An Exactly Solvable Model of Random Site-Specific Recombinations

TL;DR

This paper presents an exactly solvable statistical model for site-specific recombination, analyzing the diversity of sequences generated by inversions and excisions, with implications for genetic tools like Brainbow.

Contribution

It introduces a novel, exactly solvable model for SSR, providing analytical insights into sequence diversity and probabilities in recombination processes.

Findings

Describes the set of sequences generated by multiple inversions (ergodicity theorem)

Calculates the number of possible sequences from an initial sequence

Shows that all sequences are equally likely after many inversions

Abstract

Cre-lox and other systems are used as genetic tools to control site-specific recombination (SSR) events in genomic DNA. If multiple recombination sites are organized in a compact cluster within the same genome, a series of random recombination events may generate substantial cell specific genomic diversity. This diversity is used, for example, to distinguish neurons in the brain of the same multicellular mosaic organism, within the brainbow approach to neuronal connectome. In this paper we study an exactly solvable statistical model for SSR operating on a cluster of recombination sites. We consider two types of recombination events: inversions and excisions. Both of these events are available in the Cre-lox system. We derive three properties of the sequences generated by multiple recombination events. First, we describe the set of sequences that can in principle be generated by multiple inversions operating on the given initial sequence. We call this description the ergodicity theorem. On the basis of this description we calculate the number of sequences that can be generated from an initial sequence. This number of sequences is experimentally testable. Second, we demonstrate that after a large number of random inversions every sequence that can be generated is generated with equal probability. Lastly, we derive the equations for the probability to find a sequence as a function of time in the limit when excisions are much less frequent than inversions, such as in shufflon sequences.