Digital PCR Modeling for Maximal Sensitivity, Dynamic Range and Measurement Precision

The great promise of digital PCR is the potential for unparalleled precision enabling accurate measurements for genetic quantification. A challenge associated with digital PCR experiments, when testing unknown samples, is to perform experiments at dilutions allowing the detection of one or more targets of interest at a desired level of precision. While theory states that optimal precision (Po) is achieved by targeting ~1.59 mean copies per partition (λ), and that dynamic range (R) includes the space spanning one positive (λL) to one negative (λU) result from the total number of partitions (n), these results are tempered for the practitioner seeking to construct digital PCR experiments in the laboratory. A mathematical framework is presented elucidating the relationships between precision, dynamic range, number of partitions, interrogated volume, and sensitivity in digital PCR. The impact that false reaction calls and volumetric variation have on sensitivity and precision is next considered. The resultant effects on sensitivity and precision are established via Monte Carlo simulations reflecting the real-world likelihood of encountering such scenarios in the laboratory. The simulations provide insight to the practitioner on how to adapt experimental loading concentrations to counteract any one of these conditions. The framework is augmented with a method of extending the dynamic range of digital PCR, with and without increasing n, via the use of dilutions. An example experiment demonstrating the capabilities of the framework is presented enabling detection across 3.33 logs of starting copy concentration.数字PCR（digital PCR）的巨大应用前景在于其具备无与伦比的精准度，可实现遗传定量的高精度测量。在对未知样本开展检测时，数字PCR实验面临的一项核心挑战是：需通过合理稀释配置实验体系，以在预期的精准度水平下检出一个或多个目标靶标。理论研究表明，当每个分区（partition）的平均拷贝数（λ）约为1.59时，可达到最优精准度（Po）；而动态范围（R）的覆盖区间为总分区数（n）下，从仅出现单阳性结果（λL）到仅出现单阴性结果（λU）的范围，但实验室中搭建数字PCR实验的科研人员需对这些理论结论进行适配调整。本文提出一套数学框架，用于阐明数字PCR系统中精准度、动态范围、分区数、检测体积与灵敏度之间的内在关联。随后，本文进一步探讨了假反应判定与体积偏差对灵敏度和精准度的影响。通过蒙特卡洛模拟（Monte Carlo simulations）复现实验室场景中此类情况的真实发生概率，明确了上述因素对灵敏度与精准度的综合作用效果。该模拟结果可为实验人员提供参考，指导其调整实验上样浓度以抵消任一因素带来的负面影响。本框架还补充了一种拓展数字PCR动态范围的方法：通过调整稀释梯度，可在增加或不增加总分区数（n）的前提下实现动态范围的拓展。最后，本文展示了一个验证该框架实用性的实验案例，可实现起始拷贝浓度跨3.33个对数级区间的检测。