Mitochondria and chloroplasts display similarities
with bacteria that led to the endosymbiont theory.
This theory states that an early
ancestor of eukaryotic cells engulfed an oxygen-using nonphotosynthetic
prokaryotic cell. Eventually, the engulfed
cell formed a relationship with the host cell in which it was
enclosed, becoming an endosymbiont (a cell living within
another cell). Indeed, over the course of evolution, the host
cell and its endosymbiont merged into a single organism, a
eukaryotic cell with a mitochondrion. At least one of these
cells may have then taken up a photosynthetic prokaryote,
becoming the ancestor of eukaryotic cells that contain
chloroplasts.
This theory is consistent with
many structural features of mitochondria and chloroplasts.
First, rather than being bounded by a single membrane like
organelles of the endomembrane system, mitochondria
and typical chloroplasts have two membranes surrounding
them.
There is evidence that the ancestral engulfed prokaryotes had two outer membranes, which became the
double membranes of mitochondria and chloroplasts. Second,
like prokaryotes, mitochondria and chloroplasts contain
ribosomes, as well as multiple circular DNA molecules
associated with their inner membranes. The DNA in these
organelles programs the synthesis of some organelle proteins
on ribosomes that have been synthesized and assembled
there as well. Third, also consistent with their probable
evolutionary origins as cells, mitochondria and chloroplasts
are autonomous (somewhat independent) organelles that
grow and reproduce within the cell.
source
The Endosymbiotic Theory | Evolution of mitochondria and chloroplast | Biology lecture

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How eukaryotic cell engulf bacteria? At that time prokaryotic cell was present..
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