Using kernelized partial canonical correlation analysis to study directly coupled side chains and allostery in small G proteins.

MOTIVATION: Inferring structural dependencies among a protein's side chains helps us understand their coupled motions. It is known that coupled fluctuations can reveal pathways of communication used for information propagation in a molecule. Side-chain conformations are commonly represented by multivariate angular variables, but existing partial correlation methods that can be applied to this inference task are not capable of handling multivariate angular data. We propose a novel method to infer direct couplings from this type of data, and show that this method is useful for identifying functional regions and their interactions in allosteric proteins. RESULTS: We developed a novel extension of canonical correlation analysis (CCA), which we call 'kernelized partial CCA' (or simply KPCCA), and used it to infer direct couplings between side chains, while disentangling these couplings from indirect ones. Using the conformational information and fluctuations of the inactive structure alone for allosteric proteins in the Ras and other Ras-like families, our method identified allosterically important residues not only as strongly coupled ones but also in densely connected regions of the interaction graph formed by the inferred couplings. Our results were in good agreement with other empirical findings. By studying distinct members of the Ras, Rho and Rab sub-families, we show further that KPCCA was capable of inferring common allosteric characteristics in the small G protein super-family. AVAILABILITY AND IMPLEMENTATION: https://github.com/lsgh/ismb15

Generating conformational transitions using the euclidean distance matrix.

Elastic network interpolation (ENI) is an efficient method for generating intermediate conformations between two end protein conformations. Its current formulation uses interatomic distance. We show how this can be generalized to interatomic distances-squared. This generalization is part of an effort to study protein dynamics on the set of positive semidefinite (PSD) matrices, which has a rich mathematical structure. We use lattice structures to test this interpolation scheme, and discuss some limitations observed. We conclude with some suggestions for future research.

Sparse networks of directly coupled, polymorphic, and functional side chains in allosteric proteins.

Recent studies have highlighted the role of coupled side-chain fluctuations alone in the allosteric behavior of proteins. Moreover, examination of X-ray crystallography data has recently revealed new information about the prevalence of alternate side-chain conformations (conformational polymorphism), and attempts have been made to uncover the hidden alternate conformations from X-ray data. Hence, new computational approaches are required that consider the polymorphic nature of the side chains, and incorporate the effects of this phenomenon in the study of information transmission and functional interactions of residues in a molecule. These studies can provide a more accurate understanding of the allosteric behavior. In this article, we first present a novel approach to generate an ensemble of conformations and an efficient computational method to extract direct couplings of side chains in allosteric proteins, and provide sparse network representations of the couplings. We take the side-chain conformational polymorphism into account, and show that by studying the intrinsic dynamics of an inactive structure, we are able to construct a network of functionally crucial residues. Second, we show that the proposed method is capable of providing a magnified view of the coupled and conformationally polymorphic residues. This model reveals couplings between the alternate conformations of a coupled residue pair. To the best of our knowledge, this is the first computational method for extracting networks of side chains' alternate conformations. Such networks help in providing a detailed image of side-chain dynamics in functionally important and conformationally polymorphic sites, such as binding and/or allosteric sites.

Residue-Specific Side-Chain Polymorphisms via Particle Belief Propagation.

Protein side chains populate diverse conformational ensembles in crystals. Despite much evidence that there is widespread conformational polymorphism in protein side chains, most of the X-ray crystallography data are modeled by single conformations in the Protein Data Bank. The ability to extract or to predict these conformational polymorphisms is of crucial importance, as it facilitates deeper understanding of protein dynamics and functionality. In this paper, we describe a computational strategy capable of predicting side-chain polymorphisms. Our approach extends a particular class of algorithms for side-chain prediction by modeling the side-chain dihedral angles more appropriately as continuous rather than discrete variables. Employing a new inferential technique known as particle belief propagation, we predict residue-specific distributions that encode information about side-chain polymorphisms. Our predicted polymorphisms are in relatively close agreement with results from a state-of-the-art approach based on X-ray crystallography data, which characterizes the conformational polymorphisms of side chains using electron density information, and has successfully discovered previously unmodeled conformations.

Using kernel alignment to select features of molecular descriptors in a QSAR study.

Quantitative structure-activity relationships (QSARs) correlate biological activities of chemical compounds with their physicochemical descriptors. By modeling the observed relationship seen between molecular descriptors and their corresponding biological activities, we may predict the behavior of other molecules with similar descriptors. In QSAR studies, it has been shown that the quality of the prediction model strongly depends on the selected features within molecular descriptors. Thus, methods capable of automatic selection of relevant features are very desirable. In this paper, we present a new feature selection algorithm for a QSAR study based on kernel alignment which has been used as a measure of similarity between two kernel functions. In our algorithm, we deploy kernel alignment as an evaluation tool, using recursive feature elimination to compute a molecular descriptor containing the most important features needed for a classification application. Empirical results show that the algorithm works well for the computation of descriptors for various applications involving different QSAR data sets. The prediction accuracies are substantially increased and are comparable to those from earlier studies.

Predicting multiple binding modes using a kernel method based on a vector space model molecular descriptor.

We describe the use of our Vector Space Model Molecular Descriptor (VSMMD), based on a Vector Space Model (VSM) that is suitable for kernel studies in Quantitative Structure-Activity Relationship (QSAR) modelling. Our experiments provide convincing comparative empirical evidence that this kernel method can provide sufficient discrimination to predict various biological activities of a molecule with reasonable accuracy. Furthermore, together with a kernel feature space algorithm, experiments also provide convincing empirical evidence that our VSMMD can provide sufficient information to identify different binding modes with high accuracy.

A constructive approach for discovering new drug leads: Using a kernel methodology for the inverse-QSAR problem.

BACKGROUND: The inverse-QSAR problem seeks to find a new molecular descriptor from which one can recover the structure of a molecule that possess a desired activity or property. Surprisingly, there are very few papers providing solutions to this problem. It is a difficult problem because the molecular descriptors involved with the inverse-QSAR algorithm must adequately address the forward QSAR problem for a given biological activity if the subsequent recovery phase is to be meaningful. In addition, one should be able to construct a feasible molecule from such a descriptor. The difficulty of recovering the molecule from its descriptor is the major limitation of most inverse-QSAR methods. RESULTS: In this paper, we describe the reversibility of our previously reported descriptor, the vector space model molecular descriptor (VSMMD) based on a vector space model that is suitable for kernel studies in QSAR modeling. Our inverse-QSAR approach can be described using five steps: (1) generate the VSMMD for the compounds in the training set; (2) map the VSMMD in the input space to the kernel feature space using an appropriate kernel function; (3) design or generate a new point in the kernel feature space using a kernel feature space algorithm; (4) map the feature space point back to the input space of descriptors using a pre-image approximation algorithm; (5) build the molecular structure template using our VSMMD molecule recovery algorithm. CONCLUSION: The empirical results reported in this paper show that our strategy of using kernel methodology for an inverse-Quantitative Structure-Activity Relationship is sufficiently powerful to find a meaningful solution for practical problems.