#### Title

A Mathematical Model for β1-adrenergic Regulation of the Mouse Ventricular Myocyte Contraction

#### Date of Award

5-10-2017

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics and Statistics

#### First Advisor

Vladimir E. Bondarenko

#### Second Advisor

Igor Belykh

#### Third Advisor

Yaroslav Molkov

#### Fourth Advisor

Alexandra Smirnova

#### Abstract

The β_{1}-adrenergic signaling system is one of the most important systems regulating heart function. Activation of this system leads to an increased heart rate, which can be beneficial during exercise, but can lead to cardiac hypertrophy and heart failure with continuous over-stimulation. In this dissertation, we have developed two comprehensive mathematical models of mouse ventricular myocyte contraction. The first model is based on a previously published mathematical model of action potential and Ca^{2+} handling mechanism of the mouse cardiac cell that are not modulated by the β_{1}-adrenergic signaling system. The model was verified with experimental data on mouse myocyte contraction at room temperature. In the model, we implement simplified sarcomere length variability and indirect modulation of the tropomyosin transition rates by Ca^{2+} and troponin. The resulting model describes well steady-state force-calcium relationships, dependence of contraction force on sarcomere length, time course of contraction force and myocyte shortening, frequency dependence of contraction force and cellular contraction, and experimentally measured derivatives of myocyte length variation. We emphasize the importance of including variable sarcomere length in the model for ventricular myocyte contraction and investigate the differences in contraction force and cell shortening for epicardial and endocardial ventricular myocytes. The second model of the mouse ventricular myocyte contraction includes a more advanced description of the forces involved in myocyte contraction (active, passive, viscous, and flexible forces) and the β_{1}-adrenergic signaling system. The model was verified by the simulation of major experimental protocols on measurements of steady-state force-calcium relationships, crossbridge release rate (k_{rel}) and force development rate (k_{df}), force-velocity relationship, and force redevelopment rate (k_{tr}). It also reproduces quite well frequency and isoproterenol dependencies for [Ca^{2+}]_{i} transients, total contraction force, and sarcomere shortening. The resulting mathematical model reveals the mechanisms of increased contraction force and myocyte shortening upon stimulation of β_{1}-adrenergic receptors. The developed mathematical models can be used further for simulations of contraction of ventricular myocytes from genetically modified mice and myocytes from mice which have developed chronic cardiac diseases.

#### Recommended Citation

Mullins, Paula D., "A Mathematical Model for β1-adrenergic Regulation of the Mouse Ventricular Myocyte Contraction." Dissertation, Georgia State University, 2017.

https://scholarworks.gsu.edu/math_diss/42