How small can an organism get?
In my world, I am attempting to design a primitive organism to be the ancestor of life on an artificial planet with all chemicals necessary for life. I want the organism to be as small as possible (say 50 nanometers in diameter). Is such a small size possible?
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50 nanometers is awfully small. In fact, this is on the same order as many viruses, which can be 20-300 nm in size; to a first order approximation, this figure seems a good fit for Cort Ammon's estimate of 16-18 nm DNA strands. Some viruses are smaller along one dimension, but larger along others; Wikipedia mentions that some filoviruses can be 80x1400 nm in size.
In contrast, bacteria are usually in the 500-5000 nm (0.5-5.0 µm) size range. While the issue of whether a virus constitutes life is as of yet undecided, there is little doubt that bacteria can be considered to be life.
Hence, the boundary for true life, at least in an Earth-like environment, appears to fall somewhere in the 300 to 500 nm range, which is about one order of magnitude larger than what you are aiming for.
It is possible that some extreme biology and evolutionary pressure might be able to support living organisms smaller than Earth bacteria, but I find it highly doubtful that it would be able to reduce the minimum viable size of an organism by such a large fraction. There is also no real evolutionary benefit that I can see to becoming that much smaller, hence very limited evolutionary pressure in that direction. If the limiting factor is indeed DNA base pair size and the number of nucleotides needed, then you may need some completely different biochemistry to make a significantly smaller organism viable. Based on discussion in the answers to Why would life on a different planet use DNA?, it's likely that life would settle on DNA or at least RNA, so DNA strand size could be one factor establishing a lower limit for the size of life even on a completely different planet.
At the very least, again to a first order approximation, any living organism must be large enough to support some form of procreation, even if that is done by cell division. Even cell division would appear to need the cell to be well above its minimum viable size before the division. Because they co-opt existing cells, viruses do not have that size constraint, and in fact would appear to have an evolutionary advantage to being smaller (less things to go wrong leading to higher probability of success).
You may also want to compare Are there organisms with fewer than 1000 neurons? on the Biology Stack Exchange, which appears to be peripherally related.
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