Geometric Aspects of Biological Sequence Comparison

TL;DR

This paper introduces a flexible mathematical framework for converting biological sequence similarities into quasi-metrics, accommodating asymmetric distances and a broader class of scoring schemes, with potential applications in bioinformatics.

Contribution

It presents a novel, general approach to transform sequence similarities into quasi-metrics, allowing asymmetric distances and less restrictive gap penalties, expanding the analytical tools for biological sequences.

Findings

Framework supports asymmetric distances and partial orders.

Enables conversion of similarities to distances for diverse scoring schemes.

Requires less restrictive gap penalties than traditional methods.

Abstract

We propose a general framework for converting global and local similarities between biological sequences to quasi-metrics. In contrast to previous works, our formulation allows asymmetric distances, originating from uneven weighting of strings, that may induce non-trivial partial orders on sets of biosequences. Furthermore, the $\ell^p$-type distances considered are more general than traditional generalized string edit distances corresponding to the $\ell^1$ case, and enable conversion of sequence similarities to distances for a much wider class of scoring schemes. Our constructions require much less restrictive gap penalties than the ones regularly used. Numerous examples are provided to illustrate the concepts introduced and their potential applications.