4D Single-particle tracking with asynchronous read-out single-photon avalanche diode array detector

Abstract

Single-particle tracking techniques enable investigation of the complex functions and interactions of individual particles in biological environments. Many such techniques exist, each demonstrating trade-offs between spatiotemporal resolution, spatial and temporal range, technical complexity, and information content. To mitigate these trade-offs, we enhanced a confocal laser scanning microscope with an asynchronous read-out single-photon avalanche diode array detector. This detector provides an image of the particle's emission, precisely reflecting its position within the excitation volume. This localization is utilized in a real-time feedback system to drive the microscope scanning mechanism and ensure the particle remains centered inside the excitation volume. As each pixel is an independent single-photon detector, single-particle tracking is combined with fluorescence lifetime measurement. Our system achieves 40 nm lateral and 60 nm axial localization precision with 100 photons and sub-millisecond temporal sampling for real-time tracking. Offline tracking can refine this precision to the microsecond scale. We validated the system's spatiotemporal resolution by tracking fluorescent beads with diffusion coefficients up to 10 μm²/s. Additionally, we investigated the movement of lysosomes in living SK-N-BE cells and measured the fluorescence lifetime of the marker expressed on a membrane protein. We expect that this implementation will open other correlative imaging and tracking studies.

Fig. 1. Real-time 4D single-particle tracking on a laser scanning microscope equipped with a SPAD array detector.

a The optical setup is based on a 3D laser scanning microscope, where the confocalized detection unit is substituted with a SPAD array detector, and a cylindrical lens is inserted. The detector sFoV (≈ 1.4 A U) is composed of 5 × 5 elements leading to 25 independent single-photon pulse trains. The FPGA receives the signals, calculates the emitter position r_e, and updates the 3D scanning position r_s in real time. b A 2D movement of the single particle with respect to the center of the sFoV results in a shift of the detected emission pattern and a reduction in its intensity I_m, as shown in the simulated microimages. The detector also allows the concurrent measurement of the fluorescence lifetime τ. When the re-centering condition is triggered, a new position (x_s, y_s) is estimated, and the sFoV is re-centered onto the particle with the beam positioners. c The temporal performance of each SPAD element of the array detector is similar to the single element counterpart (time jitter < 200 ps). Thus, the fluorescence lifetime of the emitter can be extracted by analyzing the emission time histogram Δt_em obtained as the delay between each pulsed excitation at time t_exc and the associated photon detection events at time t_d. d The quantitative estimation of the axial position of the particle leverages the astigmatism caused by the cylindrical lens. In fact, the symmetry and shape of the emission pattern registered in the microimage changes throughout the depth-of-field (DoF).

Fig. 2. Characterization of the planar localization and tracking uncertainties.

a–c Lateral localization uncertainty maps σ_xy(x_e, y_e). The CRB is calculated using an experimental PSF, SBR_p = 5 and N_p = 100 photons, and assuming a fixed acquisition time. The uncertainty maps of the MLE and centroid estimator are measured by using a common dataset obtained by scanning 20 times a 20 nm fluorescent bead replicating the same conditions of the CRB. λ_exc = 561 nm. Scale bar = 100 nm. d–f Axial localization uncertainty maps σ_xz(x_e, z_e). The CRB is calculated using an experimental PSF, SBR_p = 5 and N_p = 100 photons, and assuming a fixed acquisition time. The uncertainty maps of the MLE and normalized difference estimator are measured by using a common dataset obtained by scanning 33 times a 20 nm fluorescent bead replicating the same conditions of the CRB. λ_exc = 561 nm. Scale bar = 100 nm. g Imposed and tracked trajectories of a single 20 nm fluorescent bead (λ_exc = 561 nm) moved at an average tangential speed of 5.5 μm/s along a 3D Lissajous pattern. The scanning position is updated simultaneously in the lateral direction with the centroid estimator and in the axial direction with the normalized difference estimator every 100 photons (〈Δt_rc〉 = 1.9 ± 0.4 ms). The color is used to visualize time, and black lines on the colormap mark the end of each complete turn of the periodic pattern. Extended time trace of the trajectory in Supplementary Fig. 14. h Histograms of the difference between the imposed and tracked trajectories along the three directions for the experiment in (g). σ_x = 34.60 ± 0.04 nm, σ_y = 30.36 ± 0.04 nm, and σ_z = 39.13 ± 0.07 nm.

Fig. 3. 4D tracking on free fluorescent beads in water.

a Distributions of the measured diffusion coefficients for different fluorescent beads (λ_exc = 488 nm) freely diffusing in pure water. The legend reports the number of single trajectories acquired per bead size. For each single bead trajectory, the re-centering in the lateral and axial directions is performed at a fixed timing of $\mathrm{\Delta }{t}_{\mathrm{rc}}^{\mathrm{lat}}=1\mathrm{ms}$ and $\mathrm{\Delta }{t}_{\mathrm{rc}}^{\mathrm{ax}}=2\mathrm{ms}$ respectively. Cumulative distribution function in Supplementary Fig. 15a. b Distributions of the fluorescence lifetimes for the same fluorescent beads populations in (a). Each entry is calculated as the average fluorescence lifetime of a single bead trajectory. Differences in fluorescence lifetime between the populations may be due to variations in the fluorophore concentration inside the beads. Cumulative distribution function in Supplementary Fig. 15b. c Example of the MSD of three single trajectories from the beads populations in (a). The shaded area is the standard error of the mean. Each curve is fitted with a linear model, and the relative diffusion coefficient D is displayed accordingly. The legend reports the tracking time length T_L of each trajectory. d 2D projections of the spatial trajectories for the beads in (c). The color visualizes the axial direction. For a fair comparison, each trajectory is cropped at a duration of 0.5 s. Extended time trace of the trajectories in Supplementary Fig. 16. e 3D representation of the trajectory of a single 200 nm fluorescent bead (λ_exc = 488 nm) diffusing in pure water. The color visualizes the fluorescence lifetime τ. The re-centering in the lateral and axial directions is performed simultaneously at $\mathrm{\Delta }{t}_{\mathrm{rc}}^{\mathrm{all}}=1\mathrm{ms}$. The estimation of the lifetime is performed every Δt_τ = 10 ms. Extended time trace of the trajectory in Supplementary Fig. 17. f 3D representation of the same trajectory as (e), but with color used to visualize the elapsed time. g Detail of the spatial trajectory of (e) and (f) rebinned in all the directions in postprocessing with a dwell time of 20 μs. The localization is also refined by using the MLE.

Fig. 4. Investigation of lysosomes diffusion with RT-4D-SPT.

a 2D projection of the spatial trajectory of a single lysosome moving inside a living neuroblastoma SK-N-BE cell. A white star and a white romb indicate the beginning and the ending of the trajectory, respectively. The Extended time trace of the trajectory is in Supplementary Fig. 20, and the video version is in Supplementary Video SV1. The organelle is tracked by exciting the GFP expressed on a membrane protein (λ_exc = 488 nm) with the re-centering performed at a fixed timing $\mathrm{\Delta }{t}_{\mathrm{rc}}^{\mathrm{all}}=2.5\mathrm{ms}$. The reference image shows the tubulin proteins labeled with Abberior LIVE 560 (λ_exc = 561 nm) and is acquired prior to the lysosome tracking measurement. The pixel dwell time of 100 μs. b 3D plot of the trajectory shown in a. The colormap represents the temporal scale. c Mean squared displacement of lysosomes tracked in wild-type living neuroblastoma SK-N-BE cell and after the addition of nocodazole. Each curve is obtained by averaging the MSD of 15 independent single lysosome trajectories ($\mathrm{\Delta }{t}_{\mathrm{rc}}^{\mathrm{all}}=2.5\mathrm{ms}$). The shaded area is the standard error of the mean. The mean tracking time length is 53 ± 25 s in the wild-type and 5 ± 4 s after treatment. The inset plot shows an enlarged version of the curve obtained after treatment. d 3D plot of the trajectory shown in (a). The color represents the diffusion state of the lysosome. Segmentation is performed by thresholding the average time spent by the lysosome inside voxels of dimension 5 nm × 5 nm × 20 nm (see “Methods”). e Time evolution of the fluorescence lifetime τ for the trajectory in (a) (Δt_τ = 10 ms). The color represents the fluorescence intensity on a logarithmic scale. The black arrows indicate when we register a rapid increment of the photon flux of at least 1 MHz. f 3D plot of the same trajectory of (a) with the color indicating the fluorescence lifetime value. Video version in Supplementary Video SV2.