#### Date of Award

5-10-2017

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics and Statistics

#### First Advisor

Dr. Vladimir Bondarenko

#### Second Advisor

Dr. Igor Belykh

#### Third Advisor

Dr. Yaroslav Molkov

#### Fourth Advisor

Dr. Alexandra Smirnova

#### Abstract

The β_{1}- and β_{2}-adrenergic signaling systems play different roles in the functioning of cardiac cells. Experimental data shows that the activation of the β_{1}-adrenergic signaling system produces significant inotropic, lusitropic, and chronotropic effects in the heart, while the effects of the β_{2}-adrenergic signaling system is less apparent. In this dissertation, a comprehensive experimentally-based mathematical model of the combined β_{1}- and β_{2}-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^{2+} handling proteins; modifications of action potential shape and duration; and [Ca^{2+}]_{i} and [Na^{+}]_{i} dynamics upon stimulation of β_{1}- and β_{2}-adrenergic receptors (β_{1}- and β_{2}-ARs). The model reveals physiological conditions when β_{2}-ARs do not produce significant physiological effects and when their effects can be measured experimentally. Simulations demonstrated that stimulation of β_{2}-ARs with isoproterenol caused a marked increase in the magnitude of the L-type Ca^{2+} current, [Ca^{2+}]_{i} transient, and phosphorylation of phospholamban only upon additional application of pertussis toxin (PTX) or inhibition of phosphodiesterases of type 3 and 4. The model also made testable predictions of the changes in magnitudes of [Ca^{2+}]_{i} and [Na^{+}]_{i} fluxes, the rate of decay of [Na^{+}]_{i} concentration upon both combined and separate stimulation of β_{1}- and β_{2}-ARs, and the contribution of phosphorylation of PKA targets to the changes in the action potential and [Ca^{2+}]_{i} transient. A comprehensive mathematical model of the mouse ventricular myocyte overexpressing β_{2}-adrenergic receptors was also developed. It was found that most of the β_{2}-adrenergic receptors are active in control conditions in TG mice. Simulations describe the increased basal adenylyl cyclase activity; modifications of action potential; the effects on the L-type Ca^{2+} current and [Ca^{2+}]_{i} transients upon stimulation of β_{2}-adrenergic receptors in control, after the application of PTX, upon stimulation with zinterol, and upon stimulation with zinterol in the presence of PTX. The model also describes the effects of inverse agonist ICI-118,551 on adenylyl cyclase activity, action potential, and [Ca^{2+}]_{i} transients.

#### Recommended Citation

Rozier, Kelvin, "A Mathematical Model of the Combined β1- and β2-Adrenergic Signaling System in the Mouse Ventricular Myocyte." Dissertation, Georgia State University, 2017.

https://scholarworks.gsu.edu/math_diss/43