Sine-skewed toroidal distributions and their application in protein bioinformatics

TL;DR

This paper introduces sine-skewed toroidal distributions to model asymmetric dihedral angles in proteins, providing flexible, easy-to-use models that outperform symmetric ones in bioinformatics applications.

Contribution

The paper develops a new class of asymmetric toroidal distributions based on sine-skewing, with explicit properties, simple sampling algorithms, and no need for normalizing constants.

Findings

New sine-skewed toroidal models outperform symmetric models in protein data.

Explicit shape parameter expressions and simple random number generation algorithms.

Asymptotic properties of maximum likelihood estimators are established.

Abstract

In the bioinformatics field, there has been a growing interest in modelling dihedral angles of amino acids by viewing them as data on the torus. This has motivated, over the past years, new proposals of distributions on the bivariate torus. The main drawback of most of these models is that the related densities are (pointwise) symmetric, despite the fact that the data usually present asymmetric patterns. This motivates the need to find a new way of constructing asymmetric toroidal distributions starting from a symmetric distribution. We tackle this problem in this paper by introducing the sine-skewed toroidal distributions. The general properties of the new models are derived. Based on the initial symmetric model, explicit expressions for the shape parameters are obtained, a simple algorithm for generating random numbers is provided, and asymptotic results for the maximum likelihood estimators are established. An important feature of our construction is that no normalizing constant needs to be calculated, leading to more flexible distributions without increasing the complexity of the models. The benefit of employing these new sine-skewed distributions is shown on the basis of protein data, where, in general, the new models outperform their symmetric antecedents.