Multifocal plane microscopy. (a) The schematic of a multifocal plane microscope that can simultaneously image two distinct planes within the sample. The figure illustrates the effect of changing the position of the detector relative to the tube lens, which results in imaging a plane that is distinct from the plane that is imaged by the detector positioned at the design location. (b) Simulated images of a point source at different z positions when imaged through a two-plane MUM setup. Here the z locations are specified with respect to focal plane 1. When the point source is close to the plane of focus (|z₀| ≤ 250 nm) and is imaged in only one focal plane (i.e., a conventional microscope), the resulting image profiles show negligible change in their shape thereby providing very little information about the z location (see bottom row, focal plane 1). On the other hand, if, in addition, the point source is simultaneously imaged at a second focal plane that is distinct from the first one (i.e., two-plane MUM setup), then, for the same range of z values, the image profiles of the point source acquired in this second plane show significant change in their shape (top row, focal plane 2). (c) Accuracy with which the z position of a point source can be determined for a conventional microscope (°) and for a two-plane MUM setup (⋄, *). The vertical dotted lines indicate the position of the two focal planes in the MUM setup. In a conventional microscope, when the point source is close to the plane of focus (|z₀| ≤ 250 nm), there is very high uncertainty in determining its z position (number of detected photons = 2000). In contrast, in a MUM setup, the z location can be determined with relatively high accuracy when the point source is close to the plane of focus. In particular, the accuracy of the z-position determination remains relatively constant for a range of z₀ values (⋄, number of detected photons/plane = 1000). Note that by collecting more photons from the point source per plane, the accuracy of the z-position determination can be consistently improved for a range of z₀ values (*, number of detected photons/plane = 2000). In all the plots, the numerical aperture of the objective lens is set to 1.45; the wavelength is set to 655 nm, the pixel array size is set to 11 × 11; the pixel size is set to 16 μm × 16 μm; the X-Y location coordinates of the point source are assumed to coincide with the center of the pixel array; the exposure time is set to 0.2 s or 0.4 s; and the standard deviation of the readout noise is set to 6 e⁻/pixel. For the conventional microscope (MUM setup), the photon detection rate, background and magnification are set to 10,000 photon/s (5000 photons/s per plane), 800 photons/pixel/s (400 photons/pixel/s per plane), and M = 100 (M₁ = 100, M₂ = 97.9), respectively.

Verification of MUMLA. (a) Results of z-position estimates from simulated data for a QD label. Two-plane MUM images were simulated for different z-position values, where the plane spacing between the two focal planes in the object space was assumed to be 500 nm. The z position from the simulated data was obtained using MUMLA. The plot shows the estimates of z position (°) at each value of z₀ along with the true value of z₀ (—). (b and c) Results of z-position estimates of two QD labels from experimental data. For panel b, a cell sample (stationary QD sample 1) that was pulsed with QD labeled IgG molecules and fixed was imaged in a two-plane MUM setup (focal plane spacing in object space = 300 nm). The objective was moved in 50-nm steps with a piezo-nanopositioner and at each piezo position several images of the specimen was acquired. The z position of an arbitrarily chosen QD was determined using MUMLA. The plot shows the estimates of z position (°) for one of the QDs at various piezo positions along with the mean value of the z-position estimates for each piezo position (—). For panel c, sparsely dispersed QDs on a cover glass (stationary QD sample 2) were imaged in a two-plane MUM setup (focal plane spacing in object space = 1.2 μm). The objective was moved in 200-nm steps with a piezo-nanopositioner and at each piezo position several images of the specimen were acquired. The z position of an arbitrarily chosen QD was determined using MUMLA in combination with the calibration plot (see Results for details). The plot shows the estimates of z position (°) for one of the QDs at various piezo positions along with the mean value of the z-position estimates for each piezo position (—).

Effect of signal and noise statistics on the 3D localization measure. The figure shows the variation of the 3D localization measure of z₀ for a two-plane MUM setup as a function of the expected number of detected photons per plane for readout noise levels of 6 e⁻/pixel (°) and 15 e⁻/pixel (⋄). In all the plots, the photon detection rate is set to 5000 photons/s per plane, the background rate is set to 200 photons/pixel/s per plane, and the x-axis range corresponds to an exposure time range of t = 0.1–2 s. All other numerical values are identical to those used in Fig. 1 c.

Effect of detector pixel size on the 3D localization measure. The figure shows the variation of the 3D localization measure of z₀ as a function of the detector pixel size for a two-plane MUM setup for z-position values of 250 nm (⋄) and 150 nm (*). We assume the pixel size and the readout noise statistics to be the same for both focal plane images. In all the plots, the background component is set to zero; the standard deviation of the readout noise is set to 6 e⁻/pixel; the exposure time is set to 0.2 s; the photon detection rate is set to 5000 photons/s per plane; and the pixel array is set to 500 × 500 μm. The pixel sizes were chosen such that the pixel array consists of an odd number of rows and columns. All other numerical values are identical to those used in Fig. 1 c.

Complex 3D trafficking itinerary of a QD-IgG molecule undergoing endocytosis. (a) Montages for FcRn and IgG channels along with the overlay displaying areas of interest of a transfected HMEC-1 cell with the time (in seconds) at which each image was acquired. Each row in the montage corresponds to a pair of images that was simultaneously acquired at the plasma membrane plane and at a plane that is 500 nm above the plasma membrane plane. In the overlay montage, FcRn is shown in green and IgG is shown in red. The QD-IgG molecule that is tracked is indicated by a white arrow. In some of the frames (e.g., see t = 28.05 s in the IgG channel), the image of the QD label visually appears as a very dim spot, but is detectable by MUMLA. The images in the IgG channels were acquired at a frame rate of 12 frames/s. The images shown are individual frames taken from Movie S1. Bar = 1 μm. (b) Snapshot of the raw MUM data with the FcRn and IgG channels overlaid. The white box indicates the region in the cell that is shown in the montages. The red haze seen in the membrane and top planes is due to the presence of QD-IgG molecules in the imaging medium. Bar = 5 μm. (c) 3D trajectory of the QD-IgG molecule. The trajectory is color-coded to indicate time. The color change from red to green to blue indicates increasing time. The QD-IgG positions indicated by arrows correspond to the images shown in panel a. The molecule is initially seen to be randomly diffusing on the plasma membrane. The endocytosis of the molecule is characterized by an abrupt change in its z location where the molecule moves inside the cell to a depth of 300 nm from the plasma membrane. After internalization, the molecule moves in a highly directed manner and takes an elaborate route to traffic deep inside the cell (800 nm from the plasma membrane) until it reaches a sorting endosome. The molecule briefly interacts with the sorting endosome, loops around it and then, after several repeated contacts, merges with the sorting endosome. See also Fig. S3 in Data S1 for a plot of the z₀ coordinate as a function of time.

Endocytosed QD-IgG molecule moves directly to the sorting endosome. (a) Montages for FcRn and IgG channels along with the overlay displaying areas of interest of a transfected HMEC-1 cell with the time (in seconds) at which each image was acquired. Each row in the montage corresponds to a pair of images that was simultaneously acquired at the plasma membrane plane and at a plane that is 500 nm above the plasma membrane plane. In the overlay montage, FcRn is shown in green and IgG is shown in red. The QD-IgG molecule that is tracked is indicated by a white arrow. The images in the QD channels were acquired at a frame rate of 12 frames/s. The images shown are individual frames taken from Movie S2. Bar = 1 μm. (b) Snapshot of the raw MUM data with the FcRn and IgG channels overlaid. The white box indicates the region in the cell that is shown in the montages. The red haze seen in the membrane and top planes is due to the presence of QD-IgG molecules in the imaging medium. Bar = 5 μm. (c) 3D trajectory of the QD-IgG molecule. The trajectory is color-coded to indicate time. The color change from red to green to blue indicates increasing time. The QD-IgG positions indicated by arrows correspond to the images shown in panel a. The QD-IgG molecule is initially observed to be diffusing on the plasma membrane for a significant period of time (t = 0–29.67 s). Before internalization, the molecule becomes stationary and then moves inside the cell in a highly directed manner toward a sorting endosome. See also Fig. S4 in Data S1 for a plot of the z₀ coordinate as a function of time.