Fast and accurate fitting of relaxation dispersion data using the flexible software package GLOVE

Relaxation dispersion spectroscopy is one of the most widely used techniques for the analysis of protein dynamics. To obtain a detailed understanding of the protein function from the view point of dynamics, it is essential to fit relaxation dispersion data accurately. The grid search method is commonly used for relaxation dispersion curve fits, but it does not always find the global minimum that provides the best-fit parameter set. Also, the fitting quality does not always improve with increase of the grid size although the computational time becomes longer. This is because relaxation dispersion curve fitting suffers from a local minimum problem, which is a general problem in non-linear least squares curve fitting. Therefore, in order to fit relaxation dispersion data rapidly and accurately, we developed a new fitting program called GLOVE that minimizes global and local parameters alternately, and incorporates a Monte-Carlo minimization method that enables fitting parameters to pass through local minima with low computational cost. GLOVE also implements a random search method, which sets up initial parameter values randomly within user-defined ranges. We demonstrate here that the combined use of the three methods can find the global minimum more rapidly and more accurately than grid search alone.     

Off-resonance rotating-frame relaxation dispersion experiment for 13C in aromatic side chains using L-optimized TROSY-selection

Protein dynamics on the microsecond–millisecond time scales often play a critical role in biological function. NMR relaxation dispersion experiments are powerful approaches for investigating biologically relevant dynamics with site-specific resolution, as shown by a growing number of publications on enzyme catalysis, protein folding, ligand binding, and allostery. To date, the majority of studies has probed the backbone amides or side-chain methyl groups, while experiments targeting other sites have been used more sparingly. Aromatic side chains are useful probes of protein dynamics, because they are over-represented in protein binding interfaces, have important catalytic roles in enzymes, and form a sizable part of the protein interior. Here we present an off-resonance R _1ρ experiment for measuring microsecond to millisecond conformational exchange of aromatic side chains in selectively ¹³C labeled proteins by means of longitudinal- and transverse-relaxation optimization. Using selective excitation and inversion of the narrow component of the ¹³C doublet, the experiment achieves significant sensitivity enhancement in terms of both signal intensity and the fractional contribution from exchange to transverse relaxation; additional signal enhancement is achieved by optimizing the longitudinal relaxation recovery of the covalently attached ¹H spins. We validated the L-TROSY-selected R _1ρ experiment by measuring exchange parameters for Y23 in bovine pancreatic trypsin inhibitor at a temperature of 328 K, where the ring flip is in the fast exchange regime with a mean waiting time between flips of 320 μs. The determined chemical shift difference matches perfectly with that measured from the NMR spectrum at lower temperatures, where separate peaks are observed for the two sites. We further show that potentially complicating effects of strong scalar coupling between protons (Weininger et al. in J Phys Chem B 117: 9241–9247, 2013b) can be accounted for using a simple expression, and provide recommendations for data acquisition when the studied system exhibits this behavior. The present method extends the repertoire of relaxation methods tailored for aromatic side chains by enabling studies of faster processes and improved control over artifacts due to strong coupling.     

Extending the range of amide proton relaxation dispersion experiments in proteins using a constant-time relaxation-compensated CPMG approach

Relaxation compensated constant-time Carr–Purcell–Meiboom–Gill relaxation dispersion experiments for amide protons are presented that detect s-ms time-scale dynamics of protein backbone amide sites. Because of their ten-fold larger magnetogyric ratio, much shorter 180° pulses can be applied to ¹H than to ¹⁵N spins; therefore, off-resonance effects are reduced and a wider range of effective rf fields can often be used in the case of ¹H experiments. Applications to [¹H-¹⁵N]-ubiquitin and [¹H-¹⁵N]-perdeuterated HIV-1 protease are discussed. In the case of ubiquitin, we present a pulse sequence that reduces artifacts that arise from homonuclear ³J(H_N-H) coupling. In the case of the protease, we show that relaxation dispersion of both ¹H and ¹⁵N spins provides a more comprehensive picture of slow backbone dynamics than does the relaxation dispersion of either spin alone. We also compare the relative merits of ¹H versus ¹⁵N transverse relaxation measurements and note the benefits of using a perdeuterated protein to measure the relaxation dispersion of both spin types.     

Dielectric relaxation measurements of 12 kbp plasmid DNA

The dielectric properties of 12 kbp plasmid DNA have been measured as a function of temperature in the range 5 degrees C to 40 degrees C. Time domain reflectometry was used to obtain dielectric data over the frequency range from 200 kHz to 3 GHz. Values of the frequency dependent polarisability per DNA macromolecule have been determined from the measurements. Possible mechanisms that could account for the dielectric dispersion are also discussed, in particular the counterion fluctuation model of Manning-Mandel-Oosawa.     

Conformational dynamics of yeast calmodulin in the Ca(2+)-bound state probed using NMR relaxation dispersion

Most calmodulin (CaM) in apo and Ca(2+)-bound states show a dumb-bell-like structure, involving the N- and C-terminal domains, connected with a flexible linker. However, Ca(2+)-bound yeast calmodulin (yCaM) takes on a unique globular structure; the target-binding site of this protein is autoinhibited. We applied NMR relaxation dispersion experiments to yCaM in the Ca(2+)-bound state. The amide (15)N and (1)H(N) relaxation dispersion profiles indicated the presence of conformational dynamics for specific residues at the interface between the N- and C-terminal domains. We conclude that these conformational dynamics were derived from the mobility of the C-terminal domain.     

Probing RNA dynamics via longitudinal exchange and CPMG relaxation dispersion NMR spectroscopy using a sensitive 13C-methyl label

The refolding kinetics of bistable RNA sequences were studied in unperturbed equilibrium via (13)C exchange NMR spectroscopy. For this purpose a straightforward labeling technique was elaborated using a 2'-(13)C-methoxy uridine modification, which was prepared by a two-step synthesis and introduced into RNA using standard protocols. Using (13)C longitudinal exchange NMR spectroscopy the refolding kinetics of a 20 nt bistable RNA were characterized at temperatures between 298 and 310K, yielding the enthalpy and entropy differences between the conformers at equilibrium and the activation energy of the refolding process. The kinetics of a more stable 32 nt bistable RNA could be analyzed by the same approach at elevated temperatures, i.e. at 314 and 316 K. Finally, the dynamics of a multi-stable RNA able to fold into two hairpin- and a pseudo-knotted conformation was studied by (13)C relaxation dispersion NMR spectroscopy.     

Improved discrimination of normal and malignant tissue using 1H NMR relaxation time measurements at 2.18 MHz

The 1H NMR spin-lattice relaxation time (T1), spin-spin relaxation time (T2), and spin-lattice relaxation time in the rotating frame (T1rho) were determined for Novikoff hepatoma, Walker-256 Carcinosarcoma, Sarcoma-180 and Ehrlich Ascites tumor as well as for 7 normal tissues in the rat at 2.18 MHz. T1 values yielded improved discrimination of normal and malignant tissue compared to previous results at higher frequencies.     

Thermodynamic interpretation of protein dynamics from NMR relaxation measurements

Protein dynamics and thermodynamics can be characterized through measurements of relaxation rates of side chain (2)H and (13)C, and backbone (15)N nuclei using NMR spectroscopy. The rates reflect protein motions on timescales from picoseconds to milliseconds. Backbone and methyl side chain NMR relaxation measurements for several proteins are beginning to reveal the role of protein dynamics in protein stability and ligand binding.     

The impact of window functions on NMR-based paramagnetic relaxation enhancement measurements in membrane proteins

Though challenging, solution NMR spectroscopy allows fundamental interrogation of the structure and dynamics of membrane proteins. One major technical hurdle in studies of helical membrane proteins by NMR is the difficulty of obtaining sufficient long range NOEs to determine tertiary structure. For this reason, long range distance information is sometimes sought through measurement of paramagnetic relaxation enhancements (PRE) of NMR nuclei as a function of distance from an introduced paramagnetic probe. Current PRE interpretation is based on the assumption of Lorentzian resonance lineshapes. However, in order to optimize spectral resolution, modern multidimensional NMR spectra are almost always subjected to resolution-enhancement, leading to distortions in the Lorentizian peak shape. Here it is shown that when PREs are derived using peak intensities (i.e., peak height) and linewidths from both real and simulated spectra that were produced using a wide range of apodization/window functions, that there is little variation in the distances determined (< 1 Å at the extremes). This indicates that the high degree of resolution enhancement required to obtain well-resolved spectra from helical membrane proteins is compatible with the use of PRE data as a source of distance restraints. While these conclusions are particularly important for helical membrane proteins, they are generally applicable to all PRE measurements made using resolution-enhanced data.     

An investigation of heavy meromyosin-ADP binding equilibria by proton release measurements.

The interaction of magnesium-ADP with skeletal muscle heavy meromyosin has been studied by measuring the accompanying release of protons. Total pH changes of the order of 0.03 were involved, and measurements were performed with a discrimination of some ten-thousandths of a pH unit. At pH 8.0 and 25 degrees C about 0.5 mol of protons per mol of heavy meromyosin is released at saturation. A stoichiometry of binding close to 2 mol of ADP per mol of protein was found, with a binding constant, obtained from the proton release titration curve (pH 8.0, 25 degrees C), of 2 X 10(5) M-1. At 5 degrees C the release of protons per mole is slightly greater, and the binding constant is somewhat increased, reflecting a negative enthalpy of binding. Similar proton release behavior is observed in the presence of manganous ions in place of magnesium. The liberation of protons is thus unrelated to the temperature-dependent isomerization of myosin in the presence of substrate. Alkylation of a reactive thiol group (SH1) does not change the proton liberation at pH 8.0. From the pH dependence of proton release, the association constant of heavy meromyosin with magnesium-ADP at other pH values can be inferred and shows an appreciable rise as the pH increases. The pH-proton release profile also allows the pK of the ionizing groups perturbed by the ligand to be deduced. At least two groups ionizing above pH 7 and one below are involved. Their pK's in the unperturbed state are assigned as 8.5, 9.3, and about 6.6, respectively; they are displaced in the complex to about 8.0, 9.1, and 6.3. A relation to the pH-activity profile of myosin ATPase is indicated. The pH-proton release profile is somewhat changed when the SH1 group is alkylated. Measurements with potassium-ADP, in the absence of magnesium, show that at pH 8.0 there is no proton release but rather a sizeable proton absorption (about 0.5 mol of protons per mol of heavy meromyosin). The association constant derived from the titration curves (pH 8.0, 25 degrees C) is 3 X 10(4) M-1.     

The feasibility of genome-scale biological network inference using Graphics Processing Units

Systems research spanning fields from biology to finance involves the identification of models to represent the underpinnings of complex systems. Formal approaches for data-driven identification of network interactions include statistical inference-based approaches and methods to identify dynamical systems models that are capable of fitting multivariate data. Availability of large data sets and so-called ‘big data’ applications in biology present great opportunities as well as major challenges for systems identification/reverse engineering applications. For example, both inverse identification and forward simulations of genome-scale gene regulatory network models pose compute-intensive problems. This issue is addressed here by combining the processing power of Graphics Processing Units (GPUs) and a parallel reverse engineering algorithm for inference of regulatory networks. It is shown that, given an appropriate data set, information on genome-scale networks (systems of 1000 or more state variables) can be inferred using a reverse-engineering algorithm in a matter of days on a small-scale modern GPU cluster.     

13C spin relaxation measurements in RNA: Sensitivity and resolution improvement using spin-state selective correlation experiments

A set of new NMR pulse sequences has been designed for the measurement of ¹³C relaxation rate constants in RNA and DNA bases: the spin-lattice relaxation rate constant R(C_z), the spin-spin relaxation rate constant R(C₊), and the CSA-dipolar cross-correlated relaxation rate constant . The use of spin-state selective correlation techniques provides increased sensitivity and spectral resolution. Sensitivity optimised C-C filters are included in the pulse schemes for the suppression of signals originating from undesired carbon isotopomers. The experiments are applied to a 15% ¹³C-labelled 33-mer RNA–theophylline complex. The measured ratios indicate that ¹³C CSA tensors do not vary significantly for the same type of carbon (C₂, C₆, C₈), but that they differ from one type to another. In addition, conformational exchange effects in the RNA bases are detected as a change in the relaxation decay of the narrow ¹³C doublet component when varying the spacing of a CPMG pulse train. This new approach allows the detection of small exchange effects with a higher precision compared to conventional techniques.     

Proton magnetic relaxation dispersion in solutions of the cuproprotein diamine oxidase.

Proton nuclear magnetic resonance relaxation measurements were made over the range 4.7--220 MHz for aqueous solutions of hog kidney diamine oxidase. The values of 1/T1 give rise in two distinct dispersions, at 16 and 75 MHz, whereas 1/T2 displays a minimum at 20 MHz. The temperature dependence of relaxation rates in all cases yield apparent activation energies less than 0.6 kcal/mol. These data indicate to us that the two Cu(II) ions of diamine oxidase are intrinsically different in terms of their electronic relaxation characteristics and hence, chemical environments. Low field limits of the two electronic relaxation times are 2 and 10 ns, with one of these correlation times being frequency dependent. The value of the frequency-dependent electronic relaxation time is governed by interactions that are modulated by a process having a correlation time of 5 ps.     

Quantification of the MR images of hydrogels by NMR relaxation measurements

Layers of hydrogel represent a diffusional barrier that retards the process of drug release. For better prediction of drug release, a method for evaluating the polymer concentration profile was developed.