Image segmentation and separation of spectrally similar dyes in fluorescence microscopy by dynamic mode decomposition of photobleaching kinetics

Abstract

Background: Image segmentation in fluorescence microscopy is often based on spectral separation of fluorescent probes (color-based segmentation) or on significant intensity differences in individual image regions (intensity-based segmentation). These approaches fail, if dye fluorescence shows large spectral overlap with other employed probes or with strong cellular autofluorescence.

Results: Here, a novel model-free approach is presented which determines bleaching characteristics based on dynamic mode decomposition (DMD) and uses the inferred photobleaching kinetics to distinguish different probes or dye molecules from autofluorescence. DMD is a data-driven computational method for detecting and quantifying dynamic events in complex spatiotemporal data. Here, DMD is first used on synthetic image data and thereafter used to determine photobleaching characteristics of a fluorescent sterol probe, dehydroergosterol (DHE), compared to that of cellular autofluorescence in the nematode Caenorhabditis elegans. It is shown that decomposition of those dynamic modes allows for separating probe from autofluorescence without invoking a particular model for the bleaching process. In a second application, DMD of dye-specific photobleaching is used to separate two green-fluorescent dyes, an NBD-tagged sphingolipid and Alexa488-transferrin, thereby assigning them to different cellular compartments.

Conclusions: Data-based decomposition of dynamic modes can be employed to analyze spatially varying photobleaching of fluorescent probes in cells and tissues for spatial and temporal image segmentation, discrimination of probe from autofluorescence and image denoising. The new method should find wide application in analysis of dynamic fluorescence imaging data.

Keywords: Autofluorescence; Fluorescence; Live-cell microscopy; Matrix methods; Photobleaching; Spatiotemporal modeling.

Fig. 1

Workflow for dynamic mode decomposition of bleaching kinetics in fluorescence microscopy. A video sequence with decaying intensity I(x, y, t) in m frames representing time points t = 1, … m (A) gets first reshaped into a space–time matrix in which each video frame having x pixels in each row u_y (here y = 3) gets reshaped into m columns with y times x elements each of a space–time matrix X (B and see Eq. 1). Following the procedure described in Eq. 2–11 the system matrix describing the fluorescence dynamics gets dimensionally reduced using a SVD and rank truncation to capture the dominant dynamics in the system. Subsequently, spectral decomposition of this truncated system matrix provides the dynamic modes (eigenfunctions), mode amplitudes and eigenvalues, which together approximate the original space–time matrix X (C). Reconstruction of the video sequence is achieved by reversing the reshaping procedure described in panel A. In this example, a rank-3 approximation of the system matrix is illustrated. See text for further explanations

Fig. 2

Comparison of simulated and reconstructed bleach stacks. A, selected frames (#1, #25, #50, #75 and #100) are plotted for the simulated bleach stack (left column) and the reconstructed image stack obtained from the DMD of the synthetic image series (middle column). Right column, absolute error between simulation and reconstruction. The intensity range is color-coded between 0 and 255 intensity units. One can see that DMD approximates the simulated images very well and is also efficient in removing image noise. B, integrated intensity of original (blue symbols) and reconstructed image stacks (red symbols). C, mean intensity in color-coded boxes (see #50 in A for location of regions of interest, ROI) for original (red, yellow and cyan lines) and reconstructed video stacks (blue, green and pink lines)

Fig. 3

Dynamic mode decomposition enables accurate segmentation of synthetic bleach stacks. A rank-3 approximation of the full matrix A was employed to decompose the simulated bleaching kinetics. A, 2D map of dynamic modes, i.e., Mode 1 (φ₁), Mode 2 (φ₂) and Mode 3 (φ₃). B, mode dynamics for each of the three modes and C, eigenvalues for each mode, ω₁ to ω₃, plotted on the unit circle. D, histogram of each dynamic mode (compare panel A) with threshold intensity value determined by the Minimum method indicated as red line. E, result of binary segmentation with white being foreground and black being background. While thresholding Mode 1 segments the slowly bleaching rectangular region, thresholding Mode 2 isolates the elliptical region with fast bleaching kinetics. Thresholding Mode 3 isolated the circular region with intermediate bleaching kinetics. F, reconstructed mode dynamics according to Eq. 11 for Mode 1 (left column), Mode 2 (middle column) and Mode 3 (right column)

Fig. 4

Comparison of experimental and reconstructed bleach stacks of DHE in C. elegans. A, B montage of selected frames (i.e., frame (#1, #25, #50, #75 and #100) of the experimental fluorescence stack of DHE labeled C. elegans (left column) and of the reconstructed image stack obtained from the DMD of rank 5 (right column). Right column, absolute error between original stack and DMD reconstruction. The intensity range is identically scaled in 16-bit format. B, integrated intensity of original (blue symbols) and reconstructed image stacks (red symbols). C, mean intensity in color-coded boxes (see #50 in A for location of regions of interest, ROI) for original (red, yellow and cyan lines) and reconstructed video stacks (blue, green and pink lines). Note that intensities of the DMD reconstruction perfectly coincide with the intensities of the original stack; therefore, only the line colors of the reconstruction are visible. Bar, 20 µm. See text for further details

Fig. 5

Dynamic mode amplitudes and eigenvalues of fluorescence images of DHE-labeled nematodes. A, B, real part of mode amplitudes of a rank-5 DMD of the experimental bleach stacks of DHE labeled C. elegans with two oscillatory modes (Mode 1 and 2, A) and three exponentially decaying amplitudes (Mode 3–5, B). C, eigenvalues λ₁ to λ₅ plotted on the unit circle. The first two eigenvalues have non-zero imaginary part (see also the corresponding oscillatory amplitudes in A). Eigenvalues 3–5 are real and smaller than one, describing decaying intensities in the bleach stacks

Fig. 6

Dynamic modes of C.elegans bleach stacks and comparison with pixel-wise fitting. A–E, mode weights for DMD modes 1–5. The real part of mode weights is shown in left panels (‘Real’), while the imaginary parts are shown in right panels (‘Imag’). F, bleach rate fitting using a stretched exponential function with bleaching amplitudes (right panel), time constant map (middle panel) and background fluorescence (right panel). The amplitude image in F shows the distribution of the rapidly bleaching DHE, while the background image resembles most of the autofluorescence

Fig. 7

DMD of C. elegans bleach stacks allows for discrimination of autofluorescence from DHE probe intensity. A, montage of individual dynamic modes shown as every second image of the corresponding image stacks. Dynamic mode 3 (‘DMD3’) resembles cellular autofluorescence of nematodes (upper row in A), while dynamic mode 4 and 5 (‘DMD4’ and ‘DMD5’) constitute DHE fluorescence (two middle rows in A). The sum of mode 4 and 5 shows the total DHE fluorescence (lower row in A). B–D, color overlay of mode decomposition with mode 3 resembling autofluorescence in red and sum of mode 4 and 5 representing DHE fluorescence in green. B, first frame, C, 10th frame and D, 20th frame of this color representation of the DMD, showing the rapid bleaching of DHE fluorescence (green) compared to autofluorescence (red). Bar, 20 µm

Fig. 8

DMD of bleach stacks of BHK cells labeled with two green probes, Alexa488-Tf and C6-NBD-SM. BHK cells were labeled with 4 µM C6-NBD-SM and with 20 µg/ml Alexa488-Tf, both emitting in green, as described in Materials and Methods. A, montage of selected frames (every 5th frame) of such double labeled cells. B, reconstruction of DMD of the bleach stack in A with the sum of dynamic modes 1, 3 and 4 shown in green (resembling the fast-bleaching C6-NBD-SM) and sum of dynamic mode 2 and 5 (resembling the slowly bleaching Alexa488-Tf) shown in red. Bar, 20 µm. C, mode amplitudes and D, eigenvalues of the DMD plotted on the unit circle