The β- and β-adrenergic signaling systems play different roles in the functioning of cardiac cells. Experimental data show that the activation of the β-adrenergic signaling system produces significant inotropic, lusitropic, and chronotropic effects in the heart, whereas the effects of the β-adrenergic signaling system is less apparent. In this paper, a comprehensive compartmentalized experimentally based mathematical model of the combined β- and β-adrenergic signaling systems in mouse ventricular myocytes is developed to simulate the experimental findings and make testable predictions of the behavior of the cardiac cells under different physiological conditions. Simulations describe the dynamics of major signaling molecules in different subcellular compartments; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca handling proteins; modifications of action potential shape and duration; and [Ca] and [Na] dynamics upon stimulation of β- and β-adrenergic receptors (β- and β-ARs). The model reveals physiological conditions when β-ARs do not produce significant physiological effects and when their effects can be measured experimentally. Simulations demonstrated that stimulation of β-ARs with isoproterenol caused a marked increase in the magnitude of the L-type Ca current, [Ca] transient, and phosphorylation of phospholamban only upon additional application of pertussis toxin or inhibition of phosphodiesterases of type 3 and 4. The model also made testable predictions of the changes in magnitudes of [Ca] and [Na] fluxes, the rate of decay of [Na] concentration upon both combined and separate stimulation of β- and β-ARs, and the contribution of phosphorylation of PKA targets to the changes in the action potential and [Ca] transient.

Transgenic (TG) mice overexpressing β-adrenergic receptors (β-ARs) demonstrate enhanced myocardial function, which manifests in increased basal adenylyl cyclase activity, enhanced atrial contractility, and increased left ventricular function in vivo. To gain insights into the mechanisms of these effects, we developed a comprehensive mathematical model of the mouse ventricular myocyte overexpressing β-ARs. We found that most of the β-ARs are active in control conditions in TG mice. The simulations describe the dynamics of major signaling molecules in different subcellular compartments, increased basal adenylyl cyclase activity, modifications of action potential shape and duration, and the effects on L-type Ca current and intracellular Ca concentration ([Ca]) transients upon stimulation of β-ARs in control, after the application of pertussis toxin, upon stimulation with a specific β-AR agonist zinterol, and upon stimulation with zinterol in the presence of pertussis toxin. The model also describes the effects of the β-AR inverse agonist ICI-118,551 on adenylyl cyclase activity, action potential, and [Ca] transients. The simulation results were compared with experimental data obtained in ventricular myocytes from TG mice overexpressing β-ARs and with simulation data on wild-type mice. In conclusion, a new comprehensive mathematical model was developed that describes multiple experimental data on TG mice overexpressing β-ARs and can be used to test numerous hypotheses. As an example, using the developed model, we proved the hypothesis of the major contribution of L-type Ca current to the changes in the action potential and [Ca] transient upon stimulation of β-ARs with zinterol. NEW & NOTEWORTHY We developed a new mathematical model for transgenic mouse ventricular myocytes overexpressing β-adrenoceptors that describes the experimental findings in transgenic mice. The model reveals mechanisms of the differential effects of stimulation of β-adrenoceptors in wild-type and transgenic mice overexpressing β-adrenoceptors.

Hopfield neural network attracts particular attention as it serves as a relatively simple mathematical model that describes some properties of the brain function. We investigate analog Hopfield neural networks with two time delays. It is shown that the neural network with all inhibitory connections demonstrates growing oscillations after exceeding the threshold, and oscillations become synchronous after a relatively short period of time of the order of the larger time delay. The oscillation amplitude of the neural network as function of the time delay in one subnetwork demonstrates resonance-like phenomena with multiple peaks. The oscillation period of the neural network with two time delays shows discrete structure and changes within relatively narrow intervals in contrast to the oscillation period of the neural network with one time delay, which shows continuous changes of oscillation amplitude and period with time delay. Multiresonance behavior is sustained for both inhibitory and excitatory connections of the second subnetwork, while the first subnetwork possesses only inhibitory connections. The oscillation period of the subnetwork with smaller time delay and equal coupling strengths dominates the whole neural network activity. Turning on and off smaller time delay in one subnetwork allows for the control of the oscillation period and demonstrates memory-like behavior. Mechanisms of the simulated phenomena are disclosed and their similarity to brain function is discussed.