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
0.7

duplication probability in each step of the simulated PCR. The parameter value is only taken into account if GC_MEAN is 'NaN'.

GC_MEAN
meanGC0.5NaN, 0 < meanGC < 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
SDGC 0.1 0 < SDGC < 1standard 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 , or, by a normal distribution  parameterized to capture GC preferential biases (default meanGC=0.5 and SDGC=0.1). Given p, the number of copies produced from a certain fragment is determined by random sampling under the cumulative binomial:

\[P_S(N)= \sum_{0}^{\lceil \frac{N}{2} \rceil}P_{S-1}(N-k) {N-k \choose k}  p^k (1-p)^{n-2k} \]

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}

\]