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Mass transport within cells helps maintain homeostasis and is disrupted by disease and stress.Here, we developed quantitative phase velocity (QPV) as a label-free method to make invisible and quantifiable mass flow within cells.We compare our method with alternative image registration methods, theoretical error models, and synthetic data.Our method tracks not only individual labeled particles or molecules, but also the flow of bulk material throughout the cell.This allowed us to measure diffusivity within different cellular compartments using a single method, which we used here to directly compare nuclear and cytoplasmic diffusivity.As a label-free method, QPV can be used for long-term tracking to capture dynamics throughout the cell cycle.
Ordered transport is essential for cell function and growth.To maintain homeostasis, cells continuously transport substances, including nutrients and bulk materials, into the cell from the surrounding environment1, and ions pass through cell membranes1, fluids2 and structural polymers into cell tubes to drive cell movement3.In turn, cellular trafficking can be affected by disease4 and stress5,6.Therefore, measuring intracellular transport can improve our understanding of cellular behavior, disease, response to environmental stress, and potential disease treatments.Fluorescent labels are the most commonly used tools to study intracellular trafficking because they provide unique signals with low background, making them easy to track7,8,9,10,11.Although fluorescent labels are widely used in transport studies, fluorescence has the disadvantage of photobleaching and phototoxicity, which can cause stress and alter cellular behavior12,13.There is also a limited number of components labeled at one time14 and fluorescence tracking cannot measure the velocity of unlabeled regions, limiting its ability to measure intracellular bulk material transport.
Label-free methods offer an alternative to fluorescence for transmission measurements.Label-free methods, such as phase contrast, differential interference contrast (DIC) and Raman imaging, have been applied to measure intracellular dynamics in whole cells 15, 16 , vesicles 17, 18 and lipid droplets 19 .However, DIC only measures phase gradients in a single direction, and phase contrast images contain halos that make quantitative analysis difficult.
Quantitative phase imaging (QPI) is a label-free imaging technique that measures the phase shift that occurs when light passes through materials with higher refractive indices21.The phase shift measured with QPI is proportional to the distribution of dry mass in the sample22.Therefore, by providing quantitative data on the movement of bulk materials within cells, QPIs are better candidates for long-term transport studies within cells.Previous collaborations with QPI have used contrast produced by local changes in biomass density to track well-defined subcellular components as well as the overall average rate of mass movement23,24.Spatial and temporal power spectra from QPI data have also been used to quantify cell-averaged rheological properties 25, 26 , erythrocyte dynamics 27 and local diffusivity 28 .
In this work, we combine automated image velocimetry and label-free QPI to develop a method we call quantitative phase velocity (QPV), which measures unstable intracellular velocity fields to capture large amounts of cellular material over long periods of time transportation.To understand the source of the QPV error, we developed a theoretical model of the QPV error that matched the experimental results.We then applied QPV to measure intracellular dry matter transport during cell cycle progression.Using these data, we quantified the dynamics of intracellular diffusion in the nucleus and cytoplasm during the cell cycle.We see that nuclear spreading decreases with cell cycle progression, whereas cytoplasmic spreading decreases with the transition from G1 to S phase.
We developed QPV to measure intracellular dry mass velocity from QPI data (Figure 1).We captured QPI data using an inverted microscope with a four-wave transverse shear interferometer (QWLSI) wavefront sensing camera (Fig. 1a) to obtain images of cell mass distribution over time.QWLSI uses a diffraction grating to create interference between light passing through adjacent regions of the sample, thereby projecting an interference pattern onto the camera sensor.The wavefront aberrations caused by the different refractive indices and thicknesses of the sample are then captured as deformations of this interference pattern, from which the sample-induced phase shift can be reconstructed.The QPI of retinal pigment epithelium (RPE) cells (Fig. 1b) showed the distribution of cell dry mass over time.In particular, QPI data revealed regions of high mass density in the nucleus, low mass podia, and small-scale puncta in the cell, which can be characterized as velocimetry (Fig. 1b).Differences between QPI images over time illustrate the shift in the quality of QPI captures (Fig. 1c).In this example, this difference image represents the overall movement of cell dry matter from the upper right corner to the lower left corner of the image frame.QPV uses these data to measure the movement of the mass through the principle of particle image velocimetry (PIV).As expected in this individual example cell, the distribution of intracellular dry mass velocities determined by QPV shows a dry mass velocity vector pointing from the upper right corner of the frame to the lower left corner, as well as a local deviation from the general trend (Fig. 1d) ).
Quantitative phase velocity (QPV) measures intracellular dry matter movement.(a) Quantitative phase imaging (QPI) measures the phase shift of light passing through the cell and is used to calculate the dry mass distribution of the cell over time.(b) Dry mass distribution in RPE cells imaged at 120x magnification at t = 0 min.Scale bar represents 10 µm length.(c) Differences in the QPI mass distribution of RPE cells in (b) and images taken after t = 10 min minus images at 0 min showing cell movement.The inset in (c) shows a 15 × 15 pixel interrogation window illustrating the change in the location of individual subcellular features from those marked with red arrows to those marked with black arrows.The color scale shows the difference in dry mass between time 0 and 10 minute frames (red: massive increase in quality, blue: massive decrease in quality).(d) Intracellular biomass velocity field calculated using the quantitative phase velocity method (QPV).Velocity amplitudes are represented on a 0.5 µm/min scale.
In order to select the most compatible image registration method for developing QPV, we compared the performance of commonly used methods for PIV: normalized cross-correlation (NCC)31, optical flow reconstruction (OFR)32, mutual information (MI)33 and sum-of-squares difference (SSD, Figure S1) 34.Using each method, we estimated the resolution and accuracy of velocity measurements for fixed RPE and MCF7 cells moving at known velocities as velocity criteria, since fixed cells have the same distribution of intracellular characteristics as living cells (Figure 2 and Figure 2). S2, S3).After a total of 1.5 µm of downward stage movement, the displacement distributions calculated by the QPV of the example stationary cell showed a uniform displacement distribution across all interrogation windows pointing in the direction of stage movement (Fig. 2a and Fig. S2).
SSD image registration measures intracellular velocity from QPI data and is more accurate than OFR, MI, and NCC at most interrogation window sizes.(a) QPV on RPE-fixed cells measures intracellular displacement during microscope stage translation.(b) Comparison of displacement errors, the percent difference between measured and expected displacements, for mutual information (MI), normalized cross-correlation (NCC), optical flow reconstruction (OFR), and for intracellular velocity calculations. Sum of squared differences (SSD) QPI data for different interrogation window sizes showed that SSD had the highest accuracy at most window sizes (number of cells, n = 11, error bars show standard error of the mean, SEM).(c) Velocity accuracy versus interrogation window size and displacement for RPE fixed cells using OFR shows that OFR is limited to measuring a very narrow range of displacements (n = 11) with acceptable accuracy.Yellow/white – high precision, red/black – low precision.(d) When the interrogation window size is smaller than the displacement to be measured, the QPV velocity measurement accuracy is typically less than 10% in relation to the interrogation window size and the displacement of fixed RPE cells, and the area with an error of less than 5% is represented by the dashed line (n = 11).
Our velocimetry method requires a small interrogation window size to achieve high spatial resolution of the velocity field.Using each method, we calculated the measurement accuracy of 0.1 µm (0.42 × single pixel) displacement of fixed cells, with an interrogation window size ranging from 5 to 59 pixels (1.19 µm to 14 µm) square.We calculated displacement error as the percent difference between the measured displacement and the expected displacement (see Methods).Displacement error is a key determinant of computational velocity error because the time between frames is tightly controlled during imaging.Among the four methods tested, SSD, NCC, and OFR work well for all window sizes, while MI works well for large windows (Fig. 2b and Fig. S3a).The performance of SSD and NCC is expected to be similar because SSD is related to cross-correlation (see Methods).However, due to the uneven background energy density of the QPI data, the cross-correlation alone showed poor performance compared to SSD or NCC (Fig. S4).Although MI and OFR have large errors when applied to QPI data, they reduce computation time relative to NCC and SSD.SSD in particular shows reduced computation time and smaller query window size (Fig. S5).
Image registration methods for QPV should also perform well over a wide range of displacements, as cells typically display a wide range of motion ranging from subpixel motion in the nucleus to highly deformed multi-pixel displacement in the cytoplasmic podopod region.Based on their performance at small and medium window sizes and fundamentally different image registration methods, we further measure the displacement errors of SSD and OFR with displacements from 0.1 to 10 µm and interrogation window sizes from 1 to 14 µm.Results of OFR with fixed RPE and MCF7 cells showed greater than 50% error in displacement measurements above 1 µm at all interrogation window sizes tested (Fig. 2c and Fig. S3c).The use of Gaussian blur improves OFR performance at large displacements (Fig. S6).However, Gaussian blurring comes at the cost of losing the ability to resolve small-scale differences in intracellular deformation.On the other hand, the error of SSD for any displacement is less than 10% as long as the computed window size is at least as large as the displacement itself and less than 5% for a subset of the region (Fig. 3).2d).We also evaluated that the error of SSD in displacement direction measurement is smaller than OFR (Fig. S7).For different cells, SSD also outperforms OFR (Fig. S8).Therefore, considering the accuracy, spatial resolution, and ability to measure large-scale displacements, we chose SSD as the image registration method for QPV despite a modest increase in computation time (Fig. S5).
To understand the sources of error in QPV, we developed a model that accounts for key parameters that contribute to measurement noise.These are: the size range of cellular features that influence the spread of cellular components and the ability to visualize displacement by the chosen interrogation window size, the interrogation window size that determines the maximum measurable displacement, and the optical resolution limit of the microscope.
To investigate how the distribution of spatial features and noise affects the performance of QPV, we generated a correlation between size and mean particle size observed in RPE and MCF7 cells (Fig. 3b and Fig. S9i).The Perlin noise added to the synthetic data matched the continuously locally varying background noise in our QPI data (Fig. 3a, lower middle and lower right).Therefore, the Perlin noise has a power spectrum similar to that of the background noise in QPI and reduces the magnitude of the power spectral density (Fig. S9i).Synthesized Perlin background noise gave results comparable to adding noise from real QPI images (Fig. S9i).Synthetic Perlin noise is then used to create a fully synthetic dataset that is independent of real images, used to identify fundamental features that limit the measurements, and an easily generated synthetic dataset to evaluate the method.The power spectra of RPE-fixed cells, MCF7-fixed cells, and polystyrene beads imaged at 20X magnification best matched those of heterogeneous synthetic data with Perlin noise (Figure 3b and Figure S9i).Therefore, based on this power spectral analysis, QPI images are best approximated with non-uniform spatial features and added low spatial frequency noise.The QPV on the synthetic data showed less than 5% error for both data with uniform and non-uniform spatial features (Fig. S10).
The simulated QPV displacement measurement errors are consistent with the experimental measurements.(a) Comparison of background-corrected QPI images of RPE-fixed cells at 120X (top left) and polystyrene beads at 20X (bottom left) to synthetically generated uniform and non-uniform circular data, with Perlin noise added (top middle and right ) and no Perlin noise added (bottom middle and bottom right) (b) the power spectrum of the QPI data (green and magenta) and (a) the synthesized data with noise (black) showing the QPI data synthesized with a non-uniform circle similarity data.(c) Power spectral density versus effective particle size of RPE-fixed cells (n = 3).The power spectral densities corresponding to the 5 µm and 40 µm structures are shown.Subpanels show structures within the 40 µm RPE fixed cell, illustrating the range of features captured by QPI.Scale bars show 5 µm (blue) and 40 µm (red).The colormap shows dry mass density in pg/µm2.(d) Theoretical displacement estimation error (percentage difference between expected and measured displacements) at four effective particle sizes for all tested displacements and window sizes.(e) The size-dependent model results in (d) are averaged, weighted by the actual distribution of particle sizes (c) to give a prediction error consistent with (f) the error measured from a matched RPE cell using experimental data.The colormaps in (e) and (f) are the same.
Converting frequencies to equivalent particle sizes showed that the QPV could potentially track features ranging in size from organelle-sized blobs to whole cells (Fig. 3c).To account for the range of feature sizes captured by QPI and their individual contributions to measurement error, we calculated the theoretical error for all particle sizes in a cell up to 40 µm, the size of the entire cell (Fig. 3d, Fig. S11c–d), These particle errors are then weighted averaged according to the power spectrum of the cell (Fig. 3c, Fig. S11b).The predictions of displacement magnitude errors (Fig. 3f, Fig. S11e) are in good agreement with the experimentally calculated errors for RPE (Fig. 3e) and MCF7 cells (Fig. S11f).Both the prediction error and the measurement error show large errors if the displacement is larger than the window size, and also large when the displacement is smaller than the diffraction limit (0.48 µm in our case).
We achieved diffraction-limited optical resolution by adjusting the phase pixel size to half the diffraction limit, thus satisfying the Nyquist criterion (Fig. S12a–c).We then experimentally observe high-speed estimation errors at displacements below the microscope optical resolution limit (Fig. 3f) and predict (Fig. 3e) displacement magnitudes.To estimate the effect of optical sectioning on our velocity estimates, we first calculated the depth of field of the system to be 1.7 µm, which is quite large due to the use of a low condenser aperture and large effective pixel size.We can then use the calculated optical thickness of the sample, known as the optical path length (OPL), to estimate the thickness of the cells we imaged with the QPV.Assuming a refractive index of 1.3374 for DMEM cell culture medium and a typical refractive index of 1.365 for cell contents, we estimate that cells with an OPL less than about 0.04 µm will be within the system depth of field (DOF).We observed that the maximum optical path lengths in RPE cells were mostly in this range (Fig. S12d).Furthermore, we note that while some features beyond the depth of field will be observed as blurry features, previous work on PIV shows that this does not have a large impact on velocity estimation accuracy.We also observed reasonable agreement between predicted and measured displacement orientation errors (Fig. S13).Application and validation of this model allowed us to predict the minimum window size for accurate intracellular tachymetry.For example, for RPE and MCF7 cells imaged every 1 min at 120X magnification, typical observed displacements ranged from 0 to 14 pixels outside the very fast moving podia.Therefore, we used an interrogation window of 15 x 15 pixels, corresponding to an area of ​​12.75 µm2.We note that the QPV can accommodate faster moving cells by increasing the interrogation window size or by increasing the imaging rate, thus capturing greater motion between shorter time intervals with reasonable error when using suitable optics until approaching Diffraction-limited motion.
QPV accuracy also depended on cell type and varied according to feature density, suggesting that the effective particle counts tracked by QPV varied between different regions within the cell (Fig. S12).Intracellular velocity errors in example RPE and (Fig. S14a–c) MCF7-fixed cells (Fig. S14d–f) were higher at the edges of cells with flat featureless regions.Furthermore, the lower power spectral density in RPE cells relative to MCF7 cells (Fig. S14g) suggests that the power density of larger particles is more dominant in RPE cells.This moderately reduces the accuracy of the QPV.The velocities of different interrogation windows in cells also showed increased error in windows with lower power densities (Fig. S14h–i).
QPV tracks overall cell deformation as well as movement of individual regions within the cell.As a method to measure dry mass distribution based on QPI, QPV measures the displacement of dry mass.Example results for RPE cells are shown in Figure 4.The deformation of the uniform grid overlaid on the RPE cell image from time 0 min (Fig. 4a) to 30 min (Fig. 4b) shows the compression of grid points in the grid.The spacing of the midpoints of the nuclear and podia regions (Fig. 4b), reflecting the observed compression of the cell as its podia move upward within the image frame (Movie S1).Each square surrounded by four grid points in Figure 4a represents a volume that contains a specific amount of dry mass in the cells.Using QPV, we track the movement and deformation of each dry mass region over time.Thus, QPV quantified the magnitude and direction of intracellular velocity in every volume within the cell, including high-velocity tubular regions (Fig. S15).The movement of five such volumes in the nuclear and cytoplasmic regions of the RPE cells shown shows the upward movement of the control volume and the movement of the cells over 30 min (Fig. 4c–d and Movie S2).From these trajectories, we can see that the mass from the central region of the cell is more directional and has smaller scale fluctuations than the mass from the low-density region of the cytoplasm.
QPV shows the spatial and temporal dynamics of intracellular biomass movement.(a) Grid markers at 120X magnification (b) depicting the centroid of the 4 x 4 pixel intracellular volume overlaid on RPE cells, which deformed from (a) to (b) due to cell movement over 30 min .(c) The dry mass initial position within the control volume marked with the magenta box travels along the black line to the final position indicated with the green box in (d) within 30 min.(e) Deformation velocity, the whole-cell velocity minus the intracellular velocity distribution of RPE intracellular dry matter, gives the magnitude of the deviation of each cell’s volumetric motion from its expected position.(f) Deformation velocity of dry matter in the nucleus and cytoplasm of RPE cells, indicating the magnitude of local cellular deformation, showing higher deformation in the cytoplasm than in the nucleus (n = 59, error bars show standard error of the mean).*p < 0.05, **p < 0.01.
QPV data quantifies the overall speed of mass transport across each region within the cell.The distribution of average velocities within the cells over 30 min showed higher average velocities in the cytoplasmic regions and moderate velocities in the nuclear regions (Fig. S16a).To more systematically assess the differences between the cytoplasm and the nucleus, we segmented the nuclear region from the cytoplasm of RPE cells using fluorescence images of expressed FUCCI markers 37, 38 .Separating the velocities in the nucleus and cytoplasm and comparing them with cytocentroid velocities showed no difference, as the nucleus and most of the cytoplasm moved with the cell (n = 59 cells, Figure S16b), with maximum velocities up to ~1 μm/min (Fig. S16c).These maximum velocities correspond to displacements of up to 14 pixels over a 1-minute imaging interval, well within the acceptable error range determined by our error characterization (eg Figure 3).We calculated the deformation velocity as the velocity of the intracellular control volume relative to the velocity of the cell’s centroid.If the cell is moving as a rigid body, the deformation velocity calculates how much each cell’s volume motion deviates from its expected position.It is defined as the difference between each intracellular volume motion relative to the overall motion of the cell’s centroid (often tracked, for example in motility studies).The deformation velocity map (Fig. 4e) overlaid on RPE cells showed a similar distribution to the overall distribution of intracellular velocities (Fig. S16a).However, the velocity magnitudes of regions showing minimal deformation, such as nuclei, decrease to around zero (Fig. 4e).The average deformation velocities of the nucleus and cytoplasm also reflected the larger deformation in the cytoplasm compared with the nucleus (Fig. 4f).Therefore, the nuclei of RPE cells are more in line with the movement of the whole cell body relative to the cytoplasm, and in particular the pods show greater velocities relative to the velocity of the whole cell.We also observed higher activity in the nucleus and cytoplasm during the G1 to S phase transition (Fig. 4f) likely due to increased G1-S transcriptional activity in preparation for DNA replication.
Using QPV, we tracked the intracellular dynamics of mass within each control volume within the cell (Fig. 4c,d) to continuously measure mass transport for 8 h, while monitoring cell cycle progression using the FUCCI cell cycle indicator.Then, based on these data, we performed mean square displacement (MSD) analysis of all tracked intracellular mass deformations or displacements relative to cell centroid displacements for the QPV of RPE cells during the cell cycle (Figure 5).The slope and intercept of the MSD plots were used to measure the abnormal constant and diffusion coefficient, respectively, of each intracellular region tracked with QPV (Fig. 5a–c).To validate our MSD calculations, we compared the abnormality and diffusion constants of live RPE cells to fixed cells that were moved artificially on a platform that displayed an effective zero diffusion rate (Fig. S17).Nuclear boundaries were determined by alignment with fluorescent images of FUCCI cell cycle markers (Fig. 5b, Fig. S18).These data suggest that although the cytoplasmic material exhibits a larger range of displacements than the material within the nucleus (Fig. 5e,f), these displacements indicate a lower average effective diffusivity (Fig. S19a).Both nuclear and cytoplasmic diffusion were consistent with moderate subdiffusion (Fig. 5g), abnormal diffusion (Fig. 5h).
Mean square displacement (MSD) analysis showed that the diffusion coefficient in RPE cells decreased with cell cycle progression.(a) QPI image of a single RPE cell showing red nuclei and black cytoplasmic borders.(b) Abnormally constant distribution within RPE cells from (a).(c) Diffusion coefficient distribution within RPE cells from (a).(e) Log of MSD versus time lag of RPE nuclear volume in (a).The black line shows the mean of all nuclear volumes.(f) Time lag of logarithm of MSD versus intracellular cytoplasmic volume of RPE cells in (a).The black line shows the mean of all cytoplasmic volumes.(g) Separation of diffusion coefficients in the nucleus and cytoplasm of RPE live cells showing a modest but not significant decrease in diffusion coefficients in the cytoplasm relative to the nucleus.(h) Abnormal constants from MSD analysis of the same cells showing moderate subdiffusive transport in both the nucleus and cytoplasm.(i) Nuclear and cytoplasmic diffusion coefficients of RPE cells throughout the cell cycle starting from n = 119 cells.Error bars show standard error of the mean.– p > 0.05 (not significant), **p < 0.01, ***p < 1 × 10-3, ****p < 1 × 10-4.
The average diffusion coefficient in the nucleus was slightly higher than that in the cytoplasm and varied widely (Fig. 5g).To understand this change, we classified diffusion coefficients according to cell cycle stage (Fig. 5g, Fig. S19).These data indicate that nuclear diffusion coefficients decrease with cell cycle progression and cytoplasmic diffusion coefficients decrease through G1 to the onset of S phase, and are consistent with estimates of spatially variable intracellular diffusion rates on similar timescales using quantum dots.The range of diffusion coefficients is also similar to that estimated using genetically encoded multi-measurement nanoparticles (GEMs)41, nanometer-sized particles that can freely pass through the cytoplasm and nucleus.However, QPV showed the opposite trend that the cytosol diffusion coefficient was higher than that of the nucleus.This may be expected because QPV involves diffusion of the intracellular organelle network rather than liquid flow, thereby reducing the effective diffusion coefficient value.As a method to track the mass of intracellular components, we can apply QPI to determine the dependence of the measured diffusivity on its mass for each control volume (Fig. S20a), and perform it separately in different compartments of the cell (e.g., the nucleus) The same analysis (Fig. S20c) and cytoplasm (Fig. S20b).This is close to the expected scale of D ~ m-1/3 predicted from a Stokes-Einstein-type scale, assuming a mass scale with cubic effective particle size, but with significant deviations at the level of individual control volumes.We estimated the effective size of particles tracked by QPV from the power spectrum of the QPI image (Fig. 3a), limited to particles within the window size used for QPV.This resulted in a roughly constant effective particle size throughout the cell cycle (Fig. S19b).
We developed QPV to measure the unstable velocity field of bulk intracellular transport from QPI.Bulk intracellular transport measured with QPV is the transport of all cellular material within the cell, compared to bulk transport across the cell membrane and into the cell.As a label-free method, QPV can be used directly to measure long-term mass transport within cells, such as throughout the cell cycle, and to directly compare cellular compartments.We also applied QPV to quantify the transport properties of subcellular trajectories to measure intracellular effective diffusivity throughout the cell cycle.
Our error contribution model for QPV points to possible improvements.A key insight is that particle size distribution is critical for determining the accuracy of QPV.This suggests that the high-pass filtering scheme can improve the accuracy of QPV by reducing the effective particle size.However, this would lose the applicability of tracking the displacement of the entire cell, since the resulting velocity field would be used for a subset of the intracellular particles.We also note that although Brownian motion was found to be a key limitation in velocity estimation accuracy, as PIV was previously applied to microscopy data to measure flow within microchannels, we found an effect of Brownian motion on QPV.We estimated the effect of the smallest particle size imaged to be less than 3%, while the effect of the largest particle tracked was negligible.We also note that, as an approach based on image registration rather than particle tracking, QPV should be able to handle some degree of particle disappearance and reappearance, for example due to fusion and fission.However, in low feature density regions, the QPV error in fixed cells is generally higher than in feature dense regions, and the appearance/disappearance of individual particles will further increase the error in live cells.
While our presentation focuses on the QWLSI approach to QPI, there are various alternative methods for acquiring 2D or 3D QPI data that may be analyzed using QPV.For example, other 2D QPI methods, such as digital holographic microscopy44, capture a single phase pixel per camera sensor pixel, potentially increasing the number of pixels available for analysis.This would increase the possible interrogation area (eg, allow imaging of more than one cell or cells with a larger spread) and correspondingly increase the computational cost.QPV can also potentially be extended for use with 3D QPI data provided by 3D tomographic QPI imaging45,46.This will come at the cost of increased computation time.As we found, the computation time of the SSD method increases with the size of the query window, which is similar to extending the query window to an extra dimension.However, we anticipate that applying QPV to 3D QPI can be used to resolve 3D transport and study thicker samples, such as round cells and tissue sections.Labeling different organelles in a cell using 3D QPIs can also more accurately reveal the distribution of organelles across the cell height, enabling separation of cellular compartments (such as the nucleus) from the cytoplasm, or quantification of trafficking in individual organelle systems, which can further reveal relevant Organelle Information Interaction of different organelles within the cell.
QPV offers many advantages over alternative methods for studying intracellular mass transport.Unlike many other label-free methods, QPV automatically tracks intracellular features based on PIV.Furthermore, as a label-free method, QPV avoids the problems of phototoxicity, photobleaching, or dilution of the label over time, while still giving intracellular diffusivity results comparable to methods that require labeling.Another major advantage of QPV is that it uses the same analysis for the nucleus and cytoplasm, allowing direct comparison of these two compartments that are difficult to label consistently with other methods.Overall, this work demonstrates that QPVs are invaluable tools for studying intracellular transport and biophysics.
We performed QPI using an Olympus IX83 inverted microscope (Olympus Corporation, Japan) in brightfield with a 100X, 1.3 numerical aperture oil immersion objective and 1.2X magnification to match the Nyquist standard for diffraction-limited imaging with QWLSI (Fig. S12) wavefront propagation Sensor camera 29 (Phasics SID4-4MP (Phasics, France) camera).A 120 ms exposure was performed for QPI image acquisition using red LED illumination (623 nm, DC2200, Thorlabs, USA).We used MATLAB (Mathworks, USA) for automated image acquisition.We connected the illumination source, Retiga camera and stage with MicroManager open source microscopy software47.An Olympus IX83 microscope (Olympus Corporation, Japan) and a Phasics camera were directly connected through MATLAB.At 30 imaging locations in each dataset, QPI images were captured every 1 min and fluorescence images were captured every 30 min.A flip-mirror setup (IX3-RSPCA, Olympus Corporation. USA) enabled alternating fluorescence and QPI.X-Cite 120LED light source (Excelitas Technologies, USA) and Retiga R1 camera (Cairn Research Ltd, UK) at 300 ms exposure for fluorescence, Olympus U-FBNA filter cube for green mAG fluorophore and Semrock mCherry-B -000 filter cube (IDEX Health & Science, USA) for imaging the red mKO2 fluorophore.Homogeneous conditions of 37°C and 5% CO2 were maintained using an Okolab bench top incubator (Okolab, Italy) and a custom-made objective heating ring, the temperature was controlled by a Thorlabs temperature controller (Thorlabs, USA).For live-cell imaging, cells were plated at 30% confluency in Ibidi µ-high-treated dishes.Cells were incubated for two hours after seeding and then moved to the microscope for imaging, starting 40 minutes after transferring the cells to the microscope stage to ensure an even temperature distribution in the dish.For each imaging session, groups of 30 live cells were imaged for 8 hours.
Cell culture procedures were in accordance with University of Utah BSL-2 guidelines.Welm lab (HCI, Utah) donated MCF7 (mammary epithelial cell) cell line in Dulbecco’s Modified Eagle Medium (DMEM) (Gibco™ 11,330,057, Thermo Fisher Scientific, 10% fetal bovine serum (FBS) (Corning™ 35015CV) USA), Fisher Scientific, USA).mKO2-hCdt1 and mAG-hGem-tagged FUCCI expressing RPE-1 cells from Edgar lab (HCI, Utah), prepared by Yiqin Ma, were cultured in Gibco DMEM containing 10% FBS and 5% penicillin-streptomycin.Remove penicillin-streptomycin when imaging cells.Cells divide in a ratio of 1 to 6 to 1 to 3 at less than 80% confluency at a frequency based on their growth rate.
RPE cells donated by the laboratory of Bruce Edgar (University of Utah) received mAG-hGem and mKO2-hCDt1-tagged FUCCI.Cells express the mKO2 tag on Cdt1 in the nucleus during G1 phase (red nucleus) and the addition of the mKO2 tag on Geminin in the nucleus during the G1 to S phase transition (yellow nucleus due to the combination of red mKO2 and green mAG) and mKO2 The loss of -hCdt1, which initiates S phase, results in green fluorescently labeled nuclei in S phase and G2 phase.Fluorescence images of FUCCI-labeled nuclei captured every 30 minutes were segmented using the k-mean algorithm (available as a built-in function in MATLAB) and overlaid with QPI images.We regarded three hours immediately after the nuclear marker turned green and three hours before cytokinesis as the G2 phase of the cell cycle, dividing cells into S and G2 phases.
We stained fixed cells with DAPI (Fisher-NC9677247), grown 80% to 90% confluent after permeabilizing nuclei with methanol at 4ºC to test for mycoplasma contamination.DAPI-stained cells were imaged using a Retiga R1 camera with an exposure time of 500 ms and an Olympus U-FUNA filter cube, illuminated by an X-Cite 120LED.We examined the presence of DAPI-stained puncta outside the nucleus as an indicator of mycoplasma contamination.
The Phasics SID4BIO camera for QPI uses a modified Hartmann mask diffraction grating to calculate phase gradients in two orthogonal directions, which are converted to phase measurements using the Phasics Matlab SDK (Phasics, France).Convert the phase shift to dry mass using an assumed specific refractive index increment of 0.18 µm3/pg of cellular material.The phase shift (\(\phi )\) of light expressed as optical path length is directly related to the dry mass (m) at a given pixel by a specific refractive index increment (α)48 as follows:
where A is the area of ​​each pixel of the phase-shifted image.The QPI images were then background corrected by fitting a fourth-order polynomial curve to regions in the extracellular phase image.
RPE and MCF7 cells were seeded at 40% confluency in Ibidi µ-high treated dishes.Cells were fixed by removing cell culture medium, washing with PBS, and incubating in 4% paraformaldehyde (PFA) for 10 min at 37ºC.PFA was further removed, cells were washed with PBS, refilled with fresh PBS and sealed and stored until imaging.During imaging, 40 min before imaging, warm the dishes to 37ºC in the Okolab bench top incubator to avoid condensation.Cells were imaged as they were translated in each 0.05 µm step in the vertical direction.
SSD was then performed on overlapping discretization interrogation windows of 15 x 15 pixels, spaced 1 pixel apart, in the background-corrected QPI images.The SSD calculation for the two image regions is as follows:
where f and g are two interrogation windows of consecutive images matched using SSD, where x and y are the positions of the pixels that make up the image, M and N are the width and length of the image (in pixels), and u and v are the incoming The displacement of is in each iteration of the SSD calculation.
the second term in the equation.(3) contains the cross-correlation, while the third term is related to the non-uniform energy density of the QPI data.Therefore, SSD can be considered as a method of normalizing the cross-correlation.
The NCC between interrogation windows was measured using the MATLAB function normxcorr2.This function calculates the cross-correlation in the Fourier plane based on the normalized cross-correlation equation to improve computational efficiency.
Here, f and g are the images, and \(\overline{g }\) and \({\overline{f} }\) are the averages of the images.The displacement of the highest pixel from the center pixel in the normalized correlation plane was used to calculate the displacement for each interrogation window.Similar to SSD, NCC normalizes the cross-correlation plane by image autocorrelation division.
Here I(t + \(\Delta\)t) and I(t) are the intensity of the image, the time interval \(\Delta\)t, in our case 1 minute.We use the code provided by 32 for OFR displacement calculations.The BlurSize parameter used to blur the image with Gaussian blur before OFR in the code is set to 1.BlurStd parameters were set to 1, 2, 5, 8 and 12 to understand the effect of Gaussian blur (Fig. S4 c, d).
MI is calculated using a method implemented in MATLAB that extracts mutual information from the joint histogram and joint entropy of the registered images, which is adapted to perform mutual information (MI) on a sliding interrogation window within a grayscale QPI image Image registration calculation.
Our QPV implementation is based on the SSD image registration method34 applied to an interrogation window of 15 x 15 pixels (3.57 x 3.57 µm) within cells.A magnified view of a 15 x 15 pixel interrogation window within the example cell difference image (Fig. 1c) shows the movement of individual cellular components (indicated by red arrows) to positions on the left side of the window, indicated by black arrows (15 x 15 pixels in Fig. 1c). illustration).When this quality pattern within the interrogation window overlaps between two shifted windows from consecutive imaging frames, SSD produces the smallest sum of squared differences (Fig. S1a).Computing a Gaussian fit to the neighborhood of a 3 x 3 pixel region near the SSD minimum gave the subpixel localization of the displacement (Fig. S1b).This leads to the measured displacement that forms the basis of the QPV (Fig. S1c).Spurious velocities were removed using a conditional median filter, thus preserving the original calculated values ​​of subcellular velocities.From these displacement measurements, we calculated mass transport velocities based on known time intervals between frames set during cell imaging (Fig. 1d).Processed using computing resources allocated by the University of Utah Center for High Performance Computing (CHPC).The code is available on GitHub (https://github.com/Zangle-Lab/Quantitative_Phase_Velocimetry).The relative computation time of each image registration method (Fig. S4) was estimated by computing intracellular velocity maps of 10 RPE fixed-cell images per set of interrogation window size on a general-purpose computer with 6 CPU cores Intel i7 8700 K , 3.7 GHz processor and 16 GB RAM.
where Dreal is the actual displacement amplitude introduced by the stage movement and Dmeasured is the average measured displacement amplitude.Dreal, the velocity magnitude, is measured from the x-component (Vx) and y-component (Vy) of the velocity:
The orientation error (Edir) is calculated as the angle between the calculated and actual displacement vector:
θreal is the actual displacement angle introduced by the platform, and the measured \(\theta\) is the average angle measured by the image registration method.Calculated from the x-component (Vx) and y-component (Vy) of the velocity using the four-quadrant arctangent:
fft is the Fourier transform of the image, fftshift rearranges the Fourier transform to move the zero frequency component to the center of the array.Azimuth averaging is performed on the power spectrum of the cell image to convert the power density image into a two-dimensional plot of power density versus frequency.
where λ is the wavelength of the light and NA is the numerical aperture of the objective used for imaging, assuming an illumination of NA = 0 to generate a spatially coherent plane wave for the QPI29.The code to build the granularity-dependent error model is also available on GitHub (https://github.com/Zangle-Lab).
We perform QPV intracellular velocity measurements on 2D QPI images.As a result, features outside the microscope’s depth of field will be out of focus and thus blurred.The depth of field (DOF) of incoherent light illumination can be calculated from the following equation51,
where λ is the wavelength of light, n is the refractive index of the medium between the objective and the sample, NA is the numerical aperture of the objective, M is the magnification, and e is the camera resolution on the CCD plane, used here as the size of the phase pixel.Equation (5) gives a depth of field of 0.85 µm.However, we use near-coherent illumination (NAcondenser ≈ 0) by turning off the condenser as much as possible.Therefore, the depth of field of our system is approximately twice the depth of field calculated by the equation.(12)51, which is 1.7 µm.