Simulation of convective polymerase chain reaction based on multiphase Lagrangian particle tracking model

Abstract

The article considers the issues of modeling the convective polymerase chain reaction (PCR) under the assumption that the solution of DNA molecules is a dispersed medium. The Lagrangian model of multiphase flows serves as a basis for simulations. In the framework of this approach, we consider the liquid phase to be continuous, applying the Navier-Stokes equations to describe its dynamics. To model the dispersed phase, we integrate the equation of motion of individual particles (DNA molecules) along their trajectories. Since the volume fraction of DNA molecules during the PCR reaction is small enough, the interphase interaction is assumed to be one-sided: molecular phases do not affect the motion and heat exchange of the solvent. Therefore, the general problem is split into two subproblems: the hydrodynamic part and the transport-reaction problem for particles. The mathematical model incorporates the Navier-Stokes equations written in the Hele-Shaw approximation, the motion equations for DNA molecules, and the specific condition for the PCR reactions. To model the reaction, we develop an original technique in which the history of particle movement through the reaction zone determines the criterion for transformation of a particle from one type to another. A numerical simulation of the convective PCR in a Hele-Shaw cell was carried out. The distribution fields of DNA molecules and the hydrodynamic and thermal fields were obtained. Zones with ongoing reactions were visualized. The dependence of the number of DNA molecules on the reaction time and the doubling time of the number of molecules were established. The results are consistent with the data of other convective PCR models. The positive aspects of the model used are that it provides complete information about the behavior of individual particles, including their coordinates, velocities, residence times in reaction zones, and traveled distances. Additionally, the developed approach can be used to ensure fine-tuning of the reaction kinetics. Due to this, the scope of applicability of the model and the range of related problems can be expanded.