An exactly solvable model of stochastic Cre-Lox recombinations

Biology – Quantitative Biology – Quantitative Methods

Scientific paper

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Scientific paper

Cre-Lox system is used as a genetic tool to control site specific recombination events in genomic DNA. If multiple recombination sites are organized in a compact cluster within the same genome, a series of stochastic 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 site specific recombination 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. Second, we demonstrate that after a large number of stochastic 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.

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