What can be observed in real time PCR and when does it show?
Artikel i vetenskaplig tidskrift, 2017

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 in [11], and based on Michaelis-Menten type enzyme kinetical considerations from [22]. 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 succesful 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 adressed elsewhere.

Population dynamics · PCR · initial number · Michaelis-Menten · branching processes · population size dependence


Peter Jagers

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Fima C. Klebaner

Pavel Chigansky

Journal of Mathematical Biology

0303-6812 (ISSN) 1432-1416 (eISSN)



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