Mathematical modeling physiological effects of the overexpression of β2-adrenoceptors in mouse ventricular myocytes

Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations

The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.

A Systematic Review of Inverse Agonism at Adrenoceptor Subtypes

As many, if not most, ligands at G protein-coupled receptor antagonists are inverse agonists, we systematically reviewed inverse agonism at the nine adrenoceptor subtypes. Except for β₃-adrenoceptors, inverse agonism has been reported for each of the adrenoceptor subtypes, most often for β₂-adrenoceptors, including endogenously expressed receptors in human tissues. As with other receptors, the detection and degree of inverse agonism depend on the cells and tissues under investigation, i.e., they are greatest when the model has a high intrinsic tone/constitutive activity for the response being studied. Accordingly, they may differ between parts of a tissue, for instance, atria vs. ventricles of the heart, and within a cell type, between cellular responses. The basal tone of endogenously expressed receptors is often low, leading to less consistent detection and a lesser extent of observed inverse agonism. Extent inverse agonism depends on specific molecular properties of a compound, but inverse agonism appears to be more common in certain chemical classes. While inverse agonism is a fascinating facet in attempts to mechanistically understand observed drug effects, we are skeptical whether an a priori definition of the extent of inverse agonism in the target product profile of a developmental candidate is a meaningful option in drug discovery and development.

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 Na_V1.5 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.