Euclidian space and grouping of biological objects

Abstract

Motivation: Biological objects tend to cluster into discrete groups. Objects within a group typically possess similar properties. It is important to have fast and efficient tools for grouping objects that result in biologically meaningful clusters. Protein sequences reflect biological diversity and offer an extraordinary variety of objects for polishing clustering strategies. Grouping of sequences should reflect their evolutionary history and their functional properties. Visualization of relationships between sequences is of no less importance. Tree-building methods are typically used for such visualization. An alternative concept to visualization is a multidimensional sequence space. In this space, proteins are defined as points and distances between the points reflect the relationships between the proteins. Such a space can also be a basis for model-based clustering strategies that typically produce results correlating better with biological properties of proteins. Results: We developed an approach to classification of biological objects that combines evolutionary measures of their similarity with a model-based clustering procedure. We apply the methodology to amino acid sequences. On the first step, given a multiple sequence alignment, we estimate evolutionary distances between proteins measured in expected numbers of amino acid substitutions per site. These distances are additive and are suitable for evolutionary tree reconstruction. On the second step, we find the best fit approximation of the evolutionary distances by Euclidian distances and thus represent each protein by a point in a multidimensional space. The Euclidian space may be projected in two or three dimensions and the projections can be used to visualize relationships between proteins. On the third step, we find a non-parametric estimate of the probability density of the points and cluster the points that belong to the same local maximum of this density in a group. The number of groups is controlled by a σ-parameter that determines the shape of the density estimate and the number of maxima in it. The grouping procedure outperforms commonly used methods such as UPGMA and single linkage clustering.