Objective clustering protocol for single-molecule data: A lifetime vs. intensity study

TL;DR

This work tackles the problem of subjective and noisy analysis in single-molecule spectroscopy by introducing an objective, scalable clustering pipeline for 2D lifetime–intensity data. It combines a grouping step to denoise resolved intensity levels with Gaussian Mixture Modeling, selecting the number of clusters via the Bayesian Information Criterion (BIC) and adopting the first meaningful local minimum to avoid overfitting. The method is validated on simulated data and applied to Alexa Fluor 647, QD 605, and multichromophoric complexes LHCII and PB, revealing 2–3 clusters in most cases and identifying physically meaningful states while enabling robust switching-rate analyses. The approach improves reliability and reproducibility of subpopulation identification in SMS, with potential applicability to higher-dimensional parameter correlations and broader data types beyond lifetime–intensity, enhancing interpretation of noisy single-molecule datasets.

Abstract

Single-molecule spectroscopy (SMS) is an exceptionally sensitive technique, but its inherently limited photon budget produces noisy data that can readily lead to subjective analyses, fitting errors, and reduced statistical power, obscuring true subpopulations and their dynamics. Here, we present an unbiased, objective method to cluster two-dimensional single-molecule data and demonstrate it on fluorescence lifetime-intensity correlations. The clustering method is based on Gaussian mixture modeling, with the optimal number of clusters determined through the Bayesian information criterion (BIC). The BIC score per cluster, which displays in general a non-monotonically decreasing trend, presents multiple local minima as candidate solutions for the number of fitted clusters. We also demonstrate the usefulness of statistically grouping resolved levels. The clustering protocol was benchmarked on simulated data and applied to experimental data from the Alexa Fluor 647 dye, QD 605, and the main light-harvesting complexes of plants and cyanobacteria. The combined application of grouping and clustering achieves substantial noise reduction and the identification of relevant, physically meaningful states that would typically be obscured by manual inspection.

Figures (10)

• Figure 1: Results of the clustering protocol performed on the two-state simulated dataset with 300 simulated particles, each with a time trace of 10 min. A. Representative example of a simulated two-state intensity trace (using $40$-ms binning for display). B. Lifetime--intensity distribution of this set of 300 simulated particles. C. Corresponding BIC score plot. D. Outcome of clustering, showing cluster centers (black crosses) and 0.9 confidence ellipses, estimated from the mean and covariance.
• Figure 2: Influence of the excitation light polarization on the simulated intensity of a molecular dipole. A. Example intensity trace (with 40 ms binning) for circularly polarized light and a dipole orientation of $\theta=\frac{2\pi}{3}$ and $\phi=\frac{3\pi}{4}$, simulated for a time of 10 min. B. Lifetime--intensity distribution of a set of 300 fixed but randomly oriented dipoles. C. Corresponding BIC score plot. D. Cluster centers for a two-cluster model. E. Excitation probability histogram of a set of $10^6$ randomly oriented dipoles for circularly ($\epsilon=1$, red), elliptically ($\epsilon=0.7$, blue), and linearly ($\epsilon=0$, green) polarized light. F. Clustering results using three clusters, with cluster centers indicated by black crosses. Ellipses indicate the region of data that belongs to each cluster, at a confidence of $0.9$.
• Figure 3: Comparison of the performance of the clustering protocol on the ungrouped (left column) and grouped (right column) Alexa data with 52 particles. A and B. Example intensity traces over 10-s windows, with grey representing the 40-ms binned intensity data and green showing the ungrouped (A) or grouped (B) trace. C and D. Lifetime--intensity distributions for the corresponding datasets. E and F. BIC score plots, indicating local minima used to determine the optimal number of clusters. G and H. Clustering outcomes using three clusters, with cluster centers indicated by black crosses, with corresponding 0.85 confidence ellipses.
• Figure 4: Clustering results for the statistically small QD 605 data with $\sim 30$ particles. A. Representative example intensity trace showing 40-ms binned data (grey) and resolved intensity levels (green). B and C. Lifetime--intensity distribution for the ungrouped (B) and grouped (C), respectively. D and E. Corresponding BIC score plots. F and G. Clustering both the ungrouped and grouped datasets using two clusters, with cluster centers indicated with black crosses, and ellipses (at a confidence of $0.85)$ indicating the assignment of data points to each cluster.
• Figure 5: Clustering outcome for the LHCII data, comparing the ungrouped (left) and grouped (right) results for a system of 102 particles. A. Example intensity trace with 40-ms binned data (grey) and the resolved levels (green). B and C. Lifetime--intensity distributions for the ungrouped (B) and grouped (C) LHCII data. D and E. BIC scores plots for the ungrouped and grouped data, respectively. F and G. Corresponding clustering results using three clusters, with cluster centers indicated by black crosses, and ellipses drawn at a confidence of $0.85$.