The cell, the fundamental unit of life, consists of a package of information-bearing molecules (DNA) wrapped in some material that delineates it from the outer world (lipid membrane). Basically, a cell is a highly organised and compartmentalised bag of fat and acid. Nothing much to see here...
The story is not so simple however. Multiple nuclei occupying one cytoplasm is a fairly common situation, as are holes (channels) between cells in multicellular organisms. This has even led to discussions about using an alternative "Cell Body" concept instead of the conventional cell (Baluska et al. 2004 Annals Bot. (free access)) - although perhaps it's not worth the bother to panic over redefining everything.
Apparently, some coenocytic algal nuclei can survive plasma-membrane-less upon release from a wounded cell. The nucleoplasm is then surrounded by a gelatinous envelope and subsequently forms a plasma membrane and cell wall. (Ram & Babbar 2002, BioEssays). That could be just a special case, a byproduct of coenocytic wound repair mechanisms.
But there is an organism that specialises in firing its nuclei into the host to take it over! (kinda like installing trojans on your computer...) Meet Choreocolax, a filamentous red algal parasite that leeches off Polysiphonia (another red alga).
(Goff & Coleman 1984 PNAS; free access)
It forms 'planetic' nuclei which are then injected into Polysiphonia by forming pit connections. These planetic nuclei then multiply vigorously in the host cytoplasm and 'take over' the cell:
(PN - planetic nucleus; HN - host nucleus)
The molecular aspect of this process must be pretty awesome -- would love to see that thing's genome sequence (sadly unlikely; this thing isn't particularly popular or well-known. Yet.) and hear about the various pathways involved in taking over the host... and how the nucleus can survive in a foreign cytoplasm in the first place!
There's only one lab studying Choreocolax, it appears. That needs to change...
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