Simulation of the effects of moderate stimulation/inhibition of the β₁-adrenergic signaling system and its components in mouse ventricular myocytes

Abstract

The β1-adrenergic signaling system is one of the most important protein signaling systems in cardiac cells. It regulates cardiac action potential duration, intracellular Ca(2+) concentration ([Ca(2+)]i) transients, and contraction force. In this paper, a comprehensive experimentally based mathematical model of the β1-adrenergic signaling system for mouse ventricular myocytes is explored to simulate the effects of moderate stimulations of β1-adrenergic receptors (β1-ARs) on the action potential, Ca(2+) and Na(+) dynamics, as well as the effects of inhibition of protein kinase A (PKA) and phosphodiesterase of type 4 (PDE4). Simulation results show that the action potential prolongations reach saturating values at relatively small concentrations of isoproterenol (∼0.01 μM), while the [Ca(2+)]i transient amplitude saturates at significantly larger concentrations (∼0.1-1.0 μM). The differences in the response of Ca(2+) and Na(+) fluxes to moderate stimulation of β1-ARs are also observed. Sensitivity analysis of the mathematical model is performed and the model limitations are discussed. The investigated model reproduces most of the experimentally observed effects of moderate stimulation of β1-ARs, PKA, and PDE4 inhibition on the L-type Ca(2+) current, [Ca(2+)]i transients, and the sarcoplasmic reticulum Ca(2+) load and makes testable predictions for the action potential duration and [Ca(2+)]i transients as functions of isoproterenol concentration.

Distinct physiological effects of β1- and β2-adrenoceptors in mouse ventricular myocytes: insights from a compartmentalized mathematical model

“…A mathematical model for the combined ␤1and ␤2-adrenergic signaling system in mouse ventricular myocytes is a natural extension of the previously published model for the ␤1-adrenergic signaling system in mouse ventricular myocytes (6,27) (Fig. 1).…”

“…The fast Na ϩ current, INa, 20% of the L-type Ca 2ϩ channels (the L-type Ca 2ϩ current, ICaL), the phospholemman (PLM), which regulates the Na ϩ -K ϩ pump, INaK, and the time-independent K ϩ current, IK1, are localized in the caveolar compartment; the ultra-rapidly activating delayed rectifier K ϩ current, IKur, the rapidly inactivating transient outward K ϩ current, IKto,f, 80% of the L-type Ca 2ϩ channels, and the ryanodine receptors, RyRs, are localized in the extracaveolar compartment; and phospholamban and troponin I are localized in the cytosolic compartment. The detailed description of the model development for the ␤ 1-adrenergic signaling system can be found elsewhere (6,27). In this section we describe modifications of the model (6): the combined ␤1and ␤2-adrenergic receptor module with activation of G s and Gi proteins, and the adenylyl cyclase module.…”

“…To estimate the mathematical model's stability and major contributing factors to the changes in the action potential and [Ca 2ϩ ] i transient, we performed a sensitivity analysis. In the previous paper (27), where the mathematical model included only the ␤ 1 -adrenergic signaling system, we carried out a sensitivity analysis with respect to the major repolarization currents. With the model presented in this paper, we obtained very similar results.…”

“…As the interbeat changes in the concentrations of signaling proteins did not produce measurable effects on the action potential and [Ca 2ϩ ] i transient, we explored a method of analysis different from that in Ref. 27. We ran the model cell for 300 s for the control set of the model parameters and for the case in which one protein concentration increased by 5%.…”

“…Therefore, we developed and explored a compartmentalized mathematical model of mouse ventricular myocytes that includes both the ␤ 1 -and ␤ 2 -adrenergic signaling systems to describe the effects of stimulation of ␤ 1 -and ␤ 2 -ARs on the behavior of cardiac cells. The model is based on the previously developed mathematical model of the ␤ 1 -adrenergic signaling system in mouse ventricular cells, which was extensively verified by the experimental data on the activation of ␤ 1 -ARs (6,27). The model (6) was also recently used by Esprito Santo et al (23) for simulation of the larger susceptibility of isoproterenol-stimulated mouse cardiac cells to DADs with I NaCa overexpression.…”