Cell Physiology

Three-dimensional mitochondrial arrangement in ventricular myocytes: from chaos to order

Rikke Birkedal, Holly A. Shiels, Marko Vendelin


We have developed a novel method to quantitatively analyze mitochondrial positioning in three dimensions. Using this method, we compared the relative positioning of mitochondria in adult rat and rainbow trout (Oncorhynchus mykiss) ventricular myocytes. Energetic data suggest that trout, in contrast to the rat, have two subpopulations of mitochondria in their cardiomyocytes. Therefore, we speculated whether trout cardiomyocytes exhibit two types of mitochondrial patterns. Stacks of confocal images of mitochondria were acquired in live cardiomyocytes. The images were processed and mitochondrial centers were detected automatically. The mitochondrial arrangement was analyzed by calculating the three-dimensional probability density and distribution functions describing the distances between neighboring mitochondrial centers. In the rat (8 cells with a total of 7,546 mitochondrial centers), intermyofibrillar mitochondria are highly ordered and arranged in parallel strands. These strands are separated by ∼1.8 μm and can be found in any transversal direction relative to each other. Neighboring strands exhibit the same mitochondrial periodicity. In contrast to the rat, trout ventricular myocytes (22 cells; 5,528 mitochondrial centers) exhibit a relatively chaotic mitochondrial pattern. Neighboring mitochondria can be found in any direction relative to each other. Thus, two potential subpopulations of mitochondria in trout are not distinguishable by their pattern. The developed method required minor interaction in the filtering of the mitochondrial centers. It is therefore a practical approach to describe intracellular organization and may also be used for analysis of time-dependent organizational changes. The obtained quantitative description of mitochondrial organization is a requisite for accurate mathematical analysis of mitochondrial systems biology.

  • confocal microscopy
  • quantitative analysis
  • rat
  • rainbow trout
  • probability density function

quantitative analysis of intracellular energy fluxes and interaction of mitochondria with other intracellular structures requires a description of intracellular organization that can be used in mathematical models. In rat cardiomyocytes, the intermyofibrillar mitochondria are arranged in a very regular manner. According to electron microscope images of fixed cells, intermyofibrillar mitochondria are approximately the size of a sarcomere and are arranged in longitudinal rows in clefts between myofibrils (26). A similar pattern of the mitochondria is found in live cardiomyocytes, when mitochondria are studied under a confocal microscope (2, 11, 20). The mitochondria appear as rectangles, and quantitative analyzes of the relative position of their centers suggest that they are organized in a highly ordered, crystal-like, pattern (34).

The organization of mitochondria may have important functional consequences. Cardiomyocytes seem to be divided into functional compartments called intracellular energetic units (ICEUs), in which adenine nucleotides are channeled between ATPases and mitochondria without being released to the cytosolic bulk solution (14, 23, 24, 35). This compartmentation is expected from experiments showing that mitochondria in skinned fibers and cardiomyocytes have a low apparent affinity for exogenous ADP in the surrounding medium but not endogenous ADP produced by ATPases. Furthermore, a competitive exogenous ADP trapping system consisting of pyruvate kinase and phosphoenolpyruvate is not able to inhibit mitochondrial consumption of endogenous ADP by >40%, although it has a 100 times higher ADP consumption capacity (28). These experimental results can only be reproduced by mathematical models if they assume large and rather localized diffusion restriction that separates mitochondria and endogenous ATPases from the surrounding solution (35). The functional advantage of such a compartmentation should be to increase the coupling of energy production to energy consumption diminishing the risk of the cardiomyocytes experiencing energy deficit (25). However, disruption of the mitochondrial regular pattern with trypsin increases the apparent affinity for exogenous ADP without affecting the maximal respiration capacity of mitochondria (23, 34). This suggests that disruption of the mitochondrial crystal-like pattern diminishes intracellular compartmentation and hence channeling of adenine nucleotides. This may in turn reduce the coupling between energy consumption and energy production leading to a compromise of the energetic status.

The overall structure and mitochondrial distribution in cardiomyocytes seem to differ between species. As noted above, rat cardiomyocytes have several longitudinal rows of mitochondria interchanged with rows of myofibrils (26, 32). The situation seems to be different in cardiomyocytes from rainbow trout (Oncorhynchus mykiss). Trout cells have a much smaller diameter and one single cylinder-shaped layer of myofibrils situated immediately beneath the sarcolemma. According to electron microscope images, this layer surrounds a central core of mitochondria with no obvious pattern (38). Despite this difference, rainbow trout cardiomyocytes also seem to be divided into functional compartments with mitochondria and ATPases forming ICEUs (5, 6). However, the fixation and dehydration of cells during their preparation for electron microscopy may produce histological artifacts (21), and to our knowledge there is currently no quantitative description of the mitochondrial pattern in live trout cardiomyocytes. Interestingly, a closer look at the energetic data reveals that skinned trout cardiac fibers actually exhibit both a low and a high apparent ADP affinity, suggesting the existence of two mitochondrial subpopulations (4). In rat, a low apparent ADP affinity is reflecting, in the first approximation, the overall diffusion restriction between the solution surrounding the fiber and mitochondrial inner membrane (23). Assuming that in the rat a low apparent ADP affinity is related to the organization of the mitochondria (34), we speculated whether the two potential subpopulations in trout might be distinguishable by their pattern.

The aim of the present study was to quantitatively analyze and compare the relative positioning of mitochondria in live rat and trout cardiomyocytes. For this, the two-dimensional quantitative approach from a previous study (34) was elaborated to encompass three dimensions. Our quantitative analysis of mitochondrial organization in the three-dimensional (3D) space shows large differences in mitochondrial patterns in trout and rat. In rat, the intermyofibrillar mitochondria are highly ordered. In contrast to rat, the arrangement of mitochondria in trout is rather random, or chaotic.


All animal procedures were performed in accordance with United Kingdom regulations (The Animals Scientific Procedures Act 1986).

Isolated cardiomyocytes.

Isolated rat cardiomyocytes were kindly provided by Louise Miller and were prepared according to the procedure of Eisner et al. (12). They were kept at room temperature in a solution consisting of (in mM) 115 NaCl, 10 HEPES, 11.1 glucose, 1.2 NaH2PO4, 1.2 MgSO4, 4 KCl, 50 taurine, and 0.1 CaCl2, titrated to pH 7.34 with NaOH.

Rainbow trout were obtained from Chirk Trout Farm and kept in freshwater tanks at 15°C. They were kept at a 12:12-h light:dark cycle and regularly fed with commercial trout pellets. Rainbow trout cardiomyocytes were isolated, as described in Shiels et al. (29). Briefly, the fish were humanely killed by a Schedule 1 method according to the Animal Scientific Procedures Act 1986 published by the United Kingdom Home Office, and the heart was quickly excised and transferred to ice-cold isolation solution consisting of (in mM) 100 NaCl, 10 KCl, 12 KH2PO4, 4 MgSO4, 50 taurine, 20 glucose, and 10 HEPES (adjusted to pH 6.9 using KOH). A cannula was inserted into the ventricle through the bulbus arteriosus, and the heart was perfused in a retrograde manner with isolation solution bubbled with 99% O2. After the heart was perfused with Ca2+-free isolation solution for 10 min to clear the myocardium of blood and relax the myofibrils, the perfusion solution was changed to a digestion solution consisting of isolation solution containing trypsin, collagenase, and BSA. Perfusion with digestive enzymes lasted ∼14 min. The heart was then taken off the cannula, quickly dried on a piece of paper to remove any solution with digestive enzymes, and transferred to fresh, ice-cold isolation solution. The ventricle was cut into small pieces, which were triturated with a Pasteur pipette to obtain isolated ventricular myocytes. The trout cardiomyocytes were kept in isolation solution in a refrigerator until use.

Confocal imaging of mitochondria in cardiomyocytes.

MitoTracker red CMXRos is a membrane-permeable derivative of the redox-sensitive dye X-rosamine. Visible dye therefore accumulates in the mitochondria in a potential-dependent manner. At least 15 min before the cardiomyocytes were used, 0.2 μM MitoTracker red CMXRos was added to trout cardiomyocytes in isolation solution and rat cardiomyocytes in Ringer solution, respectively. To visualize the sarcolemma in trout cardiomyocytes, 2 μM 4-{2-[6-(dioctylamino)-2-naphthalenyl]ethenyl}1-(3-sulfopropyl)-pyridinium (di-8-ANEPPS) at least 15 min before use.

A suspension of dye-loaded cells was put on a glass coverslip and the cells were visualized with the use of an inverted confocal microscope (Leica Microsystems, Heidelberg, Germany) with a ×63 water-immersion objective (1.2 numerical aperture) at room temperature. MitoTracker red CMXRos was excited with a 543-nm laser and emission was recorded at 570–690 nm. Di-8-ANEPPS was excited with 488 nm and emission was recorded at 550–700 nm range. For each cell, a 3D image was generated by scanning several confocal planes (XY) at different depths (Z) of the cell (Fig. 1). This 3D image was used for further analysis. It should be noted that the z-resolution was lower than the x- and y-resolution, and that this is reflected in the results in as much as pixels are elongated in the z-direction.

Fig. 1.

Method used to analyze distribution of mitochondria in three-dimensional (3D) space. A: first, series of Z-stack confocal images of nonpermeabilized cardiomyocytes have been acquired after preloading the cells with MitoTracker Red (scheme in A). Second, the local maxima (small squares in A) of fluorescence were found, taking into account recorded fluorescence in several consecutive images as explained in the text. As indicated in the scheme, the maxima are not always on the same image in the stack. Note that sometimes two fluorescence maxima seem to be found per mitochondrion (as illustrated in A). Next, the closest neighbors were found for each mitochondrion, one per sector (the projections of the sector borders in two dimensions are shown by dashed lines in A). In this scheme, the mitochondrion, in which neighbors are sought, is highlighted, and the closest neighbors to this mitochondrion are indicated by arrows. Note that the closest mitochondria in some sectors are not always from the same image in the stack, as indicated in A. The relative coordinates of the closest neighbors, i.e., the coordinates relative to the highlighted mitochondria, are stored and analyzed further. B: division of 3D space into the sectors with sectors shown by the different level of gray. The mitochondrion for which neighbors are sought is positioned at the origin of coordinate system. Here, the coordinate axis y corresponds to the fiber orientation. The sector names are shown in the scheme B.

Analysis of mitochondrial distribution.

Relative mitochondrial distribution was analyzed with the following procedure. First, the 3D stack of images were blurred using a Gaussian function with standard deviations equal to 0.25 μm in x- and y-directions and 0.32 μm in z-direction. Since we wanted to determine the positioning of mitochondrial centers with high precision, we oversampled our images in all directions. The standard deviation used for blurring corresponded to ∼8 pixels on the image in x- and y-directions and ∼2–3 images in the stack in z-direction. With the use of the blurred stack of images, local fluorescence maxima were found. Only the maxima that had a large fluorescence in ±0.25 μm (x- and y-directions) and ±0.32 μm (z-direction) were recorded for further analysis. Blurring and recording only local maxima that are largest in a relatively large box, allowed us to effectively remove stochastic fluorescence maxima that always occur during the recording of the images. The local fluorescence maxima were typically found in the mitochondrial center, although deviations may occur, and this may result in a higher spread of the data than is actually the case. However, the following calculations are based on the assumption that fluorescence maxima are found at the mitochondrial centers, and therefore, throughout the text, fluorescence maxima are referred to as mitochondrial centers. Second, for rat cardiomyocytes, subsarcolemmal mitochondria, and mitochondria around the nucleus (perinuclear mitochondria) were filtered out as judged by the eye. No filtering was applied for trout. Third, for each fluorescence maximum, the relative positions of other maxima, which were within a 6-μm radius from each other, were recorded. Fourth, the 3D probability density was computed describing the distribution of relative positions of mitochondrial centers. The density was found by dividing 3D space into 0.08 × 0.08 × 0.33 μm (x × y × z) boxes and counting the relative positions falling into each of the boxes. Fifth, the overall fiber orientation was found assuming that the two symmetrically distributed maxima of the probability density were along the fiber. The computed fiber orientation was similar to cell orientation, as judged visually. Next, the relative distances found in the third step were recalculated taking into account the fiber orientation and assuming that the y-axis was aligned along the fiber.

The statistical analysis of relative positions of mitochondrial centers was performed by either calculating the probability densities (in 3D) for all mitochondria that were within a radius of 6 μm from each other or dividing the space around each of the mitochondria into the sectors and analyzing the distributions in each sector separately. Both methods were used here for analysis. The division of the space surrounding each mitochondrion is shown in Fig. 1. The sectors used in this study are based on two-dimensional analysis of mitochondrial arrangement in rat cardiomyocytes (34).

In addition to the probability densities, the relative distribution of mitochondrial centers was characterized by the cumulative distribution function. The distribution function shows the fraction of mitochondria as a function of the distance in a given direction. For this, the sectors were pooled according to the direction of their median: the two opposing sectors whose medians coincided with the x-, y-, and z-axes were termed X, Y, and Z, respectively, the four sectors whose medians coincided with y = x were termed XY, and the four sectors whose medians coincided with z = y were termed YZ (Fig. 1B). The pooling of opposing sectors is justified by the symmetry of the calculated probability density functions (see figures in results).

The programs developed for this analysis were written in Python and are available upon request. The positioning of mitochondrial centers on the image stacks was checked using IMOD [http://bio3d.colorado.edu/imod, The Boulder Laboratory for 3D Electron Microscopy of Cells Department of Molecular, Cellular, and Developmental Biology, University of Colorado (17)]. The 3D probability densities were visualized and examined using OpenDX (http://www.opendx.org).


Figure 2 shows representative pictures of rat and trout cardiomyocytes in the XY- and XZ-planes (longitudinal and cross-sectional, respectively). Note the large difference in mitochondrial organization between the two species. In the rat (see Fig. 2, A and B), intermyofibrillar mitochondria are highly organized. In the trout (Fig. 2, C and D), most of the mitochondria seem to form a tubular network in the central part of the cell. A relatively large distance between sarcolemma and mitochondria was evident in trout (Fig. 2, C and D) but was absent in rat (not shown).

Fig. 2.

Representative confocal images (A, C) and reconstructed cross-sections (B, D) of nonpermeabilized cardiomyocytes from the rat (A, B) and trout (C, D). Mitochondria were visualized with MitoTracker Red CMXRos (red color on images). In addition, trout cardiomyocytes were preloaded with 4-{2-[6-(dioctylamino)-2-naphthalenyl]ethenyl}1-(3-sulfo-propyl)-pyridinium (di-8-ANEPPS) to visualize the sarcolemma (green color on images). Note that the range and excitation wavelength used to record di-8-ANEPPS fluorescence covers autofluorescence of FAD as well. Thus, due to co-localization of fluorescence coming from the MitoTracker (red) and autofluorescence of FAD (green), trout mitochondria are orange (C and D). In rat cardiomyocytes (A and B), intermyofibrillar mitochondria are rather regularly spaced forming a mesh throughout a cardiomyocyte. In trout cardiomyocytes (C and D), mitochondria form a tubular network. In all images, the fluorescence maxima are shown by white dots. Note that only few mitochondria have centers on the shown images. All other mitochondria have centers on the stack images either below or above the shown ones. Sizes of images: A, 39.7 μm × 39.7 μm; B, 39.7 μm × 10.2 μm; C, 31.7 μm × 31.7 μm; D, 31.7 μm × 5.4 μm.

To analyze mitochondrial distribution, fluorescence maxima were identified as explained in materials and methods. As shown in Fig. 2A, the fluorescence maxima in rat intermyofibrillar mitochondria were frequently found in pairs next to each other. It is not clear whether these paired fluorescence maxima are within the same mitochondrion or correspond to two mitochondria that are very close to each other. Therefore, both maxima were considered in our analysis as mitochondrial centers (discussed below). The representative maxima found by our method are shown in Fig. 3. Because of the blurring of the original images used in the algorithm, the found maxima are quite close to geometric center, judged by eye. Since it is difficult, even impossible, to determine the borders of mitochondria from the confocal images due to the resolution of the microscope, we were not able to check quantitatively how close the found maxima were to the geometrical center.

Fig. 3.

Detection of fluorescence maxima in rat (A) and trout (B) cardiomyocytes. Here, one of the centers found in the rat (Fig. 2A) and one of the centers found in the trout (Fig. 2C) is zoomed and shown in 3D (top), the XY-plane (middle), and the XZ-plane (bottom). The fluorescence intensity is shown in pseudo-color with dark blue corresponding to a low fluorescence and red corresponding to a high fluorescence. On each subplot, the zoomed center is marked with a dark gray dot (other centers are not shown for clarity). In the rat, the fluorescence maxima frequently occur in pairs very close to each other, and it is uncertain whether they belong to two separate mitochondria or a single, dog bone-shaped mitochondrion. This was not observed in the trout. In contrast to the algorithm used to find the fluorescence maxima, only light blurring was used in shown images to reduce the noise. Block sizes: A, 3.06 μm × 3.06 μm × 3.06 μm; B, 2.44 μm × 2.44 μm × 2.44 μm.

For the rat, confocal image stacks from eight cells were acquired, and a total of 7,546 fluorescence maxima were found. For trout, confocal image stacks from 22 cells were acquired with a total of 5,528 fluorescence maxima found. The distribution of the mitochondrial centers is described below. Note that a coordinate system was used where the y-axis in 3D space was aligned along fibers and the z-axis was perpendicular to the confocal images.

Probability density of all mitochondria within a distance of 6 μm.

The probability density of all neighboring mitochondria within a radius of 6 μm is shown for rat and trout cardiomyocytes in Figs. 4 and 5, respectively. For each mitochondrial center, the relative position of neighboring mitochondrial centers within a radius of 6 μm was found and statistically analyzed. The 3D probability density found on the basis of these data is shown in Figs. 4 and 5. The six upper frames show XY-planes that cut the 3D space perpendicular to the z-axis at different z values. Since the probability density is symmetric with respect to the origin of the coordinate system (0,0,0), the planes cutting at positive z values are shown only. Likewise, the six lower frames show XZ-planes taken at different y-positions. Because local fluorescence maxima within a distance of 0.25 μm in each x- and y-direction, and within 0.32 μm in each z-direction were filtered out as described in materials and methods, there is a central box of 0.50 × 0.50 × 0.64 μm (x × y × z) in which the probability density is zero.

Fig. 4.

Probability density describing the 3D distribution of mitochondria in rat cardiomyocytes. This density indicates the probability of finding a mitochondrial center on a certain position relative to the mitochondrion at the origin of the coordinate system (0,0,0). In the present diagrams, the probability density describes the distribution of all mitochondrial centers which are within a radius of 6 μm from the each other. 3D space was cut by planes perpendicular to the z-axis (XY planes, top) or y-axis (XZ planes, bottom) at different positions (indicated in the top right corner of each subplot). The value of the probability density is indicated by colors as shown on the bar to the right. In rat cardiomyocytes, mitochondria are aligned along the fiber (y-axis) a certain distance from each other. The probability density shows several maxima indicating the regular arrangement pattern of mitochondria.

Fig. 5.

Probability density describing the 3D distribution of mitochondria in trout cardiomyocytes. As in Fig. 4, the probability density describes the distribution of all mitochondrial centers within a radius of 6 μm from each other (see Fig. 4 for description of notation). In trout cardiomyocytes, mitochondria are mainly aligned on one plane (bottom subplots). In addition, while there are maxima of density along the fiber, the positioning of mitochondrial centers in all other directions is relatively random.

In rat cardiomyocytes, the highest probability density is found in a narrow, highly delimited strand along the y-axis (Fig. 4, top). This is clear on both the XY-plane at z = 0.00 μm and on the XZ-planes showing a central, highly delimited probability density maximum (Fig. 4, bottom). Around this central maximum, there is a ring of low probability density surrounded by a ring of relatively high probability density, which slowly decreases toward the edge of the diagram (Fig. 4, bottom). A mitochondrial pattern is distinguishable by several regularly spaced, local probability density maxima along the y-axis that indicate the periodicity of mitochondria. Parallel to the central strand, neighboring strands seem to show the same mitochondrial periodicity (Fig. 4, top, z = 0.00 μm).

In trout cardiomyocytes, the probability density distribution is more diffuse. As in the rat, the maximal probability density is found along the y-axis. However, in contrast to the rat, it is not delimited to the sides (Fig. 5, top). This continuity of the probability density is also observed cross-sectionally (Fig. 5, bottom). In contrast to rat, there is no ring of low probability density around the central maximum. Notably, the probability density decreases with distance from the center, but the decrease is much steeper vertically than horizontally (Fig. 5, bottom). This indicates that mitochondria are mainly distributed around a plane in trout. In contrast to rat, there is no distinguishable mitochondrial pattern: there are only two local fluorescence maxima, one on each side of the center along the y-axis.

Probability density of closest neighbors in sectors.

On the basis of the regular pattern of intermyofibrillar mitochondria in rat cardiomyocytes, the considered sphere around each mitochondrial center was divided into sectors (Fig. 1). For each sector, the distribution of the closest neighboring mitochondria was described by the probability density. Figures 6 and 7 show the results from the rat and trout, respectively, and the top and bottom panels are as in Figs. 4 and 5 showing the values of the density at different planes cutting 3D space. When only the closest neighbors are considered (Figs. 6 and 7), the probability density is refined and the distances between mitochondrial centers can be identified with a greater accuracy.

Fig. 6.

Probability density of the closest mitochondrial centers in each of the sectors in rat cardiomyocytes. The space around each mitochondrial center was divided into sectors, and the distribution of the closest mitochondrial centers in each sector was analyzed. As in Fig. 4, the space was cut by planes perpendicular to z-axis (XY planes, top) or y-axis (XZ planes, bottom) at different positions to show the 3D probability density. Note in the XY planes, the mitochondrial centers are packed in certain areas. In cross-sections (XZ planes), mitochondrial centers are either highly concentrated in the center or distributed in a circle around the center.

Fig. 7.

Probability density of the closest mitochondrial centers in each of the sectors in trout cardiomyocytes. See description of Fig. 6 for notation. Note that in contrast to rat cardiomyocytes, the neighboring mitochondrial centers are distributed relatively randomly, resembling an ellipsoid around the origin (0,0,0) in both XY and XZ planes.

The highest probability density is found along the y-axis in rat cardiomyocytes, similar to Fig. 4. Notably, there tends to be at least two local maxima in each of the y-sectors (Fig. 6, top; section z = 0.00 μm and z = 0.33 μm). In section z = 0.00 μm, on each side of the central strand of maxima, there is a parallel strand of local maxima. As these two parallel strands come closer together in z = 0.33 μm and z = 0.65 μm, and fuse in z = 1.30 μm and z = 1.95 μm, they show that the periodicity of mitochondrial positioning is maintained. The cross-sections show a narrow central, highly delimited maximum. This is surrounded by a ring of low probability density, which is in turn surrounded by a ring of relatively high activity (Fig. 6, bottom). This is similar to what was shown in Fig. 4. Notably, and now in contrast to Fig. 4, when only the closest neighboring mitochondria are considered, the ring of relatively high probability density is delimited.

In trout cardiomyocytes, despite the fact that sectors are considered separately, their probability density distributions fuse together so that the center is surrounded by an ellipsoid with a continuous, high probability density (Fig. 7, top and bottom). The probability is highest near the center and slowly decreases with distance.

Distance between mitochondrial centers.

The sector-dependent distance between mitochondrial centers relative to each other (Fig. 8A) and the y-axis (Fig. 9A) was analyzed statistically using the same sectors as for Figs. 6 and 7. Opposing x-, y- and z-sectors, and diagonal sectors whose median had the same absolute angle to the XY-plane, and to the YZ-plane, were pooled because of the symmetrical mitochondrial arrangement. Here, the statistical analysis of the distances is presented using cumulative distribution functions, which show the fraction of mitochondria that are closer either to the origin (Fig. 8) or to the y-axis (Fig. 9) than a given distance.

Fig. 8.

Cumulative distribution function of the distance between centers of neighboring mitochondria. A: the distance R between the mitochondrial center in the origin (○) and the closest mitochondrial center in each of the sectors is considered. This distance is statistically analyzed for the rat (B) and trout (C). The names of the sectors are indicated in the insets of the plots. B: in the rat, there are three groups of distributions corresponding to longitudinal (Y), transversal (X and Z) and diagonal (XY and YZ) directions. C: in the trout, only distributions of mitochondria in the transversal directions (X and Z) are relatively close to each other.

Fig. 9.

A: cumulative distribution function of the distance from the y-axis to the neighboring mitochondrial centers (RXZ). Note the difference between vectors R (in Fig. 8A) and RXZ in this scheme. As can be expected from the partitioning of space into the sectors (Fig. 1), the neighboring mitochondria in longitudinal sectors (Y) are very close to the y-axis, leading to a small RXZ distance. This is observed for both rat (B) and trout (with somewhat larger spread; C). However, only in rat, do the neighboring mitochondria in transversal (X and Z) and diagonal (XY and YZ) sectors have relatively similar distance from the y-axis.

The distances between mitochondrial centers are summarized in Fig. 8. In rat cardiomyocytes, the distribution functions of the five sector types seemed to fall into three groups. Namely, the cumulative distribution functions of the transversal X and Z and the diagonal XY and YZ were very close (Fig. 8B). The closest neighboring mitochondria were found in longitudinal Y-sectors. Notably, this distribution function seemed to increase in a stepwise manner with a first step ∼1 μm, and a second step ∼1.8 μm. These two steps in the cumulative distribution function, while not very strong, are separated by a region where a smaller amount of mitochondrial centers are found leading to relatively small derivative of the distribution function ∼1.4 μm. The stepwise increase confirms the observation in Fig. 6 of at least two local maxima in each of the Y-sectors. Most of the mitochondria in X- and Z-sectors are slightly further away than in Y-sectors. The cumulative distribution curve rises smoothly and more steeply suggesting a lower spread of mitochondria in these directions. Not surprisingly, the mitochondria are further away in the diagonal sectors XY and YZ than in the longitudinal (Y) and transversal (X and Z) sectors. In trout cardiomyocytes, in contrast to the situation in rat, mitochondria in Y-sectors were furthest away (Fig. 8C). The cumulative distribution function for Y-sectors tended to group with the functions of the diagonal XY- and YZ-sectors at the smaller distances. The closest mitochondria were found in the transverse X- and Z-sectors.

Calculating the cumulative distribution functions for the distance to the y-axis revealed a different pattern (Fig. 9). In rat, the Y-distribution function rose steeply, suggesting a small spread around the y-axis (Fig. 9B). The distribution functions for all the other sectors could be grouped together. This indicates that transverse spacing between longitudinal rows of mitochondria does not change in the longitudinal direction, i.e., the rows are parallel. In addition, this transverse spacing is the same in Y, Z, and diagonal directions.

In trout cardiomyocytes, the situation was different (Fig. 9C). The rise of the Y-distribution function was less steep suggesting a higher spread around the y-axis. Furthermore, the distance of diagonal mitochondria from the y-axis was lower than that of transversal mitochondria confirming the observations in Figs. 5 and 7 that in trout cardiomyocytes, there is no regular spacing between mitochondria.


The present study quantified the 3D arrangement of mitochondria in cardiomyocytes from rainbow trout and rat. Our results show that the 3D mitochondrial arrangement is highly variable between the two species. In rat cardiomyocytes, intermyofibrillar mitochondria are highly ordered and arranged in parallel strands (Figs. 2, 4, and 6). Notably, neighboring strands even show the same periodicity of the mitochondria (Figs. 4 and 6). In contrast, in trout cardiomyocytes the mitochondrial pattern is relatively chaotic (Figs. 2, 5, and 7). The mitochondria tend to align longitudinally as indicated by a higher probability density along the fiber, but the probability density is relatively high in all directions (Figs. 5 and 7). Thus, if trout cardiomyocytes exhibit two mitochondrial populations, these are not distinguishable by their arrangement. In this work, an approach was developed that was relatively simple to use and required only minor interaction in filtering the data. This makes it useful for analysis of large data sets and allows analyzing changes of the mitochondrial arrangement in time.

The mitochondrial arrangement, especially in rat cardiomyocytes, is related to the overall cell structure and myofibrillar arrangement. Rat cardiomyocytes have relatively large diameter (∼20 μm; Ref. 27), and electron microscope images show several rows of myofibrils interchanged with rows of mitochondria (32). Indeed, in the rat, the probability of finding a neighboring intermyofibrillar mitochondrial strand in the immediate vicinity of the central mitochondrial strand is very low (Figs. 4 and 6), and this is likely because each strand of mitochondria is surrounded by a ring of myofibrils. Outside this surrounding layer of myofibrils, parallel strands of mitochondria can be found in any direction as indicated by the cylinder of high probability density around the central strand (Figs. 4 and 6). The cumulative distribution function shows that the average distance between parallel rows of mitochondrial centers is ∼1.8 μm (Fig. 9). This value differs from that found in a previous study, in which the transversal distance was 1.43 μm (34). However, that study was carried out in two dimensions, and thus parallel mitochondrial rows in different planes were projected onto each other leading to underestimation of transversal distance between the mitochondrial centers.

In rat cardiomyocytes, intermyofibrillar mitochondria in parallel rows are arranged with more or less the same periodicity. Moreover, the periodicity in neighboring strands is in phase (Figs. 4 and 6), and this is what gives rise to the “crystal-like” pattern of rat mitochondria (34). While we have not determined the position of mitochondria relative to the sarcomere, this periodicity is consistent with the finding that intermyofibrillar mitochondria are mainly found at the level of the A-band of the myofilaments (18, 26, 31, 32). Thus mitochondrial periodicity is imposed by regular pattern of myofilaments in the cell. Our results differ from a previous study (34) in as much as the cumulative distribution function for the closest neighboring mitochondria in the longitudinal sectors seems to rise in several steps (Fig. 8, Y-sector). In accordance with this, the probability density in the Y-sectors seems to exhibit two local maxima: one at ∼1 μm and one at ∼1.8 μm (Fig. 6). This suggests that there are mainly two possible distances to the closest neighboring mitochondrial center. Indeed, Figs. 2A and 3A show that mitochondrial centers frequently occur in pairs. Thus the shorter distance is between paired centers and the longer distance is between single centers. This was not noted in a previous study, in which mitochondrial centers were consistently ∼2.0 μm apart (34). For comparison, the sarcomere length in relaxed cardiac muscle is ∼1.9 μm (32). The finding of paired centers may be due to differences between cardiomyocyte preparations or automatic rather than manual treatment of the data. It is uncertain whether paired centers represent two separate mitochondria or one single dog bone-shaped mitochondrion (Fig. 3A). In both cases two fluorescence maxima would be detected by the software.

The diameter of trout cardiomyocytes is relatively small (5–8 μm; Refs. 30 and 38). Figure 2B shows that in trout cardiomyocytes there is a gap between the sarcolemma and the central mitochondrial network. According to electron microscope images, this gap is due to a cylinder-shaped single layer of myofibrils that lies immediately beneath the sarcolemma and surrounds a central core of mitochondria (38). Therefore, in contrast to the rat, there is no regular transverse spacing between mitochondria. A longitudinal periodicity is lacking as well and the region with high probability density is ellipsoid shaped. This is confirmed by the cumulative distribution functions, which show that in the trout, mitochondria in the diagonal (XY and YZ) sectors compared with transverse (X and Z) sectors are closer to the y-axis (Fig. 9C). In the rat, these distributions are similar (Fig. 9B).

Skinned rat cardiomyocytes exhibit a low apparent mitochondrial ADP affinity because the intracellular environment is divided into functional compartments (ICEUs) in which adenosine nucleotides are locally channeled between ATPases and mitochondria (24). Tentatively, this compartmentation, which is specific to red muscle fibers (37), increases the coupling of energy consumption to energy production (25). In rat cardiomyocytes, a low apparent ADP affinity is related to the highly ordered organization of intermyofibrillar mitochondria (34). Intriguingly, despite the absence of an ordered mitochondrial pattern in trout cardiomyocytes, skinned fibers also exhibit a low apparent ADP affinity (46). Furthermore, recent evidence strongly suggests that this is due to their functional compartmentation into ICEUs (6). A closer look at skinned trout cardiac fibers reveals that they actually exhibit two apparent ADP affinities (4). This suggests the existence of two mitochondrial populations, possibly with different arrangements. However, from our present analysis, we were not able to determine the mitochondrial patterns that could be responsible for this. Thus the potential causes of two mitochondrial populations are still not clear and require further investigations.

The quantitative description of mitochondrial arrangements can be used to analyze intracellular energy fluxes and interactions between mitochondria in the cells. For example, mathematical models of oxygen transport in muscle cells, intracellular diffusion of metabolites, and propagation of mitochondrial oscillations require a geometric description of intracellular arrangement (2, 3, 36). In addition, the changes in mitochondrial organization in the heart muscle cells during ischemia (7, 15, 19) can be taken into account by the next generation of metabolic models. The quantitative approach developed by us and used to describe the organization of cardiac muscle cells gives not only the mean distances between mitochondrial centers, but the variability as well. The analysis of variability is expected to become an important aspect of intracellular modeling. Indeed, the nonlinear models used to analyze complex intracellular processes can be sensitive to small changes in parameter values indicating instability of some processes. The influence of mitochondrial arrangement and its variability can now be taken into account using the probability densities and cumulative distribution functions found in the present study for rat and trout cardiomyocytes.

In addition to the relative position of mitochondria determined in our work, several morphological aspects have to be taken into account for modeling of mitochondria in the cells. Mitochondrial morphology in many cells is not fixed but can change when the balance between fission and fusion is disturbed (22). For example, when the cardiac muscle cells are challenged by hypoxia, gigantic mitochondria, which are longer than several sarcomeres, can form (33). This is in contrast to mitochondrial morphology in normal conditions in adult rat cardiac muscle cells, where mitochondria are approximately the size of a sarcomere and are squarish and flattened in shape (26). In addition to the changes in size, depending on the cell type, the mitochondria can form an electrically continuous network (1, 13) or not (9). In adult rat cardiomyocytes, the mitochondria were found to be morphologically heterogeneous and not coupled electrically (8, 10). To our knowledge, the electric continuity has not been studied yet in trout cardiomyocytes. Another aspect of mitochondrial organization that is important for modeling oxygen fluxes in vivo is the regional intracellular differences in mitochondrial densities. For example, the mitochondrial volume density is higher near capillaries than in regions far from capillaries (16). Since we treated in our analysis all cell parts simultaneously, such gradients were ignored. Our method can be refined to take into account the regional differences in mitochondrial distribution by analyzing each region separately.

To summarize, we quantified 3D distribution of mitochondria in rat and rainbow trout cardiomyocytes by determining relative position of mitochondrial centers. While intermyofibrillar mitochondria were found to be highly ordered in the rat, mitochondria in trout are arranged in rather random pattern. The quantitative description of the arrangement can be used in the mathematical models of intracellular energy fluxes, diffusion of oxygen, and interactions between mitochondria in the cells.


This work was supported by the Marie Curie International Re-Integration Grant (to M. Vendelin), and the Biotechnology and Biological Sciences Research Council and the Danish Natural Science Research Council grants (to R. Birkedal).


We thank Louise Miller for providing the rat cardiomyocytes; Andrew W. Trafford, and David Eisner of the University of Manchester for the use of a confocal microscope.


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