Date of Award
Master of Science (MS)
Mathematics and Statistics
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 and annealing stages may significantly reduce the total time for a PCR run.
Garlick, Martha J., "Mathematically Modeling PCR: An Asymptotic Approximation with Potential for Optimization" (2007). All Graduate Plan B and other Reports. 1286.