Lattice model of replicators: aplication on prebiotic models and herpes ulcer / Dinâmica de replicação na rede: aplicações em modelos de evolução pré-biótica e de formação de úlceras

AUTOR(ES)

Cláudia Pio Ferreira

DATA DE PUBLICAÇÃO

2001

RESUMO

Two fundamental questions in the study of prebiotic evolution (origin of life) are concerned to the requisites for the persistence of small colonies of self-replicating molecules (replicators) and to the possibility that complex organisms evolve from simpler organisms as a result of mutations. These issues have been studied mainly in the chemical kinetics formulation of well-mixed medium, which is similar to the mean-field limit of statistical physics. In this work, we address these issues using a cellular automaton formulation, in which the replicators are kept fix in the lattice sites (contact process). In the stationary regime, we find that the system can be characterized by the presence (active phase) and the absence (empty phase) of replicators in the lattice. The detailed study of the phase transitions separating those two phases is carried out using the spreading analysis of Grassberger and de La Torre, in which one concentrates on the spreading behavior of a few active cells in the center of an otherwise empty infinite lattice. The nature of the phase transition, whether continuous or discontinuous, depends on the mechanisms of replication. In particular, in the case that the phase transition is continuous, we find that it is in the universality class of the directed percolation. Complementing this study, we irivestigate the possibility that a small colony of replicators invade a settled population of replicators of another species. Contrary to the results of the mean-field limit, we show that in the contact process limit, complex replicators (such as sexual reproducing ones) have a nonvanishing probability to invade a settled population of simpler replicators (such as asexual reproducing ones). In agreement with the mean-field results, we find that two different species of replicators can never coexist in an equilibrium situation. Finally, using the spreading analysis mentioned before we study the critical properties of a cellular automaton model proposed to describe the spreading of infection of the Herpes Simplex Virus (HSV-I) in the corneal tissue. The model takes into account different cell susceptibilities to the viral infection, as suggested by experimental findings, in order to explain the different shapes of the ulcers - dentritic and amoeboid - that result from the infection. We show that the phase transition separating the regimes where one of the shapes dominates is in the universality class of the ordinary percolation.

ASSUNTO(S)

cellular automata prebiotic models evolução pré-biótica herpes ulcers Úlceras autômatos celulares

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