|Evolution of DNA -
Once Fred got going and a few more Freds were on the scene, we can imagine that the Sofia molecule would spend most of its time hanging out with a Fred or one of its progeny, cranking out additional copies of Fred.
Of course not all of the Fred transcriptions would be perfect Freds. Some versions might lack an amino acid, or have an extra one. Some version might have a mistranscription, or some entirely different substance inserted in the chain. After all, it was still the world of random chemistry, and it was just not possible to attain the high levels of accuracy that are possible in modern biochemical systems. And to be honest, Fred had a rather flaky transcription system that would have made many mistakes.
Some of those 'differently enabled' versions of Fred would have slightly different properties. Some would be drastically different.
It may not have taken long at all for a Fred descendant to end up with a similar structure, but with a slightly different active group at its knee. We'll call this mutant Fred a Roscoe (short for Replicator Of Some Chains, Oldest Enzyme).
Roscoe has a similar setup to Fred, with an elbow that 'reads' chain elements, and a polymerizing knee that is linked to the elbow. So far just like Fred. The difference is that Roscoe's knee is a slightly different shape from Fred's, and it happens to polymerize chain molecules, rather than amino acids.
Read a purine at the elbow, and add a purine at the knee. Read a pyrimidine, and add a pyrimidine. Or perhaps some sort of similar action on entirely different compounds, in a aromatic chain composed of entirely different molecules.
The result? With some moderate probability, in an environment that includes a high concentration of just two chain molecules, Roscoe can replicate a genetic chain. It reads one Sofia, and create another.
Roscoe in Pictures
Let's take a closer look at Roscoe, step by step, since this is also very important.
Sofia is still the same old aromatic chain, made from two different chain molecules that could be just about anything. Meanwhile, Roscoe is a lot like Fred, with an elbow at the top, and a knee at the bottom, and with two possible conformational states.
Here is the very first genetic replication, step by step:
1. Roscoe's elbow loosely binds to the first element of the Sofia aromatic chain.
2. A chain element molecule attaches to Roscoe's knee.
3. That jiggles Roscoe on to the next chain molecule. Another of the same chain molecule binds at the knee.
4. Another day on the chain (gang).
5. Now Roscoe has jiggled on to a different chain molecule. Its conformation changes. The knee is now structured so it attracts a different chain molecule, and binds it to the chain.
6. A few more jiggles, and Roscoe has moved further along the chain.
7. Eventually it reaches the end. Along the way, it has produced a relatively exact copy of Sofia.
More about Roscoe
Now let's poke at some of the details for this Roscoe thing.
Complementary Base Pairs
If you know anything about genetics, the first thing you might notice is that this replication has not used complimentary base pairs (as happens in modern replication of DNA and RNA).
The reason? Well, first of all, it seems very unlikely that DNA or RNA would even exist in quantity, at this point in pre-history. Not only that, but there is no reason to suppose that the two random chain molecules would be complementary to each other. We definitely improve the plausibility of this replication event actually happening, if it can use any old sequence of whatever molecules that happened to form a chain in this particular neighborhood.
Even if our chain did contain RNA or DNA nucleotides, we only have two of the four base pairs right now. It was lucky enough to get a high local concentration of two chain-forming molecules, and we don't want to press our luck by expecting four.
Even if our chain happened to be DNA, it's not going to replicate reliably by base pairing in the soup. That happens only in an extremely pure solution of DNA molecules, with the assistance of enzymes such as DNA replicase. The C-G and A-T pairing system in the DNA molecule is extremely cool, but it won't happen spontaneously when you just have a few nucleotides floating in a mixed solution of random organic chemicals.
Remember that we are still in a chaotic soup, and all we have to work with is simple diffusion, hydrogen bonding, oil/water interactions, and other very simple chemistry. Replicases and other enzymes are not in the picture yet. Pure solutions of RNA or DNA are extremely unlikely (and even if they occurred, they would tend to clump up into intractable blobs).
Roscoe is not the best replicator in the world, but it kinda works. And it is similar enough to Fred it could have arisen fairly quickly, from a bad transcription of Sofia.
Roscoe has pretty much the same replication issues as Fred.
It probably made many mistakes, even in a puddle with a huge excess of just two chain-forming molecules. Sometimes it would cough, and plug in the wrong molecule. Sometimes it would skip a molecule, or add an accidental duplicate. Sometimes a similar compound would sneak in (though Roscoe is rather dense, so it might still read it as the correct shape, and create a correct chain again, the next time around).
In the open ocean, or in any pool with mixed ingredients, Roscoe would just produce random chains with an exceedingly low chance of creating another Sofia. It only works in the right locations that already contain a high concentration of two chain-forming molecules, without many similar compounds in the neighborhood.
How long would it have taken for Roscoe to appear?
Once Fred formed and started to self-replicate, it probably didn't take long at all for a Roscoe to show up-- since it has an almost identical function. It may have only required that one or two polar amino acids change to hydrophobic ones, so the knee would attract an aromatic chain molecule instead of an amino acid.
The jump from protein transcription to chain replication may have only taken minutes, hours, days or years. Practically an instant, in geological time scales.