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Predicting interactions between proteins is one of the most important yet challenging problems in structural bioinformatics. Intrinsically, potential function sites in protein surfaces are determined by both geometric and chemical features.…

Novel sampling algorithms can significantly impact open questions in computational biology, most notably the in silico protein folding problem. By using computational methods, protein folding aims to find the three-dimensional structure of…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

Computational modeling of a complex system is limited by the parts of the system with the least information. While detailed models and high-resolution data may be available for parts of a system, abstract relationships are often necessary…

In this paper, we propose finite mixtures of multivariate skew Laplace distributions to model both skewness and heavy-tailedness in the heterogeneous data sets. The maximum likelihood estimators for the parameters of interest are obtained…

Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…

Accurate prediction of protein-ligand binding affinity is crucial for rapid and efficient drug development. Recently, the importance of predicting binding affinity has led to increased attention on research that models the three-dimensional…

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of…

The hydrogen-bonded structure of methanol-water mixtures is investigated over the entire alcohol concentration range (from $x_{\mathrm{Methanol}}=$ 0.1 to 1.0) at several temperatures, from 300 K down to the freezing point of the given…

Structure predictions of helical membrane proteins have been designed to take advantage of the structural autonomy of secondary structure elements, as postulated by the two-stage model of Engelman and Popot. In this context, we investigate…

In this work we examine thermodynamics of fluid with "molecules" represented by two fused hard spheres, decorated by the attractive square-well sites. Interactions between these sites are of short-range and cause association between the…

Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools.…

We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…

The Gene or DNA sequence in every cell does not control genetic properties on its own; Rather, this is done through translation of DNA into protein and subsequent formation of a certain 3D structure. The biological function of a protein is…

Natural protein sequences somehow encode the structural forms that these molecules adopt. Recent developments in structure-prediction are agnostic to the mechanisms by which proteins fold and represent them as static objects. However, the…

Protein folding is one of the age-old biological problems that refers to the mechanism of understanding and predicting how a protein's linear sequence of amino acids folds into its specific three dimensional structure.This structure is…

Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers…

This paper deepens into the analysis of the protein secondary structure using Frenet frame to describe the curvature and torsion of the discrete curve formed by the protein $\alpha$-carbons. We show how a simple criterion based on the…

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…