A General Probabilistic Model of the PCR Process


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Department of Computer Science, Virginia Polytechnic Institute & State University


This paper rigorously derives a general probabilistic model for the PCR process; this model includes as a special case the Velikanov-Kapral model where all nucleotide reaction rates are the same. In this model the probability of binding of deoxy-nucleoside triphosphate (dNTP) molecules with template strands is derived from the microscopic chemical kinetics. A recursive solution for the probability distribution of binding of dNTPs is developed for a single cycle and is used to calculate expected yield for a multicycle PCR. The model is able to reproduce important features of the PCR amplification process quantitatively. With a set of favorable reaction conditions, the amplification of the target sequence is fast enough to rapidly outnumber all side products. Furthemore, the final yield of the target sequence in a multicycle PCR run always approaches an asymptotic limit that is less than one. The amplification process itself is highly sensitive to initial concentrations and the reaction rates of addition to the template strand of each type of dNTP in the solution.