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 
. More invasive methods of preparation such as extraction of the microtubule network can allow electron microscopy to generate traceable images, but are no longer representative of intact cells 
. Fluorescence microscopy, on the other hand, can be used to obtain information about proteins at monomer-level resolution of localization without interference from other cell components in intact cells with high-throughput data.
One reason for studying microtubule distributions across cell lines is to begin to search for explanations of how expression of microtubule-associated proteins (MAPs) may account for any differences observed. The expression levels of many proteins vary across cell lines 
, and there are cell-specific proteins that regulate microtubules 
. In this paper, the cell lines chosen are from varying lineages, such as mesenchymal, epithelial and glial tumors, which may differ in their expression of MAPs. Our analyses show that some cell lines do have significant differences in the estimated parameters of the number and length distribution of microtubules. In future work, we hope to establish whether and how these differences results from variation in expression of specific MAPS.
There is evidence that the number and length of microtubules are correlated with the size of the cell 
. We therefore computed the area of the center slice (sum of pixels of the binary image) as the value reflecting the size of cytosolic space of the cell, for each of the cell lines. To quantify the correlation, we computed the correlation coefficient between the estimated total polymerized tubulin and the area of cytosolic space for each cell line. The plot of these two quantities for all cells is shown in . The correlation coefficients varied from 0.46 to 0.81 which are intermediate to high. They add more confidence to the estimates of our automated approach and further confirm the existing hypothesis using alternative approaches.
Scatter plot of the estimated total amount of polymerized tubulin versus the area of cytosolic space (sum of pixels) for real cells from eleven cell lines.
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 high-content 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.