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A Dynamic Model of Excitation-Contraction Coupling during Acidosis in Cardiac Ventricular Myocytes

Bioengineering Institute and Department of Engineering Science, University of Auckland, Auckland, New Zealand

Correspondence: Address reprint requests to Edmund J. Crampin, Bioengineering Institute, University of Auckland, Private Bag 92019, Auckland, New Zealand. Tel.: 64-9-373-7599 ext. 88168; E-mail: e.crampin{at}auckland.ac.nz.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Acidosis in cardiac myocytes is a major factor in the reduced inotropy that occurs in the ischemic heart. During acidosis, diastolic calcium concentration and the amplitude of the calcium transient increase, while the strength of contraction decreases. This has been attributed to the inhibition by protons of calcium uptake and release by the sarcoplasmic reticulum, to a rise of intracellular sodium caused by activation of sodium-hydrogen exchange, decreased calcium binding affinity to Troponin-C, and direct effects on the contractile machinery. The relative contributions and concerted action of these effects are, however, difficult to establish experimentally. We have developed a mathematical model to examine altered calcium-handling mechanisms during acidosis. Each of the alterations was incorporated into a dynamical model of pH regulation and excitation-contraction coupling to predict the time courses of key ionic species during acidosis, in particular intracellular pH, sodium and the calcium transient, and contraction. This modeling study suggests that the most significant effects are elevated sodium, inhibition of sodium-calcium exchange, and the direct interaction of protons with the contractile machinery; and shows how the experimental data on these contributions can be reconciled to understand the overall effects of acidosis in the beating heart.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Acidosis is a major factor underlying the damage that occurs as a result of disrupted blood supply during coronary heart disease. Reduced intracellular pH disrupts each of the steps in excitation-contraction coupling, and severely affects the ability of the myocyte to generate tension, with dire consequences for the pumping capacity of the heart. Considerable experimental data exists on the effects of acidosis on different processes in cardiac myocytes. Typically, in these studies respiratory acidosis is induced by raising extracellular CO₂, which causes intracellular pH to fall.

Despite the important implications of acidosis, the relative significance of the various mechanisms by which decreased intracellular pH affects the steps of excitation-contraction coupling and force generation remain under debate. This is largely due to two factors that make data difficult to interpret unambiguously. First is the manner in which pH, ionic concentrations, and developed tension vary with time during acidosis. For example, when acidosis is induced by increasing extracellular CO₂ concentration, tension shows a biphasic response, with an initial rapid decline followed by a slower partial recovery (see Fig. 1). This response is due to the competing effects of acidosis on cellular processes involved in calcium handling, as well as direct effects on the contractile proteins. Secondly, the effects of acidosis on intracellular Ca²⁺ and tension are the result of the interactions between multiple coupled cellular processes, each with its own nonlinear dependencies and intrinsic timescale.

View larger version (5K): [in this window] [in a new window]   FIGURE 1  The effect of acidosis on intracellular Ca2+ and contractile force in rat papillary muscle, reproduced from Orchard et al. (57). Intracellular calcium (as indicated by photoprotein aquorin light intensity; top) and developed tension (bottom) during respiratory acidosis induced by raising CO2 from 5% to 20% with held constant. (Reproduced from The Journal of General Physiology, 1987, 90:145–165 by copyright permission of the Rockefeller University Press.)

The cytosolic Ca²⁺ transients that initiate contraction are strongly sensitive to pH. Studies have found consistently that acidosis raises diastolic Ca²⁺ (1) and decreases the rate of decline of the calcium transient (2). Systolic Ca²⁺, however, has been shown to increase (2,3) or show no change (4) during acidosis (or, in voltage-clamped myocytes, even to decrease (5)). The mechanisms by which these changes are effected and the reasons for the discrepancies are not completely clear. Acidosis inhibits most, if not all, of the steps in excitation-contraction coupling outlined above. Calcium release from the SR was found by Kentish and Xiang (6) to be reduced by >50% when pH was lowered to 6.5, attributed at least in part to competitive binding of protons at cytosolic Ca²⁺ activation sites. Moreover, fractional SR release decreases as pH is lowered. Therefore, it appears contrary that peak systolic calcium concentration may actually rise during acidosis despite depressed Ca²⁺ release.

There are, however, established mechanisms that contribute to an increase in cytosolic Ca²⁺. Protons displace Ca²⁺ from TnC binding sites, reducing Ca²⁺ buffering within the cell. Diastolic calcium concentration increases in acidosis, which under normal circumstances would lead to increased SR loading via calcium uptake by the SR Ca²⁺-pump—potentially a mechanism to increase the size of the transient. SERCA is, however, directly inhibited by protons; the slowed uptake of calcium into the SR is thought to underlie the marked slowing in the decline of the transient (6). Yet many studies have found that SR calcium content increases during acidosis (4,7), although others have reported a decrease (6). Pathways for Ca²⁺ removal from the cytosol are also inhibited at low pH, which would increase the amount of Ca²⁺ in the cell. Na⁺-Ca²⁺ exchange is directly inhibited by protons (8–10); however, during acidosis intracellular Na⁺ rises, due to Na⁺-coupled extrusion of protons. This decreases Na⁺-coupled Ca²⁺ efflux, which further contributes to rising cytosolic Ca²⁺. Bountra and Vaughan-Jones (11) showed that this inotropic effect can at least partially compensate for the direct inhibitory effects of lowered intracellular pH.

Finally, acidic pH has also been shown to affect the Ca²⁺-tension curve (12). Acidosis decreases the apparent sensitivity of the regulatory sites of TnC to Ca²⁺, shifting the activation curve to higher Ca²⁺ with little change in its shape and slope. This effect arises from direct competition for the low affinity binding sites of TnC (2,13). Additionally, a drop in pH decreases the maximum (Ca²⁺-saturating) tension, producing a 30% reduction at pH 6.5 (2).

The intracellular environment is highly regulated, and intracellular pH is no exception. Cellular proton concentration is strongly buffered, approximately equally by CO₂-dependent and CO₂-independent intrinsic buffers under normal conditions. pH is also regulated by four sarcolemmal transporters: sodium-bicarbonate co-transport (NBC) and sodium-hydrogen exchange (NHE) are acid extruders increasing intracellular pH, while chloride-hydroxide exchange (CHE) and bicarbonate-chloride exchange (anion exchanger, AE) are acid loaders.

In this study, we describe the development of a dynamic model of acidosis in the ventricular myocyte. Mathematical modeling provides a mechanism by which the effects of individual mechanisms can be isolated, and their significance quantified, to further our understanding of the effects of acidosis on the myocyte.

The model incorporates experimental data on pH-dependent changes to calcium-handling and buffering, and acid transport process into a coupled modeling framework for cell electrophysiology (14) and mechanics (15). Our strategy for examining the contributions of the changes to excitation-contraction coupling that occur during acidosis is to quantify the influence on the calcium transient of each mechanism in turn, before examining their collective effects on the cell. This approach is made possible with a modeling, rather than an experimental study; however, it is important to note at the outset that, for a highly coupled nonlinear system such as this, the combined effects of these mechanisms will differ from the sum of changes engendered by each mechanism individually. Nevertheless, many useful insights can be gained. We use the model to examine the effects of acidosis on each of the steps in excitation-contraction coupling over multiple beats. In particular, we focus on the dynamical changes underlying the biphasic nature of the reduced inotropy brought about by respiratory acidosis, and we seek to rationalize the discrepancies apparent in the literature regarding the effects of acidosis on SR Ca²⁺ content and release. This study develops and extends the preliminary work recently presented by Crampin et al. (16) to a dynamical modeling framework.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
We base our analysis on the Luo-Rudy-dynamic (LRd) model of myocyte electrophysiology (14,17), as that model 1), is based on Guinea-pig electrophysiology which is consistent with the majority of acid transport data; and 2), has the properties required to maintain stable voltage and ionic concentrations over multiple action potentials. Our implementation of the model follows Hund et al. (18), with modifications as described below and in the Appendix. A schematic of the model is shown in Fig. 2.

View larger version (20K): [in this window] [in a new window]   FIGURE 2  Schematic diagram of the model. Existing model components of the LRd model are shown in shading, whereas additions to the model and modified components (mechanisms regulated by pH) are shown in solid representation. Abbreviations: NCX, sodium-calcium exchanger. Acid efflux pathways: NHE, sodium-hydrogen exchanger and NBC, Na-bicarbonate cotransporter. Acid influx pathways: CHE, chloride-hydroxide exchanger and AE, anion exchanger. CMDN, calmodulin; TRPN, troponin C; CSQN, calsequestrin; JSR, junctional SR; and NSR, network SR.

Experiments in which cytosolic and SR lumenal pH were varied independently showed that the cytosolic pH is the dominant effector. As the SR is permeable to protons, we have used these data to model the inhibition. The LRd ventricular cell model does not explicitly model the kinetics of RyRs. Assuming the maximal channel conductance g_maxrel is proportional to the open channel probability, we have modified the calcium release flux to include a simple saturating inhibition, using data on the dependence of single channel open probability on pH from Xu et al. (20),

(1)

shown in Fig. 3 a, so that the pH-dependence of the conductance is given by Examination of Ca²⁺ transients in the LRd model shows that, with the published parameter set, the junctional compartment empties completely with each beat, thus the magnitude of Ca²⁺ release for each beat is determined by the filling fraction of this compartment, rather than the characteristics of the release channel. Under such a scenario, inhibition of the release mechanism will have no effect on the Ca²⁺ transient until the inhibition is severe enough that this, rather than the amount of Ca²⁺ available for release, becomes the limiting factor. Therefore we have also decreased the maximal release channel conductance by a factor of 4, so that the Ca²⁺ released is sensitive to the channel conductance, but does not change Ca²⁺ transients in the model at normal pH. Parameters are given in Table 1.

View larger version (10K): [in this window] [in a new window]   FIGURE 3  (a) pH dependence of RyR open probability, data () from Xu et al. (20); measurements at 10 µM Ca2+, maximal open probability taken as 0.7. (b) pH dependence of Ca2+ uptake flux into the SR at constant [Ca2+]i, fitted from normalized fluorescence data () from Henderson et al. (25) (at 10 mM Mg2+). (c) Proton inhibition of NCX flux, data () from Doering and Lederer (27). (d) pH-dependence of Troponin-Ca2+ affinity, half-maximal activation curve fitted to data () from Blanchard and Solaro (13). (e) pH-dependence of maximum tension, data () from Orchard and Kentish (2). Parameters for each of these fits are in Table 1.

Henderson et al. (25) reported equilibrium fluorescence studies on skeletal Ca²⁺-ATPase, which reveal sigmoidal intensity variation, increasing at higher pH. These and similar data have been interpreted as pH dependence of the conformational change between cytosol-facing and SR lumen-facing states of the protein, due to ATP binding and covalent phosphorylation (24,26). To produce a simplified model of pH inhibition of SR calcium uptake we have fitted these equilibrium data, assuming that the fluorescence change indicates a transition from an active, Ca²⁺-binding state to an inactive state of the transporter:

(2)

The pH-dependence of this flux is shown in Fig. 3 b, with parameters given in Table 1.

Na⁺-Ca²⁺ exchanger
Doering and Lederer (10,27) measured Na⁺-Ca²⁺ exchange current in giant excised patches from Guinea-pig ventricular myocytes under different cytosolic acid loading conditions, and reported a biphasic inhibition of the current after a step change in pH with a rapid initial block followed by a slower secondary phase. They also showed that proton sensitivity is abolished by the action of a protease, which leaves the exchanger functionally intact, therefore suggesting that protons interact with the exchanger at a location away from the transport site. Recent data from Egger and Niggli (28) found that the Na⁺-Ca²⁺ exchanger is also inhibited by extracellular acid, reducing the exchanger current to 70% of normal peak values at pH_e 6. As this reduction in current is 10% of the inhibitory effect of a similar fall in intracellular pH, it has not been included in the model.

We have modeled inhibition of the Na⁺-Ca²⁺ exchanger assuming that proton binding at a regulatory site affects each state of the transport cycle equally, fitting data from Doering and Lederer (27) showing the change in steady-state outward exchanger current at different pH_i (see Fig. 3 c). The pH-dependence of the current at constant ligand concentrations is

(3)

where pH_ref is a reference pH value, with parameters given in Table 1.

L-type Ca²⁺ current
Hulme and Orchard (1998) report that, under physiological conditions, the L-type Ca²⁺ current, I_CaL, is unchanged during acidosis; older studies, however, where intracellular Ca²⁺ was held constant (buffered), found I_CaL to be substantially inhibited. Under physiological conditions, [Ca²⁺]_i rises during acidosis, and this increases the activity of Ca²⁺-calmodulin-dependent protein kinase II (CaMKII), which activates I_CaL—potentially offsetting any inhibition due to H⁺ inhibition (29). Therefore, on the basis of these more recent data, we have not changed I_CaL due to acidosis in the model.

Modeling tension
Developed tension is calculated assuming isometric contraction at a sarcomere length of 2 µm using a steady-state version of the model by Hunter et al. (15). This model has two components: 1), the calcium transient and calcium binding to the thin filaments; and 2), the availability of thin-filament binding sites. At a constant extension ratio, the amount of calcium bound to the Troponin-C is a saturating function,

(4)

where is the total cellular concentration of available binding sites, as defined in the LRd model, and is the apparent binding constant for Ca²⁺.

As a result of calcium binding to Troponin-C, a conformational change in the contractile proteins occurs, making thin-filament binding sites available. The kinetics of this process are governed by the first-order equation for the fraction of available sites z,

(5)

and the tension developed at steady state is proportional to the number of available binding sites,

(6)

so that T(z = 0) = 0, and T_max is the maximum tension.

Blanchard and Solaro (13) measured the amount of Ca²⁺ bound to Troponin and determined that there is a reduction in the affinity of myofibrillar Troponin-C for calcium with acidic pH, which is responsible for the reduction in tension. We have used these data to calculate an apparent K_M for competitive binding of protons at the low affinity Ca²⁺ binding sites, Fig. 3 d. The apparent binding constant is given by

(7)

where the LRd model value was used for K_M,trpn.

The Blanchard and Solaro (13) study on intact myofibrils reported no change in maximum tension generated (for saturating Ca²⁺). Studies on skinned fibers have, however, shown a marked decrease in maximum force during acidosis (2). Furthermore, there is evidence of reduced maximal Ca²⁺-activated force (developed pressure) with falling pH in intact hearts (30), and, more recently, in intact papillary muscle preparations (31). Evidence is now accumulating that the thin-filament protein Troponin I (TnI) is also regulated by pH (32). We have included this effect as a simple empirical fit to data from Orchard and Kentish (2), to find the dependence of maximum tension on pH, Fig. 3 e,

(8)

where T_ref is the maximal tension obtained at the reference pH.

The Ca²⁺-tension curves corresponding to these equations are plotted in Fig. 4, which correspond well to experimental curves measured by Orchard and Kentish (2).

View larger version (11K): [in this window] [in a new window]   FIGURE 4  Steady-state pCa-tension curves normalized to maximum tension at pH 7, compared to experimental data points from Fig. 4 in Orchard and Kentish (2).

(9)

(in the absence of buffers, [B₁] = [B₂] = 0, the resultant term in Eq. 9 reflects the translation from flux of [H⁺] to rate of pH change). CO₂-dependent buffering is via the CO₂ hydration reaction,

(10)

for which buffering power increases with increasing pH (from 15 mM/pH unit at pH 6.9 to 50 mM/pH unit at pH 7.3; (35)). This reaction is relatively slow, and is modeled as a flux according to

(11)

Parameters for Eqs. 9 and 11 were taken from Leem et al. (35), reproduced in Table 2.

View this table: [in this window] [in a new window]   TABLE 2  Parameters for intrinsic and CO2-dependent proton buffering, from Leem et al. (35)

(12)

where J_nhe and J_che are fluxes for the transporters NHE and CHE, respectively. Assuming the sarcolemma is permeable to CO₂ and impermeable to bicarbonate, transport of bicarbonate and CO₂ are given by

(13)

(14)

where J_nbc and J_ae are the NBC and AE fluxes, and J_CO2 is the diffusive flux of CO₂ across the membrane

(15)

Here, p_CO2 is the CO₂ permeability of the cell membrane, A_m is the membrane area, and V_myo is the myocyte volume.

The CO₂ hydration reaction is the mechanism by which varying extracellular CO₂ brings about a change in intracellular pH, which is how respiratory acidosis (acidosis arising from increased extracellular CO₂) occurs. CO₂ readily diffuses through the cell membrane (Eq. 15). Thus, increasing extracellular CO₂ causes an influx of CO₂ into the cell, which disequilibrates the CO₂-bicarbonate reaction. As the reaction reestablishes equilibrium, some of this intracellular CO₂ combines with water to form bicarbonate, releasing a proton, causing the rapid drop in pH_i. In our simulations of respiratory acidosis, we assume that extracellular bicarbonate does not change, and so extracellular pH also falls in response to the change in CO₂, so that the CO₂-bicarbonate equilibrium is maintained outside the cell.

Acid transporters
The experimental data available on the pH-dependence of the four sarcolemmal acid-equivalent fluxes are sufficient to model the transporters using six-state thermodynamic cycles. This explicitly represents ion-binding and transitions between intra- and extracellular conformational states of the transporters, and allosteric regulation of the transport fluxes by protons, at intracellular and extracellular binding sites, according to available pH_i and pH_e data. We employed a model reduction approach, following Smith and Crampin (36), made on the basis of rapid binding approximations, to produce simplified kinetic models for the transporters. Details can be found in the Appendix.

Na⁺-HCO₃^– cotransporter (NBC)
While both electrogenic (NBCe-1-B) and electro-neutral (NBCn-1) isoforms of the cotransporter have been identified in the heart, the electro-neutral NBCn-1 has been shown to be the dominant form in Guinea-pig ventricular myocytes (37) and so we have assumed an electroneutral 1:1 stoichiometry for NBC. We have assumed sequential ligand binding on the cotransporter at the extracellular side to be in the order of Na⁺ followed by

Additional allosteric regulation occurs via proton binding to either intracellular or extracellular sites. Data from Vaughan-Jones and Spitzer (38) suggest that NBC is stimulated via intracellular proton binding at an allosteric site. In contrast, extracellular proton concentration was shown to inhibit NBC (39). The binding kinetics of these allosteric regulatory sites are assumed to be independent of the state of the transporter and have been modeled using a fully cooperative Hill expression and hence the steady-state flux for NBC is given by

(16)

where J_cotrans is the flux through a generic compulsory-order sequential cotransporter, and is defined in the Appendix.

Na⁺-H⁺ exchanger (NHE)
NHE is the major pathway for acid efflux from the cell. We have modeled the NHE1 isoform of the transporter, found in cardiac tissue, assuming Na⁺ must be released from the intracellular site before H⁺ binds to the transporter. Data from Vaughan-Jones and Spitzer (38) suggest that acid extrusion on NHE is stimulated via protons binding at a regulatory intracellular allosteric binding site. This allosteric regulatory site is assumed to be independent of the state of the transporter and has been modeled using a fully cooperative Hill expression. Na⁺ influx on NHE is found to be slowed if pH_e is low, as during ischemia (11). Vaughan-Jones and Spitzer (38) also proposed allosteric regulation of NHE at an extracellular site, although with a significantly weaker dependence than the intracellular site (with a Hill coefficient of 1 at the extracellular site, compared to 3 at the intracellular site).

We have found that the dependence of the basic transport cycle flux on proton (ligand) binding at low extracellular pH is sufficient to fit existing experimental data (38,40), and thus no allosteric regulation of NHE by extracellular protons was included in the model. The steady-state flux is then

(17)

where the generic compulsory-order sequential exchange flux J_exch is defined in the Appendix.

Cl^–-OH^– exchanger (CHE)
There is little direct evidence for allosteric regulation, or otherwise, of acid extrusion on CHE—thus, no allosteric regulation of CHE was included in the model. The transmembrane Cl^–-OH^– exchange flux is given by

(18)

Anion exchanger (AE)
Although there is little direct evidence for allosteric regulation of the anion exchanger, to maintain the reported steady-state relationship between pH_i and pH_e over a range of extracellular pH values (38), we have found that intra- and extracellular regulation of AE was required, where the exchanger is inhibited at low intracellular pH and stimulated by extracellular protons, giving

(19)

Parameter estimation
We estimated parameters for these fluxes using a sequential quadratic programming algorithm (41) to optimize the model fit to pH_i-dependence data, measured by Leem et al. (35), and whole-cell steady-state pH_i and pH_e measurements (38,42). This approach allows multiple data sources to be used to constrain the model parameters. Additional data sources used were pH_e values required to reduce the NBC and NHE fluxes to zero (40), dependence of NBC flux on extracellular Na⁺ (39), and estimates of intra- and extracellular Cl^– concentrations (43). Full details of the procedure employed are given in the accompanying Supplementary Material. Fitted flux curves and experimental data on pH_i-dependence for the transporters are shown in Fig. 5, and parameters are given in Table 3.

View larger version (6K): [in this window] [in a new window]   FIGURE 5  pH-dependence of sarcolemmal acid-equivalent transporters. Model fits (solid lines) and experimentally measured fluxes (35) showing NBC, NHE, + CHE, and x AE.

Respiratory acidosis was simulated by increasing extracellular CO₂ from its control value of 5% with constant extracellular bicarbonate concentration. Extracellular pH is determined from the equilibrium of the CO₂ hydration reaction (see Eq. 10). Experimental studies typically induce respiratory acidosis using 15% (3,7) to 30% (2) extracellular CO₂, and so we have compared cellular responses at these two values. Most experimental studies consider the response to 3–10 min of respiratory acidosis, and so for the majority of our simulations we have imposed the rise in extracellular CO₂ for a 5-min duration.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
To study the effects of each of the pH sensitivities described above, the pH-dependent rate laws were included in the model one at a time (using rate laws at normal pH value for each of the other mechanisms). In these initial simulations we wish to distinguish between the effects of pH on Ca²⁺-handling mechanisms and direct effects of the pH regulatory processes, and therefore sarcolemmal proton transport fluxes (in particular NHE and NBC) are held at their normal (pH 7.15) values. In the absence of transmembrane acid fluxes, a step-increase in extracellular CO₂ from 5% control produces the pH profiles shown in Fig. 6. Fifteen-percent CO₂ produces a drop to pH 6.9 and 30% to 6.7. These pH values compare well with experimental records of intracellular pH with 15% CO₂, for which Harrison et al. (7) measured intracellular pH fall to 6.9, and 30% CO₂, for which Orchard and Kentish (2) estimated an intracellular pH drop of 0.4 units.

View larger version (5K): [in this window] [in a new window]   FIGURE 6  Effect of 15% and 30% extracellular CO2 on intracellular pH (a) and (b) in cell model with no pH sensitivity of the sarcolemmal proton transporters. Extracellular CO2 is increased from 5% (control) to 15% or 30% after 1 min, and returned to control after 5 min of acidosis. Corresponding extracellular pH is also shown (dotted).

Inhibition of SR Ca²⁺ release channels
Fig. 7 shows the effects on cytosolic Ca²⁺ and SR Ca²⁺ content ([Ca²⁺]_sr) produced by inhibition of Ca²⁺ release, Eq. 1, during acidosis. Fig. 7, a–d, shows [Ca²⁺]_i and [Ca²⁺]_sr with increasing acid load, indicating that, despite a reduction of the open probability to 35% of its norm-acidic value as pH approaches 6.5, there is only a relatively minor decrease in peak systolic Ca²⁺, with a small increase in diastolic Ca²⁺. The figure shows an initial decrease in peak Ca²⁺ at the onset of acidosis (60 s) which rapidly recovers to near-normal levels, despite the sustained low pH, due to loading of the SR with Ca²⁺. On the release of acidosis after 5 min, peak Ca²⁺ rises initially but rapidly returns to normal level. By contrast, the SR Ca²⁺ load rises when pH starts to fall, and the increased SR load is sustained during the period of acidosis. Thus inhibition of the SR release channels appears to have only a transient effect on cytosolic Ca²⁺. SR Ca²⁺ content increases, which closely compensates for the reduced open probability of the release channels.

View larger version (8K): [in this window] [in a new window]   FIGURE 7  Effect of pH-dependent inhibition of RYRs on intracellular Ca2+ transient (a and b), and SR Ca2+ content (c and d), with 15% (a and c), and 30% (b and d), extracellular CO2. SR Ca2+ content is calculated according to [Ca]sr = (Vnsr[Ca]nsr + Vjsr[Ca]jsr)/Vsr. (e) Intracellular Ca2+ transients (at 150 s, solid lines), with zeroed diastolic level and unit-normalized amplitude, allowing direct comparison of the recovery timescales with the normal transient (at 50 s, dotted line). Increasing CO2 is indicated by the arrow.

Inhibition of SR Ca²⁺ uptake
In simulations for which the only pH-dependence included is inhibition of Ca²⁺ uptake into the SR, using Eq. 2, the opposite effect to inhibition of the release channels is seen. Peak systolic Ca²⁺ rises at the onset of acidosis, before recovery to normal levels, accompanied by a dramatic decrease in SR Ca²⁺ load, as shown in Fig. 8, a–d. After recovery from this initial spike in cytosolic Ca²⁺, diastolic Ca²⁺ remains raised compared to normal, also recovering to control on release of the acidosis. These results show that in the absence of changes to sarcolemmal Ca²⁺ fluxes, the inhibition of SR Ca²⁺ uptake reduces SR Ca²⁺ content until near-normal cytosolic Ca²⁺ is achieved.

View larger version (9K): [in this window] [in a new window]   FIGURE 8  Effect of pH-dependent inhibition of SERCA on intracellular Ca2+ transients and SR Ca2+ content with 15% (a and c) and 30% CO2 (b and d). Normalized intracellular Ca2+ transients are shown in e. Details as for Fig. 7.

We performed simulations that combine inhibition of SR Ca²⁺ uptake and release to simulate experiments done by Kentish and Xiang (6) in permeabilized trabeculae. In these experiments the SR is loaded under constant intracellular Ca²⁺, at different pH values. SR load was estimated by measuring the caffeine-induced Ca²⁺ release. The effect on the Ca²⁺ transient was measured by triggering Ca²⁺-induced Ca²⁺ release from the SR using flash photolysis. We simulated the permeabilized membrane by uncoupling [Ca²⁺]_i from all sarcolemmal Ca²⁺ currents, and introducing a flux to maintain intracellular Ca²⁺,

(20)

where we set the extracellular Ca²⁺ to be the steady-state resting intracellular calcium concentration [Ca²⁺]_e = 4.7 x 10^–5 mM, and the time constant for calcium transfer into the permeabilized cell, _bal = 18 ms. To simulate the Kentish and Xiang experiments, we allowed the SR to load for 3 min, by which time a steady state was established, and then triggered Ca²⁺-induced Ca²⁺ release using a calcium flux of 0.00015 mM/ms for 5 ms. Results for normalized SR load and t_1/2 for the decay of the calcium transient are shown in Fig. 9.

View larger version (3K): [in this window] [in a new window]   FIGURE 9  Normalized SR Ca2+ load (a) and t1/2 for fall of Ca2+ transient (b) in permeabilized myocytes as a function of pH. (•) Experimental data from Kentish and Xiang (6) and (+) simulation results. SR Ca2+ load is measured after loading for 3 min at resting Ca2+ concentration, t1/2 is measured for the Ca2+ transient after CICR. As Kentish and Xiang did not directly measure SR calcium load, we have assumed that releasable SR calcium concentration is proportional to the initial increase in [Ca2+]i on application of caffeine, calculated from peak [Ca2+]i and t1/2 for rise, from Kentish and Xiang (their Fig. 3 B).

View larger version (10K): [in this window] [in a new window]   FIGURE 10  Effect of pH-dependent inhibition of NCX on Ca2+ transients and SR Ca2+ content with 15% (a and c) and 30% CO2 (b and d). Normalized intracellular Ca2+ transients are shown in e. Details as for Fig. 7.

During acidosis, systolic Ca²⁺ is much higher than normal and the increase in peak Ca²⁺ is greater than the rise in diastolic Ca²⁺; however, the effect on the normalized Ca²⁺ transients shown in Fig. 10 e is that recovery is slightly more rapid.

Competitive binding of protons at TnC Ca²⁺ sites
The effect of the pH-dependence for Ca²⁺ binding to Troponin-C was included using the pH-sensitive apparent binding coefficient, Eq. 7. Although TnC is one of the major buffers for Ca²⁺ in the cytosol, we found that competitive binding of protons to the low-affinity Ca²⁺ binding sites has minimal effect on the Ca²⁺ transient profile, shown in Fig. 11 e, and has much less pronounced effects on intracellular Ca²⁺ during acidosis, Fig. 11, a–d, although this is still highly important for excitation-contraction coupling due to the modified Ca²⁺-tension curve, as shown in Fig. 4. As would be expected for a reduction in buffering power, competitive binding at the Ca²⁺ sites raises systolic Ca²⁺ and lowers diastolic Ca²⁺ (showing that the cell is less able to resist changes in Ca²⁺ due to reduced buffering).

View larger version (8K): [in this window] [in a new window]   FIGURE 11  Effect of pH-dependent reduced affinity of Ca2+ binding to TnC on intracellular Ca2+ transients and SR Ca2+ content with 15% (a and c) and 30% CO2 (b and d) Normalized intracellular Ca2+ transients are shown in e. Details as for Fig. 7.

View larger version (11K): [in this window] [in a new window]   FIGURE 12  Effect of respiratory acidosis on intracellular pH (a), [] (b), [Na+] (c), and [K+] (d). Extracellular CO2 is increased from 5% (control) to 15% and 30% at 1 min, and returned to control after 5 min of acidosis. The results of two independent simulations are shown: incorporating sarcolemmal pH transporters with no other pH-dependent changes (dotted lines), and the full dynamic model (solid lines). pH and curves are indistinguishable for these two simulations.

Na⁺ influx coupled to H⁺ efflux, in addition to the Na⁺ that comes into the cell during the upstroke of the action potential, must be removed from the cytosol. Increasing Na⁺ upregulates the Na⁺-pump, which transports 3 Na⁺ out of the cell and 2 K⁺ in to the cell. Thus, the increased Na⁺ efflux is coupled to an increased K⁺ influx, raising intracellular K⁺ as shown (dotted lines) in Fig. 12 d. When extracellular CO₂ is stepped back to control, pH quickly recovers and in fact overshoots control pH to more alkaline levels in each case. As pH recovers, acid efflux, and hence coupled Na⁺ influx, falls and [Na⁺]_i starts to recover. Intracellular K⁺ continues to rise, however, as the accumulated Na⁺ is removed by the Na⁺-pump. [K⁺]_i starts to fall only after Na⁺ has recovered to near-control levels. It is worthy of note that the removal of extracellular CO₂ produces an overshoot in pH to more alkaline values, shown in Fig. 12 a, via the loading mechanism proposed by Boron and Weer (33). High membrane permeability to CO₂ means this removal quickly produces an equivalent drop in intracellular CO₂ which shifts the equilibrium of Eq. 11 to the left. Membrane impermeable bicarbonate ions that have been transported into the cell by NBC during acidosis now bind to protons producing the increase in pH.

The effects of rising intracellular Na⁺ on intracellular Ca²⁺ are shown in Fig. 13. For these simulations the rising Na⁺ is the only directly induced effect. These simulations show that reduced Ca²⁺ efflux on NCX due to rising Na⁺ leads to an increase of systolic Ca²⁺ and a slight rise of diastolic Ca²⁺, accompanied by rising SR Ca²⁺ load.

View larger version (9K): [in this window] [in a new window]   FIGURE 13  Effects of sarcolemmal acid-equivalent transport (and consequent Na+ influx) on intracellular Ca2+ transients and SR Ca2+ content with 15% (a and c) and 30% CO2 (b and d). Normalized intracellular Ca2+ transients are shown in e. Details as for Fig. 7.

View larger version (12K): [in this window] [in a new window]   FIGURE 14  Effects of acidosis on Ca2+ transients, SR Ca2+ content, and tension in the full dynamic model with 15% (a, c, and e) and 30% CO2 (b, d, and f). Normalized intracellular Ca2+ transients are shown in g. Details as for Fig. 7.

The Ca²⁺ rebound after the return to control CO₂ is somewhat paradoxical, given that, in these simulations, the total intracellular Ca²⁺ content (which is dominated by SR Ca²⁺) actually falls during acidosis (Fig. 14, c and d). The cause of the overload is the slow reaccumulation of Ca²⁺ during acidosis, which is shown by rising SR Ca²⁺ in Fig. 14 d. This gradual loading of the cell, due to the secondary reduction of Ca²⁺ efflux as Na⁺ accumulates, means that the cell has a higher Ca²⁺ content just before release of inhibition, at the return of CO₂ to control, than it did after the initial rapid change in Ca²⁺ at the onset of acidosis. Furthermore, recovery from the overload to control Ca²⁺ levels after release of acidosis takes longer than would normally be the case, because this extra Ca²⁺ must be removed while Na⁺ is still elevated. This mechanism suggests that the Ca²⁺ rebound will be greater if acidosis is maintained for a longer period (giving more time for Ca²⁺ accumulation), and this predicted increase is demonstrated in Fig. 15, in which acidosis is maintained for 10 min, twice as long as in the previous simulations.

View larger version (5K): [in this window] [in a new window]   FIGURE 15  The effect of a longer period of acidosis on Ca2+ transients (a) and SR Ca2+ content (b) with 30% CO2. Extracellular CO2 is increased from 5% (control) to 30% after 1 min, and returned to control after 10 min of acidosis.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Our modeling study enables us to dissect the effects of acidosis on excitation-contraction coupling, as well as the role of the pH-regulatory mechanisms in the cell. It is noteworthy that for each of the pH-response curves with which we have characterized the pH-dependence of the steps in excitation-contraction coupling, normal intracellular pH is on the steep part, where the sensitivity to pH changes is highest. This is an additional indication that the myocyte is highly sensitive to pH, in addition to the finding by Leem et al. (35) that the sarcolemmal proton transporters under normal conditions operate in a permissive range, in which all transporters are active at low levels to set the normal steady-state pH.

Excitation-contraction coupling during acidosis
The simulations suggest that the most significant sustained effects on cytosolic Ca²⁺ during acidosis are due to elevated [Na⁺]_i and pH-dependent inhibition of NCX, both contributing to rising diastolic and peak systolic Ca²⁺. Some earlier experimental studies reported no change or even reduced cytosolic Ca²⁺ levels at low pH. From our simulations, the only mechanism that contributes a reduction of cytosolic Ca²⁺ is inhibition of the sarcoplasmic reticulum Ca²⁺ release channels (RyRs), and this gave only a transient drop in systolic Ca²⁺ levels. Each of the other acidotic changes increases cytosolic Ca²⁺. This response to RyR inhibition appears to be consistent with the data from Choi et al. (5), who reported a drop in cytosolic Ca²⁺ during acidosis. They observed that the recovery to control levels of cytosolic Ca²⁺, after an immediate decrease at the onset of acidosis, was accompanied by an increase in SR load in voltage-clamped rat ventricular myocytes with inhibited sarcolemmal proton transporters (NHE and NBC). Similarly, when pH was returned to normal, systolic Ca²⁺ increased and subsequently recovered to control as the SR load returned to normal.

Given the significance of elevated [Na⁺]_i, it may be important to note that recent experimental evidence (45) questions the previously accepted 1:1 electroneutral stoichiometry for Guinea-pig myocytes (35), as assumed in our model. This in turn has important implications for the relative activities of NBC and NHE. Specifically, if NBC imports more than one bicarbonate ion per sodium ion it will, in effect, be sodium-sparing relative to NHE. Another interesting finding is that the Na⁺ influx on NHE during acidosis generates a greater influx of K⁺ due to increased activity of the Na⁺-pump. During ischemia this increased influx of K⁺ might usefully act against the buildup of extracellular K⁺ that is associated with arrhythmia.

SR Ca²⁺ load during acidosis
Our study indicates that the major influences on SR Ca²⁺ load during acidosis are inhibition of Ca²⁺ uptake and inhibition of NCX, which have opposing effects on SR calcium. Therefore, the overall effect on SR calcium observed in the whole cell (in the fully coupled model) during acidosis depends on the balance between mechanisms raising SR Ca²⁺ (reduction of Ca²⁺ efflux through the sarcolemma, such as NCX and to a lesser extent rising intracellular Na⁺) and those reducing the Ca²⁺ load (primarily the inhibition of the SR Ca²⁺-ATPase).

Reports on SR calcium content during acidosis in the literature are mixed. Kentish and Xiang (6), as well as several earlier reports, found that SR Ca²⁺ load decreases. Experiments on caffeine-induced calcium release from the SR at pH 6.5 showed that releasable SR Ca²⁺ was down to 40% of pH 7.1 levels. However, the majority of the other reports in the literature found that SR calcium content increases (7), but fractional release decreases during acidosis (4). It seems clear that these differences reflect the various experimental protocols and the conditions in which the measurements were made. One possibility is that experimental data obtained in nonphysiological conditions, such as in purified cell extracts, may not reflect the normal response of the intact cell, due to alterations to, or removal of, accessory or regulatory pathways in the cell. For example, although many studies have reported direct inhibition of the SR Ca²⁺-pump at low pH or during acidosis (2,12,21,23), Choi et al. (5) inferred no significant change to SERCA flux from the lack of change to the rate of decline of individual Ca²⁺ transients. Thus one possible explanation for our finding that the experimentally reported level of inhibition of the SR calcium pump leads to a substantial decrease in SR Ca²⁺ in the whole-cell response, rather than the reported increase, is that these data do not include a compensatory mechanism by which the uptake by the pump is substantially maintained. In particular, the data we have used to parameterize the inhibition of Ca²⁺-ATPase were measured in purified SR vesicles.

Several studies have found that CaMKII-related activation of SERCA may, at least partly, compensate for the direct inhibition of the pump by protons. Komukai et al. (29) showed that, in the presence of the CaMKII inhibitor KN-93, the caffeine-induced release of Ca²⁺ from the SR was lower than control during acidosis. The proposed mechanism is that elevated intracellular Ca²⁺ causes phosphorylation of the SR membrane-bound regulatory protein phospholamban by CaMKII, which enhances pump function (29,46). This could reconcile the disparate experimental data on SR Ca²⁺ load during acidosis, as is demonstrated by the model. In Fig. 16 the effects of acidosis with zero change to SR Ca²⁺ uptake are shown—the extreme case where there is no net effect on the SR Ca²⁺-pump. In this case SR Ca²⁺ rises, as would be expected, consistent with current experimental findings. This is one possible explanation for the discrepancy, at least.

View larger version (5K): [in this window] [in a new window]   FIGURE 16  Acidosis without inhibition of SERCA: simulating effects of CaMKII on intracellular Ca2+ (a) and SR Ca2+ content (b) during respiratory acidosis with 30% CO2. (See Fig. 14, b and d, for comparison.)

Inhibition of sodium-hydrogen exchange during acidosis
Harrison et al. (7) found that the slow partial recovery of contractility was blocked when NHE (and hence Na⁺ rise) was blocked by the selective NHE inhibitor amiloride. They also found that complete inhibition of SR release (by ryanodine) blocked the recovery of the twitch but did not affect the Na⁺ rise. Thus we can infer that the effect of elevated Na⁺ is mediated by increasing diastolic Ca²⁺, consistent with the model results. Therefore the slow recovery of p