The Mathematical Modeling and Computational Simulation for Error-Prone PCR

The Mathematical Modeling and Computational Simulation for Error-Prone PCR

Lixin Luo (South China University of Technology, China), Fang Zhu (South China Universityof Technology, China) and Si Deng (South China University of Technology, China)
Copyright: © 2013 |Pages: 7
DOI: 10.4018/978-1-4666-3604-0.ch042
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Abstract

Many enzymes have been widely used in industrial production, for they have higher catalytic efficiency and catalytic specificity than the traditional catalysts. Therefore, the performance of enzymes has attracted wide attention. However, due to various factors, enzymes often cannot show their greatest catalytic efficiency and the strongest catalytic ability in industrial production. In order to improve the enzyme activity and specificity, people become increasingly interested in the transformation and modification of existing enzymes. For the structure modification of proteinase, this chapter introduces a computational method for modelling error-prone PCR. Error-prone PCR is a DNA replication process that intentionally introduces copying errors by imposing mutagenic reaction condition. We then conclude about the mathematical principle of error-prone PCR which may be applied to the quantitative analysis of directed evolution in future studies.
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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 Mij stands for the mutative probability from nucleotide i to nucleotide j.

(1)

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, = Mij; when n ≥ 1, (Gregory & Costas, 2000).

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