Journal of Mathematical Biology

, Volume 78, Issue 3, pp 767–776 | Cite as

A minimally parametrized branching process explaining plateau phase of qPCR amplification

  • Qingyang LuoEmail author


Quantitative polymerase chain reaction (qPCR) is a commonly used molecular biology technique for measuring the concentration of a target nucleic acid sequence in a sample. The whole qPCR amplification process usually consists of an exponential, a linear and a plateau phase. In qPCR experiments, amplification curves of samples with different template concentrations often, even though not always, have the same plateau height. The biological theory for this phenomenon is that the plateau height is determined by reaction kinetics. Does it mean that the target concentration has no effect on the final plateau height? We proposed a branching process based on Michaelis–Menten kinetics. Our model can describe all phases of qPCR amplification despite its simplicity (it depends on only one parameter). We theoretically showed, through almost sure convergence, that amplification curves will eventually plateau at finite values in any experiment, under any condition. We conclude that the plateau height is largely determined by reaction kinetics but could also be affected by the template concentration. This is in accordance with the current biological theory.


Branching process Michaelis–Menten kinetics Quantitative polymerase chain reaction Plateau phase 

Mathematics Subject Classification

60G42 92C45 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTulane UniversityNew OrleansUSA

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