Determining Intrachain Diffusion Coefficients for Biopolymer Dynamics from Single-Molecule Force Spectroscopy Measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.     

Probing Position-Dependent Diffusion in Folding Reactions Using Single-Molecule Force Spectroscopy

Folding of proteins and nucleic acids involves a diffusive search over a multidimensional conformational energy landscape for the minimal-energy structure. When examining the projection of conformational motions onto a one-dimensional reaction coordinate, as done in most experiments, the diffusion coefficient D is generally position dependent. However, it has proven challenging to measure such position-dependence experimentally. We investigated the position-dependence of D in the folding of DNA hairpins as a simple model system in two ways: first, by analyzing the round-trip time to return to a given extension in constant-force extension trajectories measured by force spectroscopy, and second, by analyzing the fall time required to reach a given extension in force jump measurements. These methods yielded conflicting results: the fall time implied a fairly constant D, but the round-trip time implied variations of over an order of magnitude. Comparison of experiments with computational simulations revealed that both methods were strongly affected by experimental artifacts inherent to force spectroscopy measurements, which obscured the intrinsic position-dependence of D. Lastly, we applied Kramers’s theory to the kinetics of hairpins with energy barriers located at different positions along the hairpin stem, as a crude probe of D at different stem positions, and we found that D did not vary much as the barrier was moved along the reaction coordinate. This work underlines the difficulties faced when trying to deduce position-dependent diffusion coefficients from experimental folding trajectories.     

Single-Molecule Force Spectroscopy of Protein Folding

The use of force probes to induce unfolding and refolding of single molecules through the application of mechanical tension, known as single-molecule force spectroscopy (SMFS), has proven to be a powerful tool for studying the dynamics of protein folding. Here we provide an overview of what has been learned about protein folding using SMFS, from small, single-domain proteins to large, multi-domain proteins. We highlight the ability of SMFS to measure the energy landscapes underlying folding, to map complex pathways for native and non-native folding, to probe the mechanisms of chaperones that assist with native folding, to elucidate the effects of the ribosome on co-translational folding, and to monitor the folding of membrane proteins.     

Single-Molecule Force Spectroscopy of Membrane Protein Folding

Single-molecule force spectroscopy is a unique method that can probe the structural changes of single proteins at a high spatiotemporal resolution while mechanically manipulating them over a wide force range. Here, we review the current understanding of membrane protein folding learned by using the force spectroscopy approach. Membrane protein folding in lipid bilayers is one of the most complex biological processes in which diverse lipid molecules and chaperone proteins are intricately involved. The approach of single protein forced unfolding in lipid bilayers has produced important findings and insights into membrane protein folding. This review provides an overview of the forced unfolding approach, including recent achievements and technical advances. Progress in the methods can reveal more interesting cases of membrane protein folding and clarify general mechanisms and principles.     

Multimodal Measurements of Single-Molecule Dynamics Using FluoRBT

Single-molecule methods provide direct measurements of macromolecular dynamics, but are limited by the number of degrees of freedom that can be followed at one time. High-resolution rotor bead tracking (RBT) measures DNA torque, twist, and extension, and can be used to characterize the structural dynamics of DNA and diverse nucleoprotein complexes. Here, we extend RBT to enable simultaneous monitoring of additional degrees of freedom. Fluorescence-RBT (FluoRBT) combines magnetic tweezers, infrared evanescent scattering, and single-molecule FRET imaging, providing real-time multiparameter measurements of complex molecular processes. We demonstrate the capabilities of FluoRBT by conducting simultaneous measurements of extension and FRET during opening and closing of a DNA hairpin under tension, and by observing simultaneous changes in FRET and torque during a transition between right-handed B-form and left-handed Z-form DNA under controlled supercoiling. We discover unanticipated continuous changes in FRET with applied torque, and also show how FluoRBT can facilitate high-resolution FRET measurements of molecular states, by using a mechanical signal as an independent temporal reference for aligning and averaging noisy fluorescence data. By combining mechanical measurements of global DNA deformations with FRET measurements of local conformational changes, FluoRBT will enable multidimensional investigations of systems ranging from DNA structures to large macromolecular machines.     

Association Kinetics from Single Molecule Force Spectroscopy Measurements

Single molecule force spectroscopy is often used to study the dissociation of single molecules by applying mechanical force to the intermolecular bond. These measurements provide the kinetic parameters of dissociation. We present what to our knowledge is a new atomic force microscopy-based approach to obtain the activation energy of the association reaction and approximate grafting density of reactive receptors using the dependence of the probability to form molecular bonds on probe velocity when one of the interacting molecules is tethered by a flexible polymeric linker to the atomic force microscopy probe. Possible errors in the activation energy measured with this approach are considered and resulting corrections are included in the data analysis. This new approach uses the same experimental setup as traditional force spectroscopy measurements that quantify dissociation kinetics. We apply the developed methodology to measure the activation energy of biotin-streptavidin association (including a contribution from the steric factor) and obtain a value of 8 ± 1 kT. This value is consistent with the association rate measured previously in solution. Comparison with the solution-derived activation energy indicates that kinetics of biotin-streptavidin binding is mainly controlled by the reaction step.     

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.     

Studies of Ribosomal Diffusion Coefficients Using Laser Light-Scattering Spectroscopy

Using an optical beating technique, the diffusion coefficients and relative scattered intensity of Escherichia coli 70S, 50S, and 30S ribosomes are measured as a function of temperature and Mg²⁺ concentration. For solutions at 10 mM Mg²⁺ and between 0°C and about 40°C, the values of D_20,w obtained are 1.7, 1.9, and ≈2.1 × 10^-7 cm²/s, respectively. Preparative procedures drastically affect these values and equivalent hydrodynamic ellipsoids of revolution models give large axial ratios indicating extensive hydration or a deviation from the assumed shape. Calculations also indicate that the subunits expand upon dissociation. Measurements of D_20,w vs. temperature indicate that 70S particles undergo a conformational change prior to dissociation and can be heat dissociated at 30-32°C at low concentrations. Treatment of 70S ribosomes with EDTA causes a biphasic dissociation reaction. Addition of Mg²⁺ after dissociation with EDTA shows that longer waiting times yield fewer 70S particles and that even short waiting times may yield ribosomes differing from the native conformation. Addition of p-chloromercuribenzoic acid (PCMB) is shown to dissociate 70S particles, but to a lesser extent than ethylenediaminetetraacetic acid (EDTA).     

Mechanical Unfolding of Acylphosphatase Studied by Single-Molecule Force Spectroscopy and MD Simulations

Single-molecule manipulation methods provide a powerful means to study protein transitions. Here we combined single-molecule force spectroscopy and steered molecular-dynamics simulations to study the mechanical properties and unfolding behavior of the small enzyme acylphosphatase (AcP). We find that mechanical unfolding of AcP occurs at relatively low forces in an all-or-none fashion and is decelerated in the presence of a ligand, as observed in solution measurements. The prominent energy barrier for the transition is separated from the native state by a distance that is unusually long for α/β proteins. Unfolding is initiated at the C-terminal strand (β_T) that lies at one edge of the β-sheet of AcP, followed by unraveling of the strand located at the other. The central strand of the sheet and the two helices in the protein unfold last. Ligand binding counteracts unfolding by stabilizing contacts between an arginine residue (Arg-23) and the catalytic loop, as well as with β_T of AcP, which renders the force-bearing units of the protein resistant to force. This stabilizing effect may also account for the decelerated unfolding of ligand-bound AcP in the absence of force.     

Estimation of Solvent Diffusion Coefficients Using Molecular Dynamics Simulations

Abstract

Molecular dynamics simulations have been used to investigate diffusion in two commonly used industrial solvents, toluene and tetrahydrofuran. Several different models for the solvents are compared (flexible vs. rigid, all-atom vs. united atom), and it is found that united atom and all-atom models of the solvents produce very different diffusion coefficients at the experimental density. This disagreement can be explained by the pressure dependence of the diffusion coefficient, which is found to vary in accord with the Chapman-Enskog result for hard spheres. It is recommended that force fields be parametrized carefully to produce reasonable pressures at the experimental densities, or that simulations be carried out at constant pressure, if they are to be used for the purposes of calculating transport coefficients.     

Measuring “Unmeasurable” Folding Kinetics of Proteins by Single-Molecule Force Spectroscopy

Folding and unfolding are fundamental biological processes in cell and are important for the biological functions of proteins. Characterizing the folding and unfolding kinetics of proteins is important for understanding the energetic landscape leading to the active native conformations of these molecules. However, the thermal or chemical-induced unfolding of many proteins is irreversible in vitro, precluding characterization of the folding kinetics of such proteins, just as it is impossible to “un-boil” an egg. Irreversible unfolding often manifests as irreversible aggregation of unfolded polypeptide chains, which typically occurs between denatured protein molecules in response to the exposure of hydrophobic residues to solvent. An example of such a protein where thermal denaturation results in irreversible aggregation is the β-1,4 endoxylanase from Bacillus circulans (BCX). Here, we report the use of single-molecule atomic force microscopy to directly measure the folding kinetics of BCX in vitro. By mechanically unfolding BCX, we essentially allowed only one unfolded molecule to exist in solution at a given time, effectively eliminating the possibility for aggregation. We found that BCX can readily refold back to the native state, allowing us to measure its folding kinetics for the first time. Our results demonstrate that single-molecule force-spectroscopy-based methods can adequately tackle the challenge of “un-boiling eggs”, providing a general methodology to characterize the folding kinetics of many proteins that suffer from irreversible denaturation and thus cannot be characterized using traditional equilibrium methodologies.     

Single-Molecule Force Spectroscopy Study on the Mechanism of RNA Disassembly in Tobacco Mosaic Virus

To explore the disassembly mechanism of tobacco mosaic virus (TMV), a model system for virus study, during infection, we have used single-molecule force spectroscopy to mimic and follow the process of RNA disassembly from the protein coat of TMV by the replisome (molecular motor) in vivo, under different pH and Ca²⁺ concentrations. Dynamic force spectroscopy revealed the unbinding free-energy landscapes as that at pH 4.7 the disassembly process is dominated by one free-energy barrier, whereas at pH 7.0 the process is dominated by one barrier and that there exists a second barrier. The additional free-energy barrier at longer distance has been attributed to the hindrance of disordered loops within the inner channel of TMV, and the biological function of those protein loops was discussed. The combination of pH increase and Ca²⁺ concentration drop could weaken RNA-protein interactions so much that the molecular motor replisome would be able to pull and disassemble the rest of the genetic RNA from the protein coat in vivo. All these facts provide supporting evidence at the single-molecule level, to our knowledge for the first time, for the cotranslational disassembly mechanism during TMV infection under physiological conditions.     

Single-Molecule Force Spectroscopy Study on the Mechanism of RNA Disassembly in Tobacco Mosaic Virus

To explore the disassembly mechanism of tobacco mosaic virus (TMV), a model system for virus study, during infection, we have used single-molecule force spectroscopy to mimic and follow the process of RNA disassembly from the protein coat of TMV by the replisome (molecular motor) in vivo, under different pH and Ca²⁺ concentrations. Dynamic force spectroscopy revealed the unbinding free-energy landscapes as that at pH 4.7 the disassembly process is dominated by one free-energy barrier, whereas at pH 7.0 the process is dominated by one barrier and that there exists a second barrier. The additional free-energy barrier at longer distance has been attributed to the hindrance of disordered loops within the inner channel of TMV, and the biological function of those protein loops was discussed. The combination of pH increase and Ca²⁺ concentration drop could weaken RNA-protein interactions so much that the molecular motor replisome would be able to pull and disassemble the rest of the genetic RNA from the protein coat in vivo. All these facts provide supporting evidence at the single-molecule level, to our knowledge for the first time, for the cotranslational disassembly mechanism during TMV infection under physiological conditions.     

Folding and Domain Interactions of Three Orthologs of Hsp90 Studied by Single-Molecule Force Spectroscopy

1. Download high-res image (112KB)
2. Download full-size image

     

Wi-Fi Live-Streaming Centrifuge Force Microscope for Benchtop Single-Molecule Experiments

The ability to apply controlled forces to individual molecules has been revolutionary in shaping our understanding of biophysics in areas as diverse as dynamic bond strength, biological motor operation, and DNA replication. However, the methodology to perform single-molecule experiments remains relatively inaccessible because of cost and complexity. In 2010, we introduced the centrifuge force microscope (CFM) as a platform for accessible and high-throughput single-molecule experimentation. The CFM consists of a rotating microscope with which prescribed centrifugal forces can be applied to microsphere-tethered biomolecules. In this work, we develop and demonstrate a next-generation Wi-Fi CFM that offers unprecedented ease of use and flexibility in design. The modular CFM unit fits within a standard benchtop centrifuge and connects by Wi-Fi to an external computer for live control and streaming at near gigabit speeds. The use of commercial wireless hardware allows for flexibility in programming and provides a streamlined upgrade path as Wi-Fi technology advances. To facilitate ease of use, detailed build and setup instructions, as well as LabVIEW-based control software and MATLAB-based analysis software, are provided. We demonstrate the instrument’s performance by analysis of force-dependent dissociation of short DNA duplexes of 7, 8, and 9 bp. We showcase the sensitivity of the approach by resolving distinct dissociation kinetic rates for a 7 bp duplex in which one G-C basepair is mutated to an A-T basepair.     

Single-Molecule Force Spectroscopy Measures Structural Changes Induced by Light Activation and Transducer Binding in Sensory Rhodopsin II

Microbial rhodopsins are a family of seven-helical transmembrane proteins containing retinal as chromophore. Sensory rhodopsin II (SRII) triggers two very different responses upon light excitation, depending on the presence or the absence of its cognate transducer HtrII: Whereas light activation of the NpSRII/NpHtrII complex activates a signalling cascade that initiates the photophobic response, NpSRII alone acts as a proton pump.Using single-molecule force spectroscopy, we analysed the stability of NpSRII and its complex with the transducer in the dark and under illumination. By improving force spectroscopic data analysis, we were able to reveal the localisation of occurring forces within the protein chain with a resolution of about six amino acids. Distinct regions in helices G and F were affected differently, depending on the experimental conditions. The results are generally in line with previous data on the molecular stability of NpSRII. Interestingly, new interaction sites were identified upon light activation, whose functional importance is discussed in detail.     

Determination of Interaction Kinetics between the T Cell Receptor and Peptide-Loaded MHC Class II via Single-Molecule Diffusion Measurements

The binding of peptide-loaded major histocompatibility complex (pMHC) to the T cell receptor (TCR) represents the central step in T cell antigen recognition. It proceeds in the cell contact area between a T cell and an antigen-presenting cell termed the immunological synapse. An important and unresolved issue is how T cells discriminate between potentially harmful and harmless antigens. One limitation has been the difficulty to measure interaction parameters directly, that is, as they occur in the immunological synapse. Here we present a single-molecule approach to determine pMHC-TCR interaction kinetics in situ based on diffusion analysis of dye-labeled pMHC. We find synaptic off-rates >10-fold accelerated when compared to the dissociation of purified proteins measured in vitro.     

Simultaneous Characterization of Lateral Lipid and Prothrombin Diffusion Coefficients by Z-Scan Fluorescence Correlation Spectroscopy

A new (to our knowledge) robust approach for the determination of lateral diffusion coefficients of weakly bound proteins is applied for the phosphatidylserine specific membrane interaction of bovine prothrombin. It is shown that z-scan fluorescence correlation spectroscopy in combination with pulsed interleaved dual excitation allows simultaneous monitoring of the lateral diffusion of labeled protein and phospholipids. Moreover, from the dependencies of the particle numbers on the axial sample positions at different protein concentrations phosphatidylserine-dependent equilibrium dissociation constants are derived confirming literature values. Increasing the amount of membrane-bound prothrombin retards the lateral protein and lipid diffusion, indicating coupling of both processes. The lateral diffusion coefficients of labeled lipids are considerably larger than the simultaneously determined lateral diffusion coefficients of prothrombin, which contradicts findings reported for the isolated N-terminus of prothrombin.     

Estimation of Water Diffusion Coefficients in Freeze-Concentrated Matrices of Sugar Solutions Using Molecular Dynamics: Correlation Between Estimated Diffusion Coefficients and Measured Ice-Crystal Recrystallization Rates

The diffusion coefficient of the water component in a freeze-concentrated matrix is a useful parameter for predicting and controlling the recrystallization rate of ice crystals in sugar solutions relevant to frozen desserts. Herein, application of molecular dynamics (MD) for estimating the water diffusion coefficient in a freeze-concentrated matrix of sugar solutions is described. Diffusion coefficients evaluated using MD with the optimized potentials for liquid simulations all atom force field and water models of three types (simple point charge, simple point charge extended, and transferable intermolecular potential-4 point) show a good positive linear relation with measured values, indicating that the MD methods used in this study are useful for predicting differences in water diffusion coefficients in a sugar freeze-concentrated matrix. Furthermore, similarly to measured values, the estimated diffusion coefficients show a good positive correlation with recrystallization rates of ice crystals, which suggests that MD is useful to predict differences in recrystallization rates of ice crystals in frozen sugar solutions.