Configurational distribution of denatured phosphoglycerate kinase

Advanced ensemble modelling of flexible macromolecules using X-ray solution scattering

Dynamic ensembles of macromolecules mediate essential processes in biology. Understanding the mechanisms driving the function and molecular interactions of 'unstructured' and flexible molecules requires alternative approaches to those traditionally employed in structural biology. Small-angle X-ray scattering (SAXS) is an established method for structural characterization of biological macromolecules in solution, and is directly applicable to the study of flexible systems such as intrinsically disordered proteins and multi-domain proteins with unstructured regions. The Ensemble Optimization Method (EOM) [Bernadó et al. (2007 ▶). J. Am. Chem. Soc. 129, 5656-5664] was the first approach introducing the concept of ensemble fitting of the SAXS data from flexible systems. In this approach, a large pool of macromolecules covering the available conformational space is generated and a sub-ensemble of conformers coexisting in solution is selected guided by the fit to the experimental SAXS data. This paper presents a series of new developments and advancements to the method, including significantly enhanced functionality and also quantitative metrics for the characterization of the results. Building on the original concept of ensemble optimization, the algorithms for pool generation have been redesigned to allow for the construction of partially or completely symmetric oligomeric models, and the selection procedure was improved to refine the size of the ensemble. Quantitative measures of the flexibility of the system studied, based on the characteristic integral parameters of the selected ensemble, are introduced. These improvements are implemented in the new EOM version 2.0, and the capabilities as well as inherent limitations of the ensemble approach in SAXS, and of EOM 2.0 in particular, are discussed.

Large domain fluctuations on 50-ns timescale enable catalytic activity in phosphoglycerate kinase

Large-scale domain motions of enzymes are often essential for their biological function. Phosphoglycerate kinase has a wide open domain structure with a hinge near the active center between the two domains. Applying neutron spin echo spectroscopy and small-angle neutron scattering we have investigated the internal domain dynamics. Structural analysis reveals that the holoprotein in solution seems to be more compact compared to the crystal structure but would not allow the functionally important phosphoryl transfer between the substrates if the protein were static. Brownian large-scale domain fluctuation dynamics on a timescale of 50 ns was revealed by neutron spin echo spectroscopy. The dynamics observed was compared to the displacement patterns of low-frequency normal modes. The displacements along the normal-mode coordinates describe our experimental results reasonably well. In particular, the domain movements facilitate a close encounter of the key residues in the active center to build the active configuration. The observed dynamics shows that the protein has the flexibility to allow fluctuations and displacements that seem to enable the function of the protein. Moreover, the presence of the substrates increases the rigidity, which is deduced from a faster dynamics with smaller amplitude.

Protein folding, protein collapse, and tanford's transfer model: lessons from single-molecule FRET

The essential and nontrivial role of the denatured state of proteins in their folding reaction is being increasingly scrutinized in recent years. Single molecule FRET (smFRET) experiments show that the denatured state undergoes a continuous collapse (or coil-to-globule) transition as the concentration of a chemical denaturant is decreased, suggesting that conformational entropy of the denatured state is an important part of the free energy of folding. Such observations question the validity of the classical Tanford transfer model, which suggests that the folding free energy can be understood solely based on the difference in amino acid solvation between the folded state and a fixed unfolded state. An alternative to the transfer model is obtained here from a polymer theoretical analysis of a series of published smFRET data. The analysis shows that the free energy of denatured-state collapse has a linear dependence on denaturant concentration, an outcome of the interplay between enthalpic and entropic contributions. Surprisingly, the slope of the free energy of collapse agrees very well with the respective slope of the free energy of folding. This conformity of values obtained from two very different measurements shows that it is the collapse transition in the denatured state which mediates the effect of denaturants on folding. The energetics of folding are thus governed by the competition of solvation and conformational entropy in the denatured state.

Heat capacity and compactness of denatured proteins

One of the striking results of protein thermodynamics is that the heat capacity change upon denaturation is large and positive. This change is generally ascribed to the exposure of non-polar groups to water on denaturation, in analogy to the large heat capacity change for the transfer of small non-polar molecules from hydrocarbons to water. Calculations of the heat capacity based on the exposed surface area of the completely unfolded denatured state give good agreement with experimental data. This result is difficult to reconcile with evidence that the heat denatured state in the absence of denaturants is reasonably compact. In this work, sample conformations for the denatured state of truncated CI2 are obtained by use of an effective energy function for proteins in solution. The energy function gives denatured conformations that are compact with radii of gyration that are slightly larger than that of the native state. The model is used to estimate the heat capacity, as well as that of the native state, at 300 and 350 K via finite enthalpy differences. The calculations show that the heat capacity of denaturation can have large positive contributions from non-covalent intraprotein interactions because these interactions change more with temperature in non-native conformations than in the native state. Including this contribution, which has been neglected in empirical surface area models, leads to heat capacities of unfolding for compact denatured states that are consistent with the experimental heat capacity data. Estimates of the stability curve of CI2 made with the effective energy function support the present model.

Small-Angle X-Ray Scattering from RNA, Proteins, and Protein Complexes

Small-angle X-ray scattering (SAXS) is increasingly used to characterize the structure and interactions of biological macromolecules and their complexes in solution. Although still a low-resolution technique, the advent of high-flux synchrotron sources and the development of algorithms for the reconstruction of 3-D electron density maps from 1-D scattering profiles have made possible the generation of useful low-resolution molecular models from SAXS data. Furthermore, SAXS is well suited for the study of unfolded or partially folded conformational ensembles as a function of time or solution conditions. Here, we review recently developed algorithms for 3-D structure modeling and applications to protein complexes. Furthermore, we discuss the emerging use of SAXS as a tool to study membrane protein-detergent complexes. SAXS is proving useful to study the folding of functional RNA molecules, and finally we discuss uses of SAXS to study ensembles of denatured proteins.

Global Structure Analysis of Acid-Unfolded Myoglobin with Consideration to Effects of Intermolecular Coulomb Repulsion on Solution X-ray Scattering†

To obtain information on the global structure of protein in the acid-unfolded (AU) state, the structure of apomyoglobin (apoMb) was analyzed by using the solution X-ray scattering (SXS) method. SXS profiles were obtained over a wide range of protein concentrations, 1-18 mg mL-1, under strongly acidic conditions. From analysis of the SXS profile extrapolated to a zero protein concentration, the mean square radius, Rsq, of AU-apoMb at 20 mM HCl was estimated to be 4.81 +/- 0.31 nm. This estimate is more than 1.3 nm larger than those of 3.0-3.5 nm reported thus far. The difference originates from the fact that effects of Coulomb repulsive forces acting between AU-apoMb molecules have not been correctly taken into account in the conventional analysis. In fact, even at a low protein concentration of 1 mg mL-1 close to the limit of measurement in the present SXS method, the solution condition applicable to estimating accurately structural parameters of AU-apoMb is very limited. At HCl concentrations lower than 10 mM, the scattering intensity at a small scattering vector decreases remarkably through the effect of intermolecular repulsive forces and the forward scattering intensity is significantly lower than the estimate from the partial specific volume of protein. On the other hand, at HCl concentrations higher than 50 mM, some compact molten-globule-like structures emerge. As a result, the intermediate concentration of 20 mM HCl is the best choice of the solution condition for determining Rsq of AU-apoMb. The effect of intermolecular Coulomb repulsion on the SXS profile of AU-apoMb is at its maximum for forward scattering and decreases monotonously with an increase in the scattering angle to be virtually negligible at K approximately 0.63 nm(-1). Whereas urea-denatured apoMb shows a SXS profile typical of Gaussian chains, the intrinsic SXS profile of AU-apoMb differs significantly from those of Gaussian chains.

Solution structure of human von Willebrand factor studied using small angle neutron scattering

von Willebrand factor (VWF) binding to platelets under high fluid shear is an important step regulating atherothrombosis. We applied light and small angle neutron scattering to study the solution structure of human VWF multimers and protomer. Results suggest that these proteins resemble prolate ellipsoids with radius of gyration (R(g)) of approximately 75 and approximately 30 nm for multimer and protomer, respectively. The ellipsoid dimensions/radii are 175 x 28 nm for multimers and 70 x 9.1 nm for protomers. Substructural repeat domains are evident within multimeric VWF that are indicative of elements of the protomer quarternary structure (16 nm) and individual functional domains (4.5 nm). Amino acids occupy only approximately 2% of the multimer and protomer volume, compared with 98% for serum albumin and 35% for fibrinogen. VWF treatment with guanidine.HCl, which increases VWF susceptibility to proteolysis by ADAMTS-13, causes local structural changes at length scales <10 nm without altering protein R(g). Treatment of multimer but not protomer VWF with random homobifunctional linker BS(3) prior to reduction of intermonomer disulfide linkages and Western blotting reveals a pattern of dimer and trimer units that indicate the presence of stable intermonomer non-covalent interactions within the multimer. Overall, multimeric VWF appears to be a loosely packed ellipsoidal protein with non-covalent interactions between different monomer units stabilizing its solution structure. Local, and not large scale, changes in multimer conformation are sufficient for ADAMTS-13-mediated proteolysis.

Contribution of solvent water to the solution X-ray scattering profile of proteins

A theoretical framework is presented to analyze how solvent water contributes to the X-ray scattering profile of protein solution. Molecular dynamics simulations were carried out on pure water and an aqueous solution of myoglobin to determine the spatial distribution of water molecules in each of them. Their solution X-ray scattering (SXS) profiles were numerically evaluated with obtained atomic-coordinate data. It is shown that two kinds of contributions from solvent water must be considered to predict the SXS profile of a solution accurately. One is the excluded solvent scattering originating in exclusion of water molecules from the space occupied by solutes. The other is the hydration effect resulting from formation of a specific distribution of water around solutes. Explicit consideration of only two molecular layers of water is practically enough to incorporate the hydration effect. Care should be given to using an approximation in which an averaged electron density distribution is assumed for the structure factor because it may predict profiles considerably deviating from the correct profile at large K.

Characterization of the denatured states distribution of neocarzinostatin by small-angle neutron scattering and differential scanning calorimetry

The denatured states of a small globular protein, apo-neocarzinostatin (NCS), have been characterized using several techniques. Structural properties were investigated by optical spectroscopy techniques and small-angle neutron scattering (SANS), as a function of guanidinium chloride (GdmCl) concentration. SANS experiments show that in heavy water, the protein keeps its native size at GdmCl concentrations below 2.5 M. A sharp transition occurs at about 3.6 M GdmCl, and NCS behaves like an excluded volume chain above 5 M. The same behavior is observed in deuterated buffer by fluorescence and circular dichroism measurements. For the H(2)O buffer, the transition occurs with lower concentration of denaturant, the shift being about 0.6 M. 8-Anilino-1-naphthalenesulfonate (ANS) was used as a hydrophobic fluorescent probe for studying the early stages of protein unfolding. Protein denaturation modifies the fluorescence intensity of ANS, a maximum of intensity being detected close to 2 M GdmCl in hydrogenated buffer, which shows the existence of at least one intermediate state populated at the beginning of the unfolding pathway. Differential scanning calorimetry (DSC) was used to obtain thermodynamic values for NCS denaturation. The melting curves recorded between 20 and 90 degrees C in the presence of various GdmCl concentrations (0-3 M) cannot be explained by a simple two-state model. Altogether, the data presented in this paper suggest that before unfolding the protein explores a distribution of states which is centered around compact states at denaturant concentrations below 2 M in H(2)O, and then shifts to less structured states by increasing denaturant concentrations.

Change in backbone torsion angle distribution on protein folding

Understanding protein folding requires the determination of the configurational space accessible to the protein at different stages in folding. Here, computer simulation analysis of small angle neutron scattering results is used to probe the change in the distribution of configurations on strong denaturation of a globular protein, phosphoglycerate kinase, in 4 M guanidine hydrochloride solution. To do this atomic-detail ensembles of the unfolded protein chain are modeled and their scattering profiles compared with the experiment. The local conformational statistics are found to strongly influence the experimental intensity at scattering vectors between 0.05 and 0.3 A(-1). Denaturation leads to a reduction in the protein atom-pair distance distribution function over the approximately 3-15 A region that is associated with a quantifiable shift in the backbone torsional angle (phi, psi) distribution toward the beta region of the Ramachandran plot.

Hydrodynamic radii of native and denatured proteins measured by pulse field gradient NMR techniques

Pulse field gradient NMR methods have been used to determine the effective hydrodynamic radii of a range of native and nonnative protein conformations. From these experimental data, empirical relationships between the measured hydrodynamic radius (R(h)) and the number of residues in the polypeptide chain (N) have been established; for native folded proteins R(h) = 4.75N (0.29)A and for highly denatured states R(h) = 2.21N (0.57)A. Predictions from these equations agree well with experimental data from dynamic light scattering and small-angle X-ray or neutron scattering studies reported in the literature for proteins ranging in size from 58 to 760 amino acid residues. The predicted values of the hydrodynamic radii provide a framework that can be used to analyze the conformational properties of a range of nonnative states of proteins. Several examples are given here to illustrate this approach including data for partially structured molten globule states and for proteins that are unfolded but biologically active under physiological conditions. These reveal evidence for significant coupling between local and global features of the conformational ensembles adopted in such states. In particular, the effective dimensions of the polypeptide chain are found to depend significantly on the level of persistence of regions of secondary structure or features such as hydrophobic clusters within a conformational ensemble.

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.

Excluded volume in the configurational distribution of a strongly-denatured protein

The configurational distribution of phosphoglycerate kinase (PGK) strongly-denatured in 4 M guanidine hydrochloride solution is investigated using small-angle neutron scattering (SANS) and Monte Carlo computer simulation. It is shown that the experimental scattering profile can be represented by a random flexible chain of spheres of excess scattering density with excluded volume interactions, the best agreement being achieved when partial sphere intersection is allowed. The radius of gyration of the chain increases by a factor of 4 on denaturation, whereas the average length of segments approximately 5 residues long increases by only approximately 10%, consistent with a picture in which the large expansion on denaturation originates primarily from increased long-range flexibility of the polypeptide chain. The results provide a description of the chain statistics from which the construction of starting points for simulation studies of folding of the protein can be envisaged.

Repulsive interparticle interactions in a denatured protein solution revealed by small angle neutron scattering

In order to investigate the effect of concentration in biological processes such as protein folding, small angle neutron scattering measurements were used to determine the second virial coefficient of solutions of both native and strongly denatured phosphoglycerate kinase and the radius of gyration of the protein at zero concentration. The value of the second virial coefficient is a good probe of the non-ideality of a solution. The present results show that the unfolding of the protein leads to a drastic change in the repulsive intermolecular interactions. We conclude that these interactions are due mainly to the behaviour of the denatured polypeptide chain as an excluded volume polymer.

Small-angle neutron scattering by a strongly denatured protein: analysis using random polymer theory

Small-angle neutron scattering profiles are presented from phosphoglycerate kinase, in the native form and strongly denatured in 4 M guanidinium chloride (GdnHCl) solution. The data are interpreted using a model in which the excess scattering density associated with the protein is represented as a finite freely jointed chain of spheres. The similarity of the model-derived scattering function to experiment increases asymptotically with the number of spheres. The improvement of the fit obtained with more than approximately 200 spheres (i.e., two residues per sphere) is insignificant. The effects of finite size of the scattering units and of scattering length variation along the polypeptide chain are examined. Improved agreement with experiment is obtained when these effects are taken into account. A method for rapid calculation of the scattering profile of a full, all-atom configuration is examined. It is found that a representation of the chain containing two scattering units per residue, placed at the backbone and side-chain scattering length centroids, reproduces the full, all-atom profile to within 2%.

The concept of a random coil. Residual structure in peptides and denatured proteins

Non-native states of proteins are of increasing interest because of their relevance to issues such as protein folding, translocation and stability. A framework for interpreting the wealth of experimental data for non-native states emerging from rapid advances in experimental techniques involves comparison with a "random coll' state, which possesses no structure except that inherent in the local interactions. We review here the concept of a random coil, from its global to its local properties. In particular, we focus on the description of a random coil in terms of statistical distributions in psi, phi space. We show that such a model, in combination with experimental data, provides insight into the structural properties of polypeptide chains and has significance for understanding protein folding and for molecular design.

X-ray solution scattering studies of protein folding

Protein folding is a reaction in which an extended polypeptide chain acquires maximal packing through formation of secondary and tertiary structures. Compactness and shape are, therefore, critical properties characterizing the process of protein folding. Because the stability of the native state is determined by the subtle free energy balance between the native and denatured states, the characterization of the denatured state is also essential to understand the conformational stability of the native state. We show that solution X-ray scattering is the best technique available today to address these problems. Although the structural resolution of the unfolded or compact denatured states elucidated from solution X-ray scattering is low, it provides a variety of information complementary to that obtained by NMR or X-ray crystallography.

How random is a highly denatured protein?

There has been renewed interest in determining the physicochemical properties of denatured states of proteins. In many denatured states there is evidence for the existence of nonrandom configurational distributions. Here we examine the small-angle neutron scattering profile of yeast phosphoglycerate kinase in the native state and in highly denaturing conditions. We show that the denatured protein scattering profile can be interpreted using a model developed for synthetic polymers in which the chain behaves as a random coil in a good solvent, i.e. with excluded volume interactions. The implications of this result for our appreciation of the protein folding process are discussed.

Protein interactions and dynamics probed by quantum chemistry, computer simulations and neutron experiments

We review some recent experiments and calculations on aspects of the structure and dynamics of proteins and related systems. The use of quantum chemical techniques to determine geometries and energies of supramolecular complexes of biological interest is illustrated, and the concomitant development of empirical energy functions for use in protein simulations outlined. We describe how simulations of crystalline peptides and amino-acids using an empirical force field can be combined with appropriate coherent and incoherent inelastic neutron scattering experiments to elucidate the characteristics of lattice vibrations and diffusive atomic motions in the crystals. The application of molecular dynamics simulations to the interpretation of incoherent neutron scattering experiments on proteins is examined and the resulting ideas on the general characteristics of protein motion discussed in terms of their functional implications.

Modeling compact denatured states of proteins

We propose a model for the conformations of compact denatured states of globular proteins: that they are broad ensembles of chain backbone conformations that involve common localized hydrophobic clustering and helical contacts, depending on the amino acid sequence. We construct representative ensembles for chain lengths up to 136 monomers on three-dimensional cubic lattices using the "hydrophobic zippers" method (Fiebig & Dill, 1993). We find that model conformations with radii of gyration about 20% larger than native conformations commonly have bimodal distributions of P(r), of the pairwise interatomic distances, r, and Kratky plots in agreement with recent small-angle X-ray scattering (Sosnick & Trewhella, 1992; Flanagan et al., 1992; Kataoka et al., 1993; Flanagan et al., 1993) experiments on three different proteins. We also find that the lattice model of the Shortle 1-136 fragment of staphylococcal nuclease does not appear capable of forming a single hydrophobic core by hydrophobic zippering, consistent with experiments.