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It is easy to realize that the number of sequences grows exponentially with re-
spect to their length. For example, the number of sequences of length 100 over
20 elements is 20 100 , that is, a number overcoming any possibility of enumeration,
within the whole existence of the universe. Therefore, the aggregation of basic kinds
of molecules, in linear arrangements, opens an enormous possibility in the search of
complex molecules. In fact, it provides a space of molecular variability which life
can explore in the search of the complex molecular functions for assembling living
organisms, starting from molecules.
Polymers are sequences over a set of component molecules called
monomers . They have a crucial relevance in fundamental mechanisms of
life, and are the molecular basis of replication, which is essential to life
reproduction.
1.2.1
LUCA and the Sequence Paradox
What we described in Sect. 1.1.1 is more precisely a prebiotic protocell . It is only
able to maintain, for some time, an introduction-transformation-expulsion ability.
However, another feature is missing for the passage from a prebiotic protocell to a
cell in a full sense: the reproduction in two similar organisms which, in turn, are able
to perform the same task. Surely, many attempts of reproduction happened, but over
time, the reproductive ability of descendants degraded in two possible ways: i) they
lost the reproductive ability due to some internal degradation, or ii) the environment
changed and they were not able to survive. This means that, among a huge number
of attempts, possibly in different places, and in different times, life emerged, in a
full sense, when a protocell was able to produce descendants for a sufficient number
of generations. One lineage acquired the property of generating stable progenies.
Therefore:
Cells originating from that ancestor protocell, called LUCA (Least Universal
Common Ancestor) are the cells of the life we know. This event is dated
around 3.8 billions of years ago.
A different possibility for the origin of life would suggest a different scenario
where the process outlined above happened many times, providing different sources
of life. In this case, it is possible that different LUCAs cooperated, in some way,
by exchanging some molecules, by keeping a sort of similarity, and surely a kind of
competition was established, in sharing common resources [7]. On the contrary, if no
cooperation/competition had been established among biotic protocells, then almost
 
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