Implications of using approximate Bloch-McConnell equations in NMR analyses of chemically exchanging systems: application to the electron self-exchange of plastocyanin

The validity of a series of approximate solutions of the Bloch-McConnell equations normally applied in the analyses of chemically exchanging systems is evaluated, using the electron self-exchange (ESE) in the blue copper protein plastocyanin from Anabaena variabilis as an example. The evaluation is based on a comparison with the results of a complete analysis of the NMR signals of chemically exchanging nuclei that allows an independent and accurate determination of all the involved parameters. The complete analysis is based on the general solution of the Bloch-McConnell equations. It includes a simultaneous analysis of the chemical shift, and the transverse and longitudinal relaxation rates of the observed nuclei as well as the variation of these parameters with the molar fractions of the exchanging species and the rate of the chemical exchange process. The linear prediction model method was used in the data analysis to achieve the highest possible precision. Surprisingly, it is found that the fast exchange condition may not be fulfilled even in cases where a single exchange-averaged NMR signal is observed, and the Larmor frequency and relaxation rates depend linearly on the molar fractions of the exchanging species. In such cases the use of approximate solutions in the analysis of the transverse relaxation rates and the pseudo-contact shifts can lead to erroneous results. In limiting cases close to the fast exchange and slow exchange regimes correct values of some of the parameters can be obtained using the second order approximate solution of the Bloch-McConnell equations. In contrast, the complete analysis of the NMR signals results in an accurate determination of the exchange rates and the NMR parameters of the exchanging sites. This, in turn, can provide information about the structure and function of a protein undergoing chemically exchange. For the investigated plastocyanin the complete analysis results in an accurate determination of the paramagnetic enhancement of the nuclear relaxation rates, the paramagnetic chemical shift, the electron relaxation rate, the electron self-exchange rate, and the distances between the nuclei and the paramagnetic metal ion, viz. the Cu2+ ion.     

Measuring the longitudinal NMR relaxation rates of fast relaxing nuclei using a signal eliminating relaxation filter

A new experiment for selective determination of the relaxation rates of fast relaxing NMR signals is presented. The experiment is derived from the conventional inversion recovery experiment by substituting the 180 degrees inversion pulse of this experiment with a signal eliminating relaxation filter (SERF) consisting of three 180 degrees pulses separated by two variable delays, Delta1 and Delta2. The SERF experiment allows a selective suppression of signals with relaxation rates below a given limit while monitoring the relaxation of faster relaxing signals. The experiment was tested on a sample of 20% oxidized plastocyanin from Anabaena variabilis, where the fast exchange of an electron between the reduced (diamagnetic) and the oxidized (paramagnetic) form results in a series of average signals with widely different relaxation rates. To ensure an optimum extraction of information from the experimental data, the relaxation rates were obtained from the SERF experiment by a simultaneous analysis of all the FIDs of the experiment using a fast linear prediction model method developed previously. The reliability of the relaxation rates obtained from the SERF experiment was confirmed by a comparison of the rates with the corresponding rates obtained from a conventional inversion recovery experiment.     

Computational study of redox active centres of blue copper proteins: a computational DFT study

Active sites of blue copper proteins in both reduced and oxidized states were studied at the Density Functional Theory (DFT) level. Two families of these redox sites were examined: the Type A centres with methionine ligand as fourth residue and the Type B with glutamine residue. Constrained and full optimizations were performed on the protein data bank structures in vacuo and in implicit solvent model simulating protein and water environments. It was found that the redox sites do not possess optimum geometries regardless of the oxidation state. The axial Cu-ligand bond elongates/shortens in the fully optimized Cu(I)/Cu(II) complexes. The reduced centres have a tendency to decrease the coordination number, while a trend to form four ‘equivalent’ bonds is preferred in the oxidized centres. Comparison of the full and constrained optimizations also revealed that the A centres exhibit lower relaxation energies. In the constrained structures, a higher ionization potential was predicted for the A centres when compared with the B centres regardless of the influence of environment. The calculated relative difference of the redox potentials between various A and B centres is in good agreement with the experimental data. In the fully optimized complexes, the redox properties are dependent on the environment but usually higher IP for the B centres is predicted. Partial charges, MOs, and spin density distributions (obtained by natural population analysis) were analysed together with calculated electron paramagnetic resonance (EPR) spectra for deeper understanding of the results obtained.     

Evaluation of two simplified 15N-NMR methods for determining micros-ms dynamics of proteins

Two methods for estimating the microsecond-millisecond dynamics in proteins from only two 15N relaxation parameters at one magnetic field strength are investigated. Thus, the chemical exchange contribution, R(ex), to the transversal relaxation rate, which contains the dynamics information, is evaluated by two methods: (i) one in which the R(ex) term is derived from the 15N R1 and R2 relaxation rates alone, and (ii) one in which it is obtained from the transversal dipole-chemical shift anisotropy (CSA) cross-correlation rate, eta(xy), and the R2 rate. Since the R1, R2, and eta(xy) experiments are fast and sensitive, both methods are attractive in studies where large amounts of dynamical information are required. However, both methods are liable to effects that can compromise the estimation of the R(ex) terms. In the R2/R1 method, internal ps-ns dynamics and rotational anisotropy can interfere with the determination of R(ex), while in the R2/eta(xy) method it can be affected by variations in the 15N chemical shift anisotropy. Here, the applicability of the two methods is investigated using plastocyanin from Anabaena variabilis as an example, and the quality of the obtained R(ex) terms is evaluated both theoretically and experimentally. It is found that the R2/R1 method gives reliable R(ex) terms if the protein is relatively rigid and tumbles fast and nearly isotropically in solution, as for instance plastocyanin, and is preferable in such cases. In contrast, the R2/eta(xy) method gives better results if the protein is flexible or highly non-spherical and can be used for such proteins, if the sequential variation in the 15N chemical shift anisotropy is negligible. For exchange terms <1 s(-1) neither method is reliable.     

Theoretical study on interaction of cytochrome f and plastocyanin complex by a simple coarse-grained model with molecular crowding effect

ABSTRACT

We present a simple coarse-grained model with the molecular crowding effect in solvent to investigate the structure and dynamics of protein complexes including association and/or dissociation processes and investigate some physical properties such as the structure and the reaction rate from the viewpoint of the hydrophobic intermolecular interactions of protein complex. In the present coarse-grained model, a function depending upon the density of hydrophobic amino acid residues in a binding area of the complex is introduced, and the function involves the molecular crowding effect for the intermolecular interactions of hydrophobic amino acid residues between proteins. We propose a hydrophobic intermolecular potential energy between proteins by using the density-dependent function. The present coarse-grained model is applied to the complex of cytochrome f and plastocyanin by using the Langevin dynamics simulation to investigate some physical properties such as the complex structure, the electron transfer reaction rate constant from plastocyanin to cytochrome f and so on. We find that for proceeding the electron transfer reaction, the distance between metals in their active sites is necessary within about 18 Å. We discuss some typical complex structures formed in the present simulation in relation to the molecular crowding effect on hydrophobic interactions.