Dynamics and Control of DNA Sequence Amplification

TL;DR

This paper develops a control-theoretic framework for optimizing DNA amplification processes like PCR, providing a systematic way to determine the best temperature cycling strategies for maximizing amplification efficiency.

Contribution

It introduces a biophysical control system model for DNA amplification and formulates the problem of optimal temperature cycling as a control optimization task, which is novel compared to traditional heuristic methods.

Findings

Existence of an optimal temperature cycling strategy for DNA amplification.

Formulation of control problems to derive optimal temperature profiles.

Potential to design new DNA amplification protocols using control theory.

Abstract

DNA amplification is the process of replication of a specified DNA sequence \emph{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.