What can be observed in real time PCR and when does it show?

TL;DR

This paper investigates when and how the initial number of DNA molecules in real-time PCR can be determined, revealing that it is possible when the initial replication rate is one, but uncertain otherwise, using a generalized branching process model.

Contribution

It introduces a generalized branching process model incorporating enzyme kinetics to analyze the observability of initial DNA copy numbers in PCR experiments.

Findings

Initial copy number determinable when initial rate v=1

Uncertainty in initial number when v<1

Model based on Michaelis-Menten enzyme kinetics

Abstract

Real time, or quantitative, PCR typically starts from a very low concentration of initial DNA strands. During iterations the numbers increase, first essentially by doubling, later predominantly in a linear way. Observation of the number of DNA molecules in the experiment becomes possible only when it is substantially larger than initial numbers, and then possibly affected by the randomness in individual replication. Can the initial copy number still be determined? This is a classical problem and, indeed, a concrete special case of the general problem of determining the number of ancestors, mutants or invaders, of a population observed only later. We approach it through a generalised version of the branching process model introduced by Jagers and Klebaner, 2003 and based on Michaelis-Menten type enzyme kinetical considerations from Schnell and Mendoza, 1997. A crucial role is played by the Michaelis-Menten constant being large, as compared to initial copy numbers. In a strange way, determination of the initial number turns out to be completely possible if the initial rate $v$ is one, i.e all DNA strands replicate, but only partly so when $v<1$, and thus the initial rate or probability of successful replication is lower than one. Then, the starting molecule number becomes hidden behind a "veil of uncertainty". This is a special case, of a hitherto unobserved general phenomenon in population growth processes, which will be addressed elsewhere.