Polynucleotide evolution and branching processes
type: Item
instance of: scholarly article
title: Polynucleotide evolution and branching processes
zbMATH Open document ID: 0576.92020
DOI: 10.1007/BF02460034
author: Peter Schuster
author: Karl Sigmund
author: Lloyd Demetrius
published in: Bulletin of Mathematical Biology
publication date: 1985-01-01T00:00:00Z
review text: The theory of multitype branching processes has been applied to the description of the kinetics of polynucleotide replication. The stochastic model is consistent in mean with the usual kinetic differential equations of deterministic chemical kinetics. Qualitatively new consequences of the stochastic model are: after a transient period the supercritical multitype branching process either leads to extinction (corresponding to zero fluctuations) or the total population size becomes very large (corresponding to negligible relative fluctuations). The stochastic as well as the deterministic treatments of replication with errors yield error threshold relations which attest that the maximum length of faithfully replicated sequences are proportional to the inverse single digit error rate. The stochastic threshold provides a stronger condition than the deterministic relation.
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 80A30
zbMATH DE Number: 3922436
zbMATH Keywords: kinetic differential equations
zbMATH Keywords: replication error
zbMATH Keywords: genome length
zbMATH Keywords: multitype branching processes
zbMATH Keywords: kinetics of polynucleotide replication
zbMATH Keywords: deterministic chemical kinetics
zbMATH Keywords: extinction
zbMATH Keywords: total population size
zbMATH Keywords: error threshold relations
zbMATH Keywords: inverse single digit error rate
MaRDI profile type: Publication
Wikidata QID: Q49257887
cites work: Q5674726
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full work available at URL: https://doi.org/10.1007/bf02460034
OpenAlex ID: W4239262064
description: scientific article; zbMATH DE number 3922436