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Biophys J, July 2000, p. 94-115, Vol. 79, No. 1
Department of Kinesiology and Applied Physiology, The University of Colorado Cardiovascular Institute (CUCVI), University of Colorado, Boulder, Colorado 80309-0354 USA
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
SUMMARY
APPENDIX A
APPENDIX B
REFERENCES
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Cardiac contraction and relaxation dynamics result from a
set of simultaneously interacting Ca2+ regulatory
mechanisms. In this study, cardiocyte Ca2+ dynamics were
modeled using a set of six differential equations that were based on
theories, equations, and parameters described in previous studies.
Among the unique features of the model was the inclusion of
bidirectional modulatory interplay between the sarcoplasmic reticular
Ca2+ release channel (SRRC) and calsequestrin (CSQ) in the
SR lumen, where CSQ acted as a dynamic rather than simple
Ca2+ buffer, and acted as a Ca2+ sensor in the
SR lumen as well. The inclusion of this control mechanism was central
in overcoming a number of assumptions that would otherwise have to be
made about SRRC kinetics, SR Ca2+ release rates, and SR
Ca2+ release termination when the SR lumen is assumed to
act as a simple, buffered Ca2+ sink. The model was
sufficient to reproduce a graded Ca2+-induced
Ca2+ release (CICR) response, CICR with high gain, and a
system with reasonable stability. As constructed, the model
successfully replicated the results of several previously published
experiments that dealt with the Ca2+ dependence of the SRRC
(Fabiato, 1985
, J. Gen. Physiol.
85:247-289), the refractoriness of the SRRC (Cheng et al.,
1996, Am. J. Physiol. 270:C148-C159), the
SR Ca2+ load dependence of SR Ca2+ release
(Bassani et al., 1995, Am. J. Physiol. 268:C1313-C1329; Gilchrist et al., 1992,
J. Biol. Chem. 267:20850-20856), SR Ca2+
leak (Wier et al., 1994, J. Physiol.
(Lond.). 474:463-471; Bassani and Bers, 1995,
Biophys. J. 68:2015-2022), SR Ca2+ load
regulation by leak and uptake (Ginsburg et al., 1998,
J. Gen. Physiol. 111:491-504), the effect of
Ca2+ trigger duration on SR Ca2+ release
(Bers et al., 1990, Am. J. Physiol.
258:C944-C954), the apparent relationship that exists between
sarcoplasmic and sarcoplasmic reticular calcium concentrations
(Shannon and Bers, 1997, Biophys. J. 73:1524-1531), and a variety of contraction frequency-dependent alterations in sarcoplasmic [Ca2+] dynamics that are
normally observed in the laboratory, including rest potentiation, a
negative frequency-[Ca2+] relationship, and extrasystolic
potentiation. Furthermore, under the condition of a simulated
Ca2+ overload, an alternans-like state was produced. In
summary, the current model of cardiocyte Ca2+ dynamics
provides an integrated theoretical framework of fundamental cellular
Ca2+ regulatory processes that is sufficient to predict a
broad array of observable experimental outcomes.
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
SUMMARY
APPENDIX A
APPENDIX B
REFERENCES
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The regulation of cytosolic Ca2+
concentration, [Ca2+]c, in cardiac myocytes
has been recognized to be the predominant determinant of cardiac
contraction and relaxation dynamics (Bers, 1993). The experimental identification and characterization of the many
[Ca2+]c regulatory mechanisms in cardiac
myocytes have been paramount in classifying the relative importance of
the calcium-dependent factors that influence cardiac function.
Developing and testing hypotheses regarding the complex and
interdependent relationships of these [Ca2+]c
regulatory mechanisms has been the principal focus of mathematical modeling in this field. Various models have been developed to describe
[Ca2+]c regulation in cardiac myocytes
(Bers and Berlin, 1995; Earm and Noble,
1989; Hilgemann and Noble, 1987; Harrison
et al., 1992; Langer and Peskoff, 1996;
Peskoff et al., 1992; Smith et al., 1998;
Tang and Othmer, 1994; Stern, 1992;
Wong et al., 1992). Of particular importance have been
those models that have attempted to thoroughly describe the temporal
qualities of [Ca2+]c based on characteristics
of Ca2+ accumulation and release from intracellular
compartments and buffers. These types of models have evolved to the
point where they are sufficient to make reasonable predictions of
intracellular [Ca2+] dynamics under very simple simulated
experimental conditions. Collectively, these types of theoretical
models have provided invaluable insights into the concerted mechanisms
that regulate intracellular Ca2+ dynamics in the heart. In
general, however, virtually none of these models have been shown to be
sufficient to accommodate predictions of intracellular Ca2+
dynamics under multiple and more complex experimental conditions. More
recently, much of the modeling in this area has attempted to describe
hypothetical cellular mechanisms that sufficiently represent
fundamental properties of excitation-contraction coupling (Stern, 1992; Rice et al., 1999;
Jafri et al., 1998), which would include a
Ca2+-induced Ca2+ release (CICR) mechanism that
demonstrates graded responsiveness to a sarcolemmal Ca2+
trigger, high gain, and reasonable stability.
In this study, we propose a novel model of sarcoreticular
Ca2+ regulation where control of CICR exhibits the
fundamental characteristics of graded sarcoplasmic reticulum (SR)
Ca2+ release, high gain, and stability and is dependent
upon the regulation of SR Ca2+ release channels (SRRCs) by
[Ca2+] changes in a confined subspace ("fuzzy space";
Lederer et al., 1990) and by Ca2+ sensing
elements in the SR lumen. Overall, the purpose of this study was to
develop a macroscopic model of cardiocyte sarcoreticular Ca2+ regulation that 1) is based on previously described
control theories and parameter values; 2) possesses a quiescent
steady-state (starting point) condition that was self-defined by the
same model control elements that governed dynamic model responses; 3)
is sufficient to predict expected outcomes from multiple and relatively
complex experimental perturbations; 4) is designed to provide
predictions of experimentally observable whole-cell
[Ca2+]c responses; and 5) could be used as a
framework around which more "microscopic" theories of
Ca2+ regulation could be included.
As constructed, the model was sufficient to replicate the results of
several simple but very different types of experiments that appear in
the literature (Bassani and Bers, 1995; Bassani et al., 1995; Bers et al., 1990; Cheng et
al., 1996; Fabiato, 1985; Gilchrist et
al., 1992; Ginsburg et al., 1998; Shannon
and Bers, 1997; Wier et al., 1994), as well as
predictions of the sarcoplasmic [Ca2+] transient that
would be expected to occur in response to alterations in myocyte pacing
frequency, the delivery of extrasystolic intervals at a variety of
background pacing frequencies, and cellular Ca2+ overload
(alternans). Critical examination of the results of the current study
should provide insights into theoretical mechanisms of control of
sarcoreticular Ca2+ cycling in the heart.
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MATERIALS AND METHODS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
SUMMARY
APPENDIX A
APPENDIX B
REFERENCES
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Model overview
A simple schematic of the key elements of cardiocyte
Ca2+ control represented in our model is depicted in Fig.
1. Briefly, our model was constructed to
account for Ca2+ movement between an extracellular
compartment and a very small, restricted, or fuzzy space
(Lederer et al., 1990) that exists between the t-tubular
membrane and the terminal cisternal face of the sarcoplasmic reticulum.
Calcium buffering specific to the "fuzzy space" is also included.
CICR from the SR is mediated by Ca2+ movement in the fuzzy
space and the interaction of this Ca2+ with specific
binding sites on the SRRCs. In this regard, it is relevant to note that
CICR control characteristics at the level of a single fuzzy space were
modeled and then subjected to composite averaging to yield a simulation
of whole-cell Ca2+ dynamics. One of the novel features of
our model is that it contains regulatory interactions that exist
between SRRCs, SR luminal [Ca2+], and the predominant
luminal SR buffer calsequestrin (CSQ). These types of interactions are
implied by considerable experimental evidence (discussed below and in
Appendix B) and were included to account for the known effects of SR
Ca2+ load on SR Ca2+ release (Bassani et
al., 1995; Donoso et al., 1995; Ikemoto
et al., 1989, 1991; Kawasaki and Kasai,
1994; Janczewski et al., 1995; Lukyanenko
et al., 1996; Ohkura et al., 1995; Sham
et al., 1995; Shannon and Bers, 1997;
Zhang et al., 1997). The model includes a diffusional
link between Ca2+ in the fuzzy space and the cytosol. The
cytosolic compartment contains endogenous Ca2+ buffers and
could accommodate exogenous Ca2+ buffering by the
Ca2+ indicators (fura-2, fluo-3, etc). The exogenous buffer
was included to produce model predictions of the types of cytosolic
[Ca2+] characteristics that would be observed
experimentally and to render the model more amenable to laboratory
test.
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Regulation of SRRCs by Ca2+ in the fuzzy space
In our model, each contraction cycle was initiated by a brief influx of Ca2+ into the fuzzy space per the principles previously described (Tang and Othmer, 1994;
Langer and Peskoff, 1996). This general method of
initiating the model is described in Appendix A and is critically
evaluated in the Discussion. Regulation of CICR through SRRCs was
assumed to be dependent upon the occupancy of "fast" and "slow"
Ca2+ binding sites on the SRRCs (Fabiato,
1985; Coronado et al., 1994), and a high degree
of binding cooperativity between multiple fast sites was assumed
(Fabiato, 1985; Sham et al., 1995). At
the single SRRC level, four functional states were assumed and are
described in Table 1.
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Interactions between the SRRC and the SR lumen
A unique and functionally important feature of the current model is the inclusion of interactions between the SRRC and the Ca2+ load of the SR lumen. In our model, bidirectional interactions between the SRRC and Ca2+ in the SR lumen are assumed to be mediated via CSQ. The rationale for proposing this type of interaction derives from a considerable body of experimental evidence from studies on striated muscle preparations. First, in both cardiac and skeletal muscle, CSQ is known to be localized in the terminal cisternal portion of the SR and appears to be attached to the junctional face membrane in close proximity to the SRRCs (Zhang et al., 1997; Brandt et al., 1990). Furthermore,
there is now strong evidence that cardiac CSQ and the SRRCs are coupled
by junctin and triadin (Zhang et al., 1997). This type
of association is consistent with the idea that CSQ and SRRCs are
functionally linked. Second, the idea that the probability of SRRC
opening can be affected by and be proportional to SR Ca2+
load is supported by the work of Gyorke and Gyorke
(1998). This type of functional linkage has been observed in
both cardiac and skeletal muscle SR preparations (Gyorke and
Gyorke, 1998; Ikemoto et al., 1989;
Donoso et al., 1995; Lukyanenko et al.,
1996; Sitsapesan and Williams, 1997), and in
more detailed experiments (Ikemoto et al., 1989) there
has been demonstrated a CSQ dependence for this interaction between
luminal SR [Ca2+] and SRRC opening probability. Third,
the concept that the Ca2+ buffering properties of CSQ might
be influenced by the SRRC is consistent with the work of Ikemoto
et al. (1991) and Gilchrist et al. (1992), where
it was proposed that the opening of a threshold fraction of SRRCs is
sufficient to elicit a reduction in CSQ Ca2+ affinity. This
would have the effect of rapidly increasing the free
[Ca2+] gradient across the junctional SR membrane and
increasing the amount of luminal Ca2+ available for release
into the fuzzy space. In our model, the Ca2+ affinity state
of CSQ is linked to the binding of Ca2+ to the SRRC fast
site, and the Ca2+ affinity of the SRRC slow site is linked
to the binding of Ca2+ to CSQ. A detailed description of
this element of regulation can be found in Appendix B. This mechanism
is intuitively attractive because it lends a dynamic quality to a very
large Ca2+ buffering "sink" that has been assumed by
others to be governed by simple mass action.
Sarcoreticular Ca2+ cycling
The current model provides for Ca2+ diffusion from the fuzzy space to the sarcoplasm, taking into account Ca2+ buffers specific to each compartment. The predominant mechanism of Ca2+ removal from the sarcoplasm was assumed to be Ca2+ resequestration via the SR Ca2+-ATPase. Aspects of this portion of the model that are worthy of note are the inclusion of a specific thermodynamic resequestration limit that accounts for the free [Ca2+] gradient between the SR lumen and the sarcoplasm (Shannon and Bers, 1997), CSQ
as a luminal SR Ca2+ buffer that is subject to modulation
by luminal and extraluminal influences (Gilchrist et al.,
1992; Ikemoto et al., 1991), and an SR
Ca2+ pump that operates via second-order reversible
Michaelis-Menten kinetics. Ca2+ clearance from the
sarcoplasm via cellular extrusion mechanisms, primarily via
sodium-calcium exchange, was represented in a generalized form
according to principles previously described by others
(Philipson and Nishimoto, 1981; Reeves and Sutko,
1983; Tibbits et al., 1989).
Modeling methods
The mathematical representation of the Ca2+
regulatory mechanisms of a rat cardiac myocyte included a set of six
differential equations with 33 parameter constants. The development of
the differential equations is described in Appendix A. The input
parameters are listed in Table 2. The
derivation of the parameters from literature sources is explained in
Appendix B. The set of differential equations was solved using a
fourth-order Runge-Kutta numerical integration method. The required set
of initial values was determined by solving for the model's
self-defined steady state, analogous to quiescence. The quiescent state
exhibited stable qualities consistent with those typically observed in
isolated rat cardiac myocytes. For instance, it has been shown that the SR Ca2+ content does not undergo rest decay even after 5 min of quiescence (Bassani and Bers, 1995) and that
resting [Ca2+]c is quite stable (Satoh
et al., 1997). For quiescence in the model, the differential
equations were set to equal zero, the initial value of
[Ca2+]c was set to a baseline level (see
Table 2 and Appendix B), and the set of equations and unknowns was
solved using Newton's method for nonlinear algebraic equations, which
generated the set of initial values used to solve the model. This
method is important because the resting values of the processes and
states (such as SR Ca2+ load, SRRC states, and membrane
leaks) were not set, but rather were determined by the interactions of
the modeled relationships.
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To test the performance of the model, a series of experiments of
varying complexity were simulated using two different approaches. First
the model was tested in its ability to recapitulate the results of
several previously published experiments (Bassani and Bers,
1995; Bassani et al., 1995; Bers et al.,
1990; Cheng et al., 1996; Fabiato,
1985; Gilchrist et al., 1992; Ginsburg et al., 1998; Shannon and Bers, 1997; Wier
et al., 1994). In these simulations, model parameters were
varied to simulate the actual experimental interventions while the
other model parameters were held constant. Second, in a subsequent set
of simulations, model parameters were left unaltered and allowed to
respond to a variety of contraction frequency manipulations. This
provided an opportunity to determine if the model could reasonably
simulate rest potentiation, frequency-dependent alterations in
[Ca2+]c, and extrasystolic potentiation.
Experimental methods: [Ca2+]c transients
Cardiac myocytes were obtained from the left ventricle
(septum + free wall) of female Sprague-Dawley rats (Moore
et al., 1991). In electrically paced cardiocytes,
[Ca2+]c transients were estimated using
fura-2 fluorescence and ratiometric methods that have previously been
described in detail (Palmer et al., 1999a;
Szmacinski and Lakowicz, 1995). The data for the [Ca2+]c dynamics were analyzed using
custom-made software to determine the integral as well as the general
magnitude and temporal characteristics for each
[Ca2+]c transient (Palmer et al.,
1999b).
For the extrasystolic potentiation experiments, a pacing frequency of 1 or 2 Hz was used with a 2-s rest interval inserted within the pacing protocol. Potentiation was defined as the percentage increase in the integral of the post-rest-interval [Ca2+]c transient relative to the mean integral of the normally paced [Ca2+]c transient.
For the comparison of experimental versus simulated [Ca2+]c transients, a representative [Ca2+]c transient was generated using an interpolation scheme with the mean characteristics of a series of [Ca2+]c transients from six myocytes paced at 0.25 Hz. The model was fit to the representative [Ca2+]c transient, using an iterative least-squares fit algorithm. The parameter values estimated during the fit were the fura-2 concentration and dissociation constant, both of which underwent an adjustment of less than 1%.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
SUMMARY
APPENDIX A
APPENDIX B
REFERENCES
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SR load depends on [Ca2+]s limitations on uptake, [Ca2+]c, and SRRC leak
One unique feature of this model was the inclusion of a maximum
theoretical thermodynamic gradient that can exist between the SR lumen
and the sarcoplasm. Shannon and Bers (1997) clamped sarcoplasmic [Ca2+] ([Ca2+]c),
using isolated SR microsomes from rat cardiac tissue, to demonstrate
that under conditions where the SRRCs were blocked to prevent SR
Ca2+ leak, SR luminal [Ca2+]
([Ca2+]s) varied linearly in proportion to
changes in [Ca2+]c. The slope of this
relationship, which was found to be ~7000 ([Ca2+]s/[Ca2+]c),
was described as being representative of the concentration gradient
that the SR Ca2+-ATPase was able to produce given the free
energy that would be expected to be available from ATP (Shannon
and Bers, 1997). In a simple simulation of this experiment,
model parameters were adjusted to represent the actual experimental
interventions (SRRCs blocked and [Ca2+]c
varied) that were used by Shannon and Bers (1997). The
results of this simulation are found in Fig.
2 A. It is not at all
surprising that this simple simulation recapitulated a slope of 7000 ([Ca2+]s/[Ca2+]c)
because this concept was built into our model.
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More important, however, is the model prediction of the
Ca2+ gradient that should exist between the sarcoplasm and
the SR lumen under normal conditions. Simulating the above experiment
without SRRC blockade resulted in lower levels of SR Ca2+
load (Fig. 2 A). For instance, at
[Ca2+]c = 1 × 10
7 M,
the gradient was 3011 ([Ca2+]s/[Ca2+]c)
(see Table 3), in comparison to the value
of ~7000
([Ca2+]s/[Ca2+]c)
with the SRRC blocked.
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SRRC leak
There are currently several distinctly different viewpoints regarding the relative importance of SRRC Ca2+ leak and SR Ca2+ uptake (and "back-flux"; see next paragraph) in determining SR Ca2+ content. In our model, SRRC leak plays a major role. Our model produced a value of 0.06 mM/s for the leak of Ca2+ through open SRRCs during a simulated state of quiescence that compares favorably to a theoretical estimate (0.02 mM/s) reported by Wier et al. (1994) for similar
experimental conditions. However, these values are approximately two
orders of magnitude higher than an experimentally determined diastolic
Ca2+ leak estimate (0.3 µM/s) reported by Bassani
and Bers (1995). The lower leak estimate was derived under
experimental conditions where SR Ca2+ uptake was blocked
and forward Na+-Ca2+ exchange was markedly
stimulated, whereas the higher leak values were derived from
theoretical estimates under conditions where SR Ca2+ uptake
and Na+-Ca2+ exchange were unaltered. In our
model, when SR Ca2+ uptake was blocked and
Na+-Ca2+ exchange was accelerated, there was a
rapid reduction in the predicted diastolic SRRC Ca2+
release rate to 0.24 µM/s, and the subsequent time-dependent decline
in releasable SR Ca2+ content was strikingly similar to
that observed by Bassani and Bers (1995) (Fig.
2 B). The theoretical reduction in SRRC leak rate elicited
by SR pump blockade and Na+-Ca2+ exchange
acceleration occurred secondary to a reduction in
fuzzy space [Ca2+] and, to a lesser extent, a reduction
in SR Ca2+ load. Finally, it should be recognized that the
magnitude of the hypothetical leak reduction predicted by our model is
less important than the general concept that SRRC Ca2+ leak
rate and sarcoreticular Ca2+ regulation can be markedly
affected by experimental intervention, an issue that will be addressed
in the Discussion.
Recently, a very interesting hypothesis has been advanced that "SR
pump back-flux" is the primary determinant of SR Ca2+
content, whereas SRRC Ca2+ leak plays only a minor role
(Ginsburg et al., 1998; Shannon et al.,
2000). Ginsburg et al. (1998) found that in
isolated cardiocytes when SR Ca2+ uptake was increased by
74% or decreased by 39%, SR Ca2+ content was increased by
~10-20% or decreased by 5-23%, respectively (Fig.
2 C). These data were interpreted as being supportive of SR
pump back-flux. Our model does not incorporate the back-flux concept per se, but rather uses a representation of net forward SR
Ca2+ pump rate that is subject to regulation by SR luminal
and cytosolic [Ca2+]. However, when we simulated the SR
Ca2+ uptake rate interventions used by Ginsburg et
al. (1998), SR Ca2+ content increased by 18% or
decreased by 19% in response to a 74% increase or a 39% decrease in
SR Ca2+ uptake rate, respectively (Fig. 2 C).
These simulated SR Ca2+ content changes are comparable to
those observed by Ginsburg et al. (1998). These results
indicate that the findings of Ginsburg et al. (1998) can
also be explained by a regulatory scheme in which SRRC
Ca2+ leak is more dominant in determining SR
Ca2+ content.
The above findings are particularly relevant in our model for several
reasons. First, examination of the theoretical processes that give rise
to this finding provides insight into the relative importance of SR
Ca2+ uptake and leak in determining SR Ca2+
load. Second, this in turn is very important in view of the fact that
bidirectional interactions between the Ca2+ load in the SR
lumen and the SR Ca2+ release channels provide robust
control of cellular Ca2+ dynamics under a variety of more
sophisticated experimental simulations.
SR Ca2+ release depends on SR load, SRRC recovery, and Ca2+ trigger size and duration
Graded response
A characteristic that is assumed to be fundamental to cardiac muscle CICR is that the amount of Ca2+ that is released from the SR varies or is graded as a function of the trigger [Ca2+] (Gyorke and Gyorke, 1998;
Fabiato, 1985). In the classic work of Fabiato
(1985), the relationship between the trigger
[Ca2+] (pCa) and the response (tension) had the following
characteristics: 1) a threshold pCa (~ >7) at which initial tension
development was elicited; 2) a "graded response" that increases
when pCa is increased until a maximum response is achieved (pCa 
5.5); 3) a progressive inactivation of the response that occurs
with further increases in trigger [Ca2+] (see Fig.
3 A). In Fabiato's
experiments (Fabiato, 1985), it was assumed that the
tension response was reflective of a graded CICR response. This
assumption is supported by the work of Gyorke and Gyorke
(1998), who demonstrated similar characteristics when the
response metric was the cardiac SRRC channel open probability in planar
bilayer preparation. Kim et al. (1983) observed similar results when measuring Ca2+ release rates from isolated
skeletal SR vesicles.
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. While it is clear from
inspection of Fig. 3 A that the model prediction and the
experimental data of Fabiato (1985) are not perfectly
superimposable, it is important to note that the general pattern of the
modeled graded response was reasonably similar to that observed
experimentally. The reasons for this divergence will be addressed in
the Discussion.
Load dependence of SR Ca2+ release
It has been clearly demonstrated that SR Ca2+ load has a distinct effect on the SR Ca2+ release (Gilchrist et al., 1992; Bassani et al., 1995).
Specifically, SR Ca2+ release cannot be
induced until a threshold level of SR loading is reached, after which
SR Ca2+ release demonstrates a steep SR Ca2+
load dependence. This effect should be present in the model with the
inclusion of the SRRC-CSQ bidirectional feedback. To test this, the
loading scheme of Fig. 2 A was used (with no blocking of
the SRRC), and a release trigger was provided at various SR Ca2+ loads. The results of this protocol (Fig.
3 B) demonstrate a threshold followed by a steep load
dependence of SR Ca2+ release, as has previously been
demonstrated (Bassani et al., 1995).
Effect of Ca2+ trigger duration on SR Ca2+ release
CICR has been demonstrated to be independent of Ca2+ trigger duration at periods greater than 5 ms (Fig. 3 C) (Bers et al., 1990; Cannell et al.,
1987). The model reproduces this relationship and predicts the
occurrence of a graded response at durations of less than 5 ms (Fig.
3 C). More recent studies have found that the range of
durations that produce a graded response is extended after reductions
in SR Ca2+ loading or maximum Ca2+ influx
(trigger size) (Han et al., 1994; Isenberg and
Han, 1994; Spencer and Berlin, 1995). With the
simulation of a 35% decrease in trigger rate or a 25% decrease in SR
Ca2+ load, duration-dependent gradedness is predicted to
occur with trigger durations less than 15 ms or less than 40 ms,
respectively (Fig. 3 C).
Time-dependent recovery of SR Ca2+ release
This simulation was designed to resemble a study (Cheng et al., 1996) where in discrete spaces (in which "sparks" were
observable) [Ca2+] was monitored during the course of a
spontaneous SR Ca2+ release and during a subsequent
stimulated SR Ca2+ release that was invoked at variable
times after the spontaneous event. The level of the second stimulated
SR Ca2+ release increased with the amount of recovery time,
eventually approaching the original level of the spontaneous release
(see Fig. 4 A). Cheng
et al. (1996) suggested that this pattern was representative of
a refractory state of the cell's ability to release Ca2+.
The model simulation of the experiment (see Fig. 4 B)
closely resembled the time-dependent recovery pattern observed by
Cheng et al. (1996).
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Model response to alterations in contraction frequency
As mentioned earlier concerning the types of experiments that will be described in the following text, model parameters were not manipulated but simply allowed to respond to the delivery of periodic contraction stimuli. It is important to note that the model parameter values that were used all fell within value ranges that have been reported in the literature (Table 2). Using these values, we found that the simulated [Ca2+]c transient displayed characteristics that were very similar to those observed in the laboratory with fura-2 fluorescence (Fig. 5). In the "stimulated" generation of a simulated [Ca2+]c transient, we manipulated a single external control point, perturbing the model from its self-determined steady state. The model equations responded to this perturbation, producing a [Ca2+]c transient en route to a new steady state. Because the model equations were concentration driven, all of the underlying Ca2+ regulatory processes were not defined but predicted and could be quantified and compared to literature results (Table 3).
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As constructed, the model demonstrates appropriate Ca2+ delivery qualities that are consistent with our understanding of these properties from the literature. In particular, the bidirectional control loop between the SRRCs and CSQ (the SR luminal Ca2+ sensor element) was fundamentally important in the ability of the model to exhibit reasonable SRRC gain, fractional Ca2+ release from the SR, as well a proper rate of rise and time-to-peak [Ca2+]c. With regard to these latter features, it should be noted that in generating the simulated [Ca2+]c transient, we included Ca2+ buffering by fura-2 in the model. Were it not for the inclusion of fura-2 buffering in the model, the simulated transients would have had different quantitative and temporal characteristics. In several of the experiments described below, it should be noted that simulated data include a fura-2 Ca2+ buffering element and are compared with actual experimental [Ca2+]c data derived with fura-2 fluorescence.
Rest potentiation
The simplest alteration in contraction frequency is when a myocyte makes the transition from quiescence to a fixed pacing frequency. Examples of simulated transitions from quiescence to steady-state contractile activity are depicted in Fig. 6, A and B. The model output yields a relatively large initial [Ca2+]c followed by a rapid progression to a reasonably stable steady state. This behavior is strikingly similar to what is observed in the laboratory with isolated rat cardiocytes, and the initial response represents "rest potentiation." Based on the model predictions, the larger initial response would be predominantly due to greater SRRC recovery from inactivation at the time of the first stimulation relative to that of the ensuing stimulations. The pacing rate allowed for 1 s (Fig. 6 A) or 0.5 s (Fig. 6 B) of recovery time between stimulations. The model predicts that after 1 s, SR Ca2+ reuptake would be virtually completed, yet the SRRCs would not be entirely recovered from inactivation (Fig. 6, C-F). Variable [Ca2+]c transients occurred until the SRRC activation-inactivation cycle settled into a dynamic steady state. The SR Ca2+ load was predicted to remain relatively unchanged with alterations in pacing frequency, as was observed experimentally (Bouchard and Bose, 1989).
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Negative staircase
Mammalian cardiocytes are known to be sensitive to alterations in contraction frequency, and in the case of rat ventricular myocytes, they display a negative force versus frequency response (Bers, 1993). Using our model, when the pacing
frequency of a simulated rat cardiocyte is increased, the amplitude of
the [Ca2+]c response decreases (Fig.
6 G). When the model was run at a variety of pacing
frequencies that are typically used in the laboratory, a peak
[Ca2+]c versus pacing frequency relationship
was produced (Fig. 6 H). These simulated effects of pacing
frequency are strikingly similar to those observed in the laboratory
(Bers, 1989).
Extrasystolic potentiation
Once the model demonstrated the capacity to predictably simulate steady-state frequency responses, we investigated the ability of the model to accommodate a dynamic pacing frequency perturbation in the form of a delivered extrasystolic interval. In our simulations, steady-state pacing at two different frequencies was interrupted by the delivery of a 2-s extrasystolic interval, and the ensuing [Ca2+]c transients were examined (Fig. 7, A and B). In both cases, the extrasystolic [Ca2+]c response was potentiated and the potentiation was most robust when the extrasystolic interval was delivered at the higher pacing frequency. These simulated responses are strikingly similar to the responses observed in the laboratory (Fig. 7, A and B, insets; summarized in Fig. 7 C). An examination of the model output reveals that the basis for the extrasystolic response elicited at the 1- and 2-Hz pacing frequencies was largely due to the collective recovery of SRRCs to an activatable state.
|
Pulsus alternans
In a final simulation, cellular Ca2+ loading was invoked by suppressing Ca2+ efflux from the cell during pacing at 2 Hz. As can be seen in Fig. 8, the Ca2+ overload elicited an unstable and cyclic [Ca2+]c transient irregularity that qualitatively resembled the phenomenon of pulsus alternans (Kihara and Morgan, 1991; Wong et al.,
1992). In our model, the genesis of this phenomenon was due to
control feedback instabilities in the bidirectional communication
between SRRCs and CSQ, related to a disruption in the degree and timing of Ca2+ binding to the SRRC and CSQ during the cycling of
control elements associated with a [Ca2+]c
transient. It is also important to note that large and relatively long-lived fluctuations in SR Ca2+ load or fuzzy space
[Ca2+] were not necessary to generate this alternans
effect.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
SUMMARY
APPENDIX A
APPENDIX B
REFERENCES
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Insights provided by model predictions
Graded response
The graded response is a fundamental cardiac physiological behavior that is sufficiently represented by our model (Fig. 3 A). Several regulatory features included in our model were important in conferring the properties of the graded response. The use of SRRCs with several Ca2+-sensitive functional states and bidirectional modulatory interplay between SRRCs and Ca2+ buffering in the SR lumen were centrally important in this regard. An SRRC model where various functional states were governed by [Ca2+] in the fuzzy space was fundamental in our representation of the graded response. This type of Ca2+-dependent regulation of SRRC kinetics (without a fuzzy space) has been described previously (Tang and Othmer, 1994) and was sufficient for the production of a graded
response, albeit only in the context of SR Ca2+ release
channel opening. While our scheme for the regulation of functional SRRC
states via [Ca2+] changes in the fuzzy space was
sufficient to confer a graded response behavior to the model, it was
not adequate to provide for the proper amplification of the SR
Ca2+ release response. We found that inclusion of
bidirectional communication between the SRRC and Ca2+
sensing elements in the SR lumen was important for the replication of
observed whole-cell responses. A system in which SRRCs were subject to
control by events on either side of the SR terminal cisternal membrane,
and in which luminal SR buffers were subject to modulation by SRRC
functional status, was essential in controlling the quantity of and
rate at which SR Ca2+ was released and in ensuring that
Ca2+ release from the SR was graded or fractional as
opposed to all or nothing. In addition, the bidirectional control
element confers a more dynamic quality on luminal SR Ca2+
buffers and, therefore, the regulation of luminal SR
[Ca2+].
Bidirectional communication between SRRCs and SR lumen Ca2+
sensing elements was not only critical in amplifying the SR
Ca2+ release channel reaction to a whole-cell response; it
was important in providing a tightly controlled mechanism for the
cessation of SR Ca2+ release. The latter feature has been
an issue that, until very recently, has been rather inadequately dealt
with in most models of cardiocyte Ca2+ dynamics. A
mechanism for a regulated termination of Ca2+ release is
essential in a system displaying a graded response and fractional,
rather than all-or-none, release of Ca2+ from the SR. In a
recent modeling study by Rice et al. (1999) it was
proposed that Ca2+ release termination could occur
secondary to a transient local depletion of junctional SR
Ca2+ during CICR. This scheme of local Ca2+
depletion requires the existence of two distinct pools of
Ca2+ in the SR lumen: a junctional SR Ca2+
release pool and a SR Ca2+ uptake pool that ultimately
replenishes the former pool when it is depleted. In this hypothetical
mechanism, local depletion terminates SR Ca2+ release
before large amounts of Ca2+ from the uptake pool can be
made available for release in the release pool, thus ensuring that the
SR Ca2+ release process is fractional rather than all or
nothing. There is evidence, however, against such a discrete
organization of Ca2+ pools in the SR lumen (Sham et
al., 1998; Satoh et al., 1998).
Alternatively, it has been argued that if the SR is treated as a single
Ca2+ pool, a Ca2+ depletion-induced termination
of Ca2+ release would require a nearly complete emptying of
SR Ca2+; this does not occur (Delbridge et al.,
1997; Bassani et al., 1995). Complete emptying
of a single-pool SR need not occur in a system where SRRCs and CSQ are
functionally coupled. It is now known that cardiac SRRCs and CSQ are
physically coupled by junctin and triadin (Zhang et al.,
1997) and that SR Ca2+ release and SRRC
activatability are strongly influenced by SR Ca2+ content
(Bassani et al., 1995; Donoso et al.,
1995; Gyorke and Gyorke, 1998; Gilchrist
et al., 1992; Ikemoto et al., 1989;
1991; Janczewski et al., 1995;
Lukyanenko et al., 1996; Satoh et al., 1997; Shannon and Bers, 1997; Sitsapesan
and Williams, 1997). In fact, it has been demonstrated that in
systems absent of CSQ, Ca2+-induced SR Ca2+
release does not occur (Ikemoto et al., 1991;
Ohkura et al., 1995). In our model, we propose that CSQ
acts not only as a simple Ca2+ buffer, but also as a sensor
of luminal SR Ca2+ load that exerts an effect on SRRC activatability.
Briefly, we propose that Ca2+ binding to fast activation
sites on SRRCs promotes SRRC opening, the initial release of
Ca2+ from the SR, and the dissociation of Ca2+
from CSQ. The dissociation of Ca2+ from CSQ is then assumed
to be accompanied by a conformational change in the CSQ that not only
modifies the Ca2+ binding characteristics of CSQ
(Ikemoto et al., 1989; Gilchrist et al.,
1992), but also is sensed by and modulates the inactivation characteristics of the SRRC (see Appendix B for a detailed description
and rationale). This type of feedback accomplishes Ca2+
release termination in a single Ca2+ pool SR model in a
system that exhibits gradedness and fractional Ca2+
release. This arm of the hypothetical control loop between SRRC and CSQ
is perfectly consistent with the experimental observations that
Ca2+-dependent release of Ca2+ only occurs with
a steep load dependence after a threshold level of Ca2+ in
the SR is achieved (Gilchrist et al., 1992;
Bassani et al., 1995) (for simulation, see Fig.
3 B). In the absence of some sort of communication between
the SRRC and a luminal SR Ca2+ sensing element, it is
intuitively difficult to reconcile these experimental data with a
simple local Ca2+ depletion model for the termination of
Ca2+ release.
As pointed out in the Results section, our simulated version of the
graded response approximated the response observed by Fabiato
(1985) but was not superimposable on it. There are several probable reasons for this apparent quantitative disparity. First, different response metrics were used in both experiments (tension versus [Ca2+]c), and it is well known that
peak [Ca2+]c is not linearly related to
tension development (Backx et al., 1995). Second, in our
simulation of the Fabiato experiment (Fabiato, 1985), we
applied a bulk change in Ca2+ to a rat cardiocyte model,
whereas in the actual experiment, canine myocardium was used. Third, in
skinned fiber experiments (e.g., Fabiato, 1985),
cellular Ca2+ buffers might be expected to have a smaller
effect on the effectiveness of trigger Ca2+ to elicit SR
Ca2+ release at the lower [Ca2+] when
compared to whole cells (e.g., the model). This might explain the
initial sigmoidal response at lower pCa values for our simulation compared to the linear response of the actual experiment
(Fabiato, 1985). Nonetheless, all of the basic
characteristics of a graded response were produced by our model.
SR Ca2+ leak versus uptake
As stated previously, the simulations depicting the consequences of the SR thermodynamic gradient are not particularly surprising when one considers the way in which the model was constructed. However, the simulation experiments illustrated in Fig. 2 address several very fundamental concepts. There has been some dispute over whether the SR Ca2+ load is limited by SR Ca2+ uptake/back-flux (Shannon and Bers, 1997;
Ginsburg et al., 1998; Shannon et al.,
2000) or by the SR Ca2+ leak (O'Neill et
al., 1999; Lukanyenko et al., 2000). In the context of our theory of control, the simple simulations depicted in
Fig. 2 A underscore the idea that SR Ca2+ load
is maintained below the thermodynamic limit and is, therefore, determined by the dynamic interaction of the thermodynamically limited
SR Ca2+ uptake and the SR Ca2+ leak, and that a
significant avenue of Ca2+ leak may be through open SRRCs.
This latter idea is consistent with recent findings from
Lukynanenko et al. (2000), suggesting that SR
Ca2+ content is regulated by Ca2+ leak through
SRRCs. In addition, there have been observations that in SR vesicles,
Ca2+ load can only approach a thermodynamic maximum when
SRRCs are blocked (Shannon and Bers, 1997), and in
intact cardiocytes, SR Ca2+ load increases with SRRC
blockade (O'Neill et al., 1999). Our model predicts
that SR luminal Ca2+ limitations on SR uptake account for
~40% and SRRC leak for ~60% of the dynamic balance that
determines SR Ca2+ content at quiescence.
In contrast, Shannon et al. (2000) recently developed
mathematical descriptions of cellular Ca2+ fluxes in which
SRRC leak was assumed to play a minor role in the determination of SR
Ca2+ load, whereas primary control occurred via the
regulation of forward and reverse Ca2+ fluxes through the
SR Ca2+ pump. Key features in the development of the SR
pump back-flux model of Shannon et al. (2000) are that
the diastolic SRRC Ca2+ leak rate is very low
(Bassani and Bers, 1995), SR Ca2+ load is
primarily controlled by the concerted regulation of forward and
backward Ca2+ fluxes through the SR Ca2+ pump,
and that reverse flux (or back-flux) through the SR Ca2+
pump is linked to ATP production. The latter feature is intuitively very attractive because this mechanism of diastolic SR Ca2+
load control would be more favorable energetically than a scheme where
Ca2+ is cycled through the SR via SRRCs. In comparison, in
our model SR Ca2+ uptake rate is regulated by luminal
Ca2+ in a manner similar to that proposed by Shannon
et al. (2000), but back-flux per se is not represented. Our
model predicts that diastolic SRRC leak is similar to that proposed by
others (Wier et al., 1994) but is much greater than that
estimated by Bassani and Bers (1995) and assumed for the
back-flux scheme (Shannon et al., 2000). Two points are
particularly relevant regarding this apparent leak discrepancy. First,
our SR Ca2+ leak simulations (Fig. 2 B)
indicate that the SRRC Ca2+ leak rate may be experimentally
condition dependent, an idea previously acknowledged by Shannon
et al. (2000) and one worth considering as a possible
explanation for this discrepancy. Second, as pointed out by
Shannon et al. (2000), the type of sarcoreticular Ca2+ cycling represented by our model would be
expected to be less energetically economical than Ca2+
cycling via a back-flux mechanism, particularly in systems where the
heart rate is slow and diastole is prolonged. In systems where heart
rates are high (i.e., rat, 
300 bpm) and in which diastolic resting
states similar to those observed experimentally in isolated myocytes
would never be achieved, the energetic consequences of back-flux might
be of lesser importance. Nonetheless, this is clearly a concept that
should not be overlooked.
The issue regarding the quantitative importance of SRRC
Ca2+ leak and SR pump/back-flux activity in determining SR
Ca2+ load is clearly one in need of closer scrutiny.
Resolution of this issue is directly relevant to our model insofar as a
key regulatory feature of the model that is central to its ability to
handle a broad array of physiological predictions is a hypothetical, bidirectional interaction between SRRCs and CSQ. This interaction is
directly and powerfully influenced by SR Ca2+ load.
The dependence of SR Ca2+ release on SR Ca2+ load
As discussed earlier, a central element of the current model that confers a properly scaled graded response on our system is the bidirectional communication between CSQ and SRRCs. This feature is also critical to the ability of the model to recapitulate the steep SR Ca2+ load dependence of SR Ca2+ release (Fig. 3 B). The data (simulated and experimental; Bassani et al., 1995) in Fig. 3 B are conceptually
important for several reasons. First, in the context of our model, the
CSQ:SRRC mechanism is critical in conferring a threshold for SR
Ca2+ release that is strongly dependent on SR luminal
Ca2+ content (discussed in detail in Appendix B). Second, the data in Fig. 3 B also illustrate the concept that SR
Ca2+ content is limited by a dynamic balance between SR
Ca2+ uptake and leak. Collectively, these mechanisms define
the relatively narrow operating range of SR Ca2+ load in
which the load is attainable and releasable. This behavior would not be
possible if the SR acted as a simple Ca2+ pool.
Duration dependence of SR Ca2+ release varies with Ca2+ trigger and SR load
SR Ca2+ load and the Ca2+ trigger not only affect SR Ca2+ release directly (Fig. 3, A and B), but also indirectly by shifting the effect of Ca2+ trigger duration (Fig. 3 C). (Han et al., 1994; Isenberg and Han,
1994; Spencer and Berlin, 1995). The inclusion
in the model of the CSQ:SRRC mechanism is crucial in providing the
regulation of the SRRCs by Ca2+ on both sides of the SR
membrane, which is necessary to reproduce these results. Overall, SR
luminal Ca2+ feedback to the SRRCs and SR uptake is
conceptually important from an integrative standpoint as a key
connection in the interdependence of SR Ca2+ load, SR
Ca2+ release, SR leak, SR uptake,
[Ca2+]c, trigger size, and trigger duration
(Figs. 2 and 3).
Time-dependent recovery of SR Ca2+ release
The current model was sufficient to reproduce a time-dependent recovery of the ability to release Ca2+ similar to that observed experimentally (Fig. 4). From our simulations, it appears that this was primarily related to SRRC refractoriness (with a minor effect due to SR Ca2+ reuptake). It has been proposed that there could be two additional factors affecting the recovery of the CICR response: 1) recovery of the L-type channels from inactivation and 2) diffusion of SR Ca2+ from an "uptake region" to a "release region" (for a review see Bers, 1993).
Based on previous estimates, L-type Ca2+ channel recovery
should only require ~300 ms (Mokelke et al., 1997),
and intra-SR Ca2+ diffusion should take ~1 ms
(Bers, 1993). In view of the fact that the
experimentally observed (Cheng et al., 1996) and
simulated half-times for recovery of SR Ca2+ release were
>400 ms, these alternative processes appear to be too fast to be
centrally related to the SR Ca2+ release recovery process
at the pacing rates that were examined in both studies. We concede,
however, that at faster pacing frequencies such as those that would be
expected to occur physiologically in the rat (>300 bpm), at least one
of these other processes might be expected to come into play.
There was one key difference between the model simulation and the
time-dependent recovery of Ca2+ release experiment
(Cheng et al., 1996). The model was of an isolated rat
cardiac myocyte, whereas the actual experiment involved the observation
of [Ca2+] changes in spaces in which Ca2+
sparks were observed in rat cardiocytes. The phenomenon of
Ca2+ sparks is relevant to our model, although it was not
specifically incorporated. Spark studies have shown that there are
small individual cellular spaces ordered about the Z-lines within the
cardiac myocytes. These individual spaces can undergo spontaneous SR
Ca2+ release in a quiescent cell. If the SRRCs of the
adjacent spaces are not in the refractory state, the Ca2+
spark can spread to these spaces, starting a wave (Cheng et al., 1996; Satoh et al., 1997). Where this theory
applies to our model lies in the idea that with stimulation of the
cell, many of these spaces in the cell may undergo CICR at once and
become synchronized in their cycling through the refractory state. Our
model represented the composite averaging of the fuzzy spaces
undergoing CICR simultaneously, which may in turn represent a summation
of the spark mechanisms in a whole-cell response.
Contraction frequency
The control features of the current model were adequate to reproduce a variety of fundamental pacing frequency-dependent characteristics, including rest potentiation, the negative "staircase" phenomenon, and extrasystolic potentiation. The negative staircase is a phenomenon that is rather unique to the myocardium of rats and other small rodents (Bers, 1993).
In general, steady-state frequency-dependent alterations in contractile
force are thought to be due to frequency-dependent alterations in the
fractional release of Ca2+ from the SR and in the amount of
releasable Ca2+ that is present in the SR. However, unlike
myocardium from other species (Bers, 1993), several
pieces of evidence suggest that the latter mechanism is of only modest
to minor importance in rat myocardium (Stauffer et al.,
1997; Bouchard and Bose, 1989; Bers,
1989). This is relevant to our model for several reasons. In
our simulations the dominant response to steady-state increases in
contraction frequency was a reduction in the fractional release of
Ca2+ from the SR, whereas SR Ca2+ load was not
significantly influenced (Fig. 6, C and D). The frequency-dependent effect on SR Ca2+ release was
associated with the temporal characteristics with which SRRCs cycled
through their functional states (Fig. 6, E and
F), and this mechanism alone was sufficient to produce the negative staircase phenomenon. Insofar as SR Ca2+ load does
not appear to be a dominant factor in the responsiveness of rat
myocardium to pacing frequencies <2 Hz (Stauffer et al., 1997; Bouchard and Bose, 1989; Bers,
1989), it is reasonable to assume that changes in pacing
frequency do not invoke large imbalances in cellular Ca2+
influx and efflux. However, it should be recognized that our simplified
representation of sarcolemmal Ca2+ influx and efflux
processes precludes the use of our model to rigorously examine the
effects of pacing frequency on SR Ca2+ content. A more
sophisticated representation of the sarcolemma would be required if
this model were to be applied to systems in which the effect of pacing
frequency on SR Ca2+ load are known to be substantial
(i.e., guinea pig, rabbit).
Finally, an interesting and somewhat unexpected result of this
study was the creation of cyclically variable (unstable)
Ca2+ release states under conditions where cardiocyte
Ca2+ overload was simulated. The unstable state had
alternans-like characteristics that have been associated with a variety
of pathological states, including cellular Ca2+ overload
(Kihara and Morgan, 1991; Wohlfart,
1982). It has been proposed that the alternans condition is due
to cyclic alterations in the refractory state of SRRC that occur
secondary to alternating high and low fuzzy space [Ca2+]
(Kihara and Morgan, 1991; Wohlfart,
1982). However, in our model, subtle loss of control in the
bidirectional regulatory loop between SRRCs and SR luminal
Ca2+ sensing elements appeared to be a major factor in
altering SRRC refractoriness and SR Ca2+ releasability.
This potential site of acute maladaptation is particularly interesting
in view of the fact that the inclusion of the bidirectional SRRC-SR
lumen regulatory loop was centrally important in the model's ability
to recapitulate a broad array of normal, physiologically observable characteristics.
Context and limitations
It is readily recognized that the key elements of Ca2+
regulation represented in our model are intracellular processes that exist within a boundary about which key assumptions must be made. This
boundary limitation is unavoidable and inherent to all simulation models. In our model, the sarcolemma represents the boundary, or outer
shell, about which we have made several simple regulatory assumptions,
and within which the fundamental control elements of our model exist.
Our outer shell assumptions were that 1) each contraction-relaxation
cycle is initiated by a small, transient influx of Ca2+
into the cell via a fuzzy space, and 2) during a contraction steady
state, cellular Ca2+ efflux varies as a function of changes
in sarcoplasmic [Ca2+], and overall Ca2+
efflux must quantitatively approximate the magnitude of
Ca2+ influx into the cell. With only several exceptions
(Rice et al., 1999; Jafri et al., 1998),
this is the type of approach that has been taken in the development and
testing of most models of cardiocyte Ca2+ regulation to
date (Wong et al., 1992; Tang and Othmer,
1994; Peskoff et al., 1992; Langer and
Peskoff, 1996). Viewed in one way, this approach is a
limitation because it clearly oversimplifies the complex sarcolemmal
events that are known to be directly and/or indirectly involved in the
regulation of transarcolemmal Ca2+ movement. On the other
hand, it is relevant to note that in a model where sarcolemmal ion
regulatory complexities were most comprehensively represented
(Jafri et al., 1998), many of the most fundamental
Ca2+ control mechanisms that were responsible for defining
the size and shape of the cytosolic [Ca2+] transient were
distal to events that occurred at the level of the sarcolemma.
Moreover, that model was not sufficient to generate simulations of a
graded response, whereas the current model (as well as others;
Tang and Othmer, 1994
) are from Shannon and Bers (1997)
) (replotted by permission), using isolated
ferret cardiocytes. To perform this simulation (---), SR loading was
varied by using the above thermodynamic gradient protocol (without SRRC
blockade). The L-type channel rate constant, k1,
was briefly increased to trigger SR Ca2+ release.
(C) Effect of trigger duration on SR Ca2+
release. Bers et al. (1990)
25%)
(- - - -), using the loading scheme of Fig. 
