Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

Summary

This protocol outlines a novel method to create a spatially detailed finite element model of the intracellular architecture of cardiomyocytes from electron microscopy and confocal microscopy images. The power of this spatially detailed model is demonstrated using case studies in calcium signaling and bioenergetics.

Abstract

With the advent of three-dimensional (3D) imaging technologies such as electron tomography, serial-block-face scanning electron microscopy and confocal microscopy, the scientific community has unprecedented access to large datasets at sub-micrometer resolution that characterize the architectural remodeling that accompanies changes in cardiomyocyte function in health and disease. However, these datasets have been under-utilized for investigating the role of cellular architecture remodeling in cardiomyocyte function. The purpose of this protocol is to outline how to create an accurate finite element model of a cardiomyocyte using high resolution electron microscopy and confocal microscopy images. A detailed and accurate model of cellular architecture has significant potential to provide new insights into cardiomyocyte biology, more than experiments alone can garner. The power of this method lies in its ability to computationally fuse information from two disparate imaging modalities of cardiomyocyte ultrastructure to develop one unified and detailed model of the cardiomyocyte. This protocol outlines steps to integrate electron tomography and confocal microscopy images of adult male Wistar (name for a specific breed of albino rat) rat cardiomyocytes to develop a half-sarcomere finite element model of the cardiomyocyte. The procedure generates a 3D finite element model that contains an accurate, high-resolution depiction (on the order of ~35 nm) of the distribution of mitochondria, myofibrils and ryanodine receptor clusters that release the necessary calcium for cardiomyocyte contraction from the sarcoplasmic reticular network (SR) into the myofibril and cytosolic compartment. The model generated here as an illustration does not incorporate details of the transverse-tubule architecture or the sarcoplasmic reticular network and is therefore a minimal model of the cardiomyocyte. Nevertheless, the model can already be applied in simulation-based investigations into the role of cell structure in calcium signaling and mitochondrial bioenergetics, which is illustrated and discussed using two case studies that are presented following the detailed protocol.

Introduction

Excitation-contraction coupling (ECC) in the heart refers to the important and intricate coupling between electrical excitation of the cardiomyocyte membrane and the subsequent mechanical contraction of the cell during each heartbeat. Mathematical models have played a key role in developing a quantitative understanding of the interlinked biochemical processes that regulate the action potential¹, cytosolic calcium signaling², bioenergetics³, and subsequent contractile force generation. Such models have also successfully predicted changes to the heartbeat when one or several of these biochemical processes undergo alterations^4,5. The highly-organized ultrastructure of the cardiomyocyte has increasingly been recognized to play a critical role in the normal contractile function of the cell and the whole heart. Indeed, changes to the morphology and organization of components of cardiac ultrastructure occur in parallel to biochemical changes in disease conditions such as hypertrophy⁶, heart failure⁷, and diabetic cardiomyopathy⁸. Whether these structural changes are minor, adaptive, or pathological responses to the changing biochemical conditions is still largely unknown⁹. The inherently tight coupling between form and function in biology means that experimental studies alone cannot provide deeper insights than correlations between structural remodeling and cardiomyocyte function. A new generation of mathematical models that can incorporate the structural assembly of the sub-cellular components, along with the well-studied biochemical processes, are necessary to develop a comprehensive, quantitative understanding of the relationship between structure, biochemistry, and contractile force in cardiomyocytes. This protocol describes methods that can be used to generate structurally accurate finite element models of cardiomyocytes that can be used for such investigations.

The last decade has seen significant advances in 3D electron microscopy¹⁰, confocal¹¹, and super-resolution microscopy¹² that provide unprecedented, high-resolution insights into the nano-scale and micro-scale assembly of the sub-cellular components of the cardiomyocyte. Recently, these datasets have been used to generate computational models of cardiomyocyte ultrastructure^13,14,15,16. These models use a well-established engineering simulation method, called the finite element method¹⁷, to create finite element computational meshes over which biochemical processes and cardiomyocyte contractions can be simulated. However, these models are limited by the resolution and detail that a microscopy method can provide in an image dataset. For example, electron microscopy can generate nanometer-level detail of cell structure, but it is difficult to identify specific proteins within the image that would be necessary to create a model. On the other hand, super-resolution optical microscopy can provide high contrast images at resolutions on the order of 50 nm of only a select few molecular components of the cell. Only by integrating complementary information from these imaging modalities can one realistically explore the sensitivity of function to changes in structure. Correlative light and electron microscopy is still not a routine procedure and it would still suffer the limitation that only a limited number of components could be stained in the immunofluorescence view and correlated with the electron microscopy view.

This protocol presents a novel approach¹⁸ that uses statistical methods¹⁹ to analyze and computationally fuse light microscopy information on the spatial distribution of ion-channels with electron microscopy information on other cardiac ultrastructure components, such as myofibrils and mitochondria. This produces a finite element model that can be used with biophysical models of biochemical processes to study the role of cardiomyocyte sub-cellular organization on the biochemical processes that regulate cardiomyocyte contraction. For example, this protocol could be used to create models from healthy and streptozotocin-induced diabetic cardiac myocytes to study the effect of structural remodeling on cardiac cell function that is observed in diabetic animal models⁸. An additional advantage of the statistical nature of the presented method is also illustrated in the protocol: the method can generate multiple instances of finite element geometries that closely mimic the experimentally observed variations in cell structure.

As an overview, the protocol steps include: (i) preparation of cardiac tissue for electron microscopy to generate 3D images with sufficient resolution and contrast; (ii) reconstruction and segmentation of 3D image stacks from electron microscopy data using a 3D electron microscopy reconstruction and image analysis software called IMOD²⁰; (iii) using iso2mesh²¹ to generate a finite element mesh using the segmented data as input; (iv) using the novel algorithm and codes to map the distribution of ion channels onto the finite element mesh.

The premise of the approach to each step is outlined within the protocol, and representative results are provided in the accompanying figures. An overview is outlined specifying how the generated spatially detailed models can be used to study the spatial dynamics of calcium during ECC, as well as mitochondrial bioenergetics. Some of the current limitations of the protocol are discussed, as well as new developments that are underway to overcome them and further advance a quantitative understanding of the role of cell structure to cardiac systems biology. How these methods could be generalized to create finite element models of other cell types is also addressed.

Users of this protocol may skip step 1 and the reconstruction part of step 2 if they have access to a pre-existing electron microscopy image stack. Users who intend to acquire their data in collaboration with more experienced electron microscopists may wish to discuss and compare the fixation and staining procedures in step 1 with the expert to determine an optimal protocol for acquisition.

Protocol

All methods described here have been approved by the University of Auckland Animal Ethics Committee and the University of California San Diego Institutional Animal Care and Use Committee, where the tissue protocol was originally developed.

1. Experimental Preparation

1. Prepare stock solutions of 0.15 M and 0.3 M sodium cacodylate buffers at pH 7.4 according to Table 1.
2. Prepare glutaraldehyde fixative (2% paraformaldehyde (PFA) + 2.5% glutaraldehyde + 0.2% tannic acid in 0.15 M sodium cacodylate buffer at pH 7.4) using components listed in Table 1.
   1. Dissolve 2 g of PFA powder in 20 mL of distilled water at 60 °C on a hotplate with constant stirring.
   2. Add 1 M NaOH solution until the solution is clear.
   3. Wait until the temperature of the solution is below 40 °C, then add 10 mL of glutaraldehyde and 20 mL of 0.3 M sodium cacodylate.
   4. Add 0.2 g of tannic acid and dissolve it in the solution.
   5. Add 50 mL of 0.15 M sodium cacodylate.
   6. Store three or four 20 mL scintillation vials of fixative in fridge at 4 °C, or on ice if used on the same day.
3. Prepare Tyrode's solution with 20 mM 2,3- butanedione monoxime (BDM), according to the recipe in Table 1.
4. Construct a Langendorff apparatus inside a fume cupboard.
   1. Clamp two 100 mL plastic syringe tubes to two different retort stands, approximately 70 cm high from the stand base.
   2. Connect the plastic syringe tubes and a connector tube using 3 mm-inner-diameter tubing and a three-way stopcock as shown in Figure 1.
   3. Fit a 3 mm outer-diameter cannula to the bottom of the connector tubing, where the heart will be tied for perfusion fixation.
5. Fill the syringe tubes with Tyrode's solution and fixative solutions at 37 °C.
   1. Remove air bubbles within the tubing by passing the syringe solutions through them.

2. Acquire Electron Microscopy Data of Cardiomyocyte Ultrastructure

1. Prepare the animal for excision and chemical fixation of the heart.
   NOTE: This protocol details the steps to process adult male Wistar (name for a specific breed of albino rat) rat cardiac tissue. The protocol may require modifications when the cardiac tissue is sourced from other species.
   1. Anesthetize the animal by treating the rat (200-250 g by body weight) with 0.5 mL of 250 U/mL heparin via intraperitoneal injection. Wait for 10 min, then treat the rat with intraperitoneal injection of pentobarbital (210 mg/kg of body weight).
   2. Confirm a proper degree of anesthesia by testing the toe pinch reflex.
   3. Euthanize the animal by cervical dislocation.
   4. Harvest the heart using dissection procedures similar to previously published JoVE articles^22,23, then place it in ice-cold saline.
   5. Isolate the ascending aorta and cannulate. Ensure that the tip of the cannula sits just above the semi-lunar valve, where the coronary arteries branch off. Tie a thread tightly around the ascending aorta.
   6. Connect the cannula to the gravity-driven Langendorff apparatus operated at ~70 cm above the base of the system (Figure 1).
   7. Twist the stopcock on the Langendorff system to perfuse the heart with Tyrode's solution, including 20 mM BDM (a myosin inhibitor) for 2-3 min.
   8. Twist the stopcock to begin perfusion with fixative of 2% paraformaldehyde, 2.5% glutaraldehyde, and 0.2% tannic acid in 0.15 M sodium cacodylate at 37 °C for 10 min. If successful, the heart will turn pale brown and become stiff and rubbery.
   9. Using a razor blade, dissect tissue blocks from the left ventricular (lateral) free wall and obtain tissue blocks approximately 1 mm³ in size.
   10. Store the samples in pre-cooled 20 mL scintillation vials of the same fixative on ice for 2 h. Store as many samples as possible in the vials, and ensure that the samples are submerged in the solution.
       CAUTION: It is important to keep samples cold until after the 100% dehydration step below.
2. Further fixation and staining of samples for electron microscopy.
   1. Pour 100 mL of 0.15 M sodium cacodylate buffer in a glass beaker and cool it on ice.
   2. Prepare equal volumes of 4% osmium tetroxide and 0.3 M sodium cacodylate, followed by the addition of 0.08 g of potassium ferrocyanide to make a heavy metal stain solution containing 2% potassium ferrocyanide in 2% osmium tetroxide and 0.15 M sodium cacodylate. Cool the solution on ice.
   3. Pipette the fixative out and replace it with enough cold 0.15 M sodium cacodylate buffer to submerge samples in the vials. Place the vials on ice for 5 min.
   4. Repeat step 2.2.3 four more times with 0.15 M sodium cacodylate to remove excess fixative.
      CAUTION: Do not use glass pipettes because tiny shards can get into the sample and can ruin diamond knives during tissue block sectioning. It is important to pre-cool all solutions on ice before adding them to the sample. It is also important that the sample remains covered by solution all time (very brief periods of partial coverage lasting no more than a few seconds may be briefly tolerated during solution exchanges). When washing or replacing solutions, add the new solution quickly after removing the previous solution. Keep the scintillation vials on ice between washes. Note that this step is not time sensitive, the tissue blocks can be washed slightly longer, if needed.
   5. Replace sodium cacodylate buffer with ice-cold heavy metal stain solution and store it on ice overnight. Ensure that the ferrocyanide is well mixed by shaking the vial by hand; the solution should turn black.
      CAUTION: Work in the fume hood when performing this step because osmium is toxic.
   6. Dilute 4% aqueous uranyl acetate (UA) stock solution (Table 1) to 2% using equal volumes of stock UA solution and double distilled water, and cool it down on ice.
   7. Replace heavy metal stain with ice-cooled 0.15 M sodium cacodylate buffer, and let the sample incubate for 5 min on ice.
   8. Repeat step 2.2.7 four more times on ice to rinse off any excess heavy metal stain solution.
   9. Rinse the samples four times, with a 2-min wait-period in between in purified water (double-distilled is sufficient).
   10. Replace purified water with ice-cold 2% UA and let the sample incubate for 60-120 min on ice.
   11. Cool down five 20 mL scintillation vials of ethanol (enough to submerge samples) on ice that will be used in the dehydration step. The six vials have increasing percentages of ethanol in distilled water: 20%, 50%, 70%, 90%, and 100%.
   12. Pour pure acetone into another 20 mL scintillation vial and cool on ice along with the ethanol vials.
   13. Rinse samples in purified water four times with 2 min waiting periods on ice to wash excess UA.
3. Dehydrate samples in ethanol.
   1. Dehydrate in cold ethanol series by successively replacing solution within the sample vial as follows, on ice: 20% ethanol for 10 min; 50% ethanol for 10 min; 70% ethanol for 10 min; 90% ethanol for 10 min; then twice in 100% ethanol for 10 min.
   2. Transition sample to room temperature by replacing the final 100% ethanol with cooled pure acetone and place the sample vial on a room-temperature lab bench for 10 min.
   3. Perform one more 10 min wash in pure acetone at room temperature to remove condensation that is observable within the vials. While incubating, make up the acetone/resin solutions.
   4. Replace the pure acetone in the vials with 50:50 pure acetone and epoxy resin (with proportions for epoxy resin components as stated by the manufacturer). Use all components from the same batch. Leave the resin-filled sample vials overnight on a rotor.
4. Embed samples in resin.
   1. Replace 50:50 resin with 75% resin (25% acetone) and incubate for 3 h, followed by further incubation/infiltration in 100% resin for 4 h at room temperature.
   2. Replace the 100% resin with fresh 100% resin, and leave the sample vials overnight for deeper penetration of the resin into the tissue samples.
   3. Take samples out of the vials and place them in containers that are oven-friendly and have a flat base; aluminum or silver foil baking cups can be used for this purpose, for example.
   4. Gently pour (to avoid displacement of the samples) fresh resin over the samples (thus embedding samples in resin) and polymerize the resin and samples in an oven at 60 °C for 48 h.
5. Re-orient resin blocks to image cells in cross-section.
   1. Obtain 1 µm thick test sections from the resin blocks using an ultramicrotome with a glass knife to assess cell orientation²⁴.
   2. Stain the thick test sections for 20 s with 1% toluene blue and 1% borax.
   3. Examine muscle cell orientation under a bright field microscope.
   4. Based on the orientation inferred from the images of the stained test sections, re-orient longitudinally or obliquely oriented (similar to Figure 2A) resin blocks to ensure that cells are exposed to the glass knife so that they will be cut in cross-section (similar to Figure 2B).
6. Image tissue sections using electron tomography.
   1. Obtain semi-thin sections (~300 nm) of the reoriented tissue blocks using a diamond knife and transfer the sections onto copper grids²⁵.
   2. Stain the thick sections with 2% UA and Sato lead²⁵.
   3. Apply colloidal gold particles on both sides of the sections²⁵.
   4. Obtain sets of single or dual-axis tilt series of projected images from -70 ° to +70 °²⁵.
7. Use IMOD²⁰ to reconstruct the 3D image stack (a series of 2D images that provide the 3D information of a single electron tomography section) of the cell. This reconstructed stack will be segmented in the next step.

3. Segment Myofibrils and Mitochondria Regions from the EM 3D Image Dataset

1. Execute the IMOD program "3dmod".
2. Within the 3dmod graphical user interface, enter the address of the ".rec" or ".mrc" file that contains the 3D reconstructed image dataset of the cell (generated in step 2.7) into the entry box labeled "Image file(s):", then press "OK".
3. Under the "File" menu, select New Model, then save the file with an appropriate name using the "Save Model as"… menu item under "File".
   NOTE: An object in IMOD can contain a collection of segmented components that make up the "object". By default, a new model contains a new object with the id "#1".
4. Under the "Special" menu, select "Drawing Tools". This will open a new tool bar similar to that shown in Figure 3A.
   NOTE: There are several tools that can be used to create contours around the different organelle boundaries. More help on ways to use these tools can be found in the IMOD²⁰ documentation.
5. Choose the "Sculpt" option in the "Drawing Tools" menu, and move the mouse over to the image window; a circular contour centered on the mouse pointer will appear.
6. By holding the middle mouse button down over a mitochondrion (the darker regions of the image files, as illustrated by demarcations with green contour lines in Figure 3A), drag the perimeter of the circle contour into the shape of its boundary.
7. Once contouring of the mitochondrion boundary is complete, release the middle button and repeat steps 3.6 for each mitochondrion in the data. Each contour will automatically be recognized by IMOD as a new contour within the same object.
8. Under the "Edit | Object "menu, select "New" to create a new object. This will automatically increment the total number of objects by one and assign this number to the new object.
9. Repeat steps 3.6 and 3.7 to segment and save myofibril contours.
10. Repeat step 3.8, followed by step 3.6, to segment the cell boundary as well.
11. Save the model file under the "File" menu.
12. Execute the following commands in a command-line window to convert each object grouping into a binary mask as illustrated in Figure 4A-C.
    1. Extract a specific object from the model "imodextract object modelfile outputmodelfile" where "object" is the number of the object to be extracted.
    2. Create a mask for that object: imodmop -mask 255 outputmodelfile imagefile outputmask.mrc
    3. Convert the file into a tif stack: mrc2tif -s outputmask.mrc outputmask.tif

4. Create a Finite Element Mesh from the Segmented Components

1. Iso2mesh is a freely available MATLAB program to convert TIFF image stacks into volumetric tetrahedral finite element meshes. Download and add iso2mesh to the MATLAB path from iso2mesh.sourceforge.net.
2. Download the source codes and data to simulate RyR clusters on the mesh from the github website https://github.com/CellSMB/RyR-simulator.
3. Start the CardiacCellMeshGenerator MATLAB application (Figure 5).
4. Load the different organelle component masks into MATLAB using the three push buttons on the upper left hand side of the GUI.
5. Create another binary image stack that demarcates gaps between myofibrils and mitochondria as shown in Figure 6A.
   1. Open ImageJ.
   2. Using the File | Open dialog, load the myofibrils and mitochondria tiff stacks into the program.
   3. Initiate the image addition plugin by selecting "Process | Calculator Plus".
   4. Select the myofibril image stack as i1, the mitochondria image stack as i2, and choose the "Add" operator. Click "OK".
   5. After a new image stack representing the result of 4.5.4 appears, select "Edit | Invert" to produce an image stack similar to Figure 6A.
6. Load the file containing the binary image stack of the gaps between myofibrils and mitochondria by pushing the "RyRGapsFile" button on the CardiacCellMeshGenerator program.
7. Push "Generate Mesh" on the GUI. This will trigger the iso2mesh command v2m with the 'cgalmesh' option to generate a tetrahedral mesh similar to Figure 4E. Three files will be output at the end of this step: an .ele file, a .face file, and a .node file that will contain the listing of nodes that make up the elements, the nodes that make up the faces, and the coordinates of the nodes, respectively.

5. Mathematically Map the Spatially Varying Density of Ion-channels of Interest onto the Finite Element Mesh.

1. Generate the necessary inputs for the RyR-Simulator by pushing the button labelled Generate RyR-Simulator inputs on the GUI.
   NOTE: The button will trigger a function generateRyRsimulatorInputs.m, which uses the following information from step 4 to generate the inputs:
   (1) outDir: the location to output files that are necessary for RyR cluster simulation.
   (2) imres: the pixel resolution in the three directions of the image stacks.
   (3) myofibril_file: the file containing the binary image stack like that shown in Figure 4B.
   (4) sarcolemma_file: the file containing the binary image stack like that shown in Figure 4A.
   (5) ryrgaps_file: the file containing the binary image stack like that shown in Figure 5A.
   1. After this function executes, check that the following files have been created within the directory specified as the outDir path:
   • d_axial_micron.txt, which represents the axial distance between the position of the z-disc and the remainder of the pixels in the image stack.
   • d_radial_micron.txt, which represents the Euclidean distance (excluding the axial component) from each pixel in the set of possible RyR cluster locations to the pixels on the z-disc plane.
   • W_micron.txt, which represents the list of spatial coordinates of all the available positions for RyR clusters to be present.
   • The remaining 3 files in the folder contain the suffix "_pixel" rather than "_micron" to denote that the values within these files have been written out in pixel coordinate form.
2. Simulate RyR cluster distributions on the binary image stack of myofibrils.
   1. Push the button labelled "Open RyR-simulator in R" to initiate the R program.
   2. On the R-gui, select "File | Open" and find the file "settings.R" within the RyR-Simulator package (RyR-Simulator/source/settings.R).
   3. Also open the file ryr-simulator-parallel.R (located in RyR-Simulator/source/ryr-simulator-parallel.R). Environments like Rstudio (https://www.rstudio.com) or a plain command line interface can be used, e.g. using the R64 command in a shell or command window.
   4. Change the parameters in settings.R file as detailed below:
      1. Set Path2 to the folder address that contains files listed in 5.1.2 for an experimentally acquired confocal image stack of RyR clusters and myofibrils.
         NOTE: The github repository folder input-files/master-cell/ already contains files that were generated for a previously collected image stack.
      2. Set Path4 to a folder address where the files that were generated in step 5.1.2 are stored.
      3. Set Path3 point to a folder where the user wants the simulated RyR cluster locations to be saved.
      4. Set N to the number of RyR clusters to be simulated in the model (typically in the range of 200 to 300).
      5. Set etol, a tolerance setting, for the difference between the experimentally measured spatial distribution of RyR clusters and the model simulated spatial distribution of RyR clusters.
      6. Set numIter to limit the number of attempts that the RyR-Simulator should take to find a simulated RyR cluster pattern that satisfies the etol value.
         NOTE: Values for etol and numIter have been set to typical values within the settings.R file.
      7. Set numPatterns to the number of different RyR cluster patterns that the user wants to simulate (typically, it is useful practice simulating 99 patterns for statistical confidence).
      8. Set numCores to enable the use of several CPU threads (cores) for faster parallel processing with R to simulate the point patterns.
   5. Check that the following packages are installed using the package installer gui in R: snow, doSNOW, doparallel, foreach, iterators, and rgl.
   6. Execute the simulator by entering the following command in the R command window: source('path to ryr-simulator-parallel.R',chdir=TRUE)
      NOTE: The output of the RyR-Simulator program is a list of .txt files (a numPatterns file will be generated) that contain coordinate lists in N rows and 3 columns, which represent the x, y, and z coordinates of the N simulated RyR clusters.
3. Map points as spatial densities onto a computational model using the CardiacCellMeshGenerator.
   1. By selecting the button labelled "Select RyR points file", choose a simulated RyR cluster distribution text file from those that were output by the RyR-Simulator.
   2. Execute "RyR Density Mapper" on the GUI in MATLAB. This will map the spatial locations of the simulated RyR clusters in the .txt file in step 5.3.1 onto the finite element mesh that was generated in step 4.8 using a method called a spherical kernel intensity estimator method²⁶.
      NOTE: The output from this step is a file with .txt extension that contains a list of values for the numeric density of the ion-channel per unit spherical volume at each of the computational mesh nodes.

Results

Figure 2 through Figure 7 provide representative results of several key steps in this protocol: (i) visualizing and reorienting tissue blocks for cross-sectional electron microscopy views; (ii) generating a 3D electron microscopy image stack; (iii) segmenting sub-cellular ultrastructure for organelles of interest; (iv) generation of a finite element mesh using iso2mesh; (v) simulating a realistic distribution of RyR clusters on t...

Discussion

The above protocol outlines key steps to generate a novel finite element geometric model of cardiomyocyte ultrastructure. The method enables computational fusion of different microscopy (or, in principle, other data) modalities to develop a more comprehensive computational model of cardiomyocyte dynamics that includes details of spatial cell architecture. There is currently no other protocol available to create such a model of a cardiomyocyte.

Step 1 outlines a protocol for perfusion fixation....

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Materials
Sodium chloride	Sigma-Aldrich	746398
Calcium chloride	Sigma-Aldrich	C8106
Magnesium chloride	Sigma-Aldrich	M2393
Sodium bicarbonate	Sigma-Aldrich	S5761
Potassium chloride	Sigma-Aldrich	P5405
Dextrose	Sigma-Aldrich	D9434
Sodium hydroxide	Sigma-Aldrich	S8045
Probenecid	Sigma-Aldrich	P8761
2,3-Butanedione monoxime	Sigma-Aldrich	B0753
25% Glutaraldehyde EM Grade (500 ml bottle)	Merck	354400-500ML
Paraformaldehyde	Sigma-Aldrich	P6148
Tannic Acid	Sigma-Aldrich	403040-500G	100g EM grade
Sodium cacodylate	Sigma-Aldrich	C0250
Phosphate-buffered saline (PBS)	Sigma-Aldrich	P4593
Osmium Tetroxide	Sigma-Aldrich	75632-10ML	4% in water, 5 ml bottle (or 10 ml bottle also available)
Uranyl Acetate	EM Sciences	22400	25g bottle
Potassium Ferrocyanide	Merck Millipore	104973
Toluene blue	Sigma-Aldrich	T3260
Borax	Sigma-Aldrich	S9640	also termed sodium borate
Ethanol	Sigma-Aldrich	792780	Diluted to different percentages with pure water
Acetone	EM Sciences	RT10017
Resin kit	EM Sciences	14040	ACM Durcupan works well
Hydrochloric acid	Sigma-Aldrich	H9892	1Normal solution
Equipment
Ultramicrotome	Leica	EM UC7
Transmission electron microscope	ThermoFisher Scientific	Tecnai F30	http://www.leica-microsystems.com/
Retort stand	Proscitech	T752
Tubing	BioStrategy	75831-346	for langendorff perfusion apparatus, 3 mm diameter is recommended but not essential
Stopcocks	SDR	QP13813	for langendorff tubing; product is only an example, user can select any
retort stand clamps	Proscitech	T715
Plastic syringes	SDR	QPC1108	for solutions on langendorff apparatus
Cannulation silk suture, 7-0	TeleFlex	15B051000	for tieing heart on langedorff apparatus
Cannula			Made from 3 mm outer-diameter steel needle
Rubber petri dish mat	Proscitech	H068	for use as cutting board during fixed-heart dissection
Razor blades	Proscitech	L056	for cutting fixed-heart into small blocks for EM processing
Glass bottles	BioStrategy	89000-236	for storing solutions during tissue fixation and processing for EM
Beakers	BioStrategy	213-0477	for storing solutions temporarily and during perfusion
Scintillation vials	BioStrategy	548-2170	for tissue samples during EM processing
Dissection kit	Proscitech	T161	for animal dissection
Syringe Filters	Proscitech	WS3-02225S	for purification of Uranyl Acetate
Aluminium/silver foil baking cups			From any baking products store
Dupont Diamond knife	BioStrategy	102680-780	35 degree angle version produces best sections.
Colloidal Gold	BBI Solutions	EM. GC15	15 nm colloidal gold
EM mesh grids	Proscitech	GCU150	a variety of sizes can be tested: GCU150h, GCU200h for example
Plastic disposal pippettes	Proscitech	LCH20	best to use plastic disposables especially when working with resin
Software
SerialEM	University of Boulder		tomography acquisition
MATLAB	MathWorks		https://www.mathworks.com/products/matlab.html
IMOD	University of Boulder		image alignment and segmentation
iso2mesh			available at http://iso2mesh.sourceforge.net
Fiji or similar image processing software	ImageJ	Fiji is Just Image J	available at https://fiji.sc for manipulation of binary image stacks
RyR-Simulator codes/data	CellSMB group		available at https://github.com/CellSMB/RyR-simulator
CardiacCellMeshGenerator	CellSMB group		comes with RyR-Simulator under folder "gui-version"
R-statistics software	R-project		Download from https://www.r-project.org
spatstat	R-project		install via R program
rgl	R-project		install via R program
doparallel	R-project		install via R program
foreach	R-project		install via R program
doSNOW	R-project		install via R program
iterators	R-project		install via R program