First-passage time analysis of diffusion-controlled reactions in single-molecule detection

Single-molecule detection (SMD) aims to achieve the ultimate limit-of-detection (LOD) in biosensing. This method detects a countable number of targeted analyte molecules in solution, where the dynamics of molecule diffusion, capturing, identification and delivery greatly impact the SMD's efficiency and accuracy. In this study, we adopt the first-passage time method to investigate the diffusion-controlled reaction process in SMD. We analyze the influence of detection conditions on incubation time and the expected coefficient of variation (CV) under three SMD molecule capturing strategies, including solid-phase capturing (one-dimensional solid-liquid interface fixation), liquid-phase magnetic bead (MB) capturing, and liquid-phase direct fluorescence pair labeling. We find that inside a finite-sized reaction chamber, a finite average reaction time exists in all three capturing strategies, while the liquid-phase strategies are in general more efficient than the solid-phase approaches. CV can be estimated by averaging first-passage time solely in all three strategies, and the CV reduction is achievable given an extended reaction time. To further enable zeptomolar detection, extra treatments, such as adopting liquid-phase fluorescence pairs with high diffusion rates to label the molecule, or designing specific sensing devices with large effective sensing areas would be required. This framework provides solid theoretical support to guide the design of SMD sensing strategies and sensor structures to achieve desired measurement time and CV. • The diffusion-controlled process in single molecule detection is investigated by first-passage time method. • 1 D and 3D capturing strategies are analyzed. • The coefficient of variation is calculated and reduction strategy is given from simulation. • Zeptomolar detection is achievable by fluorescence pairs labeling and well-designed sensing structures.