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 effects of macromolecular crowding on the mechanical stability of protein molecules

Macromolecular crowding, a common phenomenon in the cellular environments, can significantly affect the thermodynamic and kinetic properties of proteins. A single-molecule method based on atomic force microscopy (AFM) was used to investigate the effects of macromolecular crowding on the forces required to unfold individual protein molecules. It was found that the mechanical stability of ubiquitin molecules was enhanced by macromolecular crowding from added dextran molecules. The average unfolding force increased from 210 pN in the absence of dextran to 234 pN in the presence of 300 g/L dextran at a pulling speed of 0.25 microm/sec. A theoretical model, accounting for the effects of macromolecular crowding on the native and transition states of the protein molecule by applying the scaled-particle theory, was used to quantitatively explain the crowding-induced increase in the unfolding force. The experimental results and interpretation presented could have wide implications for the many proteins that experience mechanical stresses and perform mechanical functions in the crowded environment of the cell.     

Mechanical anisotropy of ankyrin repeats

Red blood cells are frequently deformed and their cytoskeletal proteins such as spectrin and ankyrin-R are repeatedly subjected to mechanical forces. While the mechanics of spectrin was thoroughly investigated in vitro and in vivo, little is known about the mechanical behavior of ankyrin-R. In this study, we combine coarse-grained steered molecular dynamics simulations and atomic force spectroscopy to examine the mechanical response of ankyrin repeats (ARs) in a model synthetic AR protein NI6C, and in the D34 fragment of native ankyrin-R when these proteins are subjected to various stretching geometry conditions. Our steered molecular dynamics results, supported by AFM measurements, reveal an unusual mechanical anisotropy of ARs: their mechanical stability is greater when their unfolding is forced to propagate from the N-terminus toward the C-terminus (repeats unfold at ~60 pN), as compared to the unfolding in the opposite direction (unfolding force ～ 30 pN). This anisotropy is also reflected in the complex refolding behavior of ARs. The origin of this unfolding and refolding anisotropy is in the various numbers of native contacts that are broken and formed at the interfaces between neighboring repeats depending on the unfolding/refolding propagation directions. Finally, we discuss how these complex mechanical properties of ARs in D34 may affect its behavior in vivo.     

The mechanical unfolding of ubiquitin through all-atom Monte Carlo simulation with a Go-type potential

The mechanical unfolding of proteins under a stretching force has an important role in living systems and is a logical extension of the more general protein folding problem. Recent advances in experimental methodology have allowed the stretching of single molecules, thus rendering this process ripe for computational study. We use all-atom Monte Carlo simulation with a Gō-type potential to study the mechanical unfolding pathway of ubiquitin. A detailed, robust, well-defined pathway is found, confirming existing results in this vein though using a different model. Additionally, we identify the protein's fundamental stabilizing secondary structure interactions in the presence of a stretching force and show that this fundamental stabilizing role does not persist in the absence of mechanical stress. The apparent success of simulation methods in studying ubiquitin's mechanical unfolding pathway indicates their potential usefulness for future study of the stretching of other proteins and the relationship between protein structure and the response to mechanical deformation.     

Mechanical unfolding of single filamin A (ABP-280) molecules detected by atomic force microscopy

Filamin A (ABP-280), which is an actin-binding protein of 560 kDa as a dimer, can, together with actin filaments, produce an isotropic cross-linked three-dimensional network (actin/filamin A gel) that plays an important role in mechanical responses of cells in processes such as maintenance of membrane stability and translational locomotion. In this study, we investigated the mechanical properties of single filamin A molecules using atomic force microscopy. In force-extension curves, we observed sawtooth patterns corresponding to the unfolding of individual immunoglobulin (Ig)-fold domains of filamin A. At a pulling speed of 0.37 microm/s, the unfolding interval was sharply distributed around 30 nm, while the unfolding force ranged from 50 to 220 pN. This wide distribution of the unfolding force can be explained by variation in values of activation energy and the width of activation barrier of 24 Ig-fold domains of the filamin A at the unfolding transition. This unfolding can endow filamin A with great extensibility. The refolding of the unfolded chain of filamin A occurred when the force applied to the protein was reduced to near zero, indicating that its unfolding is reversible. Based on these results, we discuss here the physiological implications of the mechanical properties of single filamin A molecules.     

Periodic Forces Trigger a Complex Mechanical Response in Ubiquitin

Mechanical forces govern physiological processes in all living organisms. Many cellular forces, for example, those generated in cyclic conformational changes of biological machines, have repetitive components. In apparent contrast, little is known about how dynamic protein structures respond to periodic mechanical information. Ubiquitin is a small protein found in all eukaryotes. We developed molecular dynamics simulations to unfold single and multimeric ubiquitins with periodic forces. By using a coarse-grained representation, we were able to model forces with periods about 2 orders of magnitude longer than the protein's relaxation time. We found that even a moderate periodic force weakened the protein and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. A complex dynamic response with secondary structure refolding and an increasing importance of local interactions was revealed. Importantly, repetitive forces with broadly distributed frequencies elicited very similar molecular responses compared to fixed-frequency forces. When testing the influence of pulling geometry on ubiquitin's mechanical stability, it was found that the linkage involved in the mechanical degradation of cellular proteins renders the protein remarkably insensitive to periodic forces. We also devised a complementary kinetic energy landscape model that traces these observations and explains periodic-force, single-molecule measurements. In turn, this analytical model is capable of predicting dynamic protein responses. These results provide new insights into ubiquitin mechanics and a potential mechanical role during protein degradation, as well as first frameworks for dynamic protein stability and the modeling of repetitive mechanical processes.     

Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics

During the last 15 years, scientists have developed methods that permit the direct mechanical manipulation of individual molecules. Using this approach, they have begun to investigate the effect of force and torque in chemical and biochemical reactions. These studies span from the study of the mechanical properties of macromolecules, to the characterization of molecular motors, to the mechanical unfolding of individual proteins and RNA. Here I present a review of some of our most recent results using mechanical force to unfold individual molecules of RNA. These studies make it possible to follow in real time the trajectory of each molecule as it unfolds and characterize the various intermediates of the reaction. Moreover, if the process takes place reversibly it is possible to extract both kinetic and thermodynamic information from these experiments at the same time that we characterize the forces that maintain the three-dimensional structure of the molecule in solution. These studies bring us closer to the biological unfolding processes in the cell as they simulate in vitro, the mechanical unfolding of RNAs carried out in the cell by helicases. If the unfolding process occurs irreversibly, I show here that single-molecule experiments can still provide equilibrium, thermodynamic information from non-equilibrium data by using recently discovered fluctuation theorems. Such theorems represent a bridge between equilibrium and non-equilibrium statistical mechanics. In fact, first derived in 1997, the first experimental demonstration of the validity of fluctuation theorems was obtained by unfolding mechanically a single molecule of RNA. It is perhaps a sign of the times that important physical results are these days used to extract information about biological systems and that biological systems are being used to test and confirm fundamental new laws in physics.     

Nanomechanical Properties of Tenascin-X Revealed by Single-Molecule Force Spectroscopy

Tenascin-X is an extracellular matrix protein and binds a variety of molecules in extracellular matrix and on cell membrane. Tenascin-X plays important roles in regulating the structure and mechanical properties of connective tissues. Using single-molecule atomic force microscopy, we have investigated the mechanical properties of bovine tenascin-X in detail. Our results indicated that tenascin-X is an elastic protein and the fibronectin type III (FnIII) domains can unfold under a stretching force and refold to regain their mechanical stability upon the removal of the stretching force. All the 30 FnIII domains of tenascin-X show similar mechanical stability, mechanical unfolding kinetics, and contour length increment upon domain unfolding, despite their large sequence diversity. In contrast to the homogeneity in their mechanical unfolding behaviors, FnIII domains fold at different rates. Using the 10th FnIII domain of tenascin-X (TNXfn10) as a model system, we constructed a polyprotein chimera composed of alternating TNXfn10 and GB1 domains and used atomic force microscopy to confirm that the mechanical properties of TNXfn10 are consistent with those of the FnIII domains of tenascin-X. These results lay the foundation to further study the mechanical properties of individual FnIII domains and establish the relationship between point mutations and mechanical phenotypic effect on tenascin-X. Moreover, our results provided the opportunity to compare the mechanical properties and design of different forms of tenascins. The comparison between tenascin-X and tenascin-C revealed interesting common as well as distinguishing features for mechanical unfolding and folding of tenascin-C and tenascin-X and will open up new avenues to investigate the mechanical functions and architectural design of different forms of tenascins.     

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.     

An Improved Strategy for Generating Forces in Steered Molecular Dynamics: The Mechanical Unfolding of Titin,e2lip3 and Ubiquitin

One of the applications of Molecular Dynamics (MD) simulations is to explore the energetic barriers to mechanical unfolding of proteins such as occurs in response to the mechanical pulling of single molecules in Atomic Force Microscopy (AFM) experiments. Although Steered Molecular Dynamics simulations have provided microscopic details of the unfolding process during the pulling, the simulated forces required for unfolding are typically far in excess of the measured values. To rectify this, we have developed the Pulsed Unconstrained Fluctuating Forces (PUFF) method, which induces constant-momentum motions by applying forces directly to the instantaneous velocity of selected atoms in a protein system. The driving forces are applied in pulses, which allows the system to relax between pulses, resulting in more accurate unfolding force estimations than in previous methods. In the cases of titin, ubiquitin and e2lip3, the PUFF trajectories produce force fluctuations that agree quantitatively with AFM experiments. Another useful property of PUFF is that simulations get trapped if the target momentum is too low, simplifying the discovery and analysis of unfolding intermediates.     

The study of protein mechanics with the atomic force microscope.

The unfolding and folding of single protein molecules can be studied with an atomic force microscope (AFM). Many proteins with mechanical functions contain multiple, individually folded domains with similar structures. Protein engineering techniques have enabled the construction and expression of recombinant proteins that contain multiple copies of identical domains. Thus, the AFM in combination with protein engineering has enabled the kinetic analysis of the force-induced unfolding and refolding of individual domains as well as the study of the determinants of mechanical stability.     

Tuning the mechanical stability of fibronectin type III modules through sequence variations

Cells can switch the functional states of extracellular matrix proteins by stretching them while exerting mechanical force. Using steered molecular dynamics, we investigated how the mechanical stability of FnIII modules from the cell adhesion protein fibronectin is affected by natural variations in their amino acid sequences. Despite remarkably similar tertiary structures, FnIII modules share low sequence homology. Conversely, the sequence homology for the same FnIII module across multiple species is notably higher, suggesting that sequence variability is functionally significant. Our studies find that the mechanical stability of FnIII modules can be tuned through substitutions of just a few key amino acids by altering access of water molecules to hydrogen bonds that break early in the unfolding pathway. Furthermore, the FnIII hierarchy of mechanical unfolding can be changed by environmental conditions, such as pH for FnIII10, or by forming complexes with other molecules, such as heparin binding to FnIII13.     

Different molecular mechanics displayed by titin's constitutively and differentially expressed tandem Ig segments

Titin is a giant elastic protein responsible for passive force generated by the stretched striated-muscle sarcomere. Passive force develops in titin's extensible region which consists of the PEVK segment in series with tandemly arranged immunoglobulin (Ig)-like domains. Here we studied the mechanics of tandem Ig segments from the differentially spliced (I65-70) and constitutive (I91-98) regions by using an atomic force microscope specialized for stretching single molecules. The mechanical stability of I65-70 domains was found to be different from that of I91-98 domains. In the range of stretch rates studied (0.05-1.00 microm/s) lower average domain unfolding forces for I65-70 were associated with a weaker stretch-rate dependence of the unfolding force, suggesting that the differences in the mechanical stabilities of the segments derive from differences in the zero force unfolding rate (K(0)(u)) and the characteristic distance (location of the barrier) along the unfolding reaction coordinate (DeltaX(u)). No effect of calcium was found on unfolding forces and persistence length of unfolded domains. To explore the structural basis of the differences in mechanical stabilities of the two fragment types, we compared the amino acid sequence of I65-70 domains with that of I91-98 domains and by using homology modeling analyzed how sequence variations may affect folding free energies. Simulations suggest that differences in domain stability are unlikely to be caused by variation in the number of hydrogen bonds between the force-bearing beta-strands at the domain's N- and C-termini. Rather, they may be due to differences in hydrophobic contacts and strand orientations.     

Fluctuations of primary ubiquitin folding intermediates in a force clamp

Folding experiments of single ubiquitin molecules under force clamp using an atomic force microscope revealed a dynamic long-lived intermediate with nanometer scale end-to-end distance fluctuations along an unexpectedly complex folding pathway. To examine the nature of this intermediate at the atomic level as well as the driving forces that give rise to the observed fluctuations, we performed molecular dynamics refolding simulations of unfolded ubiquitin under constant force. After an initial fast collapse, we find a highly dynamic, broad ensemble of conformations with partial and continuously changing secondary structure and side chain interactions. This ensemble resembles a molten-globule-like state, similar in nature to the previously described non-native state of ubiquitin in solution, but stretched by the external force. The scale of the end-to-end distance fluctuations derived from the simulations compares well with experiment. Transient formation of unspecific and metastable hydrophobic clusters along the chain are found to give rise to the observed end-to-end distance fluctuations. These distinct collapses, interpreted as folding attempts, imply an upper limit for the folding attempt frequency of approximately 10 ns. Our results suggest possible relations between force-induced unfolding and temperature or chemically induced denaturation.     

Unraveling proteins: a molecular mechanics study

An internal coordinate molecular mechanics study of unfolding peptide chains by external stretching has been carried out to predict the type of force spectra that may be expected from single-molecule manipulation experiments currently being prepared. Rather than modeling the stretching of a given protein, we have looked at the behavior of simple secondary structure elements (alpha-helix, beta-ribbon, and interacting alpha-helices) to estimate the magnitude of the forces involved in their unfolding or separation and the dependence of these forces on the way pulling is carried out as well as on the length of the structural elements. The results point to a hierarchy of forces covering a surprisingly large range and to important orientational effects in the response to external stress.     

Stability of bacteriorhodopsin alpha-helices and loops analyzed by single-molecule force spectroscopy

The combination of high-resolution atomic force microscopy imaging and single-molecule force spectroscopy allows the identification, selection, and mechanical investigation of individual proteins. In a recent paper we had used this technique to unfold and extract single bacteriorhodopsins (BRs) from native purple membrane patches. We show that subsets of the unfolding spectra can be classified and grouped to reveal detailed insight into the individualism of the unfolding pathways. We have further developed this technique and analysis to report here on the influence of pH effects and local mutations on the stability of individual structural elements of BR against mechanical unfolding. We found that, although the seven transmembrane alpha-helices predominantly unfold in pairs, each of the helices may also unfold individually and in some cases even only partially. Additionally, intermittent states in the unfolding process were found, which are associated with the stretching of the extracellular loops connecting the alpha-helices. This suggests that polypeptide loops potentially act as a barrier to unfolding and contribute significantly to the structural stability of BR. Chemical removal of the Schiff base, the covalent linkage of the photoactive retinal to the helix G, resulted in a predominantly two-step unfolding of this helix. It is concluded that the covalent linkage of the retinal to helix G stabilizes the structure of BR. Trapping mutant D96N in the M state of the proton pumping photocycle did not affect the unfolding barriers of BR.     

Single-Molecule Studies on PolySUMO Proteins Reveal Their Mechanical Flexibility

Proteins with β-sandwich and β-grasp topologies are resistant to mechanical unfolding as shown by single-molecule force spectroscopy studies. Their high mechanical stability has generally been associated with the mechanical clamp geometry present at the termini. However, there is also evidence for the importance of interactions other than the mechanical clamp in providing mechanical stability, which needs to be tested thoroughly. Here, we report the mechanical unfolding properties of ubiquitin-like proteins (SUMO1 and SUMO2) and their comparison with those of ubiquitin. Although ubiquitin and SUMOs have similar size and structural topology, they differ in their sequences and structural contacts, making them ideal candidates to understand the variations in the mechanical stability of a given protein topology. We observe a two-state unfolding pathway for SUMO1 and SUMO2, similar to that of ubiquitin. Nevertheless, the unfolding forces of SUMO1 (∼130 pN) and SUMO2 (∼120 pN) are lower than that of ubiquitin (∼190 pN) at a pulling speed of 400 nm/s, indicating their lower mechanical stability. The mechanical stabilities of SUMO proteins and ubiquitin are well correlated with the number of interresidue contacts present in their structures. From pulling speed-dependent mechanical unfolding experiments and Monte Carlo simulations, we find that the unfolding potential widths of SUMO1 (∼0.51 nm) and SUMO2 (∼0.33 nm) are much larger than that of ubiquitin (∼0.19 nm), indicating that SUMO1 is six times and SUMO2 is three times mechanically more flexible than ubiquitin. These findings might also be important in understanding the functional differences between ubiquitin and SUMOs.     

Characterization of the mechanical unfolding of RNA pseudoknots

The pseudoknot is an important RNA structural element that provides an excellent model system for studying the contributions of tertiary interactions to RNA stability and to folding kinetics. RNA pseudoknots are also of interest because of their key role in the control of ribosomal frameshifting by viral RNAs. Their mechanical properties are directly relevant to their unfolding by ribosomes during translation. We have used optical tweezers to study the kinetics and thermodynamics of mechanical unfolding and refolding of single RNA molecules. Here we describe the unfolding of the frameshifting pseudoknot from infectious bronchitis virus (IBV), three constituent hairpins, and three mutants of the IBV pseudoknot. All four pseudoknots cause −1 programmed ribosomal frameshifting. We have measured the free energies and rates of mechanical unfolding and refolding of the four frameshifting pseudoknots. Our results show that the IBV pseudoknot requires a higher force than its corresponding hairpins to unfold. Furthermore, its rate of unfolding changes little with increasing force, in contrast with the rate of hairpin unfolding. The presence of Mg²⁺ significantly increases the kinetic barriers to unfolding the IBV pseudoknot, but has only a minor effect on the hairpin unfolding. The greater mechanical stability of pseudoknots compared to hairpins, and their kinetic insensitivity to force supports the hypothesis that −1 frameshifting depends on the difficulty of unfolding the mRNA.     

Force-Clamp Analysis Techniques Give Highest Rank to Stretched Exponential Unfolding Kinetics in Ubiquitin

Force-clamp spectroscopy reveals the unfolding and disulfide bond rupture times of single protein molecules as a function of the stretching force, point mutations, and solvent conditions. The statistics of these times reveal whether the protein domains are independent of one another, the mechanical hierarchy in the polyprotein chain, and the functional form of the probability distribution from which they originate. It is therefore important to use robust statistical tests to decipher the correct theoretical model underlying the process. Here, we develop multiple techniques to compare the well-established experimental data set on ubiquitin with existing theoretical models as a case study. We show that robustness against filtering, agreement with a maximum likelihood function that takes into account experimental artifacts, the Kuiper statistic test, and alignment with synthetic data all identify the Weibull or stretched exponential distribution as the best fitting model. Our results are inconsistent with recently proposed models of Gaussian disorder in the energy landscape or noise in the applied force as explanations for the observed nonexponential kinetics. Because the physical model in the fit affects the characteristic unfolding time, these results have important implications on our understanding of the biological function of proteins.     

Mechanical unfolding of human telomere G-quadruplex DNA probed by integrated fluorescence and magnetic tweezers spectroscopy

Single-molecule techniques facilitate analysis of mechanical transitions within nucleic acids and proteins. Here, we describe an integrated fluorescence and magnetic tweezers instrument that permits detection of nanometer-scale DNA structural rearrangements together with the application of a wide range of stretching forces to individual DNA molecules. We have analyzed the force-dependent equilibrium and rate constants for telomere DNA G-quadruplex (GQ) folding and unfolding, and have determined the location of the transition state barrier along the well-defined DNA-stretching reaction coordinate. Our results reveal the mechanical unfolding pathway of the telomere DNA GQ is characterized by a short distance (<1 nm) to the transition state for the unfolding reaction. This mechanical unfolding response reflects a critical contribution of long-range interactions to the global stability of the GQ fold, and suggests that telomere-associated proteins need only disrupt a few base pairs to destabilize GQ structures. Comparison of the GQ unfolded state with a single-stranded polyT DNA revealed the unfolded GQ exhibits a compacted non-native conformation reminiscent of the protein molten globule. We expect the capacity to interrogate macromolecular structural transitions with high spatial resolution under conditions of low forces will have broad application in analyses of nucleic acid and protein folding.