Cited by 49Stochastic processes and statistical mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsMolecular Biology Techniques and Applications

Random variation and concentration effects in PCR

Jagers, Peter, Klebaner, Fima·2003·Journal of Theoretical Biology

Abstract

Even though the efficiency of the polymerase chain reaction (PCR) reaction decreases, analyses are made in terms of Galton-Watson processes, or simple deterministic models with constant replication probability (efficiency). Recently, Schnell and Mendoza have suggested that the form of the efficiency, can be derived from enzyme kinetics. This results in the sequence of molecules numbers forming a stochastic process with the properties of a branching process with population size dependence, which is supercritical, but has a mean reproduction number that approaches one. Such processes display ultimate linear growth, after an initial exponential phase, as is the case in PCR. It is also shown that the resulting stochastic process for a large Michaelis-Menten constant behaves like the deterministic sequence x(n) arising by iterations of the function f(x)=x+x/(1+x).

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Crossref · 10.1016/s0022-5193(03)00166-8

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  • PCR is an exponential process, so small random variations early on in amplification can have a large impact on distribution.

    “PCR is an exponential process, so small random variations early on in amplification can have a large impact on distribution18–24.”

    From Quantifying Molecular Bias in DNA Data Storage (2019) · cites this paper as [18]

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Authors
Jagers, P., & Klebaner, F.
Affiliations
  • Chalmers University of Technology (SE)
  • Monash University (AU)
Corresponding author
Jagers, Peter
Venue
Journal of Theoretical Biology
Publisher
Elsevier BV
Published
2003-10
Volume
224
Issue
3
Pages
299-304
ISSN
0022-5193 (ISSN-L)
OpenAlex
W1984872787
Cited by
49
References
22
Citations by year
2025: 1 · 2024: 2 · 2023: 1 · 2022: 2 · 2020: 3 · 2019: 3 · 2018: 2 · 2017: 4 · 2015: 2 · 2013: 1 · 2012: 1
FWCI
3.40
Type
journal article
Language
en
Open access
closed
Locations
  • Journal of Theoretical Biology (publishedVersion)
  • PubMed (publishedVersion)
  • Chalmers Publication Library (Chalmers University of Technology) (submittedVersion)
  • Chalmers Research (Chalmers University of Technology) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
  • Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Molecular Biology Techniques and Applications
Keywords
PCR, PCR efficiency, stochastic modeling, branching processes, Galton-Watson process, enzyme kinetics, Michaelis-Menten kinetics, supercritical branching processes, concentration effects, random variation, deterministic approximation
MeSH terms
Sensitivity and Specificity, Genetic Variation, Models, Statistical, Polymerase Chain Reaction

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