Single-cell imaging of ERK signaling using fluorescent biosensors

Summary

Single-cell analysis of the mitogen-activated protein kinase (MAPK) extracellular signal regulated kinase (ERK) activity provides a means to perform highly detailed kinetic studies, assess heterogeneity between cells, and distinguish the subcellular localization of ERK activity. We describe here the methods needed to perform such measurements in a cell type of the investigator’s choosing. We discuss the selection of appropriate reporters, and provide detailed methods for stably introducing reporters, collecting live-cell data, and automatically extracting quantitative information from individual cells.

1. Introduction

Single-cell measurements of signaling proteins are essential to accurately quantify and model their activity within cells. A classic example of the importance of single-cell measurements is the distinction between all-or-none vs. graded control of activity [1]. Signaling pathways are often assumed to operate under graded control, where each cell’s signaling response varies over a continuum to reflect the level of stimulus. However, many signaling pathways exhibit “all-or-none” control, in which at sub-maximal levels of stimulation, some cells respond with maximal levels of signaling, while other cells do not engage signaling at all [2]. Many techniques, such as immunoblotting or ELISA, use homogenized samples that effectively average the pathway’s activity level across a large number of cells, and therefore a half-maximal graded response is indistinguishable from a half-maximal all-or-none response. Beyond the simple examples of graded and all-or-none control, there are numerous other potential scenarios, such as sustained [3], damped [4], or stochastic [5] oscillations in kinase activity. Challenges also arise in tracking signaling kinetics at the population level. For example, the duration of response is a key variable in determining the cellular response to ERK activation [6,7], and cell-to-cell heterogeneity in the deactivation time of the signal can significantly skew population average measurements of signal half-life. With the emergence of single-cell imaging tools, it has become clear that even genetically identical cells display substantial heterogeneity in the responses of many pathways. Because of these considerations, live-cell techniques have become an essential tool for quantitative studies of signal transduction. In the study of ERK/MAPK signaling in particular, these tools have uncovered a range of interesting kinetics and spatial effects that were previously undetectable using classic biochemical methods [8,9,3,10,11,5].

A second advantage of live-cell measurements is the ability to obtain data at high temporal and spatial resolution. Unlike methods in which cells must be fixed or lysed, live-cell measurements are limited only by the speed at which images can be acquired and stored (typically seconds or less). Each image also typically contains multiple cells (often hundreds), and sufficient resolution to distinguish multiple subcellular locations (e.g. nucleus, cytosol, plasma membrane). Of course, such measurements rely on accurate reporters. While live-cell microscopy was once limited to labs with access to the appropriate equipment and expertise, recent advances have substantially improved the dynamic range, sensitivity, and overall usability of numerous reporters. At the same time, standard microscopy equipment has become more sophisticated, making time-lapse capabilities available at most institutions. Here, we focus on reporters for ERK because 1) the kinetics of its activation are known to play an important role in determining cell fate choices, 2) it serves as a model system in many systems biology studies, and 3) it has been investigated using multiple single-cell methods, providing a useful illustration of the different strategies that can be employed for tracking kinase activity.

There are a number of established strategies for tracking ERK activity in living cells, most of which rely on engineering of various fluorescent protein (FP) variants, such that ERK activity results in a change in fluorescence pattern or intensity within the cell. Because the genes encoding these reporter proteins can be integrated into the genome of the cell of interest and expressed constitutively, they represent a relatively low-cost and convenient means for making repeated measurements of ERK activity. It is also possible to express these reporter genes transiently, but stable expression allows much higher quality data to be collected by ensuring a steady level of expression in a high percentage of cells throughout the experiment. Several caveats must be kept in mind when using such reporters. First, there exists the possibility that reporter expression can result in significant changes to endogenous signaling kinetics, for example by providing additional substrates for ERK that act as competitive inhibitors to endogenous substrates. This possibility has been investigated in several cases, using alternate methods to monitor signaling and to compare behavior between naïve and reporter-transfected cells [8,10]. Changes in signaling as a result of reporter expression have been reported to be minimal, but nonetheless should be investigated when establishing a new reporter cell line. Second, it must be kept in mind that all reporters for ERK (or any other enzyme) produce an indirect measure of the activity of the kinase. The readout of a reporter is affected by the kinetics of interaction with the enzyme, the availability of inactive reporter, and the reversibility of the visualized reaction, and all of these factors may vary over the course of the experiment. One useful approach is to incorporate the process of reporter activation into quantitative models of the system being studied [12], or to develop “data models” that allow raw reporter data to be converted to an estimate of the actual kinase activity [13].

The earliest strategy for live-cell ERK measurements relied on ERK-FP fusion proteins, exploiting the tendency of ERK itself to translocate to the nucleus upon its activation by MEK [14]. In cells where an ERK-FP fusion is expressed either from the endogenous genomic locus [4] or from an exogenous sequence [3], ERK activation can be monitored by quantifying the intensity of nuclear relative to cytosolic fluorescence. A challenge in using such reporters lies in expressing the ERK-FP fusion at a sufficient level to enable detection, but not overexpressing it to the extent that its activity alters the endogenous signaling pathway through negative feedback. A second issue is that, while nuclear localization of ERK coincides with its activity immediately following pathway stimulation, ERK localization and activity can diverge significantly after 30 minutes [9], making ERK-FP fusions unsuitable for measuring long-term activity.

A more recent variant on the nuclear-to-cytosolic translocation assay, termed a kinase translocation reporter (KTR), consists of an FP fused to a synthetic substrate peptide in which a nuclear localization sequence (NLS), a nuclear export sequence (NES), and an ERK phosphorylation motif are interspaced in such a way that phosphorylation suppresses the effect of the NLS and leads to export of the FP from the nucleus to the cytosol [13]. Dephosphorylation of the reporter favors import into the nucleus, and activity of ERK can therefore be assessed by the ratio of cytosolic to nuclear fluorescence. While the readout mode is the same as for ERK-FP, this construct more directly indicates the kinase activity of ERK, rather than its localization.

A widely used approach based on Forster Resonance Energy Transfer (FRET), has also proved highly effective for ERK activity measurements [15,16]. Several generations of FRET-based ERK activity reporters have been constructed, using variants of cyan and yellow fluorescent proteins (CFP and YFP respectively) as a donor-acceptor pair for FRET [17,11,18]. In each of these versions, the CFP and YFP proteins are joined as a single polypeptide by a linker that features a docking and phosphorylation motif for ERK, a flexible region, and a phospho-amino acid binding domain (PAABD; typically a WW domain). Upon phosphorylation of target sequence by ERK, intramolecular binding of the PAABD domain to the phosphorylated residue forces CFP and YFP into close proximity, resulting in a FRET interaction that can be detected by ratiometric imaging. These reporters respond rapidly to ERK signals and can provide spatial resolution within the cell.

A fourth strategy for ERK activity measurement utilizes naturally occurring peptide sequences from immediate-early genes such as c-Fos and Fra-1 that target them for proteasome-mediated hydrolysis [10]. Phosphorylation of these sequences by ERK delays degradation [19]. When these sequences are fused to an FP, the resulting protein has a half-life dependent on its ERK phosphorylation status [10]. Like other degradation-based reporters [20], this strategy has a large dynamic range, but responds relatively slowly, on the scale of 30-60 minutes, to changes in ERK activity. Consequently, this reporter is best suited for long-term or endpoint measurements.

The cell culture, imaging, and analysis methods described in this chapter can be applied to any of the reporters listed above. Each reporter has its own advantages and drawbacks, and the choice of reporter must be made carefully with respect to the system being used and the objective of the study. Sensitivity, dynamic range, response time, and ability to resolve spatial effects vary between the reporters (Table 1), and it must be determined whether these characteristics are sufficient to effectively perform the desired experiment. One must, for example, consider the biological effects mediated by ERK that are under study; if the effects of ERK on migration are to be studied, the spatial resolution and rapid response time of a FRET reporter would be best, whereas a study of ERK’s involvement in gene expression may favor a slower but more sensitive degradation-based reporter. A small number of studies have directly or indirectly compared some of these reporters, and can be a useful resource in deciding which reporter is best suited for the system to be studied [11,9,10]. For example, direct comparison of FRET- and translocation-based ERK activity reporters indicated a high concordance between these different types of reporters, with minor kinetic differences on the scale of 1-3 minutes during the activation and deactivation phases [11]. A more comprehensive comparison across all reporter types has yet to be performed.

Table 1.

Characteristics of different ERK reporters

Reporter	Spatial resolution of activity	Dynamic range	Response time (time to half- max)	Sensitivity of detection of ERK activity	Preferred delivery method	Choice of FP color	Sensitive to cell shape
FP-ERK	No	+	~3min	+	Viral	Any	Yes
FRET	Yes	+	~1 min	++	Transposon	Limited to FRET pairs	No
KTR	No	++	~3 min	++	Viral	Any	Yes
degron	No	+++	~150 min	+++	Viral	Any	No

In the following sections, we present a step-by-step guide to single-cell analysis of ERK activity, beginning with the introduction of reporters into the cells of interest using retroviral transduction (see Note 1), followed by preparation for live-cell microscopy and collection of time-lapse images. We also present a detailed guide to extracting quantitative data on individual cells from raw time-lapse image files. This data processing “pipeline” comprises several steps: (1) Segment each image to find cell centroids and create masks for nucleus regions; (2) track cell centroid positions over time; (3) link tracked positions to nuclear masks, create masks for cytoplasm regions, and calculate intensity values within each mask. The result is a dynamic trace over time for each cell (Figure 1). The pipeline performs step 1 on all images in a time series before moving on to step 2 to track cells from image to image, and then step 3 on each image sequentially again (Figure 3A).

Figure 1.

Example data from an MCF-10A cell line expressing ERK-KTR. All steps for experimental setup and data analysis were performed essentially as described in the text, and the ERK activity was calculated as the cytosolic to nuclear ratio of ERK-KTR fluorescence. The top two panels depict two representative individual cells; the third panel shows the population mean (line) and 25^th to 75^th percentile range (shaded area) for >500 cells. In the heatmap shown in the bottom panel, each row depicts one cell, with activity indicated by color shading. All panels are aligned to the same time scale on the horizontal axis. Note the differences between individual cells and population mean behavior.

Figure 3.

A) Flowchart summarizing the data processing procedure. B) Sample image with a cytoplasmic reporter, showing a background region, centroids (left) and masks (right, inner light circle: nuclear mask, outer dark circles: donut-shaped cytoplasm mask). Some centroids and masks omitted. C) Segmentation thresholds, after gradient filtering, shown as shaded slices into a 3D version of the image. Darker shades are below more slices. Each slice yields a binary image, with masks in white that are then filtered for nucleus-like shape.

2. Materials

2.1. Cell lines

1. 293T cells for non-viral transduction and packaging of viral vector, (such as 293T/17 from American Type Culture Collection).

2. Target cells of interest. We have successfully applied the methods described here to a wide range of cells, including human and mouse cell lines of both tumor and non-tumor origin, and non-immortalized primary human fibroblasts.

2.2. Culture media and viral production reagents

1. 293T cell growth media (supplies obtained from Life Technologies): DMEM supplemented with 10% Fetal Bovine Serum and Penicillin (50 units/ml)/Streptomycin (50 μg/ml).

2. 0.25% Trypsin-EDTA solution (Life Technologies)

3. Sterile 6-well tissue culture plates (Corning)

4. Polybrene (hexadimethrine bromide) 4 mg/ml in water (Sigma-Aldrich)

5. Selection antibiotic (optional)

6. Poly-D-Lysine plate coating: Prepare 0.1 mg/ml solution of poly-D-lysine by dissolving 5 mg of poly-D-lysine (Sigma-Aldrich) in 50ml of sterile distilled, deionized water. Filter the solution through a 0.22 μm filter in a sterile biosafety cabinet and store at 4°C.

7. Optimem (Life Technologies)

8. FuGENE HD Transfection Reagent (Promega)

9. 10 ml syringe

10. 0.45 um syringe filter

11. Viral packaging vectors, such as psPAX2 (Addgene #12260) and pMD2.G (Addgene #12259). Select packaging vectors that are compatible with the viral vector being used to carry the reporter and the target cell line. (See Note 2 on vector selection).

2.3. Live-cell imaging materials and reagents

1. Collagen coating solution (20 μg/ml) for plates: Prepare 0.1 N acetic acid by adding 46 μl glacial acetic acid to 40 ml ultrapure water (prepared from deionized water purified to 18 MΩ cm at 25° C) in a sterile 50 ml conical tube. Filter the acetic acid through a steriflip filter (Millipore) in a sterile tissue culture hood. Add 267 μl rat tail collagen I (Gibco A10483-01, 3mg/ml) (see Note 3) to the sterile acetic acid and mix well. Store at 4° C. This collagen preparation is suitable for mammary epithelial cells (MCF-10A) but different collagen preparations may be optimal for other cell types.

2. Multi-well plates for cell imaging: Sterile well plates for imaging with high performance glass were obtained from Cellvis.com (24 well: P24-1.5H-N; 96 well: P96-1.5H-N) and Brooks Life Science Systems, Brooks.com, (square 96 well: MGB096-1-2-LG-L).

3. Pipetting supplies: 20 μl, 1 μl pipettors; 5-300 μl 8 or 12 channel multipipettor, multichannel aspirating tool (See Note 4), sterile reagent reservoirs (Costar 4871 sterile 50 ml reagent reservoirs)

4. Imaging medium for cells. In principle, regular growth medium can be used, but due to the fluorescence of several medium components, background levels will be high. Medium formulations lacking the primary contributors to background fluorescence - phenol red, riboflavin, and folic acid - are recommended for optimal data collection. Fluorbrite medium from Invitrogen is one such low-fluorescence DMEM alternative; customized media formulations suited to the cells of interest are available from a number of vendors.

5. Wide-field epifluorescence microscope equipped with a digital camera and an environmental control chamber for samples. We employ a Nikon Eclipse Ti (with the associated NIS Elements software), an Andor Zyla 5.5 camera, a Lumencor Sola light source, and an In Vivo Scientific stage-top incubator.

2.4. Image processing equipment

1. Image processing workstation: Processing the time lapse image data requires a computer with at least 4 GB RAM (see Note 5), capable of running scripting software; we use Windows (see Note 6) computers running MATLAB.

3. Methods

All work should be performed in a sterile tissue culture hood using sterile technique. Follow your usual procedures for cell culture of the cells of interest.

3.1. Cell line construction

1. Prepare purified plasmid DNA for the reporter of choice and appropriate viral packaging plasmids. (see Note 7 on plasmid purity)

2. Coat 6-well plates with 1 ml of poly-D-lysine solution for 1 hour at 37° C, to promote cell adhesion during transduction process.

3. Aspirate poly-D-lysine from the 6-well plate and allow the plate to dry.

4. Rinse a 10-cm plate of 293T cells at >70% confluence with 5 ml PBS, then add 2 ml of Trypsin/EDTA. Incubate for 5 minutes at 37° C.

5. Add 10 ml of 293T growth medium to 10-cm plate, and pipet repeatedly to remove cells from the surface. Transfer the cell suspension to a 15 ml conical tube and centrifuge at 300xg for 3 minutes.

6. Remove supernatant, and resuspend the cell pellet in 10 ml 293T growth medium.

7. Transfer 20 μl of cell resuspension to a hemocytometer and perform cell counting.

8. Seed 6-well plate with 750,000 293T cells per well, in a total volume of 2-3 ml growth medium.

9. Incubate 293T cells overnight at 37° C with 5% CO₂. On day two, 293T cells should be approximately 70% confluent.

10. Adjust growth media volume on 293T cells by aspirating media and pipetting 900 μl of fresh growth media to each well in the six well plate.

11. Prepare one transfection mixture for each well. In the following order combine reagents in a 1.5ml Eppendorf tube: 100 μl Optimem, 3 μl FuGENE HD, 1 μg packaging plasmid, and 1 μg retroviral plasmid DNA.

12. Incubate transfection mixture for 5-10 minutes at room temperature.

13. Add transfection mixture dropwise to each well of the 6-well plate.

14. Incubate 293T cells at 37° C with 5% CO₂ for 6 hours. Alternatively, 293T cells can be incubated overnight.

15. Aspirate medium and replace with 1ml growth medium.

16. At 24 hours and 48 hours after removing the transfection mixture collect the growth medium using a syringe. Filter the virus-containing media through a 0.45 μm syringe filter and into a collection tube.

17. Replace 293T growth media with another 1 ml of growth media, or discard the plate if no additional virus is needed. We typically do two collections, but 293T media can continue to be collected for up to 72 hours if more virus is needed.

18. Store viral particles for up to two weeks at 4° C or up to 1 year at −80° C.

19. Seed target cells in 6 well plate at an optimized seeding density. For human mammary epithelial cell lines (such as MCF-10A or 184A1), we use a concentration of 100,000 cells per well. At this concentration, cells are within the linear phase of cell growth and become confluent at the time of selection (4 days post seeding).

20. Incubate cells overnight at 37° C with 5% CO₂.

21. Prepare the transduction mixture by combining 500 μl of target cell growth media, 500 μl of filtered viral particles, and 1 μl of 4 mg/ml polybrene, and mix gently by pipetting. A final concentration of 4 μg/ml polybrene promotes adsorption of viral particles and limits cytotoxicity in MCF-10A cells, but up to 10 μg/ml can be used in difficult to transduce cell lines. Additionally, the volume of virus-containing media can be adjusted as needed (see Note 8).

22. Aspirate media from target cells.

23. Add transduction mixture dropwise to target cells and incubate overnight at 37° C with 5% CO₂.

24. Aspirate medium and replace with 2 ml growth media, and incubate overnight at 37° C with 5% CO_2.

25. After incubating cells for approximately 24 hours post transduction, check cells for reporter expression using a fluorescent microscope.

26. If viral reporter construct included an antibiotic resistance cassette, add the appropriate concentration of the selection antibiotic to the target cells (see Note 9).

27. Monitor cells daily during selection process and change media containing the selection antibiotic every 3-4 days. When selection is complete, only cells stably expressing the reporter construct will remain growing in 6-well plate. See Note 10 regarding optional further selection steps.

3.2. Plating cells for live-cell microscopy experiments

In the protocol described here, a cell monolayer is created on a small (2-5 mm diameter) spot within a 24-well plate (Figure 2). Covering just a small portion of the well surface reduces the number of cells in the well to just what is needed for imaging, while maintaining the same cell density that would be used in other assays. Because cells actively deplete growth factors and nutrients from the medium, using a smaller number of cells is highly preferable for long-term imaging experiments because it allows a more constant medium composition to be maintained throughout the experiment. For variations in which the entire well surface is used, see Note 11.

Figure 2.

Schematic of cell plating process in 24-well plates for imaging. To enable a small number of cells to be grown at normal density within a larger-volume well, a small region in the center of the well is first coated with collagen. Cells are then allowed to adhere to this region before a large volume of medium is added. This process reduces the rate of nutrient depletion from the medium and enables cells to be maintained in a relatively constant environment for longer periods of time during imaging within a multi-well plate.

1. Use a 20 μl pipettor to spot 3 μl of collagen coating in the center of each well (see Note 12). Allow the collagen drop to just touch the plate with no contact from the pipet tip. Cover the plate and incubate for 30 min to 1 hr in a sterile hood.

2. Use a Pasteur pipet attached to a vacuum line to aspirate any liquid collagen remaining on the spots. Gently add 1 ml sterile PBS along the sides of the wells to rinse the collagen spot. Avoid pipetting directly on the spot. Aspirate the PBS and remove the last bit of PBS adhering to the spot by barely touching the pipet tip to the top surface of the fluid. Avoid touching the tip of the pipet to the glass plate as it will leave a mark.

3. Trypsin treat and passage your cells as usual to obtain a suspension of single cells (see Note 13).

4. We typically load 5,000 cells in 10 μl media to each spot in the wells. To calculate the proper cell dilution, thoroughly mix the cell suspension and count on a hemocytometer (see Note 14).

5. Cells will settle, so remix the cell stock and make 1 ml of the calculated cell dilution in a sterile Eppendorf tube. Mix well by pipetting up and down with a 1 ml pipettor. Use a 20 μl pipettor and apply 10 μl of cell solution to the dried collagen spots in each well. Avoid touching the glass plate. Cells will settle out so continue mixing the cell solution if the spot pipetting step takes more than a few minutes.

6. Add PBS to all spaces in the plate between wells to raise the humidity in the plate and help prevent drying of the cell spots. Cover the plate and incubate in a 37° incubator for approximately 2 to 2.5 hrs.

7. Look at your cell spots using an inverted microscope. If the cells look more elongated or have small processes you can add more media. If the cells are spherical they likely need more time to attach.

8. When cells are attached to the plate, gently add 0.5 ml growth media by slowly pipetting the media down the side of the well. View with a microscope to make sure your cells are still attached. Incubate at 37° overnight to allow cells to fully attach.

9. Check cells with a microscope. When cells are fully attached you may start experimental treatments. We use a specially formulated imaging media with reduced autofluorescence for microscopy experiments.

3.3. Collecting live-cell microscopy data

1. Turn on microscope, computer, and environmental control box, start NIS Elements software. Allow the temperature and CO₂ levels to stabilize.

2. Transfer plate to microscope and mount securely in plate holder. Make sure all set screws are tightened.

3. In NIS Elements, open the ND Acquisition panel.

4. Set path and filename for saving data. Data are automatically saved when experiment is complete.

5. In the Time tab select the imaging interval and total imaging duration. (See Note 15)

6. In the Wavelength tab select the desired fluorescent channels for the experiment.

7. Navigate to the first well in the imaging sequence and find cells. Turn on “Perfect Focus” and set the appropriate focal plane using the focus wheel.

8. Open the Zyla Settings panel and set the exposure for each channel to be used in imaging experiment.

9. Using the joystick, navigate to a suitable area for imaging; try to avoid areas where cells are overcrowded.

10. In the ND Acquisition panel select the XY tab. Navigate to the first desired ROI using the joystick and select the XY point by checking the box in the XY selection tab. (See Note 16)

11. Continue selecting ROIs in each desired well by navigating to each ROI and selecting the coordinate using the checkbox. Adjust focal plane at each ROI as necessary using Perfect Focus. (See Note 17)

12. To select a background ROI (optional), navigate to an XY position which contains no cells in the field of view. This will be used later to calculate background during image processing.

13. When all ROIs have been selected return to first ROI and check that focus and exposure are set correctly and that the plate has not shifted.

14. Start imaging experiment by hitting the “Run Now” button.

15. To add treatments (such as inhibitors or growth factors) during imaging, pause imaging experiment using the “Pause” button on the Acquisition Window. (See Note 18).

16. Remove plate lid and environmental control box, add treatments to each well. Try to minimize contact with plate to avoid shifting plate position.

17. Return lid and environmental control box to plate.

18. Resume imaging using the “Resume” button on the Acquisition Window.

19. Once the time course has completed, the file will be saved in the location specified during imaging set up. Alternatively, terminate the image acquisition using the “Finish” button.

20. Close NIS Elements and shutdown microscope.

3.4. Data analysis to extract single-cell kinetics from raw image data

1. Install necessary software per distributor instructions (see Note 19). MATLAB requires a license purchased from Mathworks, which can be acquired individually if not available via an institution. The uTrack toolbox used for tracking cell positions over time can be obtained from the Danuser Lab website, http://lccb.hms.harvard.edu/software.html (see Note 20). The Bio-Formats toolbox for MATLAB is useful for reading image data directly from a variety of file types, including Nikon’s ND2 files, and is available from http://downloads.openmicroscopy.org/bio-formats/5.1.7/ (see Note 21).

2. Access image data from storage. This is specific to the imaging software used to operate the microscope. Nikon’s ND2 files can be directly accessed using Bio-Formats

   bfopen

   and

   bfGetReader

   functions. Steps 3 – 9 are then performed for each image, one at a time, then 10 – 11 are performed to track cells between images, followed by steps 12 – 13 to align tracked cells and store values as a dynamic trace (see Note 22).

3. Remove background intensity from the image. Select a region of only background (no cells, etc.) and evaluate the mean value (Figure 3B). To do so in NIS Elements, start with the image opened and select from the top menus, “ROI” > “Draw Rectangular ROI…”. Use the cursor to click and drag a box over the desired region. The box may be moved and resized afterward. To get mean intensities in the region, select “Measure” > “Measure Field and ROIs…”; ensure the pop-up has “Current Frame” selected and click OK. To view values, select “View” > “Analysis Controls” > “Automated Measurement Results”. The mean values for each channel in your image will be shown at the end of the table displayed (see Note 23). Subtract the background level from each image.

4. Prepare the image for segmentation by filtering to reduce noise. Define a Gaussian filter sized to cover approximately 1/10^th of a cell nucleus (see Note 24), and apply it to the image. MATLAB code to implement is provided below, where maxNucD is the maximum estimated diameter of a nucleus, in pixels, and im is the image, as a 2-D matrix (see Note 25).

   fltsz = floor( maxNucD/10 );
   gaussianFilter = fspecial('gaussian', fltsz.*[1, 1], fltsz/2);
   im = imfilter(im, gaussianFilter, ‘replicate’);
   

5. (Optional) If the only reliable marker in the image is located in the cytoplasm, apply a gradient filter to emphasize ‘edges’, where the intensity changes quickly, i.e. the border between nucleus and cytoplasm; then invert the image to make nuclear regions bright. Filter for the magnitude of gradients by applying a Sobel filter in both X and Y directions and taking the square root of the sum of each filtered image squared (see Note 26). Invert the resulting gradient magnitude image by subtracting the image from its maximum value. Example MATLAB code is provided below, where im is the image, as a 2-D matrix.

   hy = fspecial('sobel');   hx = hy';
   im = sqrt(imfilter(im, hx, 'replicate').^2 …
            + imfilter(im, hy, 'replicate').^2);
   im = max(im(:)) − im;
   

6. Segment features in the image by examining regions that exceed a threshold value, for a series of different thresholds. Determine thresholds to use by selecting 20 linearly spaced values between the 5^th and 95^th percentile image intensity values (see Note 27). For each threshold, create a binary map, true where the image exceeds the threshold (Figure 3C). Perform steps 7 and 8 for each threshold before continuing to the next. Example MATLAB code, where s is an index to operate on a single threshold at a time, as in a for loop:

   thresholds = quantile(im(:), linspace(0.05, 0.95, 20) );
   tim = im > thresholds(s);
   

7. Remove “salt and pepper” noise in the binary image by morphological dilation and erosion (see Note 28). Example MATLAB code (in a for loop over thresholds, the structuring elements can be defined above the loop):

   st1 = strel('disk', ceil(fltsz/4));  
   tim = imdilate(tim, st1);
   tim = imerode(tim, strel('disk', 2*ceil(fltsz/4)));
   tim = imdilate(tim, st1);
   

8. Identify each binary feature and filter for those matching the feasible size and shape of a cell nucleus (see Note 29). Size is evaluated by the total area, and shape by the squared ratio of the ideal perimeter for a circle of that area to the actual perimeter. For each threshold, retain features passing the filter by setting corresponding pixels to true in an initially all false image (here

   imkeep

   ). Example MATLAB code, where

   minNucD, maxNucD

   are predefined based on the expected diameter of a cell nucleus in the image, and

   minFormfactor

   by the expected circularity:

   maxNucArea = round(pi*maxNucD^2/4);
   minNucArea = round(pi*minNucD^2/4);
   S = regionprops(tim, 'Area', 'Perimeter', 'PixelIdxList');
   nucArea  = cat(1,S.Area);
   nucPerim = cat(1,S.Perimeter);
   nucFormfactor = 4*pi*nucArea./(nucPerim.^2);
   szScore = (nucArea - minNucArea).*(maxNucArea - nucArea);
   shScore = nucFormfactor - minFormfactor;
   scorePass  = szScore >= 0 & shScore >= 0;
   for ss = find(scorePass)'; imkeep(S(ss).PixelIdxList) = true; end
   

9. Create a data structure (

   movieInfo

   here) for the uTrack function to use, defining coordinates under fieldnames

   xCoord

   and

   yCoord

   , and an amplitude as amp (see Notes 30 and 31). Provide the area as the amplitude. Example MATLAB code:

   S = regionprops(imkeep, 'Centroid', 'Area');
   coord = cat(1,S.Centroid);
   nCoord = size(coord,1);
   movieInfo.xCoord = [coord(:,1), zeros(nCoord,1)];
   movieInfo.yCoord = [coord(:,2) , zeros(nCoord,1)];
   movieInfo.amp = [cat(1, S.Area) , zeros(nCoord,1)];
   

10. Track cell positions over time to link values into dynamic traces, using particle tracking software (uTrack 2.0, here). Provide the data structure movieInfo and operational parameters for uTrack (see Note 32). Many operational parameters are employed and we set the relevant time window and spatial radius of interest by scaling (see Note 33), based on the time interval between samples (

    tsamp

    ) and the size of pixels (

    PixSizeX and PixSizeY

    ). Example MATLAB code:

    tWin = ceil(15*5/tsamp);
    iRad = 25/sqrt(p.PixSizeX.^2 + PixSizeY.^2);
    
    gapCloseParam.timeWindow = tWin;
    gapCloseParam.mergeSplit = 1;
    gapCloseParam.minTrackLen = 3;
    gapCloseParam.diagnostics = 0;
    
    costMatrices(1).funcName = …
         'costMatRandomDirectedSwitchingMotionLink';
    parameters.linearMotion = 0;
    parameters.minSearchRadius = 2;
    parameters.maxSearchRadius = iRad;
    parameters.brownStdMult = 6;
    parameters.useLocalDensity = 1;
    parameters.nnWindow = tWin;
    parameters.kalmanInitParam = [];
    costMatrices(1).parameters = parameters;
    clear parameters
    
    costMatrices(2).funcName = …
         'costMatRandomDirectedSwitchingMotionCloseGaps';
    parameters.linearMotion = 0;
    parameters.minSearchRadius = 2;
    parameters.maxSearchRadius = iRad;
    parameters.brownStdMult = 6*ones(tWin,1);
    parameters.brownScaling = [0.25 0.25];
    parameters.timeReachConfB = 1;
    parameters.ampRatioLimit = [0.4 3];
    parameters.lenForClassify = 5;
    parameters.useLocalDensity = 1;
    parameters.nnWindow = tWin;
    parameters.linStdMult = 6;
    parameters.linScaling = [0.25 0.25];
    parameters.timeReachConfL = 1;
    parameters.maxAngleVV = 360;
    parameters.gapPenalty = 1;
    parameters.resLimit = [];
    costMatrices(2).parameters = parameters;
    clear parameters
    
    kalmanFunctions.reserveMem  = 'kalmanResMemLM';
    kalmanFunctions.initialize  = 'kalmanInitLinearMotion';
    kalmanFunctions.calcGain    = 'kalmanGainLinearMotion';
    kalmanFunctions.timeReverse = 'kalmanReverseLinearMotion';
    
    saveResults = 0;  verbose = 0;   probDim = 2; 
    tracksFinal = trackCloseGapsKalmanSparse(movieInfo, …
         costMatrices, gapCloseParam, kalmanFunctions, probDim, …
         saveResults, verbose);
    

11. Extract tracked coordinates from the uTrack output. uTrack returns a structure (

    tracksFinal

    ) that contains track coordinate information (in the field

    tracksCoordAmpCG

    ) and event timing information (in the field

    seqOfEvents

    ). Together these identify the start and end of each track, including when tracks appear to split or merge, and the associated coordinates (see Note 34). Extract the major track from each entry (from the true start to the true end). Example MATLAB code:

    nT = max( arrayfun(@(x)x.seqOfEvents(end,1), tracksFinal) );
    nC = length(tracksFinal);
    c = nan(nC, nT, 2);
    for s = 1:nC
         truei = isnan(tracksFinal(s).seqOfEvents(:,4));
         starti = tracksFinal(s).seqOfEvents(:,2) == 1;
         [tm, ti] = …
    	  min( tracksFinal(s).seqOfEvents(starti & truei, 1) );
         li = tracksFinal(s).seqOfEvents(ti,3);
         ct1 = (tracksFinal(s).seqOfEvents(:,3) == li);
         sf = tracksFinal(s).seqOfEvents( ct1 & truei & starti, 1);
         ef = tracksFinal(s).seqOfEvents( ct1 & truei & ~starti, 1);
         nf = ef-sf + 1;
         c(s, sf:ef, 1) = …
    	  tracksFinal(s).tracksCoordAmpCG(li,1:8:8*nf);
         c(s, sf:ef, 2) = …
    	  tracksFinal(s).tracksCoordAmpCG(li,2:8:8*nf);
    end
    

12. Align tracking with nuclear masks for each image. This step, along with 13 and 14, are repeated for each image. In this step, the stored mask image is re-labeled using

    bwlabel

    to uniquely identify each nuclear region, and the index value at each track coordinate is found (see Note 35). Here, the coordinates,

    c

    , are only the values at one time point (one column of

    c

    from step 11, e.g.

    c(:,4,:)

    for time point 4). Similarly, imkeep represents the mask image from the same time point (each stored from the previous processing). Example MATLAB code for one time point:

    c = round(c);
    lind = sub2ind( sz, c(:,1,2), c(:,1,1) );
    gi = find(lind>0);   lind = lind( gi );
    nuclm = bwlabel(imkeep);
    lbl = nuclm(lind);
    

13. Create masks in the cytoplasm region by forming an annulus around each nuclear mask. Dilate the nuclear mask to create a larger (filled) version that extends into the cytoplasm, then remove a smaller dilation to make a hole over the nuclear area (see Note 36). The size of dilations to use can be scaled with the expected nucleus size (see Note 37). Example MATLAB code for one time point:

    ncgap  = floor((0.05*maxNucD)) + 2;
    ncring = floor((0.05*maxNucD)) + 1;
    ncexpand = ncgap + ncring;
    expdisk = strel('disk', ncexpand);
    cytlm = imdilate(nuclm, expdisk);
    ctemp = nuclm; ctemp(ctemp == 0) = Inf;
    ctemp = -imdilate(-ctemp, expdisk);
    ctemp(ctemp == Inf) = 0;  cytlm(~(ctemp==cytlm)) = 0;
    cytlm = cytlm.*~(imdilate(nuclm, strel('disk', ncgap))>0);
    

14. Calculate mean values for each nucleus and cytoplasm mask. This is done serially for each mask. Note that the image im used here should be the original image, background subtracted (see Notes 38 and 39). Here, gi and lbl are used to align the calculated values with tracking to form complete dynamic traces vmean. Example MATLAB code for one time point:

    for s = find(lbl)'
         nmask = nuclm == lbl(s); cmask = cytlm == lbl(s); 
         vals = im(nmask);  pctb = prctile(vals,[20,80]);
         vmean(gi(s),1,1) = …
    	  mean(vals(vals > pctb(1) & vals < pctb(2)));
         vals = im(cmask);  pctb = prctile(vals, [20,80]);
         vmean(gi(s),1,2) = …
    	  mean(vals(vals > pctb(1) & vals < pctb(2)));
    end