Disorder and Power-law Tails of DNA Sequence Self-Alignment Concentrations in Molecular Evolution

TL;DR

This paper investigates the power-law behavior of DNA sequence self-alignment concentrations, revealing how disorder influences the emergence of multiple scaling regimes through a fragmentation model that accounts for molecular evolution processes.

Contribution

It introduces a fragmentation model incorporating disorder effects, explaining the observed power-law tails and multiple scaling regimes in DNA sequence alignments.

Findings

Power-law tails in DNA self-alignment concentrations are explained by a fragmentation model with disorder.

Multiple algebraic scaling regimes are observed in self-alignment data, consistent with theoretical predictions.

Disorder in molecular evolution leads to diverse scaling behaviors at different genomic scales.

Abstract

The self-alignment concentrations, $c(x)$, as functions of the length, $x$, of the identically matching maximal segments in the genomes of a variety of species, typically present power-law tails extending to the largest scales, i.e., $c(x) \propto x^{\alpha}$, with similar or apparently different negative $\alpha$s ($<-2$). The relevant fundamental processes of molecular evolution are segmental duplication and point mutation, and that recently the stick fragmentation phenomenology has been used to account the neutral evolution. However, disorder is intrinsic to the evolution system and, by freezing it in time (quenching) for the setup of a simple fragmentation model, we obtain decaying, steady-state and the general full time-dependent solutions, all $\propto x^{\alpha}$ for $x\to \infty$, which is in contrast to the only power-law solution, $x^{-3}$ for $x\to 0$ of the pure model (without disorder). %Other algebraic terms may dominate at intermediate scales, which seems to be confirmed by some species, such as rice. We also present self-alignment results showing more than one scaling regimes, consistent with the theoretical results of the existence of more than one algebraic terms which dominate at different regimes.