A defining characteristic of eukaryotes is the fact that they posses organelles and a differentiated nucleus.
A very important type of those organelles are the mitochondria.
It is an accepted hypothesis that mitochondria used to be prokaryotic organisms that established some sort of symbiosis with eukaryotes, and eventually lost their ability to live on their own (for example, mitochondria usually import cytoplasmic tRNA for transcription of mitochondrial DNA), this is know as the endosymbiotic theory.
Now, something crossed my mind the other day: Do all known eukaryotes have mitochondria?
It seems obvious that there must have been a time when eukaryotes lacked mythocondria.
We also know that eukaryotes are able of obtaining energy in other ways than not respiration. Even human cells are cable of anaerobic (lactic acid fermentation) processes.
We can, however, understand that having mitochondria provides Eukaryotes with a huge advantage.
In Biology energy is usually measured in terms of the maximum theoretical number of units of ATP (adenosine triphospate) produced per unit of glucose. Well, lactic fermentation in our muscles is capable of producing only 2 units of ATP per unit of glucose while aerobic respiration is capable of producing 36-38, that’s around 18-19 times more! (bear in mind that these are estimations for the ideal case!)
So the question remains: do all known eukaryotes have mitochondria?
Well we know some eukaryotic organisms which seem to be amitochondrial, i.e. they lack mitochondria, such as members of the genus Giardia. One can, however, detect remnants of mitochondrial DNA in their nuclear DNA.  Also, it seems these organisms, have some organelles that appear to be derived from mitochondria such as hydrogenosomes and mitosomes. [4,5] So it seems that even though they lack the organelle, they are descendant from some eurakyote that used to contain mitochondria. It is also quite plausible, that some of the proteins coded in mitochondria are still produced and that somehow they retain some of the functions (note that the it would make perfect sense for mitochondria’s proteins to be coded in our nuclear DNA. The fact that it is not, seems to simply imply that after the endosymbiosis took place there was either no evolutionary pressure for that or it was advantageous to keep both genomes apart).
Anyway, after this long dissertation it seems that there is agreement in the scientific community that no known eukaryote has a totally amitochondrial lineage, even though some seem to have lost mitochondria during evolution.
As it is stated in : “Since Trimastix retains genetic evidence of a mitochondriate ancestry, we can now say definitively that all known living eukaryote lineages descend from a common ancestor that had mitochondria.”
So while the simple answer to my question is “Yes, there are eukaryotes that lack mitochondria”, the full scenario is a tad more complex and more interesting than that…
 William F. Martin and Miklós Müller, Origin of Mitochondria and Hydrogenosomes (Springer, 2010).
 Eldon Enger, Frederick Ross and David Bailey, Concepts in Biology (McGraw-Hill, 2011).
 Jorge Tovar et al., Mitochondrial remnant organelles of Giardia function in iron-sulphur protein maturation. Nature, 426(6963), Nov 2003.
 M. van der Giezen, Hydrogenosomes and mitosomes: conservation and evolution of functions. J Eukaryot Microbiol. , 56(3), May-Jun 2009.
 R. E. Schneider et al., The Trichomonas vaginalis hydrogenosome proteome is highly reduced relative to mitochondria, yet complex compared with mitosomes. Int J Parasitol., 41(13-14), Nov 2011.
 Hampl V, Silberman JD, Stechmann A, Diaz-Triviño S, Johnson PJ, et al., Genetic Evidence for a Mitochondriate Ancestry in the ‘Amitochondriate’ Flagellate Trimastix pyriformis. PLoS ONE 3(1): e1383.
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