Optimizing 1-μs-Resolution Single-Molecule Force Spectroscopy on a Commercial Atomic Force Microscope

Quantifying a light-induced energetic change in bacteriorhodopsin by force spectroscopy

Ligand-induced conformational changes are critical to the function of many membrane proteins and arise from numerous intramolecular interactions. In the photocycle of the model membrane protein bacteriorhodopsin (bR), absorption of a photon by retinal triggers a conformational cascade that results in pumping a proton across the cell membrane. While decades of spectroscopy and structural studies have probed this photocycle in intricate detail, changes in intramolecular energetics that underlie protein motions have remained elusive to experimental quantification. Here, we measured these energetics on the millisecond time scale using atomic-force-microscopy-based single-molecule force spectroscopy. Precisely, timed light pulses triggered the bR photocycle while we measured the equilibrium unfolding and refolding of the terminal 8-amino-acid region of bR's G-helix. These dynamics changed when the EF-helix pair moved ~9 Å away from this end of the G helix during the "open" portion of bR's photocycle. In ~60% of the data, we observed abrupt light-induced destabilization of 3.4 ± 0.3 kcal/mol, lasting 38 ± 3 ms. The kinetics and pH-dependence of this destabilization were consistent with prior measurements of bR's open phase. The frequency of light-induced destabilization increased with the duration of illumination and was dramatically reduced in the triple mutant (D96G/F171C/F219L) thought to trap bR in its open phase. In the other ~40% of the data, photoexcitation unexpectedly stabilized a longer-lived putative misfolded state. Through this work, we establish a general single-molecule force spectroscopy approach for measuring ligand-induced energetics and lifetimes in membrane proteins.

Non-contact non-resonant atomic force microscopy method for measurements of highly mobile molecules and nanoparticles

Atomic force microscopy (AFM) is nowadays indispensable versatile scanning probe method widely employed for fundamental and applied research in physics, chemistry, biology as well as industrial metrology. Conventional AFM systems can operate in various environments such as ultra-high vacuum, electrolyte solutions, or controlled gas atmosphere. Measurements in ambient air are prevalent due to their technical simplicity; however, there are drawbacks such as formation of water meniscus that greatly increases attractive interaction (adhesion) between the tip and the sample, reduced spatial resolution, and too strong interactions leading to tip and/or sample modifications. Here we show how the attractive forces in AFM under ambient conditions can be used with advantage to probe surface properties in a very sensitive way even on highly mobile molecules and nanoparticles. We introduce a stable non-contact non-resonant (NCNR) AFM method which enables to reliably perform measurements in the attractive force regime even in air by controlling the tip position in the intimate surface vicinity without touching it. We demonstrate proof-of-concept results on helicene-based macrocycles, DNA on mica, and nanodiamonds on SiO2. We compare the results with other conventional AFM regimes, showing NCNR advantages such as higher spatial resolution, reduced tip contamination, and negligible sample modification. We analyze principle physical and chemical mechanisms influencing the measurements, discuss issues of stability and various possible method implementations. We explain how the NCNR method can be applied in any AFM system by a mere software modification. The method thus opens a new research field for measurements of highly sensitive and mobile nanoscale objects under air and other environments.

Nonlinear effects in optical trapping of titanium dioxide and diamond nanoparticles

Optical trapping in biophysics typically uses micron-scale beads made of materials like polystyrene or glass to probe the target of interest. Using smaller beads made of higher-index materials could increase the time resolution of these measurements. We characterized the trapping of nanoscale beads made of diamond and titanium dioxide (TiO2) in a single-beam gradient trap. Calculating theoretical expectations for the trapping stiffness of these beads, we found good agreement with measured values. Trap stiffness was significantly higher for TiO2 beads, owing to notable enhancement from nonlinear optical effects, not previously observed for continuous-wave trapping. Trap stiffness was over 6-fold higher for TiO2 beads than polystyrene beads of similar size at 70 mW laser power. These results suggest that diamond and TiO2 nanobeads can be used to improve time resolution in optical tweezers measurements.

The role of single protein elasticity in mechanobiology

In addition to biochemical signals and genetic considerations, mechanical forces are rapidly emerging as a master regulator of human physiology. Yet the molecular mechanisms that regulate force-induced functionalities across a wide range of scales, encompassing the cell, tissue or organ levels, are comparatively not so well understood. With the advent, development and refining of single molecule nanomechanical techniques, enabling to exquisitely probe the conformational dynamics of individual proteins under the effect of a calibrated force, we have begun to acquire a comprehensive knowledge on the rich plethora of physicochemical principles that regulate the elasticity of single proteins. Here we review the major advances underpinning our current understanding of how the elasticity of single proteins regulates mechanosensing and mechanotransduction. We discuss the present limitations and future challenges of such a prolific and burgeoning field.

Extract Motive Energy from Single-Molecule Trajectories

Single-molecule trajectories from nonequilibrium unfolding experiments are widely used to recover a biomolecule's intrinsic free-energy profile. Trajectories of molecular motors from similar single-molecule experiments may be mapped to biased diffusion over an inclined free-energy profile. Such an effective potential is not a static equilibrium property anymore, and how it can benefit molecular motor study is unclear. Here, we introduce a method to deduce this effective potential from motor trajectories with realistic temporal-spatial resolution and find that the potential yields a motor's stall force─a quantity that not only characterizes a motor's force-generating capacity but also largely determines its energy efficiency. Interestingly, this potential allows the extraction of a motor's stall force from trajectories recorded at a single resisting force or even zero force, as verified with trajectories from two molecular motor models and also experimental trajectories from a real artificial motor. This finding drastically reduces the difficulty of stall force measurement, making it accessible even to force-incapable optical tracking experiments (commonly regarded as irrelevant to stall force determination). This study further provides a method for experimentally measuring a second-law-decreed least energy price for submicroscopic directionality─a previously elusive but thermodynamically important quantity pertinent to efficient energy conversion of molecular motors.

High-resolution Single-molecule Magnetic Tweezers

Single-molecule magnetic tweezers deliver magnetic force and torque to single target molecules, permitting the study of dynamic changes in biomolecular structures and their interactions. Because the magnetic tweezer setups can generate magnetic fields that vary slowly over tens of millimeters-far larger than the nanometer scale of the single molecule events being observed-this technique can maintain essentially constant force levels during biochemical experiments while generating a biologically meaningful force on the order of 1-100 pN. When using bead-tether constructs to pull on single molecules, smaller magnetic beads and shorter submicrometer tethers improve dynamic response times and measurement precision. In addition, employing high-speed cameras, stronger light sources, and a graphics programming unit permits true high-resolution single-molecule magnetic tweezers that can track nanometer changes in target molecules on a millisecond or even submillisecond time scale. The unique force-clamping capacity of the magnetic tweezer technique provides a way to conduct measurements under near-equilibrium conditions and directly map the energy landscapes underlying various molecular phenomena. High-resolution single-molecule magnetic tweezers can thus be used to monitor crucial conformational changes in single-protein molecules, including those involved in mechanotransduction and protein folding. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Recent Progress on Single-Molecule Detection Technologies for Food Safety

Rapid and sensitive detection technologies for food contaminants play vital roles in food safety. Due to the complexity of the food matrix and the trace amount distribution, traditional methods often suffer from unsatisfying accuracy, sensitivity, or specificity. In past decades, single-molecule detection (SMD) has emerged as a way to realize the rapid and ultrasensitive measurement with low sample consumption, showing a great potential in food contaminants detection. For instance, based on the nanopore technique, simple and effective methods for single-molecule analysis of food contaminants have been developed. To our knowledge, there has been a rare review that focuses on SMD techniques for food safety. The present review attempts to cover some typical SMD methods in food safety, including electrochemistry, optical spectrum, and atom force microscopy. Then, recent applications of these techniques for detecting food contaminants such as biotoxins, pesticides, heavy metals, and illegal additives are reviewed. Finally, existing research challenges and future trends of SMD in food safety are also tentatively proposed.

Atomic force microscopy for quantitative understanding of peptide-induced lipid bilayer remodeling

A number of peptides are known to bind lipid bilayer membranes and cause these natural barriers to leak in an uncontrolled manner. Though membrane permeabilizing peptides play critical roles in cellular activity and may have promising future applications in the therapeutic arena, significant questions remain about their mechanisms of action. The atomic force microscope (AFM) is a single molecule imaging tool capable of addressing lipid bilayers in near-native fluid conditions. The apparatus complements traditional assays by providing local topographic maps of bilayer remodeling induced by membrane permeabilizing peptides. The information garnered from the AFM includes direct visualization and statistical analyses of distinct bilayer remodeling modes such as highly localized pore-like voids in the bilayer and dispersed thinned membrane regions. Colocalization of distinct remodeling modes can be studied. Here we examine recent work in the field and outline methods used to achieve precise AFM image data. Experimental challenges and common pitfalls are discussed as well as techniques for unbiased analysis including the Hessian blob detection algorithm, bootstrapping, and the Bayesian information criterion. When coupled with robust statistical analyses, high precision AFM data is poised to advance understanding of an important family of peptides that cause poration of membrane bilayers.

Angle-dependent strength of a single chemical bond by stereographic force spectroscopy

A wealth of chemical bonds and polymers have been studied with single-molecule force spectroscopy, usually by applying a force perpendicular to the anchoring surface. However, the direction-dependence of the bond strength lacks fundamental understanding. Here we establish stereographic force spectroscopy to study the single-bond strength for various pulling angles. Surprisingly, we find that the apparent bond strength increases with increasing pulling angle relative to the anchoring surface normal, indicating a sturdy mechanical anisotropy of a chemical bond. This finding can be rationalized by a fixed pathway for the rupture of the bond, resulting in an effective projection of the applied pulling force onto a nearly fixed rupture direction. Our study is fundamental for the molecular understanding of the role of the direction of force application in molecular adhesion and friction. It is also a prerequisite for the nanoscale tailoring of the anisotropic strength of bottom-up designed materials.

Stereographic force spectroscopy reveals that a chemical bond ruptures along a fixed pathway such that the apparent bond strength strongly depends on the angle of force application.

Quantifying molecular- to cellular-level forces in living cells

Mechanical cues have been suggested to play an important role in cell functions and cell fate determination, however, such physical quantities are challenging to directly measure in living cells with single molecule sensitivity and resolution. In this review, we focus on two main technologies that are promising in probing forces at the single molecule level. We review their theoretical fundamentals, recent technical advancements, and future directions, tailored specifically for interrogating mechanosensitive molecules in live cells.

Free-energy changes of bacteriorhodopsin point mutants measured by single-molecule force spectroscopy

Single amino acid mutations provide quantitative insight into the energetics that underlie the dynamics and folding of membrane proteins. Chemical denaturation is the most widely used assay and yields the change in unfolding free energy (ΔΔG). It has been applied to >80 different residues of bacteriorhodopsin (bR), a model membrane protein. However, such experiments have several key limitations: 1) a nonnative lipid environment, 2) a denatured state with significant secondary structure, 3) error introduced by extrapolation to zero denaturant, and 4) the requirement of globally reversible refolding. We overcame these limitations by reversibly unfolding local regions of an individual protein with mechanical force using an atomic-force-microscope assay optimized for 2 μs time resolution and 1 pN force stability. In this assay, bR was unfolded from its native bilayer into a well-defined, stretched state. To measure ΔΔG, we introduced two alanine point mutations into an 8-amino-acid region at the C-terminal end of bR's G helix. For each, we reversibly unfolded and refolded this region hundreds of times while the rest of the protein remained folded. Our single-molecule-derived ΔΔG for mutant L223A (-2.3 ± 0.6 kcal/mol) quantitatively agreed with past chemical denaturation results while our ΔΔG for mutant V217A was 2.2-fold larger (-2.4 ± 0.6 kcal/mol). We attribute the latter result, in part, to contact between Val²¹⁷ and a natively bound squalene lipid, highlighting the contribution of membrane protein-lipid contacts not present in chemical denaturation assays. More generally, we established a platform for determining ΔΔG for a fully folded membrane protein embedded in its native bilayer.

Modulation of a protein-folding landscape revealed by AFM-based force spectroscopy notwithstanding instrumental limitations

Single-molecule force spectroscopy is a powerful tool for studying protein folding. Over the last decade, a key question has emerged: how are changes in intrinsic biomolecular dynamics altered by attachment to μm-scale force probes via flexible linkers? Here, we studied the folding/unfolding of α₃D using atomic force microscopy (AFM)-based force spectroscopy. α₃D offers an unusual opportunity as a prior single-molecule fluorescence resonance energy transfer (smFRET) study showed α₃D's configurational diffusion constant within the context of Kramers theory varies with pH. The resulting pH dependence provides a test for AFM-based force spectroscopy's ability to track intrinsic changes in protein folding dynamics. Experimentally, however, α₃D is challenging. It unfolds at low force (<15 pN) and exhibits fast-folding kinetics. We therefore used focused ion beam-modified cantilevers that combine exceptional force precision, stability, and temporal resolution to detect state occupancies as brief as 1 ms. Notably, equilibrium and nonequilibrium force spectroscopy data recapitulated the pH dependence measured using smFRET, despite differences in destabilization mechanism. We reconstructed a one-dimensional free-energy landscape from dynamic data via an inverse Weierstrass transform. At both neutral and low pH, the resulting constant-force landscapes showed minimal differences (∼0.2 to 0.5 k _B T) in transition state height. These landscapes were essentially equal to the predicted entropic barrier and symmetric. In contrast, force-dependent rates showed that the distance to the unfolding transition state increased as pH decreased and thereby contributed to the accelerated kinetics at low pH. More broadly, this precise characterization of a fast-folding, mechanically labile protein enables future AFM-based studies of subtle transitions in mechanoresponsive proteins.

Quantifying the Native Energetics Stabilizing Bacteriorhodopsin by Single-Molecule Force Spectroscopy

We quantified the equilibrium (un)folding free energy ΔG_{0} of an eight-amino-acid region starting from the fully folded state of the model membrane-protein bacteriorhodopsin using single-molecule force spectroscopy. Analysis of equilibrium and nonequilibrium data yielded consistent, high-precision determinations of ΔG_{0} via multiple techniques (force-dependent kinetics, Crooks fluctuation theorem, and inverse Boltzmann analysis). We also deduced the full 1D projection of the free-energy landscape in this region. Importantly, ΔG_{0} was determined in bacteriorhodopsin's native bilayer, an advance over traditional results obtained by chemical denaturation in nonphysiological detergent micelles.

Detailed balance for diffusion in a potential with trapping and forward-backward symmetry of trapping time distributions

For particles diffusing in a potential, detailed balance guarantees the absence of net fluxes at equilibrium. Here, we show that the conventional detailed balance condition is a special case of a more general relation that works when the diffusion occurs in the presence of a distributed sink that eventually traps the particle. We use this relation to study the lifetime distribution of particles that start and are trapped at specified initial and final points. It turns out that when the sink strength at the initial point is nonzero, the initial and final points are interchangeable, i.e., the distribution is independent of which of the two points is initial and which is final. In other words, this conditional trapping time distribution possesses forward–backward symmetry.

From Nonequilibrium Single-Molecule Trajectories to Underlying Dynamics

Single-molecule observations of biomolecular dynamics and folding are commonly rationalized using the model of diffusive dynamics on a free-energy landscape, which is inferred via the Boltzmann inversion of the equilibrium distribution of the experimental observable. Can the same model be applied to high-resolution single-molecule trajectories of molecular machines that lack thermal equilibrium so that the Boltzmann inversion method is inapplicable? In this Letter, we discuss two approaches to reconstructing the underlying free-energy landscape in such nonequilibrium systems and explore the performance of this model in application to trajectories with complex underlying dynamics.

Membrane-Protein Unfolding Intermediates Detected with Enhanced Precision Using a Zigzag Force Ramp

Precise quantification of the energetics and interactions that stabilize membrane proteins in a lipid bilayer is a long-sought goal. Toward this end, atomic force microscopy has been used to unfold individual membrane proteins embedded in their native lipid bilayer, typically by retracting the cantilever at a constant velocity. Recently, unfolding intermediates separated by as few as two amino acids were detected using focused-ion-beam-modified ultrashort cantilevers. However, unambiguously discriminating between such closely spaced states remains challenging, in part because any individual unfolding trajectory only occupies a subset of the total number of intermediates. Moreover, structural assignment of these intermediates via worm-like-chain analysis is hindered by brief dwell times compounded with thermal and instrumental noise. To overcome these issues, we moved the cantilever in a sawtooth pattern of 6-12 nm, offset by 0.25-1 nm per cycle, generating a "zigzag" force ramp of alternating positive and negative loading rates. We applied this protocol to the model membrane protein bacteriorhodopsin (bR). In contrast to conventional studies that extract bR's photoactive retinal along with the first transmembrane helix, we unfolded bR in the presence of its retinal. To do so, we introduced a previously developed enzymatic-cleavage site between helices E and F and pulled from the top of the E helix using a site-specific, covalent attachment. The resulting zigzag unfolding trajectories occupied 40% more states per trajectory and occupied those states for longer times than traditional constant-velocity records. In total, we identified 31 intermediates during the unfolding of five helices of EF-cleaved bR. These included a previously reported, mechanically robust intermediate located between helices C and B that, with our enhanced resolution, is now shown to be two distinct states separated by three amino acids. Interestingly, another intermediate directly interacted with the retinal, an interaction confirmed by removing the retinal.

Memory effects in single-molecule force spectroscopy measurements of biomolecular folding

Folding is generally assumed to be a Markov process, without memory. When the molecular motion is coupled to that of a probe as in single-molecule force spectroscopy (SMFS) experiments, however, theory predicts that the coupling to a second Markov process should induce memory when monitoring a projection of the full multi-dimensional motion onto a reduced coordinate. We developed a method to evaluate the time constant of the induced memory from its effects on the autocorrelation function, which can be readily determined from experimental data. Applying this method to both simulated SMFS measurements and experimental trajectories of DNA hairpin folding measured by optical tweezers as a model system, we validated the prediction that the linker induces memory. For these measurements, the timescale of the induced memory was found to be similar to the time required for the force probe to respond to changes in the molecule, and in the regime where the experimentally observed dynamics were not significantly perturbed by probe-molecule coupling artifacts. Memory effects are thus a general feature of SMFS measurements induced by the mechanical connection between the molecule and force probe that should be considered when interpreting experimental data.

High-speed force spectroscopy: microsecond force measurements using ultrashort cantilevers

Complete understanding of the role of mechanical forces in biological processes requires knowledge of the mechanical properties of individual proteins and living cells. Moreover, the dynamic response of biological systems at the nano- and microscales span over several orders of magnitude in time, from sub-microseconds to several minutes. Thus, access to force measurements over a wide range of length and time scales is required. High-speed atomic force microscopy (HS-AFM) using ultrashort cantilevers has emerged as a tool to study the dynamics of biomolecules and cells at video rates. The adaptation of HS-AFM to perform high-speed force spectroscopy (HS-FS) allows probing protein unfolding and receptor/ligand unbinding up to the velocity of molecular dynamics (MD) simulations with sub-microsecond time resolution. Moreover, application of HS-FS on living cells allows probing the viscoelastic response at short time scales providing deep understanding of cytoskeleton dynamics. In this mini-review, we assess the principles and recent developments and applications of HS-FS using ultrashort cantilevers to probe molecular and cellular mechanics.

Generalized Langevin Equation as a Model for Barrier Crossing Dynamics in Biomolecular Folding

Conformational memory in single-molecule dynamics has attracted recent attention and, in particular, has been invoked as a possible explanation of some of the intriguing properties of transition paths observed in single-molecule force spectroscopy (SMFS) studies. Here we study one candidate for a non-Markovian model that can account for conformational memory, the generalized Langevin equation with a friction force that depends not only on the instantaneous velocity but also on the velocities in the past. The memory in this model is determined by a time-dependent friction memory kernel. We propose a method for extracting this kernel directly from an experimental signal and illustrate its feasibility by applying it to a generalized Rouse model of a SMFS experiment, where the memory kernel is known exactly. Using the same model, we further study how memory affects various statistical properties of transition paths observed in SMFS experiments and evaluate the performance of recent approximate analytical theories of non-Markovian dynamics of barrier crossing. We argue that the same type of analysis can be applied to recent single-molecule observations of transition paths in protein and DNA folding.

Improved free-energy landscape reconstruction of bacteriorhodopsin highlights local variations in unfolding energy

Precisely quantifying the energetics that drive the folding of membrane proteins into a lipid bilayer remains challenging. More than 15 years ago, atomic force microscopy (AFM) emerged as a powerful tool to mechanically extract individual membrane proteins from a lipid bilayer. Concurrently, fluctuation theorems, such as the Jarzynski equality, were applied to deduce equilibrium free energies (ΔG₀) from non-equilibrium single-molecule force spectroscopy records. The combination of these two advances in single-molecule studies deduced the free-energy of the model membrane protein bacteriorhodopsin in its native lipid bilayer. To elucidate this free-energy landscape at a higher resolution, we applied two recent developments. First, as an input to the reconstruction, we used force-extension curves acquired with a 100-fold higher time resolution and 10-fold higher force precision than traditional AFM studies of membrane proteins. Next, by using an inverse Weierstrass transform and the Jarzynski equality, we removed the free energy associated with the force probe and determined the molecular free-energy landscape of the molecule under study, bacteriorhodopsin. The resulting landscape yielded an average unfolding free energy per amino acid (aa) of 1.0 ± 0.1 kcal/mol, in agreement with past single-molecule studies. Moreover, on a smaller spatial scale, this high-resolution landscape also agreed with an equilibrium measurement of a particular three-aa transition in bacteriorhodopsin that yielded 2.7 kcal/mol/aa, an unexpectedly high value. Hence, while average unfolding ΔG₀ per aa is a useful metric, the derived high-resolution landscape details significant local variation from the mean. More generally, we demonstrated that, as anticipated, the inverse Weierstrass transform is an efficient means to reconstruct free-energy landscapes from AFM data.

High-Precision Single-Molecule Characterization of the Folding of an HIV RNA Hairpin by Atomic Force Microscopy

The folding of RNA into a wide range of structures is essential for its diverse biological functions from enzymatic catalysis to ligand binding and gene regulation. The unfolding and refolding of individual RNA molecules can be probed by single-molecule force spectroscopy (SMFS), enabling detailed characterization of the conformational dynamics of the molecule as well as the free-energy landscape underlying folding. Historically, high-precision SMFS studies of RNA have been limited to custom-built optical traps. Although commercial atomic force microscopes (AFMs) are widely deployed and offer significant advantages in ease-of-use over custom-built optical traps, traditional AFM-based SMFS lacks the sensitivity and stability to characterize individual RNA molecules precisely. Here, we developed a high-precision SMFS assay to study RNA folding using a commercial AFM and applied it to characterize a small RNA hairpin from HIV that plays a key role in stimulating programmed ribosomal frameshifting. We achieved rapid data acquisition in a dynamic assay, unfolding and then refolding the same individual hairpin more than 1,100 times in 15 min. In comparison to measurements using optical traps, our AFM-based assay featured a stiffer force probe and a less compliant construct, providing a complementary measurement regime that dramatically accelerated equilibrium folding dynamics. Not only did kinetic analysis of equilibrium trajectories of the HIV RNA hairpin yield the traditional parameters used to characterize folding by SMFS (zero-force rate constants and distances to the transition state), but we also reconstructed the full 1D projection of the folding free-energy landscape comparable to state-of-the-art studies using dual-beam optical traps, a first for this RNA hairpin and AFM studies of nucleic acids in general. Looking forward, we anticipate that the ease-of-use of our high-precision assay implemented on a commercial AFM will accelerate studying folding of diverse nucleic acid structures.

Structural-elastic determination of the force-dependent transition rate of biomolecules

The force-dependent unfolding/refolding of protein domains and ligand-receptor association/dissociation are crucial for mechanosensitive functions, while many aspects of how force affects the transition rate still remain poorly understood. Here, we report a new analytical expression of the force-dependent rate of molecules for transitions overcoming a single barrier. Unlike previous models derived in the framework of Kramers theory that requires a presumed one-dimensional free energy landscape, our model is derived based on the structural-elastic properties of molecules which are not restricted by the shape and dimensionality of the underlying free energy landscape. Importantly, the parameters of this model provide direct information on the structural-elastic features of the molecules between their transition and initial states. We demonstrate the applications of this model by applying it to explain force-dependent transition kinetics for several molecules and predict the structural-elastic properties of the transition states of these molecules.

Communication: Transition-path velocity as an experimental measure of barrier crossing dynamics

Experimental observation of transition paths-short events when the system of interest crosses the free energy barrier separating reactants from products-provides an opportunity to probe the dynamics of barrier crossing. Yet limitations in the experimental time resolution usually result in observing trajectories that are smoothed out, recross the transition state fewer times, and exhibit apparent velocities that are much lower than the instantaneous ones. Here we show that it is possible to define (and measure) an effective transition-path velocity which preserves exact information about barrier crossing dynamics in the following sense: the exact transition rate can be written in a form resembling that given by transition-state theory, with the mean thermal velocity replaced by the transition-path velocity. In addition, the transition-path velocity (i) ensures the exact local value of the unidirectional reactive flux at equilibrium and (ii) leads to the exact mean transition-path time required for the system to cross the barrier region separating reactants from products. We discuss the coordinate dependence of the transition path velocity and derive analytical expressions for it in the case of diffusive dynamics. These results can be used to discriminate among models of barrier crossing dynamics in single-molecule force spectroscopy studies.

Communication: Coordinate-dependent diffusivity from single molecule trajectories

Single-molecule observations of biomolecular folding are commonly interpreted using the model of one-dimensional diffusion along a reaction coordinate, with a coordinate-independent diffusion coefficient. Recent analysis, however, suggests that more general models are required to account for single-molecule measurements performed with high temporal resolution. Here, we consider one such generalization: a model where the diffusion coefficient can be an arbitrary function of the reaction coordinate. Assuming Brownian dynamics along this coordinate, we derive an exact expression for the coordinate-dependent diffusivity in terms of the splitting probability within an arbitrarily chosen interval and the mean transition path time between the interval boundaries. This formula can be used to estimate the effective diffusion coefficient along a reaction coordinate directly from single-molecule trajectories.

Going Vertical To Improve the Accuracy of Atomic Force Microscopy Based Single-Molecule Force Spectroscopy

Single-molecule force spectroscopy (SMFS) is a powerful technique to characterize the energy landscape of individual proteins, the mechanical properties of nucleic acids, and the strength of receptor-ligand interactions. Atomic force microscopy (AFM)-based SMFS benefits from ongoing progress in improving the precision and stability of cantilevers and the AFM itself. Underappreciated is that the accuracy of such AFM studies remains hindered by inadvertently stretching molecules at an angle while measuring only the vertical component of the force and extension, degrading both measurements. This inaccuracy is particularly problematic in AFM studies using double-stranded DNA and RNA due to their large persistence length (p ≈ 50 nm), often limiting such studies to other SMFS platforms (e.g., custom-built optical and magnetic tweezers). Here, we developed an automated algorithm that aligns the AFM tip above the DNA's attachment point to a coverslip. Importantly, this algorithm was performed at low force (10-20 pN) and relatively fast (15-25 s), preserving the connection between the tip and the target molecule. Our data revealed large uncorrected lateral offsets for 100 and 650 nm DNA molecules [24 ± 18 nm (mean ± standard deviation) and 180 ± 110 nm, respectively]. Correcting this offset yielded a 3-fold improvement in accuracy and precision when characterizing DNA's overstretching transition. We also demonstrated high throughput by acquiring 88 geometrically corrected force-extension curves of a single individual 100 nm DNA molecule in ∼40 min and versatility by aligning polyprotein- and PEG-based protein-ligand assays. Importantly, our software-based algorithm was implemented on a commercial AFM, so it can be broadly adopted. More generally, this work illustrates how to enhance AFM-based SMFS by developing more sophisticated data-acquisition protocols.

High-Resolution AFM-Based Force Spectroscopy

Atomic force microscopy (AFM)-based force spectroscopy is a powerful technique which has seen significant enhancements in both force and time resolution in recent years. This chapter details two AFM cantilever modification procedures that yield high force precision over different temporal bandwidths. Specifically, it explains a fairly straightforward method to achieve sub-pN force precision and stability at low frequencies (<50 Hz) by removing the metal coatings from a commercially available cantilever. A more involved procedure utilizing a focused ion beam milling machine is required to maintain high force precision at enhanced bandwidths. Both modification methods allow site-specific attachment of biomolecules onto the apex area of the tips for force spectroscopy. The chapter concludes with a comparative demonstration using the two cantilever modification methods to study a lipid-protein interaction.

High-Speed Force Spectroscopy for Single Protein Unfolding

Single-molecule force spectroscopy (SMFS) measurements allow for quantification of the molecular forces required to unfold individual protein domains. Atomic force microscopy (AFM) is one of the long-established techniques for force spectroscopy (FS). Although FS at conventional AFM pulling rates provides valuable information on protein unfolding, in order to get a more complete picture of the mechanism, explore new regimes, and combine and compare experiments with simulations, we need higher pulling rates and μs-time resolution, now accessible via high-speed force spectroscopy (HS-FS). In this chapter, we provide a step-by-step protocol of HS-FS including sample preparation, measurements and analysis of the acquired data using HS-AFM with an illustrative example on unfolding of a well-studied concatamer made of eight repeats of the titin I91 domain.

Force Spectroscopy with 9-μs Resolution and Sub-pN Stability by Tailoring AFM Cantilever Geometry

Atomic force microscopy (AFM)-based single-molecule force spectroscopy (SMFS) is a powerful yet accessible means to characterize the unfolding/refolding dynamics of individual molecules and resolve closely spaced, transiently occupied folding intermediates. On a modern commercial AFM, these applications and others are now limited by the mechanical properties of the cantilever. Specifically, AFM-based SMFS data quality is degraded by a commercial cantilever's limited combination of temporal resolution, force precision, and force stability. Recently, we modified commercial cantilevers with a focused ion beam to optimize their properties for SMFS. Here, we extend this capability by modifying a 40 × 18 μm² cantilever into one terminated with a gold-coated, 4 × 4 μm² reflective region connected to an uncoated 2-μm-wide central shaft. This "Warhammer" geometry achieved 8.5-μs resolution coupled with improved force precision and sub-pN stability over 100 s when measured on a commercial AFM. We highlighted this cantilever's biological utility by first resolving a calmodulin unfolding intermediate previously undetected by AFM and then measuring the stabilization of calmodulin by myosin light chain kinase at dramatically higher unfolding velocities than in previous AFM studies. More generally, enhancing data quality via an improved combination of time resolution, force precision, and force stability will broadly benefit biological applications of AFM.

Hidden dynamics in the unfolding of individual bacteriorhodopsin proteins

Protein folding occurs as a set of transitions between structural states within an energy landscape. An oversimplified view of the folding process emerges when transiently populated states are undetected because of limited instrumental resolution. Using force spectroscopy optimized for 1-microsecond resolution, we reexamined the unfolding of individual bacteriorhodopsin molecules in native lipid bilayers. The experimental data reveal the unfolding pathway in unprecedented detail. Numerous newly detected intermediates-many separated by as few as two or three amino acids-exhibited complex dynamics, including frequent refolding and state occupancies of <10 μs. Equilibrium measurements between such states enabled the folding free-energy landscape to be deduced. These results sharpen the picture of the mechanical unfolding of membrane proteins and, more broadly, enable experimental access to previously obscured protein dynamics.

Rapid Characterization of a Mechanically Labile α-Helical Protein Enabled by Efficient Site-Specific Bioconjugation

Atomic force microscopy (AFM)-based single-molecule force spectroscopy (SMFS) is a powerful yet accessible means to characterize mechanical properties of biomolecules. Historically, accessibility relies upon the nonspecific adhesion of biomolecules to a surface and a cantilever and, for proteins, the integration of the target protein into a polyprotein. However, this assay results in a low yield of high-quality data, defined as the complete unfolding of the polyprotein. Additionally, nonspecific surface adhesion hinders studies of α-helical proteins, which unfold at low forces and low extensions. Here, we overcame these limitations by merging two developments: (i) a polyprotein with versatile, genetically encoded short peptide tags functionalized via a mechanically robust Hydrazino-Pictet-Spengler ligation and (ii) the efficient site-specific conjugation of biomolecules to PEG-coated surfaces. Heterobifunctional anchoring of this polyprotein construct and DNA via copper-free click chemistry to PEG-coated substrates and a strong but reversible streptavidin-biotin linkage to PEG-coated AFM tips enhanced data quality and throughput. For example, we achieved a 75-fold increase in the yield of high-quality data and repeatedly probed the same individual polyprotein to deduce its dynamic force spectrum in just 2 h. The broader utility of this polyprotein was demonstrated by measuring three diverse target proteins: an α-helical protein (calmodulin), a protein with internal cysteines (rubredoxin), and a computationally designed three-helix bundle (α₃D). Indeed, at low loading rates, α₃D represents the most mechanically labile protein yet characterized by AFM. Such efficient SMFS studies on a commercial AFM enable the rapid characterization of macromolecular folding over a broader range of proteins and a wider array of experimental conditions (pH, temperature, denaturants). Further, by integrating these enhancements with optical traps, we demonstrate how efficient bioconjugation to otherwise nonstick surfaces can benefit diverse single-molecule studies.

Post-Translational Sortase-Mediated Attachment of High-Strength Force Spectroscopy Handles

Single-molecule force spectroscopy greatly benefits from site-specific surface immobilization and specific probing with a functionalized cantilever. Here, we describe a streamlined approach to such experiments by covalently attaching mechanically stable receptors onto proteins of interest (POI) to improve pickup efficiency and specificity. This platform provides improved throughput, allows precise control over the pulling geometry, and allows for multiple constructs to be probed with the same ligand-modified cantilever. We employ two orthogonal enzymatic ligation reactions [sortase and phosphopantetheinyl transferase (Sfp)] to covalently immobilize POI to a pegylated surface and to subsequently ligate the POI to a mechanically stable dockerin domain at the protein's C-terminus for use as a high-strength pulling handle. Our configuration permits expression and folding of the POI to proceed independently from the mechanically stable receptor used for specific probing and requires only two short terminal peptide sequences (i.e., ybbR-tag and sortase C-tag). We applied this system successfully to proteins expressed using in vitro transcription and translation reactions without a protein purification step and to purified proteins expressed in Escherichia coli.

Measuring Force-Induced Dissociation Kinetics of Protein Complexes Using Single-Molecule Atomic Force Microscopy

Proteins respond to mechanical force by undergoing conformational changes and altering the kinetics of their interactions. However, the biophysical relationship between mechanical force and the lifetime of protein complexes is not completely understood. In this chapter, we provide a step-by-step tutorial on characterizing the force-dependent regulation of protein interactions using in vitro and in vivo single-molecule force clamp measurements with an atomic force microscope (AFM). While we focus on the force-induced dissociation of E-cadherins, a critical cell-cell adhesion protein, the approaches described here can be readily adapted to study other protein complexes. We begin this chapter by providing a brief overview of theoretical models that describe force-dependent kinetics of biomolecular interactions. Next, we present step-by-step methods for measuring the response of single receptor-ligand bonds to tensile force in vitro. Finally, we describe methods for quantifying the mechanical response of single protein complexes on the surface of living cells. We describe general protocols for conducting such measurements, including sample preparation, AFM force clamp measurements, and data analysis. We also highlight critical limitations in current technologies and discuss solutions to these challenges.

Improved Force Spectroscopy Using Focused-Ion-Beam-Modified Cantilevers

Atomic force microscopy (AFM) is widely used in biophysics, including force-spectroscopy studies of protein folding and protein-ligand interactions. The precision of such studies increases with improvements in the underlying quality of the data. Currently, data quality is limited by the mechanical properties of the cantilever when using a modern commercial AFM. The key tradeoff is force stability vs short-term force precision and temporal resolution. Here, we present a method that avoids this compromise: efficient focused-ion-beam (FIB) modification of commercially available cantilevers. Force precision is improved by reducing the cantilever's hydrodynamic drag, and force stability is improved by reducing the cantilever stiffness and by retaining a cantilever's gold coating only at its free end. When applied to a commonly used short cantilever (L=40μm), we achieved sub-pN force precision over 5 decades of bandwidth (0.01-1000Hz) without significantly sacrificing temporal resolution (~75μs). Extending FIB modification to an ultrashort cantilever (L=9μm) also improved force precision and stability, while maintaining 1-μs-scale temporal resolution. Moreover, modifying ultrashort cantilevers also eliminated their inherent underdamped high-frequency motion and thereby avoided applying a rapidly oscillating force across the stretched molecule. Importantly, fabrication of FIB-modified cantilevers is accessible after an initial investment in training. Indeed, undergraduate researchers routinely modify 2-4 cantilevers per hour with the protocol detailed here. Furthermore, this protocol offers the individual user the ability to optimize a cantilever for a particular application. Hence, we expect FIB-modified cantilevers to improve AFM-based studies over broad areas of biophysical research.

Perspective: Mechanochemistry of biological and synthetic molecules

Coupling of mechanical forces and chemical transformations is central to the biophysics of molecular machines, polymer chemistry, fracture mechanics, tribology, and other disciplines. As a consequence, the same physical principles and theoretical models should be applicable in all of those fields; in fact, similar models have been invoked (and often repeatedly reinvented) to describe, for example, cell adhesion, dry and wet friction, propagation of cracks, and action of molecular motors. This perspective offers a unified view of these phenomena, described in terms of chemical kinetics with rates of elementary steps that are force dependent. The central question is then to describe how the rate of a chemical transformation (and its other measurable properties such as the transition path) depends on the applied force. I will describe physical models used to answer this question and compare them with experimental measurements, which employ single-molecule force spectroscopy and which become increasingly common. Multidimensionality of the underlying molecular energy landscapes and the ensuing frequent misalignment between chemical and mechanical coordinates result in a number of distinct scenarios, each showing a nontrivial force dependence of the reaction rate. I will discuss these scenarios, their commonness (or its lack), and the prospects for their experimental validation. Finally, I will discuss open issues in the field.

Quantifying Instrumental Artifacts in Folding Kinetics Measured by Single-Molecule Force Spectroscopy

Force spectroscopy is commonly used to measure the kinetics of processes occurring in single biological molecules. These measurements involve attaching the molecule of interest to micron-sized or larger force probes via compliant linkers. Recent theoretical work has described how the properties of the probes and linkers can alter the observed kinetics from the intrinsic behavior of the molecule in isolation. We applied this theory to estimate the errors in measurements of folding made using optical tweezers. Errors in the folding rates arising from instrument artifacts were only ∼20% for constant-force measurements of DNA hairpins with typical choices of linker length and probe size. Measurements of transition paths using a constant trap position at high trap stiffness were also found to be in the low-artifact limit. These results indicate that typical optical trap measurements of kinetics reflect the dynamics of the molecule fairly well, and suggest practical limitations on experimental design to ensure reliable kinetic measurements.