In the 1970s, Manfred Eigen launched a very
impressive research attack on the life origin problem [1,2].
M. Eigen and his coworkers tried to imagine the transient stages
between the molecular chaos in a prebiotic soup and simple
macromolecular self-reproducing systems. They developed several
mathematical models, illustrating the hypothetical macromolecular
systems; quasispecies and hypercycles are the most significant. The
models were intensively analyzed mathematically as well as
compared with biochemical experiments and discussed from
different points of view.
Quasispeciesis a model of a
Darwinian evolution of a population of the polynucleotide strings
(analogous to RNA), which are supposed to have certain
replication abilities. Polynucleotide strings are modeled by
informational sequences. The model implies that there is a master
sequence, having a maximal selective value (a selective value is
a sequence fitness). The selective values of other sequences are
defined as follows: the more similar is the particular sequence
to the master sequence, the greater is its selective value. The
evolution process includes the selection (according to the
selective values) and the mutations of informational sequences.
The final result of an evolution is a quasispecie, that
is the distribution of sequences in the neighborhood of the
The model of quasispecies was analyzed
mathematically by a number of authors [1-6], and the
particularities, concerning a final sequence distribution, a
restriction on the sequence length, and a rate of evolution were
quantitatively estimated. A short review of these mathematical
results as well as a formal description of the model are given in
the child node quasispecies.
M.Eigen et al interpreted quasispecies as a model
of a primitive RNA-sequences origin. Taking into account the
nucleotide coupling abilities, they deduced that the length of
these primitive RNA-sequences could not be greater than 100
nucleotides. As the further stage of macromolecular evolution,
M.Eigen and P.Schuster proposed a model of hypercycles,
which include the polynucleotide RNA-sequences as well as
polypeptide enzymes .
Hypercycle is a self-reproducing
macromolecular system, in which RNAs and enzymes cooperate in the
following manner: there are n RNAs; i-th RNA
codes i-th enzyme (i = 1,2,...,n); the
enzymes cyclically increase RNA's replication rates, namely, 1-st
enzyme increases replication rate of 2-nd RNA, 2-nd enzyme
increases replication rate of 3-rd RNA, ..., n-th enzyme
increases replication rate of 1-st RNA; in addition, the
described system possesses primitive translation abilities, so
the information stored in RNA-sequences is translated into
enzymes, analogously to the usual translation processes in
biological objects. For effective competition (i.e. for surviving
the hypercycle with greatest reaction rate and accuracy), the
different hypercycles should be placed in separate compartments,
for example into A.I.Oparin's coacervates . M.Eigen and
P.Schuster consider hypercycles as predecessors of protocells
(primitive unicellular biological organisms) . As
quasispecies, hypercycles were also analyzed mathematically in
details. The child node hypercycles
describes formally this model.
The models of quasispecies and hypercycles were
rather well developed and provide certain consequent description
of hypothetical process of first molecular-genetic system origin.
But they are not unique. The life origin problem is very
intriguing, and there is diversity of this problem
investigations. We mention here only some of them.
F.H.C.Crick discussed in details the possible
steps of genetic code origin .
F.J.Dyson proposed the model of "phase
transition from chaos to order" to interpret the stages of
cooperative RNA-enzyme systems origin .
P.W.Anderson et al used the physical spin-glass
concept in order to model a simple polynucleotide sequence
evolution . This model is similar to the quasispecies.
H.Kuhn considered the creation of the aggregates
of RNAs as a stage for an origin of a simple ribosome-like
translation device .
So, the approaches to the molecular-genetic
system origin modeling are different in many relations. However,
some convergence points do exist. In the early 1980s, V.A.Ratner
and V.V.Shamin (Novosibirsk, Russia), D.H.White (California), and
R.Feistel (Berlin) independently proposed the same model [12-14].
V.A.Ratner called it "syser" (the abbreviation
from SYstem of SElf-Reproduction).
Syser is a system of
catalytically interacting macromolecules, it includes the
polynucleotide matrix and several proteins; there are two
obligatory proteins: the replication enzyme and the translation
enzyme; syser can also include some structural proteins and
additional enzymes. The polynucleotide matrix codes proteins, the
replication enzyme provides the matrix replication process, the
translation enzyme provides the protein synthesis according to an
information coded in the matrix; structural proteins and
additional enzymes can provide optional functions. Analogously to
hypercycles, different sysers should be inserted into different
compartments for effective competition. Mathematical description
of sysers (see Sysers
for details) is similar to that of hypercycles.
As compared with hypercycles, sysers are more
similar to simple biological organisms. The concept of sysers
provides the ability to analyze evolutionary stages from a
mini-syser, which contains only matrix and replication and
translation enzymes, to protocells, having rather real biological
features. For example, "Adaptive
syser"  includes a simple molecular control system,
which "turns on" and "turns off" synthesis of
some enzyme in response to the external medium change; the scheme
of this molecular regulation is similar to the classical model by
F.Jacob and J.Monod . The control system of the adaptive
syser could be the first control system, which was
"invented" by biological evolution.
Additionally, it should be noted, that the scheme
of sysers is similar to that of the Self-Reproducing Automata,
which were proposed and investigated at the sunrise of modern
computer era by J.von Neumann .
Conclusion. The considered
models of course can't explain the real life origin process,
because these models are based on various plausible assumptions
rather than on a strong experimental evidences. Nevertheless,
quasispecies, hypercycles, and sysers provide a well defined
mathematical background for understanding of the first
molecular-genetic systems evolution. These models can be used to
develop the scenarios of the first cybernetic systems origin,
they can be juxtaposed with biochemical data to interpret
qualitatively the corresponding experiments, and can be
considered as a step for developments of more powerful models.
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Vol.58. P. 465.
2. M.Eigen, P.Schuster. "The
hypercycle: A principle of natural self-organization".
Springer Verlag: Berlin etc. 1979.
3. C.J.Tompson, J.L.McBride. Math.
Biosci. 1974. Vol.21. P.127.
4. B.L.Jones, R.H.Enns, S.S. Kangnekar.
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Mathematical models of evolutionary genetics. Novosibirsk: ICG,
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"Theory of self-reproducing automata". Univ. of
Illinois Press, Urbana IL, 1966.