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In the present work we address to the oligomerization of amino acids under plausible prebiotic conditions and within the framework of a simple stochastic mathematical model. A main premise of our approach is that the reactivity of such monomers is different, as experimental results suggest. Such condition would lead to the synthesis of random but biased polymers and not to purely random polymers. Another manner to phrase such result is to say that synthesized prebiotic oligopeptides have a limited randomness. To consider oligomerization of amino acids, we follow a classification of amino acids into 4 groups: Polar positive (p+ ), polar negative (p– ), neutral (n), and non-polar (np). Besides, we choose to use Markov chains to evaluate the reactivity among them, as it is a process or succession of events developing in time in which the result in any stage depends on chance, according to pre-established probabilities of reaction. So, we arrange all possible pair-wise electromagnetic interactions into a 4 x 4 reactivity matrix. Then we apply this mathematical model to every stage of the diketopiperazine reaction: Its initiation and elongation stages. The chemical nature of the amino acid monomers provides only a limited number of initiators to the oligomerization process. Besides, on close examination of the elongation stage it is revealed that oligopeptides are produced only the odd-mer species, but none pair-mer peptides. Furthermore, the mathematical model predicts the existence of a Markov chain steady state which limits still more the variability in the population of synthesized oligomers. We emphasize then that the polypeptides that were produced in a prebiotic environment were random, of course, but were biased and had a restricted randomness, due to differences in the polarity of the participating amino acids. Another important observation from this study is that it can be envisaged that contiguous alike charges or monomers will not be favored in the oligomerization process under consideration, based on simple physical criteria. On the contrary, it would be easier to unite contiguous charges of different polarity. With this background, we predict that for the oligopeptides so produced, the heteropeptides would be more prevalent than the homoligopeptides. Such conditions will be useful in the prebiotic environment because presumably heteroligopeptides would have more pre-catalytic activities than homoligopeptides. We see, then, a natural emergence and predominance of complex polypeptides (co-polypeptides and hetero-polypeptides) over simpler homo-polypeptides. This is undoubtedly an interesting result. Finally, in respect to the biased principle, it is obviously insufficient drawing conclusions from scarce experimental results and from very short oligomers (i.e. tripeptides). A quantitative evaluation of the extent of bias has to be done. The extent and effectiveness of such principle will remain an open question.

An interpretation of the oligomerization of amino acids under prebiotic conditions