The Mathematical Modeling and Computational Simulation for Error-Prone PCR

Modeling For Error-Prone Pcr

The top priority of mutagenic PCR is to introduce various types of mutations in an unbiased form rather than to achieve a high overall level of amplification (Cadwell & Joyce, 1994). As in the regular PCR, the first step is the denaturing which the double-stranded DNA is separated into two single strands by heating; the second step is the annealing which is the primer binds to the complementary single-strand DNA; the third step is extension which the template sequence is extended by DNA polymerase. As non-complementary nucleotides can bind to the extended-chain, mutation occurs in the third step (Gregory & Costas, 2000). The error rate of Taq polymerase is the highest of the known thermostable DNA polymerases, in the range of 0.1×10^-4 to 2×10^-4 per nucleotide per pass of the polymerase, and depending on reaction conditions (Leung et al., 1989). It is important to control these highly variable copying errors for obtaining “useful” mutations and excluding “useless” mutations (Gregory & Costas, 2000). Simulation technique has become extremely important in almost every aspect of scientific and engineering endeavor(Neim, 1995). Simulation is experimentation with models(Korn & Wait, 1978).Therefore, we introduce computational method model into error-prone PCR and make a conclusion about mathematic law of error-prone PCR, then it can play a guiding role in the analysis.

In the proposed model, mutations will occur during the extending process and every mutation can be considered as a contrary event to the others. Let ω represent different mutation rates and a single mutation rate M_ij stands for the mutative probability from nucleotide i to nucleotide j.

These values depend on the experimental conditions. ω can be used to describe mutation rate ωⁿ after n extension steps. When n=0, =0 (but if i=j,=1); when n=1, = M_ij; when n ≥ 1, (Gregory & Costas, 2000).