Topological Pressure

David Koslicki
Mathematical Biosciences Institute, The Ohio State University

(September 27, 2012 10:20 AM - 11:15 AM)

Topological Pressure

Abstract

Inspired by concepts from ergodic theory, we give new insight into coding sequence (CDS) density estimation for the human genome. Our approach is based on the introduction and study of topological pressure: a numerical quantity assigned to any finite sequence based on an appropriate notion of `weighted information content'. For human DNA sequences, each codon is assigned a suitable weight, and using a window size of approximately 60,000bp, we obtain a very strong positive correlation between CDS density and topological pressure. The weights are selected by an optimization procedure, and can be interpreted as quantitative data on the relative importance of different codons for the density estimation of coding sequences. This gives new insight into codon usage bias which is an important subject where long standing questions remain open. Inspired again by ergodic theory, we use the weightings on the codons to define a probability measure on finite sequences. We demonstrate that this measure is effective in distinguishing between coding and non-coding human DNA sequences of lengths approximately 5,000bp. We emphasize that topological pressure is a flexible tool and we expect it to be useful for the investigation of many other features of DNA sequences such as interspecies comparison of codon usage bias. We give a first result in this direction, investigating CDS density in the mouse genome and comparing our results with those for the human genome.