational problem for the brain to solve. The brain needs to control a nonlinear, nonstationary neuromuscular system, with redundant and occasionally undesired degrees of freedom, in an uncertain environment using a body in which information transmission is subject to delays and noise. To gain insight into the mechanisms of motor control, here we survey movement laws and invariances that shape our everyday motion. We then examine the major solutions to each of these problems in the three parts of the sensorimotor control system, sensing, planning, and acting. We focus on how the sensory system, the control architectures, and the structure and operation of the muscles serve as complementary mechanisms to overcome deviations and disturbances to motor behavior and give rise to skillful motor performance. We conclude with possible future research directions based on suggested links between the operation of the sensorimotor system across the movement stages. © 2024 American Physiological Society. Compr Physiol 14:5179-5224, 2024.

Evidence for multi-scale power amplification in skeletal muscle

Many animals use a combination of skeletal muscle and elastic structures to amplify power output for fast motions. Among vertebrates, tendons in series with skeletal muscle are often implicated as the primary power-amplifying spring, but muscles contain elastic structures at all levels of organization, from the muscle tendon to the extracellular matrix to elastic proteins within sarcomeres. The present study used ex vivo muscle preparations in combination with high-speed video to quantify power output, as the product of force and velocity, at several levels of muscle organization to determine where power amplification occurs. Dynamic ramp-shortening contractions in isolated frog flexor digitorum superficialis brevis were compared with isotonic power output to identify power amplification within muscle fibers, the muscle belly, free tendon and elements external to the muscle tendon. Energy accounting revealed that artifacts from compliant structures outside of the muscle-tendon unit contributed significant peak instantaneous power. This compliance included deflection of clamped bone that stored and released energy contributing 195.22±33.19 W kg-1 (mean±s.e.m.) to the peak power output. In addition, we found that power detected from within the muscle fascicles for dynamic shortening ramps was 338.78±16.03 W kg-1, or approximately 1.75 times the maximum isotonic power output of 195.23±8.82 W kg-1. Measurements of muscle belly and muscle-tendon unit also demonstrated significant power amplification. These data suggest that intramuscular tissues, as well as bone, have the capacity to store and release energy to amplify whole-muscle power output.

The Problem with Inventing Molecular Mechanisms to Fit Thermodynamic Equations of Muscle

Almost every model of muscle contraction in the literature to date is a molecular power stroke model, even though this corpuscular mechanism is opposed by centuries of science, by 85 years of unrefuted evidence that muscle is a thermodynamic system, and by a quarter century of direct observations that the molecular mechanism of muscle contraction is a molecular switch, not a molecular power stroke. An ensemble of molecular switches is a binary mechanical thermodynamic system from which A.V. Hill's muscle force-velocity relationship is directly derived, where Hill's parameter a is the internal force against which unloaded muscle shortens, and Hill's parameter b is the product of the switch displacement, d, and the actin-myosin ATPase rate. Ignoring this model and the centuries of thermodynamics that preceded it, corpuscularians continue to develop molecular power stroke models, adding to their 65-year jumble of "new", "innovative", and "unconventional" molecular mechanisms for Hill's a and b parameters, none of which resemble the underlying physical chemistry. Remarkably, the corpuscularian community holds the thermodynamicist to account for these discrepancies, which, as outlined here, I have done for 25 years. It is long past time for corpuscularians to be held accountable for their mechanisms, which by all accounts have no foundation in science. The stakes are high. Molecular power stroke models are widely used in research and in clinical decision-making and have, for over half a century, muddied our understanding of the inner workings of one of the most efficient and clean-burning machines on the planet. It is problematic that corpuscularians present these models to stakeholders as science when in fact corpuscularians have been actively defending these models against science for decades. The path forward for scientists is to stop baseless rejections of muscle thermodynamics and to begin testing corpuscular and thermodynamic mechanisms with the goal of disproving one or the other of these hypotheses.

Cells solved the Gibbs paradox by learning to contain entropic forces

As Nature's version of machine learning, evolution has solved many extraordinarily complex problems, none perhaps more remarkable than learning to harness an increase in chemical entropy (disorder) to generate directed chemical forces (order). Using muscle as a model system, here I describe the basic mechanism by which life creates order from disorder. In short, evolution tuned the physical properties of certain proteins to contain changes in chemical entropy. As it happens these are the "sensible" properties Gibbs postulated were needed to solve a paradox that has intrigued and challenged scientists and philosophers for over 100 years.

Appearance of de Gennes length in force-induced transitions

Using Langevin dynamic simulations, a simple coarse-grained model of a DNA protein construct is used to study the DNA rupture and the protein unfolding. We identify three distinct states: (i) zipped DNA and collapsed protein, (ii) unzipped DNA and stretched protein, and (iii) unzipped DNA and collapsed protein. Here, we find a phase diagram that shows these states depending on the size of the DNA handle and the protein. For a less stable protein, unfolding is solely governed by the size of the linker DNA, whereas if the protein's stability increases, complete unfolding becomes impossible because the rupture force for DNA has reached a saturation regime influenced by the de Gennes length. We show that unfolding occurs via a few intermediate states by monitoring the force-extension curve of the entire protein. We extend our study to a heterogeneous protein system, where similar intermediate states in two systems can lead to different protein unfolding paths.

A single filament biomechanical study of the enteropathogenic Escherichia coli Type III secretion system reveals a high elastic aspect ratio

Type III secretion systems (T3SSs) are syringe-like protein complexes used by some of the most harmful bacterial pathogens to infect host cells. While the T3SS filament, a long hollow conduit that bridges between bacteria and host cells, has been characterized structurally, very little is known about its physical properties. These filaments should endure shear and normal stresses imposed by the viscous mucosal flow during infection within the intestinal tract. We used atomic force microscopy (AFM) to probe the longitudinal and radial mechanical response of individual T3SS filaments by pulling on filaments extending directly from bacterial surfaces and later pressing into filaments that were detached from the bacteria. The measured longitudinal elastic moduli were higher by about two orders of magnitude than the radial elastic moduli. These proportions are commensurate with the role of the T3SS filament, which requires horizontal flexibility while maintaining its structural integrity to withstand intense stresses during infection.

Molecular mechanisms of muscle contraction: A historical perspective

Studies of muscle structure and function can be traced to at least 2,000 years ago. However, the modern era of muscle contraction mechanisms started in the 1950s with the classic works by AF Huxley and HE Huxley, both born in the United Kingdom, but not related and working independently. HE Huxley was the first to suggest that muscle contraction occurred through the sliding of two sets of filamentous structures (actin or thin filaments and myosin or thick filaments). AF Huxley then developed a biologically inspired mathematical model suggesting a possible molecular mechanism of how this sliding of actin and myosin might take place. This model then evolved from a two-state to a multi-state model of myosin-actin interactions, and from one that suggested a linear motor causing the sliding to a rotating motor. This model, the cross-bridge model of muscle contraction, is still widely used in biomechanics, and even the more sophisticated cross-bridge models of today still contain many of the features originally proposed by AF Huxley. In 2002, we discovered a hitherto unknown property of muscle contraction that suggested the involvement of passive structures in active force production, the so-called passive force enhancement. It was quickly revealed that this passive force enhancement was caused by the filamentous protein titin, and the three-filament (actin, myosin, and titin) sarcomere model of muscle contraction evolved. There are many suggestions of how these three proteins interact to cause contraction and produce active force, and one such suggestion is described here, but the molecular details of this proposed mechanism still need careful evaluation.

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.

Folding-unfolding asymmetry and a RetroFold computational algorithm

We treat protein folding as molecular self-assembly, while unfolding is viewed as disassembly. Fracture is typically a much faster process than self-assembly. Self-assembly is often an exponentially decaying process, since energy relaxes due to dissipation, while fracture is a constant-rate process as the driving force is opposed by damping. Protein folding takes two orders of magnitude longer than unfolding. We suggest a mathematical transformation of variables, which makes it possible to view self-assembly as time-reversed disassembly, thus folding can be studied as reversed unfolding. We investigate the molecular dynamics modelling of folding and unfolding of the short Trp-cage protein. Folding time constitutes about 800 ns, while unfolding (denaturation) takes only about 5.0 ns and, therefore, fewer computational resources are needed for its simulation. This RetroFold approach can be used for the design of a novel computation algorithm, which, while approximate, is less time-consuming than traditional folding algorithms.

Two-Molecule Force Spectroscopy on Proteins

Many elastomeric proteins, which play important roles in a wide range of biological processes, exist as parallel/antiparallelly arranged dimers or multimers to perform their mechanobiological functions. For example, in striated muscle sarcomeres, the giant muscle protein titin exists as hexameric bundles to mediate the passive elasticity of muscles. However, it has not been possible to directly probe the mechanical properties of such parallelly arranged elastomeric proteins. And it remains unknown if the knowledge obtained from single-molecule force spectroscopy studies can be directly extrapolated to such parallelly/antiparallelly arranged systems. Here, we report the development of atomic force microscopy (AFM)-based two-molecule force spectroscopy to directly probe the mechanical properties of two elastomeric proteins that are arranged in parallel. We developed a twin-molecule approach to allow two parallelly arranged elastomeric proteins to be picked up and stretched simultaneously in an AFM experiment. Our results clearly revealed the mechanical features of such parallelly arranged elastomeric proteins during force-extension measurements and allowed for the determination of mechanical unfolding forces of proteins in such an experimental setting. Our study provides a general and robust experimental strategy to closely mimic the physiological condition of such parallel elastomeric protein multimers.

Bond clusters control rupture force limit in shear loaded histidine-Ni2+ metal-coordinated proteins

Dynamic noncovalent interactions are pivotal to the structure and function of biological proteins and have been used in bioinspired materials for similar roles. Metal-coordination bonds, in particular, are especially tunable and enable control over static and dynamic properties when incorporated into synthetic materials. Despite growing efforts to engineer metal-coordination bonds to produce strong, tough, and self-healing materials, the systematic characterization of the exact contribution of these bonds towards mechanical strength and the effect of geometric arrangements is missing, limiting the full design potential of these bonds. In this work, we engineer the cooperative rupture of metal-coordination bonds to increase the rupture strength of metal-coordinated peptide dimers. Utilizing all-atom steered molecular dynamics simulations on idealized bidentate histidine-Ni²⁺ coordinated peptides, we show that histidine-Ni²⁺ bonds can rupture cooperatively in groups of two to three bonds. We find that there is a strength limit, where adding additional coordination bonds does not contribute to the additional increase in the protein rupture strength, likely due to the highly heterogeneous rupture behavior exhibited by the coordination bonds. Further, we show that this coordination bond limit is also found natural metal-coordinated biological proteins. Using these insights, we quantitatively suggest how other proteins can be rationally designed with dynamic noncovalent interactions to exhibit cooperative bond breaking behavior. Altogether, this work provides a quantitative analysis of the cooperativity and intrinsic strength limit for metal-coordination bonds with the aim of advancing clear guiding molecular principles for the mechanical design of metal-coordinated materials.

Temperature dependent mechanical unfolding and refolding of a protein studied by thermo-regulated optical tweezers

Temperature is a useful system variable to gather kinetic and thermodynamic information from proteins. Usually, free energy and the associated entropic and enthalpic contributions are obtained by quantifying the conformational equilibrium based on melting experiments performed in bulk conditions. Such experiments are suitable only for those small single-domain proteins whose side reactions of irreversible aggregation are unlikely to occur. Here, we avoid aggregation by pulling single-protein molecules in a thermo-regulated optical tweezers. Thus, we are able to explore the temperature dependence of the thermodynamic and kinetic parameters of MJ0366 from Methanocaldococcus jannaschii at the single-molecule level. By performing force-ramp experiments between 2°C and 40°C, we found that MJ0366 has a nonlinear dependence of free energy with temperature and a specific heat change of 2.3 ± 1.2 kcal/mol∗K. These thermodynamic parameters are compatible with a two-state unfolding/refolding mechanism for MJ0366. However, the kinetics measured as a function of the temperature show a complex behavior, suggesting a three-state folding mechanism comprising a high-energy intermediate state. The combination of two perturbations, temperature and force, reveals a high-energy species in the folding mechanism of MJ0366 not detected in force-ramp experiments at constant temperature.

Emulating Titin by a Multidomain DNA Structure

Titin, a giant protein containing multiple tandem domains, is essential in maintaining the superior mechanical performance of muscle. The consecutive and reversible unfolding and refolding of the domains are crucial for titin to serve as a modular spring. Since the discovery of the mechanical features of a single titin molecule, the exploration of biomimetic materials with titin-emulating modular structures has been an active field. However, it remains a challenge to prepare these modular polymers on a large scale due to the complex synthesis process. In this study, we propose modular DNA with multiple hairpins (MH-DNA) as the fundamental block for the bottom-up design of advanced materials. By analyzing the unfolding and refolding dynamics of modular hairpins by atomic force microscopy (AFM)-based single-molecule force spectroscopy (SMFS), we find that MH-DNA shows comparable stability to those of polyproteins like titin. The unique low hysteresis of modular hairpin makes it an ideal molecular spring with remarkable mechanical efficiency. On the basis of the well-established DNA synthesis techniques, we anticipate that MH-DNA can be used as a promising building block for advanced materials with a combination of superior structural stability, considerable extensibility, and high mechanical efficiency.

Thermodynamics and Kinetics of a Binary Mechanical System: Mechanisms of Muscle Contraction

Biological motors function at the interface of biology, physics, and chemistry, and it remains unsettled what rules from which disciplines account for how these motors work. Myosin motors are enzymes that catalyze the hydrolysis of ATP through a mechanism involving a switch-like myosin structural change (a lever arm rotation) induced by actin binding that generates a small displacement of an actin filament. In muscle, individual myosin motors are widely assumed to function as molecular machines having mechanical properties that resemble those of muscle. In a fundamental departure from this perspective, here, I show that muscle more closely resembles a heat engine with mechanical properties that emerge from the thermodynamics of a myosin motor ensemble. The transformative impact of thermodynamics on our understanding of how a heat engine works guides a parallel transformation in our understanding of how muscle works. I consider the simplest possible model of force generation: a binary mechanical system. I develop the mechanics, energetics, and kinetics of this system and show that a single binding reaction generates force when muscle is held at a fixed length and performs work when muscle is allowed to shorten. This creates a network of thermodynamic binding pathways that resembles many of the characteristic mechanical and energetic behaviors of muscle including the muscle force-velocity relationship, heat output by shortening muscle, four phases of a muscle tension transient, spontaneous oscillatory contractions, and force redevelopment. Analogous to the thermodynamic (Carnot) cycle for a heat engine, isothermal and adiabatic binding and detachment reactions create a thermodynamic cycle for muscle that resembles cardiac pressure-volume loops (i.e., how the heart works). This paper provides an outline for how to re-interpret muscle mechanic data using thermodynamics - an ongoing effort that will continue providing novel insights into how muscle and molecular motors work.

Extract Motive Energy from Single-Molecule Trajectories

Single-molecule trajectories from nonequilibrium unfolding experiments are widely used to recover a biomolecule's intrinsic free-energy profile. Trajectories of molecular motors from similar single-molecule experiments may be mapped to biased diffusion over an inclined free-energy profile. Such an effective potential is not a static equilibrium property anymore, and how it can benefit molecular motor study is unclear. Here, we introduce a method to deduce this effective potential from motor trajectories with realistic temporal-spatial resolution and find that the potential yields a motor's stall force─a quantity that not only characterizes a motor's force-generating capacity but also largely determines its energy efficiency. Interestingly, this potential allows the extraction of a motor's stall force from trajectories recorded at a single resisting force or even zero force, as verified with trajectories from two molecular motor models and also experimental trajectories from a real artificial motor. This finding drastically reduces the difficulty of stall force measurement, making it accessible even to force-incapable optical tracking experiments (commonly regarded as irrelevant to stall force determination). This study further provides a method for experimentally measuring a second-law-decreed least energy price for submicroscopic directionality─a previously elusive but thermodynamically important quantity pertinent to efficient energy conversion of molecular motors.

Single-molecule mechanical studies of chaperones and their clients

Single-molecule force spectroscopy provides access to the mechanics of biomolecules. Recently, magnetic and laser optical tweezers were applied in the studies of chaperones and their interaction with protein clients. Various aspects of the chaperone-client interactions can be revealed based on the mechanical probing strategies. First, when a chaperone is probed under load, one can examine the inner workings of the chaperone while it interacts with and works on the client protein. Second, when protein clients are probed under load, the action of chaperones on folding clients can be studied in great detail. Such client folding studies have given direct access to observing actions of chaperones in real-time, like foldase, unfoldase, and holdase activity. In this review, we introduce the various single molecule mechanical techniques and summarize recent single molecule mechanical studies on heat shock proteins, chaperone-mediated folding on the ribosome, SNARE folding, and studies of chaperones involved in the folding of membrane proteins. An outlook on significant future developments is given.

Ensemble Force Spectroscopy of a G-Quadruplex Cluster on a Single-Molecule Platform

Single-molecule methods offer high sensitivities with precisions superior to bulk assays. However, these methods are low in throughput and cannot repetitively interrogate the same cluster of molecular units. In this work, we investigate a tandem array of G-quadruplexes on a single-molecule DNA template with a throughput of at least two orders of magnitude higher than single-molecule force spectroscopy. During mechanical unfolding by optical tweezers, the array of G-quadruplexes experiences identical force, temperature, and ionic conditions, which not only reduce environmental noise but also render unfolding transitions indistinguishable among individual G-quadruplexes. The resultant ensemble behaviors are analyzed by scanning force diagrams, which reveals accurate F1/2 values, where 50% of G-quadruplexes are unfolded. Independent of the number of G-quadruplexes (n > 15) contained in a cluster, F1/2 can effectively evaluate G-quadruplex ligands in a new method called differential scanning forcemetry. When the same G-quadruplex cluster is subject to a series of constant forces in force-jump experiments, unfolding rate constants of G-quadruplexes can be effectively evaluated as a function of force. The high precision demonstrated in all of these measurements reflects the power of repetitive sampling on the same cluster of single-molecule entities under identical conditions. Since biomolecules such as DNA, RNA, and proteins can be conveniently incorporated in a tandem array, we anticipate that this ensemble assay on single-molecule entities (EASE) provides a generic means of ensemble force spectroscopy to amalgamate the accuracy of ensemble measurements with the precision of single-molecule methods.

Stability matters, too - the thermodynamics of amyloid fibril formation

Amyloid fibrils are supramolecular homopolymers of proteins that play important roles in biological functions and disease. These objects have received an exponential increase in attention during the last few decades, due to their role in the aetiology of a range of severe disorders, most notably some of a neurodegenerative nature. While an overwhelming number of experimental studies exist that investigate how, and how fast, amyloid fibrils form and how their formation can be inhibited, a much more limited body of experimental work attempts to answer the question as to why these types of structures form (i.e. the thermodynamic driving force) and how stable they actually are. In this review, I attempt to give an overview of the types of experiments that have been performed to-date to answer these questions, and to summarise our current understanding of amyloid thermodynamics.

Application of optical tweezers in cardiovascular research: More than just a measuring tool

Recent advances in the field of optical tweezer technology have shown intriguing potential for applications in cardiovascular medicine, bringing this laboratory nanomechanical instrument into the spotlight of translational medicine. This article summarizes cardiovascular system findings generated using optical tweezers, including not only rigorous nanomechanical measurements but also multifunctional manipulation of biologically active molecules such as myosin and actin, of cells such as red blood cells and cardiomyocytes, of subcellular organelles, and of microvessels in vivo. The implications of these findings in the diagnosis and treatment of diseases, as well as potential perspectives that could also benefit from this tool, are also discussed.

Mechanical role of the submembrane spectrin scaffold in red blood cells and neurons

Spectrins are large, evolutionarily well-conserved proteins that form highly organized scaffolds on the inner surface of eukaryotic cells. Their organization in different cell types or cellular compartments helps cells withstand mechanical challenges with unique strategies depending on the cell type. This Review discusses our understanding of the mechanical properties of spectrins, their very distinct organization in red blood cells and neurons as two examples, and the contribution of the scaffolds they form to the mechanical properties of these cells.

What Can We Learn from Single Sarcomere and Myofibril Preparations?

Sarcomeres are the smallest functional contractile unit of muscle, and myofibrils are striated muscle organelles that are comprised of sarcomeres that are strictly aligned in series. Furthermore, passive forces in sarcomeres and myofibrils are almost exclusively produced by the structural protein titin, and all contractile, regulatory, and structural proteins are in their natural configuration. For these mechanical and structural reasons single sarcomere and myofibril preparations are arguably the most powerful to answer questions on the mechanisms of striated muscle contraction. We developed and optimized single myofibril research over the past 20 years and were the first to mechanically isolate and test single sarcomeres. The results from this research led to the uncovering of the crucial role of titin in muscle contraction, first molecular explanations for the origins of the passive and the residual force enhancement properties of skeletal and cardiac muscles, the discovery of sarcomere length stability on the descending limb of the force-length relationship, and culminating in the formulation of the three-filament theory of muscle contraction that, aside from actin and myosin, proposes a crucial role of titin in active force production. Aside from all the advantages and possibilities that single sarcomere and myofibril preparations offer, there are also disadvantages. These include the fragility of the preparation, the time-consuming training to master these preparations, the limited spatial resolution for length and force measurements, and the unavailability of commercial systems for single sarcomere/myofibril research. Ignoring the mechanics that govern serially linked systems, not considering the spatial resolution and associated accuracies of myofibril systems, and neglecting the fragility of myofibril preparations, has led to erroneous interpretations of results and misleading conclusions. Here, we will attempt to describe the methods and possible applications of single sarcomere/myofibril research and discuss the advantages and disadvantages by focusing on specific applications. It is hoped that this discussion may contribute to identifying the enormous potential of single sarcomere/myofibril research in discovering the secrets of muscle contraction.

The Mechanisms of Thin Filament Assembly and Length Regulation in Muscles

The actin containing tropomyosin and troponin decorated thin filaments form one of the crucial components of the contractile apparatus in muscles. The thin filaments are organized into densely packed lattices interdigitated with myosin-based thick filaments. The crossbridge interactions between these myofilaments drive muscle contraction, and the degree of myofilament overlap is a key factor of contractile force determination. As such, the optimal length of the thin filaments is critical for efficient activity, therefore, this parameter is precisely controlled according to the workload of a given muscle. Thin filament length is thought to be regulated by two major, but only partially understood mechanisms: it is set by (i) factors that mediate the assembly of filaments from monomers and catalyze their elongation, and (ii) by factors that specify their length and uniformity. Mutations affecting these factors can alter the length of thin filaments, and in human cases, many of them are linked to debilitating diseases such as nemaline myopathy and dilated cardiomyopathy.

Measuring (biological) materials mechanics with atomic force microscopy. 3. Mechanical unfolding of biopolymers

Biopolymers, such as polynucleotides, polypeptides and polysaccharides, are macromolecules that direct most of the functions in living beings. Studying the mechanical unfolding of biopolymers provides important information about their molecular elasticity and mechanical stability, as well as their energy landscape, which is especially important in proteins, since their three‐dimensional structure is essential for their correct activity. In this primer, we present how to study the mechanical properties of proteins with atomic force microscopy and how to obtain information about their stability and energetic landscape. In particular, we discuss the preparation of polyprotein constructs suitable for AFM single molecule force spectroscopy (SMFS), describe the parameters used in our force‐extension SMFS experiments and the models and equations employed in the analysis of the data. As a practical example, we show the effect of the temperature on the unfolding force, the distance to the transition state, the unfolding rate at zero force, the height of the transition state barrier, and the spring constant of the protein for a construct containing nine repeats of the I27 domain from the muscle protein titin.

Nonexponential kinetics in captured in sequential unfolding of polyproteins over a range of loads

While performing under mechanical loads in vivo, polyproteins are vitally involved in cellular mechanisms such as regulation of tissue elasticity and mechano-transduction by unfolding their comprising domains and extending them. It is widely thought that the process of sequential unfolding of polyproteins follows an exponential kinetics as the individual unfolding events exhibit identical and identically distributed (iid) Poisson behavior. However, it was shown that under high loads, the sequential unfolding kinetics displays nonexponential kinetics that alludes to aging by a subdiffusion process. Statistical order analysis of this kinetics indicated that the individual unfolding events are not iid, and cannot be defined as a Poisson (memoryless) process. Based on numerical simulations it was argued that this behavior becomes less pronounced with lowering the load, therefore it is to be expected that polyproteins unfolding under lower forces will follow a Poisson behavior. This expectation serves as the motivation of the current study, in which we investigate the effect of force lowering on the unfolding kinetics of Poly-L₈ under varying loads, specifically high (150, 100 ​pN) and moderate-low (45, 30, 20 ​pN) forces. We found that a hierarchy among the unfolding events still exists even under low loads, again resulting in nonexponential behavior. We observe that analyzing the dwell-time distributions with stretched-exponentials and power laws give rise to different phenomenological trends. Using statistical order analysis, we demonstrated that even under the lowest load, the sequential unfolding cannot be considered as iid, in accord with the power law distribution. Additional free energy analysis revealed the contribution of the unfolded segments elasticity that scales with the force on the overall one-dimensional contour of the energy landscape, but more importantly, it discloses the hierarchy within the activation barriers during sequential unfolding that account for the observed nonexponentiality.

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Poly-L₈ unfolding shows nonexponential kinetics at forces ranging from 150 to 20 ​pN.

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Different phenomenological trends are observed for the dwell-time distributions.

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The unfolding events were shown to be dependent and not identically distributed.

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Free energy analysis reveals elastic impact and hierarchy in the unfolding barriers.

Contribution of Hydrophobic Interactions to Protein Mechanical Stability

The role of hydrophobic and polar interactions in providing thermodynamic stability to folded proteins has been intensively studied, but the relative contribution of these interactions to the mechanical stability is less explored. We used steered molecular dynamics simulations with constant-velocity pulling to generate force-extension curves of selected protein domains and monitor hydrophobic surface unravelling upon extension. Hydrophobic contribution was found to vary between one fifth and one third of the total force while the rest of the contribution is attributed primarily to hydrogen bonds. Moreover, hydrophobic force peaks were shifted towards larger protein extensions with respect to the force peaks attributed to hydrogen bonds. The higher importance of hydrogen bonds compared to hydrophobic interactions in providing mechanical resistance is in contrast with the relative importance of the hydrophobic interactions in providing thermodynamic stability of proteins. The different contributions of these interactions to the mechanical stability are explained by the steeper free energy dependence of hydrogen bonds compared to hydrophobic interactions on the relative positions of interacting atoms. Comparative analyses for several protein domains revealed that the variation of hydrophobic forces is modest, while the contribution of hydrogen bonds to the force peaks becomes increasingly important for mechanically resistant protein domains.

High-resolution Single-molecule Magnetic Tweezers

Single-molecule magnetic tweezers deliver magnetic force and torque to single target molecules, permitting the study of dynamic changes in biomolecular structures and their interactions. Because the magnetic tweezer setups can generate magnetic fields that vary slowly over tens of millimeters-far larger than the nanometer scale of the single molecule events being observed-this technique can maintain essentially constant force levels during biochemical experiments while generating a biologically meaningful force on the order of 1-100 pN. When using bead-tether constructs to pull on single molecules, smaller magnetic beads and shorter submicrometer tethers improve dynamic response times and measurement precision. In addition, employing high-speed cameras, stronger light sources, and a graphics programming unit permits true high-resolution single-molecule magnetic tweezers that can track nanometer changes in target molecules on a millisecond or even submillisecond time scale. The unique force-clamping capacity of the magnetic tweezer technique provides a way to conduct measurements under near-equilibrium conditions and directly map the energy landscapes underlying various molecular phenomena. High-resolution single-molecule magnetic tweezers can thus be used to monitor crucial conformational changes in single-protein molecules, including those involved in mechanotransduction and protein folding. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Biophysical Approaches for Applying and Measuring Biological Forces

Over the past decades, increasing evidence has indicated that mechanical loads can regulate the morphogenesis, proliferation, migration, and apoptosis of living cells. Investigations of how cells sense mechanical stimuli or the mechanotransduction mechanism is an active field of biomaterials and biophysics. Gaining a further understanding of mechanical regulation and depicting the mechanotransduction network inside cells require advanced experimental techniques and new theories. In this review, the fundamental principles of various experimental approaches that have been developed to characterize various types and magnitudes of forces experienced at the cellular and subcellular levels are summarized. The broad applications of these techniques are introduced with an emphasis on the difficulties in implementing these techniques in special biological systems. The advantages and disadvantages of each technique are discussed, which can guide readers to choose the most suitable technique for their questions. A perspective on future directions in this field is also provided. It is anticipated that technical advancement can be a driving force for the development of mechanobiology.

Nano-Precision Tweezers for Mechanosensitive Proteins and Beyond

Mechanical forces play pivotal roles in regulating cell shape, function, and fate. Key players that govern the mechanobiological interplay are the mechanosensitive proteins found on cell membranes and in cytoskeleton. Their unique nanomechanics can be interrogated using single-molecule tweezers, which can apply controlled forces to the proteins and simultaneously measure the ensuing structural changes. Breakthroughs in high-resolution tweezers have enabled the routine monitoring of nanometer-scale, millisecond dynamics as a function of force. Undoubtedly, the advancement of structural biology will be further fueled by integrating static atomic-resolution structures and their dynamic changes and interactions observed with the force application techniques. In this minireview, we will introduce the general principles of single-molecule tweezers and their recent applications to the studies of force-bearing proteins, including the synaptic proteins that need to be categorized as mechanosensitive in a broad sense. We anticipate that the impact of nano-precision approaches in mechanobiology research will continue to grow in the future.

Resonator nanophotonic standing-wave array trap for single-molecule manipulation and measurement

Nanophotonic tweezers represent emerging platforms with significant potential for parallel manipulation and measurements of single biological molecules on-chip. However, trapping force generation represents a substantial obstacle for their broader utility. Here, we present a resonator nanophotonic standing-wave array trap (resonator-nSWAT) that demonstrates significant force enhancement. This platform integrates a critically-coupled resonator design to the nSWAT and incorporates a novel trap reset scheme. The nSWAT can now perform standard single-molecule experiments, including stretching DNA molecules to measure their force-extension relations, unzipping DNA molecules, and disrupting and mapping protein-DNA interactions. These experiments have realized trapping forces on the order of 20 pN while demonstrating base-pair resolution with measurements performed on multiple molecules in parallel. Thus, the resonator-nSWAT platform now meets the benchmarks of a table-top precision optical trapping instrument in terms of force generation and resolution. This represents the first demonstration of a nanophotonic platform for such single-molecule experiments.

Applications of nanophotonic tweezers have been limited by the low trapping force. Here, the authors present enhanced force generation in a nanophotonic standing-wave array trap by integrating a critically-coupled resonator design and demonstrate common single-molecule experiments.

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.

Drag force of polyethyleneglycol in flows of polymer solutions measured using a scanning probe microscope

The drag force of polyethyleneglycol thiol (mPEG-SH) attached to a cantilever probe in the flows of glycerol and polyethyleneglycol (PEG) solutions was measured. The effects of the molecular weights of mPEG-SH, solute, and molecular weights of PEGs in the flows on the drag force were investigated. The drag force of mPEG-SH with any molecular weight in the flows of glycerol solutions was described well by the stem and ellipsoidal-flower model proposed in a previous study. However, the drag force further increased in the flow of the PEG solutions. To describe the increment, an assumption of polymer entanglement with mPEG-SH attached to the probe in the flow was employed. The modified stem and ellipsoidal-flower model that employed polymer entanglements fit well to the drag force of mPEG-SH with any molecular weight in the flow of the polymer solution.

Mechanobiology of muscle and myofibril morphogenesis

Muscles generate forces for animal locomotion. The contractile apparatus of muscles is the sarcomere, a highly regular array of large actin and myosin filaments linked by gigantic titin springs. During muscle development many sarcomeres assemble in series into long periodic myofibrils that mechanically connect the attached skeleton elements. Thus, ATP-driven myosin forces can power movement of the skeleton. Here we review muscle and myofibril morphogenesis, with a particular focus on their mechanobiology. We describe recent progress on the molecular structure of sarcomeres and their mechanical connections to the skeleton. We discuss current models predicting how tension coordinates the assembly of key sarcomeric components to periodic myofibrils that then further mature during development. This requires transcriptional feedback mechanisms that may help to coordinate myofibril assembly and maturation states with the transcriptional program. To fuel the varying energy demands of muscles we also discuss the close mechanical interactions of myofibrils with mitochondria and nuclei to optimally support powerful or enduring muscle fibers.

Force Dependence of Proteins' Transition State Position and the Bell-Evans Model

Single-molecule force spectroscopy has opened a new field of research in molecular biophysics and biochemistry. Pulling experiments on individual proteins permit us to monitor conformational transitions with high temporal resolution and measure their free energy landscape. The force–extension curves of single proteins often present large hysteresis, with unfolding forces that are higher than refolding ones. Therefore, the high energy of the transition state (TS) in these molecules precludes kinetic rates measurements in equilibrium hopping experiments. In irreversible pulling experiments, force-dependent kinetic rates measurements show a systematic discrepancy between the sum of the folding and unfolding TS distances derived by the kinetic Bell–Evans model and the full molecular extension predicted by elastic models. Here, we show that this discrepancy originates from the force-induced movement of TS. Specifically, we investigate the highly kinetically stable protein barnase, using pulling experiments and the Bell–Evans model to characterize the position of its kinetic barrier. Experimental results show that while the TS stays at a roughly constant distance relative to the native state, it shifts with force relative to the unfolded state. Interestingly, a conversion of the protein extension into amino acid units shows that the TS position follows the Leffler–Hammond postulate: the higher the force, the lower the number of unzipped amino acids relative to the native state. The results are compared with the quasi-reversible unfolding–folding of a short DNA hairpin.

Binding of SARS-COV-2 (COVID-19) and SARS-COV to human ACE2: Identifying binding sites and consequences on ACE2 stiffness

The SARS-CoV-2 coronavirus (COVID-19) that is causing the massive global pandemic exhibits similar human cell invasion mechanism as the coronavirus SARS-CoV, which had significantly lower fatalities. The cell membrane protein Angiotensin-converting enzyme 2 (ACE2) is the initiation point for both the coronavirus infections in humans. Here, we model the molecular interactions and mechanical properties of ACE2 with both SARS-CoV and COVID-19 spike protein receptor-binding domains (RBD). We report that the COVID-19 spike RBD interacts with ACE2 more strongly and at only two protein residues, as compared to multi-residue interaction of the SARS-CoV. Although both coronaviruses stiffen the ACE2, the impact of COVID-19 is six times larger, which points towards differences in the severity of the reported respiratory distress. The recognition of specific residues of ACE2 attachments to coronaviruses is important as the residues suggest potential sites of intervention to inhibit attachment and subsequent entry of the COVID-19 into human host cells

Interpretation of Single-Molecule Force Experiments on Proteins Using Normal Mode Analysis

Single-molecule force spectroscopy experiments allow protein folding and unfolding to be explored using mechanical force. Probably the most informative technique for interpreting the results of these experiments at the structural level makes use of steered molecular dynamics (MD) simulations, which can explicitly model the protein under load. Unfortunately, this technique is computationally expensive for many of the most interesting biological molecules. Here, we find that normal mode analysis (NMA), a significantly cheaper technique from a computational perspective, allows at least some of the insights provided by MD simulation to be gathered. We apply this technique to three non-homologous proteins that were previously studied by force spectroscopy: T4 lysozyme (T4L), Hsp70 and the glucocorticoid receptor domain (GCR). The NMA results for T4L and Hsp70 are compared with steered MD simulations conducted previously, and we find that we can recover the main results. For the GCR, which did not undergo MD simulation, our approach identifies substructures that correlate with experimentally identified unfolding intermediates. Overall, we find that NMA can make a valuable addition to the analysis toolkit for the structural analysis of single-molecule force experiments on proteins.

Single-Molecule Force Spectroscopy Studies of Missense Titin Mutations That Are Likely Causing Cardiomyopathy

The giant muscle protein titin plays important roles in heart function. Mutations in titin have emerged as a major cause of familial cardiomyopathy. Missense mutations have been identified in cardiomyopathy patients; however, it is challenging to distinguish disease-causing mutations from benign ones. Given the importance of titin mechanics in heart function, it is critically important to elucidate the mechano-phenotypes of cardiomyopathy-causing mutations found in the elastic I-band part of cardiac titin. Using single-molecule atomic force microscopy (AFM) and equilibrium chemical denaturation, we investigated the mechanical and thermodynamic effects of two missense mutations, R57C-I94 and S22P-I84, found in the elastic I-band part of cardiac titin that were predicted to be likely causing cardiomyopathy by bioinformatics analysis. Our AFM results showed that mutation R57C had a significant destabilization effect on the I94 module. R57C reduced the mechanical unfolding force of I94 by ∼30-40 pN, accelerated the unfolding kinetics, and decelerated the folding. These effects collectively increased the unfolding propensity of I94, likely resulting in altered titin elasticity. In comparison, S22P led to only modest destabilization of I84, with a decrease in unfolding force by ∼10 pN. It is unlikely that such a modest destabilization would lead to a change in titin elasticity. These results will serve as the first step toward elucidating mechano-phenotypes of cardiomyopathy-causing mutations in the elastic I-band.

Protein Unfolding: Denaturant vs. Force

While protein refolding has been studied for over 50 years since the pioneering work of Christian Anfinsen, there have been a limited number of studies correlating results between chemical, thermal, and mechanical unfolding. The limited knowledge of the relationship between these processes makes it challenging to compare results between studies if different refolding methods were applied. Our current work compares the energetic barriers and folding rates derived from chemical, thermal, and mechanical experiments using an immunoglobulin-like domain from the muscle protein titin as a model system. This domain, I83, has high solubility and low stability relative to other Ig domains in titin, though its stability can be modulated by calcium. Our experiments demonstrated that the free energy of refolding was equivalent with all three techniques, but the refolding rates exhibited differences, with mechanical refolding having slightly faster rates. This suggests that results from equilibrium-based measurements can be compared directly but care should be given comparing refolding kinetics derived from refolding experiments that used different unfolding methods.

Single-Molecule Force Spectroscopy of Protein Folding

The use of force probes to induce unfolding and refolding of single molecules through the application of mechanical tension, known as single-molecule force spectroscopy (SMFS), has proven to be a powerful tool for studying the dynamics of protein folding. Here we provide an overview of what has been learned about protein folding using SMFS, from small, single-domain proteins to large, multi-domain proteins. We highlight the ability of SMFS to measure the energy landscapes underlying folding, to map complex pathways for native and non-native folding, to probe the mechanisms of chaperones that assist with native folding, to elucidate the effects of the ribosome on co-translational folding, and to monitor the folding of membrane proteins.