Mixtures of concentrated multivariate sine distributions with applications to bioinformatics

Directional Support Vector Machines

Several phenomena are represented by directional—angular or periodic—data; from time references on the calendar to geographical coordinates. These values are usually represented as real values restricted to a given range (e.g., [ 0 , 2 π ) ), hiding the real nature of this information. In order to handle these variables properly in supervised classification tasks, alternatives to the naive Bayes classifier and logistic regression were proposed in the past. In this work, we propose directional-aware support vector machines. We address several realizations of the proposed models, studying their kernelized counterparts and their expressiveness. Finally, we validate the performance of the proposed Support Vector Machines (SVMs) against the directional naive Bayes and directional logistic regression with real data, obtaining competitive results.

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

Contact:lsoltang@uwaterloo.ca

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.