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Expansion of gene clusters, circular orders, and the shortest Hamiltonian path problem. (English) Zbl 1397.92465
Summary: Clusters of paralogous genes such as the famous HOX cluster of developmental transcription factors tend to evolve by stepwise duplication of its members, often involving unequal crossing over. Gene conversion and possibly other mechanisms of concerted evolution further obfuscate the phylogenetic relationships. As a consequence, it is very difficult or even impossible to disentangle the detailed history of gene duplications in gene clusters. In this contribution we show that the expansion of gene clusters by unequal crossing over as proposed by Walter Gehring leads to distinctive patterns of genetic distances, namely a subclass of circular split systems. Furthermore, when the gene cluster was left undisturbed by genome rearrangements, the shortest Hamiltonian paths with respect to genetic distances coincide with the genomic order. This observation can be used to detect ancient genomic rearrangements of gene clusters and to distinguish gene clusters whose evolution was dominated by unequal crossing over within genes from those that expanded through other mechanisms.
MSC:
92D10 Genetics and epigenetics
92D15 Problems related to evolution
05C45 Eulerian and Hamiltonian graphs
05C90 Applications of graph theory
62P10 Applications of statistics to biology and medical sciences; meta analysis
92-08 Computational methods for problems pertaining to biology
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