© 1998 American Heart Association, Inc.
Original Contributions |
Mechanisms of Stretch-Induced Changes in [Ca2+]i in Rat Atrial Myocytes
Role of Increased Troponin C Affinity and Stretch-Activated Ion Channels
From the Departments of Physiology and Physical Sciences/Division of Biophysics and Biocenter Oulu, University of Oulu, Oulu, Finland.
Correspondence to Matti Weckström, MD, PhD, Department of Physiology, University of Oulu, Kajaanintie 52A, FIN-90220 Oulu, Finland. E-mail matti.weckstrom{at}oulu.fi
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Abstract—To study the effects of stretch on the function of rat left atrium, we recorded contraction force, calcium transients, and intracellular action potentials (APs) during stretch manipulations. The stretch of the atrium was controlled by intra-atrial pressure. The Frank-Starling behavior of the atrium was manifested as a biphasic increase of the contraction force after increasing the stretch level. The development of the contraction force after step increase of the stretch (intra-atrial pressure from 1 to 3 mm Hg) was accompanied by the increase in the amplitude of the calcium transients (P<0.05, n=4) and decrease in the time constant of the Ca2+ transient decay. The APs of the individual myocytes were also affected by stretch; the duration of the AP was decreased at positive voltages (AP duration at 15% repolarization level, P<0.001; n=13) and increased at negative voltages (AP duration at 90% repolarization level, P<0.01; n=13). To study the mechanisms causing these changes we developed a mathematical model describing [Ca2+]i and electrical behavior of single rat atrial myocytes. Stretch was simulated in the model by increasing the troponin (TnC) sensitivity and/or applying a stretch-activated (SA) calcium influx. We mimicked the Ca2+ influx by introducing a nonselective cationic conductance, the SA channels, into the membrane. Neither of the 2 plausible mechanosensors (TnC or SA channels) alone could produce similar changes in the Ca2+ transients or APs as seen in the experiments. The model simulated the effects of stretch seen in experiments best when both the TnC affinity and the SA conductance activation were applied simultaneously. The SA channel activation led to gradual augmentation of Ca2+ transients, which modulated the APs through increased Na+/Ca2+-exchanger inward current. The role of TnC affinity change was to modulate the Ca2+ transients, stabilize the diastolic [Ca2+]i, and presumably to produce the immediate increase of the contraction force after stretch seen in experiments. Furthermore, we found that the same mechanism that caused the normal physiological responses to stretch could also generate arrhythmogenic afterpotentials at high stretch levels in the model.
Key Words: stretch • myocyte • Frank-Starling • Ca2+ • action potential
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Introduction |
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The stretch-induced changes in heart muscle are prototypically manifested as an increase in the contraction force, the well-known Frank-Starling mechanism.1 Although it is known that mechanical stimulation can influence the free intracellular calcium,2 3 4 5 contraction force,6 and electrical action of the myocytes,7 8 the underlying mechanisms have not been resolved. It has been reported that the stretch-dependent changes in the cardiac contraction force has 2 components.9 Immediately after stretch the contraction force is increased. This increase is followed by additional slow increase in force. Increase of the muscle length produces a gradual increase in Ca2+ transient amplitude.10 The stretch sensitivity of troponin C (TnC)11 12 and mechanical changes in the crossbridge attachments, like the reduction of double thin-filament overlap13 14 15 might explain the fast increase in contraction force, causing additional buffering of Ca2+ by the contractile element and increase in contraction force. However, it is not possible to augment the Ca2+ transients by the increased sensitivity of TnC. A complementary explanation for the increase of the Ca2+ transients during stretch would be activation of stretch-activated (SA) channels, first reported by Guharay and Sachs,16 which have also been found in cardiac myocytes.17 18 19 20 21 22 The aim of the current study was to define the stretch-induced changes in the isolated rat atrium in which stretch could be controlled by intra-atrial pressure. From the physiological point of view the plausible candidates (TnC and SA channels) for the mechanosensation in the heart are not easy to study. Usually ion channel function is studied by blockers or activators of the channel in question. In the case of SA channels, selective blockers are not known presently. The SA channel blockers previously used are fairly unspecific. For example, gadolinium blocks SA channels23 but also L-type Ca2+ channels24 and delayed rectifier K+ channels.25 The function of the TnC is also difficult to study in intact (or semi-intact) cardiac tissue. The central role of TnC in contraction makes it fairly inaccessible to study by physiological methods. It is also difficult to distinguish the effects of TnC on the function of the cardiac cells from other regulators of the contractile element (eg, troponins I and T).
The role of SA channels in the generation of the pathological effects of stretch has been widely studied previously.26 27 From the physiological point of view, if SA channels exist in the cardiac myocytes, the major function of these channels would be the participation in the normal stretch-dependent changes in the heart muscle (such as Frank-Starling [F-S] relation), rather than generation of pathological phenomena. On the basis of this hypothesis, we studied the influence of stretch on the APs, contraction force, and intracellular [Ca2+]i in the rat atrium. To keep the stretch in the range of the rising phase of the Frank-Starling relation, we used only small stretch stimuli. To complement the experimental part of the study, we developed a mathematical model by which we could further study the role of TnC and SA channels in the stretch-induced changes at the level of individual myocytes. We found that during the stretch activation of rat atrium, which included prolongation of APs, biphasic increase of the contraction force, and augmentation of the Ca2+ transients, at least 2 different mechanisms were involved. We show that the model could produce similar changes in Ca2+ balance and APs as seen in experiments only when a stretch-dependent Ca2+ influx (mimicking SA channel activation) was included in the simulation. The model simulations resembled the experiments closest when stretch was simulated by SA channel activation and increased Ca2+ affinity of TnC.
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Animals, Preparation, and Superfusion
Male Sprague-Dawley rats (n=60) weighing 290 to 400 g were used. The care and use of animals were approved by the committee of laboratory animal experimentation at the University of Oulu. They were kept at 20°C to 22°C and had free access to tap water and standard food. The rats were decapitated, and their hearts were rapidly removed and placed in oxygenated cool (25°C) buffer solution consisting of (in mmol/L) NaCl 137, KCl 5.6, CaCl2 2.2, HEPES 5.0, MgCl2 1.2, and glucose 2.5 (pH 7.4), which was also used for superfusion of the atrial preparation.
The experimental model used in this study was the isolated rat atrial appendix, prepared as described previously.28 Briefly, an X-branch polyethylene adapter was inserted into the lumen of the left auricle, and the tissue was placed in a constant-temperature (37°C) organ bath. Another tube with smaller diameter was inserted inside the adapter to carry perfusate inflow into the lumen of the auricle. The outflow from the lumen came from 1 cross-branch of the X-cannula. The stretch of the atrium was produced by changing intra-atrial pressure. Pressure inside the atrium was increased by increasing the height of the outflow tube. The other cross-branch of the X-cannula was connected to a pressure transducer (TCB 100, Millar Instruments, Inc), so that the pressure in the lumen of the auricle could be recorded. Inflow and outflow (3 mL/min) both to the auricle lumen and to the organ bath with constant temperature were controlled by a peristaltic pump (7553-85, Cole-Parmer Instrument Co).
Electrophysiological Recordings and
Data Analysis
Membrane potentials were recorded using glass
microelectrodes filled with a solution of 2 mol/L potassium acetate and
5 mmol/L KCl, pH 7.0. The resistances of the electrodes in tissue
were 70 to 120 M
. A chloride-treated silver wire, used
as a reference, was placed in contact with the superfusion medium in
the organ bath. The electrode holder connected to a micromanipulator
was a spring of chloride-treated silver wire (diameter 0.3 mm).
The atrial appendix (being the left one) was quiescent unless
stimulated electrically through bipolar Ag/AgCl electrodes placed in
contact with the auricle. Electrical stimulation (steps of duration 1
ms, 50% over threshold voltage) was provided by a stimulator (S44;
Grass Instruments Co). All electrical signals were amplified with an
intracellular amplifier (Dagan 8100-1; Dagan Co) and stored by a
data recorder (Biologic DTR-1800; Biologic Ltd). Data
analysis was done with DT VEE (Data Translation Inc) and MATLAB
(The Math Inc) programs. Sampling frequency was 3 kHz in all
recordings.
Calcium Measurements
To record intracellular Ca2+
transients from the Indo 1–loaded rat atria, a fiber optic silica
cable was led through the bottom of the perfusion chamber to make
contact with the tissue. In the detection end, the fiber cable consists
of 
100 unorganized fibers (diameter 100 µm), which are
further divided into 3 individual fiber bunches consisting of 30
individual fibers each. One branch guided the 355-nm filtered
excitation light to the tissue provided by 75-W xenon light source
(Hamamatsu), and the 2 remaining branches conducted the emitted light
that was filtered (405±5 nm and 495±5 nm) and detected with
photomultiplier tubes (Hamamatsu). The emission signal was further
amplified (x8) and filtered with an adjustable Kemo filter (Kemo Corp)
at 50 Hz. The Indo 1 emission ratio (405/495) was calculated online
from an A/D-converted (Data Translation) signal by Testpoint (Capital
Equipment Corp) custom-created software. The atrium was paced with 2
platinum electrodes at 1 Hz.
Loading the Atria With Indo 1
For Ca2+ measurements the left atrial
preparation was attached, prior to loading, to the perfusion system to
measure the autofluorescence from each atrium. The
autofluorescence at both emission wavelengths was determined
and then subtracted from the signals after loading. Together with the
autofluorescence the contraction force (developed pressure) was
measured at the low pressure (1 mm Hg), which was compared with
the contraction force after loading. For Indo 1 AM loading,
the preparation connected to the plastic tube was attached to a
separate loading chamber. In this chamber, the atria were superfused
for 25 to 40 minutes (flow 7 mL/min) with HEPES buffer (4 mL)
containing 10 µmol/L Indo 1 AM dissolved to 100 µL DMSO with
20% Pluronic, 0.5 mmol/L probenecid, and 1.5% BSA. To
avoid loading of the intracellular organelles such as sarcoplasmic
reticulum (SR) and mitochondria, the temperature in the chamber was
kept between 25°C and 30°C during the entire loading period. After
loading the fluorescence was 20 times greater than the
autofluorescence before loading. The contraction force
(developed pressure), which was 1 mm Hg before loading, was
3.1±0.4 and 3.17±0.4 mm Hg after loading (NS, n=15). This
indicates that Indo itself does not buffer calcium ions enough to
influence the contraction. It has been shown previously that when
epifluorescence of the heart muscle is used in estimation of
the intracellular calcium of the myocytes, part of the
fluorescence signal may originate from cells other than
myocytes,29 forming a possible source of error.
When cardiac tissue is loaded with fluorescence indicators such
as Fura-2 and Indo 1 through coronary arteries, a great portion
of the epifluorescence comes from the
endothelial cells.29 Here we
tried to avoid this by not using the coronary circulation in
loading; instead we used direct perfusion of the tissue. The source of
fluorescence was also under visual control (ie, when the atria
were attached to the perfusion system the areas of clearly greater
fluorescence intensity were avoided, and the atria were
measured from the areas with low total fluorescence intensity
and no visually detectable "hot spots"). In some preparations the
contraction and stretch of the tissue caused a prominent movement
artifact, and these atria were not used.
Mathematical Model
The model used in this study is based on that developed by Luo
and Rudy.30 31 32 Since the original model was
designed to model the guinea pig ventricular cell, we had
to make extensive modification to fit the model to our and previously
published experimental results from rat atrial myocytes. Together with
the species-specific modifications (see Appendix), we introduced a more
complex method of Ca2+ handling into the model on
the basis of recent reports. The calcium release in atrial myocytes is
a combination of the release from 2 different compartments of the
SR.33 34 The basic idea of this 2-step Ca-release
model is that the calcium entering through L-type channels triggers
calcium release from the first release compartment
(peripheral SR), and the Ca2+
released from the first compartment triggers release from the second
compartment (corbular SR) in an all-or-none manner. The trigger
threshold of the second compartment was set at the value equal to the
half of the calcium peak of normal release from the first compartment,
with the time constants of activation and inactivation 40 and 10 ms,
respectively. Time delay between release from first and second
compartments was 5 ms based on the calcium wave propagation velocity
and calcium gradients in atrial myocytes.33 35 36
These adjustments made the calcium release from the second compartment
slower than from the first compartment, consistent with
experimental data.34
Simulation of Stretch by the Model
The SA channels in the cardiac myocytes have reportedly a near
linear voltage dependence,22 no
adaptation,37 and nonselectivity over
cations.19 The reversal potential of the SA
channel current is –3.2 mV in rat atrial
myocytes.19 The SA channel formalism was adapted
from previous models,38 with small
modifications.
The SA channel current is given elegantly by
Sachs38 by the following equation:
 | (1) |
is the parameter defining the stretch
sensitivity (3), 
is channel density
(0.015/µm2), and 
is single-channel
conductance (25 pS). The iteration of the SA current was based
on our experimental data. To simulate the stretch effects seen in our
experiments, only 5% of the previously suggested
value38 (0.3/µm2) of the
SA channel current was needed in the model. To simulate stretch of the
rat atrium caused by the increase of the intra-atrial pressure from 1
to 3 mm Hg, increase of the current density during
diastole from –0.03 to –0.32 µA/µF was used. In our
experiments we have not measured the sarcomere lengths. However, in the
model (using the definitions of Sachs38 ), this SA
channel current increase corresponds to an increase of sarcomere length
from 1.2 to 1.9 µm, increasing the open probability of the SA
channels from 0.03 to 0.16.
Gulati et al12 showed that the calcium affinity
of the contractile element increased after a length change, whereby
Kd (for Ca2+) of the
TnC decreased 42% when the sarcomere length of skinned cardiac muscle
was increased from 1.7 to 2.2 µm, which almost corresponds to
the overall sarcomere length change during the rising phase of the F-S
relation in rat trabeculae.39
According to these observations, we approximated that the overall
increase of the TnC affinity during the rising phase of the F-S
relation is 50%. Knowing that the rising phase of the F-S relation
in rat left atrium is within intra-atrial pressure between 0 and
10 mm Hg,40 we approximated that the
increase of the intra-atrial pressure in our experiments from 1 to
3 mm Hg produces a 25% decrease of the
Kd in the TnC. This value was used in
modeling the stretch caused by increase of the intra-atrial pressure
from 1 to 3 mm Hg (Figure 1
). The
simulation of the stretch in the model was based on the following
assumptions. First, the relation of the TnC affinity change between 0%
and 50% increase and sarcomere length is linear. Secondly, the SA
channel current density (open probability of the channel) increases
with increased sarcomere length, giving the maximum open probability of
the channel at a sarcomere length that produces maximal developed
tension. Thus, the current density increase from 0% to 100% is
achieved during the rising phase of the F-S relation in the model.
Figure 1 shows the SA current density and TnC affinity change at
different sarcomere lengths in the model. In extrapolating to
pathological stretch levels we used SA channel current density from 0.2
to 1.54 µA/µF, and at the same time the TnC affinity was increased
from 20% to 50%. The assumptions are based on the scarce published
data on the mechanisms, and, if the relationships between the modeled
components of stretch sensitivity are more complex, this would
probably introduce more complex behavior into the model but does not
change the basic results.
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, demonstration of how SA current is connected
to the stretching pressure used in the experiments. 
, values of TnC
affinity used to model the stretch effects. See text for details.
Materials
HEPES was obtained from Sigma; KCl, glucose,
CaCl2, and MgCl2 from
Merck; NaCl and potassium acetate from FF-Chemicals AB; Indo 1-AM,
poloxamer, and probenecid
(p-[dipropylsulfamoyl]-benzoic acid) from Molecular Probes
Europe BV.
Statistical Analysis
Statistical testing was done by the SPSS (SPSS Inc) and
SigmaStat programs (Jandel Scientific). The AP data were tested with
1-way ANOVA. The data from contraction and Indo fluorescence
were tested with a paired t test. In all cases, P
values less than 0.05 were considered statistically significant.
Variances are expressed as ±SEM.
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Results |
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Stretch-Induced Changes in APs
In the first series of experiments we investigated the effects of a stained moderate stretch on APs of rat atrial myocytes. The tissue was stretched by the intra-atrial (diastolic) pressure. Criteria for acceptable experiments were a stable recording with a resting potential (RP) of least –70 mV and an overshoot of the AP of at least 10 mV. The atria were kept at constant pressure (1 or 3 mm Hg) for 5 minutes until recordings were started. At low pressure (1 mm Hg), myocytes with RP of –75.1±0.7 mV generated APs (n=9) with amplitude of 95.8±1.2 mV. When the pressure was 3 mm Hg, AP duration at 90% repolarization level (APD90%) and APD10% decreased (Table
, Figure 2).
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Because the sustained stretch changed the AP shape, we recorded APs
during the pressure manipulations to observe the time course of the
changes. These recordings were found to be extremely difficult,
and only a very few of the attempts were successful. Before each
recording the atrium was kept at steady pressure (1
mm Hg) until acceptable impalement (stable recordings, RPs at
least –70 mV and overshoot at least 10 mV) was achieved. After the
recording had been stable for at least 20 s, pressure
inside the atria was gradually increased from 1 to 3 mm Hg over
10 seconds and then kept constant (3 mm Hg) for at least 1
minute. Figure 3 shows a
representative trace (out of 3 successful experiments,
in which the impalement was still stable after at least 1 minute of
stretch) of the changes that increased stretch (from 1 to 3
mm Hg) causes in the APs of myocytes. Immediately after the increase
of stretch the shape of the APs was changed. The duration decreased at
positive voltages (at 10% repolarization level from 3.75 to 3.25 ms)
and increased at negative membrane potentials (at 90% repolarization
level from 43 to 47 ms). After 60 seconds of onset of stretch, some of
the changes in AP were even more prominent
(APD90%, 52.5 ms). All cells studied were able
to maintain fairly constant RP during pressure manipulations.
Depolarization of the measured potential (during diastole)
was always associated with the changes in the cell-electrode impalement
(resistance and capacitance) caused by the electrode leaving the
cell.
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To see whether the AP lengthening corresponds to the development of the
contraction force after stretch, the APD90% was
plotted together with the change in contraction force. Figure 4 shows that the development of the slow
increase of force (within 1 minute) in rat atrial tissue is accompanied
by the lengthening of the AP (APD90%) of the
individual myocytes with a similar time course.
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Effects of Stretch on Atrial Contraction and Ca2+
Transients
Figure 5 shows the effect of stretch
on the contraction force and the calcium transients in the rat atrium.
When the intra-atrial pressure was increased from 1 to 3 mm Hg,
the contraction force was increased biphasically. The immediate
increase was followed by a secondary, slower increase in force, as can
be seen from the example recording in the Figure 5A. The
Ca2+ transients (as Indo 1 fluorescence
ratio) show that the increase of contraction force is accompanied by an
increase in amplitude of the calcium transients (Figure 5B), without
any change in the diastolic Indo 1 fluorescence
ratio (NS, n=4). The pooled and normalized data in Figure 5C show the
contraction force at different times after onset of stretch. Although
increase of the contraction force is fast (ie, 10 seconds of stretch
more than doubles the force), there is still a significant increase
between 10 seconds and 2 minutes after stretch (P<0.01,
n=4). This slower increase of force is likely to be due to the increase
of Ca2+ transients that were also augmented
during the same time scale (Figure 5D; P<0.01, n=4).
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On the basis of the data presented in the Figure 5C
and 5D, it
is evident that most of the effects of stretch are actually manifested
during the 10 seconds after the onset of stretch. To study the time
courses of these changes, we analyzed the first 10
Ca2+ transients and contraction pulses from each
recording (n=4). It can readily be seen from Figure 6A and 6B that the development of
contraction force is faster than the increase of the calcium transient
amplitude. This indicates that the fast component of the contraction
force development is not due to the increase of the calcium transient
amplitude, but is probably caused by the increased sensitivity of the
contractile element to Ca2+. If this were true,
increased buffering of the Ca2+ by the
contractile element should alter the shape of the
Ca2+ transients. The 1-exponential fits to the
decay of Ca2+ transients revealed that, in fact,
the decay becomes faster after stretch (Figure 6C). However, it has
been shown that the decay of the Ca2+ transient
is accelerated by increased Ca2+ transient
amplitude.41 Because of this, the effect of
Ca2+ transient amplitude had to be estimated in
order to use the decay as an indicator of the
Ca2+ buffering of the cells. As the rate of free
Ca2+ decline increases in a parabolic
manner,41 proportional to
[Ca2+]2 , we calculated
the ratio between the decay and the square of the amplitude of the
Ca2+ transients. In theory, any intervention that
increases buffering of the Ca2+ should reduce the
ratio, but if the changes in the decay are caused by bigger
Ca2+ transients, this ratio is not changed.
Figure 6D shows that the decay of the Ca2+
transient is accelerated during the first 10 seconds after the onset of
the stretch, with no significant change thereafter (NS, n=4),
independently of the amplitude of the Ca2+
transients. This is likely to be caused by the stretch sensitivity of
the contractile element.
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Model Predictions
The main findings of the experimental part of the study can be
summarized as follows. Moderate stretch causes increase in the
amplitude of the Ca2+ transients and decrease of
the time constant of the decay of the transients without a significant
change in the diastolic
[Ca2+]i. These changes
were accompanied by lengthening of the APs of the myocytes and a
biphasic increase of the contraction force of the atrium. In the second
part of the study we tried to reproduce similar changes in the
Ca2+ balance and APs by modulating the TnC
affinity and/or calcium influx mimicking SA channel activation in the
model.
Role of TnC
One candidate for mechanosensation in heart cells is the TnC,
calcium-binding part of the contractile machinery, which is known to be
sensitive to stretch.11 12 We increased the TnC
affinity to Ca2+ by decreasing the dissociation
constant (Kd) of TnC by 25% in our model
(see Materials and Methods). This caused a biphasic behavior of the
Ca2+ transients. First transients were smaller,
but amplitude stabilized near the control value (Figure 7A) within 1 minute. Even when the
systolic [Ca2+]i
had returned to the control value, the decay of the
Ca2+ transient was faster (time constant
decreased from 118 to 105 ms; Figure 7C). When control APs were
compared with steady-state APs after a simulated stretch, only modest
changes were observed, the most prominent change being the small
increase of the APD90% (+2.4 ms; Figure 7B). The
increased Ca2+ affinity of the TnC modulated
slightly the Ca2+ dependent currents, the peak
value of the L-type Ca2+ current (Figure 7D) was
increased from –10.3 to –10.5 µA/µF, and the inward current of
the Na+/Ca2+ exchanger
(Figure 7E) was decreased from –1.09 to –1.05 µA/µF. This result
indicates that the TnC affinity change alone cannot produce similar
changes as observed in experiments, since the TnC affinity change could
not augment the Ca2+ transients or lengthen the
APs.
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Role of SA Channels
When stretch of the myocyte was simulated by applying the SA
channel conductance into the cell membrane in our model, the amplitude
of the calcium transients were gradually increased (Figure 8A). The activation of a cation-selective
SA channel increased the systolic
[Ca2+] gradually from 0.88 to 1.04
µmol/L within 1 minute (+15.4%). The decay of the calcium transients
decreased (as measured by the time constant of the 1-exponential fits)
from 115 to 114 ms (Figure 8C). Only a small change in the
diastolic [Ca2+] was observed
(Figure 8A). Greater Ca2+ transients increased
the late duration of the APs (Figure 8B), the time course of the AP
lengthening being related to the increase of the amplitude of the
calcium transients. The APD90% increased from
52.2 to 61.4 ms within 1 minute after the increased SA channel current.
This was probably due to the increase of the inward current carried by
Na+/Ca2+ exchanger (Figure 8E), which was increased from –1.09 to –1.16 µA/µF. Bigger
Ca2+ transients decreased the peak value of the
L-type Ca2+ current (by increasing inactivation)
from –10.3 to –10.1 µA/µF (Figure 8D) and made the decay of the
current a little faster.
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Combination of SA Channel and TnC Effects
Neither of the 2 candidates of the mechanosensation (SA channels
and TnC) could faithfully produce similar changes in the model cell as
seen in experiments. The TnC affinity change could not produce the
gradual increase of the amplitude of the Ca2+
transients or increase of the APD90%. The
activation of the SA channels produced both effects, but not the
prominent change in the decay of the transients. Furthermore, the SA
channel activation cannot explain the fast increase of the contraction
force seen in experiments, since it caused a slow and gradual
augmentation of Ca2+ transients during stretch.
To better fit the model predictions to experimental findings, we
combined these 2 mechanisms in the next round of modeling (Figure 9). When the stretch was simulated by
increasing the TnC affinity together with the activation of the SA
current, the Ca2+ transient amplitude gradually
increased by 20.2% from 0.88 to 1.09 µmol/L (Figure 9A and 9C).
The increase of the amplitude of the Ca2+
transients was accompanied by the decrease of the time constant of the
decay of the transients from 119 to 96 ms (Figure 9C). Increased
calcium mobilization during the AP caused a simultaneous
lengthening of the AP (Figure 9B). The APD90%
increased from 52.2 to 63.8 ms within 1 minute, and time course of the
AP lengthening was related to the increase of the calcium transients.
Since the peak value and the decay of the L-type
Ca2+ current was unaffected (Figure 9D), we may
conclude that the increase of the inward current carried by
Na+/Ca2+ exchanger from
–1.09 to –1.19 µA/µF (Figure 9E) increased the late duration of
the APs.
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Role of SR
If the Ca2+ release kinetics is not altered,
the amount of Ca2+ in SR contributes prominently
to the released Ca2+ during
excitation.42 Figure 10 shows how different strategies of
the stretch simulation (TnC affinity, SA channels, or both) influence
the amount of Ca2+ in the SR. When stretch was
simulated solely by increasing the TnC affinity by 25% (Figure 10A),
the SR Ca2+ content was affected only slightly.
The diastolic Ca2+ in the SR
increased from 1.65 to 1.69 mmol/L within 1 minute. Activation of
SA channels without any change in TnC affinity (Figure 10B) increased
the diastolic SR Ca2+ content from
1.65 to 1.79 mmol/L. The effects of TnC affinity change and
activation of SA channels were additive (as shown in Figure 10C); SR
calcium content increased from 1.65 to 1.88 mmol/L. This modeling
result indicates that augmentation of the Ca2+
transient in the model during simulated stretch is due to the increased
amount of Ca2+ in the SR. Furthermore, SA channel
activation does not cause direct increase of the
Ca2+ transient, but the effect is mediated by the
Ca2+ release from SR.
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Electrical Changes Caused by the Simulation of the Stretch
Since the combination of SA channel activation and the increased
affinity of TnC simulated fairly well the effects of stretch observed
in the experiments, we investigated whether this approach causes
simultaneous changes in Ca2+
transients and APs and whether the time course of this change is
similar to those in the experiments. Figure 11 shows the AP train (A), calcium
transients (B), and APD90% (C) when the stretch
was simulated by increasing the SA channel current and calcium affinity
of the TnC. The augmentation of the Ca2+
transient lengthened the APs by 10 ms within 1 minute, as indicated by
the APD90%, in line with our experimental
findings (Figures 2 through 4).
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Pathological Effects of Stretch
In addition to the physiological effects, the
stretch of the cardiac tissue also causes pathological phenomena. It is
known that intensive stretch can trigger arrhythmias caused by
early or delayed afterdepolarizations of the membrane
potential.40 The mechanism suggested to be
responsible for these arrhythmias is the calcium overload
caused by stretch.43 We investigated whether the
same mechanisms that cause the physiological
effects of stretch could be responsible for the pathological
stretch-induced changes in the function of the heart. To do this, we
simulated the effects of incremental stretch on the function of the
model cell. It is natural to assume that if a cationic current through
SA channels, with reversal potential more positive than the RP, is
activated, it should cause a depolarization of the membrane
potential. Because SA channels also pass Ca2+
ions,19 the depolarization would be followed by
an increase of the
[Ca2+]i. Both of these
effects were seen when SA current density was increased gradually from
0.1 to 1.6 µA/µF (Figure 12A and 12B; see also Materials and Methods for details), at the same time that
the TnC affinity was increased from 20% to 50%, respectively. The RP
depolarized up to –68 mV (from –80.5 mV) at the same time when
diastolic
[Ca2+]i was increased
from 0.1 to 0.16 µmol/L.
|
Figure 13 shows that the model can
produce an arrhythmogenic effect when the SA channel current density is
8 times as high as needed in the model to produce the
physiological effects seen in our experiments.
Similarly, as in other simulations, augmentation of the
Ca2+ transients (Figure 13B) modulated the APs
(Figure 13A) through increased
Na+/Ca2+ current (Figure 13D). When 80% of the channels present in our model were open, the
augmented Ca2+ transient reduced the L-type
Ca2+ current (Figure 13C) from –10.4 to –8.2
µA/µF. Because the
Na+/Ca2+-exchanger inward
current was increased from –1.2 to –2.6 µA/µF, it generated an
afterpotential that resembles the early afterdepolarizations of the
atrial myocytes.44 These results show that the
same mechanisms that mimic the physiological
effects of stretch can also produce the arrhythmogenic changes in the
function of myocytes.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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The present study demonstrates that stretch, in this case diastolic pressure, has a wide variety of actions in isolated rat atrium. The experimental part of the study shows that contractile function has a biphasic response to stretch, associated with augmentation of the Ca2+ transients, without a significant change in the diastolic [Ca2+]i. Diastolic calcium concentration remains fairly constant because the Ca2+ buffering power of the cell is increased, indicated by the faster decay of the Ca2+ transients during stretch. APs of the myocytes reflect the changes in Ca2+ transients and contraction force. The most prominent change in APs during stretch was the increase of the late duration of the APs. The modeling part of the study demonstrates that both affinity change of the TnC and activation of the SA channel current are needed to reproduce these effects seen in experiments. The model also suggests that SA channels do not directly modulate the function of the myocytes but instead increase the SR calcium stores, causing greater release of Ca2+ during systole. A bigger Ca2+ transient modulates the membrane voltage during APs through increased Na+/Ca2+-exchanger inward current. The same mechanisms can also induce arrhythmogenic afterpotentials, a rise in diastolic [Ca2+]i, and depolarization of the RP when high enough amounts of SA channels are activated in the model.
Properties of the Model
A mathematical model based on the Luo-Rudy
model30 31 32 was used to support the experimental
study of the stretch-dependent mechanisms. The model could reproduce
the phenomena as observed in the experiments. First, it has to be
clarified to what extent the model reflects the function of the cardiac
myocytes. It is clear that a model cannot posses all the components in
the real cells, since many of them are not known in detail
presently. Despite the scarcity of facts, we have tried to obtain
as holistic point of view as possible in the development of the model.
Therefore, the validity of the model could be judged by how well it can
reproduce documented physiological behavior. Our
model can produce fairly similar APs as recorded from rat atrial
myocytes, which are also modulated by calcium transients in the model.
Because we wanted to study the Ca2+ balance of
the myocytes during stretch, the model parameters relevant
to the Ca2+ handling are essential. In modeling
the calcium-induced calcium release (CICR), it has usually been assumed
that there is only 1 cytosolic pool of calcium, the concentration of
which controls the release of calcium from the SR. To this pool,
calcium enters from both the SR and sarcolemmal calcium
current.45 The CICR model we used is a common
pool model with 2 different release sites. The release from the first
compartment is controlled by the L-type current, whereas the release
from the second compartment is controlled by the release from the first
compartment (see Materials and Methods and Appendix for details). In
this respect, our model differs from all the other models used
previously to study the stretch-dependent changes in the cardiac
myocytes. The well-documented role of TnC in the stretch-dependent
changes of the heart muscle11 12 has been
previously modeled to evaluate TnC-induced changes during stretch by
several authors.13 14 15 46 The works by Landesberg
and Sideman,13 14
Landesberg,15 and Katsnelson and
Markhasin46 have thoroughly investigated, by
modeling, the role and function of the length-dependent changes in the
contractile apparatus, including increase of calcium
affinity and reduction of the double thin-filament overlap. Their
results show similar changes in the
[Ca2+]i, as in our work.
In contrast to those works, we wanted to investigate the
[Ca2+]i in terms of
time-dependent changes in the function of the myocytes, including the
APs, Ca2+ transients, and membrane currents.
Although in the modeling we had to approximate the TnC affinity change
during stretch, our model produced changes very similar to those
observed in the experiments. The SA channel formalism used in our model
is similar to what has been used before.38
[Ca2+]i During Stretch
A considerable agreement exists that mechanical stimulation
can influence the
[Ca2+]i of the myocytes.
The length increase produces a gradual increase in
Ca2+ transient amplitude in isolated cardiac
preparations10 and also in isolated rat cardiac
myocytes.47 The results concerning the change of
the diastolic
[Ca2+]i are somewhat
controversial. Some studies show a clear increase in
diastolic
[Ca2+]i,48 49 50
but others indicate that cardiac myocytes can maintain constant
diastolic calcium concentration during
stretch.47 Concerning systolic
[Ca2+], Allen et al2
suggested that augmentation of the Ca2+
transients during stretch might be due to a change in
diastolic
[Ca2+]i. Other studies
indicate that Ca2+ transients are augmented
without a change in diastolic
[Ca2+]i in isolated rat
myocytes.47 This was also the finding in isolated
rat atria in the present study. On the other hand, the development
of the increase of the amplitude of the Ca2+
transients over a period of several minutes10
indicates that even small changes in diastolic calcium
concentration might contribute to these changes. The
fluorescent Ca2+ indicators have
relatively high Kd values when compared
with the low [Ca2+]i
during diastole. This suggests that small changes in
diastolic
[Ca2+]i are hard to
detect with these indicators. In general, a prominent rise in
diastolic calcium concentration in heart myocytes indicates
that Ca2+ buffers are unable to remove or bind
the calcium. This is known to happen in several pathological situations
such as ischemia,51 in which the
Ca2+ buffers of the cell are incapacitated.
Usually this leads to a Ca2+ overload, causing
abnormal electrical and contractile behavior of the tissue. It is clear
that stretch can be severe enough to be pathological and cause the
calcium overload. However, a rise in diastolic
Ca2+ concentration may lead also to an increase
in resting tension of the tissue that may reduce stretch of the cell
membrane. The present study shows, experimentally, that a small
amount of stretch increases the amplitude of the
Ca2+ transients without any detectable change in
diastolic calcium concentration. Our model simulations
support the idea, since they can reproduce significant increase
in Ca2+ transients without prominent change in
diastolic
[Ca2+]i.
Role of TnC
The calcium-binding part of the contractile machinery, the
TnC,52 is known to be sensitive to muscle
length.11 12 In addition to biochemical studies,
many physiologically oriented reports suggest
the prominent role of TnC in the length-dependent activation of the
cardiac tissue of different species.4 5 10 53 54 55
If Ca2+ sensitivity of TnC increases with
stretch, this might influence the function of the myocytes in several
ways, as follows. First, fast increase of the affinity would increase
the contraction force and decrease the systolic
[Ca2+]i. Secondly, the
decay of the Ca2+ transients during stretch would
be faster than what would be expected on the basis of enzyme kinetics
alone, as previously demonstrated,56 because the
calcium binding "eats into" the calcium transient. Thirdly, the
affinity change would favor the formation of the
TnC-Ca2+ complex, leading to a slower off-rate of
the complex, and so the time course of the contraction would be
prolonged. Our experimental data demonstrate that stretch decreases the
decay of the calcium transients significantly, and the model simulation
shows that TnC affinity increase, alone or in combination with SA
channel activation, leads to similar changes (Figures 7 and 9). The
decline of the Ca2+ transients immediately after
the onset of stretch was not seen in the experiments, suggesting that a
rise in systolic
[Ca2+]i and increased TnC
affinity are smoothly graded. However, in the model, a transient
decrease of the amplitude of the Ca2+ transients
was produced when the TnC affinity was increased (Figure 7). According
to our results, the TnC sensitivity increase contributes to the
stretch-induced changes by providing an additional buffering of the
Ca2+ ions during stretch. Increased buffering by
TnC leads to an increase of the contraction force during systole, most
prominently manifested during the fast increase in contraction force
following stretch. During diastole this mechanism would
balance the [Ca2+]i or
even slightly lower the diastolic
[Ca2+]i.
Role of SA Channels
Stretch-induced changes in heart function might be possible to
explain by SA ion channels located in the plasmalemma of
cardiac myocytes. These channels have been described, and their open
probability has been found to depend on mechanical stress of the
membrane.57 After the initial discovery of SA
channels,16 several types of SA channels have
been documented in isolated adult
cardiocytes17 18 21 and in cultured
neonatal cardiocytes.19 20 22 The
majority of SA channels seems to be of a type with considerable
permeability to both monovalent and divalent
cations.58 In isolated myocytes mechanical
loading increases intracellular Ca2+
concentration,3 and interestingly, this increase
can be inhibited by gadolinium
(Gd3+),59 a blocker of SA
channels.23 Our model reproduced a gradual
increase of the calcium transients only when an additional calcium
influx through plasma membrane was activated. The SA channel we
used in our model has a permeability ratio of 1:1:1 for
Na+:Ca2+:K+,
similar to what has been reported earlier from rat atrial
myocytes.19 Activation of the SA channel leads to
an increase in [Ca2+]i by
direct Ca2+ influx. Since the SA channel is
permeable to Na+, increased sodium leads to the
activation of the Na+/Ca2+
exchanger and to an additional accumulation of
Ca2+ ions into the cell. The increased
[Ca2+]i is pumped to the
SR by the Ca2+ pump.60
Increased amount of calcium in SR causes a greater release of
Ca2+ during systole. In this scheme, potassium
ions may serve as a countercurrent mechanism that stabilizes the
membrane potential during diastole. Our study does not rule
out the possibility that the additional calcium flux comes via channels
or exchangers other than the SA channels. Since the stretch-dependent
increase of the contraction force in the heart muscle
preparations9 and even isolated
cells61 has 2 distinct components (fast part and
slow part), one has to consider the
[Ca2+]i changes as a
2-step process. If the TnC affinity change and the overlap of the actin
and myosin filaments are responsible for the fast part as previously
suggested, the additional activation of Ca2+ flux
would contribute to the slow part by modulating the
[Ca2+]i of the cells. In
fact, as shown in Figure 6, the increase of the contraction force after
stretch seems to consist of the 2 components, increased TnC affinity
and increase of the Ca2+ transients, of which the
latter is much slower than the former.
Role of SR
CICR in cardiac myocytes can be modulated by the trigger, the
L-type current through membrane, or by the release of the
Ca2+ from SR. On the basis of our results, the
amount of the trigger current is not significantly changed by stretch.
This leads to the conclusion that the Ca2+
transient augmentation is mediated by the release of the
Ca2+ from the SR. It has been reported that SR
calcium content is increased slowly after a step increase of cardiac
muscle length.62 Our model produced an increase
in SR content concomitantly with the augmentation of the
Ca2+ transient amplitude when SA channels were
introduced to the model cell (Figure 10). However, SR calcium content
increased only 12.2%, whereas amplitude of calcium transients
increased 20.2%, indicating a nonlinear correlation between SR calcium
content and the amount of calcium released during systole. The reason
for this is probably the positive feedback in
CICR,63 caused by the fact that with a higher
amount of calcium in SR a bigger proportion is released during
systole.64 On the premise that our model, which
has simpler Ca2+ dynamics than the real cells,
can reproduce this effect, we can assume that this positive feedback is
a fundamental feature of the CICR. On the basis of our experimental and
modeling data, we can conclude that during the normal stretch-dependent
activation in rat atrium, the SR has a crucial role in augmentation of
the Ca2+ transients.
Electrical Activity of the Myocyte During Stretch
Since calcium transient modulates the AP65
and vice versa,66 the changes in
[Ca2+]i during stretch
should change the shape of the APs of the myocytes. It is known that
inotropic interventions, such as stretch, increase the late duration of
the APs67 in cardiac myocytes with a short
plateau.68 69 This happens apparently via the
increased
Na+/Ca2+-exchanger inward
current that is boosted by augmentation of the calcium
transients.65 In rat myocytes, the
Na+/Ca2+-exchanger current
is proportional to
[Ca2+]i.70
The present study demonstrates that stretch influences the APs of
the rat atrial myocytes. The APD90% was
lengthened during the slow phase of the contraction development. The
model simulated similar changes in APs when the simulation included SA
channel activation. The mechanism suggested by the modeling was the
increased
Na+/Ca2+-exchanger inward
current generated by bigger Ca2+
transients.71 The data support the idea that SA
channels do not, during moderate stretch, directly modulate APs, but
instead, the effects are mediated by the SR through the increased
Ca2+ release during systole. Many reports
indicate that stretch causes a depolarization of the RP of cardiac
myocyte.3 7 72 In the present study the RP of
the myocytes was not significantly altered by moderate stretch, neither
in experiments nor in the model. The reason for this was that only a
very small SA current (depolarizing current) is needed to reproduce the
normal physiological time-dependent changes in rat
atrial function.
Pathological Changes Caused by Stretch
The effects of stretch on the function of the heart muscle have
previously been studied on the premise that stretch can cause many
pathological phenomena.73 These effects include
changes in conduction,74
excitability,73 75 and generation of
afterpotentials.40 We show that the same
mechanism that produces typical Frank-Starling responses during
moderate stretch in the rat atrium can also induce pathological changes
in cardiac myocytes when they are subjected to a more intense stretch.
These effects were manifested in our model as depolarization of the RP
and increase of the diastolic
[Ca2+]i. During the
stretch-induced Ca2+ overload, the
Ca2+-induced inactivation of the L-type
Ca2+ current opens a time window in which the
increased Na+/Ca2+ current
can trigger early afterpotentials.
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Appendix 1 |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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The Mathematical Model of the Rat Atrial Myocyte
The mathematical model we used is a further development of the one by Luo and Rudy.30 31 32 Like their model, it includes the ionic currents responsible for generation of the AP (Na+, K+, and Ca2+) and the Na+/Ca2+-exchanger current. It also includes the Ca2+ release mechanisms and intracellular buffers. The model has been built with MATLAB software in a UNIX workstation and uses the optimized integration algorithms therein to solve numerically the resulting multiple differential equations. The integration algorithm used to solve the differential equations was based on hybrid methods.76 77 An adaptive time step was used to shorten calculation times from 500 to 10 µs. Before any interventions or observations, the model was allowed to run until a steady state was reached.
A full description of the model is beyond the scope of this paper, but certain crucial modifications as compared with the Luo-Rudy model have to be recapitulated. The cell geometry has been changed to correspond to that of the rat atrial myocytes, including cell size and the size of the SR compartment. Ionic concentrations have been modified to be the same as those used in our experimental work. Concerning the ionic currents, the only current that has been fundamentally changed is the K+ current, which has been modeled with 2 time- and voltage-dependent currents (based on fast and slow inactivating channels) and 1 time-independent (noninactivating) current. The Ca2+ balance has been modeled using the knowledge that in rat about 90% of the calcium transient comes from the intracellular stores (SR), and only about 10% comes directly via L-type Ca2+ channels. The calcium release from the stores also includes 2 phases, the first directly coupled to the L-type Ca2+ current (release from the junctional SR) and the second triggered by this initial release from neighboring (nonjunctional or network) SR.
The Depolarization-Activated Outward Current
The depolarization-activated outward current
(Iout) was the main repolarization-inducing
current. The subtypes of the outward current have been described in
detail previously.78 In our model, the
Iout is modeled with 3 components, the
rapidly inactivating
(Ik,fast), slowly inactivating
(Ik,slow), and nonactivating
(Ik,ss) K+
current. We adapted the values of forward and reverse activation rate
constants given by Boyle and Nerbonne78 and
VanWagoner et al79 with the MATHCAD modeling tool
to get the activation and inactivation into the format used in
H-H–type formulae. The Iout is given
according to the H-H model, as follows:
 | (2) |
 |
 |
Parameter Details
Cell geometry (largely after Schaper et
al80 ):
Cell volume: Vcell=12x10–6 µL
SR volume: Vsr=Vcellx0.1
JSR volume: Vjsr=Vsrx0.02
NSR volume: Vnsr=Vsrx0.98
Capacitive membrane area: Acap=0.7x10–4 cm2 Extracellular ionic concentrations used:
[K]o=5.9 mmol/L
[Na]o=131 mmol/L
[Ca]o=2.5 mmol/L [Ca2+]i:
Calcium release from second release compartment:
on=40 ms; off=10
ms
The trigger threshold of calcium release from second compartment is half of the calcium release from first release compartment
The time delay of second calcium release compartment is 5 ms
First calcium release compartment: maximum conductance, Grel=6 ms–1
Second calcium release compartment: maximum conductance, Grel=0.046 ms–1 Ca2+ pump in SR: Km.up=0.46 µmol/L L-type Ca2+ channel:
Pca=1.62x10–4 cm/s
Km,ca=0.27 µmol/L Voltage-dependent outward current Iout:
Maximum conductance:
GK=0.154
(Ko/5.4)
Voltage-independent K+ current:
Maximum conductance:
GK=0.382(Ko/5.4)
Initial values:
Ki=140 mmol/L; Nai=131.4 mmol/L; Cai=0.07 µmol/L
Cajsr=1.73 mmol/L; Cansr=1.73 mmol/L; Vo=-82.1 mV Pacing stimulus:
Intensity=-80 µA/µF
Duration=0.5 ms
Received June 8, 1998; accepted September 16, 1998.
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