Protein structural motif recognition via NMR residual dipolar couplings.

NMR residual dipolar couplings have great potential to provide rapid structural information for proteins in the solution state. This information even at low resolution may be used to advantage in proteomics projects that seek to annotate large numbers of gene products for entire genomes. In this paper, we describe a novel approach to the structural interpretation of dipolar couplings which is based on structural motif pattern recognition, where a predefined gapless structural template for a motif is used to search a set of residual dipolar couplings for good matches. We demonstrate the applicability of the method using synthetic and experimental data. We also provide an analysis of the statistical power of the method and the effects of order tensor frame orientation, motif size, and structural complexity on motif detection. Finally, we discuss remaining problems that must be overcome before the method can be used routinely to identify protein homologies.

Protein backbone structure determination using only residual dipolar couplings from one ordering medium.

Residual dipolar couplings provide significant structural information for proteins in the solution state, which makes them attractive for the rapid determination of protein folds. Unfortunately, dipolar couplings contain inherent structural ambiguities which make them difficult to use in the absence of additional information. In this paper, we describe an approach to the construction of protein backbone folds using experimental dipolar couplings based on a bounded tree search through a structural database. We filter out false positives via an overlap similarity measure that insists that protein fragments assigned to overlapping regions of the sequence must have self-consistent structures. This allows us to determine a backbone fold (including the correct Calpha-Cbeta bond orientations) using only residual dipolar coupling data obtained from one ordering medium. We demonstrate the applicability of the method using experimental data for ubiquitin.

Lipari-Szabo mapping: A graphical approach to Lipari-Szabo analysis of NMR relaxation data using reduced spectral density mapping.

In this paper, we explore connections between the Lipari-Szabo formalism and reduced spectral density mapping, and show how spectral density estimates can be associated with Lipari-Szabo parameters via a simple geometric construction which we call Lipari-Szabo mapping. This relationship can be used to estimate Lipari-Szabo parameters from spectral density estimates without the need for nonlinear optimization, and to perform 'model selection' in a graphical manner. The Lipari-Szabo map also provides insight into the Lipari-Szabo model, and allows us to determine when a given set of experimental spectral densities are inconsistent with the Lipari-Szabo formalism. Practical applications of Lipari-Szabo mapping in conjunction with more traditional analysis methods are discussed.

A Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data.

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. In this paper, we show how commonly used NMR relaxation data (R(1), R(2), and NOE) obtained at two spectrometer frequencies can be analyzed using a Bayesian statistical approach to reliably detect and quantify the degree of rotational diffusion anisotropy. Our approach differs from previous methods in that it does not make assumptions concerning the internal motions experienced by the residues which are used to quantify the diffusion anisotropy, but rather averages the results over all internal motions consistent with the data. We demonstrate our method using synthetic data corresponding to isotropic, axially symmetric anisotropic, and fully asymmetric anisotropic rotational diffusion, as well as experimental NMR data. We compare the Bayesian statistical approach with a widely used method for extracting tumbling parameters using both synthetic and experimental data. While it can be difficult to separate the effects of chemical exchange from rotational anisotropy using this "standard" method, these effects are readily separated using Bayesian statistics. In addition, we find that the Bayesian statistical approach requires considerably less CPU time than an equivalent standard analysis.

Estimation of dynamic parameters from NMR relaxation data using the Lipari-Szabo model-free approach and Bayesian statistical methods.

In order to analyze NMR relaxation data in terms of parameters which describe internal motion, one must first obtain a description of the overall tumbling of the macromolecule in solution. Methods currently used to estimate these global parameters may not always provide reliable estimates of their values and uncertainties. In this paper, we present a general data analysis formalism based on products of Bayesian marginal probability densities which can be used to efficiently combine the information content from multiple experiments, such as R(1), R(2), and NOE data collected at multiple magnetic field strengths, or data from cross-correlation or rotating frame relaxation dispersion experiments. Our approach allows the estimation of global tumbling and internal dynamical parameters and their uncertainties without some of the assumptions which are made in the commonly-used methods for model-selection and global parameter estimation. Compared to an equivalent classical statistical approach, the Bayesian method not only is more computationally efficient, but also provides greater insight into the information content of the data. We demonstrate that this approach can be used to estimate both the isotropic rotational correlation time in the context of the original and "extended" Lipari-Szabo formalisms [Lipari & Szabo, J. Am. Chem. Soc. 1982, 104, 4546; Clore et al., J. Am. Chem. Soc. 1990, 112, 4989], as well as the rotational diffusion coefficients for axially symmetric anisotropic tumbling.

Order matrix analysis of residual dipolar couplings using singular value decomposition.

The measurement of anisotropic spin interactions, such as residual dipolar couplings, in partially ordered solutions can provide valuable information on biomolecular structure. While the information can be used to refine local structure, it can make a unique contribution in determining the relative orientation of remote parts of molecules, which are locally well structured, but poorly connected based on NOE data. Analysis of dipolar couplings in terms of Saupe order matrices provides a concise description of both orientation and motional properties of locally structured fragments in these cases. This paper demonstrates that by using singular value decomposition as a method for calculating the order matrices, principal frames and order parameters can be determined efficiently, even when a very limited set of experimental data is available. Analysis of 1H-15N dipolar couplings, measured in a two-domain fragment of the barley lectin protein, is used to illustrate the computational method.

Propagation of experimental uncertainties using the Lipari-Szabo model-free analysis of protein dynamics.

In this paper we make use of the graphical procedure previously described [Jin, D. et al. (1997) J. Am. Chem. Soc., 119, 6923-6924] to analyze NMR relaxation data using the Lipari-Szabo model-free formalism. The graphical approach is advantageous in that it allows the direct visualization of the experimental uncertainties in the motional parameter space. Some general 'rules' describing the relationship between the precision of the relaxation measurements and the precision of the model-free parameters and how this relationship changes with the overall tumbling time (tau m) are summarized. The effect of the precision in the relaxation measurements on the detection of internal motions not close to the extreme narrowing limit is analyzed. We also show that multiple timescale internal motions may be obscured by experimental uncertainty, and that the collection of relaxation data at very high field strength can improve the ability to detect such deviations from the simple Lipari-Szabo model.

A Metropolis Monte Carlo implementation of bayesian time-domain parameter estimation: application to coupling constant estimation from antiphase multiplets.

The Bayesian perspective on statistics asserts that it makes sense to speak of a probability of an unknown parameter having a particular value. Given a model for an observed, noise-corrupted signal, we may use Bayesian methods to estimate not only the most probable value for each parameter but also their distributions. We present an implementation of the Bayesian parameter estimation formalism developed by G. L. Bretthorst (1990, J. Magn. Reson. 88, 533) using the Metropolis Monte Carlo sampling algorithm to perform the parameter and error estimation. This allows us to make very few assumptions about the shape of the posterior distribution, and allows the easy introduction of prior knowledge about constraints among the model parameters. We present evidence that the error estimates obtained in this manner are realistic, and that the Monte Carlo approach can be used to accurately estimate coupling constants from antiphase doublets in synthetic and experimental data.

Performance of a neural-network-based determination of amino acid class and secondary structure from 1H-15N NMR data.

A neural network which can determine both amino acid class and secondary structure using NMR data from 15N-labeled proteins is described. We have included nitrogen chemical shifts, 3JHNH alpha coupling constants, alpha-proton chemical shifts, and side-chain proton chemical shifts as input to a three-layer feed-forward network. The network was trained with 456 spin systems from several proteins containing various types of secondary structure, and tested on human ubiquitin, which has no sequence homology with any of the proteins in the training set. A very limited set of data, representative of those from a TOCSY-HSQC and HNHA experiment, was used. Nevertheless, in 60% of the spin systems the correct amino acid class was among the top two choices given by the network, while in 96% of the spin systems the secondary structure was correctly identified. The performance of this network clearly shows the potential of the neural network algorithm in the automation of NMR spectral analysis.

Quantitation of chemical exchange rates using pulsed-field-gradient diffusion measurements.

A new approach to the quantitation of chemical exchange rates is presented, and its utility is illustrated with application to the exchange of protein amide protons with bulk water. The approach consists of a selective-inversion exchange HMQC experiment in which a short spin echo diffusion filter has been inserted into the exchange period. In this way; the kinetics of exchange are encoded directly in an apparent diffusion coefficient which is a function of the position of the diffusion filter in the pulse sequence. A detailed theoretical analysis of this experiment indicates that, in addition to the measurement of simple exchange rates, the experiment is capable of measuring the effect of mediated exchange, e.g. the transfer of magnetization from bulk water to an amide site mediated by an internal bound water molecule or a labile protein side-chain proton in fast exchange with bulk water. Experimental results for rapid water/amide exchange in acyl carrier protein are shown to be quantitatively consistent with the exchange rates measured using a selective-inversion exchange experiment.

Amide exchange rates in Escherichia coli acyl carrier protein: correlation with protein structure and dynamics.

The acyl carrier protein (ACP) of Escherichia coli is a 77-amino acid, highly negatively charged three-helix protein that plays a central role in fatty acid biosynthesis. Previous NMR studies have suggested the presence of multiple conformations and marginally stable secondary structural elements. The stability of these elements is now examined by monitoring amide exchange in apo-ACP using NMR-based methods. Because ACP exhibits many rapid exchange rates, application of traditional isotope exchange methods is difficult. In one approach, heteronuclear correlation experiments with pulsed field-gradient coherence selection have reduced the time needed to collect two-dimensional 1H-15N correlation spectra to the point where measurement of exchange of amide protons for deuterium on the timescale of minutes can be made. In another approach, water proton selective inversion-exchange experiments were performed to estimate the exchange rates of protons exchanging on timescales of less than a second. Backbone amide protons in the region of helix II were found to exchange significantly more rapidly than those in helices I and III, consistent with earlier structural models suggesting a dynamic disruption of the second helix. Highly protected amides occur on faces of the helices that may pack into a hydrophobic core present in a partially disrupted state.