Fractal-like Distributions over the Rational Numbers in High-throughput Biological and Clinical Data

TL;DR

This paper introduces fractal-like distributions over rational numbers that emerge in high-throughput biological and clinical data analysis, revealing self-similar structures useful for understanding sequencing errors, tumor genomics, disease prevalence, and viral diversity.

Contribution

It identifies and characterizes a new class of distributions with fractal properties that appear across various biological and clinical data analyses.

Findings

Distributions are discontinuous on rationals but continuous on irrationals.

Self-similar, fractal-like structure observed in sequencing error rates.

Applications include tumor genomics, disease prevalence, and viral diversity analysis.

Abstract

Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are some examples of such technologies. Extracting meaningful information from those technologies requires careful analysis of the large volumes of data they produce. In this note, we present a set of distributions that commonly appear in the analysis of such data. These distributions present some interesting features: they are discontinuous in the rational numbers, but continuous in the irrational numbers, and possess a certain self-similar (fractal-like) structure. The first set of examples which we present here are drawn from a high-throughput sequencing experiment. Here, the self-similar distributions appear as part of the evaluation of the error rate of the sequencing technology and the identification of tumorogenic genomic alterations. The other examples are obtained from risk factor evaluation and analysis of relative disease prevalence and co-mordbidity as these appear in electronic clinical data. The distributions are also relevant to identification of subclonal populations in tumors and the study of the evolution of infectious diseases, and more precisely the study of quasi-species and intrahost diversity of viral populations.