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Circularity of mitochondrial genomes has been taken as evidence for a bacterial origin of mitochondria, but linear as well as circular forms of mitochondrial DNA exist. In principle, the potential existence of incomplete end replication can indicate the evolutionary origin of linear DNA because this phenomenon makes evolutionary transitions between the two forms not trivial. When linear DNA is being replicated, the transcription machinery cannot replicate the very first couple of residues of each strand, potentially leading to a shortening of the chromosome with each replication (see here). So, any transition from circular to linear mitochondrial chromosomes must circumvent the potential shortening of chromosomes caused by the incomplete end replication. All organisms that contain linear chromosomes contain mechanisms that avoid the end replication problem by having special end regions called telomeres and the important question is how they evolved.

The telomeres at the end of the linear chromosomes in the nucleus of eukaryotes make incomplete end replication irrelevant since the end of the chromosomes are actively extended by a specific protein called telomerase. This enzyme adds extra DNA onto the ends of the chromosomes, preempting any potential shortening. Also, in linear mitochondrial chromosomes various different mechanisms to ‘prevent’ shortening exist, ranging from hairpin loops and self-priming to protein-assisted primer synthesis (see here). The telomeric regions of mitochondrial chromosomes do not seem to have a direct phylogenetic relation since they use other proteins and mechanisms than nuclear telomeres. Thus, it is difficult to deduce evolutionary pathways purely based on phylogenetic data on telomeres and mechanisms for end replication.

The transition from a circular genome to a linear genome is not trivial  because there has to be an immediate and efficient solution available to counter incomplete end replication. Linear forms of mitochondrial DNA have arisen multiple times in evolution without a direct relationship to nuclear or bacterial telomeres. The insertion of a plasmid vector into circular mitochondrial DNA can linearize DNA and provide a telomere at the same time (here), indicating that linearization of circular mitochondrial DNA is not a major hurdle. A circular form as the ancestral state seems the most parsimonious scenario because linear chromosomes as the ancestral state would require a concomitant targeting of telomere machinery to the mitochondria. In contrast, circularization of linear DNA can be seen as a reduction in complexity which could provide efficiency advantages. Circular mitochondrial DNA could have been obtained directly from the nuclear genome by circularization upon entry, but also in already circularized form through an intermediate vector (discussed here [todo]).

In conclusion, circular or linear forms hardly give any direction to the origin of mitochondrial DNA. The eukaryotic theory for the origin of mitochondria is not contradicted by either form. Both circular or linear mitochondrial form could have been ancestral in this theory, although a circular origin seems the most parsimonious.