Abstract
The polymerase chain reaction is a central component of current molecular biology. It is a cyclic process, in each early cycle of which the template DNA approximately doubles. An indicator which fluoresces when bound to DNA quantifies the DNA present at the end of each cycle, giving rise to a fluorescence curve which is characteristically sigmoid in shape. The fluorescence curve quantifies the amount of DNA initially present; the more the initial DNA, the earlier the rise in the fluorescence. Accordingly the amount of DNA initially present in two samples can be compared: the sample with the less DNA gives rise to a relatively delayed fluorescence curve and the ratio of the DNAs can be deduced from the separation of the curves. There is, however, a second determinant of this separation, the fold increase in DNA per cycle: ideally a twofold increase but frequently less. Current guidelines recommend that this be determined experimentally by carrying out PCR on a series of dilutions. If the value of the fold increase is known, then the algorithm for determining the separation can be reduced to a relatively simple computation, rather than employing a multidimensional nonlinear optimization such as the Marquardt-Levenberg as currently employed.
Highlights
The polymerase chain reaction (PCR) introduced by Mullis et al [1] is a cyclic process, each cycle of which involves three stages: denaturation, annealing, and extension
As resources are depleted and as template DNA strands bind to their complement rather than to primer, the value of (1 + p) in (1) diminishes: the fluorescence curve is sigmoid rather than exponential
There is between replicates, a variation in the scale, in that the plateau level that the fluorescence approaches varies. These considerations give rise to a collection of models for the fluorescence curve seen in PCR
Summary
The polymerase chain reaction (PCR) introduced by Mullis et al [1] is a cyclic process, each cycle of which involves three stages: denaturation, annealing (to a primer, possibly to some forms of fluorescent probe), and extension. A and B which initially comprise Na and Nb strands, have the same value of the probability p and if they exhibit the same fluorescence after Ca and Cb cycles, respectively, . As resources are depleted and as template DNA strands bind to their complement rather than to primer, the value of (1 + p) in (1) diminishes: the fluorescence curve is sigmoid rather than exponential. There is a background fluorescence present initially and not indicative of DNA, and this background varies between replicates. There is between replicates, a variation in the scale, in that the plateau level that the fluorescence approaches varies These considerations give rise to a collection of models for the fluorescence curve seen in PCR. The open-source facility “qpcR” [2] offers ten nonlinear sigmoidal models (and nine others) that
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