Unsupervised Machine Learning Methods for Determining Special Points of the Polymerase Chain Reaction Fluorescence Accumulation Curve

The polymerase chain reaction (PCR) method is a cyclic process based on the repeated copying of a certain fragment of DNA using enzymes in vitro. The main molecular mechanism of PCR is amplification, that is, the accumulation of copies of the selected nucleotide sequence. A real-time polymerase chain reaction, which is one of the varieties of the PCR method, allows determining not only the presence of the target nucleotide sequence in the sample, but also measuring the number of its copies. The efficiency of a real-time polymerase chain reaction is characterized by the exponential section of the fluorescence accumulation curve (PCR kinetic curve). This curve consists of a baseline, an exponential phase and a plateau phase. Of both theoretical and practical interest is the analytical determination of the moments of the transition of the PCR kinetic curve from linear to exponential growth, and then reaching a plateau. Unsupervised machine learning methods can be used to solve this problem. If we consider amplification as a quasi-deterministic discrete random process, for which the fluorescence accumulation curves are monotonically increasing trajectories, then the moments of the transition from the baseline to the exponential phase and from the exponential phase to the plateau phase are trajectory anomalies. Their detection is possible with the help of quadratic forms of approximation-estimation tests.