Efficient enumeration and visualization of helix-coil ensembles.

Helix-coil models are routinely used to interpret circular dichroism data of helical peptides or predict the helicity of naturally-occurring and designed polypeptides. However, a helix-coil model contains significantly more information than mean helicity alone, as it defines the entire ensemble-the equilibrium population of every possible helix-coil configuration-for a given sequence. Many desirable quantities of this ensemble are either not obtained as ensemble averages or are not available using standard helicity-averaging calculations. Enumeration of the entire ensemble can allow calculation of a wider set of ensemble properties, but the exponential size of the configuration space typically renders this intractable. We present an algorithm that efficiently approximates the helix-coil ensemble to arbitrary accuracy by sequentially generating a list of the M highest populated configurations in descending order of population. Truncating this list of (configuration, population) pairs at a desired accuracy provides an approximating sub-ensemble. We demonstrate several uses of this approach for providing insight into helix-coil ensembles and folding mechanisms, including landscape visualization.

Multiple Modes of Zinc Binding to Histatin 5 Revealed by Buffer-Independent Thermodynamics.

Histatin 5 (Hist5) is an antimicrobial peptide found in human saliva as part of the innate immune system. Hist5 can bind several metal ions in vitro, and Zn2+ has been shown to function as an inhibitory switch to regulate the peptide's biological activity against the opportunistic fungal pathogen Candida albicans in cell culture. Here, we studied Zn2+ binding to Hist5 at four temperatures from 15 to 37 °C using isothermal titration calorimetry to obtain thermodynamic parameters that were corrected for competing buffer effects. Hist5 bound Zn2+ with a buffer-dependent association constant of ∼105 M-1 and a buffer-independent association constant of ∼6 × 106 M-1 at pH 7.4 and at all temperatures tested. Zn2+ binding was both enthalpically and entropically favorable, with larger entropic contributions at 15 °C and larger enthalpic contributions at 37 °C. Additionally, the Zn:Hist5 binding stoichiometry increased from 1:1 to 2:1 as temperature increased. The enthalpy-entropy compensation and the variable stoichiometry lead us to propose a model in which the Zn-Hist5 complex exists in an equilibrium between two distinct binding modes with different Zn:Hist5 stoichiometries. The in-depth thermodynamic analysis presented herein may help illuminate the biophysical basis for Zn-dependent changes in the antifungal activity of Hist5.

Exposing Hidden High-Affinity RNA Conformational States.

RNA recognition frequently results in conformational changes that optimize intermolecular binding. As a consequence, the overall binding affinity of RNA to its binding partners depends not only on the intermolecular interactions formed in the bound state but also on the energy cost associated with changing the RNA conformational distribution. Measuring these "conformational penalties" is, however, challenging because bound RNA conformations tend to have equilibrium populations in the absence of the binding partner that fall outside detection by conventional biophysical methods. In this study we employ as a model system HIV-1 TAR RNA and its interaction with the ligand argininamide (ARG), a mimic of TAR's cognate protein binding partner, the transactivator Tat. We use NMR chemical shift perturbations and relaxation dispersion in combination with Bayesian inference to develop a detailed thermodynamic model of coupled conformational change and ligand binding. Starting from a comprehensive 12-state model of the equilibrium, we estimate the energies of six distinct detectable thermodynamic states that are not accessible by currently available methods. Our approach identifies a minimum of four RNA intermediates that differ in terms of the TAR conformation and ARG occupancy. The dominant bound TAR conformation features two bound ARG ligands and has an equilibrium population in the absence of ARG that is below detection limit. Consequently, even though ARG binds to TAR with an apparent overall weak affinity (Kdapp ≈ 0.2 mM), it binds the prefolded conformation with a Kd in the nM range. Our results show that conformational penalties can be major determinants of RNA-ligand binding affinity as well as a source of binding cooperativity, with important implications for a predictive understanding of how RNA is recognized and for RNA-targeted drug discovery.

Injectable tissue integrating networks from recombinant polypeptides with tunable order.

Emergent properties of natural biomaterials result from the collective effects of nanoscale interactions among ordered and disordered domains. Here, using recombinant sequence design, we have created a set of partially ordered polypeptides to study emergent hierarchical structures by precisely encoding nanoscale order-disorder interactions. These materials, which combine the stimuli-responsiveness of disordered elastin-like polypeptides and the structural stability of polyalanine helices, are thermally responsive with tunable thermal hysteresis and the ability to reversibly form porous, viscoelastic networks above threshold temperatures. Through coarse-grain simulations, we show that hysteresis arises from physical crosslinking due to mesoscale phase separation of ordered and disordered domains. On injection of partially ordered polypeptides designed to transition at body temperature, they form stable, porous scaffolds that rapidly integrate into surrounding tissue with minimal inflammation and a high degree of vascularization. Sequence-level modulation of structural order and disorder is an untapped principle for the design of functional protein-based biomaterials.

Author Correction: Injectable tissue integrating networks from recombinant polypeptides with tunable order.

In the version of this Article originally published, one of the authors' names was incorrectly given as Jeffery Schaal; it should have been Jeffrey L. Schaal. This has been corrected in all versions of the Article.

Spontaneous Unfolding-Refolding of Fibronectin Type III Domains Assayed by Thiol Exchange: THERMODYNAMIC STABILITY CORRELATES WITH RATES OF UNFOLDING RATHER THAN FOLDING.

Globular proteins are not permanently folded but spontaneously unfold and refold on time scales that can span orders of magnitude for different proteins. A longstanding debate in the protein-folding field is whether unfolding rates or folding rates correlate to the stability of a protein. In the present study, we have determined the unfolding and folding kinetics of 10 FNIII domains. FNIII domains are one of the most common protein folds and are present in 2% of animal proteins. FNIII domains are ideal for this study because they have an identical seven-strand ß-sandwich structure, but they vary widely in sequence and thermodynamic stability. We assayed thermodynamic stability of each domain by equilibrium denaturation in urea. We then assayed the kinetics of domain opening and closing by a technique known as thiol exchange. For this we introduced a buried Cys at the identical location in each FNIII domain and measured the kinetics of labeling with DTNB over a range of urea concentrations. A global fit of the kinetics data gave the kinetics of spontaneous unfolding and refolding in zero urea. We found that the folding rates were relatively similar, ∼0.1-1 s-1, for the different domains. The unfolding rates varied widely and correlated with thermodynamic stability. Our study is the first to address this question using a set of domains that are structurally homologous but evolved with widely varying sequence identity and thermodynamic stability. These data add new evidence that thermodynamic stability correlates primarily with unfolding rate rather than folding rate. The study also has implications for the question of whether opening of FNIII domains contributes to the stretching of fibronectin matrix fibrils.

Conformational kinetics reveals affinities of protein conformational states.

Most biological reactions rely on interplay between binding and changes in both macromolecular structure and dynamics. Practical understanding of this interplay requires detection of critical intermediates and determination of their binding and conformational characteristics. However, many of these species are only transiently present and they have often been overlooked in mechanistic studies of reactions that couple binding to conformational change. We monitored the kinetics of ligand-induced conformational changes in a small protein using six different ligands. We analyzed the kinetic data to simultaneously determine both binding affinities for the conformational states and the rate constants of conformational change. The approach we used is sufficiently robust to determine the affinities of three conformational states and detect even modest differences in the protein's affinities for relatively similar ligands. Ligand binding favors higher-affinity conformational states by increasing forward conformational rate constants and/or decreasing reverse conformational rate constants. The amounts by which forward rate constants increase and reverse rate constants decrease are proportional to the ratio of affinities of the conformational states. We also show that both the affinity ratio and another parameter, which quantifies the changes in conformational rate constants upon ligand binding, are strong determinants of the mechanism (conformational selection and/or induced fit) of molecular recognition. Our results highlight the utility of analyzing the kinetics of conformational changes to determine affinities that cannot be determined from equilibrium experiments. Most importantly, they demonstrate an inextricable link between conformational dynamics and the binding affinities of conformational states.

Suppression of conformational heterogeneity at a protein-protein interface.

Staphylococcal protein A (SpA) is an important virulence factor from Staphylococcus aureus responsible for the bacterium's evasion of the host immune system. SpA includes five small three-helix-bundle domains that can each bind with high affinity to many host proteins such as antibodies. The interaction between a SpA domain and the Fc fragment of IgG was partially elucidated previously in the crystal structure 1FC2. Although informative, the previous structure was not properly folded and left many substantial questions unanswered, such as a detailed description of the tertiary structure of SpA domains in complex with Fc and the structural changes that take place upon binding. Here we report the 2.3-Å structure of a fully folded SpA domain in complex with Fc. Our structure indicates that there are extensive structural rearrangements necessary for binding Fc, including a general reduction in SpA conformational heterogeneity, freezing out of polyrotameric interfacial residues, and displacement of a SpA side chain by an Fc side chain in a molecular-recognition pocket. Such a loss of conformational heterogeneity upon formation of the protein-protein interface may occur when SpA binds its multiple binding partners. Suppression of conformational heterogeneity may be an important structural paradigm in functionally plastic proteins.

Electrostatic Energetics of Bacillus subtilis Ribonuclease P Protein Determined by Nuclear Magnetic Resonance-Based Histidine pKa Measurements.

The pKa values of ionizable groups in proteins report the free energy of site-specific proton binding and provide a direct means of studying pH-dependent stability. We measured histidine pKa values (H3, H22, and H105) in the unfolded (U), intermediate (I), and sulfate-bound folded (F) states of RNase P protein, using an efficient and accurate nuclear magnetic resonance-monitored titration approach that utilizes internal reference compounds and a parametric fitting method. The three histidines in the sulfate-bound folded protein have pKa values depressed by 0.21 ± 0.01, 0.49 ± 0.01, and 1.00 ± 0.01 units, respectively, relative to that of the model compound N-acetyl-l-histidine methylamide. In the unliganded and unfolded protein, the pKa values are depressed relative to that of the model compound by 0.73 ± 0.02, 0.45 ± 0.02, and 0.68 ± 0.02 units, respectively. Above pH 5.5, H22 displays a separate resonance, which we have assigned to I, whose apparent pKa value is depressed by 1.03 ± 0.25 units, which is ∼0.5 units more than in either U or F. The depressed pKa values we observe are consistent with repulsive interactions between protonated histidine side chains and the net positive charge of the protein. However, the pKa differences between F and U are small for all three histidines, and they have little ionic strength dependence in F. Taken together, these observations suggest that unfavorable electrostatics alone do not account for the fact that RNase P protein is intrinsically unfolded in the absence of ligand. Multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.

Ligand concentration regulates the pathways of coupled protein folding and binding.

Coupled ligand binding and conformational change plays a central role in biological regulation. Ligands often regulate protein function by modulating conformational dynamics, yet the order in which binding and conformational change occurs are often hotly debated. Here we show that the "conformational selection versus induced fit" distinction on which this debate is based is a false dichotomy because the mechanism depends on ligand concentration. Using the binding of pyrophosphate (PPi) to Bacillus subtilis RNase P protein as a model, we show that coupled reactions are best understood as a change in flux between competing pathways with distinct orders of binding and conformational change. The degree of partitioning through each pathway depends strongly on PPi concentration, with ligand binding redistributing the conformational ensemble toward the folded state by both increasing folding rates and decreasing unfolding rates. These results indicate that ligand binding induces marked and varied changes in protein conformational dynamics, and that the order of binding and conformational change is ligand concentration dependent.

Multiple ligand-specific conformations of the ß2-adrenergic receptor.

Seven-transmembrane receptors (7TMRs), also called G protein-coupled receptors (GPCRs), represent the largest class of drug targets, and they can signal through several distinct mechanisms including those mediated by G proteins and the multifunctional adaptor proteins ß-arrestins. Moreover, several receptor ligands with differential efficacies toward these distinct signaling pathways have been identified. However, the structural basis and mechanism underlying this 'biased agonism' remains largely unknown. Here, we develop a quantitative mass spectrometry strategy that measures specific reactivities of individual side chains to investigate dynamic conformational changes in the ß(2)-adrenergic receptor occupied by nine functionally distinct ligands. Unexpectedly, only a minority of residues showed reactivity patterns consistent with classical agonism, whereas the majority showed distinct patterns of reactivity even between functionally similar ligands. These findings demonstrate, contrary to two-state models for receptor activity, that there is significant variability in receptor conformations induced by different ligands, which has significant implications for the design of new therapeutic agents.

Picomole-scale characterization of protein stability and function by quantitative cysteine reactivity.

The Gibbs free energy difference between native and unfolded states ("stability") is one of the fundamental characteristics of a protein. By exploiting the thermodynamic linkage between ligand binding and stability, interactions of a protein with small molecules, nucleic acids, or other proteins can be detected and quantified. Determination of protein stability can therefore provide a universal monitor of biochemical function. Yet, the use of stability measurements as a functional probe is underutilized, because such experiments traditionally require large amounts of protein and special instrumentation. Here we present the quantitative cysteine reactivity (QCR) technique to determine protein stabilities rapidly and accurately using only picomole quantities of material and readily accessible laboratory equipment. We demonstrate that QCR-derived stabilities can be used to measure ligand binding over a wide range of ligand concentrations and affinities. We anticipate that this technique will have broad applications in high-throughput protein engineering experiments and functional genomics.

Efficient Enumeration and Visualization of Helix-coil Ensembles.

Helix-coil models are routinely used to interpret CD data of helical peptides or predict the helicity of naturally-occurring and designed polypeptides. However, a helix-coil model contains significantly more information than mean helicity alone, as it defines the entire ensemble - the equilibrium population of every possible helix-coil configuration - for a given sequence. Many desirable quantities of this ensemble are either not obtained as ensemble averages, or are not available using standard helicity-averaging calculations. Enumeration of the entire ensemble can allow calculation of a wider set of ensemble properties, but the exponential size of the configuration space typically renders this intractable. We present an algorithm that efficiently approximates the helix-coil ensemble to arbitrary accuracy, by sequentially generating a list of the M highest populated configurations in descending order of population. Truncating this list of (configuration, population) pairs at a desired accuracy provides an approximating sub-ensemble. We demonstrate several uses of this approach for providing insight into helix-coil ensembles and folding mechanisms, including landscape visualization.

Conformational selection or induced fit: a flux description of reaction mechanism.

The mechanism of ligand binding coupled to conformational changes in macromolecules has recently attracted considerable interest. The 2 limiting cases are the "induced fit" mechanism (binding first) or "conformational selection" (conformational change first). Described here are the criteria by which the sequence of events can be determined quantitatively. The relative importance of the 2 pathways is determined not by comparing rate constants (a common misconception) but instead by comparing the flux through each pathway. The simple rules for calculating flux in multistep mechanisms are described and then applied to 2 examples from the literature, neither of which has previously been analyzed using the concept of flux. The first example is the mechanism of conformational change in the binding of NADPH to dihydrofolate reductase. The second example is the mechanism of flavodoxin folding coupled to binding of its cofactor, flavin mononucleotide. In both cases, the mechanism switches from being dominated by the conformational selection pathway at low ligand concentration to induced fit at high ligand concentration. Over a wide range of conditions, a significant fraction of the flux occurs through both pathways. Such a mixed mechanism likely will be discovered for many cases of coupled conformational change and ligand binding when kinetic data are analyzed by using a flux-based approach.

A miniaturized technique for assessing protein thermodynamics and function using fast determination of quantitative cysteine reactivity.

Protein thermodynamic stability is a fundamental physical characteristic that determines biological function. Furthermore, alteration of thermodynamic stability by macromolecular interactions or biochemical modifications is a powerful tool for assessing the relationship between protein structure, stability, and biological function. High-throughput approaches for quantifying protein stability are beginning to emerge that enable thermodynamic measurements on small amounts of material, in short periods of time, and using readily accessible instrumentation. Here we present such a method, fast quantitative cysteine reactivity, which exploits the linkage between protein stability, sidechain protection by protein structure, and structural dynamics to characterize the thermodynamic and kinetic properties of proteins. In this approach, the reaction of a protected cysteine and thiol-reactive fluorogenic indicator is monitored over a gradient of temperatures after a short incubation time. These labeling data can be used to determine the midpoint of thermal unfolding, measure the temperature dependence of protein stability, quantify ligand-binding affinity, and, under certain conditions, estimate folding rate constants. Here, we demonstrate the fQCR method by characterizing these thermodynamic and kinetic properties for variants of Staphylococcal nuclease and E. coli ribose-binding protein engineered to contain single, protected cysteines. These straightforward, information-rich experiments are likely to find applications in protein engineering and functional genomics.

Osmolyte-induced folding of an intrinsically disordered protein: folding mechanism in the absence of ligand.

Understanding the interconversion between thermodynamically distinguishable states present in a protein folding pathway provides not only the kinetics and energetics of protein folding but also insights into the functional roles of these states in biological systems. The protein component of the bacterial RNase P holoenzyme from Bacillus subtilis (P protein) was previously shown to be unfolded in the absence of its cognate RNA or other anionic ligands. P protein was used in this study as a model system to explore general features of intrinsically disordered protein (IDP) folding mechanisms. The use of trimethylamine N-oxide (TMAO), an osmolyte that stabilizes the unliganded folded form of the protein, enabled us to study the folding process of P protein in the absence of ligand. Transient stopped-flow kinetic traces at various final TMAO concentrations exhibited multiphasic kinetics. Equilibrium "cotitration" experiments were performed using both TMAO and urea during the titration to produce a urea-TMAO titration surface of P protein. Both kinetic and equilibrium studies show evidence of a previously undetected intermediate state in the P protein folding process. The intermediate state is significantly populated, and the folding rate constants are relatively slow compared to those of intrinsically folded proteins similar in size and topology. The experiments and analysis described serve as a useful example for mechanistic folding studies of other IDPs.

Probing the folding intermediate of Bacillus subtilis RNase P protein by nuclear magnetic resonance.

Protein folding intermediates are often imperative for overall folding processes and consequent biological functions. However, the low population and transient nature of the intermediate states often hinder their biochemical and biophysical characterization. Previous studies have demonstrated that Bacillus subtilis ribonuclease P protein (P protein) is conformationally heterogeneous and folds with multiphasic kinetics, indicating the presence of an equilibrium and kinetic intermediate in its folding mechanism. In this study, nuclear magnetic resonance (NMR) spectroscopy was used to study the ensemble corresponding to this intermediate (I). The results indicate that the N-terminal and C-terminal helical regions are mostly unfolded in I. 1H−15N heteronuclear single-quantum coherence NMR spectra collected as a function of pH suggest that the protonation of His 22 may play a major role in the energetics of the equilibria among the unfolded, intermediate, and folded state ensembles of P protein. NMR paramagnetic relaxation enhancement experiments were also used to locate the small anion binding sites in both the intermediate and folded ensembles. The results for the folded protein are consistent with the previously modeled binding regions. These structural insights suggest a possible role for I in the RNase P holoenzyme assembly process.

Continuous Interdomain Orientation Distributions Reveal Components of Binding Thermodynamics.

The flexibility of biological macromolecules is an important structural determinant of function. Unfortunately, the correlations between different motional modes are poorly captured by discrete ensemble representations. Here, we present new ways to both represent and visualize correlated interdomain motions. Interdomain motions are determined directly from residual dipolar couplings, represented as a continuous conformational distribution, and visualized using the disk-on-sphere representation. Using the disk-on-sphere representation, features of interdomain motions, including correlations, are intuitively visualized. The representation works especially well for multidomain systems with broad conformational distributions.This analysis also can be extended to multiple probability density modes, using a Bingham mixture model. We use this new paradigm to study the interdomain motions of staphylococcal protein A, which is a key virulence factor contributing to the pathogenicity of Staphylococcus aureus. We capture the smooth transitions between important states and demonstrate the utility of continuous distribution functions for computing the reorientational components of binding thermodynamics. Such insights allow for the dissection of the dynamic structural components of functionally important intermolecular interactions.

Statistical estimation of statistical mechanical models: helix-coil theory and peptide helicity prediction.

Analysis of biopolymer sequences and structures generally adopts one of two approaches: use of detailed biophysical theoretical models of the system with experimentally-determined parameters, or largely empirical statistical models obtained by extracting parameters from large datasets. In this work, we demonstrate a merger of these two approaches using Bayesian statistics. We adopt a common biophysical model for local protein folding and peptide configuration, the helix-coil model. The parameters of this model are estimated by statistical fitting to a large dataset, using prior distributions based on experimental data. L(1)-norm shrinkage priors are applied to induce sparsity among the estimated parameters, resulting in a significantly simplified model. Formal statistical procedures for evaluating support in the data for previously proposed model extensions are presented. We demonstrate the advantages of this approach including improved prediction accuracy and quantification of prediction uncertainty, and discuss opportunities for statistical design of experiments. Our approach yields a 39% improvement in mean-squared predictive error over the current best algorithm for this problem. In the process we also provide an efficient recursive algorithm for exact calculation of ensemble helicity including sidechain interactions, and derive an explicit relation between homo- and heteropolymer helix-coil theories and Markov chains and (non-standard) hidden Markov models respectively, which has not appeared in the literature previously.

Methionine oxidation of monomeric lambda repressor: the denatured state ensemble under nondenaturing conditions.

Although poorly understood, the properties of the denatured state ensemble are critical to the thermodynamics and the kinetics of protein folding. The most relevant conformations to cellular protein folding are the ones populated under physiological conditions. To avoid the problem of low expression that is seen with unstable variants, we used methionine oxidation to destabilize monomeric lambda repressor and predominantly populate the denatured state under nondenaturing buffer conditions. The denatured ensemble populated under these conditions comprises conformations that are compact. Analytical ultracentrifugation sedimentation velocity experiments indicate a small increase in Stokes radius over that of the native state. A significant degree of alpha-helical structure in these conformations is detected by far-UV circular dichroism, and some tertiary interactions are suggested by near-UV circular dichroism. The characteristics of the denatured state populated by methionine oxidation in nondenaturing buffer are very different from those found in chemical denaturant.