Mathematics Commons^™

Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …