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A Bayesian Approach to the Quantitative Polymerase Chain Reaction

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Mathematical Modeling of Biological Systems, Volume II

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Summary

The quantitative polymerase chain reaction aims at determining the initial amount X0 of a specific portion of DNA molecules from the observation of the amplification process of the DNA molecules’ quantity. This amplification process is achieved through successive replication cycles. It depends on the efficiency {pnn} of the replication of the molecules, pn being the probability that a molecule will duplicate at replication cycle n. Modelling the amplification process by a branching process and assuming pn = p for all n, we estimate the unknown parameter Θ = (p, X0) using Markov chain Monte Carlo methods under a Bayesian framework.

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Author information

Authors and Affiliations

  1. EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

    Nadia Lalam

  2. INRA, Unit of Applied Mathematics and Informatics, 78352 Jouy-en-Josas Cedex, France

    Christine Jacob

Authors
  1. Nadia Lalam
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  2. Christine Jacob
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Editor information

Editors and Affiliations

  1. Center for Information Services and High Performance Computing, Technische Universität Dresden, 01062 Dresden, Germany

    Andreas Deutsch

  2. Departamento de Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain

    Rafael Bravo de la Parra

  3. Department of Theoretical Biology, Utrecht University, Padualaan 8, 3584 CD Utrecht, The Netherlands

    Rob J. de Boer

  4. Mathematisch Instituut, Utrecht University, Budapestlaan 6, 3584 CH Utrecht, The Netherlands

    Odo Diekmann

  5. Mathematical Sciences, Chalmers University of Technology, Göteborg University, 412 96 Göteborg, Sweden

    Peter Jagers

  6. Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2b, 00014 Helsinki, Finland

    Eva Kisdi

  7. Fakultät für Gesundheitswissenschaften, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld, Germany

    Mirjam Kretzschmar

  8. Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague 4, Czech Republic

    Petr Lansky

  9. Section Theoretical Evolutionary Biology, Institute of Evolutionary and Ecological Sciences, Rijksuniversiteit Leiden, Kaiserstraat 63, 2311 GP Leiden, The Netherlands

    Hans Metz

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© 2008 Birkhäuser Boston

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Lalam, N., Jacob, C. (2008). A Bayesian Approach to the Quantitative Polymerase Chain Reaction. In: Deutsch, A., et al. Mathematical Modeling of Biological Systems, Volume II. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4556-4_27

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