Single-molecule force-clamp spectroscopy: dwell time analysis and practical considerations

Single-molecule force-clamp spectroscopy has become a powerful tool for studying protein folding/unfolding, bond rupture, and enzymatic reactions. Different methods have been developed to analyze force-clamp spectroscopy data on polyproteins to obtain kinetic parameters characterizing the mechanical unfolding of proteins, which are often modeled as a two-state process (a Poisson process). However, because of the finite number of domains in polyproteins, the statistical analysis of the force-clamp spectroscopy data is different from that of a classical Poisson process, and the equivalency of different analysis methods remains to be proven. In this article, we show that these methods are equivalent and lead to accurate measurements of the unfolding rate constant. We also demonstrate that distinct from the constant-pulling-velocity experiments, in which the unfolding rate extracted from the data is dependent on the number of protein domains in the polyproteins (the N effect), force-clamp experiments do not show any N effect. Using a simulated data set, we also highlighted important practical considerations that one needs to take into account when using the single-molecule force-clamp spectroscopy technique to characterize the unfolding energy landscape of proteins.     

Loading device effect on protein unfolding mechanics

Single-molecule mechanical manipulation has enabled quantitative understanding of not only the kinetics of both bond rupture and protein unfolding, but also the free energy landscape of chemical bond and/or protein folding. Despite recent studies reporting the role of loading device in bond rupture, a loading device effect on protein unfolding mechanics has not been well studied. In this work, we have studied the effect of loading-device stiffness on the kinetics of both bond rupture and protein unfolding mechanics using Brownian dynamics simulations. It is shown that bond rupture forces are dependent on not only loading rate but also the stiffness of loading device, and that protein unfolding mechanics is highly correlated with the stiffness of loading device. Our study sheds light on the importance of loading device effect on the mechanically induced bond ruptures and protein unfolding.     

Evidence of an intermediate and parallel pathways in protein unfolding from single-molecule fluorescence

Determining how proteins fold into their native structures is a subject of great importance, since ultimately it will allow protein structure and function to be predicted from primary sequence data. In addition, there is now a clear link between protein unfolding and misfolding events and many disease states. However, since proteins fold over rugged, multidimensional energy landscapes, this is a challenging experimental and theoretical problem. Single-molecule fluorescence methods developed over the past decade have the potential to follow the unfolding/folding of individual molecules. Mapping out the landscape without ensemble averaging will enable the identification of intermediate states which may not be significantly populated, in addition to the presence of multiple pathways. To date, there have been only a limited number of single-molecule folding/unfolding studies under nonequilibrium conditions and no intermediates have been observed. Here, for the first time, we present a single-molecule study of the unfolding of a large autofluorescent protein, Citrine, a variant of green fluorescent protein. Single-molecule fluorescence techniques are used to directly detect an intermediate on the unfolding/folding pathway and the existence of parallel unfolding pathways. This work, and the novel methods used, shows that single-molecule fluorescence can now provide new, hitherto experimentally inaccessible, insights into the folding/unfolding of proteins.     

Mechanical Deformation Accelerates Protein Ageing

A hallmark of tissue ageing is the irreversible oxidative modification of its proteins. We show that single proteins, kept unfolded and extended by a mechanical force, undergo accelerated ageing in times scales of minutes to days. A protein forced to be continuously unfolded completely loses its ability to contract by folding, becoming a labile polymer. Ageing rates vary among different proteins, but in all cases they lose their mechanical integrity. Random oxidative modification of cryptic side chains exposed by mechanical unfolding can be slowed by the addition of antioxidants such as ascorbic acid, or accelerated by oxidants. By contrast, proteins kept in the folded state and probed over week‐long experiments show greatly reduced rates of ageing. We demonstrate a novel approach whereby protein ageing can be greatly accelerated: the constant unfolding of a protein for hours to days is equivalent to decades of exposure to free radicals under physiological conditions.     

Direct Comparison of Lysine versus Site-Specific Protein Surface Immobilization in Single-Molecule Mechanical Assays**

Single-molecule force spectroscopy (SMFS) is powerful for studying folding states and mechanical properties of proteins, however, it requires protein immobilization onto force-transducing probes such as cantilevers or microbeads. A common immobilization method relies on coupling lysine residues to carboxylated surfaces using 1-ethyl-3-(3-dimethyl-aminopropyl) carbodiimide and N-hydroxysuccinimide (EDC/NHS). Because proteins typically contain many lysine groups, this strategy results in a heterogeneous distribution of tether positions. Genetically encoded peptide tags (e.g., ybbR) provide alternative chemistries for achieving site-specific immobilization, but thus far a direct comparison of site-specific vs. lysine-based immobilization strategies to assess effects on the observed mechanical properties was lacking. Here, we compared lysine- vs. ybbR-based protein immobilization in SMFS assays using several model polyprotein systems. Our results show that lysine-based immobilization results in significant signal deterioration for monomeric streptavidin-biotin interactions, and loss of the ability to correctly classify unfolding pathways in a multipathway Cohesin-Dockerin system. We developed a mixed immobilization approach where a site-specifically tethered ligand was used to probe surface-bound proteins immobilized through lysine groups, and found partial recovery of specific signals. The mixed immobilization approach represents a viable alternative for mechanical assays on in vivo-derived samples or other proteins of interest where genetically encoded tags are not feasible.     

Capturing the Mechanical Unfolding Pathway of a Large Protein with Coiled‐Coil Probes

The folding behaviors and mechanisms of large multidomain proteins have remained largely uncharacterized, primarily because of the lack of appropriate research methods. To address these limitations, novel mechanical folding probes have been developed that are based on antiparallel coiled‐coil polypeptides. Such probes can be conveniently inserted at the DNA level, at different positions within the protein of interest where they minimally disturb the host protein structure. During single‐molecule force spectroscopy measurements, the forced unfolding of the probe captures the progress of the unfolding front through the host protein structure. This novel approach allows unfolding pathways of large proteins to be directly identified. As an example, this probe was used in a large multidomain protein with ten identical ankyrin repeats, and the unfolding pathway, its direction, and the order of sequential unfolding were unequivocally and precisely determined. This development facilitates the examination of the folding pathways of large proteins, which are predominant in the proteasomes of all organisms, but have thus far eluded study because of the technical limitations encountered when using traditional techniques.     

Mechanically untying a protein slipknot: multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations

Protein structure is highly diverse when considering a wide range of protein types, helping to give rise to the multitude of functions that proteins perform. In particular, certain proteins are known to adopt a knotted or slipknotted fold. How such proteins undergo mechanical unfolding was investigated utilizing a combination of single molecule atomic force microscopy (AFM), protein engineering, and steered molecular dynamics (SMD) simulations to show the mechanical unfolding mechanism of the slipknotted protein AFV3-109. Our results reveal that the mechanical unfolding of AFV3-109 can proceed via multiple parallel unfolding pathways that all cause the protein slipknot to untie and the polypeptide chain to completely extend. These distinct unfolding pathways proceed via either a two- or three-state unfolding process involving the formation of a well-defined, stable intermediate state. SMD simulations predict the same contour length increments for different unfolding pathways as single molecule AFM results, thus providing a plausible molecular mechanism for the mechanical unfolding of AFV3-109. These SMD simulations also reveal that two-state unfolding is initiated from both the N- and C-termini, while three-state unfolding is initiated only from the C-terminus. In both pathways, the protein slipknot was untied during unfolding, and no tightened slipknot conformation was observed. Detailed analysis revealed that interactions between key structural elements lock the knotting loop in place, preventing it from shrinking and the formation of a tightened slipknot conformation. Our results demonstrate the bifurcation of the mechanical unfolding pathway of AFV3-109 and point to the generality of a kinetic partitioning mechanism for protein folding/unfolding.     

Thermal unfolding of proteins

Thermal unfolding of proteins is compared to folding and mechanical stretching in a simple topology-based dynamical model. We define the unfolding time and demonstrate its low-temperature divergence. Below a characteristic temperature, contacts break at separate time scales and unfolding proceeds approximately in a way reverse to folding. Features in these scenarios agree with experiments and atomic simulations on titin.     

Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin. Unfolding rates calculated from simulations over a broad range of stretching forces, for different pulling directions, reveal a remarkable "turnover" from a force-independent process at low force to a force-dependent process at high force, akin to the "roll-over" in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrate that it can occur for dynamics in just two dimensions. We relate the turnover to the quality of the pulling direction as a reaction coordinate for the intrinsic folding mechanism. A novel pulling direction, designed to be the most relevant to the intrinsic folding pathway, results in the smallest turnover. Our results are in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.     

Mechanical unfolding of segment-swapped protein G dimer: results from replica exchange molecular dynamics simulations

The protein G dimer (pdb code 1Q10) is a mutated dimeric form of the immunoglobulin-binding domain B1 of streptococcal protein G, in which the two monomeric units have swapped elements of their secondary structure. We have used replica exchange molecular dynamics simulations to study how this dimer responds to a mechanical force that pulls the N-terminus of one unit and the C-terminus of the other apart. We have further compared the mechanical response of the dimer to that of the protein G monomer. When the pulling force is low enough, the mechanical unfolding can be viewed as a thermally activated barrier crossing process. For each protein, we have computed the corresponding free energy barrier and its dependence on the pulling force. While the dimer is found to be less resistant to mechanical unfolding than its monomeric counterpart, the two proteins exhibit essentially the same mechanical unfolding mechanism involving separation of the terminal parallel strands. On the basis of our results, we speculate that the mechanical properties of natural adhesives, composites, fibers, and other materials may be optimized not only at a single molecule level but also at the mesoscopic level through the interactions among individual chains.     

Topography of the free-energy landscape probed via mechanical unfolding of proteins

Single-molecule experiments in which proteins are unfolded by applying mechanical stretching forces generally force unfolding to proceed along a reaction coordinate that is different from that in chemical or thermal denaturation. Here we simulate the mechanical unfolding and refolding of a minimalist off-lattice model of the protein ubiquitin to explore in detail the slice of the multidimensional free-energy landscape that is accessible via mechanical pulling experiments. We find that while the free-energy profile along typical "chemical" reaction coordinates may exhibit two minima, corresponding to the native and denatured states, the free energy G(z) is typically a monotonic function of the mechanical coordinate z equal to the protein extension. Application of a stretching force along z tilts the free-energy landscape resulting in a bistable (or multistable) free energy G(z)-fz probed in mechanical unfolding experiments. We construct a two-dimensional free-energy surface as a function of both chemical and mechanical reaction coordinates and examine the coupling between the two. We further study the refolding trajectories after the protein has been prestretched by a large force, as well as the mechanical unfolding trajectories in the presence of a large stretching force. We demonstrate that the stretching forces required to destabilize the native state thermodynamically are larger than those expected on the basis of previous experimental estimates of G(z). This finding is consistent with the recent experimental studies, indicating that proteins may refold even in the presence of a substantial stretching force. Finally, we show that for certain temperatures the free energy of a polyprotein chain consisting of multiple domains is a linear function of the chain extension. We propose that the recently observed "slow phase" in the refolding of proteins under mechanical tension may be viewed as downhill diffusion in such a linear potential.     

Free energy for protein folding from nonequilibrium simulations using the Jarzynski equality

The equilibrium free energy difference between two long-lived molecular species or "conformational states" of a protein (or any other molecule) can in principle be estimated by measuring the work needed to shuttle the system between them, independent of the irreversibility of the process. This is the meaning of the Jarzynski equality (JE), which we test in this paper by performing simulations that unfold a protein by pulling two atoms apart. Pulling is performed fast relative to the relaxation time of the molecule and is thus far from equilibrium. Choosing a simple protein model for which we can independently compute its equilibrium properties, we show that the free energy can be exactly and effectively estimated from nonequilibrium simulations. To do so, one must carefully and correctly determine the ensemble of states that are pulled, which is more important the farther from equilibrium one performs simulations; this highlights a potential problem in using the JE to extract the free energy from forced unfolding experiments. The results presented here also demonstrate that the free energy difference between the native and denatured states of a protein measured in solution is not always equal to the free energy profile that can be estimated from forced unfolding simulations (or experiments) using the JE.     

Mechanical properties of bovine rhodopsin and bacteriorhodopsin: possible roles in folding and function

Molecular interactions and mechanical properties that contribute to the stability and function of proteins are complex and of fundamental importance. In this study, we used single-molecule dynamic force spectroscopy (DFS) to explore the interactions and the unfolding energy landscape of bovine rhodopsin and bacteriorhodopsin. An analysis of the experimental data enabled the extraction of parameters that provided insights into the kinetic stability and mechanical properties of these membrane proteins. Individual structural segments of rhodopsin and bacteriorhodopsin have different properties. A core of rigid structural segments was observed in rhodopsin but not in bacteriorhodopsin. This core may reflect differences in mechanisms of protein folding between the two membrane proteins. The different structural rigidity of the two proteins may also reflect their adaptation to differing functions.     

Mesoscopic model for mechanical characterization of biological protein materials

Mechanical characterization of protein molecules has played a role on gaining insight into the biological functions of proteins, because some proteins perform the mechanical function. Here, we present the mesoscopic model of biological protein materials composed of protein crystals prescribed by Go potential for characterization of elastic behavior of protein materials. Specifically, we consider the representative volume element (RVE) containing the protein crystals represented by C(alpha) atoms, prescribed by Go potential, with application of constant normal strain to RVE. The stress-strain relationship computed from virial stress theory provides the nonlinear elastic behavior of protein materials and their mechanical properties such as Young's modulus, quantitatively and/or qualitatively comparable with mechanical properties of biological protein materials obtained from experiments and/or atomistic simulations. Further, we discuss the role of native topology on the mechanical properties of protein crystals. It is shown that parallel strands (hydrogen bonds in parallel) enhance the mechanical resilience of protein materials.     

Single molecule force spectroscopy using polyproteins

In recent years single molecule force spectroscopy has emerged as a powerful new tool to explore the mechanical stability and folding pathways of individual proteins. This technique is used to apply a stretching force between two points of a protein, unfolding the protein to an extended state. By measuring the unfolding and folding trajectories of individual proteins, insight can be gained into the physical mechanisms of protein folding. In this tutorial review we introduce the reader to single molecule force spectroscopy using the atomic force microscope (AFM), and explain the two main modes of operation of the AFM for force spectroscopy: force-extension and force-clamp. We introduce the approach of using polyproteins to obtain a clear mechanical fingerprint for monitoring the response of proteins to an applied mechanical force. In addition, we provide an informative and representative review of recent research on proteins using single molecule force spectroscopy. We focus on areas which have made a significant contribution to the single molecule protein folding field and highlight emerging areas of research which have wider implications for the general scientific community.     

Protein folding kinetics under force from molecular simulation

Despite a large number of studies on the mechanical unfolding of proteins, there are still relatively few successful attempts to refold proteins in the presence of a stretching force. We explore refolding kinetics under force using simulations of a coarse-grained model of ubiquitin. The effects of force on the folding kinetics can be fitted by a one-dimensional Kramers theory of diffusive barrier crossing, resulting in physically meaningful parameters for the height and location of the folding activation barrier. By comparing parameters obtained from pulling in different directions, we find that the unfolded state plays a dominant role in the refolding kinetics. Our findings explain why refolding becomes very slow at even moderate pulling forces and suggest how it could be practically observed in experiments at higher forces.     

Single-molecule fluorescence spectroscopy of protein folding.

Single-molecule spectroscopy is an important new approach for studying the intrinsically heterogeneous process of protein folding. This Review illustrates how different single-molecule fluorescence techniques have improved our understanding of mechanistic aspects in protein folding, exemplified by a series of recent experiments on a small protein.     

New insights into the folding–unfolding mechanism and conformations of cytochrome C

Metalloproteins account for over one-third of all proteins in nature and play important roles in biological processes. The formation of the native structures of metalloproteins requires not only the correct folding of the polypeptide chains but also the proper incorporation of metal cofactors. Understanding the folding mechanism of metalloproteins has been challenging. Horse heart cytochrome C (cytc) is a classical model system for protein folding studies. Although a large number of ensemble studies have been carried out to characterize the folding mechanism of cytc, there is still a significant debate on the folding mechanism and the existence of the proposed “foldons”. Here, we used single-molecule optical tweezers to probe the mechanical folding–unfolding behaviors of cytc at the single-molecule level. By directly monitoring the folding and unfolding of holo-cytc, we revealed novel insights into the folding of cytc. Our results showed that the structural elements that are distant from the N- and C-termini can exist as a short-lived intermediate, a finding that contrasts with the general belief that the folding and packing of the N- and C-terminal helices are prerequisites for the folding of other structural elements in cytc. In addition, our results present strong evidence that apo-cytc, which has been long believed to be a random coil, is not a true random coil, and weak interactions within the unfolded polypeptide chain exist. Our results bring new insights into our understanding of the folding mechanisms of heme proteins as well as the role of heme in the folding process.

Optical trapping experiments offer new insights into the folding and unfolding of cytochrome C.     

Single‐Molecule Detection Reveals Knot Sliding in TrmD Denaturation

An increasing number of proteins are found to contain a knot in their polypeptide chain. Although some studies have looked into the folding mechanism of knotted proteins, why and how these complex topologies form are still far from being fully answered. Moreover, no experimental information about how the knot moves during the protein‐folding process is available. Herein, by combining single‐molecule fluorescence resonance energy transfer (smFRET) experiments with molecular dynamics (MD) simulations, we performed a detailed study to characterize the knot in the denatured state of TrmD, a knotted tRNA (guanosine‐1) methyltransferase from Escherichia coli, as a model system. We found that the knot still existed in the unfolded state of TrmD, consistent with the results for two other knotted proteins, YibK and YbeA. More interestingly, both smFRET experiments and MD simulations revealed that the knot slid towards the C‐terminal during the unfolding process, which could be explained by the relatively strong interactions between the β‐sheet core at the N terminal of the native knot region. The size of the knot in the unfolded state is not larger than that in the native state. In addition, the knot slid in a “downhill” mode with simultaneous chain collapse in the denatured state.