Expected behavior system of ODEs.

We present a model for the noise and inherent stochasticity of fluorescence signals in both continuous wave (CW) and time-gated (TG) conditions. When the fluorophores are subjected to an arbitrary excitation photon flux, we apply the model and compute the evolution of the probability mass function (pmf) for each quantum state comprising a fluorophore’s electronic structure, and hence the dynamics of the resulting emission photon flux. Both the ensemble and stochastic models presented in this work have been verified using Monte Carlo molecular dynamic simulations that utilize the Gillespie algorithm. The implications of the model on the design of biomolecular fluorescence detection systems are explored in three relevant numerical examples. For a given system, the quantum-limited signal-to-noise ratio (QSNR) and limits of detection are computed to demonstrate how key design tradeoffs are quantified. We find that as systems scale down to micro- and nano- dimensions, the interplay between the fluorophore’s photophysical qualities and use of CW or TG has ramifications on optimal design strategies when considering optical component selection, measurement speed, and system energy requirements. While CW systems remain a gold standard, TG systems can be leveraged to overcome cost and system complexity hurdles when paired with the appropriate fluorophore.

本研究提出了一种适用于连续波（continuous wave, CW）与时间门控（time-gated, TG）条件下荧光信号噪声及固有随机性的建模方法。当荧光团受到任意激发光子通量作用时，借助该模型可计算包含荧光团电子结构的各量子态的概率质量函数（probability mass function, pmf）的演化过程，进而推导出对应发射光子通量的动力学特性。本文提出的系综模型与随机模型均通过采用吉莱斯皮（Gillespie）算法的蒙特卡洛分子动力学模拟完成了验证。本模型对生物分子荧光检测系统设计的指导价值，通过三个相关数值算例进行了探讨。针对特定系统，通过计算其量子极限信噪比（quantum-limited signal-to-noise ratio, QSNR）与检测限，可量化分析关键设计权衡关系。研究发现，当系统尺寸缩减至微米与纳米级别时，若需综合考量光学元件选型、测量速度与系统能量需求，荧光团的光物理特性与CW或TG激发模式的协同作用会对最优设计策略产生影响。尽管CW系统仍是当前的金标准，但搭配适配的荧光团时，TG系统可用于克服成本与系统复杂度方面的障碍。