Toward an integrative computational model of the Guinea pig cardiac myocyte

Abstract

The local control theory of excitation-contraction (EC) coupling asserts that regulation of calcium (Ca(2+)) release occurs at the nanodomain level, where openings of single L-type Ca(2+) channels (LCCs) trigger openings of small clusters of ryanodine receptors (RyRs) co-localized within the dyad. A consequence of local control is that the whole-cell Ca(2+) transient is a smooth continuous function of influx of Ca(2+) through LCCs. While this so-called graded release property has been known for some time, its functional importance to the integrated behavior of the cardiac ventricular myocyte has not been fully appreciated. We previously formulated a biophysically based model, in which LCCs and RyRs interact via a coarse-grained representation of the dyadic space. The model captures key features of local control using a low-dimensional system of ordinary differential equations. Voltage-dependent gain and graded Ca(2+) release are emergent properties of this model by virtue of the fact that model formulation is closely based on the sub-cellular basis of local control. In this current work, we have incorporated this graded release model into a prior model of guinea pig ventricular myocyte electrophysiology, metabolism, and isometric force production. The resulting integrative model predicts the experimentally observed causal relationship between action potential (AP) shape and timing of Ca(2+) and force transients, a relationship that is not explained by models lacking the graded release property. Model results suggest that even relatively subtle changes in AP morphology that may result, for example, from remodeling of membrane transporter expression in disease or spatial variation in cell properties, may have major impact on the temporal waveform of Ca(2+) transients, thus influencing tissue level electromechanical function.

Keywords: calcium cycling; calcium-induced calcium-release; cardiac myocyte; computational model; excitation-contraction coupling; mitochondrial energetics.

Figure 1

Overview of guinea pig coupled model. (A) Schematic illustration of the model structure. (B) LCC (top) and RyR (bottom) Markov model structures. (C) The 40-state LCC:RyR model representing each possible pairing of LCC and RyR states.

Figure 2

Validation of the L-type Ca²⁺ current. (A) Current-voltage relation for the model (blue) compared with experimental data from Rose et al. (; green), Linz and Meyer (; red), Grantham and Cannell (; teal), and Allen (; purple). Recordings from Rose et al. (1992), Linz and Meyer (1998), and Allen (1996) were adjusted to 37°C using the Q₁₀ value from Cavalié et al. (1985). (B) Steady-state availability in the presence of CDI and VDI (black) and with VDI only (blue) from the model (lines) is compared to experimental data from Linz and Meyer (; squares) and Hadley and Lederer (; triangles). (C) Model traces of I_Ca,L vs. time for 400 ms test pulses from a pre-clamp of −40 mV. (D) Experimental I_Ca,L traces from Linz and Meyer (1998), also from a pre-clamp of −40 mV. For the top set of traces in (C,D), the square represents a test potential of −10 mV and the triangle a test potential of 0 mV. For the bottom set, test potentials are 10, 30, and 50 mV for the circle, diamond, and triangle, respectively. (D) Was reproduced with copyright permission of John Wiley and Sons.

Figure 3

Sarcoplasmic reticulum load-dependence of fractional release. Model SR load vs. fractional release (solid line) compared to experimental data from Shannon et al. (2000) in rabbit (dots) and Bassani et al. (1995) in ferret (triangles).

Figure 4

Integrated cytosolic Ca²⁺ fluxes. Cytosolic Ca²⁺ uptake is given as the sum of SERCa, NCX, and sarcolemmal Ca²⁺-pump fluxes (A). SERCa contributes 65.9% of uptake, NCX 28.9%, and SL Ca-pump 5.1%. In this model mitochondria contribute significant beat-to-beat buffering. The mitochondrial uniporter predominates during the first 300 ms of the cycle, resulting in a net uptake of Ca²⁺ from the cytosol (B). For the remainder of the cycle, mitochondrial Na⁺-Ca²⁺ exchanger predominates, resulting in Ca²⁺ being transferred back out of the mitochondria to the cytosol. The mitochondria release an amount of Ca²⁺ equal to 12.7% of the net integrated Ca²⁺ uptake flux into the cytosol during relaxation. Integrating over the entire 1000 ms period (B), fluxes into the cytosol are given as positive and fluxes removing Ca²⁺ from the cytosol are negative. Fluxes shown represent SERCa (blue), NCX (red), SL Ca-pump (green), mitochondria (teal), background Ca²⁺ current (magenta), L-type Ca²⁺ current (yellow), SR release (gray), and total (black).

Figure 5

Action potential and Ca²⁺ transient. Steady-state AP at 1 Hz pacing from the model (A) and experiment (Sipido et al., 1995b) (B) along with the corresponding Ca²⁺ transients (D,E). Note that the peak of the model transient is aligned with the middle of the AP plateau phase (dashed line), approximately 127 ms after stimulus. Experimental data in (E) show a similar delay in the Ca²⁺ transient peak of approximately 190 ms. L-type Ca²⁺ flux (J_LCC) (C) shows a large, but brief peak aligned with the initial AP depolarization followed by a slow peak during the AP plateau. RyR flux (F) increases slowly and reaches its maximum in parallel with the J_LCC slow peak and AP plateau. Dashed lines in (C,F) correspond to the time of Ca²⁺ transient peak from (D). Flux measurements are given with respect to subspace volume. (B,E) Were reproduced with copyright permission from The Physiological Society.

Figure 6

I_Ca,L during the AP. Simulated I_Ca,L trace during steady-state AP at 1 Hz pacing (black) and experimental I_Ca,L trace from a guinea pig ventricular myocyte undergoing 1 Hz pacing at 35–37°C (blue). Blue trace is reproduced from Grantham and Cannell (1996) by copyright permission of the American Heart Association.

Figure 7

Inactivation of the L-type Ca²⁺ current during the AP. (A) Model 1 Hz AP. (D) Simulated LCC availability during the AP shown in (A). Experimental data from Linz and Meyer (1998) showing the AP clamp waveform (B) and LCC availability during the AP clamp (E) for guinea pig myocytes at 35°C. (C) Shows model membrane potential output using the trace from (B) as an AP clamp. The LCC availability during the AP clamp is given in (F). (B,E) Were reproduced by copyright permission of John Wiley and Sons.

Figure 8

Voltage-dependence of flux through LCCs and RyRs and ECC gain. (A) Voltage-dependence of maximal Ca²⁺ flux through LCCs (blue) and RyRs (green). (B) Normalized fluxes from (A). (C) ECC gain, as formulated by the ratio of maximal LCC flux to maximal RyR flux.

Figure 9

Predicted subspace Ca²⁺ levels. Model cytosolic Ca²⁺ transient during a steady-state 1 Hz AP (blue) and subspace Ca²⁺ transient averaged across all dyads (green). While the average subspace Ca²⁺ is approximately four times higher than that of the cytosol, the maximum subspace Ca²⁺ for a single dyad may reach 45 μM, measured as the maximum subspace Ca²⁺ for the open-open LCC-RyR configuration during a release event.

Figure 10

Restitution of APD. (A) APD restitution curves from guinea pig experimental data and models. Blue dots show 2000 ms BCL data from Bjornstad et al. (1993) connected by the biexponential fit reported by those authors. Green, red, and teal respectively show epicardial, midmyocardial, and endocardial experimental data from Sicouri et al. (1996). The purple line depicts output from the LRd07 model (Faber et al., 2007) and yellow is from the present model. A standard S1–S2 protocol was used to simulate APD restitution, starting from 0.5 Hz steady-state as in the protocol used by Sicouri et al. (1996). The single exponential time constant for restitution of the present model is 165 ms, compared with approximately 40 ms for Bjornstad et al. (1993) and approximately 46, 27, and 31 ms for Sicouri et al. (1996) epicardial, midmyocardial, and endocardial, respectively. (B) Alteration of the model restitution curve by reverting to the unmodified IKs formulation from Zeng et al. (1995). Blue is LRd07 model, green is the present model. Solid lines are simulations using the latest IKs formulation (one fast gate, one slow), dashed lines are for simulations with 1995 IKs formulation (two fast gates). Curves are normalized to the 2000-ms steady-state APD₉₀ for each model, respectively.

Figure 11

Frequency-dependence of APD and Force. (A) Comparison of model (blue) dependence of APD on frequency to that of Szigligeti et al. (; green). (B) Comparison of model (blue) dependence of force on frequency to that of Szigligeti et al. (; green). See Section “Frequency-Dependence of APD and ECC” of the text for conversion of normalized model output to force units.

Figure 12

Frequency-dependence of NADH levels. (A) Simulation of NADH concentration for a pacing protocol consisting of 100 s at 0.25 Hz [see labels above (A)], 200 s at higher pacing frequencies of 0.5, 1.0, 1.5, and 2.0 Hz then 200 s recovery at 0.25 Hz. Each 500 s protocol is started from 0.25 Hz steady-state initial conditions. (B) Moving average of model force output using a 4000-ms window. Force ranges from approximately 0.9 mN/mm² at 0.25 Hz to 16.4 mN/mm² at the end of the 2-Hz pacing period. (C) Model mitochondrial Ca²⁺ concentration. (D) Experimental data from Brandes and Bers (1999) follow a similar protocol. NADH signal is normalized to 0.25 Hz level. (D) Was reproduced from Brandes and Bers (1999) by copyright permission of the Biophysical Society.

Figure 13

Effect of mitochondrial uniporter block. (A) Model results show the effect of 75% block of the mitochondrial uniporter (simulated by reducing the parameter Vmuni to 25% of its control value). Cytosolic Ca²⁺ transient magnitude is increased and (B) mitochondrial Ca²⁺ transient magnitude is decreased. Experimental data (Maack et al., 2006) for cytosolic Ca²⁺ levels (C) and mitochondrial Ca²⁺ levels (D) with addition of 10 nM Ru, a blocker of the mitochondrial uniporter.

Figure 14

Action potential shape causes delayed Ca²⁺ transient and force. Normalized output from the guinea pig model is used to compare the kinetics of the AP, [Ca]_i transient, and force transient. As seen above, the [Ca]_i transient peaks near the end of the AP plateau. The force transient peak is further delayed and occurs after almost full repolarization of the cell.

Figure 15

Impact of guinea pig and canine AP morphology on I_Ca,L and [Ca]_i transients. In all panels blue traces are guinea pig model output and green traces are canine model output. (A) Comparison of APs from guinea pig and canine models (Greenstein et al., 2006). The canine AP has a significant early repolarization notch and a significantly longer APD. (B) L-type current traces peak near the same value, but guinea pig shows a much larger amount of late current. (C) Canine [Ca]_i transient peak is approximately aligned with the AP notch, while the guinea pig [Ca]_i transient peak occurs during the late plateau phase. (D) On the first beat after adding I_to,fast as in the Shannon et al. (2004) model with conductance of 0.2 mS/μF, the guinea pig AP exhibits a rapid initial repolarization and APD approaches that of canine. (E) With addition of I_to,fast, the guinea pig I_Ca,L trace exhibits a relation between fast peak and late current more similar to canine. The fast peak amplitude also increases substantially. (F) The peak of the guinea pig [Ca]_i transient is now aligned with that of the canine model.