The authors have declared that no competing interests exist.
Conceived and designed the experiments: JL AS EL GKR RFM. Performed the experiments: JL AS MW. Analyzed the data: JL AS EL GKR RFM. Wrote the paper: JL AS EL GKR RFM.
Microtubules are filamentous structures that are involved in several important cellular processes, including cell division, cellular structure and mechanics, and intracellular transportation. Little is known about potential differences in microtubule distributions within and across cell lines. Here we describe a method to estimate information pertaining to 3D microtubule distributions from 2D fluorescence images. Our method allows for quantitative comparisons of microtubule distribution parameters (number of microtubules, mean length) between different cell lines. Among eleven cell lines compared, some showed differences that could be accounted for by differences in the total amount of tubulin per cell while others showed statistically significant differences in the balance between number and length of microtubules. We also observed that some cell lines that visually appear different in their microtubule distributions are quite similar when the model parameters are considered. The method is expected to be generally useful for comparing microtubule distributions between cell lines and for a given cell line after various perturbations. The results are also expected to enable analysis of the differences in gene expression underlying the observed differences in microtubule distributions among cell types.
Microtubules play an indispensable role in subcellular processes such as cell movement, cell division and intracellular transportation. In turn, these processes are known to play a role in other biological phenomena such as wound healing, and cancer metastasis. Extracting information about the organization of microtubules in different cell lines could potentially shed light on the roles of microtubule associated proteins in that organization. While limited information is available about variation in microtubule distributions
Electron microscopy can be used to trace microtubules, but the specimen preparation for imaging does not allow for intact cells to be imaged. Fluorescence microscopy can be used to image intact cells, but microtubules typically overlap and are often densely packed inside cells. It is very difficult, if not impossible, to manually trace each individual microtubule in a confocal or widefield fluorescence microscopy image in order to obtain accurate estimates of microtubule distribution parameters. Hence previous work comparing cell lines has often focused on the tips of microtubules where tracing is possible, or the comparison has been only qualitative
We therefore previously developed an indirect method for estimating natural, interpretable and quantitative parameters such as the number and the mean length of microtubules from 3D fluorescence microscopy images of microtubules
Each microtubule starts from the centrosome, and randomly grows to the second point on the lateral surface of a cone whose aperture is 2α. Then the microtubule grows the same way until it hits the cell or nuclear shape boundary and is not able to step further within the cytosolic area. At this time, we relax the collinearity requirement but still confine the next direction under the local constraint α_{local}. Moreover, we also keep on checking a consecutive multiple (30) steps, and require that there are less than or equal to 3 pairwise vector angles that are larger than the global constraint α_{global}. Beginning with an empty (black) cytosolic area (shaped by cell and nuclear boundary), we add one to the intensity of the pixel which a microtubule crosses. In this paper, we used every step of growth to be 0.2 microns (1 pixel). For the two constraints on the collinearity which controls the curvature of each microtubule and the local and global rebounding issues, we used α_{local} to be 63.9 degrees and α_{global} to be 120 degrees. The figure only illustrates the procedure of growth in 2D for better visualization but can be easily imagined to extend to 3D.
The framework contains two subsystems, one for generating 3D synthetic images of distributions of microtubules (A), and one for estimating and comparing the model parameters of distribution of microtubules from real 2D images of eleven cell lines (B).
Using this indirect method, we estimate the model parameters for 2D images from eleven human cell lines, and analyze the resulting parameters.
In our earlier work, we described an indirect approach to estimate parameters of a generative model of microtubules that was conditioned on the shape of the cell and the nucleus
(
To test the accuracy of estimating microtubule parameters from 2D images, we applied our new 2D method (see Methods) using the central slice (at half height of the cell) of 3D HeLa cell images and compared the estimated parameters with those from the 3D method. The half height was chosen as the preferred slice because the 2D images used later were also acquired at half the height of the cell. We computed the mean absolute percentage error (MAPE) in each of the parameters estimated from the 2D images assuming that the estimated parameters from the 3D method were correct. Results are shown in
Number of microtubules  Mean of length distribution  Collinearity (cos 
Cell Height 
23.9±19.7  43.1±23.9  1.96±2.72  21.4±13.1 
We estimated how well our recovery method can perform using simulated images for which the correct parameters were known. For one cell geometry (cell shape and nucleus shape), a library of 3D synthetic images was generated with predefined parameters as a validation bed; then 5 other testing libraries were generated using different random seeds. The predefined parameters for the validation bed were estimated from each testing library separately. The resulting errors are shown in
Library  Number of microtubules  Mean of length distribution  Collinearity 
1  4.32±9.95  5.52±11.1  0.61±0.82 
2  4.89±11.9  8.52±24.2  0.58±0.78 
3  3.96±9.53  6.24±17.9  0.68±0.86 
4  4.10±10.6  4.63±10.6  0.57±0.76 
5  3.62±8.55  5.08±11.6  0.61±0.86 
3D microtubule model parameters were estimated from 2D fluorescence microscopy images of eleven cell lines collected as described previously
2D real images are shown on the left, and center slices of the bestmatching 3D synthetic images are shown on the right. (A) A431 cell line, Number of microtubules = 250, Mean of length distribution = 30 microns, Collinearity = 0.97000; (B) U2OS cell line, Number of microtubules = 250, Mean of length distribution = 30 microns, Collinearity = 0.98466; (C) U251MG cell line, Number of microtubules = 250, Mean of length distribution = 20 microns, Collinearity = 0.99610.
There are two sets of three columns for the model parameters (number of microtubules, mean of the length distribution and collinearity) in each row. The cell lines (from top to bottom) are U251MG, A549, MCF7, HepG2, A431 and HeLa in the left column, and CaCo2, PC3, RT4, Hek293, and U20S in the right.
The ellipses are centered at the bivariate means of the two parameters and contain about 67% to 80% of the cells for a particular cell line (at most 1.5 standard deviations from the means).
We compared the bivariate distribution of the estimated number of microtubules and the mean of length across different cell lines. We first compared the covariances using
The trees were built on the pairwise
U251MG  CaCo2  A549  PC3  MCF7  RT4  HepG2  Hek293  A431  U2OS  HeLa  
U251MG (94)  NA 










CaCo2(77)  1  NA 









A549(66)  0.077  1  NA 








PC3(110)  1  1  1  NA 







MCF7(54)  1  1  1  1  NA 






RT4(38)  0.11  0.030*  5.4e4*  0.067  1  NA 





HepG2(51)  5.7e4*  1  1  2.0e3*  0.081  1.0e4*  NA 




Hek293(70)  4.3e3*  0.92  1  0.26  0.12  2.0e9*  1  NA 



A431(112)  1.5e4*  8.7e6*  2.7e9*  0.012*  0.059  7.1e3*  0*  0*  NA 


U2OS(114)  2.6e7*  1.1e5*  1.9e4*  0.12  4.1e3*  8.6e6*  0*  2.9e11*  1  NA 

HeLa(35)  0*  0*  0*  0*  0*  0*  0*  0*  0*  0*  NA 
As a comparison to these statistical tests of indirect parameter estimates, we repeated the calculations mentioned above using features calculated directly from real cell images. We used the first two principal components, which accounted for 99.99% of the total variance in feature space, to represent the multivariate features. The
We compared the amount of polymerized tubulin, estimated as the product of the number and mean length of the microtubules, to the total intensity of each cell image. The plot of these two quantities for real cells from eleven cell lines is shown in
The correlation coefficient for each cell line is shown in the legend.
We have developed an automated method to estimate 3D microtubule model parameters from 2D confocal immunofluorescence microscopy images in an indirect manner. The method is dependent on the 3D structure of the cell and the nucleus, and the centrosome location. We describe an automated approach in the method to generate an approximate 3D cell and nuclear morphology using only the 2D microtubule image and 2D nucleus image acquired at the center (half height) of the cell. We applied this method to generate distributions of microtubules in cells and utilized an indirect feature matching algorithm to estimate model parameters from 821 images of cells and 11 cell lines. Then the two quantitative parameters, number of microtubules and mean length of microtubules, were compared across cell lines. These two parameters are important because they demonstrate the fundamental physical characteristics of microtubules in cells.
To our knowledge, this study is the first attempt to quantify the number and mean of the length distribution of microtubules in intact cells across different cell lines. Methods such as electron microscopy can image intact cells, but have interference from other cell components
One reason for studying microtubule distributions across cell lines is to begin to search for explanations of how expression of microtubuleassociated proteins (MAPs) may account for any differences observed. The expression levels of many proteins vary across cell lines
There is evidence that the number and length of microtubules are correlated with the size of the cell
The correlation coefficient for each cell line is shown in the legend.
The methods described here have potential applications in a range of experimental approaches. For example, microtubule interacting drugs (mitotic inhibitors) are commonly used for cancer chemotherapy, and our method could provide a quantitative measure of the effects of these drugs on different cancer cell types. It also could be used in highcontent screening to distinguish different types of effects of compounds that disrupt microtubule dynamics.
Finally, we note that our estimation procedure is only appropriate for images and cell lines for which the majority of microtubules originate at the centrosome because we explicitly modeled all microtubules as starting from it. Therefore, the centrosomes may appear more focused in some synthetic images compared to the corresponding experimental ones for cell types that are less organized by centrosomes. Future work could include modifications to our modeling procedure so that it can be used with a more diverse set of experimental images and cell lines.
We used 3D images of HeLa cells previously obtained by three color confocal immunofluorescence microscopy to visualize three cell components: the cell membrane, nucleus and microtubules
The data used here are confocal immunofluorescence microscopy images of fixed and interphase cells of eleven different cell lines: A431, U2OS, U251MG, RT4, PC3, HepG2, HeLa, CaCo2, A549, Hek293 and MCF7 from the HPA. They are human cell lines widely used in current research. The images were acquired as described previously
The field images were segmented into single cell regions using a seeded watershed method on the tubulin channel with the nuclei in the nuclear channel as seeds. The 2D cell and nuclear boundaries were found by thresholding the single cell regions and the nuclei respectively. These were used for cell size calculation and for 3D morphology generation (see below).
The confocal PSF was generated computationally based on a theoretical model using the SVI PSF calculator for the Zeiss LSM 510 confocal microscope for the first three cell lines and the Leica SP5 for the other eight cell lines (
The 3D coordinate of the centrosome was estimated by breaking the problem into two parts. First, the XYcoordinate was estimated and then the Zcoordinate. The XYcoordinate was chosen as the pixel with the maximum intensity value in the vicinity of the nucleus after smoothing with an averaging filter of size 25 pixels on the tubulin channel image (as for cell image). For the Zcoordinate, we used linear regression to estimate the location as a function of the following predictor variables: (i) Maximum intensity of the microtubule image, (ii) Mean intensity of the microtubule image, and (iii) pixel intensity of the XY coordinate in the microtubule image. The coefficients of the linear regression were estimated from the 3D HeLa images where the 3D centrosome as described previously
The single microtubule intensity for each cell line was estimated using the method described previously
In order to estimate the cell shape, we firstly required the following two estimates: (1) the cell shape at the bottom, where the cell membrane interacts with a substrate (e.g. petridish), and (2) cell shape decay from the bottom of the cell to the top.
For estimating the bottom shape of the cell, we used the microtubule channel image acquired at the center of the cell, i.e. z = Z/2, where Z is the height of the cell in pixel dimensions. This image contains information about the cell boundary at the bottommost region because the outoffocus light from the bottom slice is visible in the center slice (as microtubules being of relatively lower intensity). Hence, the boundary of the bottom slice (bottom shape) was found by thresholding for above zero intensity pixels. (see
The growth model of microtubule patterns (
Sample
Sort lengths from longest to shortest;
Iterate until all lengths are generated, starting with the longest microtubule:
use the generated microtubule length;
remove chosen microtubule from storage;
Generate a microtubule using the method in
add to storage and regenerate the microtubule.
Finally the generated image was convolved with the estimated PSF and was then multiplied with the corresponding estimated single microtubule intensity to make the intensity comparable to real images.
As described previously
Number of microtubules = 5, 50, 100, 150, 200, 250, 300, 350, 400, 450;
Mean of length distribution = 5, 10, 15, 20, 25, 30, 35, 40, 45 microns;
Collinearity (
Cell Height = 1.2, 1.4, 1.6 microns.
For each 2D real cell image and all the central 2D slices from its 3D simulated images in the library, 2D versions of the features that were used previously
We thank other members of the Human Protein Atlas project team and the Murphy and Rohde groups for helpful discussions.