Mathematical Modeling of PCR with Variable Concentrations of DNA and Taq Polymerase

Polymerase Chain Reaction (PCR) is one of the important techniques in molecular biology for many diagnostics and research applications. In this current theoretical PCR optimization research, out of its seven recipe reagents, two of the important constituents e.g., DNA which might be very rare in forensic cases and polymerase enzyme due to its high cost were mathematically modeled and computationally simulated using MATLAB programming platform. Chemical equations of PCR stages were established using the law of mass action followed by differential equations derivations from each of the DNA amplification phases. Firstly, a mathematical model of Taq polymerase enzyme with its variable concentrations ranging from 0.05-0.35 IU/L was formulated which showed the best PCR product of 0.61 ng/L obtained with 0.2 IU/L of polymerase. Similarly, by fixing the optimal polymerase concentration obtained in the previous simulation, the prime-DNA variable concentrations ranging from 0.5-3.5 ng/L were further simulated which showed the best PCR product of 0.94 ng/L at 2.0 ng/L of DNA. PCR wet-lab experimentation and gel-electrophoresis visualization validated mathematically simulated optimized concentrations of the aforementioned two reagents which vary the PCR product considerably. Current findings indicate that mathematically optimized concentrations of Taq-polymerase and template-DNA may reduce the PCR cost, time and energy, but other factors of target-sequence specificity, purity/concentrations of the other reagents, working hygiene, technical intricacies, biosafety and biosecurity factors may also contribute the desired yield of the amplicon.