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**Harvard**

Jagers, P., Klebaner, F. och Chigansky, P. (2017) *What can be observed in real time PCR and when does it show?*.

** BibTeX **

@article{

Jagers2017,

author={Jagers, Peter and Klebaner, Fima C. and Chigansky, Pavel},

title={What can be observed in real time PCR and when does it show?},

journal={Journal of Mathematical Biology},

issn={0303-6812},

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 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.},

year={2017},

keywords={Population dynamics · PCR · initial number · Michaelis-Menten · branching processes · population size dependence },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 250300

A1 Jagers, Peter

A1 Klebaner, Fima C.

A1 Chigansky, Pavel

T1 What can be observed in real time PCR and when does it show?

YR 2017

JF Journal of Mathematical Biology

SN 0303-6812

AB 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.

LA eng

DO 10.1007/s00285-017-1154-1

LK http://publications.lib.chalmers.se/records/fulltext/250300/local_250300.pdf

LK http://dx.doi.org/10.1007/s00285-017-1154-1

OL 30