© 2000 American Heart Association, Inc.
Cellular Biology |
Electrophysiological Effects of Remodeling Cardiac Gap Junctions and Cell Size
Experimental and Model Studies of Normal Cardiac Growth
From the Departments of Pediatrics (M.S.S., J.F.H.), Cell Biology (M.S.S.), and Biomedical Engineering (R.C.B.), Duke University Medical Center, and Department of Surgery (P.C.D.), Veterans Affairs Medical Center, Durham, NC.
Correspondence to Madison S. Spach, Box 3475, Duke University Medical Center, Durham, NC 27710. E-mail cspach{at}acpub.duke.edu
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Abstract |
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Abstract—The increased incidence of arrhythmias in structural heart disease is accompanied by remodeling of the cellular distribution of gap junctions to a diffuse pattern like that of neonatal cardiomyocytes. Accordingly, it has become important to know how remodeling of gap junctions due to normal growth hypertrophy alters anisotropic propagation at a cellular level (
max) in
relation to conduction velocities measured at a macroscopic level. To
this end, morphological studies of gap junctions (connexin43) and in
vitro electrical measurements were performed in neonatal and adult
canine ventricular muscle. When cells enlarged, gap
junctions shifted from the sides to the ends of ventricular
myocytes. Electrically, normal growth produced different patterns of
change at a macroscopic and microscopic level. Although the
longitudinal and transverse conduction velocities were greater in adult
than neonatal muscle, the anisotropic velocity ratios were the same. In
the neonate, mean max was not different during
longitudinal (LP) and transverse (TP) propagation. However, growth
hypertrophy produced a selective increase in mean TP
max (P<0.001), with no significant
change in mean LP max. Two-dimensional neonatal and
adult cellular computational models show that the observed increases in
cell size and changes in the distribution of gap junctions are
sufficient to account for the experimental results. Unexpectedly, the
results show that cellular scaling (cell size) is as important (or more
so) as changes in gap junction distribution in determining TP
properties. As the cells enlarged, both mean TP max
and lateral cell-to-cell delay increased. max
increased because increases in cell-to-cell delay reduced the electric
current flowing downstream up to the time of max,
thus enhancing max. The results suggest that in
pathological substrates that are arrhythmogenic, maintaining cell size
during remodeling of gap junctions is important in sustaining a maximum
rate of depolarization.
Key Words: gap junctions • structural remodeling • max • cellular scaling • anisotropic propagation
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Introduction |
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TopAbstractIntroductionExperimental ProceduresBiophysical Mechanisms: Adult...DiscussionReferences |
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Differences in the distribution of gap junctions are now considered to be an important factor in the origin of reentrant arrhythmias.1 Changes in the arrangement and number of gap junctions have been documented in hearts undergoing normal growth hypertrophy after birth,2 3 4 with aging,5 and in disease states such as ischemic heart disease.6 7 8 9 Gourdie et al10 suggested that alteration of coupling patterns in diseased mature hearts may result from pathological reiteration of developmental processes that determine the normal cellular organization of gap junctions. Accordingly, it has become important to know how electrophysiological changes at the cellular level (
max) correlate with changes at a
macroscopic-size scale, such as effective conduction velocity. However,
we have been unable to find information concerning longitudinal and
transverse propagation (LP and TP, respectively) in the neonatal
ventricle, except for preliminary results we recently presented
in a study of the foot of the action potential.11 Nor
could we find information about the effects of cellular scaling
(consequences of differences in size12 ) on anisotropic
conduction. Therefore, we hypothesized that the anisotropic electrical
effects of growth hypertrophy are due primarily to the
combined effects of two factors: cellular scaling and changes in the
distribution of the gap junctions.
Mean max is greater during TP than LP in adult
myocardium.1 13 Fast and
Kléber,14 however, found no significant difference
in mean max during LP and TP in neonatal cell
cultures. Stimulated by their results, we obtained preliminary
max results in neonatal ventricular
muscle as part of our recent study of the action potential foot, which
can vary independently of max.11
Similar to the neonatal cellular cultures,14 mean
max was not significantly different during LP and TP
in neonatal ventricle. We interpreted the similar LP-TP
max relationships in neonatal
ventricular muscle and in neonatal cell cultures to be due
to the diffuse cellular distribution of the gap junctions in both
preparations.11 14
Mathematical models incorporating a representation of the irregularly arranged microstructural components, eg, cell shapes and gap junction distribution,15 were necessary to understand structural mechanisms of conduction events in different anisotropic substrates.16 Such electrical descriptions of the microstructure make the analysis tractable by representing the irregularly arranged microstructural components.15 Such structural models represent the corollary of the step-by-step development of increasingly complex and comprehensive models of ionic channels, pumps, and exchangers within individual cells.17 18 19 20 21 22
Accordingly, the first purpose of this study was to document the
relationships between the mean values of max and the
associated macroscopic conduction velocities during anisotropic
propagation in neonatal and adult ventricular muscle. The
second, and major, objective was to gain insight into the underlying
microstructural events and into their biophysical mechanisms by
determining whether the observed differences in gap junction
distribution and in cell size could account for the
max and conduction velocity results. We
analyzed microscopic propagation events produced by (1) our
adult two-dimensional (2D) cellular model;15 23 and (2) a
neonatal 2D cellular model that we developed on the basis of the
distribution of connexin43 in neonatal canine ventricular
muscle and the geometry of isolated neonatal myocytes. The model
predictions show that the observed changes in cell size and in the
distribution of the gap junctions are sufficient to account for the
experimental results. A noteworthy feature was that cellular scaling
(differences in cell size) was as important as differences in gap
junction distribution in determining TP properties.
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Experimental Procedures |
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Experimental Materials and Methods
We studied in vitro ventricular epimyocardial preparations from the hearts of 6 adult dogs (weight 9 to 21 kg) and 6 neonatal dogs (age 1 day to 6 weeks). The electrophysiological methods used to study anisotropic propagation have been reported in previous articles.11 13 15 Glass microelectrodes were used to measure the intracellular potential
i at a depth of
~150 µm.11 The potential just outside each
impaled cell was measured as the extracellular potential
e. The transmembrane potential
(Vm) was obtained as the difference between
i and e.11 15 LP and TP
max values at the same site were used in the final
analysis, which consisted of 4 sites from each of 6 adult and 6
neonatal preparations. Double labeling with anti-connexin43 antibodies
and wheat germ agglutinin was applied to sections of adult and neonatal
hearts to study the distribution of the gap junctions.24
To develop the neonatal 2D cellular model, isolated single myocytes
were obtained from neonatal hearts.25 26 Photomicrographs
of 33 neonatal myocytes were chosen for the neonatal
model.27 An expanded Materials and Methods section is available online at http://www.circresaha.org.
Experimental Results
Anisotropic Propagation Events in Adult and Neonatal
Ventricular Muscle
In both adult and neonatal preparations, max
increased or decreased at each impalement site when conduction was
changed from LP to TP.15 In the adult (Figure 1A
), the mean TP max
value (155 V/s) was significantly greater than the mean LP
max value (120 V/s) (P<0.0001).
Contrariwise, in the neonate the mean TP (124 V/s) and LP (118 V/s)
max values were not significantly different
(P=0.36). Figure 1B shows that, although there was no
significant difference in the mean LP max values in
the adult and neonatal preparations (P=0.62), mean TP
max was significantly greater in adult than in
neonatal ventricular muscle (P<0.0001;
n=24).
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In adult preparations, the average macroscopic conduction velocity was 0.50 m/s during LP and 0.17 m/s during TP, with a LP/TP velocity ratio of 2.94. In the neonatal preparations, the average velocities were lower, ie, 0.33 m/s during LP and 0.12 m/s during TP. However, the neonatal LP/TP velocity ratio of 2.75 was essentially the same as that of the adult.
Changes in the Distribution of Gap Junctions and in Cell
Size
In adult ventricular myocytes (Figure 2, top), gap junctions were located at
the transverse-oriented intercalated disks. This association produced a
pattern of gap junctions located primarily near the ends of the cells,
with large areas along the lateral cell borders having no gap
junctions, consistent with prior
descriptions.2 3 28 In the neonatal cells (Figure 2, bottom), however, gap junctions were distributed in a relatively
uniform manner with a periodicity of 4 to 11 µm along the
perimeter of the myocytes, a pattern similar to neonates of other
species2 3 4 and the neonatal monolayers of Fast et
al.29 To compare cell size and shape, Figure 3A shows representative
isolated adult and neonatal left ventricular myocytes.
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Biophysical Mechanisms: Adult and Neonatal Cellular Models |
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Development of the Neonatal Model
Details of the adult 2D cellular model have been presented previously.15 23 Here, we present the new neonatal model, which was based on the gap junction distribution and the geometry of the isolated neonatal myocytes illustrated in Figures 2
and 3A. Values of the adult and neonatal 2D
cellular model parameters are presented in Table 1.
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Myocytes
Each neonatal cell was divided into segments with
x-y dimensions of 25 µm2
(
x, y=5 µm) and a depth of 5.6
µm. Cytoplasmic segments were interconnected by low resistances,
consistent with a specific resistivity of 250 
·
cm35 (Table 1B). To represent cell boundaries,
adjacent segments were isolated from one another in the designated
directions, except at sites of gap junctions. The membrane area of each
segment was 94 µm2, which produced a surface
area-to-volume ratio of 0.66 µm-1, with a mean cell
volume of 4948 µm3 (Table 1A). The basic unit of the
neonatal model consisted of 33 myocytes (Figure 3C), and multiple units
formed large cellular arrays.
Gap Junctions
A punctate gap junction was positioned every 5 to 10
µm along the lateral borders and at the ends of the cells (Figure 3C), which resulted in each neonatal cell being connected to an average
of 6 cells (Table 1B). Normally, there are a few gap junction channels
in small cells with large input resistances
(Rin), and large cells with small input
resistances have a large number of gap junction
channels.46 47 In our case, the neonatal-adult
relationships of Rin and cell size (Table 1A)
predict that isolated neonatal cell pairs should have a lower effective
coupling conductance gj(eff) than that of adult
cell pairs. We therefore assigned each neonatal gap junction a
conductance (gj) of 0.16 µS, because this
value produced a mean gj(eff) value of 0.63 µS
between neonatal cells in isolated pairs (n=50), a value 18% less than
that in isolated adult cell pairs (Table 1B).
Calculations and Data Output
As done previously,11 15 23 we used the
Hodgkin-Huxley model48 with Ebihara-Johnson
kinetics18 to approximate the fast Na+ current
INa as
 | (1) |
Na is the maximal sodium conductance (28
mS/cm2), m and h are gating
parameters, and VNa is the sodium
equilibrium potential (33.45 mV). We approximated a repolarization
current IR by the equation
 | (2) |
R is the repolarization
conductance (0.05 mS/cm2) and VR is
the equilibrium potential of the repolarization current (-80 mV).
The mathematical formulation and computation procedures have been
presented previously.11 15 23 The space constant
was determined as the distance at which the value of
Vm decreased to 0.37 times its greatest
value when current was injected intracellularly along a longitudinally
or transversely oriented line.23 Cytoplasmic
time49 was ascertained as the difference between the
earliest and latest time of max within each cell.
Cell-to-cell conduction delays were obtained as the time difference of
max at segments on each side of the end-to-end gap
junctions during LP and across the lateral midcell gap junctions during
TP.
An expanded neonatal model section is available online at http://www.circresaha.org.
Adult and Neonatal Cellular Model Results
Macroscopic Conduction Velocities Related to Anisotropic
Passive Properties
In the adult cellular model, the longitudinal and transverse
macroscopic conduction velocities were 0.48 m/s and 0.17 m/s,
respectively. In the neonatal model, the LP velocity was 0.36 m/s, and
the TP velocity was 0.13 m/s. These conduction velocities agreed
favorably with the experimental data in the adult and neonatal
ventricular preparations (Table 1C). As found
experimentally, the adult and neonatal models produced almost the same
LP-to-TP velocity ratios (Table 1C).
To evaluate whether the averaged effects of the irregular-shaped cells
and the gap junction distribution in the adult model produced realistic
passive properties at the macroscopic level, we determined the space
constants L and T (Table 1D). The
computed L value of 1.21 mm was within the range of
0.76 to 1.3 mm measured in adult canine ventricular
muscle.42 43 We know of no experimental data to compare
with the computed T value of 0.37 mm.
We then used continuous cable equations50 to obtain the
effective axial resistivity13 along the longitudinal and
transverse axes according to
 | (3) |
 | (4) |
is the space constant in either the longitudinal or
transverse direction, Rm has a value of 20
K · cm2, and a is the radius of a
continuous cable that has the cross-sectional area of the individual
segments (113 µm2) in the adult model. Table 1D
shows that the derived Ra values along the
longitudinal and transverse axes of the adult model agreed favorably
with Clerc’s45 experimental results in bovine
ventricular muscle; ie, RaL=410
cm (Clerc: 402 · cm), and RaT=4382
· cm (Clerc: 3620 · cm).
To make certain that the neonatal and Ra
values related to the adult values at a macroscopic level as expected
by cable analysis in relation to conduction velocity, we
determined and Ra for the neonatal 2D
cellular model. Both L (0.73 mm) and
T (0.21 mm) were less, and
Ra was greater, in the neonatal than in the
adult cellular model (Table 1D), results consistent with the
lower LP and TP velocities in the neonate compared with the adult in
accordance with continuous cable theory.45 50 We know of
no anisotropic experimental data for comparisons of these neonatal
model results. However, the values of L and
T in the neonatal model were close to the of
0.36 mm measured by Jongsma and van Rijn44 in
isotropic cellular cultures of neonatal rat myocytes.
max Mean Values and Cell-to-Cell Delays
In the adult cellular model, the TP max mean
value of 178 V/s was significantly greater than the LP
max mean value of 164 V/s (Figure 4A), as expected (P<0.001,
n=490).15 However, in the neonatal cellular network there
was no significant difference in the mean values of TP
max (164 V/s) and LP max (163.9
V/s) (P=0.83, n=490). Thus, the LP-TP mean
max relationships in the adult and neonatal cellular
models were in good agreement with the experimental data of Figure 1.
Additional experimental max relationships reproduced
were the following: (1) mean LP max was not
significantly different in the adult and neonatal cellular networks
(P=0.52), and (2) mean TP max was
significantly greater in the adult than in the neonatal model
(P<0.001). The max values of Figure 4A
were slightly higher than those measured in vitro (Figure 1), probably
because of the Na value (28
mS/cm2) used in all segments of both models. Although
overall increases or decreases in Na
produced corresponding changes in max, the above
LP-TP max relationships of the adult and neonatal
models were maintained.
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The mean delays of impulse transfer between cells during LP and TP had
the same relationships as the mean max values in the
adult and neonatal cellular networks (Figure 4B), which suggested that
these 2 parameters were linked. In the adult, the mean
cell-to-cell delay was much greater during TP (178 µs) than during LP
(90 µs) (P<0.001). In the neonatal cellular network
(Figure 4B, right), however, there was no significant difference in the
mean cell-to-cell delays during LP (68 µs) and TP (75 µs)
(P=0.28).
Intracellular max Variations During LP and TP in
Adult and Neonatal Cells
The representative result of Figure 5 (left) shows that TP
max exceeded LP max throughout
most adult cells. In a few adult cells, LP max
exceeded TP max in small regions near the
intercalated disks (not shown).15 In groups of neonatal
cells, LP max exceeded TP max
throughout some cells, and the opposite relationship occurred in other
cells (Figure 5, right). Averaging the changing dominance of LP versus
TP max from 1 cell to the next accounted for the
similar neonatal LP and TP mean max values.
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To gain insight into the relation between max and
the excitation sequence inside cells, we analyzed 25 adult and
25 neonatal cells, considered as pairs. Each neonatal cell was
approximately one-half the size of the adult cell. During LP in both
adult and neonatal cells, the lowest max values
occurred in the region of slowest conduction near the input gap
junctions (Figure 6A).
max fluctuations were greater in the adult than in
the neonatal cells. In the input region, max was
lower in the adult cell than in its neonatal counterpart, whereas in
the central-to-distal region, this relationship reversed. Consequently,
averaging the different LP max relationships in the
proximal and distal intracellular regions produced similar adult and
neonatal LP max mean values.
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A major feature of TP (Figure 6B) was the almost
simultaneous excitation of the membrane throughout both
adult and neonatal cells (14 to 28 µs). At the ends of a few adult
cells, max decreased to values below those in
neonatal cells (Figure 6B1). However, these few low
max values had little influence on overall
significantly greater TP max in the adult cells.
Microcollisions
To determine whether the development of intracellular
microcollisions29 accounted for the increasing TP
max secondary to growth hypertrophy, we
compared TP excitation sequences and max values
within the 25 adult-neonatal cell pairs. We did not find
microcollisions within neonatal cells, a result similar to that of Fast
et al.29 in dense neonatal cell cultures. Four adult cells
(16%) demonstrated microcollisions, and these cells had
max values in the highest range encountered, 192 to
202 V/s (Figure 6B1). Contrariwise, 9 other adult cells (36%) without
microcollisions demonstrated similar max values
within this range (Figure 6B2).
To determine whether an absence of microcollisions altered the overall
LP-TP mean max relationships in the adult cellular
network, we compared LP and TP max at 160 randomly
chosen sites in adult cells without microcollisions. In the absence of
microcollisions in adult cells, mean TP max (179
V/s) remained unchanged from the original value (178 V/s), and mean TP
max also remained significantly greater than mean LP
max (P<0.001). Consequently,
microcollisions did not account for the increase in TP
max produced by growth hypertrophy, nor
did microcollisions account for the greater TP than LP mean
max in adult cells.
Why Does TP max Increase Relative to LP
max?
In the longitudinal direction, the shift of connexin43 from the
sides to the ends of the cells (Figure 2) maintains tight end-to-end
coupling between myocytes as they enlarge, as evidenced by the small
change in mean cell-to-cell delay during LP (Figure 4B). Consequently,
LP remained overall a smooth process in both cellular networks. In the
transverse direction, the cells became increasingly isolated from their
lateral neighbors when they enlarged. During TP, the increased lateral
detachment produced a prominent increase in mean lateral cell-to-cell
delay of 103 µs (from 75 to 178 µs; P<0.001), but the
very short mean cytoplasmic time of 26 µs in the neonatal cells was
not significantly different from that of the cytoplasmic time of the
adult cells (23 µs; P=0.72).
To understand more easily the mechanism involved in the delays between
cells, we simplified the problem by considering the membrane of 2
segments in juxtaposed cells (Figure 7A).
As the capacitance of the membrane in the segment of the upstream cell
(proximal segment X) is discharged up to the time of its
max, depolarization will be slowed, because segment
X also supplies current to a similar segment in the next cell
downstream (distal segment Y). Furthermore, up to the time at which its
max occurs, segment X will supply relatively less of
its current to distal segment y in the presence of longer than shorter
cell-to-cell delays. As a corollary, at the time of
max in segment X, its depolarization should be more
rapid in the presence of a longer delay of transfer of the action
potential to segment Y in the next cell.
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2.4 ms.
Figure 7A illustrates how a quantitative index of this electrotonic
mechanism can be obtained during TP by analyzing the action potential
upstrokes in the two segments. The intracellular current
Ii supplied to segment X up to the time of its
max is distributed in the following 2 ways: (1) the
net charge Qx that discharges the membrane
capacitance of segment X, and (2) the net charge
Qy that concurrently discharges the membrane
capacitance of a similar segment in the next cell at segment Y.
(Smaller amounts of charge, which are ignored here, are also
distributed to cells beyond Y.) Thus, an index of the downstream
current load on proximal segment x at the time of its
max is the percentage of the total charge
(Qx+Qy) that is supplied to distal segment Y,
given as
 | (5) |
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and 7C (the time of max in segment x) can
be calculated as
Qm=CmVm,
where Cm is the membrane capacitance (1
µF/cm2) and Vm is the difference
between the resting potential and the membrane potential at that time;
eg, 1 mV depolarization=1 nC/cm2 net charge displaced. As
long as there is no significant charge supplied to the distal segment
by its own Na+ current, all of Qy is
supplied from an upstream segment. During TP in the adult network (long
cell-to-cell delays), none of the distal segments (n=15) demonstrated
activation of INa before max
in the proximal segment (vertical line in Figure 7C). In the neonatal
network (short cell-to-cell delays), all distal segments demonstrated
that the earliest phase of INa activation had
started by this time (vertical line in Figure 7B), but the charge
supplied by the beginning of INa activation in
distal segment y was small, averaging only 0.33 nC/cm2
(n=15). For example, it was 1.4% (0.7 nC/cm2) of the
47.5-nC/cm2 depolarizing charge of segment y at the time of
the vertical line in Figure 7B. Thus, in both neonatal and adult
cellular networks, during TP essentially all of the depolarizing
current of segment y was electrotonic up to the time of the vertical
line in Figure 7B and 7C. The results were not model-dependent, as we
found similar results using the Luo-Rudy phase 1
model.19
There was also no significant contribution of the slow inward current
Isi (L-type calcium current17 19 )
on charge transfer from segment X to segment Y. The longest TP delay we
encountered was 0.31 ms. During this interval,
Isi cumulative charge was 0.33
nC/cm2 in proximal segment X, only 0.7% of the total
charge to the time of max in distal segment Y. In
the normal action potentials of this study, Isi
turn-on began at max, and during the next 5 ms the
cumulative Isi charge was only 2.5
nC/cm2 (1.4% of total Isi). This
result is consistent with that of Joyner et al,51
who found that drug effects on this current are limited to
discontinuous conditions with conduction delays of 5 ms or greater.
Figure 7 illustrates the percentage of total charge that the proximal
segment, up to the time of its max, supplied to the
distal segment. This percentage was greater in neonatal cells (44%)
with their short cell-to-cell delays than in the adult cells (34%),
which had longer delays. Thus, the smaller amount of current flowing to
the next cell downstream before the time of max was
consistent with the higher mean TP max
values in adult than in neonatal cells.
Cell Size Versus Gap Junction Distribution
Numerical experiments in 4 cellular networks were devised to
separate the effects of cell size from those of gap junction
distribution. Two networks were the adult and neonatal 2D models
(Figure 3B and 3C). To reverse the relationship between cell size and
gap junction topology in these models, we created 2 hypothetical
cellular networks, as follows: (1) a network that approximated the
adult large cell geometry but with the neonatal gap junction
distribution and gj values (Figure 8A, cell type b), and (2) another network
that approximated the neonatal small cell geometry but with the adult
gap junction distribution and gj values (Figure 8A, cell type c). These 4 networks represented the 4
possible combinations of differences in adult and neonatal cell size
and gap junction topology. In each network, cell-to-cell conduction was
analyzed in 15 cell pairs using the method illustrated in
Figure 7.
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All of the networks maintained very short mean TP cytoplasmic times (21
to 29 µs). Figure 8A shows the results for mean lateral cell-to-cell
delay, mean TP max, and mean value of the percentage
total charge supplied to the distal segment (Equation 5). Across the
different networks, the mean cell-to-cell delay strongly correlated
with mean TP max (r=0.99;
P<0.01). Furthermore, the percentage of total charge
supplied to the distal segment strongly correlated in an inverse manner
with both mean TP max (r=-0.99;
P<0.01) and the mean cell-to-cell delay
(r=-0.98; P<0.01). Comparing cells a, b, c, and
d, we saw that cell size had larger effects than gap junction
distribution.
LP Versus TP
The electrotonic mechanism of cell-to-cell charge transfer
illustrated in Figure 7 for TP might also be involved in producing the
effects on max of the delay of action potential
transfer between cells during LP and TP (Figure 4). We therefore
performed a similar analysis during LP of the "percentage of
total charge supplied to the distal segment" in 15 pairs of adult and
neonatal cells connected end-to-end in which segment X was located at
the end of the proximal cell and distal segment Y was located just
across the end-to-end junction in the next cell. Figure 8B shows that
the mean values of the percentage of total charge supplied to the
distal segment had the inverse pattern of the adult and neonatal LP-TP
mean max values of Figures 1 and 4A. That is, (1)
there was no significant difference in the relatively high percentage
total charge supplied to the distal segment during LP and TP in the
neonatal cellular network, and (2) the percentage total charge supplied
to the distal segment was significantly lower during TP than during LP
(P<0.001) in the adult network.
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Functional Importance of Cell Size
The major result of this study is the emergence of the unexpected importance of cell size in considering the anisotropic electrophysiological properties of adult and neonatal hearts. Initially, we attributed the different LP-TP mean
max relationships in neonatal versus adult
ventricular muscle (Figure 1) to the associated differences
in the cellular distribution of gap junctions (Figure 2). The results
of Figure 8, however, suggest that cell size may be more important, or
at least as important, as gap junction distribution for explaining the
different TP-LP max relationships in adult and
neonatal myocardium. For example, in 2D models composed of
small neonatal cells, a change from the neonatal diffuse cellular
distribution of gap junctions to the adult gap junction pattern
(maintaining the original gj values) produced
little change during TP in max, lateral cell-to-cell
delays, or the percentage of total charge an upstream segment supplied
to a similar segment in the next cell downstream (Figure 8A).
Similarly, reversal of the neonatal-adult gap junction distributions
(maintaining the original gj values) in 2D
networks of large adult cells produced little change in these
parameters during TP. However, with either an adult or
neonatal gap junction distribution, a shift from the neonatal small
cell network to the adult large cell network produced large increases
in each of these parameters during TP (Figure 8A). Because
there was no significant difference in mean LP max
in neonatal versus adult ventricular muscle, the results
indicate that the role of cell size (cellular scaling) is important in
explaining the anisotropic
electrophysiological effects of changes in
gap junction distribution.
It will be important to develop some idea of the relative importance of
the individual contributions of cell size and intercellular coupling
changes. As an initial test for changes in mean LP and TP
max, we increased the resistance
(rj) of each gap junction in steps up to 100%
above the original values in the neonatal and adult 2D cellular models.
The results showed a linear slope of change in LP and TP mean
max, and the slopes of max change
were considerably greater in the large adult cells than in the small
neonatal cells. A 100% increase in rj produced
an associated increase in TP mean max of 5 V/s in
the neonatal model and 19 V/s in the adult model, whereas LP mean
max increased minimally (1.5 V/s) in the neonatal
model and 7 V/s in the adult model. Thus, from an experimental
viewpoint, the same relative change in gap junction resistance induced
by drugs could result in different interpretations about the effects on
max of altering rj in tissues
with large versus small cells.
The results reported here suggest the following general principles: as
the degree of coupling between cells (number of connexons per unit area
of sarcolemma) decreases in relation to the size of cells, conduction
becomes more discontinuous. Conversely, for a given cell size,
increase in the number of connexons along the sides (TP) or at
the ends of the myocytes (LP), or a decrease in cell size for a given
number of connexons, decreases the discontinuous nature of conduction
(decreased mean cell-to-cell delay and decreased mean
max).
Role of Intracellular Ion Channel Distribution in Adult
Myocytes
Recent research has shown that localization of Kv1.5
K+ channel52 and Na+
channel53 proteins is increased adjacent to the gap
junctions (intercalated disks) in adult cardiomyocytes.
However, the Kv1.5 K+ channel is distributed evenly
throughout neonatal cardiomyocytes52
(presumably neonatal cells also have a diffuse Na+ channel
distribution). Because technological limitations prevent measurement of
the effects of differences in intracellular ion channel distribution,
we used the adult 2D cellular model to analyze these
differences. We increased Na from 28 to
35 ms/cm2 in segments adjacent to gap junctions while
decreasing Na throughout the remainder of
each cell, thus having no change in total
Na (number of Na+ channels)
within each adult myocyte.
The results show that the fluctuating intracellular
max values during LP and TP remained essentially the
same as those of Figure 5 (left). Even though
Na was highest at the ends of each cell,
the lowest max values remained at these sites, and
each max maximum remained at the middle of each cell
even though that area had the lowest Na
value. We further tested the effect of redistributing the density of
Na+ channels by increasing Na
at the center of each cell while decreasing
Na at the gap junctions (without changing
total cellular Na). Again, the same adult
LP and TP intracellular pattern of fluctuating max
values occurred as shown in Figure 5. Neither of the 2 altered
intracellular distributions of Na+ channels
(Na) produced more than 0.8 V/s
difference from the original mean LP max (164 V/s)
and TP max (178 V/s) adult values of Figure 4A
(n=564 sites), and the intracellular fluctuating max
values strongly correlated across the three different
Na distributions (r=0.95 to
0.99; P<0.001; n=564 sites) during LP and during TP.
Furthermore, neither of the altered Na
distributions produced a significant difference from the mean adult
cell-to-cell delay values of Figure 4B during LP or TP. These
preliminary results suggest that the electrical loading effects of the
normal discrete cellular structure of cardiac muscle15
produce (1) intracellular variations in max that are
not significantly altered by differences in the intracellular
distribution of the Na+ channels and (2) differences in the
intracellular distribution of Na+ channels do not
significantly affect the cell-to-cell delay of impulse transfer.
Application to Pathological Remodeling of Gap Junctions
Because cellular scaling emerged as an important determinant of
the delay of impulse transfer between cells and of mean
max, the results have important implications for
pathological remodeling of the gap junctions. For example, there is
"reappearance" of diffusely distributed gap junctions (connexin43)
along the side of cells after ventricular
infarction.6 7 Peters and Wit54 showed this
type of gap junction remodeling to occur in the infarct border zone
that involves reentrant circuits. In addition, Yao et
al.55 demonstrated reduced electrical coupling between
cell pairs from the border zone. However, the influence of cell size on
the electrophysiological responses that
occur in response to pathological remodeling of the gap junctions is
unknown. Our results suggest that maintaining the size of mature cells
during pathological remodeling of gap junctions plays an important role
in sustaining max at a maximum level for a given
state of the Na+ current.56 Thus,
investigation of the effects of cellular scaling is an important area
for future studies. Such studies may be especially important in
evaluating the magnitude of
electrophysiological responses of small
versus large hearts in the application of molecular genetic strategies
to alter gap junction–mediated intercellular
communication.57
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Acknowledgments |
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This work was supported by the National Heart, Lung, and Blood Institute of the NIH (Grant HL 50537) and The North Carolina Supercomputing Center.
Received September 16, 1999; accepted November 22, 1999.
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References |
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