Luo Qingyang
Department of Mathematics, Tulane University, New Orleans, USA.
J Math Biol. 2019 Feb;78(3):767-776. doi: 10.1007/s00285-018-1291-1. Epub 2018 Aug 27.
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.
定量聚合酶链反应（qPCR）是一种常用的分子生物学技术，用于测量样品中目标核酸序列的浓度。整个qPCR扩增过程通常包括指数期、线性期和平台期。在qPCR实验中，不同模板浓度的样品的扩增曲线常常（尽管并非总是如此）具有相同的平台高度。这种现象的生物学理论是平台高度由反应动力学决定。这是否意味着目标浓度对最终的平台高度没有影响？我们基于米氏动力学提出了一个分支过程。我们的模型尽管简单（仅依赖于一个参数），却能描述qPCR扩增的所有阶段。我们通过几乎必然收敛从理论上表明，在任何实验、任何条件下，扩增曲线最终都会在有限值处达到平台期。我们得出结论，平台高度在很大程度上由反应动力学决定，但也可能受到模板浓度的影响。这与当前的生物学理论相符。
