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Modelling the PCR amplification process by a size-dependent branching process and estimation of the efficiency

Part of: Markov processes Applications Parametric inference

Published online by Cambridge University Press:  01 July 2016

N. Lalam ,
C. Jacob  and
P. Jagers
N. Lalam*
Affiliation:
Institut National de la Recherche Agronomique, Jouy-en-Josas
C. Jacob*
Affiliation:
Institut National de la Recherche Agronomique, Jouy-en-Josas
P. Jagers*
Affiliation:
Chalmers University of Technology, Göteborg
*
∗ Current address: Eurandom, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: [email protected]
∗∗ Postal address: INRA, Laboratoire de Biométrie, 78352 Jouy-en-Josas Cedex, France. Email address: [email protected]
∗∗∗ Chalmers University of Technology, S-412 96 Göteborg, Sweden. Email address: [email protected]
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Abstract

We propose a stochastic modelling of the PCR amplification process by a size-dependent branching process starting as a supercritical Bienaymé-Galton-Watson transient phase and then having a saturation near-critical size-dependent phase. This model allows us to estimate the probability of replication of a DNA molecule at each cycle of a single PCR trajectory with a very good accuracy.

Keywords

Polymerase chain reactionsize-dependent branchingkinetic modelconditional least squares

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 62F12: Asymptotic properties of estimators
Secondary: 62P10: Applications to biology and medical sciences
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 2 , June 2004 , pp. 602 - 615
Copyright
Copyright © Applied Probability Trust 2004 

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