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Early afterdepolarizations (EADs) are abnormal depolarizations during the plateau phase of the action potential, which are known to be associated with lethal arrhythmias in the heart. There are two major hypotheses for EAD genesis based on experimental observations, i.e., the voltage (Vm)-driven and intracellular calcium (Ca)-driven mechanisms. In ventricular myocytes, Ca and Vm are bidirectionally coupled, which can affect each other's dynamics and result in new dynamics, however, the roles of Ca cycling and its coupling with Vm in the genesis of EADs have not been well understood. In this study, we use an action potential model that is capable of independent Vm and Ca oscillations to investigate the roles of Vm and Ca coupling in EAD genesis. Four different mechanisms of EADs are identified, which are either driven by Vm oscillations or Ca oscillations alone, or oscillations caused by their interactions. We also use 5 other ventricular action potential models to assess these EAD mechanisms and show that EADs in these models are mainly Vm-driven. These mechanistic insights from our simulations provide a theoretical base for understanding experimentally observed EADs and EAD-related arrhythmogenesis.

Ventricular arrhythmias (VAs) in heart failure are enhanced by sympathoexcitation. However, radiotracer studies of catecholamine uptake in failing human hearts demonstrate a proclivity for VAs in patients with reduced cardiac sympathetic innervation. We hypothesized that this counterintuitive finding is explained by heterogeneous loss of sympathetic nerves in the failing heart. In a murine model of dilated cardiomyopathy (DCM), delayed PET imaging of sympathetic nerve density using the catecholamine analog [11C]meta-Hydroxyephedrine demonstrated global hypoinnervation in ventricular myocardium. Although reduced, sympathetic innervation in 2 distinct DCM models invariably exhibited transmural (epicardial to endocardial) gradients, with the endocardium being devoid of sympathetic nerve fibers versus controls. Further, the severity of transmural innervation gradients was correlated with VAs. Transmural innervation gradients were also identified in human left ventricular free wall samples from DCM versus controls. We investigated mechanisms underlying this relationship by in silico studies in 1D, 2D, and 3D models of failing and normal human hearts, finding that arrhythmogenesis increased as heterogeneity in sympathetic innervation worsened. Specifically, both DCM-induced myocyte electrical remodeling and spatially inhomogeneous innervation gradients synergistically worsened arrhythmogenesis. Thus, heterogeneous innervation gradients in DCM promoted arrhythmogenesis. Restoration of homogeneous sympathetic innervation in the failing heart may reduce VAs.

Progressive tissue remodeling after myocardial infarction (MI) promotes cardiac arrhythmias. This process is well studied in young animals, but little is known about pro-arrhythmic changes in aged animals. Senescent cells accumulate with age and accelerate age-associated diseases. Senescent cells interfere with cardiac function and outcome post-MI with age, but studies have not been performed in larger animals, and the mechanisms are unknown. Specifically, age-associated changes in timecourse of senescence and related changes in inflammation and fibrosis are not well understood. Additionally, the cellular and systemic role of senescence and its inflammatory milieu in influencing arrhythmogenesis with age is not clear, particularly in large animal models with cardiac electrophysiology more similar to humans than previously studied animal models. Here, we investigated the role of senescence in regulating inflammation, fibrosis, and arrhythmogenesis in young and aged infarcted rabbits. Aged rabbits exhibited increased peri-procedural mortality and arrhythmogenic electrophysiological remodeling at the infarct border zone (IBZ) compared to young rabbits. Studies of the aged infarct zone revealed persistent myofibroblast senescence and increased inflammatory signaling over a 12-week timecourse. Senescent IBZ myofibroblasts in aged rabbits appear to be coupled to myocytes, and our computational modeling showed that senescent myofibroblast-cardiomyocyte coupling prolongs action potential duration (APD) and facilitates conduction block permissive of arrhythmias. Aged infarcted human ventricles show levels of senescence consistent with aged rabbits, and senescent myofibroblasts also couple to IBZ myocytes. Our findings suggest that therapeutic interventions targeting senescent cells may mitigate arrhythmias post-MI with age.

Math anxiety (MA), i.e. a trait factor describing the feelings of tension, apprehension, and fear during mathematics-related situations, has attracted increasing interest in recent years, due to its importance in people's daily life and career development, especially in our modern digital world. Although the measurement of individuals' trait MA has mostly relied on self-reported psychological scales, emerging studies are seeking for objective measurement by using behavioral or neurophysiological data. The present study, for the first time, investigated the neurophysiological signatures of trait MA in a cohort of high school students during their 90-minute real final-term math exam. Wrist-worn wearable devices were used for recording their autonomic nervous system activities, including skin conductance (SC) and heart rate (HR). The calculation of pairwise correlation revealed that both SC and HR could reflect the individual's math evaluation anxiety (MEA) score, which is one of the two sub-components of trait MA. Specifically, the tonic level of SC was negatively correlated with MEA during the 5-minute pre-exam period when the students were anticipating the exam, whereas HR was positively correlated with MEA at two later time windows during the exam (63-65 minutes and 82-85 minutes, after the start of the exam). A leave-one-out regression analysis revealed a correlation (r =.349 , p =.094 ) between the self-reported MEA scores and the scores predicted by these neurophysiological signatures. Our findings provide neurophysiological evidence of trait MA in a real-life context and demonstrate the potential of implementing an objective measurement of trait MA based on neurophysiological signals.

In order to study the causes of arch foot cracking, a multiscale numerical simulation method was used to establish the finite element model of Xizha Bridge during the construction stage of the Xiaoqing River restoration project in Jinan by using Midas Civil, and the internal forces under adverse conditions were extracted. On this basis, Abaqus was used to establish the local model of arch foot, and the plastic damage model parameters were introduced to conduct stress analysis. The results show that the anchorage stress of prestressed steel bundle is too high. On the one hand, the stress component produced by the bending of the prestressed steel bundle can squeeze the concrete inside the bending angle, and on the other hand, it will stretch the concrete outside the bending angle, resulting in concrete cracking. There is a tendency of relative displacement between arch rib and arch foot, and the interface surface of arch foot and arch rib is pulled by the displacement of arch rib, resulting in cracking. Arch foot inner bend produces a certain tensile stress, and if this place is not paid enough attention to, insufficient reinforcement will produce large cracks. Finally, it is suggested that concrete cracking can be avoided by arranging enough reinforcement bars under anchor and sealing reinforcement bars, encrypting steel mesh, arranging shear studs, and extending insertion depth.

Hypertrophic cardiomyopathy (HCM) is the most common heritable cardiovascular disease and often results in cardiac remodeling and an increased incidence of sudden cardiac arrest (SCA) and death, especially in youth and young adults. Among thousands of different variants found in HCM patients, variants of TNNT2 (cardiac troponin T—TNNT2) are linked to increased risk of ventricular arrhythmogenesis and sudden death despite causing little to no cardiac hypertrophy. Therefore, studying the effect of TNNT2 variants on cardiac propensity for arrhythmogenesis can pave the way for characterizing HCM in susceptible patients before sudden cardiac arrest occurs. In this study, a TNNT2 variant, I79N, was generated in human cardiac recombinant/reconstituted thin filaments (hcRTF) to investigate the effect of the mutation on myofilament Ca2+ sensitivity and Ca2+ dissociation rate using steady-state and stopped-flow fluorescence techniques. The results revealed that the I79N variant significantly increases myofilament Ca2+ sensitivity and decreases the Ca2+ off-rate constant (koff). To investigate further, a heterozygous I79N+/−TNNT2 variant was introduced into human-induced pluripotent stem cells using CRISPR/Cas9 and subsequently differentiated into ventricular cardiomyocytes (hiPSC-CMs). To study the arrhythmogenic properties, monolayers of I79N+/− hiPSC-CMs were studied in comparison to their isogenic controls. Arrhythmogenesis was investigated by measuring voltage (Vm) and cytosolic Ca2+ transients over a range of stimulation frequencies. An increasing stimulation frequency was applied to the cells, from 55 to 75 bpm. The results of this protocol showed that the TnT-I79N cells had reduced intracellular Ca2+ transients due to the enhanced cytosolic Ca2+ buffering. These changes in Ca2+ handling resulted in beat-to-beat instability and triangulation of the cardiac action potential, which are predictors of arrhythmia risk. While wild-type (WT) hiPSC-CMs were accurately entrained to frequencies of at least 150 bpm, the I79N hiPSC-CMs demonstrated clear patterns of alternans for both Vm and Ca2+ transients at frequencies >75 bpm. Lastly, a transcriptomic analysis was conducted on WT vs. I79N+/−TNNT2 hiPSC-CMs using a custom NanoString codeset. The results showed a significant upregulation of NPPA (atrial natriuretic peptide), NPPB (brain natriuretic peptide), Notch signaling pathway components, and other extracellular matrix (ECM) remodeling components in I79N+/− vs. the isogenic control. This significant shift demonstrates that this missense in the TNNT2 transcript likely causes a biophysical trigger, which initiates this significant alteration in the transcriptome. This TnT-I79N hiPSC-CM model not only reproduces key cellular features of HCM-linked mutations but also suggests that this variant causes uncharted pro-arrhythmic changes to the human action potential and gene expression.

Mitochondria fulfill the cell’s energy demand and affect the intracellular calcium (Ca2+) dynamics via direct Ca2+ exchange, the redox effect of reactive oxygen species (ROS) on Ca2+ handling proteins, and other signaling pathways. Recent experimental evidence indicates that mitochondrial depolarization promotes arrhythmogenic delayed afterdepolarizations (DADs) in cardiac myocytes. However, the nonlinear interactions among the Ca2+ signaling pathways, ROS, and oxidized Ca2+/calmodulin-dependent protein kinase II (CaMKII) pathways make it difficult to reveal the mechanisms. Here, we use a recently developed spatiotemporal ventricular myocyte computer model, which consists of a 3-dimensional network of Ca2+ release units (CRUs) intertwined with mitochondria and integrates mitochondrial Ca2+ signaling and other complex signaling pathways, to study the mitochondrial regulation of DADs. With a systematic investigation of the synergistic or competing factors that affect the occurrence of Ca2+ waves and DADs during mitochondrial depolarization, we find that the direct redox effect of ROS on ryanodine receptors (RyRs) plays a critical role in promoting Ca2+ waves and DADs under the acute effect of mitochondrial depolarization. Furthermore, the upregulation of mitochondrial Ca2+ uniporter can promote DADs through Ca2+-dependent opening of mitochondrial permeability transition pores (mPTPs). Also, due to much slower dynamics than Ca2+ cycling and ROS, oxidized CaMKII activation and the cytosolic ATP do not appear to significantly impact the genesis of DADs during the acute phase of mitochondrial depolarization. However, under chronic conditions, ATP depletion suppresses and enhanced CaMKII activation promotes Ca2+ waves and DADs.

Intracellular calcium (Ca) cycling in the heart plays key roles in excitation–contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.

Abstract Early afterdepolarizations (EADs) are abnormal depolarizations during the repolarizing phase of the action potential, which are associated with cardiac arrhythmogenesis. EADs are classified into phase‐2 and phase‐3 EADs. Phase‐2 EADs occur during phase 2 of the action potential, with takeoff potentials typically above −40 mV. Phase‐3 EADs occur during phase 3 of the action potential, with takeoff potential between −70 and −50 mV. Since the amplitude of phase‐3 EADs can be as large as that of a regular action potential, they are also called triggered activities (TAs). This also makes phase‐3 EADs and TAs much more arrhythmogenic than phase‐2 EADs since they can propagate easily in tissue. Although phase‐2 EADs have been widely observed, phase‐3 EADs and TAs have been rarely demonstrated in isolated ventricular myocytes. Here we carry out computer simulations of three widely used ventricular action potential models to investigate the mechanisms of phase‐3 EADs and TAs. We show that when the T‐type Ca2+ current (ICa,T) is absent (e.g., in normal ventricular myocytes), besides the requirement of increasing inward currents and reducing outward currents as for phase‐2 EADs, the occurrence of phase‐3 EADs and TAs requires a substantially large increase of the L‐type Ca2+ current and the slow component of the delayed rectifier K+ current. The presence of ICa,T (e.g., in neonatal and failing ventricular myocytes) can greatly reduce the thresholds of these two currents for phase‐3 EADs and TAs. This implies that ICa,T may play an important role in arrhythmogenesis in cardiac diseases.

Mitochondria are vital organelles inside the cell and contribute to intracellular calcium (Ca2+) dynamics directly and indirectly via calcium exchange, ATP generation, and production of reactive oxygen species (ROS). Arrhythmogenic Ca2+ alternans in cardiac myocytes has been observed in experiments under abnormal mitochondrial depolarization. However, complex signaling pathways and Ca2+ cycling between mitochondria and cytosol make it difficult in experiments to reveal the underlying mechanisms of Ca2+ alternans under abnormal mitochondrial depolarization. In this study, we use a newly developed spatiotemporal ventricular myocyte computer model that integrates mitochondrial Ca2+ cycling and complex signaling pathways to investigate the mechanisms of Ca2+ alternans during mitochondrial depolarization. We find that elevation of ROS in response to mitochondrial depolarization plays a critical role in promoting Ca2+ alternans. Further examination reveals that the redox effect of ROS on ryanodine receptors and sarco/endoplasmic reticulum Ca2+-ATPase synergistically promote alternans. Upregulation of mitochondrial Ca2+ uniporter promotes Ca2+ alternans via Ca2+-dependent mitochondrial permeability transition pore opening. Due to their relatively slow kinetics, oxidized Ca2+/calmodulin-dependent protein kinase II activation and ATP do not play significant roles acutely in the genesis of Ca2+ alternans after mitochondrial depolarization, but their roles can be significant in the long term, mainly through their effects on sarco/endoplasmic reticulum Ca2+-ATPase activity. In conclusion, mitochondrial depolarization promotes Ca2+ alternans acutely via the redox effect of ROS and chronically by ATP reduction. It suppresses Ca2+ alternans chronically through oxidized Ca2+/calmodulin-dependent protein kinase II activation.

Biological excitable media, such as cardiac or neural cells and tissue, exhibit memory in which a change in the present excitation may affect the behaviors in the next excitation. For example, a change in calcium (Ca2+) concentration in a cell in the present excitation may affect the Ca2+ dynamics in the next excitation via bi-directional coupling between voltage and Ca2+, forming a delayed feedback loop. Since the Ca2+ dynamics inside the excitable cells are spatiotemporal while the membrane voltage is a global signal, the feedback loop is then a delayed global feedback (DGF) loop. In this study, we investigate the roles of DGF in the genesis and stability of spatiotemporal excitation patterns in periodically-paced excitable media using mathematical models with different levels of complexity: a model composed of coupled FitzHugh-Nagumo units, a 3-dimensional physiologically-detailed ventricular myocyte model, and a coupled map lattice model. We investigate the dynamics of excitation patterns that are temporal period-2 (P2) and spatially concordant or discordant, such as subcellular concordant or discordant Ca2+alternans in cardiac myocytes or spatially concordant or discordant Ca2+ and repolarization alternans in cardiac tissue. Our modeling approach allows both computer simulations and rigorous analytical treatments, which lead to the following results and conclusions. When DGF is absent, concordant and discordant P2 patterns occur depending on initial conditions with the discordant P2 patterns being spatially random. When the DGF is negative, only concordant P2 patterns exist. When the DGF is positive, both concordant and discordant P2 patterns can occur. The discordant P2 patterns are still spatially random, but they satisfy that the global signal exhibits a temporal period-1 behavior. The theoretical analyses of the coupled map lattice model reveal the underlying instabilities and bifurcations for the genesis, selection, and stability of spatiotemporal excitation patterns.

Early afterdepolarizations (EADs) are spontaneous depolarizations during the repolarization phase of an action potential in cardiac myocytes. It is widely known that EADs are promoted by increasing inward currents and/or decreasing outward currents, a condition called reduced repolarization reserve. Recent studies based on bifurcation theories show that EADs are caused by a dual Hopf-homoclinic bifurcation, bringing in further mechanistic insights into the genesis and dynamics of EADs. In this study, we investigated the EAD properties, such as the EAD amplitude, the inter-EAD interval, and the latency of the first EAD, and their major determinants. We first made predictions based on the bifurcation theory and then validated them in physiologically more detailed action potential models. These properties were investigated by varying one parameter at a time or using parameter sets randomly drawn from assigned intervals. The theoretical and simulation results were compared with experimental data from the literature. Our major findings are that the EAD amplitude and takeoff potential exhibit a negative linear correlation; the inter-EAD interval is insensitive to the maximum ionic current conductance but mainly determined by the kinetics of ICa,L and the dual Hopf-homoclinic bifurcation; and both inter-EAD interval and latency vary largely from model to model. Most of the model results generally agree with experimental observations in isolated ventricular myocytes. However, a major discrepancy between modeling results and experimental observations is that the inter-EAD intervals observed in experiments are mainly between 200 and 500 ms, irrespective of species, while those of the mathematical models exhibit a much wider range with some models exhibiting inter-EAD intervals less than 100 ms. Our simulations show that the cause of this discrepancy is likely due to the difference in ICa,L recovery properties in different mathematical models, which needs to be addressed in future action potential model development.

BackgroundHeart failure (HF) is associated with increased arrhythmia risk and triggered activity. Abnormal Ca2+ handling is thought to underlie triggered activity, and mitochondria participate in Ca2+ homeostasis. Methods and ResultsA model of nonischemic HF was induced in C57BL/6 mice by hypertension. Computer simulations were performed using a mouse ventricular myocyte model of HF. Isoproterenol‐induced premature ventricular contractions and ventricular fibrillation were more prevalent in nonischemic HF mice than sham controls. Isolated myopathic myocytes showed decreased cytoplasmic Ca2+ transients, increased mitochondrial Ca2+ transients, and increased action potential duration at 90% repolarization. The alteration of action potential duration at 90% repolarization was consistent with in vivo corrected QT prolongation and could be explained by augmented L‐type Ca2+ currents, increased Na+‐Ca2+ exchange currents, and decreased total K+ currents. Of myopathic ventricular myocytes, 66% showed early afterdepolarizations (EADs) compared with 17% of sham myocytes (P

Multicellular spheroids generated through cellular self-assembly provide cytoarchitectural complexities of native tissue including three-dimensionality, extensive cell-cell contacts, and appropriate cell-extracellular matrix interactions. They are increasingly suggested as building blocks for larger engineered tissues to achieve shapes, organization, heterogeneity, and other biomimetic complexities. Application of these tissue culture platforms is of particular importance in cardiac research as the myocardium is comprised of distinct but intermingled cell types. Here, we generated scaffold-free 3D cardiac microtissue spheroids comprised of cardiac myocytes (CMs) and/or cardiac fibroblasts (CFs) and used them as building blocks to form larger microtissues with different spatial distributions of CMs and CFs. Characterization of fusing homotypic and heterotypic spheroid pairs revealed an important influence of CFs on fusion kinetics, but most strikingly showed rapid fusion kinetics between heterotypic pairs consisting of one CF and one CM spheroid, indicating that CMs and CFs self-sort in vitro into the intermixed morphology found in the healthy myocardium. We then examined electrophysiological integration of fused homotypic and heterotypic microtissues by mapping action potential propagation. Heterocellular elongated microtissues which recapitulate the disproportionate CF spatial distribution seen in the infarcted myocardium showed that action potentials propagate through CF volumes albeit with significant delay. Complementary computational modeling revealed an important role of CF sodium currents and the spatial distribution of the CM-CF boundary in action potential conduction through CF volumes. Taken together, this study provides useful insights for the development of complex, heterocellular engineered 3D tissue constructs and their engraftment via tissue fusion and has implications for arrhythmogenesis in cardiac disease and repair.

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart's susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism.

Calcium (Ca) sparks are elementary events of biological Ca signaling. A normal Ca spark has a brief duration in the range of 10 to 100 ms, but long-lasting sparks with durations of several hundred milliseconds to seconds are also widely observed. Experiments have shown that the transition from normal to long-lasting sparks can occur when ryanodine receptor (RyR) open probability is either increased or decreased. Here, we demonstrate theoretically and computationally that long-lasting sparks emerge as a collective dynamical behavior of the network of diffusively coupled Ca release units (CRUs). We show that normal sparks occur when the CRU network is monostable and excitable, while long-lasting sparks occur when the network dynamics possesses multiple metastable attractors, each attractor corresponding to a different spatial firing pattern of sparks. We further highlight the mechanisms and conditions that produce long-lasting sparks, demonstrating the existence of an optimal range of RyR open probability favoring long-lasting sparks. We find that when CRU firings are sparse and sarcoplasmic reticulum (SR) Ca load is high, increasing RyR open probability promotes long-lasting sparks by potentiating Ca-induced Ca release (CICR). In contrast, when CICR is already strong enough to produce frequent firings, decreasing RyR open probability counter-intuitively promotes long-lasting sparks by decreasing spark frequency. The decrease in spark frequency promotes intra-SR Ca diffusion from neighboring non-firing CRUs to the firing CRUs, which helps to maintain the local SR Ca concentration of the firing CRUs above a critical level to sustain firing. In this setting, decreasing RyR open probability further suppresses long-lasting sparks by weakening CICR. Since a long-lasting spark terminates via the Kramers' escape process over a potential barrier, its duration exhibits an exponential distribution determined by the barrier height and noise strength, which is modulated differently by different ways of altering the Ca release flux strength.

BACKGROUND:Remodeling of cardiac repolarizing currents, such as the downregulation of slowly activating K+ channels (IKs), could underlie ventricular fibrillation (VF) in heart failure (HF). We evaluated the role of Iks remodeling in VF susceptibility using a tachypacing HF model of transgenic rabbits with Long QT Type 1 (LQT1) syndrome. METHODS AND RESULTS:LQT1 and littermate control (LMC) rabbits underwent three weeks of tachypacing to induce cardiac myopathy (TICM). In vivo telemetry demonstrated steepening of the QT/RR slope in LQT1 with TICM (LQT1-TICM; pre: 0.26±0.04, post: 0.52±0.01, P

In this review, we examine cardiovascular metabolism from three different, but highly complementary, perspectives. First, from the abstract perspective of a metabolite network, composed of nodes and links. We present fundamental concepts in network theory, including emergence, to illustrate how nature has designed metabolism with a hierarchal modular scale-free topology to provide a robust system of energy delivery. Second, from the physical perspective of a modular spatially compartmentalized network. We review evidence that cardiovascular metabolism is functionally compartmentalized, such that oxidative phosphorylation, glycolysis, and glycogenolysis preferentially channel ATP to ATPases in different cellular compartments, using creatine kinase and adenylate kinase to maximize efficient energy delivery. Third, from the dynamics perspective, as a network of dynamically interactive metabolic modules capable of self-oscillation. Whereas normally, cardiac metabolism exists in a regime in which excitation-metabolism coupling closely matches energy supply and demand, we describe how under stressful conditions, the network can be pushed into a qualitatively new dynamic regime, manifested as cell-wide oscillations in ATP levels, in which the coordination between energy supply and demand is lost. We speculate how this state of “metabolic fibrillation” leads to cell death if not corrected and discuss the implications for cardioprotection.

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

Protein ubiquitination and degradation play important roles in many biological functions and are associated with many human diseases. It is well known that for biochemical oscillations to occur, proper degradation rates of the participating proteins are needed. In most mathematical models of biochemical reactions, linear degradation kinetics has been used. However, the degradation kinetics in real systems may be nonlinear, and how nonlinear degradation kinetics affects biological oscillations are not well understood. In this study, we first develop a biochemical reaction model of protein ubiquitination and degradation and calculate the degradation rate against the concentration of the free substrate. We show that the protein degradation kinetics mainly follows the Michaelis-Menten formulation with a time delay caused by ubiquitination and deubiquitination. We then study analytically how the Michaelis-Menten degradation kinetics affects the instabilities that lead to oscillations using three generic oscillation models: 1) a positive feedback mediated oscillator; 2) a positive-plus-negative feedback mediated oscillator; and 3) a negative feedback mediated oscillator. In all three cases, nonlinear degradation kinetics promotes oscillations, especially for the negative feedback mediated oscillator, resulting in much larger oscillation amplitudes and slower frequencies than those observed with linear kinetics. However, the time delay due to protein ubiquitination and deubiquitination generally suppresses oscillations, reducing the amplitude and increasing the frequency of the oscillations. These theoretical analyses provide mechanistic insights into the effects of specific proteins in the ubiquitination-proteasome system on biological oscillations.

The reaction-diffusion equations have been widely used in physics, chemistry, and other areas. Forest fire can also be described by such equations. We here propose a fighting forest fire model. By using the normal form approach theory and center manifold theory, we analyze the stability of the trivial solution and Hopf bifurcation of this model. Finally, we give the numerical simulations to illustrate the effectiveness of our results.

In normal cardiac myocytes, the action potential duration (APD) is several hundred milliseconds. However, experimental studies showed that under certain conditions, APD could be excessively long (or ultralong), up to several seconds. Unlike the normal APD, the ultralong APD increases sensitively with pacing cycle length even when the pacing rate is very slow, exhibiting a sensitive slow rate-dependence. In addition, these long action potentials may or may not exhibit early afterdepolarizations (EADs). Although these phenomena are well known, the underlying mechanisms and ionic determinants remain incompletely understood. In this study, computer simulations were performed with a simplified action potential model. Modifications to the L-type calcium current (I(Ca,L)) kinetics and the activation time constant of the delayed rectifier K current were used to investigate their effects on APD. We show that: 1) the ultralong APD and its sensitive slow rate-dependence are determined by the steady-state window and pedestal I(Ca,L) currents and the activation speed and the recovery of the delayed rectifier K current; 2) whether an ultralong action potential exhibits EADs or not depends on the kinetics of I(Ca,L); 3) increasing inward currents elevates the plateau voltage, which in general prolongs APD, however, this can also shorten APD when the APD is already ultralong under certain conditions; and 4) APD alternans occurs at slow pacing rates due to the sensitive slow rate-dependence and the ionic determinants are different from the ones causing APD alternans at fast heart rates.