Reference-free alignment and sorting of single-molecule force spectroscopy data

Single-molecule force spectroscopy has become a versatile tool for investigating the (un)folding of proteins and other polymeric molecules. Like other single-molecule techniques, single-molecule force spectroscopy requires recording and analysis of large data sets to extract statistically meaningful conclusions. Here, we present a data analysis tool that provides efficient filtering of heterogeneous data sets, brings spectra into register based on a reference-free alignment algorithm, and determines automatically the location of unfolding barriers. Furthermore, it groups spectra according to the number of unfolding events, subclassifies the spectra using cross correlation-based sorting, and extracts unfolding pathways by principal component analysis and clustering methods to extracted peak positions. Our approach has been tested on a data set obtained through mechanical unfolding of bacteriorhodopsin (bR), which contained a significant number of spectra that did not show the well-known bR fingerprint. In addition, we have tested the performance of the data analysis tool on unfolding data of the soluble multidomain (Ig27)(8) protein.     

Direct observation of markovian behavior of the mechanical unfolding of individual proteins

Single-molecule force-clamp spectroscopy is a valuable tool to analyze unfolding kinetics of proteins. Previous force-clamp spectroscopy experiments have demonstrated that the mechanical unfolding of ubiquitin deviates from the generally assumed Markovian behavior and involves the features of glassy dynamics. Here we use single molecule force-clamp spectroscopy to study the unfolding kinetics of a computationally designed fast-folding mutant of the small protein GB1, which shares a similar β-grasp fold as ubiquitin. By treating the mechanical unfolding of polyproteins as the superposition of multiple identical Poisson processes, we developed a simple stochastic analysis approach to analyze the dwell time distribution of individual unfolding events in polyprotein unfolding trajectories. Our results unambiguously demonstrate that the mechanical unfolding of NuG2 fulfills all criteria of a memoryless Markovian process. This result, in contrast with the complex mechanical unfolding behaviors observed for ubiquitin, serves as a direct experimental demonstration of the Markovian behavior for the mechanical unfolding of a protein and reveals the complexity of the unfolding dynamics among structurally similar proteins. Furthermore, we extended our method into a robust and efficient pseudo-dwell-time analysis method, which allows one to make full use of all the unfolding events obtained in force-clamp experiments without categorizing the unfolding events. This method enabled us to measure the key parameters characterizing the mechanical unfolding energy landscape of NuG2 with improved precision. We anticipate that the methods demonstrated here will find broad applications in single-molecule force-clamp spectroscopy studies for a wide range of proteins.     

Molecular force modulation spectroscopy revealing the dynamic response of single bacteriorhodopsins

Recent advances in atomic force microscopy allowed globular and membrane proteins to be mechanically unfolded on a single-molecule level. Presented is an extension to the existing force spectroscopy experiments. While unfolding single bacteriorhodopsins from native purple membranes, small oscillation amplitudes (6-9 nm) were supplied to the vertical displacement of the cantilever at a frequency of 3 kHz. The phase and amplitude response of the cantilever-protein system was converted to reveal the elastic (conservative) and viscous (dissipative) contributions to the unfolding process. The elastic response (stiffness) of the extended parts of the protein were in the range of a few tens pN/nm and could be well described by the derivative of the wormlike chain model. Discrete events in the viscous response coincided with the unfolding of single secondary structure elements and were in the range of 1 microNs/m. In addition, these force modulation spectroscopy experiments revealed novel mechanical unfolding intermediates of bacteriorhodopsin. We found that kinks result in a loss of unfolding cooperativity in transmembrane helices. Reconstructing force-distance spectra by the integration of amplitude-distance spectra verified their position, offering a novel approach to detect intermediates during the forced unfolding of single proteins.     

Single-molecule force spectroscopy reveals the individual mechanical unfolding pathways of a surface layer protein

Surface layers (S-layers) represent an almost universal feature of archaeal cell envelopes and are probably the most abundant bacterial cell proteins. S-layers are monomolecular crystalline structures of single protein or glycoprotein monomers that completely cover the cell surface during all stages of the cell growth cycle, thereby performing their intrinsic function under a constant intra- and intermolecular mechanical stress. In gram-positive bacteria, the individual S-layer proteins are anchored by a specific binding mechanism to polysaccharides (secondary cell wall polymers) that are linked to the underlying peptidoglycan layer. In this work, atomic force microscopy-based single-molecule force spectroscopy and a polyprotein approach are used to study the individual mechanical unfolding pathways of an S-layer protein. We uncover complex unfolding pathways involving the consecutive unfolding of structural intermediates, where a mechanical stability of 87 pN is revealed. Different initial extensibilities allow the hypothesis that S-layer proteins adapt highly stable, mechanically resilient conformations that are not extensible under the presence of a pulling force. Interestingly, a change of the unfolding pathway is observed when individual S-layer proteins interact with secondary cell wall polymers, which is a direct signature of a conformational change induced by the ligand. Moreover, the mechanical stability increases up to 110 pN. This work demonstrates that single-molecule force spectroscopy offers a powerful tool to detect subtle changes in the structure of an individual protein upon binding of a ligand and constitutes the first conformational study of surface layer proteins at the single-molecule level.     

Analyzing forced unfolding of protein tandems by ordered variates, 2: dependent unfolding times

Statistical analyses of forced unfolding data for protein tandems, i.e., unfolding forces (force-ramp) and unfolding times (force-clamp), used in single-molecule dynamic force spectroscopy rely on the assumption that the unfolding transitions of individual protein domains are independent (uncorrelated) and characterized, respectively, by identically distributed unfolding forces and unfolding times. In our previous work, we showed that in the experimentally accessible piconewton force range, this assumption, which holds at a lower constant force, may break at an elevated force level, i.e., the unfolding transitions may become correlated when force is increased. In this work, we develop much needed statistical tests for assessing the independence of the unobserved forced unfolding times for individual protein domains in the tandem and equality of their parent distributions, which are based solely on the observed ordered unfolding times. The use and performance of these tests are illustrated through the analysis of unfolding times for computer models of protein tandems. The proposed tests can be used in force-clamp atomic force microscopy experiments to obtain accurate information on protein forced unfolding and to probe data on the presence of interdomain interactions. The order statistics-based formalism is extended to cover the analysis of correlated unfolding transitions. The use of order statistics leads naturally to the development of new kinetic models, which describe the probabilities of ordered unfolding transitions rather than the populations of chemical species.     

Mechanical design of proteins studied by single-molecule force spectroscopy and protein engineering

Mechanical unfolding and refolding may regulate the molecular elasticity of modular proteins with mechanical functions. The development of the atomic force microscopy (AFM) has recently enabled the dynamic measurement of these processes at the single-molecule level. Protein engineering techniques allow the construction of homomeric polyproteins for the precise analysis of the mechanical unfolding of single domains. alpha-Helical domains are mechanically compliant, whereas beta-sandwich domains, particularly those that resist unfolding with backbone hydrogen bonds between strands perpendicular to the applied force, are more stable and appear frequently in proteins subject to mechanical forces. The mechanical stability of a domain seems to be determined by its hydrogen bonding pattern and is correlated with its kinetic stability rather than its thermodynamic stability. Force spectroscopy using AFM promises to elucidate the dynamic mechanical properties of a wide variety of proteins at the single molecule level and provide an important complement to other structural and dynamic techniques (e.g., X-ray crystallography, NMR spectroscopy, patch-clamp).     

Single-molecule unfolding force distributions reveal a funnel-shaped energy landscape

The protein folding process is described as diffusion on a high-dimensional energy landscape. Experimental data showing details of the underlying energy surface are essential to understanding folding. So far in single-molecule mechanical unfolding experiments a simplified model assuming a force-independent transition state has been used to extract such information. Here we show that this so-called Bell model, although fitting well to force velocity data, fails to reproduce full unfolding force distributions. We show that by applying Kramers' diffusion model, we were able to reconstruct a detailed funnel-like curvature of the underlying energy landscape and establish full agreement with the data. We demonstrate that obtaining spatially resolved details of the unfolding energy landscape from mechanical single-molecule protein unfolding experiments requires models that go beyond the Bell model.     

Mechanical Characterization of Protein L in the Low-Force Regime by Electromagnetic Tweezers/Evanescent Nanometry

Mechanical manipulation at the single molecule level of proteins exhibiting mechanical stability poses a technical challenge that has been almost exclusively approached by atomic force microscopy (AFM) techniques. However, due to mechanical drift limitations, AFM techniques are restricted to experimental recordings that last less than a minute in the high-force regime. Here we demonstrate a novel combination of electromagnetic tweezers and evanescent nanometry that readily captures the forced unfolding trajectories of protein L at pulling forces as low as 10 ∼ 15 pN. Using this approach, we monitor unfolding and refolding cycles of the same polyprotein for a period of time longer than 30 min. From such long-lasting recordings, we obtain ensemble averages of unfolding step sizes and rates that are consistent with single-molecule AFM data obtained at higher stretching forces. The unfolding kinetics of protein L at low stretching forces confirms and extends the observations that the mechanical unfolding rate is exponentially dependent on the pulling force within a wide range of stretching forces spanning from 13 pN up to 120 pN. Our experiments demonstrate a novel approach for the mechanical manipulation of single proteins for extended periods of time in the low-force regime.     

The Molecular Mechanism Underlying Mechanical Anisotropy of the Protein GB1

Mechanical responses of elastic proteins are crucial for their biological function and nanotechnological use. Loading direction has been identified as one key determinant for the mechanical responses of proteins. However, it is not clear how a change in pulling direction changes the mechanical unfolding mechanism of the protein. Here, we combine protein engineering, single-molecule force spectroscopy, and steered molecular dynamics simulations to systematically investigate the mechanical response of a small globular protein GB1. Force versus extension profiles from both experiments and simulations reveal marked mechanical anisotropy of GB1. Using native contact analysis, we relate the mechanically robust shearing geometry with concurrent rupture of native contacts. This clearly contrasts the sequential rupture observed in simulations for the mechanically labile peeling geometry. Moreover, we identify multiple distinct mechanical unfolding pathways in two loading directions. Implications of such diverse unfolding mechanisms are discussed. Our results may also provide some insights for designing elastomeric proteins with tailored mechanical properties.     

A novel pattern recognition algorithm to classify membrane protein unfolding pathways with high-throughput single-molecule force spectroscopy

MOTIVATION: Misfolding of membrane proteins plays an important role in many human diseases such as retinitis pigmentosa, hereditary deafness and diabetes insipidus. Little is known about membrane proteins as there are only very few high-resolution structures. Single-molecule force spectroscopy is a novel technique, which measures the force necessary to pull a protein out of a membrane. Such force curves contain valuable information on the protein structure, conformation, and inter- and intra-molecular forces. High-throughput force spectroscopy experiments generate hundreds of force curves including spurious ones and good curves, which correspond to different unfolding pathways. Manual analysis of these data is a bottleneck and source of inconsistent and subjective annotation. RESULTS: We propose a novel algorithm for the identification of spurious curves and curves representing different unfolding pathways. Our algorithm proceeds in three stages: first, we reduce noise in the curves by applying dimension reduction; second, we align the curves with dynamic programming and compute pairwise distances and third, we cluster the curves based on these distances. We apply our method to a hand-curated dataset of 135 force curves of bacteriorhodopsin mutant P50A. Our algorithm achieves a success rate of 81% distinguishing spurious from good curves and a success rate of 76% classifying unfolding pathways. As a result, we discuss five different unfolding pathways of bacteriorhodopsin including three main unfolding events and several minor ones. Finally, we link folding barriers to the degree of conservation of residues. Overall, the algorithm tackles the force spectroscopy bottleneck and leads to more consistent and reproducible results paving the way for high-throughput analysis of structural features of membrane proteins.     

A mechanical unfolding intermediate in an actin-crosslinking protein

Many F-actin crosslinking proteins consist of two actin-binding domains separated by a rod domain that can vary considerably in length and structure. In this study, we used single-molecule force spectroscopy to investigate the mechanics of the immunoglobulin (Ig) rod domains of filamin from Dictyostelium discoideum (ddFLN). We find that one of the six Ig domains unfolds at lower forces than do those of all other domains and exhibits a stable unfolding intermediate on its mechanical unfolding pathway. Amino acid inserts into various loops of this domain lead to contour length changes in the single-molecule unfolding pattern. These changes allowed us to map the stable core of approximately 60 amino acids that constitutes the unfolding intermediate. Fast refolding in combination with low unfolding forces suggest a potential in vivo role for this domain as a mechanically extensible element within the ddFLN rod.     

Observing the osmophobic effect in action at the single molecule level

Protecting osmolytes are widespread small organic molecules able to stabilize the folded state of most proteins against various denaturing stresses in vivo. The osmophobic model explains thermodynamically their action through a preferential exclusion of the osmolyte molecules from the protein surface, thus favoring the formation of intrapeptide hydrogen bonds. Few works addressed the influence of protecting osmolytes on the protein unfolding transition state and kinetics. Among those, previous single molecule force spectroscopy experiments evidenced a complexation of the protecting osmolyte molecules at the unfolding transition state of the protein, in apparent contradiction with the osmophobic nature of the protein backbone. We present single-molecule evidence that glycerol, which is a ubiquitous protecting osmolyte, stabilizes a globular protein against mechanical unfolding without binding into its unfolding transition state structure. We show experimentally that glycerol does not change the position of the unfolding transition state as projected onto the mechanical reaction coordinate. Moreover, we compute theoretically the projection of the unfolding transition state onto two other common reaction coordinates, that is, the number of native peptide bonds and the weighted number of native contacts. To that end, we augment an analytic Ising-like protein model with support for group-transfer free energies. Using this model, we find again that the position of the unfolding transition state does not change in the presence of glycerol, giving further support to the conclusions based on the single-molecule experiments.     

Exact low-force kinetics from high-force single-molecule unfolding events

Mechanical forces play a key role in crucial cellular processes involving force-bearing biomolecules, as well as in novel single-molecule pulling experiments. We present an exact method that enables one to extrapolate, to low (or zero) forces, entire time-correlation functions and kinetic rate constants from the conformational dynamics either simulated numerically or measured experimentally at a single, relatively higher, external force. The method has twofold relevance: 1), to extrapolate the kinetics at physiological force conditions from molecular dynamics trajectories generated at higher forces that accelerate conformational transitions; and 2), to extrapolate unfolding rates from experimental force-extension single-molecule curves. The theoretical formalism, based on stochastic path integral weights of Langevin trajectories, is presented for the constant-force, constant loading rate, and constant-velocity modes of the pulling experiments. For the first relevance, applications are described for simulating the conformational isomerization of alanine dipeptide; and for the second relevance, the single-molecule pulling of RNA is considered. The ability to assign a weight to each trace in the single-molecule data also suggests a means to quantitatively compare unfolding pathways under different conditions.     

Configurational entropy modulates the mechanical stability of protein GB1

Configurational entropy plays important roles in defining the thermodynamic stability as well as the folding/unfolding kinetics of proteins. Here we combine single-molecule atomic force microscopy and protein engineering techniques to directly examine the role of configurational entropy in the mechanical unfolding kinetics and mechanical stability of proteins. We used a small protein, GB1, as a model system and constructed four mutants that elongate loop 2 of GB1 by 2, 5, 24 and 46 flexible residues, respectively. These loop elongation mutants fold properly as determined by far-UV circular dichroism spectroscopy, suggesting that loop 2 is well tolerant of loop insertions without affecting GB1′s native structure. Our single-molecule atomic force microscopy results reveal that loop elongation decreases the mechanical stability of GB1 and accelerates the mechanical unfolding kinetics. These results can be explained by the loss of configurational entropy upon closing an unstructured flexible loop using classical polymer theory, highlighting the important role of loop regions in the mechanical unfolding of proteins. This study not only demonstrates a general approach to investigating the structural deformation of the loop regions in mechanical unfolding transition state, but also provides the foundation to use configurational entropy as an effective means to modulate the mechanical stability of proteins, which is of critical importance towards engineering artificial elastomeric proteins with tailored nanomechanical properties.     

High-speed atomic force microscopy: Imaging and force spectroscopy

Atomic force microscopy (AFM) is the type of scanning probe microscopy that is probably best adapted for imaging biological samples in physiological conditions with submolecular lateral and vertical resolution. In addition, AFM is a method of choice to study the mechanical unfolding of proteins or for cellular force spectroscopy. In spite of 28 years of successful use in biological sciences, AFM is far from enjoying the same popularity as electron and fluorescence microscopy. The advent of high-speed atomic force microscopy (HS-AFM), about 10 years ago, has provided unprecedented insights into the dynamics of membrane proteins and molecular machines from the single-molecule to the cellular level. HS-AFM imaging at nanometer-resolution and sub-second frame rate may open novel research fields depicting dynamic events at the single bio-molecule level. As such, HS-AFM is complementary to other structural and cellular biology techniques, and hopefully will gain acceptance from researchers from various fields. In this review we describe some of the most recent reports of dynamic bio-molecular imaging by HS-AFM, as well as the advent of high-speed force spectroscopy (HS-FS) for single protein unfolding.     

Computational investigation of the effect of thermal perturbation on the mechanical unfolding of titin I27

The emergence of single-molecule force measurement experiments has facilitated a better understanding of protein folding pathways and the thermodynamics involved. Computational methods such as steered molecular dynamics (SMD) simulations are helpful in providing atomistic level information on the unfolding pathways. Recent experimental studies have showed that combinations of single-molecule experiments with traditional methods such as chemical and/or thermal denaturation yield additional insights into the folding phenomenon. In this study, we report results from extensive computations (a total of about 60 SMD simulations with a total length of about 0.4 μs) that address the effect of thermal perturbation on the mechanical stability of the I27 domain of the protein titin. A wide range of temperatures (280-340 K) were considered for the pulling, which was done at both constant velocity and constant force using SMD simulations. Good agreement with experimental data, such as for the trends in changes in average force and the maximum force with respect to the temperature, was obtained. This study identifies two competing pathways for the mechanical unfolding of I27, and illustrates the significance of combining various techniques to examine protein folding.     

Force-clamp spectroscopy of single-protein monomers reveals the individual unfolding and folding pathways of I27 and ubiquitin

Single-protein force experiments have relied on a molecular fingerprint based on tethering multiple single-protein domains in a polyprotein chain. However, correlations between these domains remain an issue in interpreting force spectroscopy data, particularly during protein folding. Here we first show that force-clamp spectroscopy is a sensitive technique that provides a molecular fingerprint based on the unfolding step size of four single-monomer proteins. We then measure the force-dependent unfolding rate kinetics of ubiquitin and I27 monomers and find a good agreement with the data obtained for the respective polyproteins over a wide range of forces, in support of the Markovian hypothesis. Moreover, with a large statistical ensemble at a single force, we show that ubiquitin monomers also exhibit a broad distribution of unfolding times as a signature of disorder in the folded protein landscape. Furthermore, we readily capture the folding trajectories of monomers that exhibit the same stages in folding observed for polyproteins, thus eliminating the possibility of entropic masking by other unfolded modules in the chain or domain-domain interactions. On average, the time to reach the I27 folded length increases with increasing quenching force at a rate similar to that of the polyproteins. Force-clamp spectroscopy at the single-monomer level reproduces the kinetics of unfolding and refolding measured using polyproteins, which proves that there is no mechanical effect of tethering proteins to one another in the case of ubiquitin and I27.     

Complex stability of single proteins explored by forced unfolding experiments

In the last decade atomic force microscopy has been used to measure the mechanical stability of single proteins. These force spectroscopy experiments have shown that many water-soluble and membrane proteins unfold via one or more intermediates. Recently, Li and co-workers found a linear correlation between the unfolding force of the native state and the intermediate in fibronectin, which they suggested indicated the presence of a molecular memory or multiple unfolding pathways (1). Here, we apply two independent methods in combination with Monte Carlo simulations to analyze the unfolding of alpha-helices E and D of bacteriorhodopsin (BR). We show that correlation analysis of unfolding forces is very sensitive to errors in force calibration of the instrument. In contrast, a comparison of relative forces provides a robust measure for the stability of unfolding intermediates. The proposed approach detects three energetically different states of alpha-helices E and D in trimeric BR. These states are not observed for monomeric BR and indicate that substantial information is hidden in forced unfolding experiments of single proteins.     

原子力显微镜单分子力谱研究生物分子间相互作用

原子力显微镜单分子力谱是近年来发展起来的能在单分子水平研究生物分子相互作用的新工具。本文综述了单分子力谱的测定原理、方法及其在研究蛋白．蛋白、蛋白-DNA相互作用,蛋白质去折叠和活细胞上配体／受体结合中的应用进展。     

Probing force-induced unfolding intermediates of a single staphylococcal nuclease molecule and the effect of ligand binding

Single-molecule manipulation techniques have given experimental access to unfolding intermediates of proteins that are inaccessible in conventional experiments. A detailed characterization of the intermediates is a challenging problem that provides new possibilities for directly probing the energy landscape of proteins. We investigated single-molecule mechanical unfolding of a small globular protein, staphylococcal nuclease (SNase), using atomic force microscopy. The unfolding trajectories of the protein displayed sub-molecular and stochastic behavior with typical lengths corresponding to the size of the unfolded substructures. Our results support the view that the single protein unfolds along multiple pathways as suggested in recent theoretical studies. Moreover, we found the drastic change, caused by the ligand and inhibitor bindings, in the mechanical unfolding dynamics.