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.

Flexible, charged biopolymers in monovalent and mixed-valence salt: Regimes of anomalous electrostatic stiffening and of salt insensitivity.

The conformations of biological polyelectrolytes (PEs), such as polysaccharides, proteins, and nucleic acids, affect how they behave and interact with other biomolecules. Relative to neutral polymers, PEs in solution are more locally rigid due to intrachain electrostatic repulsion, the magnitude of which depends on the concentration of added salt. This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. However, the applicability of this approach to flexible PEs has long been questioned. To investigate this, we use high-precision single-molecule elasticity measurements to infer the scaling with salt of the local stiffness of three flexible biopolymers (hyaluronic acid, single-stranded RNA, and single-stranded DNA) in both monovalent and mixed-valence salt solutions. In monovalent salt, we collapse the data across all three polymers by accounting for charge spacing, and find a common power-law scaling of the electrostatic persistence length with ionic strength with an exponent of 0.66±0.02. This result rules out simple OSF pictures of electrostatic stiffening. It is roughly compatible with a modified OSF picture developed by Netz and Orland; alternatively, we posit the exponent can be explained if the relevant electrostatic screening length is the interion spacing rather than the DH length. In mixed salt solutions, we find a regime where adding monovalent salt, in the presence of multivalent salt, does not affect PE stiffness. Using coarse-grained simulations, and a three-state model of condensed, chain-proximate, and bulk ions, we attribute this regime to a "jacket" of ions surrounding the PE that regulates the chain's effective charge density as ionic strength varies. The size of this jacket in simulations is again consistent with a screening length controlled by interion spacing rather than the DH length. Taken together, our results describe a unified picture of the electrostatic stiffness of polyelectrolytes in the mixed-valence salt conditions of direct relevance to cellular and intercellular biological systems.

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.

Correcting molecular transition rates measured by single-molecule force spectroscopy for limited temporal resolution.

Equilibrium free-energy-landscape parameters governing biomolecular folding can be determined from nonequilibrium force-induced unfolding by measuring the rates k for transitioning back and forth between states as a function of force F. However, bias in the observed forward and reverse rates is introduced by limited effective temporal resolution, which includes the mechanical response time of the force probe and any smoothing used to improve the signal-to-noise ratio. Here we use simulations to characterize this bias, which is most prevalent when the ratio of forward and reverse rates is far from unity. We find deviations in k(F) at high rates, due to unobserved transitions from short- to long-lived states, and at low rates, due to the corresponding unobserved transitions from long- to short-lived states. These missing events introduce erroneous curvature in log(k) vs F that leads to incorrect landscape parameter determination. To correct the measured k(F), we derive a pair of model-independent analytical formulas. The first correction accounts for unobserved transitions from short- to long-lived states, but does surprisingly little to correct the erroneous energy-landscape parameters. Only by subsequently applying the second formula, which corrects the corresponding reverse process, do we recover the expected k(F) and energy-landscape quantities. Going forward, these corrections should be applied to transition-rate data whenever the highest measured rate is not at least an order of magnitude slower than the effective temporal resolution.

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.

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.

Single-stranded nucleic acid elasticity arises from internal electrostatic tension.

Understanding of the conformational ensemble of flexible polyelectrolytes, such as single-stranded nucleic acids (ssNAs), is complicated by the interplay of chain backbone entropy and salt-dependent electrostatic repulsions. Molecular elasticity measurements are sensitive probes of the statistical conformation of polymers and have elucidated ssNA conformation at low force, where electrostatic repulsion leads to a strong excluded volume effect, and at high force, where details of the backbone structure become important. Here, we report measurements of ssDNA and ssRNA elasticity in the intermediate-force regime, corresponding to 5- to 100-pN forces and 50-85% extension. These data are explained by a modified wormlike chain model incorporating an internal electrostatic tension. Fits to the elastic data show that the internal tension decreases with salt, from [Formula: see text]5 pN under 5 mM ionic strength to near zero at 1 M. This decrease is quantitatively described by an analytical model of electrostatic screening that ascribes to the polymer an effective charge density that is independent of force and salt. Our results thus connect microscopic chain physics to elasticity and structure at intermediate scales and provide a framework for understanding flexible polyelectrolyte elasticity across a broad range of relative extensions.

Counting the ions surrounding nucleic acids.

Nucleic acids are strongly negatively charged, and thus electrostatic interactions-screened by ions in solution-play an important role in governing their ability to fold and participate in biomolecular interactions. The negative charge creates a region, known as the ion atmosphere, in which cation and anion concentrations are perturbed from their bulk values. Ion counting experiments quantify the ion atmosphere by measuring the preferential ion interaction coefficient: the net total number of excess ions above, or below, the number expected due to the bulk concentration. The results of such studies provide important constraints on theories, which typically predict the full three-dimensional distribution of the screening cloud. This article reviews the state of nucleic acid ion counting measurements and critically analyzes their ability to test both analytical and simulation-based models.

Magnetic tweezers force calibration for molecules that exhibit conformational switching.

High spatial and temporal resolution magnetic tweezers experiments allow for the direct calibration of pulling forces applied to short biomolecules. In one class of experiments, a force is applied to a structured RNA or protein to induce an unfolding transition; when the force is maintained at particular values, the molecule can exhibit conformational switching between the folded and unfolded states or between intermediate states. Here, we analyze the degree to which common force calibration approaches, involving the fitting of model functions to the Allan variance or power spectral density of the bead trajectory, are biased by this conformational switching. We find significant effects in two limits: that of large molecular extension changes between the two states, in which alternative fitting functions must be used, and that of very fast switching kinetics, in which the force calibration cannot be recovered due to the slow diffusion time of the magnetic bead. We use simulations and high-resolution RNA hairpin data to show that most biophysical experiments do not occur in either of these limits.

Quantifying the ion atmosphere of unfolded, single-stranded nucleic acids using equilibrium dialysis and single-molecule methods.

To form secondary structure, nucleic acids (NAs) must overcome electrostatic strand-strand repulsion, which is moderated by the surrounding atmosphere of screening ions. The free energy of NA folding therefore depends on the interactions of this ion atmosphere with both the folded and unfolded states. We quantify such interactions using the preferential ion interaction coefficient or ion excess: the number of ions present near the NA in excess of the bulk concentration. The ion excess of the folded, double-helical state has been extensively studied; however, much less is known about the salt-dependent ion excess of the unfolded, single-stranded state. We measure this quantity using three complementary approaches: a direct approach of Donnan equilibrium dialysis read out by atomic emission spectroscopy and two indirect approaches involving either single-molecule force spectroscopy or existing thermal denaturation data. The results of these three approaches, each involving an independent experimental technique, are in good agreement. Even though the single-stranded NAs are flexible polymers that are expected to adopt random-coil configurations, we find that their ion atmosphere is quantitatively described by rod-like models that neglect large-scale conformational freedom, an effect that we explain in terms of the competition between the relevant structural and electrostatic length scales.

A thin permeable-membrane device for single-molecule manipulation.

Single-molecule manipulation instruments have unparalleled abilities to interrogate the structure and elasticity of single biomolecules. Key insights are derived by measuring the system response in varying solution conditions; yet, typical solution control strategies require imposing a direct fluid flow on the measured biomolecule that perturbs the high-sensitivity measurement and/or removes interacting molecules by advection. An alternate approach is to fabricate devices that permit solution changes by diffusion of the introduced species through permeable membranes, rather than by direct solution flow through the sensing region. Prior implementations of permeable-membrane devices are relatively thick, disallowing their use in apparatus that require the simultaneous close approach of external instrumentation from two sides, as occurs in single-molecule manipulation devices like the magnetic tweezer. Here, we describe the construction and use of a thin microfluidic device appropriate for single-molecule studies. We create a flow cell of only ∼500 µm total thickness by sandwiching glass coverslips around a thin plastic gasket and then create permeable walls between laterally separated channels in situ through photo-induced cross-linking of poly(ethylene glycol) diacrylate hydrogels. We show that these membranes permit passage of ions and small molecules (thus permitting solution equilibration in the absence of direct flow), but the membranes block the passage of larger biomolecules (thus retaining precious samples). Finally, we demonstrate the suitability of the device for high-resolution magnetic-tweezer experiments by measuring the salt-dependent folding of a single RNA hairpin under force.

Measuring the differential stoichiometry and energetics of ligand binding to macromolecules by single-molecule force spectroscopy: an extended theory.

Many chemical techniques exist for measuring the stoichiometry of ligand binding to a macromolecule; however, these techniques are often specific to certain ligands or require the presumption of specific binding models. Here, we further develop a previously reported, general, thermodynamic method for extracting the change in number of ligands bound to a macromolecule as that macromolecule undergoes a conformational transition driven by mechanical stretching, for example, by magnetic tweezers or optical trapping. We extend the theory of this method to consider systems with many ligands, experiments conducted in different thermodynamic ensembles (e.g., constant-force, constant-extension), and experiments in which the system is not at equilibrium. Further, we show that analysis of the same single-molecule mechanical manipulation data yields a measure of the differential free energy of stabilization due to ligand binding, that is, the free energy contribution by which ligand binding favors one conformation of the macromolecule over another. We interpret an existing data set measuring ion binding to RNA and DNA in terms of this free energy.

The snakelike chain character of unstructured RNA.

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod "wormlike chain" (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a "snakelike chain," characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.

Measurement of radon and xenon binding to a cryptophane molecular host.

Xenon and radon have many similar properties, a difference being that all 35 isotopes of radon ((195)Rn-(229)Rn) are radioactive. Radon is a pervasive indoor air pollutant believed to cause significant incidence of lung cancer in many geographic regions, yet radon affinity for a discrete molecular species has never been determined. By comparison, the chemistry of xenon has been widely studied and applied in science and technology. Here, both noble gases were found to bind with exceptional affinity to tris-(triazole ethylamine) cryptophane, a previously unsynthesized water-soluble organic host molecule. The cryptophane-xenon association constant, K(a)=42,000 ± 2,000 M(-1) at 293 K, was determined by isothermal titration calorimetry. This value represents the highest measured xenon affinity for a host molecule. The partitioning of radon between air and aqueous cryptophane solutions of varying concentration was determined radiometrically to give the cryptophane-radon association constant K(a)=49,000 ± 12,000 M(-1) at 293 K.