An interpretation of the oligomerization of amino acids under prebiotic conditions

Resumen

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.