Joseph L. Greenstein

Role of the calcium-independent transient outward current I(to1) in shaping action potential morphology and duration

The Kv4.3-encoded current (IKv4.3) has been identified as the major component of the voltage-dependent Ca2+-independent transient outward current (Ito1) in human and canine ventricular cells. Experimental evidence supports a correlation between Ito1 density and prominence of the phase 1 notch; however, the role of Ito1 in modulating action potential duration (APD) remains unclear. To help resolve this role, Markov state models of the human and canine Kv4.3- and Kv1.4-encoded currents at 35°C are developed on the basis of experimental measurements. A model of canine Ito1 is formulated as the combination of these Kv4.3 and Kv1.4 currents and is incorporated into an existing canine ventricular myocyte model. Simulations demonstrate strong coupling between L-type Ca2+ current and IKv4.3 and predict a bimodal relationship between IKv4.3 density and APD whereby perturbations in IKv4.3 density may produce either prolongation or shortening of APD, depending on baseline Ito1 current level.

An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release.

The local control theory of excitation-contraction (EC) coupling in cardiac muscle asserts that L-type Ca(2+) current tightly controls Ca(2+) release from the sarcoplasmic reticulum (SR) via local interaction of closely apposed L-type Ca(2+) channels (LCCs) and ryanodine receptors (RyRs). These local interactions give rise to smoothly graded Ca(2+)-induced Ca(2+) release (CICR), which exhibits high gain. In this study we present a biophysically detailed model of the normal canine ventricular myocyte that conforms to local control theory. The model formulation incorporates details of microscopic EC coupling properties in the form of Ca(2+) release units (CaRUs) in which individual sarcolemmal LCCs interact in a stochastic manner with nearby RyRs in localized regions where junctional SR membrane and transverse-tubular membrane are in close proximity. The CaRUs are embedded within and interact with the global systems of the myocyte describing ionic and membrane pump/exchanger currents, SR Ca(2+) uptake, and time-varying cytosolic ion concentrations to form a model of the cardiac action potential (AP). The model can reproduce both the detailed properties of EC coupling, such as variable gain and graded SR Ca(2+) release, and whole-cell phenomena, such as modulation of AP duration by SR Ca(2+) release. Simulations indicate that the local control paradigm predicts stable APs when the L-type Ca(2+) current is adjusted in accord with the balance between voltage- and Ca(2+)-dependent inactivation processes as measured experimentally, a scenario where common pool models become unstable. The local control myocyte model provides a means for studying the interrelationship between microscopic and macroscopic behaviors in a manner that would not be possible in experiments.

From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales

Computer simulations of electrical behaviour in the whole ventricles have become commonplace during the last few years. The goals of this article are (i) to review the techniques that are currently employed to model cardiac electrical activity in the heart, discussing the strengths and weaknesses of the various approaches, and (ii) to implement a novel modelling approach, based on physiological reasoning, that lifts some of the restrictions imposed by current state-of-the-art ionic models. To illustrate the latter approach, the present study uses a recently developed ionic model of the ventricular myocyte that incorporates an excitation–contraction coupling and mitochondrial energetics model. A paradigm to bridge the vastly disparate spatial and temporal scales, from subcellular processes to the entire organ, and from sub-microseconds to minutes, is presented. Achieving sufficient computational efficiency is the key to success in the quest to develop multiscale realistic models that are expected to lead to better understanding of the mechanisms of arrhythmia induction following failure at the organelle level, and ultimately to the development of novel therapeutic applications.

K current changes account for the rate dependence of the action potential in the human atrial myocyte

Ongoing investigation of the electrophysiology and pathophysiology of the human atria requires an accurate representation of the membrane dynamics of the human atrial myocyte. However, existing models of the human atrial myocyte action potential do not accurately reproduce experimental observations with respect to the kinetics of key repolarizing currents or rate dependence of the action potential and fail to properly enforce charge conservation, an essential characteristic in any model of the cardiac membrane. In addition, recent advances in experimental methods have resulted in new data regarding the kinetics of repolarizing currents in the human atria. The goal of this study was to develop a new model of the human atrial action potential, based on the Nygren et al. model of the human atrial myocyte and newly available experimental data, that ensures an accurate representation of repolarization processes and reproduction of action potential rate dependence and enforces charge conservation. Specifically, the transient outward K(+) current (I(t)) and ultrarapid rectifier K(+) current (I(Kur)) were newly formulated. The inwardly recitifying K(+) current (I(K1)) was also reanalyzed and implemented appropriately. Simulations of the human atrial myocyte action potential with this new model demonstrated that early repolarization is dependent on the relative conductances of I(t) and I(Kur), whereas densities of both I(Kur) and I(K1) underlie later repolarization. In addition, this model reproduces experimental measurements of rate dependence of I(t), I(Kur), and action potential duration. This new model constitutes an improved representation of excitability and repolarization reserve in the human atrial myocyte and, therefore, provides a useful computational tool for future studies involving the human atrium in both health and disease.

Electrotonic coupling between human atrial myocytes and fibroblasts alters myocyte excitability and repolarization.

Atrial fibrosis has been implicated in the development and maintenance of atrial arrhythmias, and is characterized by expansion of the extracellular matrix and an increased number of fibroblasts (Fbs). Electrotonic coupling between atrial myocytes and Fbs may contribute to the formation of an arrhythmogenic substrate. However, the role of these cell-cell interactions in the function of both normal and diseased atria remains poorly understood. The goal of this study was to gain mechanistic insight into the role of electrotonic Fb-myocyte coupling on myocyte excitability and repolarization. To represent the system, a human atrial myocyte (hAM) coupled to a variable number of Fbs, we employed a new ionic model of the hAM, and a variety of membrane representations for atrial Fbs. Simulations elucidated the effects of altering the intercellular coupling conductance, electrophysiological Fb properties, and stimulation rate on the myocyte action potential. The results demonstrate that the myocyte resting potential and action potential waveform are modulated strongly by the properties and number of coupled Fbs, the degree of coupling, and the pacing frequency. Our model provides mechanistic insight into the consequences of heterologous cell coupling on hAM electrophysiology, and can be extended to evaluate these implications at both tissue and organ levels.

CaMKII-Induced Shift in Modal Gating Explains L-Type Ca2+ Current Facilitation: A Modeling Study

Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) plays an important role in L-type Ca(2+) channel (LCC) facilitation: the Ca(2+)-dependent augmentation of Ca(2+) current (I(CaL)) exhibited during rapid repeated depolarization. Multiple mechanisms may underlie facilitation, including an increased rate of recovery from Ca(2+)-dependent inactivation and a shift in modal gating distribution from mode 1, the dominant mode of LCC gating, to mode 2, a mode in which openings are prolonged. We hypothesized that the primary mechanism underlying facilitation is the shift in modal gating distribution resulting from CaMKII-mediated LCC phosphorylation. We developed a stochastic model describing the dynamic interactions among CaMKII, LCCs, and phosphatases as a function of dyadic Ca(2+) and calmodulin levels, and we incorporated it into an integrative model of the canine ventricular myocyte. The model reproduces behaviors at physiologic protein levels and allows for dynamic transition between modes, depending on the LCC phosphorylation state. Simulations showed that a CaMKII-dependent shift in LCC distribution toward mode 2 accounted for the I(CaL) positive staircase. Moreover, simulations demonstrated that experimentally observed changes in LCC inactivation and recovery kinetics may arise from modal gating shifts, rather than from changes in intrinsic inactivation properties. The model therefore serves as a powerful tool for interpreting I(CaL) experiments.

Integrative Systems Models of Cardiac Excitation–Contraction Coupling

Excitation–contraction coupling in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca2+ transport. The complexity and integrative nature of heart cell electrophysiology and Ca2+ cycling has led to an evolution of computational models that have played a crucial role in shaping our understanding of heart function. An important emerging theme in systems biology is that the detailed nature of local signaling events, such as those that occur in the cardiac dyad, have important consequences at higher biological scales. Multiscale modeling techniques have revealed many mechanistic links between microscale events, such as Ca2+ binding to a channel protein, and macroscale phenomena, such as excitation–contraction coupling gain. Here, we review experimentally based multiscale computational models of excitation–contraction coupling and the insights that have been gained through their application.

Superresolution Modeling of Calcium Release in the Heart

Stable calcium-induced calcium release (CICR) is critical for maintaining normal cellular contraction during cardiac excitation-contraction coupling. The fundamental element of CICR in the heart is the calcium (Ca2+) spark, which arises from a cluster of ryanodine receptors (RyR). Opening of these RyR clusters is triggered to produce a local, regenerative release of Ca2+ from the sarcoplasmic reticulum (SR). The Ca2+ leak out of the SR is an important process for cellular Ca2+ management, and it is critically influenced by spark fidelity, i.e., the probability that a spontaneous RyR opening triggers a Ca2+ spark. Here, we present a detailed, three-dimensional model of a cardiac Ca2+ release unit that incorporates diffusion, intracellular buffering systems, and stochastically gated ion channels. The model exhibits realistic Ca2+ sparks and robust Ca2+ spark termination across a wide range of geometries and conditions. Furthermore, the model captures the details of Ca2+ spark and nonspark-based SR Ca2+ leak, and it produces normal excitation-contraction coupling gain. We show that SR luminal Ca2+-dependent regulation of the RyR is not critical for spark termination, but it can explain the exponential rise in the SR Ca2+ leak-load relationship demonstrated in previous experimental work. Perturbations to subspace dimensions, which have been observed in experimental models of disease, strongly alter Ca2+ spark dynamics. In addition, we find that the structure of RyR clusters also influences Ca2+ release properties due to variations in inter-RyR coupling via local subspace Ca2+ concentration ([Ca2+]ss). These results are illustrated for RyR clusters based on super-resolution stimulated emission depletion microscopy. Finally, we present a believed-novel approach by which the spark fidelity of a RyR cluster can be predicted from structural information of the cluster using the maximum eigenvalue of its adjacency matrix. These results provide critical insights into CICR dynamics in heart, under normal and pathological conditions.

Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium.

In the mammalian heart, myocytes and fibroblasts can communicate via gap junction, or connexin-mediated current flow. Some of the effects of this electrotonic coupling on the action potential waveform of the human ventricular myocyte have been analyzed in detail. The present study employs a recently developed mathematical model of the human atrial myocyte to investigate the consequences of this heterogeneous cell-cell interaction on the action potential of the human atrium. Two independent physiological processes which alter the physiology of the human atrium have been studied. i) The effects of the autonomic transmitter acetylcholine on the atrial action potential have been investigated by inclusion of a time-independent, acetylcholine-activated K(+) current in this mathematical model of the atrial myocyte. ii) A non-selective cation current which is activated by natriuretic peptides has been incorporated into a previously published mathematical model of the cardiac fibroblast. These results identify subtle effects of acetylcholine, which arise from the nonlinear interactions between ionic currents in the human atrial myocyte. They also illustrate marked alterations in the action potential waveform arising from fibroblast-myocyte source-sink principles when the natriuretic peptide-mediated cation conductance is activated. Additional calculations also illustrate the effects of simultaneous activation of both of these cell-type specific conductances within the atrial myocardium. This study provides a basis for beginning to assess the utility of mathematical modeling in understanding detailed cell-cell interactions within the complex paracrine environment of the human atrial myocardium.

A Computational Model of Reactive Oxygen Species and Redox Balance in Cardiac Mitochondria

Elevated levels of reactive oxygen species (ROS) play a critical role in cardiac myocyte signaling in both healthy and diseased cells. Mitochondria represent the predominant cellular source of ROS, specifically the activity of complexes I and III. The model presented here explores the modulation of electron transport chain ROS production for state 3 and state 4 respiration and the role of substrates and respiratory inhibitors. Model simulations show that ROS production from complex III increases exponentially with membrane potential (ΔΨm) when in state 4. Complex I ROS release in the model can occur in the presence of NADH and succinate (reverse electron flow), leading to a highly reduced ubiquinone pool, displaying the highest ROS production flux in state 4. In the presence of ample ROS scavenging, total ROS production is moderate in state 3 and increases substantially under state 4 conditions. The ROS production model was extended by combining it with a minimal model of ROS scavenging. When the mitochondrial redox status was oxidized by increasing the proton permeability of the inner mitochondrial membrane, simulations with the combined model show that ROS levels initially decline as production drops off with decreasing ΔΨm and then increase as scavenging capacity is exhausted. Hence, this mechanistic model of ROS production demonstrates how ROS levels are controlled by mitochondrial redox balance.