© 1997 American Heart Association, Inc.
Articles |
Ionic Mechanisms of Propagation in Cardiac Tissue
Roles of the Sodium and L-type Calcium Currents During Reduced Excitability and Decreased Gap Junction Coupling
From the Cardiac Bioelectricity Research and Training Center, Case Western Reserve University, Cleveland, Ohio.
Correspondence to Yoram Rudy, Director, Cardiac Bioelectricity Research and Training Center, 505 Wickenden Bldg, Case Western Reserve University, Cleveland, OH 44106-7207. E-mail yxr{at}po.cwru.edu
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Abstract In cardiac tissue, reduced membrane excitability and reduced gap junction coupling both slow conduction velocity of the action potential. However, the ionic mechanisms of slow conduction for the two conditions are very different. We explored, using a multicellular theoretical fiber, the ionic mechanisms and functional role of the fast sodium current, INa, and the L-type calcium current, ICa(L), during conduction slowing for the two fiber conditions. A safety factor for conduction (SF) was formulated and computed for each condition. Reduced excitability caused a lower SF as conduction velocity decreased. In contrast, reduced gap junction coupling caused a paradoxical increase in SF as conduction velocity decreased. The opposite effect of the two conditions on SF was reflected in the minimum attainable conduction velocity before failure: decreased excitability could reduce velocity to only one third of control (from 54 to 17 cm/s) before failure occurred, whereas decreased coupling could reduce velocity to as low as 0.26 cm/s before block. Under normal conditions and conditions of reduced excitability, ICa(L) had a minimal effect on SF and on conduction. However, ICa(L) played a major role in sustaining conduction when intercellular coupling was reduced. This phenomenon demonstrates that structural, nonmembrane factors can cause a switch of intrinsic membrane processes that support conduction. High intracellular calcium concentration, [Ca]i, lowered propagation safety and caused earlier block when intercellular coupling was reduced. [Ca]i affected conduction via calcium-dependent inactivation of ICa(L). The increase of safety factor during reduced coupling suggests a major involvement of uncoupling in stable slow conduction in infarcted myocardium, making microreentry possible. Reliance on ICa(L) for this type of conduction suggests ICa(L) as a possible target for antiarrhythmic drug therapy.
Key Words: cardiac excitation • gap junction • cardiac ion channels
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Although the time and voltage-dependent kinetics of the major ionic membrane currents of ventricular cells are well described, their functional role in propagation of the action potential is not fully understood. The major cardiac inward currents are the fast sodium current, INa, and the L-type calcium current, ICa(L). Typically, INa is responsible for excitability and conduction, and ICa(L) is responsible for maintaining the action potential plateau. We sought to elucidate the relative role of INa and ICa(L) in maintaining multicellular ventricular propagation under both normal physiological conditions and two pathophysiological conditions: reduced membrane excitability and reduced intercellular coupling.
Reduced membrane excitability, caused by reduced availability of INa, is present during conditions of acute myocardial ischemia,1 2 3 tachycardia,3 and treatment with class I antiarrhythmic agents.4 Reduced excitability lowers the safety factor for conduction (safety factor is a dimensionless parameter that indicates the margin of safety with which the action potential propagates relative to the minimum requirements for sustained conduction). However, the precise relationship between safety factor and excitability has not been studied: it is not known whether the safety factor drops monotonically with decrease in INa availability, nor has the steepness of this relationship been characterized. For instance, does a 50% reduction in excitability bring the membrane very close or only marginally close to conduction block? Safety factor considerations usually address INa only. At highly reduced membrane excitability, it is possible that ICa(L) contributes significantly to the safety factor. In this study we attempt to determine the contribution of ICa(L) to the safety factor and its role in conduction.
Similar to the condition of reduced membrane excitability, reduced intercellular coupling at gap junctions decreases velocity of the propagating action potential. However, the magnitude of velocity reduction and the effect on safety factor for conduction may be vastly different for the two conditions. Several theoretical5 6 7 and experimental8 9 10 studies have suggested that reduced coupling can cause major reductions in velocity before conduction block and that velocity in the context of reduced coupling can potentially be much slower than velocity in the context of reduced excitability. Despite slowed conduction, evidence tends to suggest that propagation across cells with reduced coupling occurs with a high safety factor.11 12 These reports of high propagation safety with low intercellular coupling are not universal, and there exists evidence to the contrary.9
Long intercellular propagation delays associated with highly reduced gap junction coupling also suggest a potential role for ICa(L) in supporting conduction.13 14 With long intercellular delays, it is feasible that the downstream neighboring cell remains unexcited and constitutes a current sink when the upstream depolarized cell (current source) is already in its plateau phase. During the plateau phase, ICa(L) is the inward source current of the upstream cell and could be important to sustain cell-to-cell conduction. The degree of coupling reduction necessary before ICa(L) becomes a major contributor to both conduction velocity and safety factor has not been determined. Also, the phenomenon of calcium-dependent ([Ca]i) inactivation of ICa(L) suggests that there can be direct coupling between [Ca]i and propagation safety. It was recently shown in neuronal preparations (rat ganglion cells) that calcium overload reduces safety factor for conduction.15
We characterized propagation in the setting of reduced membrane excitability and reduced gap junction coupling with simulations using detailed cellular ionic models and the appropriate intercellular coupling conditions of a multicellular fiber. The individual cells were represented by the dynamic Luo-Rudy (LRd) ventricular cell formulation,16 17 18 interconnected by resistive pathways representing gap junctions. In the context of this study, it should be emphasized that the LRd model incorporates important kinetic properties of INa and ICa(L). These include fast and slow inactivation processes of INa, an order-of-magnitude faster ICa(L) activation than in previous models (eg, Beeler and Reuter19 ), and calcium-dependent inactivation of ICa(L). Safety factor of conduction was formulated using a modified version of formulations previously introduced.9 12
The results demonstrate that a decrease in membrane excitability (eg, due to ischemia, tachycardia, or treatment with antiarrhythmics) causes a monotonic decrease of the safety factor for conduction and a modest decrease of conduction velocity before the occurrence of block. In contrast, a decrease in intercellular coupling (eg, due to anisotropy of the myocardial structure, aging, elevated intracellular calcium, or infarction) can have a profound depressant effect on conduction velocity that is accompanied by a paradoxical augmentation of the safety factor for conduction. The interplay between membrane factors and gap junction factors has significant relevance to conduction under pathological conditions in which one pathophysiological change (reduced coupling) may compensate for another (reduced excitability) in terms of their opposite effects on propagation safety. Detailed studies of the ionic mechanisms of normal and pathological conduction identify the relative importance of INa and ICa(L) in supporting conduction under a given set of conditions. Such insight could be very helpful for informed treatment of cardiac arrhythmias.
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The LRd cell model and its use as the cellular element of a multicellular fiber have been described previously.16 18 20 The following is a brief description of the cell and fiber models and formulation of the safety factor of conduction (SF). In view of the strong emphasis in this study on the role of gap junctions in propagation and the detailed cable analysis required for SF computation, related methodology is presented in "Appendices 1 and 2." A description of simulation protocols is also included below.
Multicellular Fiber Model
For each cell in the fiber, the LRd model is used to compute
ionic currents and concentration changes. In this model, the guinea
pig–type ventricular action potential is numerically
constructed on the basis of experimental data. Included in the model
are the membrane ionic channel currents, represented
mathematically by a Hodgkin-Huxley type formalism, as well as ionic
pumps and exchangers. In addition, processes that regulate ionic
concentration changes, especially dynamic changes of intracellular
calcium concentration, are introduced. A diagram of the cell model is
provided in Fig 1A
, with the two major
excitatory currents (INa and ICa(L))
highlighted. Detailed tables of equations governing the model are
provided in References 1616 to 18.
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The theoretical fiber (Fig 1B
) is composed of serially arranged
ventricular cells, each of LRd formulation. The temporal
transmembrane current fluxes of the LRd model are related to spatial
(axial) current flow by a finite difference approximation6
of the cable equation21 22 23
 | (1) |
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x is the discretization element
(µm), RCG is the ratio between capacitive and geometrical
areas (RCG=2), and Ri is the axial resistance
per unit length (
cm). Ri is composed of myoplasmic
resistance (Rmyo=150 cm) and gap junction resistance
(normal Rg=1.5 cm2, which corresponds to a
conductance of gj=2.5 µs). Direct explicit solutions to
Equation 1 would necessitate a very small time increment (t) for
numeric convergence and could not guarantee stability. For faster
computing with a larger t, the relation in Equation 1 can be
expressed in implicit Crank Nicolson24 form by replacing
the second central difference with the average of the second central
difference at time t and t+t.6 The Crank and Nicolson
method is second-order accurate and is unconditionally stable. Its
solution entails, at any given time step, simultaneous
solution of membrane potential over the entire fiber once individual
ionic currents are computed.25 We always use the Crank and
Nicolson implicit method to solve for the relation in Equation 1.
Extracellular resistance, Ro, is neglected (the fiber is
assumed to be in an extensive medium). No flux (sealed ends) boundary
conditions are used by setting 
Vm/x=0 at
the beginning and end of the fiber.
Spatial discretization and distribution of fiber resistivity require
special consideration for a discontinuous fiber, as discussed in
"Appendix 1." For computations in this report,
x=100 µm (entire cell length) is used as the
discretization element with Ri reflecting the lumped
contribution of axial and gap junction resistance
(Ri=Rmyo+Rg/x). When
intracellular detail is sought, a smaller x of 21
computation elements per cell (x=4.76 µm) is used
with Rg concentrated at the edge elements of the cells. All
simulations were tested for numeric convergence and accuracy.
Regardless of fiber discretization, the intracellular calcium transient
[Ca]i, intracellular calcium buffering, and sarcoplasmic
reticulum (SR) calcium fluxes are always computed for the entire cell
as one unit. When x is less than one cell length,
sarcolemma calcium currents from each element are summed for net
calcium entry into the cell. Unless otherwise specified, the middle
element of a multi-element cell is always used for computation of
upstroke velocity, dVm/dt.
Safety Factor for Conduction
On the basis of the approach of others,9 12 we
define the safety factor for conduction (SF) as the ratio of charge
generated for the fiber by cell excitation to the minimal amount of
charge required to cause the excitation. An SF >1 indicates that more
charge was produced during cellular excitation than charge required to
cause excitation. The fraction of SF >1 indicates the margin of
safety. When SF falls <1, the charge requirements are not met and
conduction fails. The equation used to compute SF is
 | (2) |
Simulation Protocol
The theoretical fibers used in this study were between 70 and
100 cells (0.70 to 1.0 cm) in length. Rmyo (myoplasmic
resistivity) was 150 cm and gj (gap junction
conductance) varied between 0.005 and 2.5 µs (corresponding to
resistance changes between Rg=760 and 1.5
cm2, respectively). A variable time step was
introduced that tracks the propagating action potential, using small
time steps (t=0.005 ms) when membrane activity is high and large
time steps (t=1.0 ms) when membrane activity is low. The
variable time step algorithm sums the change in membrane voltage
for nine cells in each direction from the cell under consideration.
Each millisecond, the sum is evaluated for all cells of the fiber. If a
cell's sum is greater than a preset threshold (20 mV) or the cell is
within 15 ms of calcium release, then the cell's time step for the
next millisecond is small. Otherwise the time step is large. The
variable time step is used for membrane current computations only.
Axial currents are always computed every 0.005 ms. The variable
time step was always in effect, except where indicated.
The fiber was excited by applying a 0.5-ms superthreshold stimulus to cell 1 and, when multiple (n) elements per cell were used, to the middle element of cell 1. Stimulus strength (µA/µF) varied with n and gj. For n=1 and gj=2.5 µs, stimulus was -600 µA/µF. Results are independent of the stimulus used for distances greater than one space constant (about 9 cells) from the stimulus site because propagation depends on fiber axial current, not on the applied stimulus, for excitation. End effects were also restricted to within 9 cells from the fiber end.
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Propagation in a Multicellular Fiber
The theoretical fiber we used is composed of interconnected cell models rather than a membrane model with finite spatial dimensions. The difference is that individual cell models contain both membrane and intracellular processes. Excitation in the multicellular fiber by a propagating action potential results in both membrane and intracellular events (eg, the transmembrane action potential and the intracellular calcium transient). Fig 2A
shows the
profile of a computed action potential (AP) in space at time=t and
time=t+3 ms. The distance covered in 3 ms is 1.6 mm (16 cells),
which is observed in Fig 3 and can be
computed from the product of the time period (3 ms) and conduction
velocity (54 cm/s). At the head of the action potential there is a slow
electrotonic depolarizing phase (AP "foot"). Slightly further
upstream (to the left) cells are undergoing a sharp upstroke caused by
the fast sodium current (INa) depolarizing local membrane.
Further upstream (left) of the upstroke, late upstroke, and early
plateau depolarization is occurring, which is due to the L-type calcium
current (ICa(L)).
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Spread of electrical excitation in Fig 2A initiates a chain of events
that lead to calcium-induced calcium release (CICR) and a rise in
intracellular calcium. Fig 2B shows the calcium transient in space for
the same time instants as the AP profiles in Fig 2A. At each time
instant (t and t+3) the AP upstroke (wave front) is about 25 cells
ahead of the calcium transient. This spatial difference results from
the period of calcium accumulation that triggers CICR16
and the dynamics of the SR calcium release process.
The coupling between membrane excitation and calcium release is bidirectional. Calcium accumulation from calcium entry through ICa(L) during the late upstroke initiates CICR. The resulting myoplasmic calcium transients decrease local ICa(L) via calcium-dependent inactivation. Under normal conditions, CICR is sufficiently delayed from the upstroke to not interfere with conduction. However, when conduction is slowed, CICR leading to calcium-dependent inactivation of ICa(L) may become an important factor.
Fig 3 shows action potential profiles in two neighboring cells under
conditions of normal gap junction coupling (panel A) and a marginal
(10-fold) decrease in coupling (panel B). For normal coupling
(gj=2.5 µs), the gap junction conductance between cells
is equal to the myoplasmic conductance of the entire cell. The result
is equal conduction time of 0.09 ms between cells as in crossing the
cell length. On a macroscopic (many cells) scale, the result is an
apparent uniform spread of excitation as seen in Fig 3A. With only
10-fold reduction in coupling (Fig 3B) a large (0.5 ms) conduction
delay is introduced at each intercellular junction, while the entire
cell depolarizes almost simultaneously. The almost
simultaneous depolarization of the cell is due to increased
confinement of depolarizing current to the cell when intercellular
coupling is reduced, decreasing loading effects and current leakage out
of the cell. Note (Fig 3B) that propagation under these conditions is
nonuniform ("discontinuous"), with long delays at gap junctions. In
fact, the macroscopic conduction velocity over many cells is determined
by the gap junction delays rather than by the (negligible) time spent
in traveling across individual cells. With even further reduction in
coupling, the intercellular delay can be on the order of milliseconds,
providing time for calcium released from the SR to contribute to
ICa(L) inactivation, altering the balance of currents at
the head of a traveling action potential. The issues of propagation
down a fiber with reduced coupling and interaction between the calcium
transient and ICa(L) are explored in later sections of this
report. Principles observed in Figs 2 and 3 are that propagation is a
multicellular phenomenon that involves interaction between membrane
currents, gap junction properties, and intracellular ionic processes.
The interactions between these multiple factors must be considered when
propagation is analyzed and when mechanisms of normal and
abnormal conduction are investigated.
Reduced Membrane Excitability Lowers Conduction Velocity and
Propagation Safety, With Little Effect From ICa(L)
We investigated the effects of reduced membrane excitability (eg,
due to acute ischemia or class I drugs) on conduction of the
action potential impulse. The parameters used to
characterize conduction with changes in excitability are conduction
velocity (
), safety factor for conduction (SF), maximum upstroke
velocity ([dVm/dt]max), and peak sodium
current (INa,max). These computed parameters
are shown with different degrees of membrane excitability in Fig 4. Because excitability is determined by
availability of fast sodium channels, membrane excitability is reduced
by lowering ¯gNa, the maximum conductance of
INa. All four indices of conduction decrease monotonically
with excitability reduction. This result is to be expected; lower
sodium channel availability causes slower conduction of an action
potential that has a slower upstroke and is less safe. Fig 4A shows
that the minimum conduction velocity obtained before conduction failure
is 17 cm/s, indicating that the minimum possible conduction velocity
with reduction in excitability is only one third of control velocity
(54 cm/s).
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Safety factor of conduction, also in Fig 4A, decreases slowly with
excitability reduction, indicating a relative insensitivity to moderate
changes in membrane excitability. It can be recalled from the
discussion in "Methods" that SF is the ratio between charge gained
by the fiber from cell excitation to charge required for cell
depolarization. Our simulations reveal that reducing sodium channel
availability only marginally reduces charge gained by the fiber from
excitation (numerator of SF) because (1) capacitive charge gained
(first numerator term) is proportional to peak membrane potential,
which is not reduced significantly by reducing INa, and (2)
subthreshold depolarization time is not greatly reduced, resulting in
only small changes to the charge delivered downstream (second numerator
term). Our simulations also indicate that charge required to depolarize
the fiber (the denominator of SF) is not significantly increased.
Therefore less than extreme reductions in INa availability
do not constitute a great detriment to SF. At INa
availability <11.25%, the cell membrane has difficulty reaching
threshold, depolarizing charge requirements from upstream fiber start
to increase dramatically (denominator), and SF drops precipitously
toward 1. The rapid decrease of SF toward 1 in Fig 4C is indicative of
the nonlinear "all or none" response of the cell membrane.
The data in Fig 4B suggest that INa dominates
conduction for almost the entire range of membrane excitability.
Maximum upstroke velocity, an indicator of the depolarizing current
during the upstroke, follows INa,max at all levels of
reduced excitability. However, as membrane excitability is reduced
below 30% ¯gNa, INa,max decreases faster
than (dVm/dt)max, suggesting additional support
from another inward current (ICa(L)). We also found that
when ICa(L) is removed, conduction fails at slightly higher
membrane excitability (¯gNa=15% as compared with 11%
when ICa(L) is present). Therefore we examined, in Fig 5, the role of ICa(L) in
action potential conduction under conditions of depressed membrane
excitability. In Fig 5A, SF is computed for a control fiber with all
membrane currents intact (solid line) and for a fiber with
ICa(L) removed (dashed line). For most values of membrane
excitability, the presence of ICa(L) does not influence SF.
At extreme reductions of excitability (<30% availability),
ICa(L) augments SF slightly, resulting in conduction
failure at the slightly lower value of % ¯gNa.
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At extremely low membrane excitability, in the vicinity of
¯gNa=20%, a slight positive influence of
ICa(L) on SF is evident in Fig 5A. We investigated the
mechanism by which ICa(L) increases the safety of highly
depressed conduction. Fig 5B shows action potential upstrokes from the
middle cell of the fiber computed with ICa(L) (solid line)
and without ICa(L) (dashed line), both at 20%
¯gNa. Time 0 is the time of
(dVm/dt)max for the middle cell. The action
potential upstrokes, as reflected in
(dVm/dt)max, are slightly faster for the fiber
computed with ICa(L) (46 versus 35 V/s). The difference in
(dVm/dt)max is not due to different
INa,max, which is actually higher for the fiber without
ICa(L) (-48 versus -54 µA/µF, not shown), nor is the
difference due to direct local action of ICa(L), which does
not significantly activate at the negative voltage range
(around -33 mV) at which (dVm/dt)max occurs.
(dVm/dt)max is somewhat higher in the fiber
with ICa(L) because ICa(L) increases slightly
the action potential amplitude in the adjoining upstream cell (compare
action potentials with and without ICa(L) in Fig 5). Higher
action potential amplitude acts to increase the potential gradient and
the electrotonic driving force between an excited cell and its
downstream neighbor that is still undergoing depolarization. The result
is a slight increase in axial current and somewhat greater axial charge
delivery that contributes directly to the depolarization of the
downstream cell.
The quantitative role of ICa(L) in augmenting electrotonic
driving force and downstream depolarization can be established by
computing the charge (current integrated over time) generated by a cell
membrane between its own (dVm/dt)max and
(dVm/dt)max of its downstream neighbor
(identified by a thin vertical line in the figure). This computation is
a measure of charge generated by a source cell to depolarize its
downstream neighbor. Note that INa and ICa(L)
are integrated over a very short interval (to the thin vertical line)
because the downstream neighbor is activated early during the
plateau of the upstream source cell (a long intercellular delay at the
gap junction is not present). During the short interval,
INa is near its maximum value and ICa(L) is
only beginning to activate. In the inset of Fig 5B, we show
relative charge generated by INa and ICa(L) at
20% ¯gNa. The computed charge ratio
QNa:QCa is 75:1. Thus it can be concluded that
the predominant current responsible for maintaining conduction, even at
20% ¯gNa, remains INa.
The results of this section demonstrate that despite a slight influence from ICa(L) in supporting axial charge delivery at extreme levels of membrane depression, in an otherwise well-coupled fiber excitability and conduction are determined by INa. Decreased excitability decreases all parameters of conduction, ultimately leading to conduction block. In the following section we evaluate the effect of decreased intercellular coupling while the membrane currents are not directly modified.
Reduced Intercellular Coupling Reduces Conduction Velocity and Has
a Biphasic Effect on Propagation Safety, With Major Effect from
ICa(L)
Propagation transverse to fiber orientation and propagation across
areas of a healed infarct are examples of normal and
pathophysiological propagation in which
intercellular coupling is reduced. Fig 6
contains the parameters of propagation plotted against
changes in intercellular coupling conductance, gj.
Conduction velocity decreases monotonically with reduction in
intercellular coupling. This behavior is more dramatic but
qualitatively similar to that of reductions in membrane excitability.
However, as seen in both Fig 6A and 6B, safety factor for conduction
and maximum upstroke velocity of the action potential do not decrease
with decreasing levels of intercellular coupling. Both
parameters display a biphasic behavior, increasing then
decreasing, in response to reduction of gj. Across the
entire range of gj, SF is greatest at gj=0.023
µs and (dVm/dt)max is greatest at
gj=0.040 µs. Therefore, maximum values for both
parameters occur when intercellular coupling is reduced by
a factor of about 15 relative to its normal value of 2.5 µs.
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The slight monotonic decrease in INa,max with decrease in
gj, seen in Fig 6B, establishes that membrane currents are
not the cause of the biphasic changes in SF and
(dVm/dt)max. Instead, the changes of
intercellular coupling affect source-load relationships in the fiber,
which feed back on the action of membrane currents. Inward membrane
current either acts to depolarize local membrane or generates axial
current flow downstream to act on distant membrane. When coupling is
reduced, less inward current is shunted downstream (less load),
effectively increasing availability of inward current for local
depolarization. As a result of increased availability of local
depolarizing current, safety factor and
(dVm/dt)max increase. The descent of safety
factor and (dVm/dt)max at very low levels of
coupling is due to reduced availability of INa
source-current under these conditions. INa,max is small at
very low levels of intercellular coupling due to a long subthreshold
depolarization phase (slow charging process due to the small axial
current when resistance between cells is large) that provides for
dynamic inactivation of sodium channels before reaching their
activation threshold. This results in reduced sodium channel
availability at threshold and a small INa,max. Ultimately,
for very low degrees of intercellular coupling, subthreshold dynamic
inactivation of INa is not compensated for by conservation
of current for local membrane due to the reduced cellular coupling. The
result is decreased safety factor, decreased
(dVm/dt)max, and with sufficiently reduced
coupling, conduction block. The data in Fig 6B demonstrate that when
coupling is extremely reduced, INa,max is almost the sole
determinant of (dVm/dt)max (the two curves
practically overlap at this range), as occurs in an isolated
space-clamped cell (a situation that is approached by the highly
uncoupled fiber).
The results of Fig 6 illustrate that altered intercellular coupling can
cause major changes of the action of membrane currents even when the
intrinsic properties (ie, density and gating) of these membrane
currents remain unchanged. We introduced earlier the possibility that
ICa(L) can affect conduction when coupling is reduced. This
hypothesis is tested by computing the safety factor for conduction over
a full range of intercellular coupling with and without the presence of
ICa(L). Results are shown in Fig 7A that show that the two safety factor
curves have the same biphasic shape. However, a striking difference
between the curves is that conduction failed at gj=0.0056
µs for the fiber with all ionic currents intact and at a much higher
gj=0.0197 µs for the fiber computed without
ICa(L). The finding that the presence of ICa(L)
can support conduction that otherwise fails over more than a threefold
decrease in gap junction coupling strongly suggests that
ICa(L) is a major determinant of propagation under
conditions of highly reduced intercellular coupling and long
propagation delays across gap junctions.
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The interplay between INa and ICa(L) during
conduction with decreased intercellular coupling is further explored in
Fig 7B, which contains an action potential upstroke at
gj=0.020 µs, computed with (solid line) and without
(dashed line) ICa(L). Gap junction conductance of
gj=0.020 µs is used because it is slightly greater than
the conductance at which ICa(L) becomes essential for
conduction. As was explained in the context of reduced excitability,
ICa(L) does not play a direct role in local excitation but,
by maintaining a higher plateau, ICa(L) enhances the axial
driving force and the resulting electrotonic source current. When
decreased coupling causes long propagation delays, ICa(L),
which is the major depolarizing current during late upstroke and early
plateau, becomes extremely important. The role of ICa(L) in
augmenting the driving force and the electrotonic current is confirmed
by the postupstroke membrane potentials of Fig 7B. The action potential
that included ICa(L) maintains an early plateau at
significantly higher potential than the action potential without
ICa(L). It is the higher plateau that increases the driving
force, forcing more source current to the adjacent downstream cell. The
bar graph inset in Fig 7B indicates the increasing role of
ICa(L) in supporting conduction under conditions of
decreased coupling. The bars, like those of Fig 5, show the relative
charge contribution to sustain conduction from INa and from
ICa(L) and are computed by integrating these currents over
time, until the downstream neighboring cell is activated. Note
that due to the long delay at the gap junction, the downstream neighbor
is excited when the upstream source cell is well into its plateau (thin
vertical line in Fig 7B). Therefore, ICa(L), which is
active during the plateau, is integrated over a much longer time than
in the case of depressed membrane (compare with Fig 5B), and
INa, which is inactivated at the plateau, does
not contribute additional charge beyond its early contribution during
this interval. As a result, unlike the INa dominance
conditions of reduced excitability (Fig 5), charge contributions from
both currents are almost equal
(QNa:QCa(L)=1.47:1) for reduced coupling of
gj=0.020 µs. Therefore, ICa(L) under such
conditions is almost as important as INa in sustaining
conduction. With further reductions in coupling, charge contribution
from ICa(L) needed to support conduction exceeds that from
INa (ie, at gj of 0.010, 0.006, and 0.0057
µs, QNa:QCa(L) charge ratios are 0.81, 0.26,
and 0.16, respectively; the case of gj=0.006 µs is shown
in Fig 7C). Therefore, in the situation of highly reduced coupling,
INa is necessary to bring the membrane into the activation
range of ICa(L), but the major source of depolarizing
charge and the most significant current to sustain propagation is
ICa(L).
Intracellular Calcium Can Influence Conduction
There are numerous pathological conditions during which
ventricular cells experience an increase in intracellular
calcium, a condition known as calcium overload. Because
[Ca]i has a direct effect on ICa(L) via
calcium-dependent inactivation, it follows that changes in
intracellular calcium may affect conduction. We explored the effect of
elevated [Ca]i on action potential propagation by
comparing propagation in a fiber with control values of resting
[Ca]i=0.12 µM to a fiber with elevated resting
[Ca]i=0.25 µM. Considering that ICa(L)
affects propagation when coupling is reduced, we computed the safety
factor of each fiber over a full range of intercellular coupling with a
protocol similar to that of Fig 7A. We found (not shown) that calcium
overload begins to lower SF after a 100-fold reduction in
gj and causes conduction failure at slightly higher
intercellular conductance (failure occurs at gj=0.007 µs
and gj=0.0057 µs at elevated and normal
[Ca]i, respectively). Therefore, under extreme
conditions, when dependence on ICa(L) to sustain conduction
is a major factor, decreasing ICa(L) via elevated
[Ca]i will decrease propagation safety.
To confirm that [Ca]i action on ICa(L) is the
mechanism of decreased propagation safety under conditions of calcium
loading, we examined, in Fig 8, the
action potential upstroke and related calcium current that occur at low
intercellular coupling (gj=0.008 µs). Two fibers were
used, one with normal [Ca]i (solid line) and one with
elevated [Ca]i (dashed line). The action potential
upstrokes are followed by a dip, which (as recognized from previous
figures) is caused by the charging of the adjoining downstream cell.
During the dip, ICa(L) reaches a maximum value and then
decreases. The maximum values of ICa(L) are coincident with
calcium release from the SR and the following decline is due mostly to
calcium-dependent inactivation. ICa(L) decreases more for
the cell with elevated [Ca]i, reflecting greater
calcium-dependent inactivation. Greater inactivation of
ICa(L) causes (Fig 8A) faster action potential
repolarization, decreased axial driving force, and longer charging
period of the adjacent downstream cell. The inset of Fig 8B shows that
the charge from ICa(L) needed to excite the adjoining cell
is approximately the same for both fibers. Since ICa(L) is
smaller in the overloaded fiber, longer intercellular charging time is
needed, leading to decreased sodium channel availability (greater
dynamic inactivation) and reduced SF.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1Appendix 2References |
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This study establishes two types of seemingly paradoxical behavior for propagation of excitation in multicellular cardiac fibers. The first is that as conduction velocity is slowed by decreased gap junction coupling, propagation safety is increased. Conduction in the milieu of decreased coupling (such as in a zone of infarction) is slow but safe. The second is that the functional role of excitation currents (ie, INa and ICa(L)) is determined more by passive structural factors external to the membrane than by intrinsic membrane factors. Decreased intercellular coupling, not decreased sodium channel availability (reduced membrane excitability), results in a major functional role for ICa(L) in propagation. The significance of these behaviors is discussed below.
Slow Conduction and Propagation Safety
Both reduction in membrane excitability and reduction in
intercellular coupling reduce conduction velocity. However, the
mechanisms by which each pathology causes conduction slowing are
fundamentally different. Reduced excitability decreases availability of
the depolarizing membrane current, INa, slowing membrane
depolarization. Reduced coupling increases intercellular conduction
time by limiting (reducing) electrotonic axial current flow. By also
decreasing electrical load, decreased coupling confines current to the
depolarizing cell, causing an enhancement of its depolarization.
Safety factor data for the two different pathologies are compiled with
respect to conduction velocity in Fig 9.
The data establish that during conduction slowing decreased coupling
increases safety factor for conduction, whereas decreased excitability
decreases safety factor. The opposite effects on safety factor are
evident from the minimum conduction velocity obtained before block.
Reduced excitability can reduce conduction velocity only threefold (to
17 cm/s) before block occurs, whereas uncoupling can reduce conduction
velocity to an extremely low value of 0.26 cm/s before conduction
fails.
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There are differences in the literature as to whether conduction slowing with reduced coupling occurs with higher or lower safety. In a classic study, Spach et al8 found that cardiac conduction in the longitudinal (well-coupled) direction had higher conduction velocity but was less safe than conduction in the transverse (less-coupled) direction. Safety was evaluated by susceptibility to block with premature stimulation. Delgado et al9 observed the opposite, that conduction failed preferentially in the transverse direction. In their study, block was obtained by elevation of extracellular potassium concentration. A possible reason for the disparity between the two studies is the technique used to obtain block. Elevation of extracellular potassium concentration, unlike premature stimulation, alters the potassium reversal potential and depolarizes the resting membrane potential.26 27 As a result, not only do sodium channels inactivate, but distance between resting potential and threshold potential is reduced.27 28 In addition, conduction near block due to elevated extracellular potassium depends on the L-type calcium current to aid in excitation.20 Therefore an evaluation of safety factor based on elevating [K]o may include important contribution from ICa(L) and might differ from the safety factor evaluated by premature stimulation.
It is worthwhile to emphasize the magnitude of the safety factor changes caused by reduced excitability versus reduced coupling. Reduced excitability causes a monotonic reduction in SF, lowering it by 60% (from 1.6 to 1), before causing conduction failure. In contrast, reduced coupling increases SF by 200% before causing a drop in SF and block. This is evidence that, in terms of safety factor for conduction, membrane excitability properties are less influential than passive fiber properties. A slight decrease in coupling could compensate for a major decrease in membrane excitability. For example, the ischemic combination of acidosis (pH=6.5) and hyperkalemia ([K]o=10 mmol/L) decreases resting INa availability by 60%,20 lowering SF from 1.6 to 1.4. Merely decreasing gap junction coupling by a factor of three will compensate for such ischemic decrease in safety. Uncoupling is typically considered to be an attempt of the myocardium to isolate damaged cells.29 However, because reduced coupling improves the safety factor for conduction, a certain degree of uncoupling may be an important tissue-level response to ensure conduction despite depressed membrane excitability.
Roles of INa and ICa(L) in
Propagation
Under all conditions other than reduced intercellular coupling,
INa is the major ionic current that determines
excitability. This includes slow conduction due to depressed membrane.
When intercellular coupling is even marginally reduced, we found that
conduction relies on ICa(L) as well as INa.
Conduction block occurred, with all membrane currents intact, at gap
junction conductance gj=0.0057 µs. When
ICa(L) availability was reduced to zero, conduction block
occurred at gj=0.0197 µs, three times the intercellular
conductance that caused block in the presence of ICa(L).
The important role of ICa(L) under conditions of decreased
coupling is also evidenced by the total charge generated to excite an
adjoining cell. At control conditions (gj=2.5 µs) the
charge ratio QNa:QCa is 166:1, indicating
INa dominance. At gj=0.020 µs, the ratio
decreases to 1.47:1, reflecting equal roles of INa and
ICa(L) in conduction. The charge ratio decreases further
with further decreases in coupling, and at gj=0.0057 µs,
QNa:QCa is 0.16:1 indicating ICa(L)
dominance and an order of magnitude greater charge contribution by
ICa(L) than by INa.
The effect of ICa(L) at low intercellular coupling has been studied in isolated cell pairs (between two real cells, a real cell and a model cell, and two model cells) by Joyner and colleagues.13 30 They determined that if the leader cell is unable to excite a follower cell due to limited intercellular conductance or size related source-load mismatch, ICa(L) enhancement in the leader cell could successfully restore excitation in the follower cell. The converse was also true, ICa(L) inhibition in the leader cell could block otherwise successful follower cell excitation. For all conditions, ICa(L) was effective when intercellular delay was on the order of 5 ms (equivalent to conduction velocity of about 2 cm/s).
In the multicellular fiber, we found that ICa(L) influenced safety factor for conduction when gj was as high as 0.5 µs (one fifth of control), which causes an intercellular conduction delay of only 0.3 ms. As gj decreases and the conduction delay increases, the downstream cell depolarizes when the upstream source cell is "deeper" into the plateau phase of its action potential. At this phase, ICa(L) is the depolarizing current and the major contributor of depolarizing charge to the downstream cell (note that charge involves integrating the current over time). Therefore, with longer intercellular conduction delays, more of the depolarizing charge delivered to the downstream cell is generated by ICa(L). Two- and three-dimensional structural anisotropy as well as nonmyocyte inhomogeneities (eg, connective tissue septae) may cause local conduction delays even when global conduction velocity is not drastically reduced. For instance Spach and Heidlage,31 32 using a detailed two-dimensional cellular model with realistic cell geometry and gap junction distribution, observed microscopic transcellular conduction delays on the order of 1 ms. Rohr and colleagues14 33 34 found, with cultured rat heart cells patterned into a narrow strand opening into a large rectangular area (large load), that ICa(L) block caused conduction failure when activation delay at this opening was in the millisecond range. Conversely, when block of conduction from the small strand to the large area preexisted, ICa(L) enhancement with Bay K 8644 reestablished successful conduction.33 34 Fast and colleagues35 36 37 have observed in cultured rat cell monolayers that nonuniformities on different-size scales (eg, uneven gap junction distribution, connective tissue sheets, nonexcitable vascular cells) may represent predilective sites for conduction block.35 On the basis of these studies and our results, ICa(L) may then be a major component of microscopic propagation and of the safety factor for conduction at these sites even when overall macroscopic conduction velocity is not significantly reduced. ICa(L) is likely to play an important role in any situation when propagation is associated with long local conduction delays (eg, tissue expansion at Purkinje muscle junctions, increase in load on a wave front while circulating around a pivot point during reentry).
There is strong experimental evidence that the
electrophysiological characteristics of
conduction within a healed infarct zone are the result of reduced
intercellular coupling. Fractionated electrograms, observed in
infarcted regions,10 38 are associated with separation and
altered orientation of myocardial fibers.10 39 In these
cases slowed activation and very slow conduction are likely a result of
decreased intercellular coupling.38 On the basis of our
simulations (Fig 9), the very slow velocities (<1 cm/s) that are
measured in healed infarcts and that make reentry in a small region
("microreentry") possible must involve long local conduction delays
and cannot be supported by depressed excitability (which cannot support
velocity slower than 17 cm/s). Slow and discontinuous conduction within
surviving muscle of epicardial infarcts has been identified as a
mechanism of reentrant arrhythmias.40 41 42 43 The newly
recognized importance of ICa(L) in highly discontinuous
propagation that involves long conduction delays identifies the L-type
calcium channel as a possible target for antiarrhythmic therapy under
such conditions.
With our discussion focusing on the role of ICa(L), we hasten to emphasize that INa, even with reduced availability, is always required for conduction. ICa(L) activates between Vm=-40 and -30 mV.16 INa is still needed to bring the membrane potential to within the range of ICa(L) activation. [K]o elevation, and consequent depolarization of resting membrane potential, is the only scenario we know in which ICa(L) may be the sole excitatory current.20
Intracellular Calcium Transients and Propagation
Through the calcium-induced calcium release process,
excitation-contraction coupling involves coupling between sarcolemmal
calcium flux via ICa(L) and intracellular calcium
transients. That is, intracellular calcium responds to sarcolemmal
currents. In the reverse direction, ICa(L) and other
currents (eg, INaCa, IKs) are modulated by
[Ca]i. The simulations of this study indicate a possible
functional role for ICa(L) modulation by
[Ca]i in propagation of the cardiac action potential.
The L-type calcium current can be inactivated by free intracellular calcium ions.44 Sipido et al45 have shown in guinea pig cells that ICa(L) inactivation is proportional to [Ca]i. Grantham and Cannell46 found in guinea pig cells (using the ICa(L) formulation from the LRd model) that ICa(L) behavior during an action potential cannot be reconstructed correctly without calcium-dependent inactivation. Lüscher et al47 showed that replacement of calcium ions by strontium ions (also a divalent positive charge carrier) prevented action potential conduction failure in dorsal root ganglion cells, suggesting that [Ca]i-dependent inactivation of ICa(L) can affect conduction (strontium causes minimal inactivation of ICa(L)). More recently, the same team15 found that flash photolytic liberation of a calcium buffer, during trains of action potentials, which partly failed to invade the cell body, immediately lowered intracellular [Ca]i and restored safe action potential propagation. Also, the velocity of the propagated action potential was reduced when intracellular calcium was increased by flash photolysis.15
Our results demonstrate that elevated intracellular calcium can both
decrease conduction velocity and lower the safety factor for conduction
during highly discontinuous ventricular propagation, which
depends on ICa(L). Doubling the free intracellular calcium
concentration (to 0.25 µmol/L) resulted in conduction
failure at gj
0.007 µs, 23% higher than the conductance
at which it otherwise occurred. Although, for the uniform fiber,
reduction of gap junction coupling by two orders of magnitude is needed
before the effects of [Ca]i on propagation are apparent,
the principle of [Ca]i modulated conduction may have much
greater significance in conduction across tissue inhomogeneities where
large source-load mismatches exist and cause very long conduction
delays.34 By studying the direct response of
ICa(L) to changes in [Ca]i, we established
that the ionic mechanism of [Ca]i modulated propagation
is, as suggested by Lüscher et al,15 47
calcium-dependent inactivation of ICa(L).
Conclusions
The study emphasizes that reduced membrane excitability (eg,
during acute ischemia) cannot support very slow conduction and
is mostly associated with conduction failure. In contrast, slow
conduction due to gap junction decoupling is safe, and very slow
velocities can be supported by such structural changes (eg, due to
infarction).
Our results suggest that the passive myocardial structure has a major effect on the role of membrane currents in propagation of the cardiac action potential. We find it striking that a nonmembrane change (ie, decreased intercellular coupling) can cause the membrane to switch to a different process (calcium current instead of sodium current) as the major mechanism for supporting conduction. A control fiber relies on INa to sustain conduction and, except for extreme circumstances, a fiber with depressed membrane excitability still relies on INa for action potential conduction. However, reduced gap junction coupling (a nonmembrane structural change) changes the dynamics of membrane ionic currents during the action potential and switches the membrane to an ICa(L)-dependent mode of operation. This finding illustrates the strong bidirectional interaction between the membrane (source) and passive myocardial structure (sink) during action potential propagation.
In addition to its direct feedback influence on membrane dynamics, reduced gap junction coupling modulates the effects of interaction between intracellular ionic processes (eg, the calcium transient) and membrane ionic currents (eg, ICa(L)). In this study, [Ca]i-dependent inactivation of ICa(L) was shown to influence propagation only when long conduction delays at gap junctions were involved (the condition for ICa(L) involvement in sustaining conduction). This example emphasizes even more the highly interactive nature of action potential propagation in cardiac tissue.
The fact that ICa(L) plays an important role in conduction only where propagation is very slow and highly discontinuous is encouraging from the perspective of antiarrhythmic drug therapy. Such conduction requires a pathological substrate (eg, infarcted region), implying that conduction depends on ICa(L) only where the pathology exists. In healthy myocardium with normal intercellular coupling, ICa(L) is not needed to maintain propagation of excitation. With appropriate levels of universally applied ICa(L) block, conduction will be modified in the vulnerable infarcted region only, without affecting the normal myocardium, thereby ensuring specific drug action. In the same context of antiarrhythmic drug therapy, the study demonstrates that the intervention should consider the underlying pathophysiological state of the myocardium. For example, slow conduction during most phases of acute ischemia involves only INa, whereas slow conduction in a healed infarct involves long local delays and therefore ICa(L). Consequently, the targets for intervention (drug treatment, genetic modification) might be very different in treating propagation-related arrhythmias (eg, reentry) in the context of different pathophysiological conditions.
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Acknowledgments |
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This work was supported by the National Institutes of Health grants HL-49054 and HL-33343 (National Heart, Lung, and Blood Institute).
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Footnotes |
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Previously published in abstract form (Biophys J. 1997;72:A110).
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Appendix 1 |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1Appendix 2References |
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Spatial computational discretization and distribution of fiber resistivity require two separate considerations, one of numeric accuracy (convergence) and one of anatomic correctness. For a continuous fiber, numeric accuracy requires that the spatial discretization element (
x) be no longer than one tenth of
the fiber space constant so that the entire element is essentially
equipotential.7 However, a ventricular fiber
is discontinuous, consisting of intracellular myoplasm of low
resistivity separated by intercellular gap junctions of (comparatively)
high resistivity. Under normal coupling conditions, resistance over the
entire 100 µm of myoplasm is equal to the resistance across the
gap junction,48 49 which occupies no more than 80 Å. To
select a x that is both numerically accurate and reflects
the discontinuous structure of a cardiac fiber, we computed key
physiological parameters for different
values of gap junction resistance (Rg) at different levels
of spatial discretization (x). Results are shown in the
Table, which is a compilation of peak
membrane potential (Vm,peak), maximum upstroke velocity
([dVm/dt]max), action potential duration at
90% repolarization ([APD]90), and conduction velocity
(), all computed for an action potential traveling down a 7-mm
fiber. Simulations were repeated for three types of fiber
discretization: (1) a discontinuous fiber of 21 computational elements
per cell length (x=4.76 µm) with Rg
confined to the edge elements of the cell (representing the
local gap junction resistance); this high level of discretization
ensures convergence and provides a gold standard for propagation in a
discontinuous fiber; (2) a continuous fiber also discretized to 21
elements/cell length (x=4.76 µm) but with
Rg evenly distributed across the entire cell; this provides
an accurate model of propagation in a continuous fiber; and (3) a
continuous fiber discretized to computational elements equal to the
entire cell length (x=100 µm) with
Rmyo and Rg lumped together at each
discretization point. Al