Direct quantification of the attempt frequency determining the mechanical unfolding of ubiquitin protein

Arrhythmogenic cardiomyopathy-related cadherin variants affect desmosomal binding kinetics

Cadherins are calcium dependent adhesion proteins that establish and maintain the intercellular mechanical contact by bridging the gap between adjacent cells. Desmoglein-2 (Dsg2) and desmocollin-2 (Dsc2) are tissue specific cadherin isoforms of the cell-cell contact in cardiac desmosomes. Mutations in the DSG2-gene and in the DSC2-gene are related to arrhythmogenic right ventricular cardiomyopathy (ARVC) a rare but severe heart muscle disease. Here, several possible homophilic and heterophilic binding interactions of wild-type Dsg2, wild-type Dsc2, as well as one Dsg2- and two Dsc2-variants, each associated with ARVC, are investigated. Using single molecule force spectroscopy (SMFS) with atomic force microscopy (AFM) and applying Jarzynski's equality the kinetics and thermodynamics of Dsg2/Dsc2 interaction can be determined. The free energy landscape of Dsg2/Dsc2 dimerization exposes a high activation energy barrier, which is in line with the proposed strand-swapping binding motif. Although the binding motif is not affected by any of the mutations, the binding kinetics of the interactions differ significantly from the wild-type. While wild-type cadherins exhibit an average complex lifetime of approx. 0.3 s interactions involving a variant consistently show - lifetimes that are substantially larger. The lifetimes of the wild-type interactions give rise to the picture of a dynamic adhesion interface consisting of continuously dissociating and (re)associating molecular bonds, while the delayed binding kinetics of interactions involving an ARVC-associated variant might be part of the pathogenesis. Our data provide a comprehensive and consistent thermodynamic and kinetic description of cardiac cadherin binding, allowing detailed insight into the molecular mechanisms of cell adhesion.

A Density Functional Theory (DFT) Perspective on Optical Absorption of Modified Graphene Interacting with the Main Amino Acids of Spider Silk

We investigated the possible adsorption of each of the main building blocks of spider silk: alanine, glycine, leucine, and proline. This knowledge could help develop new biocompatible materials and favors the creation of new biosensors. We used ab initio density functional theory methods to study the variations in the optical absorption, reflectivity, and band structure of a modified graphene surface interacting with these four molecules. Four modification cases were considered: graphene with vacancies at 5.55% and fluorine, nitrogen, or oxygen doping, also at 5.55%. We found that, among the cases considered, graphene with vacancies is the best candidate to develop optical biosensors to detect C=O amide and differentiate glycine and leucine from alanine and proline in the visible spectrum region. Finally, from the projected density of states, the main changes occur at deep energies. Thus, all modified graphene's electronic energy band structure undergoes only tiny changes when interacting with amino acids.

Connecting conformational stiffness of the protein with energy landscape by a single experiment

The structure-function dynamics of a protein as a flexible polymer is essential to describe its biological functions. Here, using single-molecule magnetic tweezers, we have studied the effect of ionic strength on the folding mechanics of protein L, and probed its folding-associated physical properties by re-measuring the same protein in a range of ammonium sulfate concentrations from 150 mM to 650 mM. We observed an electrolyte-dependent conformational dynamics and folding landscape of the protein in a single experiment. Salt increases the refolding kinetics, while decreasing the unfolding kinetics under force, which in turn modifies the barrier heights towards the folded state. Additionally, salt enhances the molecular compaction by decreasing the Kuhn length of the protein polymer from 1.18 nm to 0.58 nm, which we have explained by modifying the freely jointed chain model. Finally, we correlated polymer chain physics to the folding dynamics, and thus provided an analytical framework for understanding compaction-induced folding mechanics across a range of ionic strengths from a single experiment.

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.

Ab Initio Study of the Interaction of a Graphene Surface Decorated with a Metal-Doped C30 with Carbon Monoxide, Carbon Dioxide, Methane, and Ozone

Using DFT simulations, we studied the interaction of a semifullerene C₃₀ and a defected graphene layer. We obtained the C₃₀ chemisorbs on the surface. We also found the adsorbed C₃₀ chemisorbs, Li, Ti, or Pt, on its concave part. Thus, the resulting system (C₃₀-graphene) is a graphene layer decorated with a metal-doped C₃₀. The adsorption of the molecules depends on the shape of the base of the semifullerene and the dopant metal. The CO molecule adsorbed without dissociation in all cases. When the bottom is a pentagon, the adsorption occurs only with Ti as the dopant. It also adsorbs for a hexagon as the bottom with Pt as the dopant. The carbon dioxide molecule adsorbs in the two cases of base shape but only when lithium is the dopant. The adsorption occurs without dissociation. The ozone molecule adsorbs on both surfaces. When Ti or Pt are dopants, we found that the O₃ molecule always dissociates into an oxygen molecule and an oxygen atom. When Li is the dopant, the O₃ molecule adsorbs without dissociation. Methane did not adsorb in any case. Calculating the recovery time at 300 K, we found that the system may be a sensor in several instances.

Direct observation of chaperone-modulated talin mechanics with single-molecule resolution

Talin as a critical focal adhesion mechanosensor exhibits force-dependent folding dynamics and concurrent interactions. Being a cytoplasmic protein, talin also might interact with several cytosolic chaperones; however, the roles of chaperones in talin mechanics remain elusive. To address this question, we investigated the force response of a mechanically stable talin domain with a set of well-known unfoldase (DnaJ, DnaK) and foldase (DnaKJE, DsbA) chaperones, using single-molecule magnetic tweezers. Our findings demonstrate that chaperones could affect adhesion proteins’ stability by changing their folding mechanics; while unfoldases reduce their unfolding force from ~11 pN to ~6 pN, foldase shifts it upto ~15 pN. Since talin is mechanically synced within 2 pN force ranges, these changes are significant in cellular conditions. Furthermore, we determined that chaperones directly reshape the energy landscape of talin: unfoldases decrease the unfolding barrier height from 26.8 to 21.7 k_BT, while foldases increase it to 33.5 k_BT. We reconciled our observations with eukaryotic Hsp70 and Hsp40 and observed their similar function of decreasing the talin unfolding barrier. Quantitative mapping of this chaperone-induced talin folding landscape directly illustrates that chaperones perturb the adhesion protein stability under physiological force, thereby, influencing their force-dependent interactions and adhesion dynamics.

Chakraborty et al. uses single-molecule magnetic tweezers to investigate the chaperone-modulated talin protein mechanics. The results showed that chaperones are involved in the regulation of talin folding/unfolding under mechanical force with some chaperones stabilizing talin and increasing the force, whereas others destabilize it and reduce the force.

Protein nanomechanics in biological context

How proteins respond to pulling forces, or protein nanomechanics, is a key contributor to the form and function of biological systems. Indeed, the conventional view that proteins are able to diffuse in solution does not apply to the many polypeptides that are anchored to rigid supramolecular structures. These tethered proteins typically have important mechanical roles that enable cells to generate, sense, and transduce mechanical forces. To fully comprehend the interplay between mechanical forces and biology, we must understand how protein nanomechanics emerge in living matter. This endeavor is definitely challenging and only recently has it started to appear tractable. Here, I introduce the main in vitro single-molecule biophysics methods that have been instrumental to investigate protein nanomechanics over the last 2 decades. Then, I present the contemporary view on how mechanical force shapes the free energy of tethered proteins, as well as the effect of biological factors such as post-translational modifications and mutations. To illustrate the contribution of protein nanomechanics to biological function, I review current knowledge on the mechanobiology of selected muscle and cell adhesion proteins including titin, talin, and bacterial pilins. Finally, I discuss emerging methods to modulate protein nanomechanics in living matter, for instance by inducing specific mechanical loss-of-function (mLOF). By interrogating biological systems in a causative manner, these new tools can contribute to further place protein nanomechanics in a biological context.

Energy Landscape of Ubiquitin Is Weakly Multidimensional

Single molecule pulling experiments report time-dependent changes in the extension (X) of a biomolecule as a function of the applied force (f). By fitting the data to one-dimensional analytical models of the energy landscape, we can extract the hopping rates between the folded and unfolded states in two-state folders as well as the height and the location of the transition state (TS). Although this approach is remarkably insightful, there are cases for which the energy landscape is multidimensional (catch bonds being the most prominent). To assess if the unfolding energy landscape in small single domain proteins could be one-dimensional, we simulated force-induced unfolding of ubiquitin (Ub) using the coarse-grained self-organized polymer-side chain (SOP-SC) model. Brownian dynamics simulations using the SOP-SC model reveal that the Ub energy landscape is weakly multidimensional (WMD), governed predominantly by a single barrier. The unfolding pathway is confined to a narrow reaction pathway that could be described as diffusion in a quasi-1D X-dependent free energy profile. However, a granular analysis using the P_fold analysis, which does not assume any form for the reaction coordinate, shows that X alone does not account for the height and, more importantly, the location of the TS. The f-dependent TS location moves toward the folded state as f increases, in accord with the Hammond postulate. Our study shows that, in addition to analyzing the f-dependent hopping rates, the transition state ensemble must also be determined without resorting to X as a reaction coordinate to describe the unfolding energy landscapes of single domain proteins, especially if they are only WMD.

Outstanding Performance of Transition-Metal-Decorated Single-Layer Graphene-like BC6N Nanosheets for Disease Biomarker Detection in Human Breath

In the present work, we report highly sensitive and selective nanosensors constructed with metal-decorated graphene-like BC6N employing nonequilibrium Green's function (NEGF) formalism combined by density functional theory (DFT) toward multiple inorganic and sulfur-containing gas molecules (NO, NO2, NH3, CO, CO2, H2S, and SO2) as disease biomarkers from human breath. Monolayer sheets of pristine BC6N and Pd-decorated BC6N were evaluated for their gas adsorption properties, electronic property changes, sensitivity, and selectivity toward disease biomarkers. The pristine BC6N nanosheets exhibited sharp drops in the bandgap when interacted with gases such as NO2 while barely affected by other gases. However, the nanosecond recovery time and low adsorption energies limit the gas sensing applications of the pristine BC6N sheet. On the other hand, the Pd-decorated BC6N-based sensor underwent a semiconductor to metal transition upon the adsorption of NO x gas molecules. The conductance change of the sensor's material in terms of I-V characteristics revealed that the Pd-decorated BC6N sensor is highly sensitive (98.6-134%) and selective (12.3-74.4 times) toward NO x gas molecules with a recovery time of 270 s under UV radiation at 498 K while weakly interacting with interfering gases in exhaled breath such as CO2 and H2O. The gas adsorption behavior suggests that metal-decorated BC6N sensors are excellent candidates for analyzing pulmonary disease and cardiovascular biomarkers, among other ailments of the stomach, kidney, and intestine.

Talin folding as the tuning fork of cellular mechanotransduction

Cells continually sample their mechanical environment using exquisite force sensors such as talin, whose folding status triggers mechanotransduction pathways by recruiting binding partners. Mechanical signals in biology change quickly over time and are often embedded in noise; however, the mechanics of force-sensing proteins have only been tested using simple force protocols, such as constant or ramped forces. Here, using our magnetic tape head tweezers design, we measure the folding dynamics of single talin proteins in response to external mechanical noise and cyclic force perturbations. Our experiments demonstrate that talin filters out external mechanical noise but detects periodic force signals over a finely tuned frequency range. Hence, talin operates as a mechanical band-pass filter, able to read and interpret frequency-dependent mechanical information through its folding dynamics. We describe our observations in the context of stochastic resonance, which we propose as a mechanism by which mechanosensing proteins could respond accurately to force signals in the naturally noisy biological environment.

The nanomechanics of individual proteins

This tutorial review provides an overview of the single protein force spectroscopy field, including the main techniques and the basic tools for analysing the data obtained from the single molecule experiments.

A modular DNA scaffold to study protein-protein interactions at single-molecule resolution

The residence time of a drug on its target has been suggested as a more pertinent metric of therapeutic efficacy than the traditionally used affinity constant. Here, we introduce junctured-DNA tweezers as a generic platform that enables real-time observation, at the single-molecule level, of biomolecular interactions. This tool corresponds to a double-strand DNA scaffold that can be nanomanipulated and on which proteins of interest can be engrafted thanks to widely used genetic tagging strategies. Thus, junctured-DNA tweezers allow a straightforward and robust access to single-molecule force spectroscopy in drug discovery, and more generally in biophysics. Proof-of-principle experiments are provided for the rapamycin-mediated association between FKBP12 and FRB, a system relevant in both medicine and chemical biology. Individual interactions were monitored under a range of applied forces and temperatures, yielding after analysis the characteristic features of the energy profile along the dissociation landscape.

Removal of a Conserved Disulfide Bond Does Not Compromise Mechanical Stability of a VHH Antibody Complex

Single-domain VHH antibodies are promising reagents for medical therapy. A conserved disulfide bond within the VHH framework region is known to be critical for thermal stability, however, no prior studies have investigated its influence on the stability of VHH antibody-antigen complexes under mechanical load. Here, we used single-molecule force spectroscopy to test the influence of a VHH domain's conserved disulfide bond on the mechanical strength of the interaction with its antigen mCherry. We found that although removal of the disulfide bond through cysteine-to-alanine mutagenesis significantly lowered VHH domain denaturation temperature, it had no significant impact on the mechanical strength of the VHH:mCherry interaction with complex rupture occurring at ∼60 pN at 103-104 pN/sec regardless of disulfide bond state. These results demonstrate that mechanostable binding interactions can be built on molecular scaffolds that may be thermodynamically compromised at equilibrium.

Probing Position-Dependent Diffusion in Folding Reactions Using Single-Molecule Force Spectroscopy

Folding of proteins and nucleic acids involves a diffusive search over a multidimensional conformational energy landscape for the minimal-energy structure. When examining the projection of conformational motions onto a one-dimensional reaction coordinate, as done in most experiments, the diffusion coefficient D is generally position dependent. However, it has proven challenging to measure such position-dependence experimentally. We investigated the position-dependence of D in the folding of DNA hairpins as a simple model system in two ways: first, by analyzing the round-trip time to return to a given extension in constant-force extension trajectories measured by force spectroscopy, and second, by analyzing the fall time required to reach a given extension in force jump measurements. These methods yielded conflicting results: the fall time implied a fairly constant D, but the round-trip time implied variations of over an order of magnitude. Comparison of experiments with computational simulations revealed that both methods were strongly affected by experimental artifacts inherent to force spectroscopy measurements, which obscured the intrinsic position-dependence of D. Lastly, we applied Kramers's theory to the kinetics of hairpins with energy barriers located at different positions along the hairpin stem, as a crude probe of D at different stem positions, and we found that D did not vary much as the barrier was moved along the reaction coordinate. This work underlines the difficulties faced when trying to deduce position-dependent diffusion coefficients from experimental folding trajectories.

Structural determinants of coiled coil mechanics

The natural abundance of coiled coil (CC) motifs in the cytoskeleton and the extracellular matrix suggests that CCs play a crucial role in the bidirectional mechanobiochemical signaling between cells and the matrix. Their functional importance and structural simplicity has allowed the development of numerous applications, such as protein-origami structures, drug delivery systems and biomaterials. With the goal of establishing CCs as nanomechanical building blocks, we investigated the importance of helix propensity and hydrophobic core packing on the mechanical stability of 4-heptad CC heterodimers. Using single-molecule force spectroscopy, we show that both parameters determine the force-induced dissociation in shear loading geometry; however, with different effects on the energy landscape. Decreasing the helix propensity lowers the transition barrier height, leading to a concomitant decrease in the distance to the transition state. In contrast, a less tightly packed hydrophobic core increases the distance to the transition state. We propose that this originates from a larger side chain dynamics, possible water intrusion at the interface as well as differences in solvation of the hydrophobic amino acids at the transition state. In conclusion, the different contributions of helix propensity and hydrophobic core packing need to be considered when tuning the mechanical properties of CCs for applications.

Mechanical Softening of a Small Ubiquitin-Related Modifier Protein Due to Temperature Induced Flexibility at the Core

Despite the growing interest in the thermal softening of proteins, the mechanistic details of it are far from understood. β-Grasp proteins have globular shape with compact structure and they are mechanically resilient. The β-clamp or mechanical clamp in them formed by the interactions between the terminal β-strands is generally associated with the protein mechanical resistance. Although previous studies showed that temperature can perturb the protein mechanical stability, the structural changes leading to the lowered mechanical resistance are not known. Here, we investigated the temperature dependent mechanical stability of small ubiquitin-related modifier 2 (SUMO2) using single-molecule force spectroscopy (SMFS) and the corresponding conformational changes using ensemble experiments. SMFS studies on the polyprotein of SUMO2 estimate a decrease in the spring constant of the protein from 4.50 to 1.35 N/m upon increasing the temperature from 5 to 45 °C. Interestingly, near-UV circular dichroism spectroscopy reveals a decrease in tertiary structure content while the overall secondary structure of the protein remains unchanged. Steady-state fluorescence and quenching studies on SUMO2 with a tryptophan mutation at the core (F60W) show that the nonpolar environment of the tryptophan is unchanged and the protein core is inaccessible to the bulk solvent, in the same temperature range. We attribute the thermal softening observed in atomic force microscopy (AFM) experiments to the reduction in tertiary structure of SUMO2. Our results provide evidence for the importance of the intramolecular interactions at the protein core along with the β-clamp or mechanical clamp in providing the mechanical resistance as well as in modulating the protein stiffness.

Segmentation and the Entropic Elasticity of Modular Proteins

Single-molecule force spectroscopy utilizes polyproteins, which are composed of tandem modular domains, to study their mechanical and structural properties. Under the application of external load, the polyproteins respond by unfolding and refolding domains to acquire the most favored extensibility. However, unlike single-domain proteins, the sequential unfolding of the each domain modifies the free energy landscape (FEL) of the polyprotein nonlinearly. Here we use force-clamp (FC) spectroscopy to measure unfolding and collapse-refolding dynamics of polyubiquitin and poly(I91). Their reconstructed unfolding FEL involves hundreds of k_B T in accumulating work performed against conformational entropy, which dwarfs the ∼30 k_B T that is typically required to overcome the free energy difference of unfolding. We speculate that the additional entropic energy caused by segmentation of the polyprotein to individual proteins plays a crucial role in defining the "shock absorber" properties of elastic proteins such as the giant muscle protein titin.

Measuring the Local Velocity along Transition Paths during the Folding of Single Biological Molecules

Transition paths are the most interesting part of folding reactions but remain little studied. We measured the local velocity along transition paths in DNA hairpin folding using optical tweezers. The velocity distribution agreed well with diffusive theories, yielding the diffusion coefficient. We used the average velocity to calculate the transmission factor in transition-state theory (TST), finding observed rates that were ∼10^{5}-fold slower than predicted by TST. This work quantifies the importance of barrier recrossing events and highlights the effectiveness of the diffusive model of folding.

Multidomain proteins under force

Advancements in single-molecule force spectroscopy techniques such as atomic force microscopy and magnetic tweezers allow investigation of how domain folding under force can play a physiological role. Combining these techniques with protein engineering and HaloTag covalent attachment, we investigate similarities and differences between four model proteins: I10 and I91-two immunoglobulin-like domains from the muscle protein titin, and two α + β fold proteins-ubiquitin and protein L. These proteins show a different mechanical response and have unique extensions under force. Remarkably, when normalized to their contour length, the size of the unfolding and refolding steps as a function of force reduces to a single master curve. This curve can be described using standard models of polymer elasticity, explaining the entropic nature of the measured steps. We further validate our measurements with a simple energy landscape model, which combines protein folding with polymer physics and accounts for the complex nature of tandem domains under force. This model can become a useful tool to help in deciphering the complexity of multidomain proteins operating under force.

Single-Molecule Protein Folding Experiments Using High-Precision Optical Tweezers

How proteins fold from linear chains of amino acids to delicate three-dimensional structures remains a fundamental biological problem. Single-molecule manipulation based on high-resolution optical tweezers (OT) provides a powerful approach to study protein folding with unprecedented spatiotemporal resolution. In this method, a single protein or protein complex is tethered between two beads confined in optical traps and pulled. Protein unfolding induced by the mechanical force is counteracted by the spontaneous folding of the protein, reaching a dynamic equilibrium at a characteristic force and rate. The transition is monitored by the accompanying extension change of the protein and used to derive conformations and energies of folding intermediates and their associated transition kinetics. Here, we provide general strategies and detailed protocols to study folding of proteins and protein complexes using optical tweezers, including sample preparation, DNA-protein conjugation and methods of data analysis to extract folding energies and rates from the single-molecule measurements.

Structure-Based Derivation of Protein Folding Intermediates and Energies from Optical Tweezers

Optical tweezers (OTs) measure the force-dependent time-resolved extension of a single macromolecule tethered between two trapped beads. From this measurement, it is possible to determine the folding intermediates, energies, and kinetics of the macromolecule. Previous data analysis generally has used the extension as a reaction coordinate to characterize the observed folding transitions. Despite its convenience, the extension poorly describes folding in the absence of force. Here, we chose the contour length of the unfolded polypeptide as a reaction coordinate and modeled the extensions of protein structures along their predicted folding pathways based on high-resolution structures of the proteins in their native states. We included the extension in our model to calculate the total extensions, energies, and transition rates of the proteins as a function of force. We fit these calculations to the corresponding experimental measurements and obtained the best-fit conformations and energies of proteins in different folding states. We applied our method to analyze single-molecule trajectories of two representative protein complexes responsible for membrane fusion, the HIV-1 glycoprotein 41 and the synaptic SNARE proteins, which involved transitions between two and five states, respectively. Nonlinear fitting of the model to the experimental data revealed the structures of folding intermediates and transition states and their associated energies. Our results demonstrate that the contour length is a useful reaction coordinate to characterize protein folding and that intrinsic extensions of protein structures should be taken into account to properly derive the conformations and energies of protein folding intermediates from single-molecule manipulation experiments.

A HaloTag Anchored Ruler for Week-Long Studies of Protein Dynamics

Under physiological conditions, protein oxidation and misfolding occur with very low probability and on long times scales. Single-molecule techniques provide the ability to distinguish between properly folded and damaged proteins that are otherwise masked in ensemble measurements. However, at physiological conditions these rare events occur with a time constant of several hours, inaccessible to current single-molecule approaches. Here we present a magnetic-tweezers-based technique that allows, for the first time, the study of folding of single proteins during week-long experiments. This technique combines HaloTag anchoring, sub-micrometer positioning of magnets, and an active correction of the focal drift. Using this technique and protein L as a molecular template, we generate a magnet law by correlating the distance between the magnet and the measuring paramagnetic bead with unfolding/folding steps. We demonstrate that, using this magnet law, we can accurately measure the dynamics of proteins over a wide range of forces, with minimal dispersion from bead to bead. We also show that the force calibration remains invariant over week-long experiments applied to the same single proteins. The approach demonstrated in this Article opens new, exciting ways to examine proteins on the "human" time scale and establishes magnetic tweezers as a valuable technique to study low-probability events that occur during protein folding under force.

Combined Constant-Force and Constant-Velocity Single-Molecule Force Spectroscopy of the Conrotatory Ring Opening Reaction of Benzocyclobutene

Single-molecule force spectroscopy (SMFS) of multi-mechanophore polymers has been used to provide kinetic and mechanistic insights into mechanochemical reactions. Whereas biological systems have benefitted from force clamp spectroscopy, synthetic polymers have been studied primarily with constant-velocity methods. Here, force clamp SMFS is applied to the mechanically accelerated conrotatory ring opening of benzocyclobutene, and a comparison with constant-velocity SMFS extends the range of available rate-versus-force data and corroborates the use of constant-velocity SMFS to extract force dependencies.

Determining intrachain diffusion coefficients for biopolymer dynamics from single-molecule force spectroscopy measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.

Transition path sampling with quantum/classical mechanics for reaction rates

Predicting rates of biochemical reactions through molecular simulations poses a particular challenge for two reasons. First, the process involves bond formation and/or cleavage and thus requires a quantum mechanical (QM) treatment of the reaction center, which can be combined with a more efficient molecular mechanical (MM) description for the remainder of the system, resulting in a QM/MM approach. Second, reaction time scales are typically many orders of magnitude larger than the (sub-)nanosecond scale accessible by QM/MM simulations. Transition path sampling (TPS) allows to efficiently sample the space of dynamic trajectories from the reactant to the product state without an additional biasing potential. We outline here the application of TPS and QM/MM to calculate rates for biochemical reactions, by means of a simple toy system. In a step-by-step protocol, we specifically refer to our implementation within the MD suite Gromacs, which we have made available to the research community, and include practical advice on the choice of parameters.

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

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

Deciphering the scaling of single-molecule interactions using Jarzynski's equality

Unravelling the complexity of the macroscopic world relies on understanding the scaling of single-molecule interactions towards integral macroscopic interactions. Here, we demonstrate the scaling of single acid-amine interactions through a synergistic experimental approach combining macroscopic surface forces apparatus experiments and single-molecule force spectroscopy. This experimental framework is ideal for testing the well-renowned Jarzynski's equality, which relates work performed under non-equilibrium conditions with equilibrium free energy. Macroscopic equilibrium measurements scale linearly with the number density of interfacial bonds, providing acid-amine interaction energies of 10.9 ± 0.2 kT. Irrespective of how far from equilibrium single-molecule experiments are performed, the Jarzynski's free energy converges to 11 ± 1 kT. Our results validate the applicability of Jarzynski's equality to unravel the scaling of non-equilibrium single-molecule experiments to scenarios where large numbers of molecules interacts simultaneously in equilibrium. The developed scaling strategy predicts large-scale properties such as adhesion or cell-cell interactions on the basis of single-molecule measurements.

Single molecule evidence for the adaptive binding of DOPA to different wet surfaces

3,4-Dihydroxyphenylalanine (DOPA) is the noncanonical amino acid widely found in mussel holdfast proteins, which is proposed to be responsible for their strong wet adhesion. This feature has also inspired the successful development of a range of DOPA-containing synthetic polymers for wet adhesions and surface coating. Despite the increasing applications of DOPA in material science, the underlying mechanism of DOPA-wet surface interactions remains unclear. In this work, we studied DOPA-surface interactions one bond at a time using atomic force microscope (AFM) based single molecule force spectroscopy. With our recently developed "multiple fishhook" protocol, we were able to perform high-throughput quantification of the binding strength of DOPA to various types of surfaces for the first time. We found that the dissociation forces between DOPA and nine different types of organic and inorganic surfaces are all in the range of 60-90 pN at a pulling speed of 1000 nm s(-1), suggesting the strong and versatile binding capability of DOPA to different types of surfaces. Moreover, by constructing the free energy landscape for the rupture events, we revealed several distinct binding modes between DOPA and different surfaces, which are directly related to the chemistry nature of the surfaces. These results explain the molecular origin of the versatile binding ability of DOPA. Moreover, we could quantitatively predict the relationship between DOPA contents and the binding strength based on the measured rupture kinetics. These serve as the bases for the quantitative prediction of the relationship between DOPA contents and adhesion strength to different wet surfaces, which is important for the design of novel DOPA based materials.

How force unfolding differs from chemical denaturation

Single-molecule force spectroscopies are remarkable tools for studying protein folding and unfolding, but force unfolding explores protein configurations that are potentially very different from the ones traditionally explored in chemical or thermal denaturation. Understanding these differences is crucial because such configurations serve as starting points of folding studies, and thus can affect both the folding mechanism and the kinetics. Here we provide a detailed comparison of both chemically induced and force-induced unfolded state ensembles of ubiquitin based on extensive, all-atom simulations of the protein either extended by force or denatured by urea. As expected, the respective unfolded states are very different on a macromolecular scale, being fully extended under force with no contacts and partially extended in urea with many nonnative contacts. The amount of residual secondary structure also differs: A significant population of α-helices is found in chemically denatured configurations but such helices are absent under force, except at the lowest applied force of 30 pN where short helices form transiently. We see that typical-size helices are unstable above this force, and β-sheets cannot form. More surprisingly, we observe striking differences in the backbone dihedral angle distributions for the protein unfolded under force and the one unfolded by denaturant. A simple model based on the dialanine peptide is shown to not only provide an explanation for these striking differences but also illustrates how the force dependence of the protein dihedral angle distributions give rise to the worm-like chain behavior of the chain upon force.

Nanomechanics of HaloTag tethers

The active site of the Haloalkane Dehydrogenase (HaloTag) enzyme can be covalently attached to a chloroalkane ligand providing a mechanically strong tether, resistant to large pulling forces. Here we demonstrate the covalent tethering of protein L and I27 polyproteins between an atomic force microscopy (AFM) cantilever and a glass surface using HaloTag anchoring at one end and thiol chemistry at the other end. Covalent tethering is unambiguously confirmed by the observation of full length polyprotein unfolding, combined with high detachment forces that range up to ∼2000 pN. We use these covalently anchored polyproteins to study the remarkable mechanical properties of HaloTag proteins. We show that the force that triggers unfolding of the HaloTag protein exhibits a 4-fold increase, from 131 to 491 pN, when the direction of the applied force is changed from the C-terminus to the N-terminus. Force-clamp experiments reveal that unfolding of the HaloTag protein is twice as sensitive to pulling force compared to protein L and refolds at a slower rate. We show how these properties allow for the long-term observation of protein folding-unfolding cycles at high forces, without interference from the HaloTag tether.

Force dependency of biochemical reactions measured by single-molecule force-clamp spectroscopy

Here we describe a protocol for using force-clamp spectroscopy to precisely quantify the effect of force on biochemical reactions. A calibrated force is used to control the exposure of reactive sites in a single polyprotein substrate composed of repeated domains. The use of polyproteins allows the identification of successful single-molecule recordings from unambiguous mechanical unfolding fingerprints. Biochemical reactions are then measured directly by detecting the length changes of the substrate held at a constant force. We present the layout of a force-clamp spectrometer along with protocols to design and conduct experiments. These experiments measure reaction kinetics as a function of applied force. We show sample data of the force dependency of two different reactions, protein unfolding and disulfide reduction. These data, which can be acquired in just a few days, reveal mechanistic details of the reactions that currently cannot be resolved by any other technique.

Mechanical activation of a multimeric adhesive protein through domain conformational change

The mechanical force-induced activation of the adhesive protein von Willebrand factor (VWF), which experiences high hydrodynamic forces, is essential in initiating platelet adhesion. The importance of the mechanical force-induced functional change is manifested in the multimeric VWF's crucial role in blood coagulation, when high fluid shear stress activates plasma VWF (PVWF) multimers to bind platelets. Here, we showed that a pathological level of high shear stress exposure of PVWF multimers results in domain conformational changes, and the subsequent shifts in the unfolding force allow us to use force as a marker to track the dynamic states of the multimeric VWF. We found that shear-activated PVWF multimers are more resistant to mechanical unfolding than nonsheared PVWF multimers, as indicated in the higher peak unfolding force. These results provide insight into the mechanism of shear-induced activation of PVWF multimers.

Energy landscape analysis of native folding of the prion protein yields the diffusion constant, transition path time, and rates

Protein folding is described conceptually in terms of diffusion over a configurational free-energy landscape, typically reduced to a one-dimensional profile along a reaction coordinate. In principle, kinetic properties can be predicted directly from the landscape profile using Kramers theory for diffusive barrier crossing, including the folding rates and the transition time for crossing the barrier. Landscape theory has been widely applied to interpret the time scales for protein conformational dynamics, but protein folding rates and transition times have not been calculated directly from experimentally measured free-energy profiles. We characterized the energy landscape for native folding of the prion protein using force spectroscopy, measuring the change in extension of a single protein molecule at high resolution as it unfolded/refolded under tension. Key parameters describing the landscape profile were first recovered from the distributions of unfolding and refolding forces, allowing the diffusion constant for barrier crossing and the transition path time across the barrier to be calculated. The full landscape profile was then reconstructed from force-extension curves, revealing a double-well potential with an extended, partially unfolded transition state. The barrier height and position were consistent with the previous results. Finally, Kramers theory was used to predict the folding rates from the landscape profile, recovering the values observed experimentally both under tension and at zero force in ensemble experiments. These results demonstrate how advances in single-molecule theory and experiment are harnessing the power of landscape formalisms to describe quantitatively the mechanics of folding.

Rate limit of protein elastic response is tether dependent

The elastic restoring force of tissues must be able to operate over the very wide range of loading rates experienced by living organisms. It is surprising that even the fastest events involving animal muscle tissues do not surpass a few hundred hertz. We propose that this limit is set in part by the elastic dynamics of tethered proteins extending and relaxing under a changing load. Here we study the elastic dynamics of tethered proteins using a fast force spectrometer with sub-millisecond time resolution, combined with Brownian and Molecular Dynamics simulations. We show that the act of tethering a polypeptide to an object, an inseparable part of protein elasticity in vivo and in experimental setups, greatly reduces the attempt frequency with which the protein samples its free energy. Indeed, our data shows that a tethered polypeptide can traverse its free-energy landscape with a surprisingly low effective diffusion coefficient D(eff) ~ 1,200 nm(2)/s. By contrast, our Molecular Dynamics simulations show that diffusion of an isolated protein under force occurs at D(eff) ~ 10(8) nm(2)/s. This discrepancy is attributed to the drag force caused by the tethering object. From the physiological time scales of tissue elasticity, we calculate that tethered elastic proteins equilibrate in vivo with D(eff) ~ 10(4)-10(6) nm(2)/s which is two to four orders magnitude smaller than the values measured for untethered proteins in bulk.