Assessment of the consistency of cell contours determined by different imaging modalities
To facilitate quantitative analysis of contours from cells with a wide variety of shapes and sizes, we sought to implement an algorithm that made no assumptions about specific cell shapes and that extracted a parameter-free contour not subject to user biases. The Morphometrics algorithm can be conceptualized in two stages. First, with a small number of user-defined parameters, discrete ‘objects’ are detected as contiguous groups of pixels through watershed and distance-transform segmentation. Second, a smooth parameter-free contour defining the boundary of each object is calculated by treating the image intensity as a metric surface on which contour ‘energy’ can be minimized, with the segmented object boundary as an initial contour guess. Further information about the algorithm can be found in the Morphometrics user manual included with the software download. Three types of images can be used for contour detection: i) phase contrast images, in which the cell interior appears dark; ii) interior fluorescence images, e.g. from uniformly distributed cytoplasmic fluorescent proteins; and iii) peripheral fluorescence images, e.g. from membrane dye. Calculating the magnitude of the image gradient transforms the first two image types into an intensity map similar to that given by a fluorescence marker on the surface, which constitutes the common basis for calculating contours.
After optional image scaling, contrast adjustment, and background removal, the software offers multiple algorithms for segmenting contiguous groups of pixels (objects) that meet specified constraints on size and intensity. Each object is checked against criteria for false-positive detection based on the ratio of interior to boundary pixel intensities and, depending on user input, these objects may be linked with objects in other frames for tracking across a set of time-lapse images (see examples in the Morphometrics user manual). Parameters may be tested on individual images before being applied to the processing of large data sets. Ultimately, each segmented region serves as a seed to begin contour fitting. Once a contiguous object composed of discrete pixels is identified, a contour is calculated by treating the intensity features of the object as an interpolated energy landscape and then fitting a closed-loop contour in continuous coordinates to the minima of that energy landscape. From the cell contours, Morphometrics can be used to calculate an interior mesh; for rod-shaped cells, this mesh defines a cellular coordinate system with a midline and associated perpendicular meshlines that connect the two sides of the cell, thereby also measuring local cell width along the midline. The contour is also used to calculate one-dimensional profiles such as curvature (a measure of the radius of the circle that best fits the contour surrounding a particular point and whether the contour is concave or convex), fluorescence signals along the cell boundary (e.g., membrane dye, surface markers [3], or membrane-bound proteins [38]), or fluorescence signals along the interior centerline of the cell, among other features. Optical shifts between fluorescence imaging channels can be corrected by translating the contour coordinates by an amount appropriate to the particular imaging system; these translation values can be determined visually using the included post-processing contour viewing software.
To illustrate the capabilities of Morphometrics for contour detection, we stained E. coli cells expressing cytoplasmic GFP with the surface marker Alexa 594-conjugated Wheat Germ Agglutinin [3] and imaged the cells using phase contrast and epifluorescence microscopy (Fig. 1a, top). Morphometrics successfully segmented isolated and dividing cells (Fig. 1a, middle) from all three imaging modalities (phase contrast (PC), interior fluorescence (IF), and peripheral fluorescence (PF)), leading to three sets of contours, with the PF contour exterior to the IF contour as expected (Fig. 1b). The meshlines for these cells (Fig. 1c) define a cellular grid that can be associated with regions of the contour or cell midline that show positive or negative curvature (Fig. 1a, bottom).
From these cells and their associated meshline grids, we measured width profiles along the midline, obtaining values that increased from 0 at the two poles to ~1 μm near the middle of the cell (Fig. 1d). As previously reported [39], there was little intracellular variability in cell width along the midline away from the poles, and all three profiles showed similar variability (Fig. 1d). The contour measurements represented an approximately cylindrical body with hemispherical endcaps (Fig. 1d), although all three contour measurements displayed slight variations in curvature (Fig. 1e) that were previously shown to correlate with MreB localization [3, 40].
PC, IF, and PF images are expected to provide distinct positions of cell boundaries. Across many cells, there were strong correlations among length measurements from the three modalities; lengths from PC images were consistently larger than those from IF or PF images by ~400 nm (Fig. 1f). Similar comparative behavior was observed in cell width measurements (Additional file 1: Figure S1). The combined effects of shifts in width (Fig. 1d, Additional file 1: Figure S1) and length (Fig. 1f) led to an increasing divergence in the area measurements of the three imaging modalities across many cells (Fig. 1g). Nonetheless, all three imaging modalities were highly correlated, indicating a consistent picture of cellular dimensions that can be applied to wide variety of organisms. To demonstrate the utility of Morphometrics for unbiased contour detection across a wide range of object shapes, we analyzed PF images of the root tissue of Arabidopsis thaliana plants (Fig. 2a), PF (Fig. 2b) and PC images (Fig. 2c) of curved rod-like Caulobacter crescentus, PC images of red blood cells (Fig. 2d), brightfield images of budding yeast Saccharomyces cerevisiae (Fig. 2e), PC images of dense Pseudomonas aeruginosa communities (Fig. 2f), transmission electron microscopy images of Neisseria gonorrhoeae (Fig. 2g), PC images of branched Bifidobacterium breve DSM20213 (Fig. 2h), brightfield images of zebrafish (Fig. 2i), and IF images of filamentous E. coli (Fig. 2j). In all cases, Morphometrics successfully segmented the cells or organisms, regardless of shape or imaging modality.
Simulated fluorescence microscopy for validation of quantitative analyses
Given the differences in cellular dimensions extracted from PC, IF, and PF data (Fig. 1), we wondered which modality accurately represented cell size. Other experimental methodologies with higher resolution such as electron microscopy still do not provide a “true” measure of cell size, since sample preparation likely perturbs the cell, for example by disrupting turgor pressure. To identify a strategy for comparing measurements with known geometric parameters, we developed BlurLab, a software package that generates simulated fluorescence images. BlurLab takes as input a set of locations of fluorescent molecules and convolves these locations with a point spread function (PSF) to generate a simulated image. The PSF can be directly measured for a particular microscope and objective using sub-diffraction-limited particles such as quantum dots or fluorescent beads; alternatively, BlurLab can generate a PSF for a given set of objective parameters (numerical aperture, wavelength, magnification, index of refraction, and pixel size). BlurLab can also mimic camera noise, thermal noise, and shot noise, yielding simulated images that are more realistic for head-to-head comparison with experimental images. Additional BlurLab functionalities include simulation of imaging at other focal planes for creating z-stacks, modeling total internal reflection fluorescence imaging, boxcar averaging of positions during simulated time-lapse imaging to account for particle motion during the exposure interval, simulating mean-field and stochastic photobleaching, and simulating fluorescence recovery after photobleaching. Detailed descriptions of these functionalities and examples can be found in the BlurLab manual.
To validate cellular dimensions and morphological features of E. coli cells, we used BlurLab to generate sets of uniformly distributed molecules at high density on the surface of cylinders with hemispherical endcaps over a range of cell widths and lengths. For an in silico cell with width 1 μm, we also simulated images of the same cell at focal planes up to 500 nm above and below the cell midplane (Fig. 3a). As the cell goes out of focus, the image attributes used for contour fitting become blurred by the PSF. Nonetheless, a bright boundary, the signature of surface-bound fluorescence, was evident in each image (Fig. 3a). We then applied Morphometrics to each simulated image and successfully resolved a cell contour at each z-offset. The width measured from these cell contours peaked at the midplane and monotonically decreased as the offset from the cell midplane increased (Fig. 3b). These data illustrate the importance of midplane focus, and provide an estimate of the deviation in width measurement when using out-of-focus cells. Interestingly, these data also show that the measured cell width (magenta line in Fig. 3b) is more robust to changes in the focal plane than the actual cell width at a given focal plane (black line in Fig. 3b).
Next, we examined the contours extracted from simulated images of in silico cells with different widths (Fig. 3c). The error in the extracted contour was practically zero for widths greater than 2 μm, but increased as cell width decreased (Fig. 3d). The extracted contours were smaller than the true midplane contours because the cell curvature introduced light from out-of-focus planes in which the cellular cross-section had a smaller width; for cell widths much larger than the wavelength of light used for imaging, this curvature became negligible (Fig. 3d). To determine the accuracy of other geometric measurements, we computed the curvature along the cell contour. The curvature along a 2-μm in silico cell was relatively accurate everywhere except in the transition region between the cylinder and the hemispherical end caps (Fig. 3e), where the PSF blurred the step-function curvature into a smooth transition. For a 1-μm in silico cell, the curvature remained accurate along the cylindrical portions of the cell (where the measured curvature was close to zero), although there was a slight overestimate of the curvature at the ends of the cell (Fig. 3e); this error was exacerbated as the cell width was further narrowed (Fig. 3e). We note that these systematic morphological errors with decreasing cell size result from the limitations of light imaging at wavelengths comparable to the cell size, not from imprecision in fluorescence simulation or contour detection.
To evaluate the overall bias, we used BlurLab to compute the difference between the actual and measured widths and areas for in silico cells 400 nm to 8 μm in width and a range of cell lengths in the peripheral fluorescence modality. The error in the width asymptotically approached zero, and was essentially undetectable in cells with width above ~1.5 μm (Fig. 3f). Error in area behaved in a similar fashion, regardless of cell length (Fig. 3g), indicating that PF measurements provide an accurate measure of cell length without systematic bias. This application illustrates the intended purpose and power of BlurLab: to assess the accuracy of imaging data in the context of a particular model by consistently comparing analyses of both experimental and simulated images (Fig. 3h).
Morphological analysis of a genomic library of nonessential gene deletions
To demonstrate the efficacy of Morphometrics for rapid quantification of bacterial morphology, we analyzed ~14,000 images of the Keio collection, a collection of single knockouts of all non-essential genes in E. coli [25]. We obtained phase contrast images from the National BioResource Project and segmented isolated cells from each strain in an unbiased manner (Methods). Mean cell width varied from ~0.8 to 1.2 μm, and mean cell length varied from ~2.5 to 4 μm (Fig. 4a, Additional file 2: Figure S2). Interestingly, mean cell width and length were strongly correlated with each other (R = 0.39, Student’s t-test: p < 0.001, Fig. 4a), as were mean cell width and length standard deviation (Additional file 3: Figure S3). From our data, we determined the distributions of morphological parameters such as mean width and length across the population of cells for each strain. Moreover, we utilized the meshing of each cell to measure the local cell width (distance across the cell at each point along the contour), from which we calculated the mean variability in cell width within individual cells in the population. Both the standard deviation across the population (Fig. 4b) and the intracellular fractional width variability (Additional file 4: Figure S4) increased with mean cell width, indicating that cells are increasingly unable to maintain cell width as they widen. Interestingly, although wild-type E. coli cells increase in cell size with nutrient-induced increases in growth rate [6], we found no significant correlations between maximal growth rate (as determined by microplate growth curves in [41]) and cell width (Fig. 4c) or length (Fig. 4d). We note that these results are not contradictory; for example, a previous study showed that cell size is not correlated with growth rate within a population of cells [14].
To identify other morphological correlations across the library or in particular strains, we aligned 150 cell contours from each strain of the Keio collection for which at least 150 contours were available in order to calculate an average cell shape, and performed PCA on the covariance matrix to identify significant shape variations. The first two, three, and four PCA modes accounted for 97.3%, 99.0% and 99.3% of variation in cell shape, respectively (Fig. 4e–h), and by far the greatest amount of variation was accounted for by a mode that clearly captured elongation (Fig. 4e). This result, which is not surprising for rod-shaped growth, indicates that length changes are the most significant source of shape variation within the Keio library. Nonetheless, the next three modes representing cell bending, widening, and tapering, respectively (Fig. 4f–h), have potential for revealing cells or strains that are shape outliers. Mean width strongly correlated with PCA mode 3 (width, R = 0.998, Student’s t-test: p < 0.001) and with the projection from mode 1 (length, R = 0.43, Student’s t-test: p < 0.001) (Fig. 4e, bottom), as expected based on the correlation between length and width noted above (Fig. 4a). There was also a significant correlation between mean width and mode 4 (tapering, R = 0.49, Student’s t-test: p < 0.001) (Fig. 4h, bottom), potentially indicating a connection between cell-width determination and cell division. Our analysis demonstrates that most of the variation in cell shape is captured by length and width, although other morphological features such as tapering may be informative for characterizing certain outlier strains. PCA of the correlation matrix, which involves rescaling that avoids heavy skewing by cell length variation, led to an increased emphasis on cell width, bending, and tapering in the decomposition, with the mode corresponding to the largest eigenvalue representing tip morphology (Additional file 5: Figure S5). Taken together, correlations among features suggest underlying feedback between elongation and division in rod-shaped cells [42].
Identification of chemical sensitivities correlated with cellular dimensions
Given the range of cellular dimensions across the Keio library and the correlations between morphological observables, we wanted to systematically probe the physiological significance of cell size. We previously found that the MreBA53T mutation led to wider cells during growth in a variety of carbon sources; cells harboring this mutation had a large gain in fitness when competed against the parental strain in glucose-rich medium [5]. However, the change in fitness was carbon-source dependent, with neutral fitness in lactose and a reduction in fitness in galactose [5]. We also previously observed that sublethal treatment with the MreB inhibitor A22 led to a dose-dependent increase in cell width in wild-type E. coli MG1655 cells [20]. Based on these data and the increase in width variability with increasing mean cell width across the Keio collection detected here (Fig. 4c), we hypothesized that wider cells may be more sensitive to A22 than thinner cells, and more generally that morphological observables may be predictive of the severity of phenotypes in certain environments or chemical treatments.
To test these hypotheses, we made use of an existing chemical genomics dataset [29] in which the Keio collection was grown as colonies on agar plates in 324 conditions including media, drugs, dyes, detergents, metal stresses, and hormones. From the colony sizes, a statistic called an S-score was previously computed to represent the severity of the growth phenotype in each condition [29]; a positive/negative S-score indicates more/less growth than expected based on the changes to wildtype in the condition of interest (Fig. 5a). We compared our quantification of cellular dimensions with the previously reported S-scores from treatment with 0.5 μg/mL A22 for each knockout, and detected a significant correlation between cell width and S-score (Fig. 5b, Pearson correlation coefficient R = −0.10, Student’s t-test: p < 10−6), consistent with our hypothesis. We then wondered whether other chemical or environmental perturbations were correlated with mean cell width or length. We calculated the correlation coefficients of these quantities with each of the 324 condition datasets (Fig. 5c) and determined statistical significance with a Bonferroni correction for multiple hypothesis testing (Methods). For cell width, A22 treatment was the most significant negative correlate; six other compounds (ignoring differences in concentration) also exhibited significant negative correlation (Additional file 6: Table S1) [29]. Of these compounds, three also targeted cell-wall synthesis (the β-lactam cefaclor, the peptide bacitracin, and the amino acid derivative D-cycloserine), possibly indicating inhibitory effects similar to those of A22. The list also included compounds targeting the membrane or proton motive force (the Ca2+-channel inhibitor verapamil and the detergent taurocholate) and translation (50S inhibitor erthyromycin) (Fig. 5d), indicating potential links between cell-width control and other metabolic processes.
There were 15 unique conditions for which the knockouts had S-scores with significant positive correlation with cell width (Additional file 6: Table S2) [29], indicating that wider cells were less sensitive. These conditions target a broader range of cellular processes, including DNA/RNA, stress, and fatty acid metabolism in addition to the ribosome and cell-wall and membrane synthesis (Additional file 6: Table S2) [29]. Carbonyl cyanide m-chlorophenyl hydrazone, a proton ionophore that inhibits oxidative phosphorylation, was positively correlated at all tested concentrations (Additional file 6: Table S2) [29]; interestingly, we observed in a separate study that this ionophore increases bending rigidity, which is an expected outcome of increased cell width based on the mechanics of a thin cylindrical shell. There was also a compound (theophylline) with an unknown target that exhibited a significant positive correlation with cell width (Additional file 6: Table S2) [29], indicating that cell-size profiling may be an effective tool for associating chemical exposure with the molecular pathways that control cell morphology.
We next considered correlations of S-scores with cell length. Six conditions were associated with significant negative correlations (Fig. 5cii): high iron, treatment with the cell-wall inhibitor ceftazidime, and four carbon-source limitations, which may reflect the known coupling of cell size with nutrient-dependent growth rate [6]. Of the eight conditions positively correlated with length (Fig. 5cii), several involved ribosomal inhibitors (n = 3), inhibitors of fatty acid and membrane synthesis (n = 2), or DNA/RNA synthesis (n = 1). In some cases, correlations indicated differences in the underlying mode of drug action; for example, the cephalosporin cefaclor was positively correlated with cell length, while the structurally similar compound ceftazidime was negatively correlated with length.
Given that the observed correlations between cell size and S-scores involved chemicals with many target processes, we conjectured that the correlations for subsets of strains deleted for genes with similar functions may yield further insight into the relationships between cell size and cellular processes. We separated genes into 23 Clusters of Orthologous Groups, a common classification scheme [43]. As compared to the correlations from the full library (Fig. 5c), we detected higher correlations between cell size and S-scores within some of these gene clusters (Fig. 5d,e; Additional file 6: Table S3) [29]. A22 again was significantly (Student’s t-test) and negatively correlated with cell width for strains harboring deletions of genes associated with signal transduction mechanisms (Fig. 5ei), indicating that signaling pathways, such as those activated in response to stress, may respond to the changes in cell width caused by A22 treatment. Although the COG for cell-cycle control, cell division, and chromosome partitioning comprises only 34 genes, sensitivity to the division inhibitor verapamil nevertheless exhibited a strong and significant correlation of −0.92 with cell width (Fig. 5eii), while S-scores for minocycline sensitivity of knockouts of genes involved in nucleotide metabolism and transport were positivity correlated with cell width (R = 0.47, Fig. 5eiii). Surprisingly, for the large number of strains carrying deletions of genes of unknown function (COG class S, n = 918 genes), mean cell width was negatively correlated with sensitivity to low iron stress and the folic acid synthesis inhibitor sulfamethizole (Fig. 5d). Strains harboring deletions in genes involved in amino-acid transport and metabolism had mean cell lengths that were negatively correlated with sensitivity to four carbon-source starvations (Fig. 5d), while cells harboring deletions in genes involved in transcription and post-translational modification, protein turnover, and chaperones had lengths positively correlated with ribosomal inhibitor sensitivity (Fig. 5eiv). As with cell width, strains deleted for genes of unknown function had lengths both positively and negatively correlated with some treatments (Additional file 6: Table S4) [29], further supporting the importance of these genes to cell shape. Taken together, our correlation analyses based on the entire Keio collection and subdivided into Clusters of Orthologous Groups suggest that a variety of intracellular factors, beyond those controlling cell-wall synthesis or turgor, contribute to the cell’s determination of its size, and that responses to some extracellular perturbations have general connections with cell size (Fig. 5d). These correlations were revealed through precise and automated measurements of cellular dimensions that were enabled by our open-source software packages Morphometrics and BlurLab.