First off, the Ghadiri self-replicator is just a single example; there are countless possibilities (I could equally, say, go into the SunY self-replicator, the hexanucleotide self-replicator, Eckland's RNA polymerase self replicator, etc). In reality, there are going to be millions of possible simple self-replicators, and many times more self-catylizing cycles (i.e., where no single chemical is a self-replicator, but together they encourage the creation of more of their components). However, let's just use the Ghadiri self-replicator:
RMKQLEEKVYELLSKVACLEYEVARLKKVGE (sp? I think I'm missing one...)
Just assuming that the Ghadiri peptide is randomly pieced together (just coincidentally, it is of a form that is ideally suited to be formed by abiotic peptide synthesis, but we'll ignore that), you would have odds of 4.29e41 for producing it. However, its subunits 6.655e20 - 6.655e20 times as common as the original self-replicating peptide. If the Ghadiri ligase was formed in an environment that tends to form peptides like itself, then its subunits are quite likely to occur there as well.
Furthermore, I might ask: when given partial subunits, will the replicator assemble a partial copy of itself? If so, then its odds of survival just vastly increased, because the partial copy is well on its way to becoming a full copy, or even a deformed copy that itself makes partial copies. Anything that turns the pool of amino acids more toward a self-replicating form is a "good thing", and a positive step on the way to creating life. I'm unable to find an article on this subject either confirming or denying this possibility in respect to the Ghadiri replicator, but it seems realistic. Catalyzation to produce chemicals similar to but not exactly like the original, is likely the first step in abiogenesis, because it would be far more common than forming a complete self-replicator. This catalyzation progresses into a full hypercycle, which progresses into an ur-cell.
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