One can of worms that one user here declared mathmatically impossible(not writting proof given or paper noted) we now have some proof that proteins can assemble on their own.
Life on Earth Was Not a Fluke
...The assembly can only produce proteins when its molecules are close enough together to react with each other. When the assembly is diluted with water, they can no longer react. This is one reason that the insides of living cells are very crowded, concentrated places: to allow the chemistry of life to work.
In order to recreate this molecular crowding, Stano added a chemical called POPC to the dilute solution. Fatty molecules such as POPC do not mix with water, and when placed into water they automatically form liposomes. These have a very similar structure to the membranes of living cells and are widely used to study the evolution of cells.
Stano reports in the journal Angewandte Chemie that many of these liposomes trapped some molecules of the assembly. But remarkably, five in every 1,000 such liposomes had all 83 of the molecules needed to produce a protein. These liposomes produced large amount of GFP and glowed green under a microscope.
Computer calculations reveal that even by chance, five liposomes in 1,000 could not have trapped all 83 molecules of the assembly. Their calculated probability for even one such liposome to form is essentially zero. The fact that any such liposomes formed and that GFP was produced means something quite unique is happening.
Since we don't know the exact makeup of promrdial Earth we can only extrapolate what was there. Though this is just one example of "unguided" protein product, we certainly can see that even in a simple experiment we get result similar to life.[/url]
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