Computer simulations of the translocation and unfolding of a protein pulled mechanically through a pore

Protein degradation by ATP-dependent proteases and protein import into the mitochondrial matrix involve the unfolding of proteins upon their passing through narrow constrictions. It has been hypothesized that the cellular machinery accomplishes protein unfolding by pulling mechanically at one end of the polypeptide chain. Here, we use Langevin dynamics simulations of a minimalist off-lattice model to examine this hypothesis and to study the unfolding of a protein domain pulled mechanically through a long narrow pore. We compute the potential of mean force (PMF) experienced by the domain as a function of its displacement along the pore and identify the unfolding intermediates corresponding to the local minima of the PMF. The observed unfolding mechanism is different from that found when the two termini are pulled apart, as in single-molecule mechanical unfolding experiments. It depends on the pore diameter, the magnitude of the pulling force, and on whether the force is applied at the N- or the C-terminus of the chain. Consequently, the translocation time exhibits a pulling force dependence that is more complex than a simple exponential function expected on the basis of simple phenomenological models of translocation.     

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.     

Highly anisotropic stability and folding kinetics of a single coiled coil protein under mechanical tension

Coiled coils are one of the most abundant protein structural motifs and widely mediate protein interactions and force transduction or sensation. They are thus model systems for protein engineering and folding studies, particularly the GCN4 coiled coil. Major single-molecule methods have also been applied to this protein and revealed its folding kinetics at various spatiotemporal scales. Nevertheless, the folding energy and the kinetics of a single GCN4 coiled coil domain have not been well determined at a single-molecule level. Here we used high-resolution optical tweezers to characterize the folding and unfolding reactions of a single GCN4 coiled coil domain and their dependence on the pulling direction. In one axial and two transverse pulling directions, we observed reversible, two-state transitions of the coiled coil in real time. The transitions equilibrate at pulling forces ranging from 6 to 12 pN, showing different stabilities of the coiled coil in regard to pulling direction. Furthermore, the transition rates vary with both the magnitude and the direction of the pulling force by greater than 1000 folds, indicating a highly anisotropic and topology-dependent energy landscape for protein transitions under mechanical tension. We developed a new analytical theory to extract energy and kinetics of the protein transition at zero force. The derived folding energy does not depend on the pulling direction and is consistent with the measurement in bulk, which further confirms the applicability of the single-molecule manipulation approach for energy measurement. The highly anisotropic thermodynamics of proteins under tension should play important roles in their biological functions.     

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.     

Single Molecule Force Spectroscopy Reveals Critical Roles of Hydrophobic Core Packing in Determining the Mechanical Stability of Protein GB1

Understanding molecular determinants of protein mechanical stability is important not only for elucidating how elastomeric proteins are designed and functioning in biological systems but also for designing protein building blocks with defined nanomechanical properties for constructing novel biomaterials. GB1 is a small α/β protein and exhibits significant mechanical stability. It is thought that the shear topology of GB1 plays an important role in determining its mechanical stability. Here, we combine single molecule atomic force microscopy and protein engineering techniques to investigate the effect of side chain reduction and hydrophobic core packing on the mechanical stability of GB1. We engineered seven point mutants and carried out mechanical ?-value analysis of the mechanical unfolding of GB1. We found that three mutations, which are across the surfaces of two subdomains that are to be sheared by the applied stretching force, in the hydrophobic core (F30L, Y45L, and F52L) result in significant decrease in mechanical unfolding force of GB1. The mechanical unfolding force of these mutants drop by 50-90 pN compared with wild-type GB1, which unfolds at around 180 pN at a pulling speed of 400 nm/s. These results indicate that hydrophobic core packing plays an important role in determining the mechanical stability of GB1 and suggest that optimizing hydrophobic interactions across the surfaces that are to be sheared will likely be an efficient method to enhance the mechanical stability of GB1 and GB1 homologues.     

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.     

Simulation of the mechanical unfolding of ubiquitin: probing different unfolding reaction coordinates by changing the pulling geometry

Motivated by the recent experimental atomic force microscopy (AFM) measurements of the mechanical unfolding of proteins pulled in different directions [D. J. Brockwell et al., Nat. Struct. Biol. 10, 731 (2003); M. Carrion-Vazquez et al., ibid 10, 738 (2003)] we have computed the unfolding free energy profiles for the ubiquitin domain when it is stretched between its (A) N and C termini, (B) Lys48 and C terminus, (C) Lys11 and C terminus, and (D) N terminus and Lys63. Our results for cases (A) and (B) are in good agreement with the experimental unfolding forces measured for the N-C and Lys48-C linked polyubiquitin, in particular, indicating a considerably lower unfolding force in the latter case. Mechanical unfolding in case (A) involves longitudinal shearing of the terminal parallel strands while in case (C) the same strands are "unzipped" by the force. The computed unfolding forces in case (C) are found to be very low, less than 50 pN for pulling rates typical of AFM experiments. The unfolding free energy barrier found in case (C) is approximately 13 kcal/mol, which corresponds to a zero-force unfolding rate constant that is comparable to the rate of chemical unfolding extrapolated to zero denaturant concentration. The unfolding barrier calculated in case (A) in the limit of zero force is much higher, suggesting that mechanical unfolding in this case follows a pathway that is different from that of thermal/chemical denaturation.     

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.     

Biomolecules under mechanical stress: a simple mechanism of complex behavior

The unfolding of a biomolecule by stretching force is commonly treated theoretically as one-dimensional dynamics along the reaction coordinate coincident with the direction of pulling. Here we explore a situation, particularly relevant to complex biomolecules, when the pulling direction alone is not an adequate reaction coordinate for the unfolding or rupture process. We show that in this case the system can respond to pulling force in unusual ways. Our theory points out a remarkably simple, but largely overlooked, mechanism of the complex responses of biomolecules to force. The mechanism originates from the basic property of the transition state to change its structure under applied force. A relationship is established between a key experimental observable--force-dependent lifetime--and the microscopic properties of the biomolecule in the form of an analytical solution to the problem of a force-induced molecular transition in two dimensions. The theory is applicable to biological contexts ranging from protein folding to ligand-receptor interactions.     

Domain swapping proceeds via complete unfolding: a 19F- and 1H-NMR study of the Cyanovirin-N protein

Domain swapping creates protein oligomers by exchange of structural units between identical monomers. At present, no unifying molecular mechanism of domain swapping has emerged. Here we used the protein Cyanovirin-N (CV-N) and (19)F-NMR to investigate the process of domain swapping. CV-N is an HIV inactivating protein that can exist as a monomer or a domain-swapped dimer. We measured thermodynamic and kinetic parameters of the conversion process and determined the size of the energy barrier between the two species. The barrier is very large and of similar magnitude to that for equilibrium unfolding of the protein. Therefore, for CV-N, overall unfolding of the polypeptide is required for domain swapping.     

New force replica exchange method and protein folding pathways probed by force-clamp technique

We have developed a new extended replica exchange method to study thermodynamics of a system in the presence of external force. Our idea is based on the exchange between different force replicas to accelerate the equilibrium process. This new approach was applied to obtain the force-temperature phase diagram and other thermodynamical quantities of the three-domain ubiquitin. Using the C(alpha)-Go model and the Langevin dynamics, we have shown that the refolding pathways of single ubiquitin depend on which terminus is fixed. If the N end is fixed then the folding pathways are different compared to the case when both termini are free, but fixing the C terminal does not change them. Surprisingly, we have found that the anchoring terminal does not affect the pathways of individual secondary structures of three-domain ubiquitin, indicating the important role of the multidomain construction. Therefore, force-clamp experiments, in which one end of a protein is kept fixed, can probe the refolding pathways of a single free-end ubiquitin if one uses either the polyubiquitin or a single domain with the C terminus anchored. However, it is shown that anchoring one end does not affect refolding pathways of the titin domain I27, and the force-clamp spectroscopy is always capable to predict folding sequencing of this protein. We have obtained the reasonable estimate for unfolding barrier of ubiquitin, using the microscopic theory for the dependence of unfolding time on the external force. The linkage between residue Lys48 and the C terminal of ubiquitin is found to have the dramatic effect on the location of the transition state along the end-to-end distance reaction coordinate, but the multidomain construction leaves the transition state almost unchanged. We have found that the maximum force in the force-extension profile from constant velocity force pulling simulations depends on temperature nonlinearly. However, for some narrow temperature interval this dependence becomes linear, as have been observed in recent experiments.     

Direct Observation of the Reversible Two‐State Unfolding and Refolding of an α/β Protein by Single‐Molecule Atomic Force Microscopy

Directly observing protein folding in real time using atomic force microscopy (AFM) is challenging. Here the use of AFM to directly monitor the folding of an α/β protein, NuG2, by using low‐drift AFM cantilevers is demonstrated. At slow pulling speeds (<50 nm s^?1), the refolding of NuG2 can be clearly observed. Lowering the pulling speed reduces the difference between the unfolding and refolding forces, bringing the non‐equilibrium unfolding–refolding reactions towards equilibrium. At very low pulling speeds (ca. 2 nm s^?1), unfolding and refolding were observed to occur in near equilibrium. Based on the Crooks fluctuation theorem, we then measured the equilibrium free energy change between folded and unfolded states of NuG2. The improved long‐term stability of AFM achieved using gold‐free cantilevers allows folding–unfolding reactions of α/β proteins to be directly monitored near equilibrium, opening the avenue towards probing the folding reactions of other mechanically important α/β and all‐β elastomeric proteins.     

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.     

Dynamic force spectroscopy on soft molecular systems: Improved analysis of unbinding spectra with varying linker compliance

Dynamic force spectroscopy makes it possible to measure the breaking of single molecular bonds or the unfolding of single proteins subjected to a time-dependent pulling force. The force needed to break a single bond or to unfold a domain in a protein depends critically on the time dependence of the applied force. In this way the elastic response couples to the unbinding force. We have performed an experimental and theoretical examination of this coupling by studying the well-known biotin–streptavidin bond in systems incorporating two common types of linkers. In the first case biotin is linked by bovine serum albumin (BSA) and it is observed that this linker has a linear elastic response. More surprisingly we find that its force constant varies significantly between repeated force curves. It is demonstrated that by sorting the force curves according to the force constant of the linker we can improve the data analysis and obtain a better agreement between experimental data and theory. In the second case biotin is linked by poly(ethylene glycol) (PEG), which has a soft nonlinear elastic response. A numerical calculation of the unbinding statistics for the polymer system agrees quantitatively with experiments. It demonstrates a clear decrease in unbinding forces resulting from the polymer linker.     

Folding thermodynamics of pseudoknotted chain conformations

We develop a statistical mechanical framework for the folding thermodynamics of pseudoknotted structures. As applications of the theory, we investigate the folding stability and the free energy landscapes for both the thermal and the mechanical unfolding of pseudoknotted chains. For the mechanical unfolding process, we predict the force-extension curves, from which we can obtain the information about structural transitions in the unfolding process. In general, a pseudoknotted structure unfolds through multiple structural transitions. The interplay between the helix stems and the loops plays an important role in the folding stability of pseudoknots. For instance, variations in loop sizes can lead to the destabilization of some intermediate states and change the (equilibrium) folding pathways (e.g., two helix stems unfold either cooperatively or sequentially). In both thermal and mechanical unfolding, depending on the nucleotide sequence, misfolded intermediate states can emerge in the folding process. In addition, thermal and mechanical unfoldings often have different (equilibrium) pathways. For example, for certain sequences, the misfolded intermediates, which generally have longer tails, can fold, unfold, and refold again in the pulling process, which means that these intermediates can switch between two different average end-end extensions.     

Reaction rates in a theory of mechanochemical pathways

If one applies mechanical stress to a molecule in a defined direction then one generates a new, effective potential energy surface (PES). Changes for minima and saddle points (SP) by the stress are described by Newton trajectories on the original PES (Quapp and Bofill, Theor. Chem. Acc. 2016, 135, 113). The barrier of a reaction fully breaks down for the maximal value of the norm of the gradient of the PES along a pulling Newton trajectory. This point is named barrier breakdown point (BBP). Depending on the pulling direction, different reaction pathways can be enforced. If the exit SP of the chosen pulling direction is not the lowest SP of the reactant valley, on the original PES, then the SPs must change their role anywhere: in this case the curve of the log(rate) over the pulling force of a forward reaction can show a deviation from the normal concave curvature. We discuss simple, two‐dimensional examples for this model to understand more deeply the mechanochemistry of molecular systems under a mechanical stress. © 2016 Wiley Periodicals, Inc.     

A toy model of polymer stretching

We present an extremely simplified model of multiple-domain polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interaction terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental sawtooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.     

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.     

Coupling between hydration layer dynamics and unfolding kinetics of HP-36

We have performed atomistic molecular dynamics simulations of aqueous solutions of HP-36 at 300 K in its native state, as well as at high temperatures to explore the unfolding dynamics of the protein and its correlation with the motion of water around it. On increasing the temperature a partially unfolded molten globule state is formed where the smallest alpha helix (helix 2) unfolds into a coil. It is observed that the unfolding is initiated around the residue Phe-18 which shows a sharp displacement during unfolding. We have noticed that the unfolding of the protein affects the density of water near the protein surface. Besides, the dynamics of water in the protein hydration layer has been found to be strongly correlated with the time evolution of the unfolding process. We have introduced and calculated a displacement time correlation function to monitor the change in water motion relative to the protein backbone during unfolding. We find that the unfolding of helix 2 is associated with an increase in mobility of water around it as compared to water around the other two helices. We have also explored the microscopic aspects of secondary structure specific and site specific solvation dynamics of the protein. The calculations reveal that unfolding influences the solvation dynamics of the protein molecule in a heterogeneous manner depending on the location of the polar probe residues. This seems to be in agreement with recent experimental findings.