Jean-Christophe Hus

Efficient analysis of macromolecular rotational diffusion from heteronuclear relaxation data

A novel program has been developed for the interpretation of 15N relaxation rates in terms of macromolecular anisotropic rotational diffusion. The program is based on a highly efficient simulated annealing/minimization algorithm, designed specifically to search the parametric space described by the isotropic, axially symmetric and fully anisotropic rotational diffusion tensor models. The high efficiency of this algorithm allows extensive noise-based Monte Carlo error analysis. Relevant statistical tests are systematically applied to provide confidence limits for the proposed tensorial models. The program is illustrated here using the example of the cytochrome c′ from Rhodobacter capsulatus, a four-helix bundle heme protein, for which data at three different field strengths were independently analysed and compared.

A novel interactive tool for rigid-body modeling of multi-domain macromolecules using residual dipolar couplings

Residual dipolar couplings (RDC), measured by dissolving proteins in dilute liquid crystal media, or by studying naturally paramagnetic molecules, have rapidly become established as routine measurements in the investigation of the structure of macromolecules by NMR. One of the most obvious applications of the previously inaccessible long-range angular information afforded by RDC is the accurate definition of domain orientation in multi-module macromolecules or complexes. In this paper we describe a novel program developed to allow the determination of alignment tensor parameters for individual or multiple domains in macromolecules from residual dipolar couplings and to facilitate their manipulation to construct low-resolution models of macromolecular structure. For multi-domain systems the program determines the relative orientation of individual structured domains, and provides graphical user-driven rigid-body modeling of the different modules relative to the common tensorial frame. Translational freedom in the common frame, and equivalent rotations about the diagonalized (x,y,z) axes are used to position the different modules in the common frame to find a model in best agreement with experimentally measured couplings alone or in combination with additional experimental or covalent information.

16-Fold Degeneracy of Peptide Plane Orientations from Residual Dipolar Couplings: Analytical Treatment and Implications for Protein Structure Determination

Residual dipolar couplings (RDCs) measured for internally rigid molecular fragments provide important information about the relative orientations of these fragments. Dependent on the symmetry of the alignment tensor and the symmetry of the molecular fragment, however, there generally exist more than one solution for the fragment orientation consistent with the measured RDCs. Analytical solutions are presented that describe the complete set of orientations of internally rigid fragments that are consistent with multiple dipolar couplings measured in a single alignment medium that is rhombic. For the first time, it is shown that, for a planar fragment such as the peptide plane, there generally exist 16 different solutions with their analytical expressions presented explicitly. The presence of these solutions is shown to be highly relevant for standard structure determination protocols using RDCs to refine molecular structures. In particular, when using standard protein structure refinement with RDCs that were measured in a single alignment medium as constraints, it is found that often more than one of the peptide plane solutions is physically viable; i.e., despite being consistent with measured RDCs, the local backbone structure can be incorrect. On the basis of experimental and simulated examples, it is rationalized why protein structures that are refined against RDCs measured in a single medium can have lower resolution (precision) than one would expect on the basis of the experimental accuracy of the RDCs. Conditions are discussed under which the correct solution can be identified.

Principal component method for assessing structural heterogeneity across multiple alignment media.

The recent availability of residual dipolar coupling measurements in a variety of different alignment media raises the question to what extent biomolecular structure and dynamics are differentially affected by their presence. A computational method is presented that allows the sensitive assessment of such changes using dipolar couplings measured in six or more alignment media. The method is based on a principal component analysis of the covariance matrix of the dipolar couplings. It does not require a priori structural or dynamic information nor knowledge of the alignment tensors and their orientations. In the absence of experimental errors, the covariance matrix has at most five nonzero eigenvalues if the structure and dynamics of the biomolecule is the same in all media. In contrast, differential structural and dynamic changes lead to additional nonzero eigenvalues. Characteristic features of the eigenvalue distribution in the absence and presence of noise are discussed using dipolar coupling data calculated from conformational ensembles taken from a molecular dynamics trajectory of native ubiquitin.

Reconstruction of interatomic vectors by principle component analysis of nuclear magnetic resonance data in multiple alignments

A general method is presented for the reconstruction of interatomic vector orientations from nuclear magnetic resonance (NMR) spectroscopic data of tensor interactions of rank 2, such as dipolar coupling and chemical shielding anisotropy interactions, in solids and partially aligned liquid-state systems. The method, called PRIMA, is based on a principal component analysis of the covariance matrix of the NMR parameters collected for multiple alignments. The five nonzero eigenvalues and their eigenvectors efficiently allow the approximate reconstruction of the vector orientations of the underlying interactions. The method is demonstrated for an isotropic distribution of sample orientations as well as for finite sets of orientations and internuclear vectors encountered in protein systems.