An approach to the mapping of internal motions in proteins. Analysis of carbon-13 NMR relaxation in the bovine pancreatic trypsin inhibitor

Model-independent interpretation of NMR relaxation data for unfolded proteins: the acid-denatured state of ACBP

We have investigated the acid-unfolded state of acyl-coenzyme A binding protein (ACBP) using 15N laboratory frame nuclear magnetic resonance (NMR) relaxation experiments at three magnetic field strengths. The data have been analyzed using standard model-free fitting and models involving distribution of correlation times. In particular, a model-independent method of analysis that does not assume any analytical form for the correlation time distribution is proposed. This method explains correlations between model-free parameters and the analytical distribution parameters found by other authors. The analysis also shows that the relaxation data are consistent with and complementary to information obtained from other parameters, especially secondary chemical shifts and residual dipolar couplings, and strengthens the conclusions of previous observations that three out of the four regions that form helices in the native structure appear to contain residual secondary structure also in the acid-denatured state.

Intermolecular electrostatic interactions and Brownian tumbling in protein solutions

It is often implicitly assumed that the long-range intermolecular electrostatic interactions in homogeneous protein solutions either are negligible for affecting protein Brownian tumbling or cause its deceleration without changing the shape of rotational auto-correlation function. This review presents a wide set of experimental data (NMR relaxation, dielectric spectroscopy and Brownian dynamics simulations) demonstrating that the interprotein electrostatic steering leads to a complication of the rotational correlation function. The key point of this effect is the rotational anisotropy caused by the interaction of the electric dipole moment of a protein with the external electric field produced by charges of neighboring proteins. Taking this effect into account in some cases might be of critical importance for the correct interpretation of various experimental data.

A new approach to visualizing spectral density functions and deriving motional correlation time distributions: applications to an alpha-helix-forming peptide and to a well-folded protein

A new approach to visualizing spectral densities and analyzing NMR relaxation data has been developed. By plotting the spectral density function, J(omega), as F(omega)=2 omega J(omega) on the log-log scale, the distribution of motional correlation times can be easily visualized. F(omega) is calculated from experimental data using a multi-Lorentzian expansion that is insensitive to the number of Lorentzians used and allows contributions from overall tumbling and internal motions to be separated without explicitly determining values for correlation times and their weighting coefficients. To demonstrate the approach, (15)N and (13)C NMR relaxation data have been analyzed for backbone NH and C(alpha)H groups in an alpha-helix-forming peptide 17mer and in a well-folded 138-residue protein, and the functions F(omega) have been calculated and deconvoluted for contributions from overall tumbling and internal motions. Overall tumbling correlation time distribution maxima yield essentially the same overall correlation times obtained using the Lipari-Szabo model and other standard NMR relaxation data analyses. Internal motional correlational times for NH and C(alpha)H bond motions fall in the range from 100 ps to about 1 ns. Slower overall molecular tumbling leads to better separation of internal motional correlation time distributions from those of overall tumbling. The usefulness of the approach rests in its ability to visualize spectral densities and to define and separate frequency distributions for molecular motions.

Main-chain dynamics of cardiotoxin II from Taiwan cobra (Naja naja atra) as studied by carbon-13 NMR at natural abundance: delineation of the role of functionally important residues

Cardiotoxin analogue II (CTX II) is an all beta-sheet, small molecular mass (6.8 kDa), basic protein possessing a wide array of biological properties. Nearly complete assignment of the protonated carbon resonances has been achieved by heteronuclear NMR experiments. The study shows that the correlation between the carbon-13 chemical shifts and CTX II structure is good in general, but interesting deviations are also noticed. To characterize the internal dynamics of CTX II, longitudinal, transverse relaxation rates and heteronuclear 13C{1H} NOEs were measured for alpha-carbons at natural abundance by two-dimensional NMR spectroscopy. Relaxation measurements were obtained in a 14.1 T spectrometer for 50 residues, which are evenly spread along the CTX II polypeptide chain. Except for five alpha-carbons, all data were analyzed from a simple two-parameter spectral density function using the model free approach of Lipari and Szabo. The microdynamical parameters (S2, taue, and Rex) were calculated with an overall rotational correlation time (taum) for the protein of 4.8 ns. For most residues, the alpha-carbons exhibit fast (taue < 30 ps) restricted libration motions (S2 = 0.79-0.89). The present study reveals that the functionally important residues located at the tips of the three loops are flexible, and the flexibility of residues in this region could be important in the binding of cardiotoxins to their putative "receptors" which are postulated to be located on the erythrocyte membrane. In addition, the results obtained in the present study support the earlier predictions on the relative role of the lysine residues in the erythrocyte lytic activity of cardiotoxins.

Protein backbone dynamics revealed by quasi spectral density function analysis of amide N-15 nuclei

Spectral density functions J(0), J(omega N), and J(omega H + omega N) of individual amide N-15 nuclei in proteins were approximated by a quasi spectral density function (QSDF). Using this function, the backbone dynamics were analyzed for seven protein systems on which data have been published. We defined J(0; omega N) as the difference between the J(0) and the J(omega N) values, which describes motions slower than 50 (or 60) MHz, and J(omega N; omega H+N) as the difference between the J(omega N) and the J(omega H + omega N) values, which describes motions slower than 450 (or 540) MHz. The QSDF analysis can easily extract the J(0; omega N) of protein backbones, which have often some relation to biologically relevant reactions. Flexible N-terminal regions in eglin c and glucose permease IIA and a loop region in eglin c showed smaller values of both the J(0; omega N) and the J(omega N; omega H+N) as compared with the other regions, indicating increases in motions faster than nanosecond. The values of the J(0; omega N) for the backbone of the FK506 binding protein showed a large variation in the apoprotein but fell in a very narrow range after the binding of FK506. Characteristic increase or decrease in the values of J(0) and J(omega N) was observed in two or three residues located between secondary structures.

Assignment of the protonated 13C resonances of apo-neocarzinostatin by 2D heteronuclear NMR spectroscopy at natural abundance

Nearly complete assignment of the protonated carbon resonances of apo-neocarzinostatin, a 113-amino acid antitumor antibiotic carrier protein, has been achieved at natural 13C abundance using heteronuclear 2D experiments. Most of the cross peaks in the proton-carbon correlation map were identified by the combined use of HMQC, HMQC-RELAY and HMQC-NOESY spectra, using already published proton chemical shifts. However, double-DEPT and triple-quantum experiments had to be performed for the edition of CH and CH2 side-chain groups, respectively, which were hardly visible on HMQC-type maps. The triple-quantum pulse sequence was adapted from its original scheme to be applicable to a natural abundance sample. The correlation between carbon chemical shifts and the apo-neocarzinostatin structure is discussed. In particular, 13C alpha secondary shifts correlate well with the backbone conformation. These shifts also yield information about the main-chain flexibility of the protein. Assignments reported herein will be used further for interpretation of carbon relaxation times in a study of the internal dynamics of apo-neocarzinostatin.

Tri- and diglycine backbone rotational dynamics investigated by 13C NMR multiplet relaxation and molecular dynamics simulations

Backbone motional dynamics in tri- and diglycine have been investigated by using 13C NMR multiplet relaxation spectroscopy. Dipolar auto- and cross-correlation times were determined as a function of pH, ionic strength, and temperature. Molecular dynamics simulations and phi,psi bond rotation energy profiles were calculated for insight into the physical nature of backbone rotations that could contribute to 13C relaxation. Various motional models were used to fit the experimental data. For internal glycine G2 in triglycine, restricted and unrestricted rotational diffusion models both underestimate internal correlation times, although they do agree that the axis of fastest internal rotation is directed closely along the C alpha-C bond. For di- and triglycine, significant pH dependencies in cross-correlation times for C-terminal glycines, and more so for those of N-terminal glycines, indicate the importance of the ionization state in internal mobility of terminal backbone positions. For terminal glycines, rotational jump models which allow for diffusive-like fluctuations within minima best explain the experimental data. phi,psi rotational fluctuation amplitudes and internal rotational energy barriers derived from the temperature dependence of 13C relaxation parameters, which range from 3 to 5 kcal/mol, agree well with those values calculated in rotational energy profiles.

Overall and internal protein dynamics in solution studied by the nonselective proton relaxation

A new algorithm for the analysis of nonselective proton relaxation data in protein solution is presented. T1 and T2 of protein protons in lysozyme and RNase solutions were measured at three resonance frequencies--11, 27 and 90 MHz. In addition we measured water T1 dispersions in lysozyme solutions over the frequency range of 10 kHz--10 MHz on a field-cycling installation. It was found that the correlation function of protein Brownian tumbling as a whole is nonexponential: in addition to a component with the usual correlation time tau t it contained also a component with a correlation time exceeding tau t by approximately an order of magnitude and with a small relative amplitude. The experiment shows that the parameters of the slow component of the tumbling correlation function depend both on the concentration and on the pH of the protein solution. To explain the results obtained one must take into account the interprotein electrostatic interactions in solution. All protein molecules in solution experience electrostatic torques from their neighbors and this gives rise to an anisotropy in the protein Brownian tumbling. The lifetime of this anisotropy is controlled by the translational diffusion of proteins.

Proton nmr relaxation study of the dynamics of anthopleurin-A in solution

Spin-spin and spin-lattice 1H-nmr relaxation times of the sea anemone polypeptide anthopleurin-A were measured at frequencies of 200, 300, 400, and 500 MHz. Relaxation times were fitted iteratively by least squares regression to the isotropic tumbling model, Woessner's model for anisotropic motion, and Lipari and Szabo's "model-independent" model. Data for aromatic and aliphatic methine protons could not be fitted satisfactority using the isotropic model. Good fits were obtained, however, using the model-independent approach, indicating that high-frequency internal motions of the polypeptide backbone were significant. In addition, a range of tau c values from 2.2 to 3.2 ns was obtained for various methine protons, suggesting that overall rotational reorientation of the molecule was anisotropic. Methyl group relaxation data were fitted satisfactorily by Woessner's model. Some assessment has been made of the effect of experimental errors on the quality of fit to the data, as well as of the contribution of experimental values at certain frequencies to definition of the spectral density function.

Spectroscopic evidence for a porphobilinogen deaminase-tetrapyrrole complex that is an intermediate in the biosynthesis of uroporphyrinogen III

Incubation of porphobilinogen (PBG) with PBG deaminase from Rhodopseudomonas sphaeroides in carbonate buffer (pH 9.2) to total PBG consumption resulted in low yields of uroporphyrinogen I (uro'gen I). In the reaction mixture a pyrrylmethane accumulated, which at longer incubation periods was transformed into uro'gen I. The accumulated pyrrylmethane gave an Ehrlich reaction which was different from that of a 2-(aminomethyl)dipyrrylmethane or 2-(aminomethyl)tripyrrane. It resembled that of a bilane (tetrapyrrylmethane) but was different from that of a 2-(hydroxymethyl)bilane. The 13C NMR spectra of incubations carried out with [11-13C]PBG indicated that the pyrrylmethane was a tetrapyrrole with methylene resonances at 22.35-22.50 ppm. It was loosely bound to the deaminase, and when separated from the enzyme by gel filtration or gel electrophoresis, it immediately cyclized to uro'gen I. No enzyme-bound methylene could be detected by its chemical shift, suggesting that its line width must be very broad. When uro'gen III-cosynthase was added to the deaminase-tetrapyrrole complex, uro'gen III was formed at the expense of the latter in about 75% yield. The tetrapyrrole could only be partially displaced from the enzyme by ammonium ions, although a small amount of 2-(aminomethyl)bilane was always formed together with the tetrapyrrole intermediate. A protonated uro'gen I structure for this intermediate was ruled out by incubations using [2,11-13C]PBG. Uro'gen III formation from 2-(hydroxymethyl)bilane (HMB) and from the deaminase-tetrapyrrole intermediate was compared by using deaminase-cosynthase and cosynthase from several sources. It was found that while the HMB inhibited uro'gen III formation at higher concentrations and longer incubation times, uro'gen III formation from the complex did not decrease with time.

New modification of model-free approach to analysis of nuclear magnetic relaxation data in proteins

A formal approach to the analysis of 13C magnetic relaxation data in proteins has been developed. It is based on the concepts of one of the authors on the internal motions in solid polymers (Fedotov, V.D., Pulse NMR in bulk polymers, Doctoral dissertation, Kazan, USSR, 1981). According to this approach the intermolecular motions in proteins are considered as anisotropic ones and described in terms of a spectrum of correlation times. To characterize the motions a set of formal microdynamic parameters has been introduced. They are: the anisotropy parameter (a measure of spatial restriction of motion), the most probable correlation time, the parameter of the correlation time distribution width. The analysis of protonated carbon relaxation in globular proteins (bovine pancreatic trypsin inhibitor and ribonuclease S) and polymers has been carried out by the model-free approach. Microdynamic parameters of CH3-, CH2-, aromatic CH-groups have been considered within the framework of the diffusional rotation-oscillation models. To explain the backbone CH-group relaxation the model of the defect diffusion has been applied. The distinctive feature of the results obtained is the broad correlation time distribution for all groups of any type. The causes of nonexponential correlation function of local motion have been discussed. To elucidate the nature of the correlation time the carbon magnetization decays in the wide range of microdynamic parameter values imitating various experimental conditions have been calculated.

Comparative studies of conformation and internal mobility in native and circular basic pancreatic trypsin inhibitor by 1H nuclear magnetic resonance in solution

A circular derivative of bovine pancreatic trypsin inhibitor (c-BPTI) with the C- and N-termini covalently linked with a peptide bond, has been studied in solution by spectroscopic techniques, principally two-dimensional 1H NMR. Near complete sequence specific assignment of the 1H NMR spectrum of c-BPTI has been obtained in a highly efficient manner, using recently developed experimental techniques. The assignments serve as the necessary background for detailed examination of the effects of the chemical modification on global and local features of the protein conformation and on the internal mobility. Analysis of chemical shifts, spin-spin coupling constants, amide proton exchange and proton-proton Overhauser enhancements indicates that perturbations of the native BPTI conformation in c-BPTI involve exclusively residues adjacent to the modification site. The strict localization and small magnitude of the conformation changes relative to native BPTI emphasize the important role of the salt bridge between the chain ends in determining the solution conformation and dynamics in the chain terminal regions of the native protein.

13C NMR studies of the molecular dynamics of selectively 13C-enriched ribonuclease complexes

13C spin-lattice (T1) relaxation times determined at four frequencies (25, 68, 100, and 125 MHz) have been used to probe the molecular dynamics of ribonuclease S' complexes prepared from synthetic amino-terminal peptides containing 13C enrichment (ca. 90%) at selected sites [Niu, C., Matsuura, S., Shindo, H., & Cohen, J. S. (1979) J. Biol. Chem. 254, 3788]. It was found that the motion of the C alpha-H bond of Ala-5 could not be determined by isotropic reorientation alone. The time scale and spatial restriction on the internal motion of this residue were determined by the model-free approach of Lipari and Sazbo [Lipari, G., & Szabo, A. (1982) J. Am. Chem. Soc. 104, 4546-4559]. It was found that the C alpha-H bond, in addition to an overall correlation time of 20 ns, underwent internal motion with a correlation time of 0.5 ns and a generalized order parameter S corresponding to a cone semiangle of 23 degrees C. The C beta-H bond had a correlation time of 37 ps, reflecting the fast rotation of the methyl group, and had an S value close to that expected if the C alpha-C beta and C alpha-H bonds have the same degree of spatial restriction.

Internal dynamics and overall motion of lysozyme studied by fluorescence depolarization of the eosin lysozyme complex

Time-resolved fluorescence depolarization on the nanosecond and sub-nanosecond time scales is a powerful technique for the study of rapid motions in the condensed phase. We apply this technique to measure the motions of proteins using both extrinsic and intrinsic probes. Eosin, which absorbs and fluoresces in the visible, forms a one-to-one complex with lysozyme binding in the hydrophobic box region and is used as an extrinsic probe of lysozyme motion. The long-time anisotropy of bound eosin is used to measure the overall rotation time of lysozyme for which refined values are presented. In addition, our measurements show a rapid restricted motion of the eosin molecule on the time scale of approximately 100 ps. The order parameter, a model independent measure of the extent of the restriction of the rapid motions, decreases with increasing temperature, indicating that the motion of the eosin is less hindered as temperature increases. We compare our results with the crystallographic measurements of least square displacements for the hydrophobic box region. Our measurements provide direct time resolved confirmation that the displacements observed in this region correspond to rapid motion.

[Dynamics of protein structures]

This review presents a survey of experimental and theoretical methods capable of providing a many-parameter characterization of internal mobility of protein molecules. Special emphasis is on applications of high-resolution nuclear magnetic resonance for studies of non-crystalline proteins and discussions of possible correlations between protein dynamics and biological functions of proteins.

Structural dynamics of erabutoxin b. A 13C nuclear magnetic resonance relaxation study of methyl groups

A detailed examination has been made of the 13C NMR relaxation times of the assigned methyl groups of erabutoxin b. Anisotropic rotation was analysed using a restricted diffusion model. The results are compared with a previous study of the 1H NMR relation times. There is good agreement on the segments of the molecule which show restricted motion. Our results are compared with those of previous studies on proteins in solution and in crystals and again the general agreement is good. We have attempted to interpret the value of the limited motion seen in the protein to the reactions of the neurotoxin.

Dynamics of erabutoxin b as studied by nuclear magnetic resonance. Relaxation studies of methyl proton resonances

Longitudinal and transverse relaxation times were measured for well-resolved and assigned methyl proton resonances of erabutoxin b at 270 MHz, 300 MHz and 500 MHz. Both longitudinal and transverse magnetization decay curves are non-exponential due to cross-relaxation and cross-correlation effects. The longitudinal and transverse relaxation rates were obtained from the initial slope of both magnetization decay curves. The correlation times for the isotropic tumbling motion of the protein were determined to be 2.82 ns at 300 K and 1.62 ns at 330 K from the analysis of the relaxation data of some alpha protons. Using these values, the relaxation data of methyl protons were fitted to various theoretical models. Most of the methyl resonances could be fitted well to a model which allowed methyl rotation (in the range 0.01-0.05 ns) and an external contribution from protons assumed to be in positions derived from X-ray coordinates. The data for a few methyl groups, however, could not be fitted in this way. For these a smaller number of external protons than predicted by the X-ray coordinates was assumed. Additionally, a larger amplitude motion had to be introduced into the model for particular residues. This additional motion requires concerted protein motion close to these residues, since the X-ray structure suggests that steric hindrance would prevent local motion. These results are consistent with the idea of a flexible and dynamic structure for proteins.