Random variation and concentration effects in PCR
Journal article, 2003
Even though the efficiency of the PCR reaction decreases, analyses are made in terms of Galton-Watson processes, or simple deterministic models with constant replication probability (efficiency).Recently Schnell and Mendoza have suggested that the form of the efficiency can be derived from enzyme kinetics. This results in the sequence
of molecules numbers forming a stochastic process with the properties of a branching process with population size
dependence, which is supercritical, but has a mean reproductionnumber that approaches one. Such processes
display ultimate linear growth, after an initial exponential
phase, as is the case in PCR. It is also shown that the resulting stochastic process for a large Michaelis Menten constant behaves like the deterministic sequence x_n
arising by iterations of the function f(x) = x+x/(1+x).