The University of Montana
Department of Mathematical Sciences

Technical report #10/2009

A Multi-Stage Model for Quantitative PCR

Emily Stone
The University of Montana

John Goldes
The University of Montana

Martha Garlick
Utah State University

Abstract

PCR (Polymerase Chain Reaction), a method which replicates a selected sequence of DNA, has revolutionized the study of genomic material, but mathematical study of the process has been limited to simple deterministic models or descriptions relying on stochastic processes. In this paper we develop a deterministic model for the reactions of quantitative PCR (Polymerase Chain Reaction) based on the law of mass action. Maps are created from DNA copy number in one cycle to the next, with ordinary differential equations describing the evolution of different molecular species during each cycle. The advantage of this type of model is the ability to vary the time spent in each stage of the reaction, which is critical to predicting optimal protocols. Qualitative analysis of the models are performed and parameters are estimated by fitting each model to data from Roche LightCycler (TM) runs.

Keywords: polymerase chain reaction, mathematical model

AMS Subject Classification: 92C45, 92C50, 92D20

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