Random variation and concentration effects in PCR.

Even though the efficiency of the polymerase chain reaction (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 reproduction number 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).

[1]  L Raeymaekers,et al.  Basic principles of quantitative PCR , 2000, Molecular biotechnology.

[2]  J. Peccoud,et al.  Estimation of the parameters of a branching process from migrating binomial observations , 1998, Advances in Applied Probability.

[3]  Consistency and fluctuation theorems for discrete time structured population models having demographic stochasticity , 2000, Journal of mathematical biology.

[4]  J. Peccoud,et al.  Inference on the initial size of a supercritical branching process from migrating binomial observations , 1996 .

[5]  A. von Haeseler,et al.  A coalescent approach to the polymerase chain reaction. , 1997, Nucleic acids research.

[6]  F. Klebaner.  Population-dependent branching processes with a threshold , 1993 .

[7]  Fengzhu Sun,et al.  The Polymerase Chain Reaction and Branching Processes , 1995, J. Comput. Biol..

[8]  Henry A. Erlich,et al.  Enzymatic amplification of ?-globin genomic sequences and restriction site analysis for diagnosis of , 1985 .

[9]  Michel Loève,et al.  Probability Theory I , 1977 .

[10]  F. Klebaner.  On population-size-dependent branching processes , 1984, Advances in Applied Probability.

[11]  K. Mullis,et al.  Primer-directed enzymatic amplification of DNA with a thermostable DNA polymerase. , 1988, Science.

[12]  J. Peccoud,et al.  Theoretical uncertainty of measurements using quantitative polymerase chain reaction. , 1996, Biophysical journal.

[13]  K. Mullis,et al.  Enzymatic amplification of beta-globin genomic sequences and restriction site analysis for diagnosis of sickle cell anemia. , 1985, Science.

[14]  Patrick J. Heagerty,et al.  Quantitative PCR: Procedures and precisions , 1992 .

[15]  J. Peccoud,et al.  Statistical Estimations of PCR Amplification Rates , 1998 .

[16]  P. Holgate,et al.  Branching Processes with Biological Applications , 1977 .

[17]  S. Schnell,et al.  Theoretical description of the polymerase chain reaction. , 1997, Journal of theoretical biology.

[18]  S. Schnell,et al.  Enzymological considerations for a theoretical description of the quantitative competitive polymerase chain reaction (QC-PCR). , 1997, Journal of theoretical biology.

[19]  J. Reiss,et al.  Polymerase chain reaction: replication errors and reliability of gene diagnosis. , 1989, Nucleic acids research.

[20]  Fima C. Klebaner.  Population and Density Dependent Branching Processes , 1997 .

[21]  C. Shaw,et al.  Exact sampling formulas for multi-type Galton-Watson processes , 2002, Journal of mathematical biology.