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| Author(s): |
Paulo Roberto de Araujo Campos
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT) |
| Defense date: | 2001-08-06 |
| Examining board members: |
Jose Fernando Fontanari;
Nestor Felipe Caticha Alfonso;
Antonio Caliri;
Tereza Cristina da Rocha Mendes;
Salomon Sylvain Mizrahi
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| Advisor: | Jose Fernando Fontanari |
| Abstract | |
The quasi-species model is the paradigm of systems composed of self-replicating molecules, which are represented by sequences of fixed length L. The replication machinery is assumed to be imperfect. Particularly, each sequence is copied exactly with probability Q=qL, where q denotes the probability of exact copy per digit. One of the most intriguing results of the model for the single-peak replication landscape, which considers the existence of a master sequence that has a selective advantage a in comparison to the other types, is the occurrence of an error threshold phenomenon beyond the biological information is completely lost. The error threshold transition can be viewed as an order-disorder phase-transition. We investigated the sharpness of the threshold and found that its characteristics persist across a range of Q of order L-1 about Qc. Other physical quantities of interest are also well described by universal functions. We formulate a stochastic version (i.e., finite population size N) for the quasispecies model, in which a Markov chain defines the dynamics. We show that the characteristic time r for the disappearance of master sequences in the population obeys a well defined scaling relation. The transition in this model is signalized by the divergente of t at Qc in the limit N → ∞, and the sharpness of the transition decreases like N -1/2. In our approach we do not use any arbitrary definition of the error threshold for finite population. As a solution for the information crisis associated to the error threshold, here we considered the hypercycle model, where the macromolecules self-replicate with the catalytic support of the other members of the hypercycle. We study analytically the error propagation in the hypercycle and obtain the phases diagrams in the space of parameters for several hypercycle sizes n. These diagrams describe the stability regions of the steady state solutions of the system. We find that for hypercicle size n ≤ 4 the error threshold is smaller than that for the quasispecies model. Since the catalytic support developed by a molecule is in fact an altruistic behavior, some models for the evolution of altruism, for instance, the selection group theory, have been investigated in the context of pre-biotic evolution. Specifically, here we analyze the evolution of enzyme production and the effects of synergism. (AU) | |