Distinguishing Signatures of Multipathway Conformational Transitions

Engineering the Mechanical Stability of a Therapeutic Affibody/PD-L1 Complex by Anchor Point Selection

Protein-protein complexes can vary in mechanical stability depending on the direction from which force is applied. Here we investigated the anisotropic mechanical stability of a molecular complex between a therapeutic non-immunoglobulin scaffold called Affibody and the extracellular domain of the immune checkpoint protein PD-L1. We used a combination of single-molecule AFM force spectroscopy (AFM-SMFS) with bioorthogonal clickable peptide handles, shear stress bead adhesion assays, molecular modeling, and steered molecular dynamics (SMD) simulations to understand the pulling point dependency of mechanostability of the Affibody:(PD-L1) complex. We observed diverse mechanical responses depending on the anchor point. For example, pulling from residue #22 on Affibody generated an intermediate unfolding event attributed to partial unfolding of PD-L1, while pulling from Affibody's N-terminus generated force-activated catch bond behavior. We found that pulling from residue #22 or #47 on Affibody generated the highest rupture forces, with the complex breaking at up to ~ 190 pN under loading rates of ~104-105 pN/sec, representing a ~4-fold increase in mechanostability as compared with low force N-terminal pulling. SMD simulations provided consistent tendencies in rupture forces, and through visualization of force propagation networks provided mechanistic insights. These results demonstrate how mechanostability of therapeutic protein-protein interfaces can be controlled by informed selection of anchor points within molecules, with implications for optimal bioconjugation strategies in drug delivery vehicles.

Theory and Examples of Catch Bonds

We discuss slip bonds, catch bonds, and the tug-of-war mechanism using mathematical arguments. The aim is to explain the theoretical tool of molecular potential energy surfaces (PESs). For this, we propose simple 2-dimensional surface models to demonstrate how a molecule under an external force behaves. Examples are selectins. Catch bonds, in particular, are explained in more detail, and they are contrasted to slip bonds. We can support special two-dimensional molecular PESs for E- and L-selectin which allow the catch bond property. We demonstrate that Newton trajectories (NT) are powerful tools to describe these phenomena. NTs form the theoretical background of mechanochemistry.

Constructing efficient strategies for the process optimization by restart

Optimization of the mean completion time of random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: how to construct a restart strategy for a process whose detailed statistics are unknown to ensure that the expected completion time will reduce? Addressing this query here we propose several constructive criteria for the effectiveness of various protocols of noninstantaneous restart in the mean completion time problem and in the success probability problem. Being expressed in terms of a small number of easily estimated statistical characteristics of the original process (MAD, median completion time, low-order statistical moments of completion time), these criteria allow informed restart decision based on partial information.

Self-driven configurational dynamics in frustrated spring-mass systems

Various physical systems relax mechanical frustration through configurational rearrangements. We examine such rearrangements via Hamiltonian dynamics of simple internally stressed harmonic four-mass systems. We demonstrate theoretically and numerically how mechanical frustration controls the underlying potential energy landscape. Then, we examine the harmonic four-mass systems' Hamiltonian dynamics and relate the onset of chaotic motion to self-driven rearrangements. We show such configurational dynamics may occur without strong precursors, rendering such dynamics seemingly spontaneous.

Free Energy Landscape of Type III Fibronectin Domain with Identified Intermediate State and Hierarchical Symmetry

The tenth domain of type III fibronectin (FNIII_{10}) mediates cell adhesion to the extracellular matrix. Despite its structural similarity to immunoglobulin domains, FNIII_{10} exhibits unique unfolding behaviors. We employed magnetic tweezers to investigate the unfolding and folding dynamics of FNIII_{10} under physiological forces (4-50 pN). Our results showed that FNIII_{10} follows a consistent transition pathway with an intermediate state characterized by detached A and G β strands. We determined the folding free energies and all force-dependent transition rates of FNIII_{10} and found that both unfolding rates from the native state to the intermediate state and from the intermediate state to the unfolded state deviate from Bell's model. We constructed a quantitative free energy landscape with well-defined traps and barriers that exhibits a hierarchical symmetrical pattern. Our findings provide a comprehensive understanding of FNIII_{10} conformational dynamics and demonstrate how free energy landscape of multistate biomolecules can be precisely mapped, illuminating the relationship between thermal stability, intermediate states, and folding rates in protein folding.

Bernoulli trial under restarts: A comparative study of resetting transitions

A Bernoulli trial describing the escape behavior of a lamb to a safe haven in pursuit by a lion is studied under restarts. The process ends in two ways: either the lamb makes it to the safe haven (success) or is captured by the lion (failure). We study the first passage properties of this Bernoulli trial and find that only mean first passage time exists. Considering Poisson and sharp resetting, we find that the success probability is a monotonically decreasing function of the restart rate. The mean time, however, exhibits a nonmonotonic dependence on the restart rate taking a minimal value at an optimal restart rate. Furthermore, for sharp restart, the mean time possesses a local and a global minima. As a result, the optimal restart rate exhibits a continuous transition for Poisson resetting while it exhibits a discontinuous transition for sharp resetting as a function of the relative separation of the lion and the lamb. We also find that the distribution of first passage times under sharp resetting exhibits a periodic behavior.

Direct Observation and Real-Time Tracking of an Extraordinarily Stable Folding Intermediate in Mitotic Arrest Deficient Protein 2 Folding by Single-Molecule Fluorescence Resonance Energy Transfer

Although ensemble experiments have suggested that mitotic arrest deficient protein 2 (Mad2), a metamorphic protein, has folding intermediates, direct evidence and characterization are not available. It remains an outstanding challenge to capture the folding intermediates in real time, which is crucial to elucidate the folding mechanism, but the folding intermediates are normally unstable and only exist transiently. By combining confocal-microscopy-based and total internal reflection fluorescence (TIRF)-microscopy-based single-molecule Förster resonance energy transfer (sm-FRET) techniques, we have investigated the folding/unfolding process of Mad2 and captured its folding intermediate at the single-molecule level. This provides direct evidence for the existence of an intermediate along the folding pathway of Mad2. The folding intermediate proved to be extraordinarily stable, with an extremely long average dwell time of 2.3 s under the conditions of 3 M GdmCl at ambient temperature. The folding trajectories obtained from TIRF experiments further suggest that the intermediate is on-pathway to native Mad2.

Free-energy landscape of two-state protein acylphosphatase with large contact order revealed by force-dependent folding and unfolding dynamics

Acylphosphatase (AcP) is a small protein with 98 amino acid residues that catalyzes the hydrolysis of carboxyl-phosphate bonds. AcP is a typical two-state protein with slow folding rate due to its relatively large contact order in the native structure. The mechanical properties and unfolding behavior of AcP has been studied by atomic force microscope. Here using stable magnetic tweezers, we measured the force-dependent folding rates within a force range 1-3 pN, and unfolding rates 15-40 pN. The obtained unfolding rates show different force sensitivities at forces below and above ∼27 pN, which determines a free-energy landscape with two energy barriers. Our results indicate that the free-energy landscape of small globule proteins have general Bactrian camel shape, and large contact order of the native state produces a high barrier dominate at low forces.

Two energy barriers and a transient intermediate state determine the unfolding and folding dynamics of cold shock protein

Cold shock protein (Csp) is a typical two-state folding model protein which has been widely studied by biochemistry and single molecule techniques. Recently two-state property of Csp was confirmed by atomic force microscopy (AFM) through direct pulling measurement, while several long-lifetime intermediate states were found by force-clamp AFM. We systematically studied force-dependent folding and unfolding dynamics of Csp using magnetic tweezers with intrinsic constant force capability. Here we report that Csp mostly folds and unfolds with a single step over force range from 5 pN to 50 pN, and the unfolding rates show different force sensitivities at forces below and above ~8 pN, which determines a free energy landscape with two barriers and a transient intermediate state between them along one transition pathway. Our results provide a new insight on protein folding mechanism of two-state proteins.

Structural dynamics of single SARS-CoV-2 pseudoknot molecules reveal topologically distinct conformers

The RNA pseudoknot that stimulates programmed ribosomal frameshifting in SARS-CoV-2 is a possible drug target. To understand how it responds to mechanical tension applied by ribosomes, thought to play a key role during frameshifting, we probe its structural dynamics using optical tweezers. We find that it forms multiple structures: two pseudoknotted conformers with different stability and barriers, and alternative stem-loop structures. The pseudoknotted conformers have distinct topologies, one threading the 5′ end through a 3-helix junction to create a knot-like fold, the other with unthreaded 5′ end, consistent with structures observed via cryo-EM and simulations. Refolding of the pseudoknotted conformers starts with stem 1, followed by stem 3 and lastly stem 2; Mg²⁺ ions are not required, but increase pseudoknot mechanical rigidity and favor formation of the knot-like conformer. These results resolve the SARS-CoV-2 frameshift signal folding mechanism and highlight its conformational heterogeneity, with important implications for structure-based drug-discovery efforts.

The RNA pseudoknot of SARS-CoV-2 promotes -1 programmed ribosomal frameshifting. Here the authors use single molecule force spectroscopy to study the folding of this pseudoknot, showing that it forms at least two different pseudoknot conformers with distinct fold topologies.

Hidden Intermediate State and Second Pathway Determining Folding and Unfolding Dynamics of GB1 Protein at Low Forces

Atomic force microscopy experiments found that GB1, a typical two-state model protein used for study of folding and unfolding dynamics, can sustain forces of more than 100 pN, but its response to low forces still remains unclear. Using ultrastable magnetic tweezers, we discovered that GB1 has an unexpected nonmonotonic force-dependent unfolding rate at 5-160 pN, from which a free energy landscape with two main barriers and a hidden intermediate state was constructed. A model combining two separate models by Dudko et al. with two pathways between the native state and this intermediate state is proposed to rebuild the unfolding dynamics over the full experimental force range. One candidate of this transient intermediate state is the theoretically proposed molten globule state with a loosely collapsed conformation, which might exist universally in the folding and unfolding processes of two-state proteins.

High force catch bond mechanism of bacterial adhesion in the human gut

Bacterial colonization of the human intestine requires firm adhesion of bacteria to insoluble substrates under hydrodynamic flow. Here we report the molecular mechanism behind an ultrastable protein complex responsible for resisting shear forces and adhering bacteria to cellulose fibers in the human gut. Using single-molecule force spectroscopy (SMFS), single-molecule FRET (smFRET), and molecular dynamics (MD) simulations, we resolve two binding modes and three unbinding reaction pathways of a mechanically ultrastable R. champanellensis (Rc) Dockerin:Cohesin (Doc:Coh) complex. The complex assembles in two discrete binding modes with significantly different mechanical properties, with one breaking at ~500 pN and the other at ~200 pN at loading rates from 1-100 nN s-1. A neighboring X-module domain allosterically regulates the binding interaction and inhibits one of the low-force pathways at high loading rates, giving rise to a catch bonding mechanism that manifests under force ramp protocols. Multi-state Monte Carlo simulations show strong agreement with experimental results, validating the proposed kinetic scheme. These results explain mechanistically how gut microbes regulate cell adhesion strength at high shear stress through intricate molecular mechanisms including dual-binding modes, mechanical allostery and catch bonds.

Correcting molecular transition rates measured by single-molecule force spectroscopy for limited temporal resolution

Equilibrium free-energy-landscape parameters governing biomolecular folding can be determined from nonequilibrium force-induced unfolding by measuring the rates k for transitioning back and forth between states as a function of force F. However, bias in the observed forward and reverse rates is introduced by limited effective temporal resolution, which includes the mechanical response time of the force probe and any smoothing used to improve the signal-to-noise ratio. Here we use simulations to characterize this bias, which is most prevalent when the ratio of forward and reverse rates is far from unity. We find deviations in k(F) at high rates, due to unobserved transitions from short- to long-lived states, and at low rates, due to the corresponding unobserved transitions from long- to short-lived states. These missing events introduce erroneous curvature in log(k) vs F that leads to incorrect landscape parameter determination. To correct the measured k(F), we derive a pair of model-independent analytical formulas. The first correction accounts for unobserved transitions from short- to long-lived states, but does surprisingly little to correct the erroneous energy-landscape parameters. Only by subsequently applying the second formula, which corrects the corresponding reverse process, do we recover the expected k(F) and energy-landscape quantities. Going forward, these corrections should be applied to transition-rate data whenever the highest measured rate is not at least an order of magnitude slower than the effective temporal resolution.

Significant Differences in RNA Structure Destabilization by HIV-1 GagDp6 and NCp7 Proteins

Retroviral nucleocapsid (NC) proteins are nucleic acid chaperones that play distinct roles in the viral life cycle. During reverse transcription, HIV-1 NC facilitates the rearrangement of nucleic acid secondary structures, allowing the transactivation response (TAR) RNA hairpin to be transiently destabilized and annealed to a complementary RNA hairpin. In contrast, during viral assembly, NC, as a domain of the group-specific antigen (Gag) polyprotein, binds the genomic RNA and facilitates packaging into new virions. It is not clear how the same protein, alone or as part of Gag, performs such different RNA binding functions in the viral life cycle. By combining single-molecule optical tweezers measurements with a quantitative mfold-based model, we characterize the equilibrium stability and unfolding barrier for TAR RNA. Comparing measured results with a model of discrete protein binding allows us to localize affected binding sites, in addition to quantifying hairpin stability. We find that, while both NCp7 and Gag∆p6 destabilize the TAR hairpin, Gag∆p6 binding is localized to two sites in the stem, while NCp7 targets sites near the top loop. Unlike Gag∆p6, NCp7 destabilizes this loop, shifting the location of the reaction barrier toward the folded state and increasing the natural rate of hairpin opening by ~10⁴. Thus, our results explain why Gag cleavage and NC release is an essential prerequisite for reverse transcription within the virion.

Non-Markov bond model for dynamic force spectroscopy

Single-molecule force spectroscopy data are conventionally analyzed using a schematic model, wherein a molecular bond is represented as a virtual particle diffusing in a one-dimensional free-energy landscape. However, this simple and efficient approach is unable to account for the "anomalous" bond-breaking kinetics increasingly observed in force spectroscopy experiments and simulations, e.g., in the form of non-exponential distributions of bond lifetimes under constant load. Here, we show that such characteristic traits arise naturally in a rigorous extension of the one-dimensional theory that accounts for the transient dynamics of a generic set of coupled degrees of freedom. These "hidden modes" affect the reaction dynamics in various ways, depending on their relaxation spectrum and the loading protocol, giving rise, in particular, to apparent static and dynamic disorder. In two complementary asymptotic limits, we are able to find exact analytical expressions for pertinent experimental observables, such as the mean rupture force and the rupture-force distribution. Intriguingly, our asymptotic results become unconditionally exact at high loading rates, thus providing us with a microscopically consistent theory of rapid force spectroscopy that avoids the usual Markov assumption.

Advances in molecular simulations of protein mechanical properties and function

Single-molecule force spectroscopy and classical molecular dynamics are natural allies. Recent advances in both experiments and simulations have increasingly facilitated a direct comparison of SMFS and MD data, most importantly by closing the gap between time scales, which has been traditionally at least 5 orders of magnitudes wide. In this review, we will explore these advances chiefly on the computational side. We focus on protein dynamics under force and highlight recent studies that showcase how lower loading rates and more statistics help to better interpret previous experiments and to also motivate new ones. At the same time, steadily increasing system sizes are used to mimic more closely the mechanical environment in the biological context. We showcase some of these advances on atomistic and coarse-grained scale, from asymmetric membrane tension to larger (multidomain/multimeric) protein assemblies under force.

Specific Nucleic Acid Chaperone Activity of HIV-1 Nucleocapsid Protein Deduced from Hairpin Unfolding

RNA and DNA hairpin formation and disruption play key regulatory roles in a variety of cellular processes. The 59-nucleotide transactivation response (TAR) RNA hairpin facilitates the production of full-length transcripts of the HIV-1 genome. Yet the stability of this long, irregular hairpin becomes a liability during reverse transcription as 24 base pairs must be disrupted for strand transfer. Retroviral nucleocapsid (NC) proteins serve as nucleic acid chaperones that have been shown to both destabilize the TAR hairpin and facilitate strand annealing with its complementary DNA sequence. Yet it has remained difficult to elucidate the way NC targets and dramatically destabilizes this hairpin while only weakly affecting the annealed product. In this work, we used optical tweezers to measure the stability of TAR and found that adding NC destabilized the hairpin and simultaneously caused a distinct change in both the height and location of the energy barrier. This data was matched to an energy landscape predicted from a simple theory of definite base pair destabilization. Comparisons revealed the specific binding sites found by NC along the irregular TAR hairpin. Furthermore, specific binding explained both the unusual shift in the transition state and the much weaker effect on the annealed product. These experiments illustrate a general method of energy landscape transformation that exposes important physical insights.

Thermal versus mechanical unfolding in a model protein

Force spectroscopy techniques are often used to learn about the free energy landscape of single biomolecules, typically by recovering free energy quantities that, extrapolated to zero force, are compared to those measured in bulk experiments. However, it is not always clear how the information obtained from a mechanically perturbed system can be related to the information obtained using other denaturants since tensioned molecules unfold and refold along a reaction coordinate imposed by the force, which is not likely to be meaningful in its absence. Here, we explore this dichotomy by investigating the unfolding landscape of a model protein, which is unfolded first mechanically through typical force spectroscopy-like protocols and next thermally. When unfolded by nonequilibrium force extension and constant force protocols, we recover a simple two-barrier landscape as the protein reaches the extended conformation through a metastable intermediate. Interestingly, folding-unfolding equilibrium simulations at low forces suggested a totally different scenario, where this metastable state plays little role in the unfolding mechanism, and the protein unfolds through two competing pathways [R. Tapia-Rojo et al., J. Chem. Phys. 141, 135102 (2014)]. Finally, we use Markov state models to describe the configurational space of the unperturbed protein close to the critical temperature. The thermal dynamics is well understood by a one-dimensional landscape along an appropriate reaction coordinate, however it is very different from the mechanical picture. In this sense, the results of our protein model for the mechanical and thermal descriptions provide incompatible views of the folding/unfolding landscape of the system, and the estimated quantities to zero force result are hard to interpret.

Critical phenomena in the temperature-pressure-crowding phase diagram of a protein

In the cell, proteins fold and perform complex functions through global structural rearrangements. Function requires a protein to be at the brink of stability to be susceptible to small environmental fluctuations, yet stable enough to maintain structural integrity. These apparently conflicting behaviors are exhibited by systems near a critical point, where distinct phases merge-a concept beyond previous studies indicating proteins have a well-defined folded/unfolded phase boundary in the pressure-temperature plane. Here, by modeling the protein phosphoglycerate kinase (PGK) on the temperature (T), pressure (P), and crowding volume-fraction (ϕ) phase diagram, we demonstrate a critical transition where phases merge, and PGK exhibits large structural fluctuations. Above the critical point, the difference between the intermediate and unfolded phases disappears. When ϕ increases, the critical point moves to lower T _c. We verify the calculations with experiments mapping the T-P-ϕ space, which likewise reveal a critical point at 305 K and 170 MPa that moves to lower T _c as ϕ increases. Crowding places PGK near a critical line in its natural parameter space, where large conformational changes can occur without costly free energy barriers. Specific structures are proposed for each phase based on simulation.

Force-Dependent Facilitated Dissociation Can Generate Protein-DNA Catch Bonds

Cellular structures are continually subjected to forces, which may serve as mechanical signals for cells through their effects on biomolecule interaction kinetics. Typically, molecular complexes interact via "slip bonds," so applied forces accelerate off rates by reducing transition energy barriers. However, biomolecules with multiple dissociation pathways may have considerably more complicated force dependencies. This is the case for DNA-binding proteins that undergo "facilitated dissociation," in which competitor biomolecules from solution enhance molecular dissociation in a concentration-dependent manner. Using simulations and theory, we develop a generic model that shows that proteins undergoing facilitated dissociation can form an alternative type of molecular bond, known as a "catch bond," for which applied forces suppress protein dissociation. This occurs because the binding by protein competitors responsible for the facilitated dissociation pathway can be inhibited by applied forces. Within the model, we explore how the force dependence of dissociation is regulated by intrinsic factors, including molecular sensitivity to force and binding geometry and the extrinsic factor of competitor protein concentration. We find that catch bonds generically emerge when the force dependence of the facilitated unbinding pathway is stronger than that of the spontaneous unbinding pathway. The sharpness of the transition between slip- and catch-bond kinetics depends on the degree to which the protein bends its DNA substrate. This force-dependent kinetics is broadly regulated by the concentration of competitor biomolecules in solution. Thus, the observed catch bond is mechanistically distinct from other known physiological catch bonds because it requires an extrinsic factor-competitor proteins-rather than a specific intrinsic molecular structure. We hypothesize that this mechanism for regulating force-dependent protein dissociation may be used by cells to modulate protein exchange, regulate transcription, and facilitate diffusive search processes.

On the Interpretation of Force-Induced Unfolding Studies of Membrane Proteins Using Fast Simulations

Single-molecule force spectroscopy has proven extremely beneficial in elucidating folding pathways for membrane proteins. Here, we simulate these measurements, conducting hundreds of unfolding trajectories using our fast Upside algorithm for slow enough speeds to reproduce key experimental features that may be missed using all-atom methods. The speed also enables us to determine the logarithmic dependence of pulling velocities on the rupture levels to better compare to experimental values. For simulations of atomic force microscope measurements in which force is applied vertically to the C-terminus of bacteriorhodopsin, we reproduce the major experimental features including even the back-and-forth unfolding of single helical turns. When pulling laterally on GlpG to mimic the experiment, we observe quite different behavior depending on the stiffness of the spring. With a soft spring, as used in the experimental studies with magnetic tweezers, the force remains nearly constant after the initial unfolding event, and a few pathways and a high degree of cooperativity are observed in both the experiment and simulation. With a stiff spring, however, the force drops to near zero after each major unfolding event, and numerous intermediates are observed along a wide variety of pathways. Hence, the mode of force application significantly alters the perception of the folding landscape, including the number of intermediates and the degree of folding cooperativity, important issues that should be considered when designing experiments and interpreting unfolding data.

Force-Dependent Regulation of Talin-KANK1 Complex at Focal Adhesions

KANK proteins mediate cross-talk between dynamic microtubules and integrin-based adhesions to the extracellular matrix. KANKs interact with the integrin/actin-binding protein talin and with several components of microtubule-stabilizing cortical complexes. Because of actomyosin contractility, the talin-KANK complex is likely under mechanical force, and its mechanical stability is expected to be a critical determinant of KANK recruitment to focal adhesions. Here, we quantified the lifetime of the complex of the talin rod domain R7 and the KN domain of KANK1 under shear-force geometry and found that it can withstand forces for seconds to minutes over a physiological force range up to 10 pN. Complex stability measurements combined with cell biological experiments suggest that shear-force stretching promotes KANK1 localization to the periphery of focal adhesions. These results indicate that the talin-KANK1 complex is mechanically strong, enabling it to support the cross-talk between microtubule and actin cytoskeleton at focal adhesions.

Unraveling the Mechanical Unfolding Pathways of a Multidomain Protein: Phosphoglycerate Kinase

Phosphoglycerate kinase (PGK) is a highly conserved enzyme that is crucial for glycolysis. PGK is a monomeric protein composed of two similar domains and has been the focus of many studies for investigating interdomain interactions within the native state and during folding. Previous studies used traditional biophysical methods (such as circular dichroism, tryptophan fluorescence, and NMR) to measure signals over a large ensemble of molecules, which made it difficult to observe transient changes in stability or structure during unfolding and refolding of single molecules. Here, we unfold single molecules of PGK using atomic force spectroscopy and steered molecular dynamic computer simulations to examine the conformational dynamics of PGK during its unfolding process. Our results show that after the initial forced separation of its domains, yeast PGK (yPGK) does not follow a single mechanical unfolding pathway; instead, it stochastically follows two distinct pathways: unfolding from the N-terminal domain or unfolding from the C-terminal domain. The truncated yPGK N-terminal domain unfolds via a transient intermediate, whereas the structurally similar isolated C-terminal domain has no detectable intermediates throughout its mechanical unfolding process. The N-terminal domain in the full-length yPGK displays a strong unfolding intermediate 13% of the time, whereas the truncated domain (yPGKNT) transitions through the intermediate 81% of the time. This effect indicates that the mechanical properties of yPGK cannot be simply deduced from the mechanical properties of its constituents. We also find that Escherichia coli PGK is significantly less mechanically stable as compared to yPGK, contrary to bulk unfolding measurements. Our results support the growing body of observations that the folding behavior of multidomain proteins is difficult to predict based solely on the studies of isolated domains.

Multiplexed protein force spectroscopy reveals equilibrium protein folding dynamics and the low-force response of von Willebrand factor

Single-molecule force spectroscopy has provided unprecedented insights into protein folding, force regulation, and function. So far, the field has relied primarily on atomic force microscope and optical tweezers assays that, while powerful, are limited in force resolution, throughput, and require feedback for constant force measurements. Here, we present a modular approach based on magnetic tweezers (MT) for highly multiplexed protein force spectroscopy. Our approach uses elastin-like polypeptide linkers for the specific attachment of proteins, requiring only short peptide tags on the protein of interest. The assay extends protein force spectroscopy into the low force (<1 pN) regime and enables parallel and ultra-stable measurements at constant forces. We present unfolding and refolding data for the small, single-domain protein ddFLN4, commonly used as a molecular fingerprint in force spectroscopy, and for the large, multidomain dimeric protein von Willebrand factor (VWF) that is critically involved in primary hemostasis. For both proteins, our measurements reveal exponential force dependencies of unfolding and refolding rates. We directly resolve the stabilization of the VWF A2 domain by Ca²⁺ and discover transitions in the VWF C domain stem at low forces that likely constitute the first steps of VWF's mechano-activation. Probing the force-dependent lifetime of biotin-streptavidin bonds, we find that monovalent streptavidin constructs with specific attachment geometry are significantly more force stable than commercial, multivalent streptavidin. We expect our modular approach to enable multiplexed force-spectroscopy measurements for a wide range of proteins, in particular in the physiologically relevant low-force regime.

Using Single-Molecule Chemo-Mechanical Unfolding to Simultaneously Probe Multiple Structural Parameters in Protein Folding

While single-molecule force spectroscopy has greatly advanced the study of protein folding, there are limitations to what can be learned from studying the effect of force alone. We developed a novel technique, chemo-mechanical unfolding, that combines multiple perturbants—force and chemical denaturant—to more fully characterize the folding process by simultaneously probing multiple structural parameters—the change in end-to-end distance, and solvent accessible surface area. Here, we describe the theoretical background, experimental design, and data analysis for chemo-mechanical unfolding experiments probing protein folding thermodynamics and kinetics. This technique has been applied to characterize parallel protein folding pathways, the protein denatured state, protein folding on the ribosome, and protein folding intermediates.

Constructing Free Energy Landscapes of Nucleic Acid Hairpin Unfolding

Single nucleic acid molecules form hairpins that may stabilize secondary and tertiary structures as well as perform enzymatic and other chemical functions. Considerable progress has been made in the effort to understand the contributions of various factors to the stability of a given hairpin sequence. For a given sequence, it is possible to compute both the most likely structural arrangements and their associated free energies over a range of experimental conditions. However, there are many observed hairpin irregularities for which the energies and function are not well understood. Here we examine the irregular RNA Transactivation Response (TAR) hairpin from the HIV-1 genome. Using single molecule optical tweezers, the hairpin is force unfolded, revealing the overall unfolding free energy and the character of the transition state. These measurements allow the construction of a simple energy landscape from unfolding measurements, which can be directly compared to a theoretical landscape. This method is easily adapted to other structures, including the effects of noncanonical bases and even ligand binding.

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.

Structural-elastic determination of the force-dependent transition rate of biomolecules

The force-dependent unfolding/refolding of protein domains and ligand-receptor association/dissociation are crucial for mechanosensitive functions, while many aspects of how force affects the transition rate still remain poorly understood. Here, we report a new analytical expression of the force-dependent rate of molecules for transitions overcoming a single barrier. Unlike previous models derived in the framework of Kramers theory that requires a presumed one-dimensional free energy landscape, our model is derived based on the structural-elastic properties of molecules which are not restricted by the shape and dimensionality of the underlying free energy landscape. Importantly, the parameters of this model provide direct information on the structural-elastic features of the molecules between their transition and initial states. We demonstrate the applications of this model by applying it to explain force-dependent transition kinetics for several molecules and predict the structural-elastic properties of the transition states of these molecules.

Conformational dynamics of the frameshift stimulatory structure in HIV-1

Programmed ribosomal frameshifting (PRF) in HIV-1 is thought to be stimulated by a hairpin in the mRNA, although a pseudoknot-like triplex has also been proposed. Because the conformational dynamics of the stimulatory structure under tension applied by the ribosomal helicase during translation may play an important role in PRF, we used optical tweezers to apply tension to the HIV stimulatory structure and monitor its unfolding and refolding dynamics. The folding and unfolding kinetics and energy landscape of the hairpin were measured by ramping the force on the hairpin up and down, providing a detailed biophysical characterization. Unexpectedly, whereas unfolding reflected the simple two-state behavior typical of many hairpins, refolding was more complex, displaying significant heterogeneity. Evidence was found for multiple refolding pathways as well as previously unsuspected, partially folded intermediates. Measuring a variant mRNA containing only the sequence required to form the proposed triplex, it behaved largely in the same way. Nonetheless, very rarely, high-force unfolding events characteristic of pseudoknot-like structures were observed. The rare occurrence of the triplex suggests that the hairpin is the functional stimulatory structure. The unusual heterogeneity of the hairpin dynamics under tension suggests a possible functional role in PRF similar to the dynamics of other stimulatory structures.

Proteins Breaking Bad: A Free Energy Perspective

Protein aging may manifest as a mechanical disease that compromises tissue elasticity. As proved recently, while proteins respond to changes in force with an instantaneous elastic recoil followed by a folding contraction, aged proteins break bad, becoming unstructured polymers. Here, we explain this phenomenon in the context of a free energy model, predicting the changes in the folding landscape of proteins upon oxidative aging. Our findings validate that protein folding under force is constituted by two separable components, polymer properties and hydrophobic collapse, and demonstrate that the latter becomes irreversibly blocked by oxidative damage. We run Brownian dynamics simulations on the landscape of protein L octamer, reproducing all experimental observables, for a naive and damaged polyprotein. This work provides a unique tool to understand the evolving free energy landscape of elastic proteins upon physiological changes, opening new perspectives to predict age-related diseases in tissues.

Chemomechanical regulation of myosin Ic cross-bridges: Deducing the elastic properties of an ensemble from single-molecule mechanisms

Myosin Ic is thought to be the principal constituent of the motor that adjusts mechanical responsiveness during adaptation to prolonged stimuli by hair cells, the sensory receptors of the inner ear. In this context myosin molecules operate neither as filaments, as occurs in muscles, nor as single or few molecules, as characterizes intracellular transport. Instead, myosin Ic molecules occur in a complex cluster in which they may exhibit cooperative properties. To better understand the motor’s remarkable function, we introduce a theoretical description of myosin Ic’s chemomechanical cycle based on experimental data from recent single-molecule studies. The cycle consists of distinct chemical states that the myosin molecule stochastically occupies. We explicitly calculate the probabilities of the occupancy of these states and show their dependence on the external force, the availability of actin, and the nucleotide concentrations as required by thermodynamic constraints. This analysis highlights that the strong binding of myosin Ic to actin is dominated by the ADP state for small external forces and by the ATP state for large forces. Our approach shows how specific parameter values of the chemomechanical cycle for myosin Ic result in behaviors distinct from those of other members of the myosin family. Integrating this single-molecule cycle into a simplified ensemble description, we predict that the average number of bound myosin heads is regulated by the external force and nucleotide concentrations. The elastic properties of such an ensemble are determined by the average number of myosin cross-bridges. Changing the binding probabilities and myosin’s stiffness under a constant force results in a mechanical relaxation which is large enough to account for fast adaptation in hair cells.

Myosin molecules are biological nanomachines that transduce chemical energy into mechanical work and thus produce directed motion in living cells. These molecules proceed through cyclic reactions in which they change their conformational states upon the binding and release of nucleotides while attaching to and detaching from filaments. The myosin family consists of many distinct members with diverse functions such as muscle contraction, cargo transport, cell migration, and sensory adaptation. How these functions emerge from the biophysical properties of the individual molecules is an open question. We present an approach that integrates recent findings from single-molecule experiments into a thermodynamically consistent description of myosin Ic and demonstrate how the specific parameter values of the cycle result in a distinct function. The free variables of our description are the chemical input and external force, both of which are experimentally accessible and define the cellular environment in which these proteins function. We use this description to predict the elastic properties of an ensemble of molecules and discuss the implications for myosin Ic’s function in the inner ear as a tension regulator mediating adaptation, a hallmark of biological sensory systems. In this situation myosin molecules cooperate in an intermediate regime, neither as a large ensemble as in muscle nor as a single or a few molecules as in intracellular transport.