Applied and Computational Mathematics Division, National Institute of Standards and Technology, 100 Bureau Dr., MS 8910, Gaithersburg, MD, 20899-8910, USA.
Department of Chemistry and Biochemistry, University of Maryland, 8051 Regents Dr., College Park, MD, 20742-4454, USA.
Bull Math Biol. 2023 Aug 14;85(9):83. doi: 10.1007/s11538-023-01182-z.
We present a new approach for relating nucleic-acid content to fluorescence in a real-time Polymerase Chain Reaction (PCR) assay. By coupling a two-type branching process for PCR with a fluorescence analog of Beer's Law, the approach reduces bias and quantifies uncertainty in fluorescence. As the two-type branching process distinguishes between complementary strands of DNA, it allows for a stoichiometric description of reactions between fluorescent probes and DNA and can capture the initial conditions encountered in assays targeting RNA. Analysis of the expected copy-number identifies additional dynamics that occur at short times (or, equivalently, low cycle numbers), while investigation of the variance reveals the contributions from liquid volume transfer, imperfect amplification, and strand-specific amplification (i.e., if one strand is synthesized more efficiently than its complement). Linking the branching process to fluorescence by the Beer's Law analog allows for an a priori description of background fluorescence. It also enables uncertainty quantification (UQ) in fluorescence which, in turn, leads to analytical relationships between amplification efficiency (probability) and limit of detection. This work sets the stage for UQ-PCR, where both the input copy-number and its uncertainty are quantified from fluorescence kinetics.
我们提出了一种新的方法，用于将核酸含量与实时聚合酶链反应（PCR）测定中的荧光相关联。通过将 PCR 的两种分支过程与 Beer 定律的荧光类似物相结合，该方法减少了荧光的偏差并量化了不确定性。由于两种分支过程区分了 DNA 的互补链，因此它允许对荧光探针与 DNA 之间的反应进行化学计量描述，并可以捕获针对 RNA 的测定中遇到的初始条件。对预期拷贝数的分析确定了在短时间内（或者，等效地，在低循环数下）发生的附加动力学，而方差的研究揭示了来自液体体积转移、不完全扩增和链特异性扩增（即，如果一条链比其互补链更有效地合成）的贡献。通过 Beer 定律类似物将分支过程与荧光联系起来，可以对背景荧光进行先验描述。它还能够对荧光进行不确定性量化（UQ），这反过来又导致了扩增效率（概率）和检测限之间的分析关系。这项工作为 UQ-PCR 奠定了基础，其中从荧光动力学中定量输入的拷贝数及其不确定性。
