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Stochastic Simulations of Branching Processes: Study on Complexity Threshold of RNA-World Species

The main reason of popularity of RNA-world hypothesis is the fact that it resolves by introduction of RNA-species the unsolved in another way problem of anteriority of DNA or proteins in the beginning of Life [1]. The problem is similar to that with an egg and a hen: the enzymatic proteins are needed for the replication of DNA strands (anteriority of proteins), however, DNA strands are required for forming enzymatic proteins (anteriority of DNA). The RNA-world eliminates both: the hen laying an egg and the egg giving the birth to a hen, and introduces the ancestral hybrid capable for performing roles of both a hen and an egg. Similarly, in hypothetical RNA-species RNA plays the role of both genetic material and enzymes (called rybozymes) required for reproduction. This is a very attractive hypothesis, and perhaps it lacks only the experimental confirmation. The problem is that the enzyme, crucial for reproduction of any RNA-species, called RNA-based RNA-replicase is yet to be discovered. The advocates of RNA-world do not treat seriously this lack of experimental confirmation, believing that it is only the matter of time when such confirmation comes. Remarkably, some enzymatic activity exhibited by RNA molecules has been already discovered, and extending this limited activity to activities performed by all enzymes required for reproduction is only one step further. Not going into hot debate between RNA-world proponents [1] and antagonists [2], we consider the problem of the complexity threshold of the RNA-species. This threshold defines a maximum sequence length, based on theory of branching processes and stochastic computer simulations. In the paper we summarize main theoretical results of Demetrius et. al. [3] and Kimmel and Axelrod [4], and further discuss them obtaining values of complexity threshold for different mutation rates and surviving probabilities. The stochastic simulations of slightly supercritical branching process for species not exceeding complexity threshold are also presented. They are performed by the software using sophisticated random number generators described in [5, 6]. This simulating branching processes software was used also in [7] to make inferences about interactions of Neanderthals and archaic H sapiens, based on the mitochondrial DNA record. It is known that different species during reproduction produce almost identical copies of themselves. The word almost is of great concern in our study (and probably in the whole history of Life) since it is responsible for rare changes (caused by mutations) on one hand, and for keeping relatively …