Computation of the thinness ratio. (A) Confocal maximum intensity projection image of a mito-DsRed2-expressing cortical neuron; original image (G(x,y)) and the absolute value of its discrete Fourier transform The maximal spatial frequency of the Fourier transform was 1/(2 × 0.075μm) = 6.67cycles/μm, where 0.075 μm is the pixel size in the space domain. For better visualization, ω is cropped at 4 c/μm. (B and C) HBP (B) and LBP (C) filter and transfer functions, f_filter(ω) and correspond to Eqs. 4 and 2, respectively. The theoretical MTF(ω) for confocal microscopy is shown by the red trace (NA = 1.3, λ = 590 nm, n_medium = 1.33, d_pinhole = 1.2 Airy units or resels (1 resel = 0.61λ/NA); see Eqs. S1–S6 and Figs. S1 and S2 in Data S1). (D and E) Fluorescence images after filtering (). Intensities can be directly measured by averaging pixel values in regions of interest, as indicated by the red dashed line. Scale bar, 5 μm. Fluorescence intensity is given in photoelectrons (the used gain settings resulted in 1.9 gray value units/photoelectron). Images are printed at γ = 1.6. See example for filtering in Data S2.

Optimization of the filter functions. (A) Scheme of the optimization. Parameters of the two filter functions corresponding to the HBP and LBP filters were determined by numeric optimization using differential evolution to find the global minimum of the p-value. (B–D) Filter functions optimized for alamethicin-evoked mitochondrial swelling in different microscope configurations. Filters are shown without normalization (Eq. 5). Optimized filter functions for wide-field imaging on astrocytes (B) (recorded as single-image plane; λ ≈ 590 nm, 0.1 μm/pixel, NA = 1.3, corresponding to Fig. 5), confocal imaging of neurons (C) (recorded as mean-intensity projected z-stacks; λ ≈ 590 nm, 0.075 μm/pixel, NA = 1.3, corresponding to Fig. 8), and wide-field imaging of mixed cortical cultures (D) (recorded as mean-intensity projected z-stacks; λ ≈ 535 nm, 0.1 μm/pixel, NA = 1.3, corresponding to Fig. 10). (E) Contour plot showing p-values of the optimization in a logarithmic scale as a function of ω_cutoff of the LBP filter and ω_cuton of the HBP filter. The diagram was generated on the same image sequence that was used for the optimization in D. The other three parameters were taken from D. See example for NMinimize in Data S2.

The TR technique estimates the diameter of mitochondria. (A) Typical imaged mitochondria (upper row) and model mitochondrion capsule bodies (lower row) are shown at the same printed pixel size. The modeling parameters were dependent on the optical configuration as indicated. Model mitochondria have diameter d = 0.34 μm and are scaled to match the resolution of the acquisition and are blurred by the theoretical MTF of the given optical configuration. (B) Model mitochondrion images were generated with increasing diameter and correspond to the confocal microscopic configuration. (C and D) Effect of mitochondrial diameter on the TR in the three indicated optical configurations using spheres (C) or capsules of l = 50 pixels (D) as models. The model images were blurred with the MTFs given in Fig. 2, B–D. Although the slopes are not intended to be used for calibration of real biological data (because the real MTF of the microscope could differ from the theoretical), the reciprocal slopes are given for the estimation of sensitivity in pixels/TR for C (▵, 2.8; □, 1.6; ○, 17.8) and for D (▵, 4.3; □, 3.1; ○, 22.2). (E) TR as a function of subpixel changes of the diameter. Model mitochondria were 50 pixels long and were placed in the same positions and orientations in each image (black trace) or in a different manner (gray trace). The latter simulation was repeated five times and the mean ± SE is shown. Comparison of all data points by ANOVA with Tukey post hoc test at p < 0.05 indicates that data points farther away from each other than an average 0.15 pixels or 15 nm had significantly different TRs. This corresponds to the optical configuration given in Fig. 2 D. (F) TR (as mean ± SE of n = 3) calculated from fluorescent bead images acquired by mean-intensity projected z-stacking wide-field microscopy in conditions similar to the images in Figs. 2 D and 10.

“Thread-grain” transition of mitochondria: swelling versus fission. (A and B) Model mitochondria shortening from l = 2.5 μm and d = 0.34 μm due to swelling (A) or fission (B). (C and D) Diameters of model mitochondria calculated as a function of length, based on the considerations of constant n and s_total for swelling (C) and constant v_total and s_total for fission (D). (E) v_total as a function of length during swelling. (F) Number of mitochondria as a function of length during fission (the starting n was 100). (G and H) Thinness ratios obtained by filtering blurred model mitochondrion images generated with the parameters given in C–F using filter functions shown in Fig. 2 D. Traces from top to bottom in C–E, and from bottom to top in F–H correspond to the starting diameters (in μm) 0.44, 0.40, 0.36, 0.32, 0.30, 0.28, 0.26, and 0.22, or to s_total/v_total ratios (constant for fission and initial for swelling from l = 7.5 μm) of (in μm⁻¹) 9, 10, 11, 12.3, 13, 14, 16, and 19. The simulation of mitochondrial swelling was started from l = 7.5 μm (black traces) and alternatively from l = 2.5 μm (gray traces) with the same starting diameters as given above. The results of the fission simulation are fully determined by the constant s_total and v_total, and therefore do not depend on the initial length.

In situ mitochondrial swelling in cortical astrocytes. (A) Raw fluorescence micrographs of a mito-DsRed2-expressing cortical astrocyte, acquired by single-plane wide-field fluorescence microscopy. (B) TR shown as pseudocolor images gated with raw intensity. Solid and open arrows indicate slender and swollen mitochondria, respectively. Open arrowheads indicate swollen, beaded (grain) mitochondria. Scale bar, 5 μm. (C–G) Time course of the TR shown as mean ± SE of single cell traces (gray) normalized to the baseline (). (C) Effect of valinomycin (0.2 and 250 nM) and alamethicin (Ala; 40 μg/ml; n = 3). Numbers in black discs refer to the frames shown in A. (D) Switch of superfusion to identical buffer (n = 4). (E) Effect of FCCP (1 μM) and alamethicin (40 μg/ml; n = 3). (F) Effect of antimycin A₃ (2 μM) plus oligomycin (2 μM) (n = 4). (G) Effect of mastoparan (10 μM) and alamethicin (40 μg/ml) (n = 3). The filter functions for the TR calculation are given in Fig. 2 B.

Light-scatter measurement of swelling in isolated mitochondria. (A and B) Brain mitochondria isolated by percoll gradient were exposed to valinomycin (0.2 and 200 nM) and to alamethicin (Ala; 40 μg/ml) (A) or to mastoparan (1 and 4 μM) and to alamethicin (Ala; 40 μg/ml) (B). (C) Liver mitochondria exposed to valinomycin (0.2 and 200 nM) and to alamethicin (Ala; 40 μg/ml). Gray traces show alamethicin-only treatments; black traces show effects of the indicated treatments. Optical density measured at 540 nm was normalized to a baseline of 1, with a value of 0 after alamethicin treatment. Traces are representative of triplicate measurements.

Three-dimensional, volume-rendered reconstruction of confocal image stacks. (A and B) An astrocyte in culture (A) and a cortical neuron expressing mito-DsRed2 (B). Both image stacks were acquired in identical imaging conditions, with the exception that finer z-steps were used for astrocytes. Grid, 3.3 μm. Note that whereas most mitochondria are in a single plane in the astrocyte, mitochondria in neurites are often at different z-coordinates, and only a section of the soma was acquired.

In situ mitochondrial swelling in cortical neurons. (A) Fluorescence micrographs of mito-DsRed2-expressing cortical neurons acquired by laser scanning confocal microscopy, shown as maximum intensity z-projections. (B and H) TR shown as pseudocolor images gated with raw intensity. Solid and open arrows indicate slender and swollen mitochondria, respectively. Open arrowheads indicate swollen, beaded mitochondria. Scale bar, 5 μm; zoom 2.5×. (C–G) The time course of TR is shown as mean ± SE of single-cell traces (gray), calculated with the filters shown in Fig. 2 C from mean-intensity projected z-stacks and normalized to the baseline (δ). (C) Effect of valinomycin (0.2 and 250 nM) and alamethicin (Ala; 40 μg/ml) (n = 4). Numbers in black discs refer to the frames shown in A and B. (D) Baseline (n = 9). (E) Effect of FCCP (1 μM) and alamethicin (40 μg/ml) (n = 4). (F and H) Effect of antimycin A₃ (2 μM) plus oligomycin (2 μM) and alamethicin (40 μg/ml) (n = 4). Numbers in black discs refer to the frames shown in H. (G) Effect of mastoparan (10 μM) and alamethicin (40 μg/ml) (n = 5). (H) Antimycin A₃ plus oligomycin triggers mitochondrial fission (depicts F). (Left) Raw and TR pseudocolor images are shown in a manner similar to that in A and B. (Right) The kymogram shows the time course of mito-DsRed2 raw fluorescence along a broken line following the dendrite containing the mitochondria. The filter functions for the TR calculations are given in Fig. 2 C.

Signal/noise ratio of the TR in different optical configurations. (A) SNR as a function of confocal pinhole size (1 resel = 0.61λ/NA). (B and C) SNR as a function of NA for confocal and wide-field microscopy, respectively. (D) SNR as a function of emission wavelength (λ). (E) SNR as a function of the mean fluorescence intensity of the PSF. The intensity units are given in photoelectrons; therefore, the variance of photon shot noise equals the intensity. Arrows show the typical detection range. For this, the sum of photoelectrons from seven image planes and 0.4 gray value units/photoelectron were used. (F) Sensitivity of the TR technique as a function of SNR. Sensitivity was defined as the absolute change of the TR, which results in p = 0.05 in a two-tailed Student's t-test comparison of two sets of five samples (calibrated to nanometers based on Fig. 3 D (circles) at 2.2 μm/TR). (E and F) The indicated arbitrary TR values were generated by decreasing the high-frequency integral component in Eq. S8 in Data S1, and this was followed by calculation of error propagation.

Comparison of astrocytes and neurons in mixed cortical cultures. (A and B) Mitochondrial swelling is indicated as a percentage of negative change of the TR. The TR was measured at baseline, and after 5- and 90-min treatment with vehicle (1:1000 ethanol), valinomycin (0.2 and 200 nM), FCCP (1 μM), and oligomycin (2 μg/ml) plus antimycin A₃ (1 μM) or mastoparan (10 μM). Bars indicate mean ± SE of baseline-normalized negative TR for the 5-min treatment (gray bars) or the 90-min treatment (black bars). The maximal-effect alamethicin (20 μg/ml) was captured after addition without delay, because of progressive lysis of mitochondria. #, p < 0.05; ##, p < 0.01; and ###, p < 0.001 compared to 0 by two-sided Student's t-test. *p < 0.05, **p < 0.01, and ***p < 0.001 compared to the vehicle treatment by ANOVA for the given time point with Dunnett's post hoc test. A representative astrocyte (C–E) and a neuron (F–H) from the same experiment are shown at baseline (C and F), after 5 min FCCP (1 μM) treatment (D and G), and after fixation at ∼2 h and staining for the astrocyte marker GFAP (red), neuronal marker MAP2 (green), and nuclear marker DAPI (blue) (E and H). Scale bar, 10 μm. Data are from four independent cell culture preparations and n > 10 cells for each condition. The filter functions for the TR calculations are given in Fig. 2 D.