TY - JOUR

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

AU - Chigansky, Pavel

AU - Jagers, Peter

AU - Klebaner, Fima C.

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2018/2/1

Y1 - 2018/2/1

N2 - 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 Jagers and Klebaner (J Theor Biol 224(3):299–304, 2003. doi:10.1016/S0022-5193(03)00166-8), and based on Michaelis–Menten type enzyme kinetical considerations from Schnell and Mendoza (J Theor Biol 184(4):433–440, 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 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.

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 Jagers and Klebaner (J Theor Biol 224(3):299–304, 2003. doi:10.1016/S0022-5193(03)00166-8), and based on Michaelis–Menten type enzyme kinetical considerations from Schnell and Mendoza (J Theor Biol 184(4):433–440, 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 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.

KW - Branching processes

KW - Initial number

KW - Michaelis–Menten

KW - PCR

KW - Population dynamics

KW - Population size dependence

UR - http://www.scopus.com/inward/record.url?scp=85021726394&partnerID=8YFLogxK

U2 - 10.1007/s00285-017-1154-1

DO - 10.1007/s00285-017-1154-1

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C2 - 28667372

AN - SCOPUS:85021726394

SN - 0303-6812

VL - 76

SP - 679

EP - 695

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

IS - 3

ER -