Genome Rearrangement in Mitochondria and Its Computational Biology

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In the first part of this paper, we investigate gene orders of closely related mitochondrial genomes for studying the properties of mutations rearranging genes in mitochondria. Our conclusions are that the evolution of mitochondrial genomes is more complicated than it is considered in recent methods, and stochastic modelling is necessary for its deeper understanding and more accurate inferring. The second part is a review on the Markov chain Monte Carlo approaches for the stochastic modelling of genome rearrangement, which seem to be the only computationally tractable way to this problem. We introduce the concept of partial importance sampling, which yields a class of Markov chains being efficient both in terms of mixing and computational time. We also give a list of open algorithmic problems whose solution might help improve the efficiency of partial importance samplers.