A compartmentalized mathematical model of the ß1- and ß2-adrenergic signaling systems in ventricular myocytes from mouse in heart failure.

Mouse models of heart failure are extensively used to research human cardiovascular diseases. In particular, one of the most common is the mouse model of heart failure resulting from transverse aortic constriction (TAC). Despite this, there are no comprehensive compartmentalized mathematical models that describe the complex behavior of the action potential, [Ca2+]i transients, and their regulation by ß1- and ß2-adrenergic signaling systems in failing mouse myocytes. In this paper, we develop a novel compartmentalized mathematical model of failing mouse ventricular myocytes after TAC procedure. The model describes well the cell geometry, action potentials, [Ca2+]i transients, and ß1- and ß2-adrenergic signaling in the failing cells. Simulation results obtained with the failing cell model are compared with those from the normal ventricular myocytes. Exploration of the model reveals the sarcoplasmic reticulum Ca2+ load mechanisms in failing ventricular myocytes. We also show a larger susceptibility of the failing myocytes to early and delayed afterdepolarizations and to a proarrhythmic behavior of Ca2+ dynamics upon stimulation with isoproterenol. The mechanisms of the proarrhythmic behavior suppression are investigated and sensitivity analysis is performed. The developed model can explain the existing experimental data on failing mouse ventricular myocytes and make experimentally testable predictions of a failing myocyte's behavior.

A compartmentalized mathematical model of mouse atrial myocytes.

Various experimental mouse models are extensively used to research human diseases, including atrial fibrillation, the most common cardiac rhythm disorder. Despite this, there are no comprehensive mathematical models that describe the complex behavior of the action potential and [Ca2+]i transients in mouse atrial myocytes. Here, we develop a novel compartmentalized mathematical model of mouse atrial myocytes that combines the action potential, [Ca2+]i dynamics, and ß-adrenergic signaling cascade for a subpopulation of right atrial myocytes with developed transverse-axial tubule system. The model consists of three compartments related to ß-adrenergic signaling (caveolae, extracaveolae, and cytosol) and employs local control of Ca2+ release. It also simulates ionic mechanisms of action potential generation and describes atrial-specific Ca2+ handling as well as frequency dependences of the action potential and [Ca2+]i transients. The model showed that the T-type Ca2+ current significantly affects the later stage of the action potential, with little effect on [Ca2+]i transients. The block of the small-conductance Ca2+-activated K+ current leads to a prolongation of the action potential at high intracellular Ca2+. Simulation results obtained from the atrial model cells were compared with those from ventricular myocytes. The developed model represents a useful tool to study complex electrical properties in the mouse atria and could be applied to enhance the understanding of atrial physiology and arrhythmogenesis.NEW & NOTEWORTHY A new compartmentalized mathematical model of mouse right atrial myocytes was developed. The model simulated action potential and Ca2+ dynamics at baseline and after stimulation of the ß-adrenergic signaling system. Simulations showed that the T-type Ca2+ current markedly prolonged the later stage of atrial action potential repolarization, with a minor effect on [Ca2+]i transients. The small-conductance Ca2+-activated K+ current block resulted in prolongation of the action potential only at the relatively high intracellular Ca2+.

A Mathematical Model of the Human Cardiac Na+ Channel.

Sodium ion channel is a membrane protein that plays an important role in excitable cells, as it is responsible for the initiation of action potentials. Understanding the electrical characteristics of sodium channels is essential in predicting their behavior under different physiological conditions. We investigated several Markov models for the human cardiac sodium channel NaV1.5 to derive a minimal mathematical model that describes the reported experimental data obtained using major voltage clamp protocols. We obtained simulation results for peak current-voltage relationships, the voltage dependence of normalized ion channel conductance, steady-state inactivation, activation and deactivation kinetics, fast and slow inactivation kinetics, and recovery from inactivation kinetics. Good agreement with the experimental data provides us with the mechanisms of the fast and slow inactivation of the human sodium channel and the coupling of its inactivation states to the closed and open states in the activation pathway.