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Veterans Affairs Medical Center, Durham, North Carolina 27705
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ABSTRACT |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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We have estimated the rate of diffusion of
calcium ions in the transverse tubules of isolated cardiocytes by
recording changes in peak calcium current
(ICa) caused by
rapid changes of the extracellular calcium concentration
([Ca]o) at various
intervals just preceding activation of
ICa. Isolated
ventricular cells of guinea pig heart and atrial cells from rabbit
heart were voltage-clamped (whole cell patch), superfused at a high
flow rate, and stimulated continuously with depolarizing pulses (0.5 Hz, 200- or 20-ms pulses from a holding potential of 
45 or
75 mV to 0 mV). In ventricular cells, the change in peak
ICa following a
sudden change of [Ca]o
increased rapidly as the delay between the solution change and
depolarization was increased, up to a delay of ~75 ms [time
constant (
) 
20 ms, 30-40% of total current change), and
then increased more slowly ( 200 ms, 60-70% of total
current change); 400-500 ms were needed to achieve 90% of the
total current increase. In atrial cells, a clear separation into two
phases was not possible and 90% of the current change occurred within
85 ms. The slow phase of current change, which was unique to the
ventricular cells, presumably reflects the slow equilibration of ions
between the bulk perfusate and the lumina of the transverse tubules. If
the lengths of the transverse tubules were equal to the cell thickness, the slow rate of change of current would be consistent with an apparent
diffusion coefficient for calcium ions of 0.95 × 10
6
cm2/s, considerably smaller than
the value in bulk solution (7.9 × 106
cm2/s). Most likely, this
discrepancy is due to a high degree of tortuosity in the transverse
tubular system in guinea pig ventricular cells or possibly to ion
binding sites within the tubular membranes and glycocalyx.
guinea pig ventricular cells; calcium; excitation-contraction coupling
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INTRODUCTION |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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THE TRANSVERSE TUBULES of cardiac ventricular muscle cells provide passageways for the exchange of solutes between the interstitial fluid and the interior of the cell. This exchange is important because nearly two-thirds of the cell membrane is in the form of transverse tubules (7), and excitation-contraction (E-C) coupling is mediated by structures residing mainly in the tubular membranes (i.e., the close apposition of plasmalemma and junctional sarcoplasmic reticulum; Refs. 12 and 20). Although the exchange of solutes between the interstitium and the interior of the cell is generally assumed to be rapid, the tubular network is known to be tortuous, consisting of both transverse and axial components (8, 7), and could impose a significant barrier to diffusion. A recent theoretical analysis suggests that substantial depletion or accumulation of ions could occur within the tubules during the passage of ionic current through the cell membrane, especially if the diffusion is slower than in bulk solution (2). Experimentally, slow movement of calcium ions within the transverse tubules of guinea pig ventricular cells has been observed in the presence of calcium-sensitive dyes (4), and slow exchange of ions between bulk perfusate and the cell surface has been observed in both rabbit and rat ventricular myocytes (30).
To attempt to determine the rate at which ions in the interstitium can exchange with those in the transverse tubules, we have studied the rate at which the peak magnitude of a rapidly activating and rapidly inactivating membrane current is changed by a very rapid change of the extracellular ion concentration. We compare the responses of guinea pig ventricular cells, which have a well-developed transverse tubular system (7), with those of rabbit atrial cells, which are similar in shape to the ventricular cells but lack transverse tubules (12, 16, 25, 27). Our results are consistent with a degree of tortuosity in the transverse tubular system that is similar to that found in skeletal muscle (1). A preliminary account of these results has been published (23).
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METHODS |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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Preparation of cells. Male guinea pigs weighing between 250 and 500 g were deeply anesthetized with 75 mg/kg pentobarbital sodium. The heart was rapidly excised and the aorta cannulated for coronary perfusion with oxygenated solutions (35-36°C). The heart was first perfused for 5 min with nominally calcium-free, low-sodium solution containing (in mM) 100 NaCl, 10 KCl, 1.2 KH2PO4, 50 taurine, 4 MgSO4, 20 glucose, and 10 HEPES at pH 6.9. The perfusate was then switched to a solution of the same composition with the addition of 1 mg/ml collagenase (type L, Sigma Chemical), 1 mg/ml fatty acid-free serum albumin (A-6003, Sigma Chemical), and 100 µM of CaCl2. CaCl2 (50 mM) was added in three aliquots during the enzyme perfusion to bring the total added calcium concentration to 200 µM. The heart was then minced and further incubated, with continuous stirring, in 5-10 ml of the same enzyme solution with the addition of 0.07 mg/ml protease (type XIV, Sigma Chemical). At 5- to 10-min intervals, the supernatant, containing dissociated cells, was drawn off and replaced by more enzyme solution. The cell suspensions were diluted into low-sodium solution to which 0.5 mM CaCl2 and 1 ml/500 ml kanamycin (Sigma Chemical) had been added and were stored at 23°C.
Atrial cells were obtained from the hearts of adult male rabbits by essentially the same method, with two changes: the perfusion solutions were prepared with calcium-free Tyrode solution rather than the modified Tyrode solution (see Voltage clamp) and the stirring times were approximately doubled. This investigation conforms with the Guide for the Care and Use of Laboratory Animals published by the National Institutes of Health [DHHS Publication No. (NIH) 85-23, Revised 1985].Voltage clamp. For experimentation, cells were placed in a Lucite chamber (3 ml) and continuously superfused with a prewarmed (35°C), modified Tyrode solution composed of (in mM) 150 NaCl, 5.4 KCl, 1.2 MgCl2, 5 HEPES, 1.8 CaCl2, and 5.5 glucose, with pH adjusted to 7.4 with NaOH. The details of our technique have been described in previous papers (22, 29). In short, the ends of an isolated cell were glued to the tips of two glass rods (diameter 76 µm) with alcian blue (25). Cells were attached in either a longitudinal or a transverse orientation (Fig. 1A). The length, width, and thickness of the cell were measured [to the nearest one-half division of the eyepiece graticule (1.25 µm)] by rotating the rod pair so that the cross-sectional area and the volume of the cell could be estimated. The mean dimensions of the principal groups of ventricular cells were (length × width × thickness) 121 ± 19 × 32 ± 5 × 12 ± 2 µm (longitudinal) and 139 ± 37 × 26 ± 4 × 13 ± 1 µm (transverse) (n = 5 in both cases). Atrial cells used in the study of calcium current (ICa) were 121 ± 20 × 16 ± 2 × 11 ± 3 µm. Most, although probably not all, of the portion of the cell lying over the glass surface was firmly attached (see DISCUSSION).
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when filled with a solution containing (in mM) 130 KCl, 10 HEPES, 5 K-oxaloacetate, 5 K-succinate, 1 MgCl2, 0.02 EGTA, and 5 mM
Na2ATP, pH 7.4. The cell
capacitance was estimated by applying a symmetrical ±5 mV pulse
while holding at 75 mV and again at 45 mV. One to two
minutes after membrane rupture, the cell was stimulated continuously at
0.5 Hz with depolarizing pulses to 0 mV. The holding potential was
45 mV for the study of
ICa and 75
mV for the study of sodium currents
(INa). After a
steady peak current was established, solution-changing protocols were
initiated. For the study of
INa, we added
250-350 µM lidocaine (6) to the control and experimental
solutions to reduce the current to a level that could be controlled.
Solution changes. Very fast extracellular solution changes were applied to a cell by means of a double-jet system (22). The position of the jets was monitored by an LED/phototransistor pair, the output of which was recorded simultaneously with the electrical and mechanical signals from a cell. In all experiments the flow velocity was ~50 mm/s, permitting a fast and highly reproducible solution change. The temperature of the perfusate was kept at 35°C throughout the experiment by switching between continuously flowing prewarmed solutions and keeping the flow rates identical for all solutions. The solution temperature was monitored by means of a thermistor placed 0.2 mm below the cell-bearing rods, 0.2 mm above the floor of the chamber, and 1 mm distal to the rod ends.
The values for the delay between the solution change and the depolarization given in Figs. 1-4 represent the difference between the first motion of the perfusion jets and the upstroke of the depolarizing pulse. The actual instant at which the solution change begins at the cell is ~19 ms following the jet motion, as estimated from exponential fits to the points describing the change in difference current as a function of the delay (see Figs. 2 and 3, described in RESULTS). This means that, for the nominally 15-ms delay (Fig. 2A), the actual solution change began ~4 ms after the peak inward current, so the difference current in that case was always zero and is omitted from the data plots.
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Recording and analysis. Current signals were digitized (Instrutech VR-100; 9-kHz channel, 4 channels) and stored on videotape with concurrent strip-chart recording (Gould 2400). Off-line analysis was made by recreating the analog signal, redigitizing each channel at 2.5 or 5.0 kHz, and analyzing the records with programs written by the authors in Asyst (Keithly-Metrobyte).
The peak inward ICa during control depolarizations (Icontrol) was visually estimated as the difference between the peak inward current and the steady-state current at the end of the pulse (10). In experiments involving INa, 10 µM verapamil was added to reduce interference from ICa; otherwise, peak currents were measured in the same way as ICa. Difference currents were obtained by subtracting the current in the depolarization immediately preceding a solution change from the current in the presence of the altered ion concentration (Fig. 1). The peak difference currents plotted in Fig. 2 were calculated as follows. For each cell, the peak difference current at each delay was divided by Icontrol in the control depolarization (Fig. 1B), and the result was averaged among all cells in an experimental group. Each set of averaged points was fitted with exponential functions, and the points were scaled so that the maximal extrapolated current change (
I)max was
equal to 100%. Thus
ICa represents the ratio
{ICa([Ca]o) ICa(0.45)}/[ICa(1.8) ICa(0.45)]. This procedure takes current rundown into account and allows direct comparison of the time course of current changes among the various cell
groups.
Data points representing the time course of
I were fitted with either
exponential functions or the one-dimensional diffusion equation by
means of a least-squares nonlinear regression program (NLREG, Phillip
Sherrod). Parameter values obtained from the fits to averaged data are
given as values ± SE of the fit. When fits to data sets from
individual cells are summarized, the results are given as means ± SE. Two-tailed t-tests were used to
determine statistical significance (Excel).
All of the critical experiments, i.e., those comparing the responses of
atrial and ventricular cells (Figs. 2 and
3), were made with cells attached to the
same glass rod in the longitudinal orientation, yielding very
reproducible results.
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Experimental approach. The relatively simple technique of making a concentration change (e.g., potassium) and observing the time course of changes in the holding current cannot readily provide a quantitative measure of diffusion times because there are multiple potassium channels with conductances that depend in complex ways on the membrane potential, the potassium equilibrium potential, the external concentration, and time. Thus the current at a given point in time after a solution change will depend on the current changes up to that time. This makes it virtually impossible to translate the time course of the current into a time course of ionic concentration, even for cells lacking transverse tubules. In accordance, our approach to exploring the extracellular space with rapid solution changes is to look at the effect of a "step" change of ionic concentration on a subsequent "delta function" conductance change in, for the present case, ICa and INa. Although neither the concentration changes nor the conductance changes used in the present study are ideally rapid, both are sufficiently so to allow us to observe compartmentalization of the extracellular space in ventricular myocytes.
A second important feature of our method is that we compare results obtained from experiments with ventricular cells with results obtained with atrial cells. This takes into account the uncertainty in the actual time course of the ionic concentration changes at the most superficial parts of the sarcolemma, as mentioned earlier. Without this comparison we could not, with any certainty, ascribe the apparently slow exchange of calcium and sodium observed in the ventricular myocytes to cellular components.| |
RESULTS |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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Effect of a rapid change of
[Ca]o.
At various intervals preceding every fifth depolarization
(delay; Fig. 1B), the calcium or
sodium concentration surrounding a cell
([Ca]o or
[Na]o) was rapidly
changed (Ca replacing Mg or, vice versa, Cs replacing Na; Fig.
1B). As the delay between the solution change and the depolarization was increased, the difference between the current in the test pulse
(Itest) and
that in the preceding conditioning pulse
(Icontrol; Fig.
1C) also increased (Fig.
2A). The change in peak
ICa following an
increase of [Ca]o from
0.45 to 1.8 mM was much more rapid in atrial cells than in ventricular
cells (Fig. 2). The difference current in the atrial cell reached 90%
of maximum by 85 ms but only 50% of maximum in that time in
ventricular cells. The mean ratio (±SE) of the extrapolated maximum
ICa to the
control current
(Imax/Icontrol)
was 1.01 ± 0.06 (n = 5)
for atrial cells and 1.24 ± 0.11 (n = 5) for longitudinally oriented
ventricular cells; i.e., the current was approximately doubled in each
cell type by increasing
[Ca]o from 0.45 to 1.8 mM. For descriptive purposes, the data points describing
ICa as a function
of the delay were fitted by the sum of two exponential functions (Fig.
2B; see details in
METHODS). For longitudinally oriented ventricular cells, the rate coefficients were 45 ± 12 and
5.1 ± 0.6 s1, with 36 ± 5% of the current change in the fast phase and 64 ± 4% in
the slow phase (estimates from fit ± SE of estimate). For atrial
cells, neither the rate coefficients (58 ± 39 and 19 ± 20 s1) nor the fractional
divisions of the overall current change (66 ± 62 and 34 ± 62%)
were sufficiently certain for us to be confident of the separation into
a fast and slow phase. On the other hand, the atrial data were well
fitted by a single exponential with a rate coefficient of 36 ± 2 s1. Irrespective of the
type of fit, the ventricular and atrial currents at each delay between
35 and 285 ms were significantly different
(P < 0.01, Wilcoxon test).
Steady-state relationship between
[Ca]o and
ICa.
Hypothetically, a difference between the time course of current change
in atrial and ventricular cells could reflect a very different
relationship between
[Ca]o and
ICa in the two
cell types. For example, the apparently rapid change of
ICa in atrial
cells could be due to saturation of
ICa at a very low
[Ca]o. However, the
measured relationship between
[Ca]o and
ICa in atrial
cells is very similar to that in ventricular cells (Fig.
2B,
inset). This relationship was found
in a separate group of cells by measuring the difference currents for
changes of [Ca]o from
0.45 mM to either 0.9, 1.35, or 1.8 mM at a delay sufficiently long
that ICa reached a steady state in both cell types [1,900 ms; for the change to 1.8 mM,
Imax/Icontrol = 1.09 ± 0.02 (n = 5) for atrial
cells and 1.06 ± 0.05 (n = 5) for
ventricular cells]. We conclude that the different time courses
of change in ICa
after a rapid concentration change are not due to different
relationships between
ICa and [Ca]o.
Slow changes in ICa?
The slow phase of current change could be due to a slow
change in the calcium channel itself, e.g., a slow shift in the level of steady-state inactivation (17). A difference between the atrial and
ventricular cell in this regard is plausible due to the markedly faster
waveform of ICa
in atrial cells, presumably due to different gating parameters of
ICa in the two
cell types (Fig. 2A). However, the
time course of change in
ICa was the same at a holding potential of either 45 or 75 mV, at which
potential any shifts in inactivation should be too small to affect
ICa (Fig. 2B, filled circles and diamonds,
respectively) (17). A less direct kind of slow change in
ICa could occur
due to changes in SR calcium content as
[Ca]o is changed.
However, there is no reason to expect a difference between atrial and
ventricular cells in this respect, and, in any case, an increase in the
SR calcium content and release would tend to reduce rather than
increase ICa
(21). This would make the change in
ICa after a
change of [Ca]o appear
faster rather than slower.
Changes in INa due to rapid changes of [Na]o. All explanations of the slow change in ICa that invoke slow changes in the calcium channel itself, either directly or indirectly, were rendered much less plausible by the finding that INa changes in the same way, qualitatively, following a change of [Na]o as does ICa following a change of [Ca]o in both atrial and ventricular cells (Fig. 3). Unfortunately, INa is too large to clamp in the absence of a channel blocker, and the presence of the blocker complicates analysis of the results due to possible interactions between sodium ions and the blocking agent. Nevertheless, the qualitative similarity of the results of the experiments with INa and ICa suggests that the different rates of change of ionic currents following a concentration change are not ascribable to the properties of a particular ion channel but rather to the properties of the cells, presumably to the difference in relative density of transverse tubules.
Estimating diffusivity of calcium ions in transverse tubules.
Because the physical basis of the slow phase of current change in
ventricular cells seems likely to be diffusion in the transverse tubules, appropriate solutions of the one-dimensional diffusion equation (1, 2, 5) should account for our data (Fig. 4). With the assumption that
[Ca]o in the solution
surrounding the cell changes exponentially with a rate coefficient of
, the solution to the diffusion equation has the form (5)
![<FR><NU>[Ca]<SUB>tt</SUB>(<IT>t</IT>, <IT>x</IT>) − [Ca]<SUB>tt</SUB>(0, <IT>x</IT>)</NU><DE>[Ca]<SUB>tt</SUB>(∞, <IT>x</IT>) − [Ca]<SUB>tt</SUB>(0, <IT>x</IT>)</DE></FR> = 1 − <FR><NU>cos <IT>x</IT>(&bgr;/<IT>D</IT>)<SUP>1/2</SUP></NU><DE>cos <IT>L</IT>(&bgr;/<IT>D</IT>)<SUP>1/2</SUP></DE></FR> <IT>e</IT><SUP>−&bgr;<IT>t</IT></SUP>](/content/vol275/issue3/fulltext/H852/img001.gif)
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and the instant at which the
extracellular solution change actually began near the cell surface
(t0) (Fig. 4,
filled squares). The fitted line corresponded to a current change that
was almost entirely attributable to the superficial cell membrane
(98%) and to a change in
[Ca]o that began at a
delay of 19 ms and proceeded at a rate of 26 s1. These values for
t0 and are
used in all subsequent analyses, although it does seem unlikely to us
that the atrial cells are actually entirely lacking in transverse
tubules. Nevertheless, fits to the ventricular data with these values
for t0 and were reasonable, and fits with other values did not significantly
change the fitted values of
D/L2,
although the fraction of current in the transverse tubules
(
tt) varied inversely with
.
The data from ventricular cells were fitted in two ways. First, we
averaged the data from each group of ventricular cells (holding
potential 45 mV) in the manner described earlier
(Fig. 2) and then fitted the cumulative data points with
Eq. 1 (Fig. 4).
D/L2
for the transverse cells was significantly larger than
D/L2
for the longitudinal cells (1.57 ± 0.19 vs. 1.13 ± 0.17 s1, respectively; value ± SE of fit, P < 0.05), whereas
values for tt were similar
(0.60 and 0.58, respectively). In the second method, nearly identical
results were obtained by fitting data sets from individual cells and
then averaging the fitted values of the parameters
[D/L2 = 1.60 ± 0.28 and 1.13 ± 0.30 s1 (means ± SD),
respectively, P = 0.03;
tt = 0.59 and 0.60],
despite a nearly twofold range of individual values for
D/L2.
The identity of the results from the two methods implies a linear addition of the values of
D/L2
from different cells and, therefore, from different regions of the same
cell. This result can be used to understand the different values for
D/L2
obtained for different cell orientations and to estimate the value of
D/L2
for cells that are not attached to any surface.
It is likely that the difference between
D/L2
for transverse and longitudinal cells reflects the fact that the
longitudinally oriented cells have one entire side of the cell facing
the glass surface, restricting access of the extracellular solution to
the tubule openings on that surface, whereas the transversely oriented cells have only 66% of one side occluded in this way. Extrapolating the fitted values of
D/L2
to the hypothetical case in which 0% of the cell surface is occluded gives a value for
D/L2
of 2.42 s1 (Fig.
4B).
However, if one side of the idealized cell were really totally attached
to the glass, and if that attachment completely occluded the
extracellular solution from that cell surface, at least on the
timescale of our solution changes, then the length of the diffusion
path through the transverse tubules would be twice that for the
completely unattached cell. Thus
D/L2
for a cell attached over 100% of its length should be one-quarter its
value when both sides of the cell are free, i.e., 2.42 s1/4 = 0.61 s1, rather than the value
we find, 1.13 s1 (Fig.
4B). This presumably means that the
portion of the cell that overlaps the rods is not actually completely
occluded. To estimate the degree of occlusion, we can imagine the cell
as having two regions, one in which both ends of the tubules are
exposed to the extracellular solution
(D/L2 = 2.42 s1) and the other
having one end totally occluded
(D/L2 = 0.61 s1). To account
for our data in this way, it is necessary to assume that only 71% of
the cell length overlapping the rods is actually attached, with the
rod-facing tubules of that portion of the cell totally occluded,
whereas the remainder has all cell surfaces and tubule mouths readily
accessible to the extracellular solution (Fig.
4B, dashed line).
This analysis does not take into account that the transversely oriented
cells were thicker on average (13 µm) than the longitudinally oriented cells (12 µm, see
METHODS). Although this difference was not statistically significant, if it is taken into account by
multiplying
D/L2
for the transverse cells by the square of the ratio of the thicknesses, the extrapolated value of
D/L2
for an unattached cell becomes 3.23 s1, and the fitted values
can be accounted for if 13% of the cell length that overlaps the rods
is actually unattached.
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DISCUSSION |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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Origin of fast phase of current change.
The apparent rate of change of ion concentration at the atrial cell
surface (26 s1, Fig. 4) is
surprisingly slow given that the linear velocity of the cell perfusate
is two to three cell widths (50 µm) per millisecond. One reason for
this is that the atrial cells almost certainly are not entirely devoid
of transverse tubules, and some of what the curve-fitting program finds
as rapid phase (Fig. 4A) is probably
actually a small slow phase, as suggested by the exponential fits to
the data (Fig. 2B) and by cell
capacitance measurements (see below). A second reason is that the
concentration change at the cell surface depends to some extent on
diffusion through a boundary layer, because the initial rate of change
of current or potential depends linearly on the flow velocity (see
METHODS). We assume in our analyses
that the rate of change of ionic concentration at the cell surface is
the same for both atrial and ventricular cells.
Origin of slow phase of current change. Our results are consistent with the idea that the slow component of current change in ventricular cells reflects a physical property of the cells, which we hypothesize is the restricted diffusion space constituted by the lumens of the transverse tubular network. It is unlikely that the small caveolae found in cardiac cell membranes are responsible for the slow exchange of extracellular calcium near the sarcolemma, because they are quite small (90 nm in diameter; Ref. 13) and are present in both atrial and ventricular cells (19). On the other hand, caveolae are more prevalent in the transverse tubules than elsewhere on the cell surface (13) and may contribute to the apparently slow diffusion in the transverse tubules.
The value for D/L2 obtained, 2.42 s1, was
obtained from cells with a mean thickness of 12.5 µm. If we were to
assume that 2L = thickness,
D would have a value of 0.95 × 106
cm2
s1, less than one-eighth
its value in bulk solution (7.9 × 106
cm2
s1; Ref. 14). The
transverse tubules would need to be ~2.8 times the cell thickness in
length to account for the fitted value of D/L2.
This degree of tortuosity is similar to that of skeletal muscle, as
derived from a study of potassium depletion (1) and estimated from
electron micrographs (11). The tortuous nature of the transverse tubules in cardiac muscle has been observed in morphological studies that document both longitudinal and transverse segments of the "transverse" tubular system (8). Unfortunately, the length of the
transverse tubules in guinea pig ventricular cells cannot be determined
even approximately from morphometric data because the diameter of the
tubules is known to vary widely within a cell (7) and because the
number of tubules per unit of surface membrane area has not been
reported for these cells. Although the tubules are certainly at least
somewhat tortuous, diffusion within the tubules might also be slowed by
calcium binding sites (3), which Bers and Peskoff (2) have shown could
account for as much as a fivefold slowing of diffusion. However, the
degree of tortuosity necessary to account for our results is within a
plausible range, and it would be necessary to postulate sodium binding
sites as well to account fully for our results.
On the other hand, it is possible that we have overestimated the value
of D in this study because of either
SR calcium loading or calcium-dependent inactivation of
ICa. The
elevation of [Ca]o before depolarization could load the SR with calcium in proportion to
the delay between the solution change and depolarization, and the extra
calcium release would inhibit
ICa (21). Thus
ICa for the
longer delays would be underestimated and the apparent rate of change
of ICa
overestimated. However, in the experiments with transversely oriented
cells, we could measure the force of contraction and compare the change
in twitch force with the change in
ICa following a
change of [Ca]o. In
those experiments, for a delay of 885 ms, the rate of rise of twitch
force was increased by a mean of 105 ± 34%, and the difference
current was 105 ± 10% of control for that delay. This result is
consistent with there being little or no SR loading, because the rate
of rise of tension is approximately proportional to
ICa for constant
SR loading (28). Calcium-dependent inactivation is unlikely to be very
important for the reasons discussed earlier. However, there were small
changes in the apparent rate of inactivation of
ICa induced by
the rapid change in
[Ca]o, which can be
seen as a slight positive overshoot of the difference current in Fig.
1. Such inactivation would affect the shape of the curves for
ICa versus delay
in the same way as does SR loading, resulting again in the
overestimation of D.
Comparison with previous studies.
A recent study using methods similar to ours (30) reported rates of
change of membrane currents and potential similar to those reported
here but differing in important ways.
ICa in rabbit ventricular myocytes was found to decline to 10% of its initial value
(t90) within
241 ms of the application of a calcium-free solution (with 2 mM EGTA).
Although this seems much faster than what we find in guinea pig
myocytes, the results cannot be directly compared, because the
relationship between current magnitude and calcium concentrations was
not given. Nevertheless, our calcium exchange rate
(t90 600 ms) does compare well
with the decline of
ICa in rat
myocytes in the same report
(t90 = 910 ms)
(30).
Comparison with morphometric studies and capacitance measurements.
The surface area-to-volume ratio of transverse tubular membrane in
guinea pig ventricle is 0.42 µm1 (7), and the ratio of
external membrane area to volume in our cells, excluding the attached
fraction described above, was 0.20 µm1. Thus the fraction of
membrane area immediately accessible to the extracellular solution
would be 0.20/0.62 = 0.32, less than the value of 0.40-0.42 we
find from the fitted data (1 tt; Fig.
4A). The discrepancy is not large
given that we estimate the cell surface area by assuming it to be a
smooth surface without caveolae or wrinkles that would increase the
true area.
Significance of ionic exchange in transverse tubules. Whatever the mechanism, slow tubular diffusion is likely to have functional significance, because the structures mediating E-C coupling are located in the tubules (12, 20). The accumulation and depletion of potassium and calcium ions could profoundly affect E-C coupling, particularly when the heart hypertrophies and the tubules apparently elongate (18). In pressure-overload hypertrophy, ventricular cell thickness has been shown to increase by as much as 50% (9, 15), which would slow diffusion by a factor >2 if the transverse tubules elongate to the same degree. From the experimentalist's point of view, a slow diffusion space surrounding 60% of the cell membrane would complicate the interpretation of experiments involving fast solution changes and could make it more difficult to voltage clamp whole cells.
Potential uses of this method. The method described here may provide a relatively simple means, perhaps the only means, for estimating the length of transverse tubules in living cardiac muscle cells. This information is difficult or impossible to obtain through morphometry and could provide insight into morphological changes occurring during development or in pathological conditions.
Also, the ability to isolate changes of ionic conductance in the tubular membranes from those in the superficial membrane in live, intact cells should be useful in identifying the cellular location of other ion transporters in the cell membrane, such as sodium-calcium exchange, which information could deepen our understanding of E-C coupling in heart muscle. This should be particularly helpful in studying the changes in transporter distribution that may occur under pathological or experimental conditions (16).| |
ACKNOWLEDGEMENTS |
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We are grateful to Dr. Rashid Nassar of Duke University for a critical reading of a previous version of this manuscript.
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FOOTNOTES |
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This work was supported by Merit Review funding from the Department of Veterans Affairs.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests: N. Shepherd, Research Service, 151, VA Medical Center, 508 Fulton St., Durham, NC 27705.
Received 10 February 1998; accepted in final form 13 May 1998.
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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, Value of
D/L2
for 100% overlap computed from value for 0% overlap, with assumption
that tubule mouths in that portion of cell that overlaps rod surface
are completely shut off from extracellular solution.