Modeling the actions of beta-adrenergic signaling on excitation--contraction coupling processes

Abstract

Activation of the beta-adrenergic (beta-AR) signaling pathway enhances cardiac function through protein kinase A (PKA)-mediated phosphorylation of target proteins involved in the process of excitation-contraction (EC) coupling. Experimental studies of the effects of beta-AR stimulation on EC coupling have yielded complex results, including increased, decreased, or unchanged EC coupling gain. In this study, we extend a previously developed model of the canine ventricular myocyte describing local control of sarcoplasmic reticulum (SR) calcium (Ca(2+)) release to include the effects of beta-AR stimulation. Incorporation of phosphorylation-dependent effects on model membrane currents and Ca(2+)-cycling proteins yields changes of action potential (AP) and Ca(2+) transients in agreement with those measured experimentally in response to the nonspecific beta-AR agonist isoproterenol (ISO). The model reproduces experimentally observed alterations in EC coupling gain in response to beta-AR agonists and predicts the specific roles of L-type Ca(2+) channel (LCC) and SR Ca(2+) release channel phosphorylation in altering the amplitude and shape of the EC coupling gain function. The model also indicates that factors that promote mode 2 gating of LCCs, such as beta-AR stimulation or activation of the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII), may increase the probability of occurrence of early after-depolarizations (EADs), due to the random, long-duration opening of LCC gating in mode 2.

FIGURE 1

Schematic representation of the CaRU. (A) Trigger Ca²⁺ influx through LCCs enters the T-SR cleft (diadic space). The rise in local Ca²⁺ level promotes the opening of RyRs and chloride channels (ClChs). Local Ca²⁺ diffuses passively from the cleft into the cytosol, and JSR Ca²⁺ is refilled via passive diffusion from the NSR. (B) The T-SR cleft (shown in cross-section) is composed of four diadic subspace volumes arranged on a 2 × 2 grid, each containing 1 LCC, 1 ClCh, and 5 RyRs. Ca²⁺ in any subspace may diffuse to a neighboring subspace (J_iss) or to the cytosol (J_xfer). J_iss,i,j,l represents Ca²⁺ flux from the j^th subspace to the l^th subspace within the i^th CaRU. Similarly J_xfer,i,j represents Ca²⁺ flux from the j^th subspace to the cytosol from the i^th CaRU.

FIGURE 2

Model and experimental APs and Ca²⁺ transients for control (black) and β-AR stimulation (gray). (A) Representative APs measured in isolated canine myocytes in control bath (black) and ISO (gray). (B) Indo-1 fluorescence ratio measured simultaneously with the APs in Fig. 1A (B. O’Rourke, unpublished data). (C) Control (black) and β-AR stimulated (gray) model APs. (D) Model cytosolic Ca²⁺ concentration (μM) corresponding to the APs in Fig. 1C.

FIGURE 3

Panels A–C show effects of β-AR stimulation using the baseline model on macroscopic peak LCC Ca²⁺ influx F_LCC(max) (A), peak RyR Ca²⁺ release flux F_RyR(max) (B), and EC-coupling gain defined as F_RyR(max)/F_LCC(max) (C) Responses include control (black circles), the baseline β-stimulated model (black triangles), and the β-stimulated model with initial control conditions for SR Ca²⁺ load (gray triangles). Panels D–F show effects of LCC open frequency and RyR Ca²⁺ sensitivity associated with β-AR stimulation on macroscopic peak LCC Ca²⁺ influx (D), peak RyR Ca²⁺ release flux (E), and EC coupling gain (F). Responses include control (circles), increased LCC open frequency (4 × f, triangles), and increased RyR Ca²⁺ sensitivity (10 × k₁₂, squares).

FIGURE 4

(A) Membrane potential (ordinate; mV) as a function of time (abscissa; Sec) for the baseline β-AR model in response to 1 Hz pacing. (B) Membrane potential (ordinate; mV) as a function of time (abscissa; Sec) for three AP simulations in which model parameters, initial conditions on state variables governed by ordinary differential equations, and initial states of each channel are identical; however, the pseudorandom number generator seeds used to produce channel open times are initialized to different values prior to each simulation.