4.4.2 - PCR Amplification

Parameter

Parameter Name	Variable	Default Value	Parameter Range	Description
PCR_DISTRIBUTION		default	{default, none, file}	parameter specifies the name of a PCR distribution file, or 'default' to use a distribution with 15 rounds and 20 bins. A value of 'none' disables PCR amplification.
PCR_PROBABILITY	$\begin{array}{l}p\end{array}$	0.7	$\begin{array}{l}0< p\leq 1\end{array}$	duplication probability in each step of the simulated PCR. The parameter value is only taken into account if GC_MEAN is 'NaN'.
GC_MEAN	mean_GC	0.5	NaN, 0 < mean_GC < 1	mean of duplication probability distribuiton with respect to GC content; the distribution is approximated by a normal distribution. A value of 'NaN' disables the GC-dependency of PCR and employs the (constant) probability PCR_PROBABILITY
GC_SD	SD_GC	0.1	0 < SD_GC < 1	standard deviation of duplication probability distribuiton with respect to GC content

Algorithm

The efficiency of the polymerase chain reaction (PCR) amplification is either specified by an universal success rate $\begin{array}{l}p\end{array}$ , or, by a normal distribution $\begin{array}{l}p= f(mean_{GC},SD_{GC})\end{array}$ parameterized to capture GC preferential biases (defaultmean_GC=0.5 and SD_GC=0.1). Given p, the number of copies produced from a certain fragment is determined by random sampling under the cumulative binomial:

$\begin{array}{l}\displaystyle P_S(N)= \sum_{0}^{\lceil \frac{N}{2} \rceil}P_{S-1}(N-k) {N-k \choose k} p^k (1-p)^{n-2k}\end{array}$

with S denoting the PCR cycle and N the number of molecules. As default, we assume 15 PCR cycles (S=15), and sample randomly the number of duplicates yielded by PCR amplification under the corresponding probability distribution P₁₅(N) for all possible values of N=[1;2¹⁵]. The recursion terminates by

$\begin{array}{l} P_0=0 \\ P_1=\left\{ \begin{array}{rl} 1 &\mbox{ if $N=1$} \\ 0 &\mbox{ otherwise} \end{array} \right. \end{array}$

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