Janet S. Anderson

Polarization and Polarizability Assessed by Protein Amide Acidity

Hydroxide-catalyzed exchange rate constants were determined for those amides of FK506-binding protein (FKBP12), ubiquitin, and chymotrypsin inhibitor 2 (CI2) that are solvent-accessible in the high-resolution X-ray structures. When combined with previous hydrogen exchange results for the rubredoxin from Pyrococcus furiosus, the acidity of these amides was calculated by continuum dielectric methods as a function of the nonpolarizable electrostatic parameter set, internal dielectric, and the charge distribution of the peptide anion. The CHARMM22 parameter set with an internal dielectric value of 3 and an ab initio-derived anion charge distribution yielded an rmsd value of 7 for the 56 amide exchange rate constants ranging from 10(0.67) to 10(9.0) M(-1) s(-1). The OPLS-AA parameter set yielded comparably robust predictions, while that of PARSE, AMBER parm99, and AMBER ff03 performed more poorly. The small value for the optimal internal dielectric, combined with the brief lifetime of the peptide anion intermediate and the uniformity of the correlation between predicted and observed amide acidities, is consistent with electronic polarizability providing the dominant contribution to dielectric shielding. By construction, nonpolarizable force fields do not model electric field attenuation by electronic polarizability. Accurate prediction of the total electrostatic energy by such force fields necessitates the hyperpolarization of the atomic charge values in order to match the average electric field energy density (1/2)epsilon(tau)E(2)(tau) when epsilon(tau) is set to the in vacuo dielectric value of 1. The resulting predictions of the experimental hydrogen exchange data demonstrate the substantial systematic errors in the predicted electrostatic potential that can arise when dielectric shielding due to electronic polarizability is neglected.

A Billion-fold Range in Acidity for the Solvent-Exposed Amides of Pyrococcus furiosus Rubredoxin

The exchange rates of the static solvent-accessible amide hydrogens of Pyrococcus furiosus rubredoxin range from near the diffusion-limited rate to a billion-fold slower for the non-hydrogen-bonded Val 38 (eubacterial numbering). Hydrogen exchange directly monitors the kinetic acidity of the peptide nitrogen. Electrostatic solvation free energies were calculated by Poisson-Boltzmann methods for the individual peptide anions that form during the hydroxide-catalyzed exchange reaction to examine how well the predicted thermodynamic acidities match the experimentally determined kinetic acidities. With the exception of the Ile 12 amide, the differential exchange rate constant for each solvent-exposed amide proton that is not hydrogen bonded to a backbone carbonyl can be predicted within a factor of 6 (10 (0.78)) root-mean-square deviation (rmsd) using the CHARMM22 electrostatic parameter set and an internal dielectric value of 3. Under equivalent conditions, the PARSE parameter set yields a larger rmsd value of 1.28 pH units, while the AMBER parm99 parameter set resulted in a considerably poorer correlation. Either increasing the internal dielectric value to 4 or reducing it to a value of 2 significantly degrades the quality of the prediction. Assigning the excess charge of the peptide anion equally between the peptide nitrogen and the carbonyl oxygen also reduces the correlation to the experimental data. These continuum electrostatic calculations were further analyzed to characterize the specific structural elements that appear to be responsible for the wide range of peptide acidities observed for these solvent-exposed amides. The striking heterogeneity in the potential at sites along the protein-solvent interface should prove germane to the ongoing challenge of quantifying the contribution that electrostatic interactions make to the catalytic acceleration achieved by enzymes.

Peptide conformer acidity analysis of protein flexibility monitored by hydrogen exchange.

The amide hydrogens that are exposed to solvent in the high-resolution X-ray structures of ubiquitin, FK506-binding protein, chymotrypsin inhibitor 2, and rubredoxin span a billion-fold range in hydroxide-catalyzed exchange rates which are predictable by continuum dielectric methods. To facilitate analysis of transiently accessible amides, the hydroxide-catalyzed rate constants for every backbone amide of ubiquitin were determined under near physiological conditions. With the previously reported NMR-restrained molecular dynamics ensembles of ubiquitin (PDB codes 2NR2 and 2K39) used as representations of the Boltzmann-weighted conformational distribution, nearly all of the exchange rates for the highly exposed amides were more accurately predicted than by use of the high-resolution X-ray structure. More strikingly, predictions for the amide hydrogens of the NMR relaxation-restrained ensemble that become exposed to solvent in more than one but less than half of the 144 protein conformations in this ensemble were almost as accurate. In marked contrast, the exchange rates for many of the analogous amides in the residual dipolar coupling-restrained ubiquitin ensemble are substantially overestimated, as was particularly evident for the Ile 44 to Lys 48 segment which constitutes the primary interaction site for the proteasome targeting enzymes involved in polyubiquitylation. For both ensembles, “excited state” conformers in this active site region having markedly elevated peptide acidities are represented at a population level that is 102 to 103 above what can exist in the Boltzmann distribution of protein conformations. These results indicate how a chemically consistent interpretation of amide hydrogen exchange can provide insight into both the population and the detailed structure of transient protein conformations.

Electrostatic stabilization and general base catalysis in the active site of the human protein disulfide isomerase a domain monitored by hydrogen exchange.

The nucleophilic Cys36 thiol of the human protein disulfide isomerase a domain is positioned over the N terminus of the α2 helix. Amides in the active site exhibit diffusion‐limited, hydroxide‐catalyzed exchange, indicating that the local positive electrostatic potential decreases the pK value for peptide anion formation by at least 2 units so as to equal or exceed the acidity of water. In stark contrast to the pH dependence of exchange for simple peptides, the His38 amide in the reduced enzyme exhibits a maximum rate of exchange at pH 5 due to efficient general base catalysis by the neutral imidazole of its own side chain and suppression of its exchange by the ionization of the Cys36 thiol. Ionization of this thiol and deprotonation of the His38 side chain suppress the Cys39 amide hydroxide‐catalyzed exchange by a million‐fold. The electrostatic potential within the active site monitored by these exchange experiments provides a means of stabilizing the two distinct transition states that lead to substrate reduction and oxidation. Molecular modeling offers a role for the conserved Arg103 in coordinating the oxidative transition‐state complex, thus providing further support for mechanisms of disulfide isomerization that utilize enzymatic catalysis at each step of the overall reaction.

Backbone conformational dependence of peptide acidity.

Electrostatic interactions at the protein surface yield over a billion-fold range of amide hydrogen exchange rates. This range is equivalent to the maximal degree of attenuation in exchange rates that have been shown to occur for amides buried within the protein interior. Continuum dielectric analysis of Ala-Ala, Ala-Gly, Gly-Ala and trans-Pro-Ala peptide conformer acidities predicts that the relative orientation of the two neighboring peptide groups can account for a million-fold variation in hydroxide-catalyzed hydrogen exchange rates. As in previous protein studies, an internal dielectric value of 3 was found to be applicable to simple model peptides, presumably reflecting the short lifetime of the peptide anion intermediate. Despite the million-fold range in conformer acidities, the small differences in the experimental exchange rates for these peptides are accurately predicted. Ala-Ala conformers with an extended N-terminal residue and the C-terminal residue in the alpha conformation are predicted to account for over 60% of the overall hydrogen exchange reaction, despite constituting only 12% of the protein coil population.

Experimentally assessing molecular dynamics sampling of the protein native state conformational distribution.

The acute sensitivity to conformation exhibited by amide hydrogen exchange reactivity provides a valuable test for the physical accuracy of model ensembles developed to represent the Boltzmann distribution of the protein native state. A number of molecular dynamics studies of ubiquitin have predicted a well-populated transition in the tight turn immediately preceding the primary site of proteasome-directed polyubiquitylation Lys 48. Amide exchange reactivity analysis demonstrates that this transition is 10(3)-fold rarer than these predictions. More strikingly, for the most populated novel conformational basin predicted from a recent 1 ms MD simulation of bovine pancreatic trypsin inhibitor (at 13% of total), experimental hydrogen exchange data indicates a population below 10(-6). The most sophisticated efforts to directly incorporate experimental constraints into the derivation of model protein ensembles have been applied to ubiquitin, as illustrated by three recently deposited studies (PDB codes 2NR2, 2K39 and 2KOX2K392KOX). Utilizing the extensive set of experimental NOE constraints, each of these three ensembles yields a modestly more accurate prediction of the exchange rates for the highly exposed amides than does a standard unconstrained molecular simulation. However, for the less frequently exposed amide hydrogens, the 2NR2 ensemble offers no improvement in rate predictions as compared to the unconstrained MD ensemble. The other two NMR-constrained ensembles performed markedly worse, either underestimating (2KOX) or overestimating (2K39) the extent of conformational diversity.

Rotational velocity rescaling of molecular dynamics trajectories for direct prediction of protein NMR relaxation

Rotational velocity rescaling (RVR) enables (15)N relaxation data for the anisotropically tumbling B3 domain of Protein G (GB3) to be accurately predicted from 1 μs of constant energy molecular dynamics simulation without recourse to any system-specific adjustable parameters. Superposition of adjacent trajectory frames yields the unique rotation axis and angle of rotation that characterizes each transformation. By proportionally scaling the rotation angles relating each consecutive pair of frames, the rotational diffusion in the RVR-MD trajectory was adjusted to correct for the elevated self-diffusion rate of TIP3P water. (15)N T(1) and T(2) values for 32 residues in the regular secondary structures of GB3 were predicted with an rms deviation of 2.2%, modestly larger than the estimated experimental uncertainties. Residue-specific chemical shift anisotropy (CSA) values reported from isotropic solution, liquid crystal and microcrystalline solid measurements less accurately predict GB3 relaxation than does applying a constant CSA value, potentially indicating structure-dependent correlated variations in (1)H-(15)N bond length and (15)N CSA. By circumventing the quasi-static analysis of NMR order parameters often applied in MD studies, a more direct test is provided for assessing the accuracy with which molecular simulations predict protein motion in the ps-ns timeframe. Since no assumption of separability between global tumbling and internal motion is required, utility in analyzing simulations of mobility in disordered protein segments is anticipated.

Assessing the native state conformational distribution of ubiquitin by peptide acidity.

At equilibrium, every energetically feasible conformation of a protein occurs with a non-zero probability. Quantitative analysis of protein flexibility is thus synonymous with determining the proper Boltzmann-weighting of this conformational distribution. The exchange reactivity of solvent-exposed amide hydrogens greatly varies with conformation, while the short-lived peptide anion intermediate implies an insensitivity to the dynamics of conformational motion. Amides that are well-exposed in model conformational ensembles of ubiquitin vary a million-fold in exchange rates which continuum dielectric methods can predict with an rmsd of 3. However, the exchange rates for many of the more rarely exposed amides are markedly overestimated in the PDB-deposited 2K39 and 2KN5 ubiquitin ensembles, while the 2NR2 ensemble predictions are largely consistent with those of the Boltzmann-weighted conformational distribution sampled at the level of 1%. The correlation between the fraction of solvent-accessible conformations for a given amide hydrogen and the exchange rate constant for that residue provides a useful monitor of the degree of completeness with which a given ensemble has sampled the energetically accessible conformational space. These exchange predictions correlate with the degree to which each ensemble deviates from a set of 46 ubiquitin X-ray structures. Kolmogorov-Smirnov analysis for the distribution of intra- and inter-ensemble pairwise structural rmsd values assisted the identification of a subensemble of 2K39 that eliminates the overestimations of hydrogen exchange rates observed for the full ensemble. The relative merits of incorporating experimental restraints into the conformational sampling process are compared to using these restraints as filters to select subpopulations consistent with the experimental data.

Assessing the chemical accuracy of protein structures via peptide acidity

Although the protein native state is a Boltzmann conformational ensemble, practical applications often require a representative model from the most populated region of that distribution. The acidity of the backbone amides, as reflected in hydrogen exchange rates, is exquisitely sensitive to the surrounding charge and dielectric volume distribution. For each of four proteins, three independently determined X-ray structures of differing crystallographic resolution were used to predict exchange for the static solvent-exposed amide hydrogens. The average correlation coefficients range from 0.74 for ubiquitin to 0.93 for Pyrococcus furiosus rubredoxin, reflecting the larger range of experimental exchange rates exhibited by the latter protein. The exchange prediction errors modestly correlate with the crystallographic resolution. MODELLER 9v6-derived homology models at ~60% sequence identity (36% identity for chymotrypsin inhibitor CI2) yielded correlation coefficients that are ~0.1 smaller than for the cognate X-ray structures. The most recently deposited NOE-based ubiquitin structure and the original NMR structure of CI2 fail to provide statistically significant predictions of hydrogen exchange. However, the more recent RECOORD refinement study of CI2 yielded predictions comparable to the X-ray and homology model-based analyses.

Statistical allosteric coupling to the active site indole ring flip equilibria in the FK506-binding domain

In solution, the Trp 59 indole ring at the base of the active site cleft in the FKBP domain protein FKBP12 is rotated by ~90° at a population level of 20%, relative to its canonical crystallographic orientation. NMR measurements on the homologous FK1 domains of human FKBP51 and FKBP52 indicate no observable indole ring flip conformation, while the V101I variant of FKBP12 decreases the population having a perpendicular indole orientation by 10-fold. A set of three parallel 400 ns CHARMM27 molecular simulations for both wild type FKBP12 and the V101I variant examined how this ring flip might be energetically coupled to a transition of the Glu 60 sidechain which interacts with the backbone of the 50s loop located ~12 Å from the indole nitrogen. Analysis of the transition matrix for the local dynamics of the Glu 60 sidechain, the Trp 59 sidechain, and of the structurally interposed α-helix hydrogen bonding pattern yielded a statistical allosteric coupling of 10 kJ/mol with negligible concerted dynamical coupling for the transitions of the two sidechains.