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A stochastic evolution model for residue Insertion–Deletion Independent from Substitution

Paper ID Volume ID Publish Year Pages File Format Full-Text
15281 1400 2010 9 PDF Available
Title
A stochastic evolution model for residue Insertion–Deletion Independent from Substitution
Abstract

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.

Keywords
Gene evolution; Stochastic model; Analytical solutions; Substitution; Insertion; Deletion; Time and sequence length; Occurrence probability; Nucleotides
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A stochastic evolution model for residue Insertion–Deletion Independent from Substitution
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Publisher
Database: Elsevier - ScienceDirect
Journal: Computational Biology and Chemistry - Volume 34, Issues 5–6, December 2010, Pages 259–267
Authors
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Subjects
Physical Sciences and Engineering Chemical Engineering Bioengineering
Get Full-Text Now
Don't Miss Today's Special Offer
Price was $35.95
You save - $31
Price after discount Only $4.95
100% Money Back Guarantee
Full-text PDF Download
Online Support
Any Questions? feel free to contact us