Self crowding of globular proteins studied by small-angle x-ray scattering.

Small-angle x-ray scattering (SAXS) was used to study the behavior of equine metmyoglobin (Mb) and bovine pancreatic trypsin inhibitor (BPTI) at concentrations up to 0.4 and 0.15 g/mL, respectively, in solutions also containing 50% D2O and 1 M urea. For both proteins, significant effects because of interference between x-rays scattered by different molecules (interparticle interference) were observed, indicating nonideal behavior at high concentrations. The experimental data were analyzed by comparison of the observed scattering profiles with those predicted by crystal structures of the proteins and a hard-sphere fluid model used to represent steric exclusion effects. The Mb scattering data were well fit by the hard-sphere model using a sphere radius of 18 Å, only slightly smaller than that estimated from the three-dimensional structure (20 Å). In contrast, the scattering profiles for BPTI in phosphate buffer displayed substantially less pronounced interparticle interference than predicted by the hard-sphere model and the radius estimated from the known structure of the protein (15 Å). Replacing the phosphate buffer with 3-(N-morpolino)propane sulfonic acid (MOPS) led to increased interparticle interference, consistent with a larger effective radius and suggesting that phosphate ions may mediate attractive intermolecular interactions, as observed in some BPTI crystal structures, without the formation of stable oligomers. The scattering data were also used to estimate second virial coefficients for the two proteins: 2.0 ×10(-4) cm(3)mol/g(2) for Mb in phosphate buffer, 1.6 ×10(-4) cm(3)mol/g(2) for BPTI in phosphate buffer and 9.2 ×10(-4) cm(3)mol/g(2) for BPTI in MOPS. The results indicate that the behavior of Mb, which is nearly isoelectric under the conditions used, is well described by the hard-sphere model, but that of BPTI is considerably more complex and is likely influenced by both repulsive and attractive electrostatic interactions. The hard-sphere model may be a generally useful tool for the analysis of small-angle scattering data from concentrated macromolecular solutions.

Minimal effects of macromolecular crowding on an intrinsically disordered protein: a small-angle neutron scattering study.

Small-angle neutron scattering was used to study the effects of macromolecular crowding by two globular proteins, i.e., bovine pancreatic trypsin inhibitor and equine metmyoglobin, on the conformational ensemble of an intrinsically disordered protein, the N protein of bacteriophage λ. The λ N protein was uniformly labeled with (2)H, and the concentrations of D2O in the samples were adjusted to match the neutron scattering contrast of the unlabeled crowding proteins, thereby masking their contribution to the scattering profiles. Scattering from the deuterated λ N was recorded for samples containing up to 0.12 g/mL bovine pancreatic trypsin inhibitor or 0.2 g/mL metmyoglobin. The radius of gyration of the uncrowded protein was estimated to be 30 Å and was found to be remarkably insensitive to the presence of crowders, varying by <2 Å for the highest crowder concentrations. The scattering profiles were also used to estimate the fractal dimension of λ N, which was found to be ∼1.8 in the absence or presence of crowders, indicative of a well-solvated and expanded random coil under all of the conditions examined. These results are contrary to the predictions of theoretical treatments and previous experimental studies demonstrating compaction of unfolded proteins by crowding with polymers such as dextran and Ficoll. A computational simulation suggests that some previous treatments may have overestimated the effective volumes of disordered proteins and the variation of these volumes within an ensemble. The apparent insensitivity of λ N to crowding may also be due in part to weak attractive interactions with the crowding proteins, which may compensate for the effects of steric exclusion.

Structure of a serine protease poised to resynthesize a peptide bond.

The serine proteases are among the most thoroughly studied enzymes, and numerous crystal structures representing the enzyme-substrate complex and intermediates in the hydrolysis reactions have been reported. Some aspects of the catalytic mechanism remain controversial, however, especially the role of conformational changes in the reaction. We describe here a high-resolution (1.46 A) crystal structure of a complex formed between a cleaved form of bovine pancreatic trypsin inhibitor (BPTI) and a catalytically inactive trypsin variant with the BPTI cleavage site ideally positioned in the active site for resynthesis of the peptide bond. This structure defines the positions of the newly generated amino and carboxyl groups following the 2 steps in the hydrolytic reaction. Comparison of this structure with those representing other intermediates in the reaction demonstrates that the residues of the catalytic triad are positioned to promote each step of both the forward and reverse reaction with remarkably little motion and with conservation of hydrogen-bonding interactions. The results also provide insights into the mechanism by which inhibitors like BPTI normally resist hydrolysis when bound to their target proteases.

Effects of macromolecular crowding on an intrinsically disordered protein characterized by small-angle neutron scattering with contrast matching.

Small-angle neutron scattering was used to examine the effects of molecular crowding on an intrinsically disordered protein, the N protein of bacteriophage λ, in the presence of high concentrations of a small globular protein, bovine pancreatic trypsin inhibitor (BPTI). The N protein was labeled with deuterium, and the D(2)O concentration of the solvent was adjusted to eliminate the scattering contrast between the solvent and unlabeled BPTI, leaving only the scattering signal from the unfolded protein. The scattering profile observed in the absence of BPTI closely matched that predicted for an ensemble of random conformations. With BPTI added to a concentration of 65 mg/mL, there was a clear change in the scattering profile representing an increase in the mass fractal dimension of the unfolded protein, from 1.7 to 1.9, as expected if crowding favors more compact conformations. The crowding protein also inhibited aggregation of the unfolded protein. At 130 mg/mL BPTI, however, the fractal dimension was not significantly different from that measured at the lower concentration, contrary to the predictions of models that treat the unfolded conformations as convex particles. These results are reminiscent of the behavior of polymers in concentrated melts, suggesting that these synthetic mixtures may provide useful insights into the properties of unfolded proteins under crowding conditions.

Modulation of functionally significant conformational equilibria in adenylate kinase by high concentrations of trimethylamine oxide attributed to volume exclusion.

The effect of an inert small molecule osmolyte, trimethyl amine N-oxide (TMAO), upon the conformational equilibria of Escherichia coli adenylate kinase was studied using time-resolved FRET. The relative populations of open and closed clefts between the LID and the CORE domains were measured as functions of the concentrations of the substrate ATP over the concentration range 0-18 mM and TMAO over the concentration range 0-4 M. A model was constructed according to which the enzyme exists in equilibrium among four conformational states, corresponding to combinations of open and closed conformations of the LID-CORE and AMP-CORE clefts. ATP is assumed to bind only to those conformations with the closed LID-CORE cleft, and TMAO is assumed to be differentially excluded as a hard spherical particle from each of the four conformations in accordance with calculations based upon x-ray crystallographic structures. This model was found to describe quantitatively the dependence of the fraction of the closed LID-CORE cleft upon the concentrations of both ATP and TMAO over the entire range of concentrations with just five undetermined parameters.

Rigidification of a flexible protease inhibitor variant upon binding to trypsin.

The Tyr35-->Gly replacement in bovine pancreatic trypsin inhibitor (BPTI) has previously been shown to dramatically enhance the flexibility of the trypsin-binding region of the free inhibitor and to destabilize the interaction with the protease by about 3 kcal/mol. The effects of this replacement on the enzyme-inhibitor interaction were further studied here by X-ray crystallography and isothermal titration calorimetry (ITC). The co-crystal structure of Y35G BPTI bound to trypsin was determined using 1.65 A resolution X-ray diffraction data collected from cryopreserved crystals, and a new structure of the complex with wild-type BPTI under the same conditions was determined using 1.62 A data. These structures reveal that, in contrast to the free protein, Y35G BPTI adopts a conformation nearly identical with that of the wild-type protein, with a water-filled cavity in place of the missing Tyr side-chain. The crystallographic temperature factors for the two complexes indicate that the mutant inhibitor is nearly as rigid as the wild-type protein when bound to trypsin. Calorimetric measurements show that the change in enthalpy upon dissociation of the complex is 2.5 kcal/mol less favorable for the complex containing Y35G BPTI than for the complex with the wild-type inhibitor. Thus, the destabilization of the complex resulting from the Y35G replacement is due to a more favorable change in entropy upon dissociation. The heat capacity changes for dissociation of the mutant and wild-type complexes were very similar, suggesting that the entropic effects probably do not arise from solvation effects, but are more likely due to an increase in protein conformational entropy upon dissociation of the mutant inhibitor. These results define the biophysical role of a highly conserved core residue located outside of a protein-binding interface, demonstrating that Tyr35 has little impact on the trypsin-bound BPTI structure and acts primarily to define the structure of the free protein so as to maximize binding affinity.

Computational simulation of the statistical properties of unfolded proteins.

A simple Monte Carlo method was used to generate ensembles of simulated polypeptide conformations that are restricted only by steric repulsion. The models used for these simulations were based on the sequences of four real proteins, ranging in size from 26 to 268 amino acid residues, and included all non-hydrogen atoms. Two sets of calculations were performed, one that included only intra-residue steric repulsion terms and those between adjacent residues, and one that included repulsion terms between all possible atom pairs, so as to explicitly account for the excluded volume effect. Excluded volume was found to increase the average radius of gyration of the chains by 20-40%, with the expansion factor increasing with chain length. Contrary to recent suggestions, however, the excluded volume effect did not greatly restrict the distribution of dihedral angles or favor native-like topologies. The average dimensions of the ensembles calculated with excluded volume were consistent with those measured experimentally for unfolded proteins of similar sizes under denaturing conditions, without introducing any adjustable scaling factor. The simulations also reproduced experimentally determined effective concentrations for the formation of disulfide bonds in reduced and unfolded proteins. The statistically generated ensembles included significant numbers of conformations that were nearly as compact as the corresponding native proteins, as well as many that were as accessible to solvent as a fully extended chain. On the other hand, conformations with as much buried surface area as the native proteins were very rare, as were highly extended conformations. These results suggest that the overall properties of unfolded proteins can be usefully described by a random coil model and that an unfolded polypeptide can undergo significant collapse while losing only a relatively small fraction of its conformational entropy.

Identification of a residue critical for maintaining the functional conformation of BPTI.

The effects of amino acid replacements on the backbone dynamics of bovine pancreatic trypsin inhibitor (BPTI) were examined using 15N NMR relaxation experiments. Previous studies have shown that backbone amide groups within the trypsin-binding region of the wild-type protein undergo conformational exchange processes on the micros time scale, and that replacement of Tyr35 with Gly greatly increases the number of backbone atoms involved in such motions. In order to determine whether these mutational effects are specific to the replacement of this residue with Gly, six additional replacements were examined in the present study. In two of these, Tyr35 was replaced with either Ala or Leu, and the other four were single replacements of Tyr23, Phe33, Asn43 or Asn44, all of which are highly buried in the native structure and conserved in homologous proteins. The Y35A and Y35L mutants displayed dynamic properties very similar to those of the Y35G mutant, with the backbone segments including residues 10-19 and 32-44 undergoing motions revealed by enhanced 15N transverse relaxation rates. On the other hand, the Y23L, N43G and N44A substitutions caused almost no detectable changes in backbone dynamics, on either the ns-ps or ms-micros time scales, even though each of these replacements significantly destabilizes the native conformation. Replacement of Phe33 with Leu caused intermediate effects, with several residues that have previously been implicated in motions in the wild-type protein displaying enhanced transverse relaxation rates. These results demonstrate that destabilizing amino acid replacements can be accommodated in a native protein with dramatically different effects on conformational dynamics and that Tyr35 plays a particularly important role in defining the conformation of the trypsin-binding site of BPTI.

Alteration of the disulfide-coupled folding pathway of BPTI by circular permutation.

The kinetics of disulfide-coupled folding and unfolding of four circularly permuted forms of bovine pancreatic trypsin inhibitor (BPTI) were studied and compared with previously published results for both wild-type BPTI and a cyclized form. Each of the permuted proteins was found to be less stable than either the wild-type or circular proteins, by 3-8 kcal/mole. These stability differences were used to estimate effective concentrations of the chain termini in the native proteins, which were 1 mM for the wild-type protein and 2.5 to 4000 M for the permuted forms. The circular permutations increased the rates of unfolding and caused a variety of effects on the kinetics of refolding. For two of the proteins, the rates of a direct disulfide-formation pathway were dramatically increased, making this process as fast or faster than the competing disulfide rearrangement mechanism that predominates in the folding of the wild-type protein. These two permutations break the covalent connectivity among the beta-strands of the native protein, and removal of these constraints appears to facilitate direct formation and reduction of nearby disulfides that are buried in the folded structure. The effects on folding kinetics and mechanism do not appear to be correlated with relative contact order, a measure of overall topological complexity. These observations are consistent with the results of other recent experimental and computational studies suggesting that circular permutation may generally influence folding mechanisms by favoring or disfavoring specific interactions that promote alternative pathways, rather than through effects on the overall topology of the native protein.

Fractal dimension of an intrinsically disordered protein: small-angle X-ray scattering and computational study of the bacteriophage λ N protein.

Small-angle X-ray scattering (SAXS) was used to characterize the bacteriophage λ N protein, a 107 residue intrinsically disordered protein (IDP) that functions as a transcriptional antitermination factor. The SAXS data were used to estimate both the average radius of gyration and the fractal dimension, a measure of the protein's internal scaling properties, under a variety of solution conditions. In the absence of denaturants, the radius of gyration was 38 ± 3.5 Å and the fractal dimension was 1.76 ± 0.05, slightly larger than the value predicted for a well-solvated polymer with excluded volume (1.7). Neither the radius of gyration nor the fractal dimension changed significantly on the addition of urea, further indicating that the protein is extensively unfolded and well solvated in the absence of denaturant. The addition of NaCl or D(2) O was found to promote aggregation, but did not appear to affect the properties of the monomeric form. The experimental SAXS profiles were also compared with those predicted by a computational model for a random-coil polypeptide, with an adjustable solvation energy term. The experimental data were well fit to the model with the solvation energy close to zero. These results indicate that the λ N protein is among the more expanded members of the broad class of IDPs, most likely because of its high content of charged residues and a large net charge (+15 at neutral pH). The expanded nature of the conformational ensemble may play a role in facilitating the interactions of the protein with other components of the dynamic transcriptional complex.

Exploration of transferability in multiscale coarse-grained peptide models.

Coarse-grained models can facilitate the efficient simulation of complex biological systems. In earlier studies the multiscale coarse-graining (MS-CG) method was employed to examine the folding landscape for two small peptides. In those studies, MS-CG force fields specific to each peptide were employed. We extend here the scope of that work with the goal of obtaining a transferable MS-CG force field which can be used to simulate the folded conformations of peptides with disparate structural motifs. Information obtained via MS-CG modeling was used to understand the characteristics of CG interactions which govern their capacity to be transferred between different peptide systems. We find that polar CG groups are least transferable in general, with interactions between CG sites representing the CO and NH groups on the peptide backbone being particularly resistant to facile transfer. Our results additionally suggest that, while there are limitations to the approach, the MS-CG method may provide a systematic path toward obtaining rigorously defined CG interactions with at least some degree of transferability. These studies also indicate that it may be possible to enhance the transferability of the MS-CG approach by identifying novel ways to combine information from different MS-CG force fields.

The Product Operator Formalism: A Physical and Graphical Interpretation.

The product-operator formalism is the most commonly used tool for describing and designing multidimensional NMR experiments. In spite of its relative simplicity and sound theoretical underpinnings, however, students and practitioners often find it difficult to relate the mathematical manipulations to a physical picture. In an effort to address this pedagogical challenge, the present paper begins with a quantum-mechanical treatment of pure populations of scalar-coupled spin-pairs, rather than the equilibrium population of spin-pairs in different quantum states, which is the usual starting point for treatments based on the density matrix and product operators. In the context of pure populations, the product operators are shown to represent quantum correlations between the nuclei in individual molecules, and a new variation on the classical vector diagram is introduced to represent these correlations. The treatment is extended to mixed populations that begin at thermal equilibrium, and the density matrix is introduced as an efficient means of carrying out quantum calculations for a mixed population. Finally, it is shown that the operators for observable magnetization and correlations can be used as a basis set for the density matrix, providing the formal justification for the widely-used rules of the product-operator treatment. Throughout the discussion, the vector diagrams are used to help maintain a connection between the mathematics and the sometimes subtle physical principles. An electronic supplement created with the Mathematica computer program is used to provide additional mathematical details and the means to carry out further calculations.

Small-angle X-ray scattering of reduced ribonuclease A: effects of solution conditions and comparisons with a computational model of unfolded proteins.

The disulfide-reduced form of bovine ribonuclease A, with the Cys thiols irreversibly blocked, was characterized by small-angle x-ray scattering. To help resolve the conflicting results and interpretations from previous studies of this model unfolded protein, we measured scattering profiles using a range of solution conditions and compared them with the profiles predicted by a computational model for a random-coil polypeptide. Analysis of the simulated and experimental profiles reveals that scattering intensities at intermediate angles, corresponding to interatomic distances in the range of 5-20 A, are particularly sensitive to changes in solvation and can be used to assess the internal scaling behavior of the polypeptide chain, expressed as a mass fractal dimension, D(m). This region of the scattering curve is also much less sensitive to experimental artifacts than is the very small angle regime (the Guinier region) that has been more typically used to characterize unfolded proteins. The experimental small-angle x-ray scattering profiles closely matched those predicted by the computational model assuming relatively small solvation energies. The scaling behavior of the polypeptide approaches that of a well-solvated polymer under conditions where it has a large net charge and at high urea concentrations. At lower urea concentrations and neutral pH, the behavior of the chain approaches that expected for theta-conditions, where the effects of slightly unfavorable interactions with solvent balance those of excluded volume, leading to scaling behavior comparable to that of an idealized random walk chain. Though detectable, the shift toward more compact conformations at lower urea concentrations does not correspond to a transition to a globule state and is associated with little or no reduction in conformational entropy. This type of collapse, therefore, is unlikely to greatly reduce the conformational search for the native state.

Functional and structural roles of the Cys14-Cys38 disulfide of bovine pancreatic trypsin inhibitor.

The disulfide bond between Cys14 and Cys38 of bovine pancreatic trypsin inhibitor lies on the surface of the inhibitor and forms part of the protease-binding region. The functional properties of three variants lacking this disulfide, with one or both of the Cys residues replaced with Ser, were examined, and X-ray crystal structures of the complexes with bovine trypsin were determined and refined to the 1.58-A resolution limit. The crystal structure of the complex formed with the mutant with both Cys residues replaced was nearly identical with that of the complex containing the wild-type protein, with the Ser oxygen atoms positioned to replace the disulfide bond with a hydrogen bond. The two structures of the complexes with single replacements displayed small local perturbations with alternate conformations of the Ser side chains. Despite the absence of the disulfide bond, the crystallographic temperature factors show no evidence of increased flexibility in the complexes with the mutant inhibitors. All three of the variants were cleaved by trypsin more rapidly than the wild-type inhibitor, by as much as 10,000-fold, indicating that the covalent constraint normally imposed by the disulfide contributes to the remarkable resistance to hydrolysis displayed by the wild-type protein. The rates of hydrolysis display an unusual dependence on pH over the range of 3.5-8.0, decreasing at the more alkaline values, as compared with the increased hydrolysis rates for normal substrates under these conditions. These observations can be accounted for by a model for inhibition in which an acyl-enzyme intermediate forms at a significant rate but is rapidly converted back to the enzyme-inhibitor complex by nucleophilic attack by the newly created amino group. The model suggests that a lack of flexibility in the acyl-enzyme intermediate, rather than the enzyme-inhibitor complex, may be a key factor in the ability of bovine pancreatic trypsin inhibitor and similar inhibitors to resist hydrolysis.

Initial disulfide formation steps in the folding of an omega-conotoxin.

To determine whether the native disulfides of omega-conotoxins are preferentially stabilized early in the folding of these small proteins, the rates and equilibria for disulfide formation were measured for three analogues of omega-conotoxin MVIIA. In each analogue, one of the three pairs of disulfide-bonded Cys residues was replaced with Ala residues, leaving four Cys residues that can form six intermediates with one disulfide and three species with two disulfides. For each analogue, all of the disulfide-bonded species were identified, and the equilibrium constants for forming the individual species via exchange with oxidized and reduced glutathione were measured. These equilibrium constants represent effective concentrations of the Cys thiols and ranged from 0.01 to 0.4 M in the fully reduced protein. There was little or no preference for forming the native disulfides, and the equilibria for forming the first and second disulfides decreased only slightly upon the addition of 8 M urea. The data for the four-Cys analogues, together with equilibrium data for the six-Cys form, were also used to estimate effective concentrations for forming a third disulfide once two native disulfides are present. These effective concentrations were approximately 100 and 10 M in the presence of 0 and 8 M urea, respectively. The results indicate that there is little or no preferential formation of native interactions in the folding of these molecules until two disulfides have formed, after which there is a high degree of cooperativity among the native interactions.

The Cys-Xaa-His metal-binding motif: [N] versus [S] coordination and nickel-mediated formation of cysteinyl sulfinic acid.

A series of peptide ligands containing the sequence -Cys-Xaa-His- (CXH; Xaa=Gly or Lys) has been prepared and the coordination chemistry of these peptides with nickel(II) investigated. Selective protection of either the N-terminal cysteine thiol or amine group gave complexes with amino or thiolato coordination, respectively, to nickel(II). Insertion of CGH into a pentapeptide, N-acetyl-Ala-Cys-Gly-His-Ala-CONH(2), allowed the formation of a square-planar thiolato Cys-Gly-His complex with nickel(II) in an internal position of the peptide. Inclusion of an N-terminal cysteine residue with a free amino terminus gave rise to pH- and dioxygen-dependent coordination behavior. Solutions of CGH-CONH(2) with nickel(II) at neutral pH yielded a red nickel-thiolate complex, but at higher pH (8.5 or above) or with exposure to dioxygen, yellow nickel complexes with N-terminal amino coordination were observed. The disulfide-bridged dimers formed from Ni(CGH-CONH(2)) in the presence of air were characterized and found to have the typical coordination found in the amino-terminal binding motif of the serum albumins. Nickel(II) coordination and thiol reactivity were also studied by determination of rates of thiol alkylation and by monitoring air oxidation in the presence of various metals. Zinc(II) effectively inhibits thiol alkylation and oxidation (disulfide formation) in all the peptides studied. Nickel(II) inhibits aerobic oxidation and alkylation of N-terminal protected peptides such as N-acetyl-Cys-Gly-His, but does not inhibit air oxidation of free amino terminal peptides such as Cys-Gly-His. Instead, nickel(II) mediates the formation an additional product under aerobic conditions, a cysteinesulfinic acid.