#### Date of Award

5-2014

#### Embargo Period

9-11-2014

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Chemical Engineering

#### Advisor(s)

Raj Chakrabarti

#### Abstract

DNA amplification or the Polymerase Chain Reactions (PCR) is the workhorse of nearly every modern molecular biology laboratory, as well as the burgeoning discipline of personalized medicine. Despite the apparent simplicity of the PCR reaction, the method is often fraught with difficulties that can decrease the cycle efficiency or result in competitive amplification of undesired side products. The focus of this work is to derive an optimal reaction condition for a given PCR using the engineering discipline of control theory that can automatically derive prescriptions for the optimal temperature cycling protocols of a PCR reaction, if a suitable kinetic model exists. We first developed a theoretical model to estimate the sequence and temperature dependent rate parameters of a oligonucleotide hybridization or annealing reaction. Rate constants that were estimated using our model is in good agreement with the experimentally estimated rate constants of the same oligonucleotide hybridization reaction. Using the theory of enzyme processivity the kinetic parameters of enzyme binding and extension reactions were estimated experimentally. Thus, a first sequence-dependent biophysical model for DNA amplification has been developed. It is shown that amplification efficiency is affected by dynamic processes that are not accurately represented in simplified models of DNA amplification that are the basis of conventional temperature cycling protocols. Based on this analysis; a modified temperature protocol that improves the PCR efficiency is suggested. Use of this sequence- dependent kinetic model in a control theoretic framework to determine the optimal dynamic operating conditions of DNA amplification reactions, for any specified amplification objective, is discussed. Using these control systems, we demonstrate that there exists an optimal temperature cycling strategy for geometric amplification of any DNA sequence and formulate optimal control problems that can be used to derive the optimal temperature control. Strategies for the optimal synthesis of the DNA amplification control trajectory are proposed. Analogous methods can be used to formulate control problems for more advanced amplification objectives corresponding to the design of new types of DNA amplification reactions. Finally, a PCR optimal control problem is solved and an optimal temperature control that maximizes the desired DNA concentration as well as minimizes the total reaction is obtained.

#### Recommended Citation

Marimuthu, Karthikeyan, "Biophysical Modeling and Optimal Control of DNA Amplification" (2014). *Dissertations*. 355.

http://repository.cmu.edu/dissertations/355