Comput Biol Chem - A stochastic evolution model for residue Insertion-Deletion Independent from Substitution.

Tópicos

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Resumo

We develop here a new class of stochastic models of gene evolution based on residue Insertion-Deletion Independent from Substitution (IDIS). Indeed, in contrast to all existing evolution models, insertions and deletions are modeled here by a concept in population dynamics. Therefore, they are not only independent from each other, but also independent from the substitution process. After a separate stochastic analysis of the substitution and the insertion-deletion processes, we obtain a matrix differential equation combining these two processes defining the IDIS model. By deriving a general solution, we give an analytical expression of the residue occurrence probability at evolution time t as a function of a substitution rate matrix, an insertion rate vector, a deletion rate and an initial residue probability vector. Various mathematical properties of the IDIS model in relation with time t are derived: time scale, time step, time inversion and sequence length. Particular expressions of the nucleotide occurrence probability at time t are given for classical substitution rate matrices in various biological contexts: equal insertion rate, insertion-deletion only and substitution only. All these expressions can be directly used for biological evolutionary applications. The IDIS model shows a strongly different stochastic behavior from the classical substitution only model when compared on a gene dataset. Indeed, by considering three processes of residue insertion, deletion and substitution independently from each other, it allows a more realistic representation of gene evolution and opens new directions and applications in this research field.

Resumo Limpo

develop new class stochast model gene evolut base residu insertiondelet independ substitut idi inde contrast exist evolut model insert delet model concept popul dynam therefor independ also independ substitut process separ stochast analysi substitut insertiondelet process obtain matrix differenti equat combin two process defin idi model deriv general solut give analyt express residu occurr probabl evolut time t function substitut rate matrix insert rate vector delet rate initi residu probabl vector various mathemat properti idi model relat time t deriv time scale time step time invers sequenc length particular express nucleotid occurr probabl time t given classic substitut rate matric various biolog context equal insert rate insertiondelet substitut express can direct use biolog evolutionari applic idi model show strong differ stochast behavior classic substitut model compar gene dataset inde consid three process residu insert delet substitut independ allow realist represent gene evolut open new direct applic research field

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