Random variation and concentration effects in PCR
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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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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