Sub-angstrom conformational changes of a single molecule captured by AFM variance analysis

Molecular Fluctuations as a Ruler of Force-Induced Protein Conformations

Molecular fluctuations directly reflect the underlying energy landscape. Variance analysis examines protein dynamics in several biochemistry-driven approaches, yet measurement of probe-independent fluctuations in proteins exposed to mechanical forces remains only accessible through steered molecular dynamics simulations. Using single molecule magnetic tweezers, here we conduct variance analysis to show that individual unfolding and refolding transitions occurring in dynamic equilibrium in a single protein under force are hallmarked by a change in the protein's end-to-end fluctuations, revealing a change in protein stiffness. By unfolding and refolding three structurally distinct proteins under a wide range of constant forces, we demonstrate that the associated change in protein compliance to reach force-induced thermodynamically stable states scales with the protein's contour length increment, in agreement with the sequence-independent freely jointed chain model of polymer physics. Our findings will help elucidate the conformational dynamics of proteins exposed to mechanical force at high resolution which are of central importance in mechanosensing and mechanotransduction.

Non-equilibrium cytoquake dynamics in cytoskeletal remodeling and stabilization

The cytoskeleton (CSK) is a tensed fiber framework that supports, shapes and stabilizes the cell. The CSK is in a constant state of remodeling, moreover, which is an active non-equilibrium thermodynamic process. We report here that cytoskeletal remodeling involves reconfigurations that are not only sudden but also are transmitted to great distances within the cell in a fashion reminiscent of quakes in the Earth's crust. Remarkably, these events in the cell conform both qualitatively and quantitatively to empirical laws typical of earthquakes, including hierarchical fault structures, cumulative energy distributions following the Gutenberg-Richter law, and rate of after-shocks following Omori's law. While it is well-established that remodeling and stabilization of the cytoskeleton are non-equilibrium process, these new unanticipated observations establish that these processes are also remarkably non-local and strongly cooperative.

Data-driven techniques for detecting dynamical state changes in noisily measured 3D single-molecule trajectories

Optical microscopes and nanoscale probes (AFM, optical tweezers, etc.) afford researchers tools capable of quantitatively exploring how molecules interact with one another in live cells. The analysis of in vivo single-molecule experimental data faces numerous challenges due to the complex, crowded, and time changing environments associated with live cells. Fluctuations and spatially varying systematic forces experienced by molecules change over time; these changes are obscured by "measurement noise" introduced by the experimental probe monitoring the system. In this article, we demonstrate how the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS) of Fox et al. [IEEE Transactions on Signal Processing 59] can be used to detect both subtle and abrupt state changes in time series containing "thermal" and "measurement" noise. The approach accounts for temporal dependencies induced by random and "systematic overdamped" forces. The technique does not require one to subjectively select the number of "hidden states" underlying a trajectory in an a priori fashion. The number of hidden states is simultaneously inferred along with change points and parameters characterizing molecular motion in a data-driven fashion. We use large scale simulations to study and compare the new approach to state-of-the-art Hidden Markov Modeling techniques. Simulations mimicking single particle tracking (SPT) experiments are the focus of this study.

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.

Mechanochemistry: one bond at a time

Single-molecule force-clamp spectroscopy offers a novel platform for mechanically denaturing proteins by applying a constant force to a polyprotein. A powerful emerging application of the technique is that, by introducing a disulfide bond in each protein module, the chemical kinetics of disulfide bond cleavage under different stretching forces can be probed at the single-bond level. Even at forces much lower than that which can rupture the chemical bond, the breaking of the S-S bond at the presence of various chemical reducing agents is significantly accelerated. Our previous work demonstrated that the rate of thiol/disulfide exchange reaction is force-dependent and well-described by an Arrhenius term of the form r = A(exp((FΔx(r) - E(a))/k(B)T)[nucleophile]). From Arrhenius fits to the force dependency of the reduction rate, we measured the bond elongation parameter, Δx(r), along the reaction coordinate to the transition state of the S(N)2 reaction cleaved by different nucleophiles and enzymes, never before observed by any other technique. For S-S cleavage by various reducing agents, obtaining the Δx(r) value can help depicting the energy landscapes and elucidating the mechanisms of the reactions at the single-molecule level. Small nucleophiles, such as 1,4-dl-dithiothreitol (DTT), tris(2-carboxyethyl)phosphine (TCEP), and l-cysteine, react with the S-S bond with monotonically increasing rates under the applied force, while thioredoxin enzymes exhibit both stretching-favored and -resistant reaction-rate regimes. These measurements demonstrate the power of the single-molecule force-clamp spectroscopy approach in providing unprecedented access to chemical reactions.

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.

Quantifying DNA melting transitions using single-molecule force spectroscopy

We stretched a DNA molecule using atomic force microscope and quantified the mechanical properties associated with B and S forms of double-stranded DNA (dsDNA), molten DNA, and single-stranded DNA (ssDNA). We also fit overdamped diffusion models to the AFM time series and used these models to extract additional kinetic information about the system. Our analysis provides additional evidence supporting the view that S-DNA is a stable intermediate encountered during dsDNA melting by mechanical force. In addition, we demonstrated that the estimated diffusion models can detect dynamical signatures of conformational degrees of freedom not directly observed in experiments.

Quantifying multiscale noise sources in single-molecule time series

When analyzing single-molecule data, a low-dimensional set of system observables typically serves as the observational data. We calibrate stochastic dynamical models from time series that record such observables. Numerical techniques for quantifying noise from multiple time scales in a single trajectory, including experimental instrument and inherent thermal noise, are demonstrated. The techniques are applied to study time series coming from both simulations and experiments associated with the nonequilibrium mechanical unfolding of titin's I27 domain. The estimated models can be used for several purposes, (1) detect dynamical signatures of "rare events" by analyzing the effective diffusion and force as a function of the monitored observable, (2) quantify the influence that conformational degrees of freedom, which are typically difficult to directly monitor experimentally, have on the dynamics of the monitored observable, (3) quantitatively compare the inherent thermal noise to other noise sources, for example, instrument noise, variation induced by conformational heterogeneity, and so forth, (4) simulate random quantities associated with repeated experiments, and (5) apply pathwise, that is, trajectory-wise, hypothesis tests to assess the goodness-of-fit of the models and even detect conformational transitions in noisy signals. These items are all illustrated with several examples.

Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models

Low-dimensional stochastic models can summarize dynamical information and make long time predictions associated with observables of complex atomistic systems. Maximum likelihood based techniques for estimating low-dimensional surrogate diffusion models from relatively short time series are presented. It is found that a heterogeneous population of slowly evolving conformational degrees of freedom modulates the dynamics. This underlying heterogeneity results in a collection of estimated low-dimensional diffusion models. Numerical techniques for exploiting this finding to approximate skewed histograms associated with the simulation are presented. In addition, statistical tests are also used to assess the validity of the models and determine physically relevant sampling information, e.g. the maximum sampling frequency at which one can discretely sample from an atomistic time series and have a surrogate diffusion model pass goodness-of-fit tests. The information extracted from such analyses can possibly be used to assist umbrella sampling computations as well as help in approximating effective diffusion coefficients. The techniques are demonstrated on simulations of Adenylate Kinase.

A fluorescence energy transfer-based mechanical stress sensor for specific proteins in situ

To measure mechanical stress in real time, we designed a fluorescence resonance energy transfer (FRET) cassette, denoted stFRET, which could be inserted into structural protein hosts. The probe was composed of a green fluorescence protein pair, Cerulean and Venus, linked with a stable alpha-helix. We measured the FRET efficiency of the free cassette protein as a function of the length of the linker, the angles of the fluorophores, temperature and urea denaturation, and protease treatment. The linking helix was stable to 80 degrees C, unfolded in 8 m urea, and rapidly digested by proteases, but in all cases the fluorophores were unaffected. We modified the alpha-helix linker by adding and subtracting residues to vary the angles and distance between the donor and acceptor, and assuming that the cassette was a rigid body, we calculated its geometry. We tested the strain sensitivity of stFRET by linking both ends to a rubber sheet subjected to equibiaxial stretch. FRET decreased proportionally to the substrate strain. The naked cassette expressed well in human embryonic kidney-293 cells and, surprisingly, was concentrated in the nucleus. However, when the cassette was located into host proteins such alpha-actinin, nonerythrocyte spectrin and filamin A, the labeled hosts expressed well and distributed normally in cell lines such as 3T3, where they were stressed at the leading edge of migrating cells and relaxed at the trailing edge. When collagen-19 was labeled near its middle with stFRET, it expressed well in Caenorhabditis elegans, distributing similarly to hosts labeled with a terminal green fluorescent protein, and the worms behaved normally.

Conformational equilibria in monomeric alpha-synuclein at the single-molecule level

Human α-Synuclein (αSyn) is a natively unfolded protein whose aggregation into amyloid fibrils is involved in the pathology of Parkinson disease. A full comprehension of the structure and dynamics of early intermediates leading to the aggregated states is an unsolved problem of essential importance to researchers attempting to decipher the molecular mechanisms of αSyn aggregation and formation of fibrils. Traditional bulk techniques used so far to solve this problem point to a direct correlation between αSyn's unique conformational properties and its propensity to aggregate, but these techniques can only provide ensemble-averaged information for monomers and oligomers alike. They therefore cannot characterize the full complexity of the conformational equilibria that trigger the aggregation process. We applied atomic force microscopy–based single-molecule mechanical unfolding methodology to study the conformational equilibrium of human wild-type and mutant αSyn. The conformational heterogeneity of monomeric αSyn was characterized at the single-molecule level. Three main classes of conformations, including disordered and “β-like” structures, were directly observed and quantified without any interference from oligomeric soluble forms. The relative abundance of the “β-like” structures significantly increased in different conditions promoting the aggregation of αSyn: the presence of Cu²⁺, the pathogenic A30P mutation, and high ionic strength. This methodology can explore the full conformational space of a protein at the single-molecule level, detecting even poorly populated conformers and measuring their distribution in a variety of biologically important conditions. To the best of our knowledge, we present for the first time evidence of a conformational equilibrium that controls the population of a specific class of monomeric αSyn conformers, positively correlated with conditions known to promote the formation of aggregates. A new tool is thus made available to test directly the influence of mutations and pharmacological strategies on the conformational equilibrium of monomeric αSyn.

Natively unstructured proteins defy the classical “one sequence–one structure” paradigm of protein science. In pathological conditions, monomers of these proteins can aggregate in the cell, a process that underlies neurodegenerative diseases such as Alzheimer and Parkinson. A key step in the aggregation process—the formation of misfolded intermediates—remains obscure. To shed light on this process, we characterized the folding and conformational diversity of αSyn, a natively unstructured protein involved in Parkinson disease, by mechanically stretching single molecules of this protein and recording their mechanical properties. These experiments permitted us to observe directly and quantify three main classes of conformations that, under in vitro physiological conditions, exist simultaneously in the αSyn sample. We found that one class of conformations, “β-like” structures, is directly related to αSyn aggregation. In fact, their relative abundance increases drastically in three different conditions known to promote the formation of αSyn fibrils. We expect that a critical concentration of αSyn with a “β-like” structure must be reached to trigger fibril formation. This critical concentration is therefore controlled by a chemical equilibrium. Novel pharmacological strategies can now be tailored to act upstream, before the aggregation process ensues, by targeting this equilibrium. To this end, single-molecule force spectroscopy can be an effective tool to tailor and test new pharmacological agents.

A single-molecule study detects structured and unstructured conformers in equilibrium in monomeric α-synuclein. The β-like conformers increase with pathological mutations and under other conditions known to promote aggregation.

Single-molecule biophysics: at the interface of biology, physics and chemistry

Single-molecule methods have matured into powerful and popular tools to probe the complex behaviour of biological molecules, due to their unique abilities to probe molecular structure, dynamics and function, unhindered by the averaging inherent in ensemble experiments. This review presents an overview of the burgeoning field of single-molecule biophysics, discussing key highlights and selected examples from its genesis to our projections for its future. Following brief introductions to a few popular single-molecule fluorescence and manipulation methods, we discuss novel insights gained from single-molecule studies in key biological areas ranging from biological folding to experiments performed in vivo.

Dynamics of single-molecule force-ramp experiments: The role of fluctuations

In the force-ramp mode of the atomic force microscope, the force with which a macromolecule is stretched is increased linearly in time by properly controlling the motion of the cantilever through a feedback loop. Using a master equation approach for the coupled cantilever-macromolecule system, we mimic such a feedback loop, to study nonequilibrium effects in the measurements of force-extension curves and fluctuations. In particular, it is shown that the fluctuations are the same for force-ramp experiments and for the more commonly used constant velocity experiments. Thus the exact same statistics suffice for the explanation of either experiment. Specific results are presented for the stretching of Dextran.

Interrogation of Single Synthetic Polymer Chains and Polysaccharides by AFM-Based Force Spectroscopy

This contribution reviews selected mechanical experiments on individual flexible macromolecules using single-molecule force spectroscopy (SMFS) based on atomic force microscopy. Focus is placed on the analysis of elasticity and conformational changes in single polymer chains upon variation of the external environment, as well as on conformational changes induced by the mechanical stress applied to individual macromolecular chains. Various experimental strategies regarding single-molecule manipulation and SMFS testing are discussed, as is theoretical analysis through single-chain elasticity models derived from statistical mechanics. Moreover, a complete record, reported to date, of the parameters obtained when applying the models to fit experimental results on synthetic polymers and polysaccharides is presented.

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.

Conformational transitions in single polymer molecules modeled with a complete energy landscape: continuous two-state model

An extension of the two-state Freely Jointed Chain model is presented in which the discrete energies of the two conformers are replaced by continuous functions of the conformer length. The statistical mechanics is initially developed in the Gibbs ensemble and leads to a conformational multi-state model. This is used to fit the equilibrium force-extension curve for Dextran. The continuous model also allows the use of Transfer Matrix methods to calculate all statistical properties in the Helmholtz ensemble, including thermal fluctuations. The latter are obtained with near perfect agreement to experiment.

Direct measurement of the full, sequence-dependent folding landscape of a nucleic acid

Nucleic acid hairpins provide a powerful model system for understanding macromolecular folding, with free-energy landscapes that can be readily manipulated by changing the hairpin sequence. The full shapes of energy landscapes for the reversible folding of DNA hairpins under controlled loads exerted by an optical force clamp were obtained by deconvolution from high-resolution, single-molecule trajectories. The locations and heights of the energy barriers for hairpin folding could be tuned by adjusting the number and location of G:C base pairs, and the presence and position of folding intermediates were controlled by introducing single-nucleotide mismatches.

Simulating force-induced conformational transitions in polysaccharides with the SMD replica exchange method

Conventional steered molecular dynamics (SMD) simulations do not readily reproduce equilibrium conditions of atomic force microscopy (AFM) stretch and release measurements of polysaccharides undergoing force-induced conformational transitions because of the gap between the timescales of computer simulations ( approximately 1 mus) and AFM measurements ( approximately 1 s). To circumvent this limitation, we propose using the replica exchange method (REM) to enhance sampling during SMD simulations. By applying REM SMD to a small polysaccharide system and comparing the results with those from AFM stretching experiments, we demonstrate that REM SMD reproduces the experimental results not only qualitatively but quantitatively, approaching near equilibrium conditions of AFM measurements. As tested in this work, hysteresis and computational time of REM SMD simulations of short polysaccharide chains are significantly reduced as compared to regular SMD simulations, making REM SMD an attractive tool for studying forced-induced conformational transitions of small biopolymer systems.