The free living version of this bacteria lives on today in the broad family of alpha-proteobacteria; the bacteria that committed to a partnership with the motile (presumably) nuclear cell is called "Mitochondria" and is rightly called the "power plant" of our cells.

(More background; molecular oxygen was created by another piece of biochemical innovation in bacteria to use water as a source of reducing power protons; previous bacteria were (and still!) use easier to split compounds, like hydrogen sulphide, but this is far rarer on earth;

water is ubiquitous, so using H2O as a source of protons was a logistical breakthrough. But one did have this pesky oxygen knocking around; an oxygen radical, a single atom, is a highly reactive thing. Molecular oxygen, O2, not only is less reactive but as a gas diffuses away

Splitting water and fixing carbon, both powered by light therefore was a big breakthrough for early cyanobacteria in evolution, with a by product of releasing oxygen. This has such as big impact one can see it in the rocks where the presence of oxygen in the atmosphere changes

geological composition - basically lots more iron oxide, aka, rust - due to this bacterial innovation. But the increasing oxygen was also a toxin to most current life being pretty reactive. Living organisms either had to hide from the oxygen, tolerate it, or use it)

Back to our bacterial partners in our our cells, mitochondria. They have kept a rump core of genome of the key "power plant" machinery. This is sophisticated, key energy generating chemistry inside our cells.

The core part is the chemical wizardry of accepting electrons with oxygen and protons, but using the insane electron desire of molecular oxygen to water to force other protons outside their cell; by having membrane largely imperneable to protons (no mean feat) >>

<< they can allow the protons to come back through a molecular motor - a ring and stalk that rotates 360 degrees - where the rotational movement crunches down one more phosphate group on to a Adensine Di-Phospate (ADP) to make ATP.

This last phosphate is really not happy being so close to two other phosphates, but is kinetically stable; it is a chemical currency in our cells where ATP can be hydrolysed by enzymes, capturing that energy; eg moving muscles or pumping ions in nerve cells.

These previously-free living bacteria - mitochondria - with their own internal core machinery - have to have their own cell cycle - they need to replicate. The partnership with the motile cell has evolved so that replication is done *by* the mother eurkaryotic cell.