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Models of molecular-genetic systems origin

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 master sequence.

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 [2].

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 [7]. M.Eigen and P.Schuster consider hypercycles as predecessors of protocells (primitive unicellular biological organisms) [2]. 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 [8].

F.J.Dyson proposed the model of "phase transition from chaos to order" to interpret the stages of cooperative RNA-enzyme systems origin [9].

P.W.Anderson et al used the physical spin-glass concept in order to model a simple polynucleotide sequence evolution [10]. 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 [11].

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" [15] 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 [16]. 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 [17].

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.


1. M.Eigen. Naturwissenshaften. 1971. 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. Bull. Math. Biol. 1976. Vol.38. N.1. P.15.

5. Von H.D.Fosterling, H.Kuhn, K.H.Tews. Ang. Chem. 1972. Jg.84. Nr.18. S. 862.

6. V.G.Red'ko. Biofizika. 1986. Vol. 31. N.3. P. 511 (In Russian).

7. A.I.Oparin. "The origin of life". New York, 1938. A.I.Oparin. "Genesis and evolutionary development of life". New York, 1968.

8. F.H.C.Crick. J. Mol. Biol. 1968. Vol. 38. N.3. P.367.

9. F.J.Dyson. J. Mol. Evol. 1982. Vol.18. N.5. P.344.

10. P.W.Anderson. Proc. Natl. Acad. Sci. USA. 1983. V.80. N.11. P.3386. Rokhsar D.S., Anderson P.W., Stein D.L. J.Mol. Evol. 1986. V.23. N.2. P.119.

11. H.Kuhn. Angew. Chem. 1972. Jg.84. Nr.18. S.838.

12. V.A.Ratner and V.V.Shamin. In: Mathematical models of evolutionary genetics. Novosibirsk: ICG, 1980. P.66. V.A.Ratner and V.V.Shamin. Zhurnal Obshchei Biologii. 1983. Vol.44. N.1. PP. 51. (In Russian).

13. D.H.White. J. Mol. Evol. 1980. Vol.16. N.2. P.121.

14. R.Feistel. Studia biophysica.1983. Vol.93. N.2. P.113.

15. V.G.Red'ko. Biofizika. 1990. Vol. 35. N.6. P. 1007 (In Russian).

16. F.Jacob and J.Monod. J. Mol. Biol. 1961. Vol. 3. P. 318.

17. J.von Neumann, A. W. Burks. "Theory of self-reproducing automata". Univ. of Illinois Press, Urbana IL, 1966.

Copyright© 1998 Principia Cybernetica - Referencing this page

V.G. Red'ko

Apr 27, 1998


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