Mechanisms and determinants of ultralong action potential duration and slow rate-dependence in cardiac myocytes.

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

A unified theory of calcium alternans in ventricular myocytes.

Intracellular calcium (Ca2+) alternans is a dynamical phenomenon in ventricular myocytes, which is linked to the genesis of lethal arrhythmias. Iterated map models of intracellular Ca2+ cycling dynamics in ventricular myocytes under periodic pacing have been developed to study the mechanisms of Ca2+ alternans. Two mechanisms of Ca2+ alternans have been demonstrated in these models: one relies mainly on fractional sarcoplasmic reticulum Ca2+ release and uptake, and the other on refractoriness and other properties of Ca2+ sparks. Each of the two mechanisms can partially explain the experimental observations, but both have their inconsistencies with the experimental results. Here we developed an iterated map model that is composed of two coupled iterated maps, which unifies the two mechanisms into a single cohesive mathematical framework. The unified theory can consistently explain the seemingly contradictory experimental observations and shows that the two mechanisms work synergistically to promote Ca2+ alternans. Predictions of the theory were examined in a physiologically-detailed spatial Ca2+ cycling model of ventricular myocytes

R-from-T as a common mechanism of arrhythmia initiation in long QT syndromes

Background: Long QT syndromes (LQTS) arise from many genetic and nongenetic causes with certain characteristic ECG features preceding polymorphic ventricular tachyarrhythmias (PVTs). However, how the many molecular causes result in these characteristic ECG patterns and how these patterns are mechanistically linked to the spontaneous initiation of PVT remain poorly understood. Methods: Anatomic human ventricle and simplified tissue models were used to investigate the mechanisms of spontaneous initiation of PVT in LQTS. Results: Spontaneous initiation of PVT was elicited by gradually ramping up I-Ca,I-L to simulate the initial phase of a sympathetic surge or by changing the heart rate, reproducing the different genotype-dependent clinical ECG features. In LQTS type 2 (LQT2) and LQTS type 3 (LQT3), T-wave alternans was observed followed by premature ventricular complexes (PVCs). Compensatory pauses occurred resulting in short-long-short sequences. As I-Ca,I-L increased further, PVT episodes occurred, always preceded by a short-long-short sequence. However, in LQTS type 1 (LQT1), once a PVC occurred, it always immediately led to an episode of PVT. Arrhythmias in LQT2 and LQT3 were bradycardia dependent, whereas those in LQT1 were not. In all 3 genotypes, PVCs always originated spontaneously from the steep repolarization gradient region and manifested on ECG as R-on-T. We call this mechanism R-from-T, to distinguish it from the classic explanation of R-on-T arrhythmogenesis in which an exogenous PVC coincidentally encounters a repolarizing region. In R-from-T, the PVC and the T wave are causally related, where steep repolarization gradients combined with enhanced I-Ca,I-L lead to PVCs emerging from the T wave. Since enhanced I-Ca,I-L was required for R-from-T to occur, suppressing window I-Ca,I-L effectively prevented arrhythmias in all 3 genotypes. Conclusions: Despite the complex molecular causes, these results suggest that R-from-T is likely a common mechanism for PVT initiation in LQTS. Targeting I-Ca,I-L properties, such as suppressing window I-Ca,I-L or preventing excessive I-Ca,I-L increase, could be an effective unified therapy for arrhythmia prevention in LQTS

Deducing topology of protein-protein interaction networks from experimentally measured sub-networks.

BackgroundProtein-protein interaction networks are commonly sampled using yeast two hybrid approaches. However, whether topological information reaped from these experimentally-measured sub-networks can be extrapolated to complete protein-protein interaction networks is unclear.ResultsBy analyzing various experimental protein-protein interaction datasets, we found that they are not random samples of the parent networks. Based on the experimental bait-prey behaviors, our computer simulations show that these non-random sampling features may affect the topological information. We tested the hypothesis that a core sub-network exists within the experimentally sampled network that better maintains the topological characteristics of the parent protein-protein interaction network. We developed a method to filter the experimentally sampled network to result in a core sub-network that more accurately reflects the topology of the parent network. These findings have fundamental implications for large-scale protein interaction studies and for our understanding of the behavior of cellular networks.ConclusionThe topological information from experimental measured networks network as is may not be the correct source for topological information about the parent protein-protein interaction network. We define a core sub-network that more accurately reflects the topology of the parent network

Computational Modeling and Numerical Methods for Spatiotemporal Calcium Cycling in Ventricular Myocytes

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown

Dynamic Properties of a Forest Fire Model

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

Spark-induced Sparks as a Mechanism of Intracellular Calcium Alternans in Cardiac Myocytes

Rationale: Intracellular calcium (Ca) alternans has been widely studied in cardiac myocytes and tissue, yet the underlying mechanism remains controversial. Objective: In this study, we used computational modeling and simulation to study how randomly occurring Ca sparks interact collectively to result in whole-cell Ca alternans. Methods and Results: We developed a spatially-distributed intracellular Ca cycling model in which Ca release units (CRUs) are locally coupled by Ca diffusion throughout the myoplasm and sarcoplasmic reticulum (SR) network. Ca sparks occur randomly in the CRU network when periodically paced with a clamped voltage waveform, but Ca alternans develops as the pacing speeds up. Combining computational simulation with theoretical analysis, we show that Ca alternans emerges as a collective behavior of Ca sparks, determined by three critical properties of the CRU network from which Ca sparks arise: randomness (of Ca spark activation), refractoriness (of a CRU after a Ca spark), and recruitment (Ca sparks inducing Ca sparks in adjacent CRUs). We also show that the steep nonlinear relationship between fractional SR Ca release and SR Ca load arises naturally as a collective behavior of Ca sparks, and Ca alternans can occur even when SR Ca is held constant. Conclusions: We present a general theory for the mechanisms of intracellular Ca alternans, which mechanistically links Ca sparks to whole-cell Ca alternans, and is applicable to Ca alternans in both physiological and pathophysiological conditions

Period-doubling Bifurcation in an Array of Coupled Stochastically-excitable Elements Subjected to Global Periodic Forcing

The collective behaviors of coupled, stochastically-excitable elements subjected to global periodic forcing are investigated numerically and analytically. We show that the whole system undergoes a period-doubling bifurcation as the driving period decreases, while the individual elements still exhibit random excitations. Using a mean-field representation, we show that this macroscopic bifurcation behavior is caused by interactions between the random excitation, the refractory period, and recruitment (spatial cooperativity) of the excitable elements

Acceleration of cardiac tissue simulation with graphic processing units

In this technical note we show the promise of using graphic processing units (GPUs) to accelerate simulations of electrical wave propagation in cardiac tissue, one of the more demanding computational problems in cardiology. We have found that the computational speed of two-dimensional (2D) tissue simulations with a single commercially available GPU is about 30 times faster than with a single 2.0 GHz Advanced Micro Devices (AMD) Opteron processor. We have also simulated wave conduction in the three-dimensional (3D) anatomic heart with GPUs where we found the computational speed with a single GPU is 1.6 times slower than with a 32-central processing unit (CPU) Opteron cluster. However, a cluster with two or four GPUs is faster than the CPU-based cluster. These results demonstrate that a commodity personal computer is able to perform a whole heart simulation of electrical wave conduction within times that enable the investigators to interact more easily with their simulations