Original Contribution |
From the Department of Physiology, University of Auckland, Auckland, NZ.
Correspondence to Dr Mark Cannell, Department of Physiology, University of Auckland, Private Bag 92019, Grafton St, Auckland, NZ. E-mail m.cannell{at}auckland.ac.nz
| Abstract |
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Key Words: heart structure t-system imaging myocyte rat
| Introduction |
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Most studies have used EM to provide sufficient resolution to identify
the tubular membranes. However, this method suffers from the
disadvantage that the specimen must be fixed (or frozen), dehydrated,
thin sectioned and heavy-metal stained. Obtaining structural
information through the thickness of a cell with EM is
problematic because of the poor penetration of the electron
beam. Even "thick EM sections" are limited to a thickness of
5 µm,8 and because of this problem only an
11x24x2µm section of the TATS in a mouse myocardial cell has been
shown.6 EM of thin sections relies on absorption and so
has no intrinsic 3-dimensional (3D) resolution. This leads to images of
thicker sections becoming blurred and losing internal detail.
Three-dimensional reconstruction from stacks of thin EM sections is
complicated by the difficulty of obtaining the necessary registration
between separate thin sections that are subject to distortion. Indeed,
the TATS has only been reconstructed over a 5.5-µm-thick segment of a
heart cell with manual section registration.7
The t-system in skeletal muscle provides a rapid propagation of electrical excitation into the cell interior.9 10 11 Evidence for such a role for the t-system in heart12 13 has been less clear, since there is no correlation between contraction speed and abundance of t-system.3 However, optical measurements of latencies for calcium release across rat ventricular cells show that the t-system provides both a rapid inward spread of electrical excitation and the calcium influx that triggers calcium release from the sarcoplasmic reticulum.14 The microarchitecture of the t-system has been suggested to be important in determining the levels of ionic accumulation/depletion during excitation.7 15 16 The t-system may not be a fixed structure within the cell, since short-term cell culture has been reported to be associated with a loss of t-tubules,17 and t-tubule proliferation occurs with hypertrophy.13 These observations suggest that a method for investigating t-tubular morphology in living myocytes may be useful for studying pathological changes in myocyte structure.
The confocal microscope provides a means for optically sectioning living specimens, thereby overcoming problems associated with fixation and dehydration. As shown by Shacklock et al18 and Cheng et al,19 it is possible to detect t-tubules by immersing cells in a soluble fluorescent marker that penetrates the tubular system. We have extended this approach by using 2-photon molecular excitation (TPME) microscopy20 and staining the extracellular compartment with a fluorescent probe that does not cross the cell membrane. Although the t-tubules themselves are generally below the optical limit of resolution, this does not preclude quantitative measurement of the fractional cell volume occupied by these structures, since the imaging properties of the microscope are known from its point-spread function (PSF). We have used this approach to obtain estimates of fractional volumes and tubule diameters in rat ventricular myocytes. A preliminary account of some of these methods has been published elsewhere.21
| Materials and Methods |
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Imaging
The t-system was visualized by immersing cells in a bathing
medium containing
1 mmol/L dextran-linked
fluorescein (molecular weight 70 000; Molecular Probes).
Images were recorded with an LSM 410 laser scanning confocal
microscope (Zeiss), which was modified for TPME
microscopy.23 Illumination for 2-photon
fluorescence excitation was supplied by a mode-locked
Ti:Sapphire laser (Mira 900F; Coherent), which generated a train of
ultrashort pulses at a repetition frequency of
76 MHz. For these
experiments, the laser was tuned to a center wavelength of 860 nm with
the intracavity prisms adjusted to produce a bandwidth of 19 nm. The
pulse width was
45 fs (measured by autocorrelation) and the average
illumination power at the sample was
4 mW. An external prism
compressor was adjusted to (re)establish minimum pulse width at
the specimen.23 The cell was imaged through a Zeiss x63
1.25-numerical aperture oil-immersion objective. Images from the
isolated cells were obtained at a nominal spacing of 200 nm along the
optical axis. The optical performance of the microscope was
determined by imaging 200-nm fluorescent latex beads
(Fluospheres, Molecular Probes). Since the PSF of the microscope
depends on the distribution of refractive index in the
sample,24 25 the PSF was measured by dispersing the
subresolution beads in the bath containing the myocytes in bathing
medium without fluorescein. Beads that spontaneously stuck
to the cell membrane were imaged at several heights above the
coverslip, and from these images a resolution of 400 nm (full width at
half maximum; FWHM) in x-y and 800 nm in z was
measured. Figure 1
illustrates the
TPME microscope PSF measured in this way. To exceed the Nyquist
criterion for image sampling, the voxel size was set to
0.1x0.1x0.2 µm (x, y, and z,
respectively). This fine voxel resolution also improved convergence of
the deconvolution procedure (see below), but it limited the cell area
that could be imaged to
102x102 µm. Since this encompassed
most of the chosen myocytes, this limitation was considered
acceptable.
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Data Processing
To improve the resolution and signal-to-noise ratio of the
volume data, digital deconvolution26 was applied to
"stacks" of images. In a recent comparison of image-restoration
methods for confocal microscopy, the Richardson-Lucy
algorithm27 was judged superior to other
algorithms.28 For this study, the deconvolution algorithm
was implemented in the language IDL (Research Systems Inc) to
produce a maximum likelihood reconstruction for the specimen in the
presence of Poisson (photon shot) noise. A Poisson noise model was
used, because the number of photons collected was probably insufficient
to justify using a gaussian noise model. The update step of the
procedure can be written as follows27 28 :
![]() | (1) |
are the convolution and
cross-correlation operators, respectively. In general, about 15
iterations of Equation 1
Volume Visualization
To assist visualization of the t-system architecture, a
topological "skeleton" was constructed from the deconvolved stack
of images. In this 3D skeleton,29 all information about
tubule signal intensity was removed by replacing tubule segments with a
thin line of uniform thickness, which followed the direction of the
t-tubule in space. Since the 3D connectivity of the skeleton is
identical to that of the t-tubular system, this method of data
presentation clarifies the organization of the t-tubular
system. In any case, the calculated t-tubule diameters (see below) were
generally less than the wavelength of light so the original light image
contained no more spatial information than the topological skeleton.
The first step in skeleton construction was generation of a binary mask
from the enhanced image stack. Pixels with intensities greater than the
mean background+5 SD were assumed to represent t-tubular
segments and were set to 1.0; all other pixels were set to 0.0. From
this 3D binary mask, a topological skeleton was generated by deleting
all pixels that did not change the connectivity of the 3D
structure.30
The need to construct a topological skeleton forced us to adopt a
lower-limit threshold for t-tubular cross-section. For the data sets
presented here, tubules less than
50 nm in diameter would be
lost in the noise and therefore missed. Since the smallest t-tubule
diameter reported in left ventricular myocytes of rat is
70 nm,31 this limit was considered acceptable. However,
more extensive signal averaging (to reduce photon noise) or a
relaxation of the stringency of the binary mask would allow any desired
lower limit to be achieved.
Estimation of Fractional t-Tubule Volume
Since we were unable to detect any entry of dextran-linked
fluorescein into the intracellular compartment, and cell
autofluorescence was negligible (not shown), the calculation of
fractional t-tubular volume FVtt was
straightforward and required no assumptions about t-tubular
microarchitecture. The total intensity of fluorescence
recorded within the boundary of the sarcolemma is directly
proportional to the amount of dye contained within the t-system, as
shown in the following:
![]() | (2) |
Estimation of t-Tubule Diameters
The peak signal from a piece of t-tubule is a function of the
tubule geometry and PSF of the microscope (see Figure 2A
) as follows:
![]() | (3) |
with
respect to the optical axis) being 1 at points inside the segment and 0
elsewhere.
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As shown in Figure 2B
, even for a (typical) PSF that is
symmetrical about the z-axis, Equation 3
remains a
function of both radius R and angle
. However, if the PSF
is completely symmetrical, then the signal does not depend on
(see
Figure 2C
) and becomes only a function of the PSF and
R, as follows:
![]() | (4) |
),
if the tubules are adequately described by cylinders and the PSF is
symmetrical. Although the microscope does not have a symmetrical PSF,
the effective PSF applied to the data (cell structure) can be made
symmetrical by convolving each of the images of the 3D data set in the
x-y plane with a gaussian kernel so that the in-plane FWHM
equals the axial FWHM (0.8 µm). Blurring the images to create
identical resolutions in x, y, and z
results in the image data losing the directional dependence of the
local fluorescence signal. For segments of t-tubules of which
the architecture is more complicated than simple nonbranching
cylindrical segments, the binary topological skeleton contains the
information needed to correct the relationship between
IR and R for any branching that
may occur in the t-system. The correction factor is obtained by
convolving the binary skeleton with the PSF used to process the data to
yield a weighting (w) that is applied to the data to allow
for elements such as blind-ended tubules (w<1.0) and
branches (w>1.0) (see Figure 2D
and wxR.
We also used the calculated distribution of tubule diameters to
estimate the total surface area of t-system within the sampled cell
volume. In the calculation, pieces of t-tubule are approximated by
cylinders of varying diameter so that a piece of tubule of length
si and radius
Ri contributes a surface area
Si=si2
Ri.
The total t-system area STT in a given
volume can then be obtained by summing all the contributions of pieces
of t-tubule within the sample volume, as follows:
![]() | (5) |
To visualize the distribution of tubule diameters, the skeleton was intensity coded according to the calculated t-tubule diameter and displayed by isosurface rendering using IrisExplorer software (Silicon Graphics).
| Results |
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1%; eg,
References 12 and 3212 32 ).
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To simplify and clarify the general macroarchitecture of the cell
t-tubular system, the volume data were reduced to a 3D skeleton (see
Materials and Methods). The 3D skeleton of a rat
ventricular myocyte t-system is shown in Figure 4
. Visual inspection of such skeletons
suggested that the overall macroarchitecture of the t-tubular system
resembles a complicated mesh with some limited regularity at the level
of the Z-line (at a regular axial spacing of
1.8 µm). There
are also a few regions relatively devoid of t-tubules that probably
coincide with the locations of cell nuclei. To quantify the
preponderance of t-tubules at the Z-lines, Figure 5A
shows a graph of tubule density as a
function of the longitudinal position inside the cell. Although 60% of
the tubule volume occurs at the Z-line (as defined by their presence in
a region 0.55 µm around Z-lines), the remaining 40% of the
tubules are found at other locations along the myofibrils. It is
apparent from Figures 4
and 5A
that a considerable amount
of the t-tubular system forms longitudinal connections between
t-tubules, although most of the t-tubules are organized in transverse
planes. However, the t-tubules do not run across the cell at the level
of the Z-lines for great distances but instead run at the level of 1
Z-line for a short distance and then change direction to join other
tubules at other Z-lines. In some places, no t-tubules ran in the
transverse direction (across the cell) but instead passed through the
cell at an angle to its longitudinal axis (see also stereo views in
Figure 6
). Having reconstructed the
skeleton of t-tubular architecture, it is straightforward to determine
the distribution of the length of t-tubular segments between branching
points. Figure 5B
shows a graph of t-tubule lengths between
branching points obtained from the skeleton data in Figure 4
.
The distribution of interbranch lengths is approximately exponential,
with short segments being most prominent and a mean branch length of
6.87 µm. To help clarify the complex macroarchitecture of the
tubular system, Figure 6A
shows an enlarged stereo view of the
tubular system from a randomly selected part of the cell. In the upper
right portion of this view, it can be seen that t-tubules form
ring-shaped connections, possibly wrapping around myofibrils. A region
almost devoid of tubules is apparent in the center of this section of
tubular network. The predominance of t-tubules in planes located at the
Z-line can be identified most clearly in the region at the left of this
view.
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Electron micrographs suggest that tubules have nearly circular cross
sections, so it is possible to calculate the apparent width of the
tubule (see Materials and Methods). The calculated tubule diameters
have been imposed on the skeletons by gray coding in Figure 6B
.
Although the majority of tubules appear to have diameters of
200 to
300 nm, there are also local increases and decreases in tubule diameter
at (apparently) random points in the cell. The data shown in Figure 6B
are summarized in a histogram of tubule diameters shown in
Figure 7
. It is apparent that the
distribution is approximately gaussian, and almost no tubules larger
than 450 nm were found. The histogram has a maximum at a diameter of
240 nm, and most t-tubules (51%) are between 180 and 280 nm wide.
Using the calculated distribution of tubule diameters to estimate the
surface area of t-tubular membrane per unit of cell volume (see
Materials and Methods), we obtained a value of
STT/VCell=0.44
µm2/µm3.
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The positions at which the t-tubules leave the cell surface can be
visualized from the same data set. In Figure 8
, the topology of the surface membrane
has been extracted from the data set and isosurface rendered. It is
apparent that the t-tubules form extensive regions of regular patterns
on an almost rectangular mesh. The tubule mouths often run for some
tens of micrometers in linear arrays with a transverse
spacing between mouths of
1.8 µm. However, there are points
within the mesh that are missing a tubule contact. Although
freeze-fracture images also support this view,33 the more
extensive data set presented here allows a greater appreciation
of the extent of order and disorder of the tubule contacts with the
surface membrane.
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| Discussion |
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Our data suggest that the fractional volume
(VFtt) of the t-tubular system is
3.6%. Earlier measurements based on EM studies suggested a much
lower VFtt in the rat (typically 1% for
adult rat; eg, References 12 and 3212 32 ). This large difference is not
easily explained by an error in our method of measurement, since the
total fluorescence from the extracellular marker should depend
only on the volume of the t-tubules and the concentration of marker
(see Materials and Methods). Although a large contribution of
autofluorescence to the recorded signal would lead to an
overestimate of VFtt, inspection of the
images shows that the autofluorescence background was barely
detectable compared with the t-tubule signal. Similar arguments rule
out the possibility that marker dye penetration into the cytoplasm
could explain the larger VFtt (since any
entry of the dye into the cell would appear as generalized cytoplasmic
staining). Although low levels of dextran binding to phospholipids have
been reported34 and such an effect would cause an
overestimate of VFtt, 4 pieces of evidence
suggest that this explanation is unlikely. (1) The reported densities
of dextran binding by phospholipids are too low (
0.4 mg D-40/g
1,2-dipalmitoyl-3-sn-phosphatidyl-choline) to
materially affect our results. (2) Our estimates of t-tubule diameters
and EM data are in reasonable agreement (see below), which suggests
that our method accurately measures t-tubules. (3) The level of
membrane binding needed to explain the difference between our results
and those of Stewart and Page32 would have led to an
elevated level of fluorescence near the cell edge, but this was
not observed. (4) Further support for the idea that EM studies have
underestimated the extent of the t-tubular system is provided by
electrophysiological studies. We estimate a
surface-to-volume ratio
STT/VCell=0.44
µm2/µm3 that is almost
3 times larger than previously reported stereological measurements from
EM data (0.15
µm2/µm3).35
A recent study of capacity/volume ratios in cardiac myocytes from
different species suggests a specific membrane capacitance
CM/VCell of
6.76 pF/pL for myocytes from young (3-month-old) and 8.88 pF/pL from
older (6-month-old) rats.36 Since the specific
membrane capacitance is
1 µF/cm2 (see, eg,
Reference 37 ), these values can be converted into a ratio
of total sarcolemmal membrane area (outer sarcolemma+ t-tubular
system) that is
STotal/VCell
0.68
µm2/µm3 for the younger
and 0.89 µm2/µm3
for older rats. For a typical myocyte 100 µm long with a
diameter of 20 µm (ie, a volume of
3.1x104 µm3, we
can estimate from our data that
STotal/VCell
would be
0.68
µm2/µm3, which is in
good agreement with the
electrophysiological data.
The above agreement between the estimate of cell capacitance and our data suggests that the lower VFtt and STT/VCell derived from previous EM studies must be in error. Since there can be problems in identifying t-tubules in electron micrographs (eg, see Reference 3838 ), as well as specimen shrinkage during section preparation, such an underestimate of VFtt and STT/VCell might easily occur. It is also possible that the method of measurement used by Stewart and Page32 will have underestimated VFtt, since, as they noted, (1) average t-tubule diameter is much less than the EM section thickness, and (2) t-tubules were assumed to run at right angles to the long axis of the cell only, whereas we have detected large amounts of t-tubules running in other directions.
"t-System" Morphology
The volume data show that the term "transverse-tubular system"
is something of a misnomer, since t-tubules run in all directions. The
general impression of the t-tubular organization is that of a rete,
although such a term does not fully describe the preponderance of
elements near the Z-lines. We have been able to confirm the presence of
large numbers of tubules running in axial directions,4 the
presence of which led to the suggestions that the t-system be referred
to as the TATS, or T-Ax.5 6 38 However, there are
also large numbers of tubules that run in neither axial nor transverse
directions, so a more accurate descriptive term might be the
"sarcolemmal Z rete" (SZR). For convenience, this nomenclature will
be adopted in the following discussion, although the possible general
acceptance of such a term will depend on the findings of future
studies on other species.
The SZR often formed complete loops around the (assumed) location of
myofibrils. However, there are also regions within the cell that are
relatively devoid of tubules. We suspect that some of these regions may
be associated with parts of the cell that are not involved in
excitation-contraction coupling (such as the nucleus), but further work
will be required to confirm this view. Visual inspection of the SZR
skeletons suggested that there was little or no correlation of tubule
width with position along the sarcomere (see Figure 6B
).
However, quantitative analysis suggested that the average
tubule diameter was
15% larger between the Z-lines than in
longitudinal elements (not shown). Since the cells were relaxed, this
increase in average diameter could be the result of the constant volume
behavior of the cell. We suspect that if the cell were stretched to
working lengths, this difference would largely disappear, and there
would be almost no correlation between tubule diameter and longitudinal
position.
Although the optical methods used here cannot resolve the fine microarchitecture of the SZR, they give good insight into the gross morphology of the SZR. For surveying the general organization of the SZR, our optical approach produces a comprehensive overview of it, which would not be possible (for any reasonable amount of effort) with EM. This is because with one image stack we are able to resolve the entire SZR within a selected myocyte. In addition, we have shown that it is straightforward to extract quantitative information about the fractional cell volume occupied by the SZR and equivalent tubule diameters. In contrast to the utility of our optical method, stereological analysis of electron micrographs is extremely time consuming. In addition, our fluorescent method does not require extensive geometrical correction factors to take account of the variations in the plane of section of t-tubules.32
Surface Membrane Topology
Using the methods introduced here, we have been able to produce
images that portray the organization of junction between the SZR and
the outer sarcolemmal surface. These images are very similar to
freeze-fracture images of myocyte surfaces.33 However, we
have been able to examine a much larger area of the cell surface than
has been achieved by freeze-fracture techniques. In addition, we can be
certain that the organization of SZR "mouths" is not confused with
caveolae. The SZR mouths are mostly arranged in linear arrays with a
longitudinal spacing of
1.8 µm. However, these linear arrays
are interrupted by missing mouths or by a misregistration with another
region of linear arrays (Figure 8
). It is possible that such an
organization may reflect the nonuniform development of the SZR during
maturation, since it is known that in some species neonatal myocytes
have no SZR (eg, cats40 ). It is likely that during
hypertrophy the SZR will grow and form new connections with
the surface membrane. Whether this occurs as a result of new
invaginations of the surface membrane or by extension of the SZR with
subsequent fusion with the surface of the cell is unknown. It may be
possible to distinguish between these possibilities by applying our
methods to myocytes that are actively undergoing
hypertrophy.
The fluid contained within the SZR can only directly exchange with the extracellular fluid at the junction of the SZR with the outer cell surface. Since accumulation/depletion phenomena will be limited by the efficiency of this exchange, it is possible that a part of the propensity of hypertrophied hearts to develop arrhythmias (eg, Reference 4141 ) may reflect a mismatch between SZR volume and the number of SZR mouths. Again, future work should be able to directly examine this possibility.
In conclusion, we have shown that it is possible to examine the gross morphology of the SZR using optical methods combined with digital image processing. The advantage of this approach is that most of the analysis and data acquisition can be automated. In addition, we can examine the cell microarchitecture in identified living myocytes that have not suffered from the extensive preprocessing required for EM.
| Acknowledgments |
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Received August 10, 1998; accepted October 6, 1998.
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