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Processus de branchement en champ moyen et réaction PCR

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Didier Piau
Didier Piau*
Affiliation:
Université Claude Bernard Lyon-I
*
∗ Adresse postale: LaPCS, UFR de Mathématiques, Université Claude Bernard Lyon-I, 43, boulevard du 11-Novembre-1918, 69622 Villeurbanne Cedex, France. Adresse email: [email protected]
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Abstract

Sun and Waterman model DNA mutations during the PCR reaction by a non-canonical branching process. Mean-field approximated values fit the simulated values surprisingly well. We prove this as a theoretical result, for a wide range of the parameters. Thus, we bound explicitly the biases, in law and in the mean, that the mean-field approximation induces in the random number of mutations of a DNA molecule, as a function of the initial number of molecules, of the number of PCR cycles, of the efficiency rate and of the mutation rate. The range where we prove that the approximation is good contains the observed mutation rates in many actual PCR reactions.

Résumé

Résumé

Sun et Waterman modélisent les mutations de l'ADN qui apparaissent au cours de la réaction PCR par un processus de branchement non canonique. Ils observent un accord surprenant entre les données simulées et une approximation de type champ moyen. Nous montrons que cette approximation est valide sur un domaine étendu de l'ensemble des parametres. Nous majorons explicitement le biais qu'elle introduit, en loi et en moyenne, dans le nombre de mutations subies par une molécule d'ADN, en fonction du nombre de molécules présentes au départ, du nombre de cycles PCR effectués, du taux d'efficacité de la réaction et du taux de mutation. Le domaine de validité que nous établissons contient en particulier les valeurs des taux de mutation observés couramment.

Keywords

Réaction PCRmutations ADNprocessus de branchementapproximation de champ moyenmarche au hasard avec branchement

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 92D20: Protein sequences, DNA sequences
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 391 - 403
Copyright
Copyright © Applied Probability Trust 2001 

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References

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