A theoretical framework for prediction of the dynamic evolution of chemical species in DNA amplification reactions, for any specified sequence and operating conditions, is reported. Using the polymerase chain reaction (PCR) as an example, we developed a sequence- and temperature-dependent kinetic model for DNA amplification using first-principles biophysical modeling of DNA hybridization and polymerization. We compare this kinetic model with prior PCR models and discuss the features of our model that are essential for quantitative prediction of DNA amplification efficiency for arbitrary sequences and operating conditions. Using this model, the kinetics of PCR is analyzed. The ability of the model to distinguish between the dynamic evolution of distinct DNA sequences in DNA amplification reactions is demonstrated. The kinetic model is solved for a typical PCR temperature protocol to motivate the need for optimization of the dynamic operating conditions of DNA amplification reactions. It is shown that amplification efficiency is affected by dynamic processes that are not accurately represented in the simplified models of DNA amplification that form the basis of conventional temperature cycling protocols. Based on this analysis, a modified temperature protocol that improves 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.
A theoretical approach to the prediction of the sequence and temperature-dependent rate constants for oligonucleotide hybridization reactions has been developed based on the theory of relaxation kinetics. One-sided and two-sided melting reaction mechanisms for oligonucleotide hybridization reactions have been considered, analyzed, modified, and compared to select a physically consistent as well as robust model for prediction of the relaxation times of DNA hybridization reactions that agrees with the experimental evidence. The temperature- and sequence-dependent parameters of the proposed model have been estimated using available experimental data. The relaxation time model that we developed has been combined with the nearest neighbor model of hybridization thermodynamics to estimate the temperature- and sequence-dependent rate constants of an oligonucleotide hybridization reaction. The model-predicted rate constants are compared to experimentally determined rate constants for the same oligonucleotide hybridization reactions. Finally, we consider a few important applications of kinetically controlled DNA hybridization reactions.
DNA amplification is the process of replication of a specified DNA sequence in vitro through time-dependent manipulation of its external environment. A theoretical framework for determination of the optimal dynamic operating conditions of DNA amplification reactions, for any specified amplification objective, is presented based on first-principles biophysical modeling and control theory. Amplification of DNA is formulated as a problem in control theory with optimal solutions that can differ considerably from strategies typically used in practice. Using the Polymerase Chain Reaction (PCR) as an example, sequence-dependent biophysical models for DNA amplification are cast as control systems, wherein the dynamics of the reaction are controlled by a manipulated input variable. 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 profile. 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.
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