Force-dependent switch in protein unfolding pathways and transition-state movements

A hydrophobic core stabilizes the residual structure in the RRM2 intermediate state of the ALS-linked protein TDP-43

Folding intermediates mediate both protein folding and the misfolding and aggregation observed in human diseases, including amyotrophic lateral sclerosis (ALS), and are prime targets for therapeutic interventions. In this study, we identified the core nucleus of structure for a folding intermediate in the second RNA recognition motif (RRM2) of the ALS-linked RNA-binding protein, TDP-43, using a combination of experimental and computational approaches. Urea equilibrium unfolding studies revealed that the RRM2 intermediate state consists of collapsed residual secondary structure localized to the N-terminal half of RRM2, while the C-terminus is largely disordered. Steered molecular dynamics simulations and mutagenesis studies yielded key stabilizing hydrophobic contacts that, when mutated to alanine, severely disrupt the overall fold of RRM2. In combination, these findings suggest a role for this RRM intermediate in normal TDP-43 function as well as serving as a template for misfolding and aggregation through the low stability and non-native secondary structure.

Molecular mechanisms of catch bonds and their implications for platelet hemostasis

Adhesive molecular bonds between blood cells are essential for thrombosis and hemostasis as they provide means for platelet adhesion, aggregation, and signaling in flowing blood. According to the nowadays conventional definition, a "catch" bond is a type of non-covalent bio-molecular bridge, whose dissociation lifetime counter-intuitively increases with applied tensile force. Following recent experimental findings, such receptor-ligand protein bonds are vital to the blood cells involved in the prevention of bleeding (hemostatic response) and infection (immunity). In this review, we examine the up-to-date experimental discoveries and theoretical insights about catch bonds between the blood cells, their biomechanical principles at the molecular level, and their role in platelet thrombosis and hemostasis.

Catch bonds in sickle cell disease: Shear-enhanced adhesion of red blood cells to laminin

Could the phenomenon of catch bonding-force-strengthened cellular adhesion-play a role in sickle cell disease, where abnormal red blood cell (RBC) adhesion obstructs blood flow? Here, we investigate the dynamics of sickle RBCs adhering to a surface functionalized with the protein laminin (a component of the extracellular matrix around blood vessels) under physiologically relevant microscale flow. First, using total internal reflectance microscopy we characterize the spatial fluctuations of the RBC membrane above the laminin surface before detachment. The complex dynamics we observe suggest the possibility of catch bonding, where the mean detachment time of the cell from the surface initially increases to a maximum and then decreases as a function of shear force. We next conduct a series of shear-induced detachment experiments on blood samples from 25 sickle cell disease patients, quantifying the number and duration of adhered cells under both sudden force jumps and linear force ramps. The experiments reveal that a subset of patients does indeed exhibit catch bonding. By fitting the data to a theoretical model of the bond dynamics, we can extract the mean bond lifetime versus force for each patient. The results show a striking heterogeneity among patients, both in terms of the qualitative behavior (whether or not there is catch bonding) and in the magnitudes of the lifetimes. Patients with large bond lifetimes at physiological forces are more likely to have certain adverse clinical features, like a diagnosis of pulmonary arterial hypertension and intracardiac shunts. By introducing an in vitro platform for fully characterizing RBC-laminin adhesion dynamics, our approach could contribute to the development of patient-specific antiadhesive therapies for sickle cell disease. The experimental setup is also easily generalizable to studying adhesion dynamics in other cell types, for example, leukocytes or cancer cells, and can incorporate disease-relevant environmental conditions like oxygen deprivation.

Using steered molecular dynamic tension for assessing quality of computational protein structure models

The native structures of proteins, except for notable exceptions of intrinsically disordered proteins, in general take their most stable conformation in the physiological condition to maintain their structural framework so that their biological function can be properly carried out. Experimentally, the stability of a protein can be measured by several means, among which the pulling experiment using the atomic force microscope (AFM) stands as a unique method. AFM directly measures the resistance from unfolding, which can be quantified from the observed force-extension profile. It has been shown that key features observed in an AFM pulling experiment can be well reproduced by computational molecular dynamics simulations. Here, we applied computational pulling for estimating the accuracy of computational protein structure models under the hypothesis that the structural stability would positively correlated with the accuracy, i.e. the closeness to the native, of a model. We used in total 4929 structure models for 24 target proteins from the Critical Assessment of Techniques of Structure Prediction (CASP) and investigated if the magnitude of the break force, that is, the force required to rearrange the model's structure, from the force profile was sufficient information for selecting near-native models. We found that near-native models can be successfully selected by examining their break forces suggesting that high break force indeed indicates high stability of models. On the other hand, there were also near-native models that had relatively low peak forces. The mechanisms of the stability exhibited by the break forces were explored and discussed.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Parallel path mechanisms lead to nonmonotonic force-velocity curves and an optimum load for molecular motor function

Molecular motors convert chemical potential energy into mechanical work and perform a great number of critical biological functions. Examples include the polymerization and manipulation of nucleic acids, the generation of cellular motility and contractility, the formation and maintenance of cell shape, and the transport of materials within cells. The mechanisms underlying these molecular machines are varied, but are almost always considered in the context of a single kinetic pathway that describes motor stepping. However, the multidimensional nature of protein energy landscapes suggests the possibility of multiple reaction pathways connecting two states. Here we investigate the properties of a hypothetical molecular motor able to utilize parallel translocation mechanisms. We explore motor velocity and force dependence as a function of the energy landscape of each path and reveal the potential for such a mechanism to result in negative differential conductance. More specifically, regimes exist where increasing opposing force leads to increased velocity and an optimum load for motor function. We explore how the presence of this optimum depends on the rates of the individual paths and show that the distribution of stepping times characterized by the randomness parameter may be used to test for parallel path mechanisms. Last, we caution that experimental data consisting solely of measurements of velocity as a function of ATP concentration and force cannot be used to eliminate the possibility of such a parallel path mechanism.

On distributions of barrier crossing times as observed in single-molecule studies of biomolecules

Single-molecule experiments that monitor time evolution of molecular observables in real time have expanded beyond measuring transition rates toward measuring distributions of times of various molecular events. Of particular interest is the first-passage time for making a transition from one molecular configuration ( a ) to another ( b ) and conditional first-passage times such as the transition path time, which is the first-passage time from a to b conditional upon not leaving the transition region intervening between a and b . Another experimentally accessible (but not yet studied experimentally) observable is the conditional exit time, i.e., the time to leave the transition region through a specified boundary. The distributions of such times contain a wealth of mechanistic information about the transitions in question. Here, we use the first and the second (and, if desired, higher) moments of these distributions to characterize their relative width for the model in which the experimental observable undergoes Brownian motion in a potential of mean force. We show that although the distributions of transition path times are always narrower than exponential (in that the ratio of the standard deviation to the distribution's mean is always less than 1), distributions of first-passage times and of conditional exit times can be either narrow or broad, in some cases displaying long power-law tails. The conditional exit time studied here provides a generalization of the transition path time that also allows one to characterize the temporal scales of failed barrier crossing attempts.

Protein Folding Dynamics as Diffusion on a Free Energy Surface: Rate Equation Terms, Transition Paths, and Analysis of Single-Molecule Photon Trajectories

The rates of protein (un)folding are often described as diffusion on the projection of a hyperdimensional energy landscape onto a few (ideally one) order parameters. Testing such an approximation by experiment requires resolving the reactive transition paths of individual molecules, which is now becoming feasible with advanced single-molecule spectroscopic techniques. This has also sparked the interest of theorists in better understanding reactive transition paths. Here we focus on these issues aiming to establish (i) practical guidelines for the mechanistic interpretation of transition path times (TPT) and (ii) methods to extract the free energy surface and protein dynamics from the maximum likelihood analysis of photon trajectories (MLA-PT). We represent the (un)folding rates as diffusion on a 1D free energy surface with the FRET efficiency as a reaction coordinate proxy. We then perform diffusive kinetic simulations on surfaces with two minima and a barrier, but with different shapes (curvatures, barrier height, and symmetry), coupled to stochastic simulations of photon emissions that reproduce current SM-FRET experiments. From the analysis of transition paths, we find that the TPT is inversely proportional to the barrier height (difference in free energy between minimum and barrier top) for any given surface shape, and that dividing the TPT into climb and descent segments provides key information about the barrier's symmetry. We also find that the original MLA-PT procedure used to determine the TPT from experiments underestimates its value, particularly for the cases with smaller barriers (e.g., fast folders), and we suggest a simple strategy to correct for this bias. Importantly, we also demonstrate that photon trajectories contain enough information to extract the 1D free energy surface's shape and dynamics (if TPT is >4-5-fold longer than the interphoton time) using the MLA-PT directly implemented with a diffusive free energy surface model. When dealing with real (unknown) experimental data, the comparison between the likelihoods of the free energy surface and discrete kinetic three-state models can be used to evaluate the statistical significance of the estimated free energy surface.

First-passage times in protein folding: exploring the native-like states vs. overcoming the free energy barrier

Using a model β-hairpin protein as a representative example of simple two-state folders whose kinetics are uncomplicated by the presence of on- and off-pathway intermediates, it is studied how the search for the protein's native state among native-like states affects the folding kinetics. It is revealed that the first-passage time (FPT) distributions are essentially single-exponential not only for the times to overcome the free energy barrier between the unfolded and native-like states but also for the times to find the native state among the native-like ones. The FPT distributions of this type are observed through all studied two-state-like regimes of protein folding, varying from a regime close to two-state folding to a regime close to downhill folding. If the protein explores native-like states for a time much longer than the time to overcome the free energy barrier, which is characteristic of high temperatures, the resulting FPT distribution to reach the native state remains close to exponential but the mean FPT (MFPT) is determined not by the height of the free energy barrier but by the time to explore native-like states. In particular, the mean time to overcome the free energy barrier is in reasonable agreement with the Kramers rate formula and generally far shorter than the overall MFPT to reach the native state. The observed increase of the overall MFPT, as a result of longer exploration of native-like states, may lead to an overestimate of the height of the free energy barrier between the unfolded and folded states when it is calculated from the overall MFPT.

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.

The Measurement of Information and Free Energy in Mechanical-Force-Driven Coil-Globule Transitions

We study the role of information (the relative entropy) for polymers undergoing coil-globule transitions driven by a time-dependent force. Pulling experiments at various speeds are performed by Brownian dynamics simulations. We obtain the work distributions for the forward and time-reversed backward processes and information stored at the end of the nonequilibrium pulling processes. We present the systematic method to measure the information from the pulling experiments and extract the information by analyzing slowly relaxing modes. When the information is incorporated, the work distributions modified by the information allow access to the proper free energy via the formulation of the generalized fluctuation theorems even if the initial states of the forward and time-reversed backward processes are out of equilibrium. This demonstrates that the work-information conversion works well for a single-molecule system with many degrees of freedom.

Reconstruction of mechanical unfolding and refolding pathways of proteins with atomic force spectroscopy and computer simulations

Most proteins in proteomes are large, typically consist of more than one domain and are structurally complex. This often makes studying their mechanical unfolding pathways challenging. Proteins composed of tandem repeat domains are a subgroup of multi-domain proteins that, when stretched, display a saw-tooth pattern in their mechanical unfolding force extension profiles due to their repetitive structure. However, the assignment of force peaks to specific repeats undergoing mechanical unraveling is complicated because all repeats are similar and they interact with their neighbors and form a contiguous tertiary structure. Here, we describe in detail a combination of experimental and computational single-molecule force spectroscopy methods that proved useful for examining the mechanical unfolding and refolding pathways of ankyrin repeat proteins. Specifically, we explain and delineate the use of atomic force microscope-based single molecule force spectroscopy (SMFS) to record the mechanical unfolding behavior of ankyrin repeat proteins and capture their unusually strong refolding propensity that is responsible for generating impressive refolding force peaks. We also describe Coarse Grain Steered Molecular Dynamic (CG-SMD) simulations which complement the experimental observations and provide insights in understanding the unfolding and refolding of these proteins. In addition, we advocate the use of novel coiled-coils-based mechanical polypeptide probes which we developed to demonstrate the vectorial character of folding and refolding of these repeat proteins. The combination of AFM-based SMFS on native and CC-equipped proteins with CG-SMD simulations is powerful not only for ankyrin repeat polypeptides, but also for other repeat proteins and more generally to various multidomain, non-repetitive proteins with complex topologies.

Conserved patterns and interactions in the unfolding transition state across SH3 domain structural homologues

Proteins with similar structures are generally assumed to arise from similar sequences. However, there are more cases than not where this is not true. The dogma is that sequence determines structure; how, then, can very different sequences fold to the same structure? Here, we employ high temperature unfolding simulations to probe the pathways and specific interactions that direct the folding and unfolding of the SH3 domain. The SH3 metafold in the Dynameomics Database consists of 753 proteins with the same structure, but varied sequences and functions. To investigate the relationship between sequence and structure, we selected 17 targets from the SH3 metafold with high sequence variability. Six unfolding simulations were performed for each target, transition states were identified, revealing two general folding/unfolding pathways at the transition state. Transition states were also expressed as mathematical graphs of connected chemical nodes, and it was found that three positions within the structure, independent of sequence, were consistently more connected within the graph than any other nearby positions in the sequence. These positions represent a hub connecting different portions of the structure. Multiple sequence alignment and covariation analyses also revealed certain positions that were more conserved due to packing constraints and stabilizing long-range contacts. This study demonstrates that members of the SH3 domain with different sequences can unfold through two main pathways, but certain characteristics are conserved regardless of the sequence or unfolding pathway. While sequence determines structure, we show that disparate sequences can provide similar interactions that influence folding and lead to similar structures.

The generic unfolding of a biomimetic polymer during force spectroscopy

With the help of force spectroscopy, several analytical theories aim at estimating the rate coefficient of folding for various proteins. Nevertheless, a chief bottleneck lies in the fact that there is still no perfect consensus on how does a force generally perturb the crystal-coil transition. Consequently, the goal of our work is in clarifying the generic behavior of most proteins in force spectroscopy; in other words, what general signature does an arbitrary protein exhibit for its rate coefficient as a function of the applied force? By employing a biomimetic polymer in molecular simulations, we focus on evaluating its respective activation energy for unfolding, while pulling on various pairs of its monomers. Above all, we find that in the vicinity of the force-free scenario, this activation energy possesses a negative slope and a negative curvature as a function of the applied force. Our work is in line with the most recent theories for unfolding, which suggest that such a signature is expected for most proteins, and thus, we further reiterate that many of the classical formulae, that estimate the rate coefficient of the crystal-coil transition, are inadequate. Besides, we also present here an analytical expression which experimentalists can use for approximating the activation energy for unfolding; importantly, it is based on measurements for the mean and variance of the distance between the beads which are being pulled. In summary, our work presents an interesting view for protein folding in force spectroscopy.

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.

Diverse Folding Pathways of HIV-1 Protease Monomer on a Rugged Energy Landscape

The modern energy landscape theory of protein folding predicts multiple folding pathways connecting a myriad of unfolded conformations and a well-defined folded state. However, direct experimental observation of heterogeneous folding pathways is difficult. Naturally evolved proteins typically exhibit a smooth folding energy landscape for fast and efficient folding by avoiding unfavorable kinetic traps. In this case, rapid fluctuations between unfolded conformations result in apparent two-state behavior and make different pathways indistinguishable. However, the landscape roughness can be different, depending on the selection pressures during evolution. Here, we characterize the unusually rugged folding energy landscape of human immunodeficiency virus-1 protease monomer using single-molecule Förster resonance energy transfer spectroscopy. Our data show that fluctuations between unfolded conformations are slow, which enables the experimental observation of heterogeneous folding pathways as predicted by the landscape theory. Although the landscape ruggedness is sensitive to the mutations and fluorophore locations, the folding rate is similar for various protease constructs. The natural evolution of the protease to have a rugged energy landscape likely results from intrinsic pressures to maintain robust folding when human immunodeficiency virus-1 mutates frequently, which is essential for its survival.

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.

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.

Mechanical unfolding of spectrin reveals a super-exponential dependence of unfolding rate on force

We investigated the mechanical unfolding of single spectrin molecules over a broad range of loading rates and thus unfolding forces by combining magnetic tweezers with atomic force microscopy. We find that the mean unfolding force increases logarithmically with loading rate at low loading rates, but the increase slows at loading rates above 1pN/s. This behavior indicates an unfolding rate that increases exponentially with the applied force at low forces, as expected on the basis of one-dimensional models of protein unfolding. At higher forces, however, the increase of the unfolding rate with the force becomes faster than exponential, which may indicate anti-Hammond behavior where the structures of the folded and transition states become more different as their free energies become more similar. Such behavior is rarely observed and can be explained by either a change in the unfolding pathway or as a reflection of a multidimensional energy landscape of proteins under force.

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.

Forced-rupture of cell-adhesion complexes reveals abrupt switch between two brittle states

Cell adhesion complexes (CACs), which are activated by ligand binding, play key roles in many cellular functions ranging from cell cycle regulation to mediation of cell extracellular matrix adhesion. Inspired by single molecule pulling experiments using atomic force spectroscopy on leukocyte function-associated antigen-1 (LFA-1), expressed in T-cells, bound to intercellular adhesion molecules (ICAM), we performed constant loading rate (r_f) and constant force (F) simulations using the self-organized polymer model to describe the mechanism of ligand rupture from CACs. The simulations reproduce the major experimental finding on the kinetics of the rupture process, namely, the dependence of the most probable rupture forces (f*s) on ln r_f (r_f is the loading rate) exhibits two distinct linear regimes. The first, at low r_f, has a shallow slope, whereas the slope at high r_f is much larger, especially for a LFA-1/ICAM-1 complex with the transition between the two occurring over a narrow r_f range. Locations of the two transition states (TSs) extracted from the simulations show an abrupt change from a high value at low r_f or constant force, F, to a low value at high r_f or F. This unusual behavior in which the CACs switch from one brittle (TS position is a constant over a range of forces) state to another brittle state is not found in forced-rupture in other protein complexes. We explain this novel behavior by constructing the free energy profiles, F(Λ)s, as a function of a collective reaction coordinate (Λ), involving many key charged residues and a critical metal ion (Mg²⁺). The TS positions in F(Λ), which quantitatively agree with the parameters extracted using the Bell-Evans model, change abruptly at a critical force, demonstrating that it, rather than the molecular extension, is a good reaction coordinate. Our combined analyses using simulations performed in both the pulling modes (constant r_f and F) reveal a new mechanism for the two loading regimes observed in the rupture kinetics in CACs.

A small single-domain protein folds through the same pathway on and off the ribosome

In vivo, proteins fold and function in a complex environment subject to many stresses that can modulate a protein's energy landscape. One aspect of the environment pertinent to protein folding is the ribosome, since proteins have the opportunity to fold while still bound to the ribosome during translation. We use a combination of force and chemical denaturant (chemomechanical unfolding), as well as point mutations, to characterize the folding mechanism of the src SH3 domain both as a stalled ribosome nascent chain and free in solution. Our results indicate that src SH3 folds through the same pathway on and off the ribosome. Molecular simulations also indicate that the ribosome does not affect the folding pathway for this small protein. Taken together, we conclude that the ribosome does not alter the folding mechanism of this small protein. These results, if general, suggest the ribosome may exert a bigger influence on the folding of multidomain proteins or protein domains that can partially fold before the entire domain sequence is outside the ribosome exit tunnel.

Unraveling the mechanism of the cadherin-catenin-actin catch bond

The adherens junctions between epithelial cells involve a protein complex formed by E-cadherin, β-catenin, α-catenin and F-actin. The stability of this complex was a puzzle for many years, since in vitro studies could reconstitute various stable subsets of the individual proteins, but never the entirety. The missing ingredient turned out to be mechanical tension: a recent experiment that applied physiological forces to the complex with an optical tweezer dramatically increased its lifetime, a phenomenon known as catch bonding. However, in the absence of a crystal structure for the full complex, the microscopic details of the catch bond mechanism remain mysterious. Building on structural clues that point to α-catenin as the force transducer, we present a quantitative theoretical model for how the catch bond arises, fully accounting for the experimental lifetime distributions. The underlying hypothesis is that force induces a rotational transition between two conformations of α-catenin, overcoming a significant energy barrier due to a network of salt bridges. This transition allosterically regulates the energies at the interface between α-catenin and F-actin. The model allows us to predict these energetic changes, as well as highlighting the importance of the salt bridge rotational barrier. By stabilizing one of the α-catenin states, this barrier could play a role in how the complex responds to additional in vivo binding partners like vinculin. Since significant conformational energy barriers are a common feature of other adhesion systems that exhibit catch bonds, our model can be adapted into a general theoretical framework for integrating structure and function in a variety of force-regulated protein complexes.

Dynamic coarse-graining fills the gap between atomistic simulations and experimental investigations of mechanical unfolding

We present a dynamic coarse-graining technique that allows one to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSMs), which we construct from molecular dynamics simulations using the pulling coordinate as an order parameter. We obtain a sequence of MSMs as a function of the discretized pulling coordinate, and the pulling process is modeled by switching among the MSMs according to the protocol applied to unfold the complex. This way we cover seven orders of magnitude in pulling speed. In the region of rapid pulling, we additionally perform steered molecular dynamics simulations and find excellent agreement between the results of the fully atomistic and the dynamically coarse-grained simulations. Our technique allows the determination of the rates of mechanical unfolding in a dynamical range from approximately 10^-8/ns to 1/ns thus reaching experimentally accessible time regimes without abandoning atomistic resolution.

How Do We Know when Single-Molecule Force Spectroscopy Really Tests Single Bonds?

Single-molecule force spectroscopy makes it possible to measure the mechanical strength of single noncovalent receptor-ligand-type bonds. A major challenge in this technique is to ensure that measurements reflect bonds between single biomolecules because the molecules cannot be directly observed. This perspective evaluates different methodologies for identifying and reducing the contribution of multiple molecule interactions to single-molecule measurements to help the reader design experiments or assess publications in the single-molecule force spectroscopy field. We apply our analysis to the large body of literature that purports to measure the strength of single bonds between biotin and streptavidin as a demonstration that measurements are only reproducible when the most reliable methods for ensuring single molecules are used.

Impact of hydrodynamic interactions on protein folding rates depends on temperature

We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collective motion with a single reaction coordinate across a folding barrier, we compared the kinetic effects of HI on the folding rates of two protein models that use a chain of single beads with distinctive topologies: a 64-residue α/β chymotrypsin inhibitor 2 (CI2) protein, and a 57-residue β-barrel α-spectrin Src-homology 3 domain (SH3) protein. When comparing the protein folding kinetics simulated with Brownian dynamics in the presence of HI to that in the absence of HI, we find that the effect of HI on protein folding appears to have a "crossover" behavior about the folding temperature. This means that at a temperature greater than the folding temperature, the enhanced friction from the hydrodynamic solvents between the beads in an unfolded configuration results in lowered folding rate; conversely, at a temperature lower than the folding temperature, HI accelerates folding by the backflow of solvent toward the folded configuration of a protein. Additionally, the extent of acceleration depends on the topology of a protein: for a protein like CI2, where its folding nucleus is rather diffuse in a transition state, HI channels the formation of contacts by favoring a major folding pathway in a complex free energy landscape, thus accelerating folding. For a protein like SH3, where its folding nucleus is already specific and less diffuse, HI matters less at a temperature lower than the folding temperature. Our findings provide further theoretical insight to protein folding kinetic experiments and simulations.

Denaturants Alter the Flux through Multiple Pathways in the Folding of PDZ Domain

Although we understand many aspects of how small proteins (number of residues less than about hundred) fold, it is a major challenge to quantitatively describe how large proteins self-assemble. To partially overcome this challenge, we performed simulations using the self-organized polymer model with side chains (SOP-SC) in guanidinium chloride (GdmCl), using the molecular transfer model (MTM), to describe the folding of the 110-residue PDZ3 domain. The simulations reproduce the folding thermodynamics accurately including the melting temperature (T_m), the stability of the folded state with respect to the unfolded state. We show that the calculated dependence of ln k_obs (k_obs is the relaxation rate) has the characteristic chevron shape. The slopes of the chevron plots are in good agreement with experiments. We show that PDZ3 folds by four major pathways populating two metastable intermediates, in accord with the kinetic partitioning mechanism. The structure of one of the intermediates, populated after polypeptide chain collapse, is structurally similar to an equilibrium intermediate. Surprisingly, the connectivities between the intermediates and hence, the fluxes through the pathways depend on the concentration of GdmCl. The results are used to predict possible outcomes for unfolding of PDZ domain subject to mechanical forces. Our study demonstrates that, irrespective of the size or topology, simulations based on MTM and SOP-SC offer a theoretical framework for describing the folding of proteins, mimicking precisely the conditions used in experiments.

The mechano-sensing role of the unique SH3 insertion in plakin domains revealed by Molecular Dynamics simulations

The plakin family of proteins, important actors in cross-linking force-bearing structures in the cell, contain a curious SH3 domain insertion in their chain of spectrin repeats (SRs). While SH3 domains are known to mediate protein-protein interactions, here, its canonical binding site is autoinhibited by the preceding SR. Under force, however, this SH3 domain could be released, and possibly launch a signaling cascade. We performed large-scale force-probe molecular dynamics simulations, across two orders of magnitude of loading rates, to test this hypothesis, on two prominent members of the plakin family: desmoplakin and plectin, obligate proteins at desmosomes and hemidesmosomes, respectively. Our simulations show that force unravels the SRs and abolishes the autoinhibition of the SH3 domain, an event well separated from the unfolding of this domain. The SH3 domain is free and fully functional for a significant portion of the unfolding trajectories. The rupture forces required for the two proteins significantly decrease when the SH3 domain is removed, which implies that the SH3 domain also stabilizes this junction. Our results persist across all simulations, and support a force-sensing as well as a stabilizing role of the unique SH3 insertion, putting forward this protein family as a new class of mechano-sensors.

Simulated Force Quench Dynamics Shows GB1 Protein Is Not a Two State Folder

Single molecule force spectroscopy is a useful technique for investigating mechanically induced protein unfolding and refolding under reduced forces by monitoring the end-to-end distance of the protein. The data is often interpreted via a "two-state" model based on the assumption that the end-to-end distance alone is a good reaction coordinate and the thermodynamic behavior is then ascribed to the free energy as a function of this one reaction coordinate. In this paper, we determined the free energy surface (PMF) of GB1 protein from atomistic simulations in explicit solvent under different applied forces as a function of two collective variables (the end-to-end-distance, and the fraction of native contacts ρ). The calculated 2-d free energy surfaces exhibited several distinct states, or basins, mostly visible along the ρ coordinate. Brownian dynamics (BD) simulations on the smoothed free energy surface show that the protein visits a metastable molten globule state and is thus a three state folder, not the two state folder inferred using the end-to-end distance as the sole reaction coordinate. This study lends support to recent experiments that suggest that GB1 is not a two-state folder.

Transition Path Times Measured by Single-Molecule Spectroscopy

The transition path is a tiny fraction of a molecular trajectory during which the free-energy barrier is crossed. It is a single-molecule property and contains all mechanistic information of folding processes of biomolecules such as proteins and nucleic acids. However, the transition path has been difficult to probe because it is short and rarely visited when transitions actually occur. Recent technical advances in single-molecule spectroscopy have made it possible to directly probe transition paths, which has opened up new theoretical and experimental approaches to investigating folding mechanisms. This article reviews recent single-molecule fluorescence and force spectroscopic measurements of transition path times and their connection to both theory and simulations.

The ribosome destabilizes native and non-native structures in a nascent multidomain protein

Correct folding is a prerequisite for the biological activity of most proteins. Folding has largely been studied using in vitro refolding assays with isolated small, robustly folding proteins. A substantial fraction of all cellular proteomes is composed of multidomain proteins that are often not amenable to this approach, and their folding remains poorly understood. These large proteins likely begin to fold during their synthesis by the ribosome, a large molecular machine that translates the genetic code. The ribosome affects how folding proceeds, but the underlying mechanisms remain largely obscure. We have utilized optical tweezers to study the folding of elongation factor G, a multidomain protein composed of five domains. We find that interactions among unfolded domains interfere with productive folding in the full-length protein. The N-terminal G-domain constitutes an independently folding unit that, upon in vitro refolding, adopts two similar states that correspond to the natively folded and a non-native, possibly misfolded structure. The ribosome destabilizes both of these states, suggesting a mechanism by which terminal misfolding into highly stable, non-native structures is avoided. The ribosome may thus directly contribute to efficient folding by modulating the folding of nascent multidomain proteins.

Analysis of the Acting Forces in a Theory of Catalysis and Mechanochemistry

The theoretical description of a chemical process resulting from the application of mechanical or catalytical stress to a molecule is performed by the generation of an effective potential energy surface (PES). Changes for minima and saddle points by the stress are described by Newton trajectories (NTs) on the original PES. From the analysis of the acting forces we postulate the existence of pulling corridors built by families of NTs that connect the same stationary points. For different exit saddles of different height we discuss the corresponding pulling corridors; mainly by simple two-dimensional surface models. If there are different exit saddles then there can exist saddles of index two, at least, between. Then the case that a full pulling corridor crosses a saddle of index two is the normal case. It leads to an intrinsic hysteresis of such pullings for the forward or the backward reaction. Assuming such relations we can explain some results in the literature. A new finding is the existence of roundabout corridors that can switch between different saddle points by a reversion of the direction. The findings concern the mechanochemistry of molecular systems under a mechanical load as well as the electrostatic force and can be extended to catalytic and enzymatic accelerated reactions. The basic and ground ansatz includes both kinds of forces in a natural way without an extra modification.

Force-Dependent Folding and Unfolding Kinetics in DNA Hairpins Reveals Transition-State Displacements along a Single Pathway

Biomolecules diffusively explore their energy landscape overcoming energy barriers via thermally activated processes to reach the biologically relevant conformation. Mechanically induced unfolding and folding reactions offer an excellent playground to feature these processes at the single-molecule level by monitoring changes in the molecular extension. Here we investigate two-state DNA hairpins designed to have the transition states at different locations. We use optical tweezers to characterize the force-dependent behavior of the kinetic barrier from nonequilibrium pulling experiments by using the continuous effective barrier approach (CEBA). We introduce the mechanical fragility and the molecular transition-state susceptibility, both useful quantities to characterize the response of the transition state to an applied force. Our results demonstrate the validity of the Leffler-Hammond postulate where the transition state approaches the folded state as force increases, implying monotonically decreasing fragility with force and a non-negative transition state susceptibility at all forces.

Phenomenological and microscopic theories for catch bonds

Lifetimes of bound states of protein complexes or biomolecule folded states typically decrease when subject to mechanical force. However, a plethora of biological systems exhibit the counter-intuitive phenomenon of catch bonding, where non-covalent bonds become stronger under externally applied forces. The quest to understand the origin of catch-bond behavior has led to the development of phenomenological and microscopic theories that can quantitatively recapitulate experimental data. Here, we assess the successes and limitations of such theories in explaining experimental data. The most widely applied approach is a phenomenological two-state model, which fits all of the available data on a variety of complexes: actomyosin, kinetochore-microtubule, selectin-ligand, and cadherin-catenin binding to filamentous actin. With a primary focus on the selectin family of cell-adhesion complexes, we discuss the positives and negatives of phenomenological models and the importance of evaluating the physical relevance of fitting parameters. We describe a microscopic theory for selectins, which provides a structural basis for catch bonds and predicts a crucial allosteric role for residues Asn82-Glu88. We emphasize the need for new theories and simulations that can mimic experimental conditions, given the complex response of cell adhesion complexes to force and their potential role in a variety of biological contexts.

The Power of Force: Insights into the Protein Folding Process Using Single-Molecule Force Spectroscopy

One of the major challenges in modern biophysics is observing and understanding conformational changes during complex molecular processes, from the fundamental protein folding to the function of molecular machines. Single-molecule techniques have been one of the major driving forces of the huge progress attained in the last few years. Recent advances in resolution of the experimental setups, aided by theoretical developments and molecular dynamics simulations, have revealed a much higher degree of complexity inside these molecular processes than previously reported using traditional ensemble measurements. This review sums up the evolution of these developments and gives an outlook on prospective discoveries.

Cytochrome c folds through foldon-dependent native-like intermediates in an ordered pathway

Previous hydrogen exchange (HX) studies of the spontaneous reversible unfolding of Cytochrome c (Cyt c) under native conditions have led to the following conclusions. Native Cyt c (104 residues) is composed of five cooperative folding units, called foldons. The high-energy landscape is dominated by an energy ladder of partially folded forms that differ from each other by one cooperative foldon unit. The reversible equilibrium unfolding of native Cyt c steps up through these intermediate forms to the unfolded state in an energy-ordered sequence, one foldon unit at a time. To more directly study Cyt c intermediates and pathways during normal energetically downhill kinetic folding, the present work used HX pulse labeling analyzed by a fragment separation-mass spectrometry method. The results show that 95% or more of the Cyt c population folds by stepping down through the same set of foldon-dependent pathway intermediates as in energetically uphill equilibrium unfolding. These results add to growing evidence that proteins fold through a classical pathway sequence of native-like intermediates rather than through a vast number of undefinable intermediates and pathways. The present results also emphasize the condition-dependent nature of kinetic barriers, which, with less informative experimental methods (fluorescence, etc.), are often confused with variability in intermediates and pathways.