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Talk Abstract
Lattice Dynamical System Model for the HIV1 Genetic Sequence Evolution

Gustavo Martinez-Mekler
Centro de Ciencias Fisicas, UNAM

The HIV1 reproductive cycle entails high mutability and strong competition. Here we present a coupled map lattice model for the evolution of the HIV1 genetic sequence which incorporates these characteristics. The equations are of the reaction-diffusion type operating in a discrete chemical composition space with time also discrete. From the variety of available virus strains we obtain the equivalent of a "quasi-species." Our formulation falls into a popullation dynamics scheme where point mutations appear as interactions amongst of strains and selective synthesis is taken into account in terms of ecological constraints. The model predicts an anticorrelation between a local concentration of certain type of codons and strain variability. For the case of the envelope (env) gene this property is verified by a statistical analysis of the gene bank data. We argue that this behavior is suggestive for a new therapeutical clue involving the ribosome. We believe that it highlights the relevance of non-local mechanisms in protein synthesis. We are presently extending our analysis to extensive portions of the genome of other organisms in order to test the validity and generality of this conjecture.


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  1998-1999 Mathematics in Biology

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