# Physical Simulation-Based Calibration for Quantitative Real-Time PCR
## 1 Introduction  
Fluorescence quantitative PCR (qPCR) instruments are utilized for various nucleic acid detection and gene analysis characterized by the polymerase chain reaction (PCR) technique, aimed at detecting DNA/RNA with extensive applications in clinical diagnostics [1, 2, 3], animal quarantine [4], forensic identification [5], adulteration identification and species identification [6, 7, 8], in vitro diagnostics [9], and pharmaceutical research and development [10]. Particularly, amidst the global outbreak of the COVID-19 pandemic, qPCR method has emerged as the gold standard [11] for nucleic acid detection, leading to a larger-scale deployment of qPCR instruments in the field of molecular biology. Furthermore, qPCR instruments are also employed in environmental monitoring, such as pathogen monitoring in wastewater [12]. With the extensive applications of qPCR instruments, its users were a comprehensive performance evaluation of the qPCR. In such evaluation, factors impacting the accuracy of the qPCR instruments results pose a significant challenge to the calibration. In comparison to qualitative PCR instruments, the factors of qPCR instruments are more intricate. Key factors include the type of chemical reagents, temperature factors of the temperature module and lid, specification of the filters, reflectors and optical path channels, sensitivity of the fluorescence receiver, mechanical components, and threshold settings in software such as baseline and S/N ratio, etc. These factors pose significant challenges for the calibration of qPCR instruments. Quality control and regular calibration of qPCR instruments are crucial, as they directly impact quantitative results including Ct values, precision, detection limit, and specificity [13]. Two main reasons for influencing the accuracy and repeatability of qPCR instrument results are edge effects and experimental errors. Edge effects are caused by defects in the optical detection system design and the temperature control module, also known as sample tray (Block). Such defects can lead to differences in the optical path lengths between edge wells and central wells of qPCR instrument Block resulting in variations in the excitation light energy received by fluorescent groups in different wells, and ultimately affecting the reliability of experimental results, namely Ct values. Similarly, temperature differences between wells within the Block can also lead to such edge effects with even small optical or temperature differences between wells may be exponentially amplified during the amplification process, ultimately affecting experimental results [14; 15]. The structural design of the optical detection system in qPCR instruments can also impact the stability and detection limit of detection [16]. Additionally, defects in the optical path design and differences in inter-well temperatures directly affect the results of melting curve analysis, leading to significant variations in resolution among different instruments. This influence can result in an inability to successfully differentiate mutant genes or misidentification of mutant genes when detecting mutations or performing single nucleotide polymorphism analysis using melting curve analysis. Regular calibration of qPCR instruments helps ensure the reliability and accuracy of the equipment, providing support for traceability and quality control. In the detection of respiratory pathogens, the Ct value of qPCR reactions is widely used as an epidemiological and clinical indicator [17; 18]. The Ct value is negatively correlated with the initial viral load, allowing for indirect quantification of the starting virus copy number [19; 20]. Typically, due to variations in reported Ct values from different PCR methods, it is necessary to use a standard curve for accurate quantification of expected virus copy number [21].