Modeling Ca²⁺ Dynamics of Mouse Cardiac Cells Points to a Critical Role of SERCA's Affinity for Ca²⁺

Abstract

The SERCA2a isoform of the sarco/endoplasmic reticulum Ca²⁺ pumps is specifically expressed in the heart, whereas SERCA2b is the ubiquitously expressed variant. It has been shown previously that replacement of SERCA2a by SERCA2b in mice (SERCA2^b/b mice) results in only a moderate functional impairment, whereas SERCA activity is decreased by a 40% lower SERCA protein expression and by increased inhibition by phospholamban. To find out whether the documented kinetic differences in SERCA2b relative to SERCA2a (i.e., a twofold higher apparent Ca²⁺ affinity, but twofold lower maximal turnover rate) can explain these compensatory changes, we simulated Ca²⁺ dynamics in mouse ventricular myocytes. The model shows that the relative Ca²⁺ transport capacity of SERCA2a and SERCA2b depends on the SERCA concentration. The simulations point to a dominant effect of SERCA2b's higher Ca²⁺ affinity over its lower maximal turnover rate. The results suggest that increased systolic and decreased diastolic Ca²⁺ levels in unstimulated conditions could contribute to the downregulation of SERCA in SERCA2^b/b mice. In stress conditions, Ca²⁺ handling is less efficient by SERCA2b than by SERCA2a, which might contribute to the observed hypertrophy in SERCA2^b/b mice. Altogether, SERCA2a might be a better compromise between performance in basal conditions and performance during β-adrenergic stress.

Introduction

The transient release of Ca²⁺ from the sarcoplasmic reticulum (SR) couples activation to contraction in skeletal and cardiac muscle. The state of filling of the SR with Ca²⁺ is thus an important factor in determining contractile strength. Ca²⁺ loading of the SR is catalyzed by SERCA Ca²⁺-transport ATPases, which pump Ca²⁺ back into the SR after its release, thereby contributing for ∼50–90% to the termination of the Ca²⁺ transient in mammalian ventricular myocytes (1). In addition, SERCA-mediated Ca²⁺ transport plays a central role in the β-adrenergic regulation of the heart via interaction with the accessory membrane protein phospholamban (2). Phosphorylation of phospholamban during β-adrenergic stress releases its inhibitory interaction, resulting in faster relaxation, augmented loading of the SR with Ca²⁺, and stronger contraction. Alterations in SERCA's Ca²⁺ pumping activity also play a central role in heart pathology. A decline in the Ca²⁺ load of the SR caused by decreased affinity of SERCA for Ca²⁺ or by decreased SERCA levels is often associated with heart failure, whereas Ca²⁺ overload of the SR can cause arrhythmia (3–6).

Although in the heart, slow skeletal muscle, and to some extent smooth muscle, express the SERCA2a splice variant, all other cell types predominantly make use of SERCA2b, which is considered the housekeeping isoform. This differential distribution suggests that SERCA2a is better adapted to function in cells like striated muscle cells, which generate faster Ca²⁺ transients than most other cell types. This raises the question of the functional link between the characteristics of cellular Ca²⁺ dynamics and those of the reticular Ca²⁺ pumps. SERCA2b differs functionally from SERCA2a in its twofold higher affinity for cytosolic Ca²⁺ and its approximately twofold lower maximal turnover rate (7,8). The physiological meaning of these characteristics was explored in the SERCA2^b/b mouse model. In these genetically modified mice, the formation of the SERCA2a splice variant is prevented and splicing to the default SERCA2b form is favored. A remarkable finding is that these interventions result in a drop of the SERCA levels to ∼60% of wild-type. Moreover, expression of the SERCA inhibitory protein phospholamban is increased, and phosphorylation of phospholamban, which removes the protein's inhibitory effect on SERCA, is decreased (9). Although the animals develop cardiac hypertrophy, Ca²⁺ transients in isolated ventricular cells appear normal except when challenged with higher Ca²⁺ loads (10). Altogether, this phenotype suggests that in the mouse heart, the higher affinity of SERCA2b for Ca²⁺ represents a more critical parameter than its lower maximal speed. An increased activity of the SERCA pump below 0.1 μM concentration of cytosolic Ca²⁺ is apparently not well tolerated in the heart, resulting in downregulation of SERCA expression and upregulation of inhibitory phospholamban. This interpretation is further supported by various crosses of the SERCA2^b/b mice with SERCA2b transgenes. Inducing a further increase of the Ca²⁺ affinity by crossing with phospholamban knockout animals results in further downregulation of the SERCA2b level to about one-third of the wild-type without severely impacting basal Ca²⁺ handling (11). Conversely, enforced expression of SERCA2b obtained in crosses with SERCA2b transgenes was compensated by an increased inhibition by phospholamban (12).

To better understand the consequences of the enforced SERCA2a-to-SERCA2b switch in mouse cardiac myocytes, we designed a computer model of the intervention that takes into consideration the presently known kinetic differences between the two isoforms. This model includes information about differences in rate constants of specific substeps of the SERCA2 catalytic cycle.

Methods

Simulation of SERCA2a and SERCA2b activity

The different kinetic properties of Ca²⁺ transport by SERCA2a and SERCA2b have been well documented (7,8,11,13). SERCA2b differs from SERCA2a in its nearly twofold lower maximal turnover rate, its approximately twofold higher affinity for cytosolic Ca²⁺ and the lower sensitivity of its maximal turnover rate to inhibition by luminal Ca²⁺ ([Ca²⁺]_SR). In addition, Dode et al. (7) have identified different kinetics of several specific partial reaction steps. Using the seven-step Post-Albers-type schema (Fig. 1 A; the multistep scheme), the changes reside in steps 3, 4, and 7, which were modified accordingly in the SERCA2b scheme (Table S1 in the Supporting Material). Fig. 1 B shows the Ca²⁺ dependence of the steady-state turnover rate of SERCA2a and SERCA2b, with [Ca²⁺]_SR set equal to [Ca²⁺]_cyt. To obtain a sufficient shift of the Ca²⁺ affinity, r₂ was assigned a smaller value also, in accordance with recent structural data suggesting a stabilization of E1Ca or E1 or both (13). These documented modifications represent a stronger decrease of reverse compared to forward rate constants, predicting that SERCA2b is able to build a steeper Ca²⁺ gradient over the SR membrane (Fig. S1). However, the kinetic scheme predicts that at lower [Ca²⁺]_SR that moderately decrease SERCA activity, SERCA2b is more easily inhibited due to the lower value of k₇ (Fig. S2). This property makes it more difficult to model the experimental data on the SERCA2^b/b mouse, which suggest a higher over-all Ca²⁺ transport rate for SERCA2b. It is possible that other unidentified differences exist in SERCA2b at the level of the luminal Ca²⁺-binding sites that alleviate this higher sensitivity to inhibition by luminal Ca²⁺, but such hypothetical modifications were not tested.

Figure 1.

Reaction scheme of the SERCA pump and its equilibrium behavior. (A) Seven-step Post-Albers-type reaction scheme of the SERCA pump. (B) Ca²⁺-activation curves of SERCA2a and SERCA2b obtained from the seven-step SERCA model using the rate constants from Table S1. S2a, SERCA2a; S2b, SERCA2b. (C) Dependence of the amount of SERCA-bound Ca²⁺ on Ca²⁺ concentration.

In addition to the seven-step Post-Albers-type cycle, we also used a single equation to represent SERCA activity (denoted as the one-step scheme) that captures the transport rate of the multistep scheme under conditions of constant [Ca²⁺]_cyt and nonjunctional SR calcium concentration ([Ca²⁺]_NSR) (see Supporting Material).

In ventricular myocytes, the SERCA level differs between animal species and correlates with the heart rate in mammals (1). In the faster-beating heart of small animals like rats (∼350 beats/min), it can reach up to 50 μmol/kg (14). In mice (600 beats/min), the SERCA level required to account for the relaxation rate is even higher. In our models, and with a V_max of ∼30 s⁻¹, a SERCA2a concentration of several tens of μM/liter cell volume was required to obtain proper relaxation rates (see Results).

Whole-cell Ca²⁺ dynamics model with a homogeneous cytosolic compartment (cell model)

This simple model considers two cellular compartments, the SR, with a Ca²⁺ pump and a Ca²⁺-release channel, and the cytosol (Fig. 2 A). SR and cytosol are both treated as homogeneous. Ca²⁺ binding to calsequestrin in the SR is instantaneous. Ca²⁺ binding to troponin C (TRPN) is described by

$$\frac{d\left[TRPNCa\right]}{dt}=\left[TRP{N}_{total}-TRPNCa\right]\times {\left[{\text{Ca}}^{2+}\right]}_{\text{cyt}}\times k{t}_{on}-\left[TRPNCa\right]\times k{t}_{off}.$$ (1)

Two different values were used for the off-rate constant of the Ca-troponin complex to obtain sufficiently strong binding to troponin during systole (kt_offsys, 25 s⁻¹) and sufficiently fast unbinding during diastole (kt_offdia, 50 s⁻¹). An increase of kt_off during the shortening phase of the heartbeat is in accordance with physiological data and is known as shortening deactivation (see Edman (15) and Hinken and Solaro (16) for review). The transitions between both kt_off values occurred linearly with time, between 20 and 60 ms (kt_offsys to kt_offdia), and between 60 ms and the end of the beat (kt_offdia to kt_offsys).

Figure 2.

Outline of the models used in the simulations. (A) The cell model. The cytosol is considered as a homogeneous compartment. Since this model is used only to simulate one isolated Ca²⁺ transient, Ca²⁺ influx and efflux are omitted. (B) Geometry of a half-sarcomere in the sarcomere model (not to scale). The region between the Z- and M-disks is divided into five concentric compartments of 0.1-μm thickness surrounded by a contractile filament-free sheet of 0.25 μm. The longitudinal direction is divided into 10 compartments of 0.1 μm each, all of which contain calmodulin and ATP and seven of which contain troponin C (shaded region). Ca²⁺ is released from the JSR into the two peripheral volumes closest to the Z-disk. SERCAs translocate Ca²⁺ from the outer compartments of segments 3–10 into the nonjunctional SR (NSR). Ca²⁺ efflux occurs from all peripheral compartments.

Since this model is only used to illustrate the implications of the SERCA model on Ca²⁺ dynamics during a single beat, Ca²⁺ influx and efflux are omitted. Parameters are given in Table S2.

The rate of change of the Ca²⁺ concentration of the cytosolic compartment due to activity of the SERCA multistep scheme is calculated according to

$$\frac{d{\left[{\text{Ca}}^{+}\right]}_{\text{cyt}}}{dt}=-\left(\left[E1\right]\times {\left[{\text{Ca}}^{2+}\right]}_{\text{cyt}}\times k_2+\left[E1Ca\right]\times {\left[{\text{Ca}}^{2+}\right]}_{\text{cyt}}\times k_3-\left[E1Ca\right]\times r_2-\left[E1P2Ca\right]\times r_3\right).$$ (2)

The rate of change of the free Ca²⁺ concentration in the SR induced by the SERCA multistep scheme is represented by

$$\frac{d{\left[\text{Ca}\right]}_{\text{SR}}}{dt}=\frac{\left(-\left[E2P\right]\times {\left[{\text{Ca}}^{2+}\right]}_{\text{SR}}\times r_6-\left[E2PCa\right]\times {\left[{\text{Ca}}^{2+}\right]}_{\text{SR}}\times r_5+\left[E2P2Ca\right]\times k_5+\left[E2PCa\right]\times k_6\right)\times \frac{Vo{l}_{\text{cyt}}}{Vo{l}_{\text{SR}}}}{1+\frac{CSQN\max \ast CSQN{K}_d}{{\left(1+\frac{CSQN{K}_{0.5}}{{\left[{\text{Ca}}^{2+}\right]}_{\text{SR}}}\right)}^2\times {\left[{\text{Ca}}^{2+}\right]}_{\text{SR}}}}.$$ (3)

CSQNmax represents the maximum Ca²⁺-binding capacity of the SR and CSQNK_d the dissociation constant for luminal Ca²⁺ binding.

When using the one-step SERCA representation, Eq. 2 and the Ca²⁺ flux part of Eq. 3 were replaced by the appropriate relations, as described in the previous section.

Changes of Ca²⁺ concentrations due to Ca²⁺ release from the SR are given by

$$\frac{d{\left[{\text{Ca}}^{2+}\right]}_{\text{SR}}}{dt}=-k_{release}\left({\left[\text{Ca}\right]}_{\text{JSR}}-{\left[\text{Ca}\right]}_{\text{cyt}}\right)=\frac{d{\left[{\text{Ca}}^{2+}\right]}_{\text{cyt}}}{dt}\frac{Vo{l}_{\text{SR}}}{Vo{l}_{\text{cyt}}}.$$ (4)

The rate constant k_release depends on time. k_release rises linearly with time during 5 ms, from zero to a peak value (k_relMax) of 180 s⁻¹, and then decreases linearly to zero, also in 5 ms.

The compartmentalized sarcomere model (sarcomere model)

The geometry and position of the various Ca²⁺ fluxes are indicated in Fig. 2 B. The SR is considered continuous around the myofibril, preserving symmetry and reducing computation time (17). Parameter values are given in Table S3. Parameters and computations are the same as for the cell model, except for the additional elements given below. The program is run until a stable state is reached, defined as a <10⁻⁴% change of the maximal level of troponin-bound Ca²⁺ between two consecutive beats.

To obtain a reasonable fast rate of Ca²⁺ diffusion, binding of Ca²⁺ to ATP and simultaneous diffusion of Ca²⁺-ATP were included (18). The flux due to diffusion between two compartments is calculated from the diffusion coefficient (D), the contact area (A), the concentration difference (ΔC) and the distance separating the centers of the compartments (Δx) by a numerical approximation of Fick's law:

$$Flux=-A\times D\times \Delta C/\Delta x.$$ (5)

Ca²⁺ influx lasts for the first 10 ms of the beat, is constant with time, and is inhibited by the calcium concentration in the junctional SR ([Ca²⁺]_JSR) according to

$$Influx=\frac{InflMax}{1+{\left(\frac{{\left[{\text{Ca}}^{2+}\right]}_{\text{JSR}}}{0.5}\right)}^{1.5}}.$$ (6)

(concentrations in mM). Maximal Ca²⁺ influx, InflMax, is set at a value such that it accounts for ∼10% of the total Ca²⁺ entering the sarcomere during regular pacing at 9 Hz in unstimulated conditions, as observed in cardiac cells of small mammals (1). In addition to this activating Ca²⁺ influx, there is a continuous background influx in longitudinal segments 1–7 amounting to 7.2 μM s⁻¹ in total.

The rate of Ca²⁺ efflux depends on the free Ca²⁺ concentration in the superficial subcompartment S_x ([Ca]_Sx) according to

$$\frac{d{\left[Ca\right]}_{Sx}}{dt}=-\frac{{\left(EV\right)}_{\max }}{1+\left(\frac{{\left(EK\right)}_{0.5}}{{\left[\text{Ca}\right]}_{cSx}}\right)}.$$ (7)

Since Ca²⁺ efflux mainly occurs via the Na⁺/Ca²⁺ exchanger, which starts to operate in the forward mode only at a sufficiently polarized membrane potential, Ca²⁺ efflux was switched off during the initial period of each beat, set at 12 ms.

For convenience, an apparent rate constant of Ca²⁺ release was used that applies to the change of the total JSR Ca²⁺ content instead of [Ca²⁺]_JSR. This apparent rate constant, k_release, depends on time and increases with increasing [Ca²⁺]_JSR to simulate the potentiating effect of SR Ca²⁺ load on the release (19). The time-dependent component (k_release,time) rises linearly with time during 5 ms from zero to a peak value (k_relMax) of 6600 L s⁻¹ and then decreases linearly to zero, also in 5 ms. k_relMax corresponds to a rate constant of 450 s⁻¹ at a [Ca²⁺]_JSR of 0.5 mM. k_release is given by (concentrations in mM)

$$k_{release}=k_{release,time}\frac{1}{\left(1+\frac{0.5}{{\left[\text{Ca}\right]}_{\text{JSR}}}\right)},$$ (8)

The maximum rate constant of Ca²⁺ leak from the JSR and NSR was set at 0.33 L s⁻¹ and dependent on [Ca²⁺]_JSR as in Eq. 8.

The change of the Ca²⁺ concentration in the peripheral compartments and in the NSR due to SERCA activity was calculated either as a single-state SERCA representation or as a multistate SERCA scheme.

Transfer of Ca²⁺ between the JSR and NSR is governed by the rate constant k_trans:

$$\frac{d{\left[\text{Ca}\right]}_{\text{JSR}}}{dt}=-k_{trans}\left({\left[\text{Ca}\right]}_{\text{JSR}}-{\left[\text{Ca}\right]}_{\text{NSR}}\right)=-\frac{d{\left[\text{Ca}\right]}_{\text{NSR}}}{dt}\frac{Vo{l}_{\text{JSR}}}{Vo{l}_{\text{NSR}}}.$$ (9)

The models were programmed in Delphi (Borland Software, Austin, TX) using the basic Euler method and run with constant time steps of 0.001 ms. To exclude possible errors arising from the discreteness of the time steps that may artifactually induce differences between models incorporating SERCA2a or SERCA2b, results were compared between runs with and runs without bookkeeping of total Ca²⁺ of the system, based on the integrated amount of Ca²⁺ influx and Ca²⁺ efflux. When the program was run with regular pacing until steady state (typically 100–300 beats), diastolic and peak systolic levels of troponin-bound Ca²⁺ differed at most by ∼0.03%. These small values demonstrate that the effect of various SERCA kinetic schemes cannot be explained by the accumulation of computing errors.

Results

The effect of various SERCA representations on myofilament activation during a single beat in the cell model

Ca²⁺ binds not only to troponin C, determining the degree of myofilament contraction, but also to SERCA before its complete translocation across the SR membrane. Thus, troponin C and SERCA compete for Ca²⁺ binding, influencing the amount of Ca²⁺ available for contraction. Multistate schemes take this into account and predict a faster rate of Ca²⁺ removal from the cytosol in the early phase of the Ca²⁺ transient than does the one-step Hill-type equation. Consequently, in such a model, a smaller fraction of all Ca²⁺ that enters the sarcomere will bind to the contractile filaments, predicting a reduced contraction. The implications for a single isolated Ca²⁺ transient, starting from the same initial conditions ([Ca²⁺]_cyt = 0.08 μM, [Ca²⁺]_SR = 0.5 mM), are shown in Fig. 3 for a model that considers the cytosol as a homogeneous compartment (cell model). The amount of Ca²⁺ release was adjusted such that it caused a peak level of ∼60% average saturation of troponin at a SERCA concentration of 40 μM using the SERCA2a multistep scheme. This value corresponds to 26 μM troponin-bound Ca²⁺ above the diastolic level (assuming 0.1 μM free Ca²⁺), close to the accepted value of ∼27 μM for rabbit myocytes (3). With the one-step SERCA2a models, a much higher peak level of troponin-bound Ca²⁺ is reached (42.2 μM compared to 28.2 μM (Table 1)). The calculated amount of Ca²⁺ that rapidly binds to SERCA also differs between SERCA2a and SERCA2b (Fig. 3 and Table 1). For example, at peak levels of calcium saturation, 48.7% of all Ca²⁺ released is bound to SERCA2a (multistep) compared to 43.3% for SERCA2b. This difference can be explained by differences in kinetics of Ca²⁺ binding during the rising phase of the Ca²⁺ transient and by the difference in steady-state Ca²⁺ affinity: as is clear from Fig. 1 C, additional Ca²⁺ binding by SERCA2b above that by SERCA2a is higher at low Ca²⁺ levels than at high concentrations, leaving less room for extra Ca²⁺ binding during systole.

Figure 3.

Simulation of a single beat in the cell model. Various SERCA schemes result in different peak values of troponin-bound Ca²⁺ transients.

Table 1.

Systolic Ca²⁺ pools (one single beat)

	Multistep		One-step
	S2a	S2b	S2a	S2b
ΔPeak Ca-troponin (μM)
Cell model	28.2	31.1	42.2	45.0
Sarcomere model	27.6	28.8	35.0	37.4
ΔPeak Ca-SERCA (μM)
Cell model	26.8	23.8
Sarcomere model	19.8	18.4
SERCA-bound Ca, % of total
Cell model	48.7	43.3
Sarcomere model	41.8	39.0

Distribution of bound Ca²⁺ over troponin and SERCA at the peak systolic level during a single isolated beat starting from identical initial conditions ([Ca²⁺]_cyt = 0.08 μM, [Ca²⁺]_SR = 0.5 mM), compared between the cell and sarcomere models and between SERCA2a and SERCA2b. Troponin-bound Ca²⁺ and SERCA-bound Ca²⁺ are represented as the difference between systolic and diastolic levels (ΔPeak) in absolute concentration, and for SERCA-bound Ca²⁺ also as the percentage of total bound Ca²⁺.

The simulations above show that the time course of the changes of [Ca²⁺]_cyt at the level of troponin C relative to that near the SERCA pumps may have implications for the effects of the SERCA2a-to SERCA2b switch.

Ca²⁺ transients during a single beat in the sarcomere model

To more faithfully reproduce the time course of the Ca²⁺ concentration changes near the Ca²⁺ pumps, we used the sarcomere model, which takes into account diffusion delays between the Ca²⁺ release sites, the cytosolic Ca²⁺ buffers, and the SR.

Fig. 4 A shows the temporal and spatial distribution of troponin-bound Ca²⁺ during a single beat in the sarcomere model incorporating SERCA2a. Ca²⁺ is rapidly bound to troponin in the segments close to the Z-disk. In the more central segments of the sarcomere, there is a short delay and the peak level is considerably lower. In cardiac muscle, intrasarcomeric Ca²⁺ gradients can be expected to be higher than in fast skeletal muscle, because in the latter, Ca²⁺ is released at sites located closer to the center of the sarcomere. Significant Ca²⁺ gradients within sarcomeres of cardiac cells have also been observed experimentally (20).

Figure 4.

Examples of the dynamics of a single beat in the sarcomere model. (A) Change of troponin-bound Ca²⁺ in space and time in the presence of SERCA2a. In each segment in the x direction (distance from Z-disk (Fig. 2B)), the concentration of troponin-bound Ca²⁺ was averaged over the five concentric rings subdividing the segment. (B) Time course of troponin-bound Ca²⁺ averaged over the whole sarcomere, using the SERCA multistep or one-step representation. (C) Time course of the luminal Ca²⁺ concentration in the JSR and NSR in the presence of SERCA2a or SERCA2b. (Inset) Initial phase for the SERCA one-step equations. (D) Time course of the change of SERCA-bound Ca²⁺. The dotted line shows Ca²⁺ bound to SERCA2b shifted down to the same level as SERCA2a (solid line) at time zero. (E) Integrated amount of Ca²⁺ removed from the cytosol by various SERCA schemes starting from the initiation of the Ca²⁺ transient at time zero.

Troponin-bound Ca²⁺ of the transient shown in Fig. 4 A averaged over the whole sarcomere is shown in Fig. 4 B (solid line). This transient started from the same initial conditions as the transient in the cell model in the previous section (Fig. 3), and with a similar amplitude. As in the cell model, the peak level of troponin-bound Ca²⁺ in the sarcomere model differs between multistep and one-step SERCA schemes and between SERCA2a and SERCA2b. However, the differences are smaller compared to the cell model (Table 1), which can be explained by a relatively slower rise of Ca²⁺ close to the SERCA pumps. Compared to the cell model, the difference in the peak troponin-bound Ca²⁺ between the SERCA2a multistep and one-step schemes was reduced from 42.2 − 28.2 = 14 to 35 − 27.6 = 7.4 μM. The difference caused by the SERCA2a-to-SERCA2b switch was reduced from 4.9 (33.1 − 28.2 μM) to 1.2 μM (28.8 − 27.6). Also, the fraction of the released Ca²⁺ that rapidly binds to SERCA2a (represented as the multistep scheme) is reduced from 48.7% to 41.8%. The respective values for SERCA2b were 43.3 and 39% (Table 1). Thus, the sarcomere model favors Ca²⁺ binding to troponin by reducing the time of diffusion of Ca²⁺ toward the filaments relative to that toward the SR, which results in less futile Ca²⁺ cycling.

In the initial phase of the Ca²⁺ reuptake, Ca²⁺ rise in the SR lumen is about equally fast for SERCA2a and SERCA2b (Fig. 4 C), which points to the lower V_max of SERCA2b having a less significant role than expected. In the later phase, when [Ca²⁺]_cyt is low, Ca²⁺ transport by SERCA2b is slightly faster due to its higher Ca²⁺ affinity, resulting in an overall higher total Ca²⁺-transport activity. With SERCA2b, a high level of troponin-bound Ca²⁺ is maintained for a longer time, thus prolonging contraction (early phase). However, this prolonged activation occurs with preservation of low diastolic levels, even below control levels (later phase) (Fig. 4 B). This is further illustrated in Fig. 4 E, which shows the time-integrated amount of Ca²⁺ removed from the cytosol, that is, the sum of Ca²⁺ translocated across the SR membrane into the lumen and Ca²⁺ bound to SERCA that is in surplus of the end-diastolic level. Ca²⁺ buffering by the multistep SERCA schemes is visible as the fast rise in the initial phase of the beat, which is slightly faster for SERCA2a than for SERCA2b (see also Fig. 4 D). The curves clearly show the faster Ca²⁺ translocation by SERCA2b in the later phase of the Ca²⁺ transient. This difference becomes more clear with time after the stimulus, resulting in a higher SR Ca²⁺ load in a resting cell (Fig. S3). Thus, these simulations show that in a single beat, Ca²⁺ availability for contraction could be more efficient in the presence of SERCA2b than in the presence of SERCA2a, an unexpected finding.

It should be noted that the differences in the amplitude of the Ca²⁺ transient caused by the SERCA2a-to-SERCA2b switch in the multistep and one-step schemes should be attributed to different, although somewhat related, explanations: the enhanced transient in the presence of SERCA2b is due to the lower V_max in the one-step model, whereas it is mainly caused by the lower Ca²⁺ buffering in the multistep scheme.

Ca²⁺ transients of the sarcomere model during regular pacing

To test whether the previous observations are also valid in conditions of regular pacing, the sarcomere model was run at specific stimulation frequencies till the output was stable. In a first set of simulations, the SERCA concentration was varied (Fig. 5). Changing the SERCA level between 20 and 100 μM has a relatively mild effect, especially on the peak level of troponin-bound Ca²⁺, demonstrating a strong autoregulatory effect. This result can be explained by the observation that decreased Ca²⁺ buffering by the pump compensates for the decreased Ca²⁺ transport. In line with this interpretation, the replacement of SERCA2a by SERCA2b, the latter presenting less Ca²⁺-buffering capacity, causes a higher peak level, and this increase is more pronounced with increasing SERCA concentration.

Figure 5.

Effect of SERCA concentration on peak systolic and diastolic levels of troponin-bound Ca²⁺ at 6- and 8-Hz pacing and for SERCA2a and SERCA2b multistep kinetic schemes.

Transients of troponin-bound Ca²⁺ at 8 Hz pacing and the effect of equimolar replacement of SERCA2a by SERCA2b are shown in Fig. 6 A. As in the simulations of one single transient, the peak amplitude is slightly enhanced by the isoform switch, and the Ca²⁺-bound state of troponin is prolonged. The enhanced amplitude cannot be explained by an increased loading of the SR with Ca²⁺, because [Ca²⁺]_SR is slightly lower with SERCA2b (Fig. 6 B). It also cannot be explained by Ca²⁺ release on top of an elevated end-diastolic Ca²⁺. To the contrary, diastolic Ca²⁺ is significantly decreased (Fig. 6, A and D). The higher peak level is explained by the lower fast Ca²⁺ buffering by SERCA2b, as demonstrated in previous sections. Ca²⁺ transients are higher with the one-step SERCA schemes, but the relative difference between SERCA2a and SERCA2b in peak amplitude is preserved. The prolongation of the duration of the transient is somewhat more pronounced.

Figure 6.

Behavior of the sarcomere model during regular pacing in the presence of SERCA2a or SERCA2b. (A) Time course of the change in troponin-bound Ca²⁺. (B) Time dependence of the free Ca²⁺ concentration in the lumen of the JSR. (C) Peak values of troponin-bound Ca²⁺ during regular pacing at the indicated frequencies until a stable state is achieved. (D) Frequency dependence of end-diastolic [Ca²⁺]_cyt.

Data on the frequency dependency of the SERCA2a to SERCA2b switch at 40 μM SERCA concentration are illustrated in Fig. 6, C and D. As expected, since a lower frequency prolongs the diastolic phase of low [Ca²⁺]_cyt, where SERCA2b is more effective, the relative performance of SERCA2b improves with decreasing frequency. This difference is accounted for by the higher loading state of the SR in the presence of SERCA2b (not shown).

To model cardiac cells of the SERCA2^b/b mouse in which the SERCA2 concentration is reduced to ∼60% of the wild-type level, SERCA2b concentrations of 40 and 24 μM were compared. The peak of the Ca²⁺ transient is only slightly shifted (Fig. 6 C). Diastolic levels of [Ca²⁺]_cyt are lower in the presence of 24 μM SERCA2b at a frequency of 6 Hz or lower, but increase at higher frequencies (Fig. 6 D).

Although at 8 Hz the peak amplitude of troponin-bound Ca²⁺ is slightly enhanced by an equimolar switch from SERCA2a to SERCA2b (Fig. 6, A and C), it should be noted that the pump function of the heart can be expected to be more significantly increased due to lower end-diastolic Ca²⁺ and because of the prolongation of the Ca²⁺-bound state of troponin (Fig. 6 A). The amount of troponin-bound Ca²⁺ integrated over time starting from its peak systolic level till it fell below 20 μM, a value well above diastolic levels (Fig. 6 A), was 9.4% higher in the presence of SERCA2b compared to SERCA2a, predicting a significant impact on contractility.

Simulations in stimulated conditions

Given the finding that SERCA2b, with a lower V_max than SERCA2a, is performing better at basal conditions, it is plausible that the lower maximal activity of SERCA2b only becomes limiting at higher Ca²⁺ concentrations. Indeed, SERCA2b became less effective during stronger activation of the contractile apparatus (Fig. 7). Stimulated conditions were implemented by increasing Ca²⁺ influx by 50% and by using a SERCA multistep model that yields Ca²⁺-activation curves with higher affinity (S2astim and S2bstim (Table S1)), thus mimicking the effect of β-adrenergic stimulation via phosphorylation of L-type Ca²⁺ channels and phospholamban, respectively. Compared to the unstimulated condition at 8 Hz, the peak level of Ca²⁺-bound troponin is increased by 10.6 μM with SERCA2a and 7.3 μM with SERCA2b, resulting in lower systolic levels and increased diastolic levels of Ca²⁺-bound troponin in SERCA2b cells. Lowering SERCA2b to 60% of control further reduces the peak amplitude of Ca²⁺-bound troponin and increases the diastolic level, which is accompanied by an increase of diastolic [Ca²⁺]_cyt from 62 nM (SERCA2a 60 μM, stimulated) to 79 nM (SERCA2b 36 μM, stimulated). This increase could contribute to the observed hypertrophy, whereas the reduced peak amplitude could underlie the impaired physiological stress test (11).

Figure 7.

Ca²⁺ activation of troponin in stimulated conditions, using SERCA schemes S2aStim and S2bStim (Table S1) and a 50% increase of the Ca²⁺ influx.

Discussion

Ca²⁺ buffering by SERCA depends on the isoform and on the simulation model

Compared to a one-step Hill equation, representing SERCA activity by a Post-Albers kinetic scheme introduces several additional degrees of freedom in the choice of parameters, since the rate constants of each partial reaction steps are not firmly established experimentally, especially at body temperature. Thus, it is possible to change the values of rate constants while preserving identical Ca²⁺-activation curves at equilibrium. The use of different sets of rate constants has implications for the extent of fast Ca²⁺ buffering, which in our scheme is moderate because of the displacement of the E1-E2 equilibrium (step 1) toward E2.

The problem of the extensive Ca²⁺ buffering by SERCA has been considered by the Baylor group in their mathematical models of Ca²⁺ transients in sarcomeres of frog and mouse fast-twitch skeletal muscle (21,22). In considering the energetic cost of a large amount of Ca²⁺ bypassing the troponin C Ca²⁺-binding sites, these authors have chosen to incorporate additional states of SERCA1 with delayed Ca²⁺ binding. There is indeed experimental evidence for the existence of SERCA states that are dead-end complexes of Ca²⁺-free intermediates with Mg²⁺ and/or H⁺ (23–25). By choosing a slow transition rate from E1MgH toward the unliganded E1 intermediate, Ca²⁺ binding to SERCA is retarded during a sudden rise of the Ca²⁺ concentration, such as during the rising phase of the Ca²⁺ transient. We have not yet implemented these additional SERCA states for several reasons. First, there is a paucity of kinetic data on the transitions that could be involved, especially for SERCA2. Second, in the mouse heart, the implications of Ca²⁺ buffering by SERCA for the Ca²⁺ signal are expected to be less severe than in fast-twitch skeletal muscle due to the lower cardiac content of SERCA. Third, excessive SERCA1a expression obtained by gene transfer leads to impaired myocyte shortening that is adequately explained by increased Ca²⁺ buffering by SERCA (26), indicating that SERCA-related Ca²⁺ buffering indeed exists. The cost of fast Ca²⁺ binding to SERCA could be offset by buffering of the physiological effects of chronic changes of SERCA activity, for example, by oxidative damage (27–29). If SERCA levels were to respond to changes in cytosolic Ca²⁺, the relatively small alteration of the Ca²⁺ transient with changing SERCA concentrations, at least in the high range of SERCA concentrations, suggests that the SERCA level might be sensitive to subtle signals. However, this outcome is not well supported by observations in mice with decreased SERCA2 levels carrying a null mutation in one copy of the SERCA2 gene (30), which show appreciably reduced Ca²⁺ transients despite compensatory changes in phospholamban phosphorylation and Na⁺/Ca²⁺-exchange activity. This result would better fit with a lower SERCA concentration, which, however, complicates an explanation of the SERCA2^b/b mouse model. On the other hand, rapid cardiac-specific ablation of the SERCA2 gene is initially well tolerated (31).

The difference in pump activity between SERCA2a and SERCA2b depends mainly on the Ca²⁺ affinity

SERCA2a has a twofold-higher catalytic turnover rate than SERCA2b, but only half the Ca²⁺ affinity of SERCA2b. Assuming that kinetic differences in Ca²⁺ transport have prompted the selective expression of SERCA2a over SERCA2b in cardiac cells, it would seem that the faster maximal turnover of SERCA2a is more appropriate for heart function than the higher Ca²⁺ affinity of SERCA2b, i.e., the higher Ca²⁺ affinity of SERCA2b appears unlikely to compensate for its lower turnover rate. However, several findings on the SERCA2^b/b mouse appear to contradict this interpretation. In these gene-modified animals, an apparently compensatory downregulation of cardiac SERCA2 levels and an increased inhibition of phospholamban are seen. Both of these alterations result in less pump activity at low cytosolic Ca²⁺ levels, suggesting that it is rather the high Ca²⁺ affinity of SERCA2b that is not well tolerated. The simulations presented here support this hypothesis for the mouse heart in unstimulated conditions. The better performance of SERCA2b under low workload is seen with both the one-step and multistep SERCA representations. This effect is explained in part by the lower competition of SERCA2b with the binding sites on troponin C, due to the lower extent of fast Ca²⁺ buffering. The contribution of SERCA buffering explains why the relative performance of SERCA2b increases with increasing SERCA concentrations entered into the model (Fig. 5). With our current knowledge about the kinetic properties of SERCA2b and the compensatory changes in the SERCA2^b/b mouse, the downregulation of SERCA in the transgenic animals can best be explained if the normal SERCA level is ∼40 μM or higher. This concentration is well within the range compatible with experimental observations (14).

Limitations of the study

The simulations presented here are the result of a particular choice of values for the model parameters, several of which may have significant quantitative effects. In particular, the value accepted for the degree of saturation of troponin with Ca²⁺ during systole in the unstimulated heart, and the relative affinity of troponin C and SERCA for Ca²⁺, can be expected to be critical parameters affecting the relative over-all transport capacity of the SERCA isoforms. As can be expected intuitively, and also confirmed by the computer simulations (not shown), relative SERCA2b performance will increase with increasing Ca²⁺ affinity of the contractile filaments because of the activation of the contractile apparatus at lower average Ca²⁺ concentrations. All simulations in basal conditions shown in this article apply to the condition of approximately equal Ca²⁺ affinities of SERCA2a and troponin C during systole. Another important constraint is the accepted systolic and diastolic levels of troponin-bound Ca²⁺.

Besides these troponin-related parameters, the concentration of SERCA and the characteristics of the Ca²⁺ efflux determine the results of the model. Because of the large contribution of Ca²⁺ buffering by SERCA and the different buffering characteristics of SERCA2a and SERCA2b, the SERCA concentration codetermines the outcome of the isoform replacement. The SERCA concentration required to sustain a specific amplitude of the Ca²⁺ signal is also determined by the maximal turnover rate. This value is not firmly established, in particular at body temperature. Furthermore, as expected intuitively, the relative effectiveness of SERCA2b increases with increasing rate of Ca²⁺ efflux in the low Ca²⁺ range relative to the higher Ca²⁺ concentrations (data not shown). When more quantitative information on the in vivo parameters is obtained, the simulations and their outcome may have to be adjusted accordingly.

Qualitatively, the better performance of SERCA2b, taking into account the known kinetic characteristics of this isoform, is a robust result of the simulations. It should also be taken into account that in the mutant mice, normal force can be maintained with lower Ca²⁺ transients because of the hypertrophied state of the heart (9). However, the existence of additional, yet unknown differences between SERCA2a and SERCA2b and unidentified compensatory or other changes in the transgenic animals may contribute as well to the downregulation of SERCA in the SERCA2^b/b mouse.

Modeling supports a predominant role for SERCA's Ca²⁺ affinity in basal conditions

Computer modeling has demonstrated that the major effects of the SERCA2a-to-SERCA2b switch result in a slightly higher peak level of the Ca²⁺ transient, a longer period of activation of the filaments, and a lower end-diastolic Ca²⁺ concentration in the unstimulated heart. This effect increases with decreasing contraction strength, as shown by the frequency dependence (Fig. 6, C and D) and by the effects in stimulated conditions (Fig. 7). [Ca²⁺]_cyt is on average lower in basal conditions than in the stimulated heart, shifting the relative importance of the difference in V_max and K_0.5 of SERCA2a and SERCA2b toward the Ca²⁺ affinity. However, since the gain of function of replacing SERCA2a by SERCA2b is not really impressive, it remains a surprising observation that in the SERCA2^b/b mouse, SERCA levels are drastically reduced to ∼60% of wild-type, moreover in combination with an upregulation of inhibitory phospholamban levels. The simulations presented here do not quantitatively account for this strong reduction. At face value, the simulations indicate that a factor contributing to the adjustment of the SERCA levels could be the diastolic Ca²⁺ concentration in basal conditions. Although normal systolic Ca²⁺ saturation of troponin C is slightly lower with SERCA2b at 60% of normal levels (Fig. 6 C), diastolic Ca²⁺ is below normal, at least at frequencies of 6 Hz or lower (Fig. 6 D). In vivo, it is likely that diastolic Ca²⁺ ends up at a higher level because of the additional upregulation of the inhibition of SERCA activity by phospholamban.

In stimulated conditions, the over-all Ca²⁺-transport capacity of SERCA2b relative to that of SERCA2a is strongly reduced. This result is in line with experimental observations on the SERCA2^b/b mouse, which show that the Ca²⁺ uptake by the SR is impaired at higher Ca²⁺ loads only (10). SERCA2a might thus be a better compromise between performance both in basal conditions and during β-adrenergic stress. The model predicts an elevated diastolic Ca²⁺ in SERCA2^b/b myocytes in stressed conditions, which may be a contributing factor to the observed hypertrophy through activation of calcineurin.