Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte

Abstract

It is now well established that characteristic properties of excitation-contraction (EC) coupling in cardiac myocytes, such as high gain and graded Ca(2+) release, arise from the interactions that occur between L-type Ca(2+) channels (LCCs) and nearby ryanodine-sensitive Ca(2+) release channels (RyRs) in localized microdomains. Descriptions of Ca(2+)-induced Ca(2+) release (CICR) that account for these local mechanisms are lacking from many previous models of the cardiac action potential, and those that do include local control of CICR are able to reconstruct properties of EC coupling, but require computationally demanding stochastic simulations of approximately 10(5) individual ion channels. In this study, we generalize a recently developed analytical approach for deriving simplified mechanistic models of CICR to formulate an integrative model of the canine cardiac myocyte which is computationally efficient. The resulting model faithfully reproduces experimentally measured properties of EC coupling and whole cell phenomena. The model is used to study the role of local redundancy in L-type Ca(2+) channel gating and the role of dyad configuration on EC coupling. Simulations suggest that the characteristic steep rise in EC coupling gain observed at hyperpolarized potentials is a result of increased functional coupling between LCCs and RyRs. We also demonstrate mechanisms by which alterations in the early repolarization phase of the action potential, resulting from reduction of the transient outward potassium current, alters properties of EC coupling.

FIGURE 1

State diagrams for the LCC and RyR Markov models and schematic diagrams of the CaRU. (A) State model of the LCC which represents a simplification of the model presented previously (see Fig. 12, A and B, of Greenstein and Winslow (18)). Upper states (green outline, states 1–3, and 6–8) encompass Mode Normal, lower states (red outline, states 4, 5, 9, and 10) encompass Mode CDI, and the backplane states (gray shading, states 6–10) encompass Mode VDI. The open state (state 3) is denoted by a circle, whereas closed states are denoted by squares. Depolarization rapidly promotes transitions from left to right, and more slowly promotes transitions into Mode VDI states, whereas downward transitions into Mode CDI states are promoted by elevation in local Ca²⁺ level. Pairs of transitions with the same arrow color share identical transition rates. (B) State model of the RyR based on a simplification described previously (see Fig. 13 C of Greenstein and Winslow (18)), where states 1 and 2 are the resting states, state 3 is the open state, and state 4 is the refractory state. Rate constants are Ca²⁺-dependent based on the assumption that four Ca²⁺ ions must bind the RyR before opening. Rate definitions for both the LCC and RyR models are provided in the Supplementary Material. (C) Schematic representation of the CaRU, which is the basis of the baseline-coupled LCC-RyR model. In the baseline model, a CaRU consists of a single LCC on the t-tubule membrane and a single RyR on the SR membrane, both facing into the dyadic space. (D) Visualization of the state diagram for the baseline-coupled LCC-RyR model. The “outer” model represents the four-state RyR model of B, and for each RyR state, there are 10 possible LCC states, shown within each RyR state as the LCC model of A. The model therefore consists of 40 states, where each state represents a unique pairing of LCC and RyR states. Each state transition of the coupled model represents a single state transition of either the LCC or the RyR. The full set of equations describing the 40-state coupled LCC-RyR model is provided in the Supplementary Material.

FIGURE 2

Properties of I_CaL. (A) Simulated whole-cell currents as a function of time in response to a family of depolarizing voltage steps from −30 mV to 40 mV in 10-mV increments. (B) Peak I-V relation for I_CaL. (C) LCC open probability (p_o, solid line), probability that Ca²⁺-dependent inactivation has not occurred (p_{not_CDI}, shaded line), and probability that voltage-dependent inactivation has not occurred (p_{not_VDI}, dashed line), in response to a voltage-clamp to 0 mV. (D) Steady-state inactivation curve obtained using a double-pulse protocol with (black line) and without (shaded line) Ca²⁺ as the charge carrier.

FIGURE 3

Ca²⁺ dependence of peak (solid line) and steady-state (dashed line) RyR open probability (p_o) for simulated maintained changes in free dyadic Ca²⁺ concentration. The response at each [Ca²⁺] level was initiated from a resting [Ca²⁺] of 0.1 μM.

FIGURE 4

Voltage dependence of LCC Ca²⁺ influx, RyR Ca²⁺ release flux, and EC coupling gain. (A) Peak LCC Ca²⁺ flux (solid circles) and peak RyR release flux (open circles) as a function of membrane voltage. (B) Peak Ca²⁺ fluxes (data in A) normalized by their respective maxima. (C) EC coupling gain as a function of membrane potential for the baseline-coupled LCC-RyR model (solid circles), in which a single model RyR is used to represent a cluster of five RyRs is compared to a model in which the five RyRs are each modeled individually (open circles).

FIGURE 5

Properties of EC coupling gain. (A) EC coupling gain as a function of membrane potential for the baseline-coupled LCC-RyR model (solid line) is compared to gain for models in which dyad size and number of channels is increased twofold (shaded line), and threefold (dashed line). The number of CaRUs in the cell is scaled such that the number of LCCs and RyRs (and total dyad volume) in the whole cell remains identical for all models. (B) Redundancy of LCC p_o as a function of time in the model with twofold increase in dyad size in response to a voltage-clamp to 0 mV. (C) Peak redundancy of LCC p_o as a function of voltage in the model with a twofold increase in dyad size. (D) EC coupling gain in the model with a twofold increase in dyad size for [Ca²⁺]_o of 2.0 mM (solid line), 1.8 mM (shaded line), 1.6 mM (black dashed line), and 1.4 mM (shaded dashed line).

FIGURE 6

Action potentials and Ca²⁺ transients. (A) Steady-state model APs for CLs of 500 ms (shaded line), 1000 ms (solid line), 2000 ms (shaded dashed line), and 4000 ms (black dashed line). (B) Cytosolic Ca²⁺ transients corresponding to the APs of A. (C) Mean subspace (dyadic) Ca²⁺ transient (dashed line) demonstrates that microdomain Ca²⁺ levels reach significantly higher levels than that in the cytosol (solid line) during the AP at 1000 ms CL. (D) Properties of I_CaL (solid line) during the AP at 1000 ms CL, demonstrating relatively strong Ca²⁺-dependent inactivation (p_{not_CDI}, shaded line) but weak voltage-dependent inactivation (p_{not_VDI}, dashed line).

FIGURE 7

Role of I_to1 on EC coupling during the AP. Control simulations (left panels) are compared to simulations in which I_to1 density is reduced threefold (right panels). (A) AP; (B) I_CaL; (C) redundancy of LCC p_o; (D) LCC Ca²⁺ influx (shaded line) and RyR Ca²⁺ release flux (solid line); and (E) cytosolic Ca²⁺ transient.