Simple Mathematical Model Of Pathologic Microsatellite Expansions: When Self-Reparation Does Not Work

TL;DR

This paper introduces a simple mathematical model for pathologic microsatellite expansions, highlighting conditions under which self-repair mechanisms succeed or fail, and explaining related phenomena like mosaicism and anticipation.

Contribution

It presents a novel, minimalistic model that explains the dynamics of microsatellite expansions and their self-repair mechanisms, including conditions for their effectiveness.

Findings

Self-repair works when expansion and contraction probabilities are equal.

Microsatellite expansions are always self-repairing under equal probabilities.

The model explains phenomena like mosaicism, anticipation, and the rarity of reverse mutations.

Abstract

We propose a simple model of pathologic microsatellite expansion, and describe an inherent self-repairing mechanism working against expansion. We prove that if the probabilities of elementary expansions and contractions are equal, microsatellite expansions are always self-repairing. If these probabilities are different, self-reparation does not work. Mosaicism, anticipation and reverse mutation cases are discussed in the framework of the model. We explain these phenomena and provide some theoretical evidence for their properties, for example the rarity of reverse mutations.