Ellipsoid localisation microscopy (ELM) software

MATLAB software for ellipsoid localisation microscopy (ELM).

Eric J. Rees and James D. Manton, University of Cambridge. 2016. License: CC-BY 4.0.

The principle of ellipsoid localisation microscopy is presented in the following open-access paper, together with measurements of some coat protein positions in B. megaterium and B. subtilis:

Julia Manetsberger, James D. Manton, Miklos J. Erdelyi, Henry Lin, David Rees, Graham Christie, Eric J. Rees. Ellipsoid localisation microscopy infers the size and order of protein layers in Bacillus spore coats. Biophysical Journal (2015).

This software package is a more developed and comprehensive version of the method used in the Manetsberger paper. The instructions and technical detail in this document accompany the paper:

[James D. Manton, Robert D. Turner, Yao Xiao, Graham Christie, Eric J. Rees. ELM: super-resolution analysis of wide-field images of fluorescent shell structures.]

Please cite these papers if you use this software for a publication.

Sample image data is supplied in the open data folders associated with some of our publications. https://www.repository.cam.ac.uk/handle/1810/251135

• The fluorescent shell analysis repository also includes preliminary code for a similar analysis of cylindrical fluorescent shells

Contents

1. Background
2. Graphical user interface
3. Preparing images for analysis
4. Examples of results
5. How to use this ELM software
6. How to read and interpret the numerical results of the ELM software
7. How to use the cylindrical shell analysis
8. Notes

1. Background

ELM is an image analysis tool designed to estimate the location of fluorescent fusion proteins in bacteria coats. Various other fluorescent shell structures (where the word 'shell' means a thin fluorescent layer around a spheroidal specimen) can also be measured.

ELM very precisely infers the size (i.e. radius, or axis lengths) of fluorescent shells with certain geometries (e.g. spherical, ellipsoidal), by analysing fluorescence image data which can be captured on a traditional fluorescence microscope. The model structures (spheres and ellipsoids) provide good approximations of the way that some GFP-fusion proteins are incorporated into the multi-layered coats of bacterial spores.

The ELM method consists of segmentation of individual spore images (which must be well-separated from each other) followed by fitting an equation or a model to each candidate. For spherical shells, the radius can be inferred with a precision better than about 10 nm, and for ellipsoidal shells the semiaxis lengths can be inferred with similar precision. (The precision depends on the brightness and uniformity of the shells.) This makes it possible to identify information such as the position of each protein in a multi-layered coat, with a precision much better than the diffraction-limited resolution of an optical microscope. Once the parameters of the spore are fitted, these values can be fed back into the equation for the spore image (with the blur parameter decreased) in order to reconstruct a super-resolution image of what the spore might look like if the image had been captured with less diffractive blur.

2. Graphical User Interface

Figure 1. This is the graphical user interface for the ELM software, once it is started in Matlab.

3. Preparing images for analysis

For the best quantitative results, fluorescence microscopy should be performed to obtain images with the following qualities:

• Separate spores. Well-separated images of individual spores. (Sparse spore images allow easy segmentation, and prevent the image-fitting from being spoiled by interference of fluorescence from overlapping candidates.)
• Lots of spores. Having lots of spore images (say 1000), provided they are well-separated, will provide a more robust average measurement of a protein layer position.
• In focus. Spores should be in-focus (e.g. the fluorescent coat should look as sharp as possible). They are assumed to all lie in the focal plane.
• A dark background. A uniformly dark background makes it easy to identify the fluorescence signal from the spore coat.
• Bright spore coats. The brighter the fluorescence of the spore coat protein, the better the fit quality, but even quite dim images have been analysed successfully.
• Not saturated. The digital image should not be saturated. The pixel values in the digital image are assumed to be linearly proportional to the optical image brightness.
• Known scale. The width of the digital pixels needs to be known. We use a 100X objective lens with a Retiga 2000R camera on an Olympus BX-51 microscope, which gives a pixel width corresponding to 74 nm on the specimen. This is a good pixel size to use, because the 'ring-shaped' image of fluorescent shells can be resolved, and this is the structure that is analysed to infer the fluorescent shell size.

The image below is an example of a 'good' image for ELM analysis, with sufficient brightness and a high, but not too high, density.

Slide preparation method 1

We find that 1 µl of B. megaterium or B. subtilis spores in suspension (sterile water), pipetted onto a slide and covered with a polylyseine cover slip works well for imaging, with the polylyseine ensuring that the spores stick to the cover slip and do not drift around in solution. As the fluorescence from a coat protein layer can be quite weak, we find it advantageous to focus the spores using phase contrast imaging and then briefly illuminate the spores for fluorescence imaging. This helps to minimise photobleaching.

Slide preparation method 2

We have also found that a dab of B. subtilis spores (approximately 1 cubic mm) can be taken directly from a petri dish if they have been prepared on agar, and placed on a microscope slide. This method does have the disadvantage that there may be immature spores or germinating spores together with mature spores, and so identifying the average size of a mature spore (if that is a desired measurement) may be hard.
Then three microliters of sterile water should be pipetted onto the dab, and the mixture should be pipetted up and down several times to disperse the spores. Firmly pressing a coverslip down onto the sample can be sufficient to immobilise these spores for imaging (although method 1 may work better).

4. Example results

The animation below shows the output from running the ELM software on one image. First, each spore is detected and segmented, with each segment being tiled for display in the first frame of the animation. The second frame shows the model fit for each spore, with the final frame demonstrating a super-resolved reconstruction, where the parameters from the model fit are fed back into the image generation pipeline, but without the effect of microscope blurring.

In addition to these images, all parameters for the model fit for each spore, along with the residual sum of squares error, are saved to a spreadsheet (CSV format) and in a Matlab .MAT data file as an array of values that can be used for quantitative analysis.

These numerical results can be used to plot graphs such as these:

Figure taken from Manetsberger_2015 (Biophysical Journal). Model-fitting estimates of a fluorescent protein layer radius in B. megaterium and B. subtilis, and in simulated calibration data with a groundtruth radius of 500 nm (Cal). (a) The average layer radius was obtained by analyzing at least three separate fields of typically 200 spores each, and the error bars indicate the standard deviation of these measurements. For the ellipsoidal models, the radius of a sphere of equal volume is presented. (b) Residual errors of fitted models. (c) The distribution of radii fitted to SleL and CotG in 200 individual B. subtilis spores. (d) The aspect ratio of ellipsoidal B. subtilis spores. (e) The polarity parameter quantifying the tendency of proteins to localize preferentially at the spore poles. To see this figure in color, go online.

5. How to use this ELM software

Download and start

1. Download the entire ELM folder from its github repository: https://github.com/quantitativeimaging/ELM .
2. Start Matlab. (Version 2016a was used for development. It may work with older versions.). Set the ELM folder as the working folder.
3. Run the file ELM.m or start it from the Matlab console with the command >>ELM. This will start the graphical user interface (GUI).

Process a folder of images

The ELM GUI will try to analyse every file in the selected input folder. The input folder should only contain image files that need to be analysed. It will save its results (images and .CSV files of numerical data that can be opened by excel) into the selected output folder.

1. Prepare a folder containing only the images to be analysed. TIF files are the intended format for input, but other image formats may work. The GUI will start with a folder of sample data selected: this folder contains a small TIF image of some approximately-spherical B. megaterium spores. There is also a folder containing a sample image of appproximately-ellipsoidal B. subtilis spores, but try processing the B. megaterium images first.
2. In the Input field, enter the location of a folder of images that you want to process. You can use the Browse button to select a folder. (Note that you are selecting a folder, not a single file.)
3. In the Output field, select a folder where you want to save the results. You can leave this as the default example_output/ folder if you want.
4. Enter the width of the pixels on the microscopy sample. It is 74 nm in the sample data. The ELM software should work OK if spore coats (radius ~ 500 nm) are imaged with a pixel width in about the range 50 nm to 100 nm, but this has not been explored much by the authors. Note that this length scale is not actually needed to run the ELM analysis, since parameters are saved in units of pixel widths. However this length scale needs to be known for later analysis.
5. If the spores are approximately spherical, select the Spherical model button. If they are approximately ellipsoidal, select the Ellipsoidal model button.

• the cylindrical model is implemented in the fluorescent shell analysis repository. It will be incorporated into the ELM GUI in a slightly different way, and should not be selected in the current version.

6. Click the Process button. The software will then try to process all the image data and save the results.

• This should take a few seconds for the spherical model with its sample data, or a few minutes for the ellipsoidal model with its sample data. The waitbar will update every time the program moves on to a new file.
• Large folders of ellipsoidal spore images are best processed overnight.

7. For each input file, the GUI will save four images to the output folder, as well as an (excel-readable) .CSV file with numerical results, and a .MAT file of Matlab-readable results. These output files will start with the same name as the corresponding input file.

6. How to read and interpret the numerical results of the ELM software

The ELM software saves both a spreadsheet (filename_params.CSV) and a Matlab file (filename_params.mat) for each input file (filename.tif). It also saves several image file showing the raw, segmented, fitted, and reconstructed images for each input file.

6.1 CSV (spreadsheet) data

The simplest way to review the numerical results is to open the .CSV results file in Excel or some other spreadsheet. The top row of the spreadsheet gives the parameter names saved by the ELM software, and each row of numerical data underneath gives the inferred values for one candidate spore.

The saved parameters are as follows

Columns 1 and 2. x segment pos and y segment pos are the rough XY-coordinates of the spore centre, estimated by the segmentation step of the image analysis. Units are pixel widths.

Columns 3 and 4. x shift and y shift are the XY-offsets to the exact centre position of the spore, obtained by the fitting step of the image analysis. Units are pixel widths. Note that the final estimate of the centre position is given by floor(x segment pos) + x shift because the rough XY-coordinates are rounded down to the nearest integer in order to obtain an integer pixel value as a starting point for the precise fitting process.

Column 5. orientation is the azimuth orientation inferred by the ellipsoidal model for a prolate ellipsoid of revolution with its long axis lying in the XY plane. This parameter is in radians, and a value of zero is recorded by default for spherical models.

Column 6. semiminor axis is the radius of a spherical shell, or the semi-minor axis of an ellipsoidal shell. Units are pixel widths.

Column 7. PSF variance describes the size of the point spread function (blur radius of the model microscope) fitted to the image data. Units are (pixel widths) squared. This is a useful parameter for quality control of the analysis. Fits with a PSF variance much larger than the value expected due to diffraction-limited microscope optics should be treated with caution or discarded.

Column 8. brightness describes the fluorescence brightness of the spore. It is useful for comparing different spores.

Column 9. aspectRatioMinusOne is needed to handle ellipsoidal spores. If the long semiaxis length is b and the short semiaxis length is a then the parameter records (b/a) - 1. A value of zero is recorded for a sphere, naturally.

Column 10. equatorialty allows for ellipsoidal spores to have non-uniform fluorescence brightness per unit of their surface area, and to be brighter at the poles (if negative) or equator (if positive). The name 'polarity' was avoided in the programming, as that name may have various biological meanings.

Column 11. residual is the sum of squared differences between the fitted pixel values and the actual values in the image data. (Actual values are after uniform background subtraction, and fitted values are fitted to the background-subtracted data.) A useful way of quantifying the error of the fit is by expressing this residual as a percentage of the sum of squared signal (total fluorescence) of the sample, which is recorded in the next column. Frequently, fitting errors less that 5% or 10% seem to be of 'good quality' whereas larger values indicate that the data is not so well described by the fitted model.

Column 12. sum_square_signal is the sum of squared pixel values (brightnesses) in the image data, after uniform background subtration.

Note the radius and semiminor_axislengths are given in pixel widths, and need to be multiplied through by the pixel width to give physical distances.

6.2 MAT file data for Matlab

The same data recorded in the spreadsheet is also saved in a more Matlab-compatible .mat file. To read the data in Matlab, drop the .mat file onto the Matlab console. A copy of the same data is saved with the header names in the string fitsHdr and the numerical parameters for each spore stored as rows in fitData.

The Matlab script \example_analysis\analyse_results.m reads all the MAT files in an output folder and can provide a summary of the combined results of all the spores in each image. (Refer to that script for details.) It can also perform a quality control step to exclude bad fits (usually by removing fits with extreme shell radii, or large blur radii) before summarising the accepted results.

The script \example_analysis\analyse_ELM_results.m does the same thing, but promts the user for parameters using a dialog window instead of using values in the script.

The image analysis results are also saved as a cell array in the MAT file, which can be read as follows. (Note, however, that reading handling cell arrays can be rather cubmersome, and for most purposes it may be easier to read the results some other way.)

fit_headers = fits{1}   % Reads the headings of the data columns
fit_data = cell2mat(fits(2:end)) % Reads the data

% Evaluate mean equivalent sphere radius of ellipsoids:
equivalent_radius = mean(fit_data(:,6).*(1+fit_data(:,9)).^(1/3))*74

7. How to use the cylindrical shell analysis

In the Manton_2017 paper, we present an equation for the image of a spherical fluorescent shell. This makes it possible to use an ELM-like method for analysing the size of cylindrical shells, such as a vegetative bacterial cell wall.

In this software package we provide a script for the cylindrical fluorescent shell equivalent of ELM. This script requires manual segmentation by the user, to select central sections of cylindrical fluorescent shells, and then it performs an ELM-like analysis that fits a cylindrical fluorescent shell model to each segment. The script then returns the key parameters (e.g. cylinder radius) and a reconstructed image of the sample with decreased blur.

To use this analysis:

1. In Matlab, open the folder \cylindrical_analysis\ and run the script cylindrical_analysis.m

2. You will be prompted to select a tif file showing some cylindrical fluorescent shells. Select the example image in the folder \example_images\cylinders\

3. You will be prompted to specify how many regions of interest you will manually select from the image. Try leaving this at the default value of one.

4. Use the cursor on the figure showing the image file to select regions of interest. This step uses the Matlab function roipoly(). You should select regions in the middle of straight, cylindrical specimens and avoid selecting the ends. You must select regions with 4 corners: larger regions will be cut down to a quadrilateral with the first four corners. Refer to the >>doc roipoly instructions for full details on how to select a region of interest -- briefly, one can left-click on the first three corners of your region of interest, then double-click on the fourth to close the quadrilateral, then right-click on it and select 'create mask' from the menu.

5. The software will fit the cylindrical model to each specified segment.

6. The reconstructed images can be saved, and the fitted parameters are available in the Matlab workspace.

8. Notes

The Advanced button opens a panel in which some image analysis settings can be adjusted. This may be necessary for images with somewhat different scale or brightness to the sample data.

Radius controls the range of circle radius, in pixel widths, which is searched for by the imfindcircles() function in the segmentation step.

Hough sensitivity controls the sensitivity of the imfindcircles() function. Higher values will detect more candidates, but probably also more spurious candidates.

Segmentation size controls the half-width of the square segments that are selected for analysis around each candidate centre. A square of side-length 1 + 2*Segmentation size will be analysed for each candidate. For example, if the segmentation size is 13, the software will crop a region of interest of 27*27 pixels around each candidate spore location found by imfindcircles().

Image border This many pixels around the edge of the microcopy image data are excluded from analysis. If any candidate segment requires pixels from this area, it is discarded.

RNG seed This sets the random number generator seed, which means that the Monte Carlo models of ellipsoidal shells should be generated consistently in repeat analyses.

Num fluorophores Sets the number of fluorophores simulated on each ellipsoidal spore model. Smaller numbers will be faster to process, but this has not been extensively tested. The number should be big enough for the modelled images to be suitably uniform.

Additional Notes

• The image segmentation step may miss a few spore images. The sensitivity parameter can be adjusted (increased) to capture more candidates, but this might introduce false positive candidates.
• The image segmentation step uses imfindcircles which often returns a warning (that the function is looking for overly small circles). With the sample data, this warning is over-cautious and can be ignored.