A Stochastic Spatiotemporal Model of Rat Ventricular Myocyte Calcium Dynamics Demonstrated Necessary Features for Calcium Wave Propagation

Making time and space for calcium control of neuron activity

Calcium directly controls or indirectly regulates numerous functions that are critical for neuronal network activity. Intracellular calcium concentration is tightly regulated by numerous molecular mechanisms because spatial domains and temporal dynamics (not just peak amplitude) are critical for calcium control of synaptic plasticity and ion channel activation, which in turn determine neuron spiking activity. The computational models investigating calcium control are valuable because experiments achieving high spatial and temporal resolution simultaneously are technically unfeasible. Simulations of calcium nanodomains reveal that specific calcium sources can couple to specific calcium targets, providing a mechanism to determine the direction of synaptic plasticity. Cooperativity of calcium domains opposes specificity, suggesting that the dendritic branch might be the preferred computational unit of the neuron.

Local Control Model of a Human Ventricular Myocyte: An Exploration of Frequency-Dependent Changes and Calcium Sparks

Calcium (Ca2+) sparks are the elementary events of excitation-contraction coupling, yet they are not explicitly represented in human ventricular myocyte models. A stochastic ventricular cardiomyocyte human model that adapts to intracellular Ca2+ ([Ca2+]i) dynamics, spark regulation, and frequency-dependent changes in the form of locally controlled Ca2+ release was developed. The 20,000 CRUs in this model are composed of 9 individual LCCs and 49 RyRs that function as couplons. The simulated action potential duration at 1 Hz steady-state pacing is ~0.280 s similar to human ventricular cell recordings. Rate-dependence experiments reveal that APD shortening mechanisms are largely contributed by the L-type calcium channel inactivation, RyR open fraction, and [Ca2+]myo concentrations. The dynamic slow-rapid-slow pacing protocol shows that RyR open probability during high pacing frequency (2.5 Hz) switches to an adapted "nonconducting" form of Ca2+-dependent transition state. The predicted force was also observed to be increased in high pacing, but the SR Ca2+ fractional release was lower due to the smaller difference between diastolic and systolic [Ca2+]SR. Restitution analysis through the S1S2 protocol and increased LCC Ca2+-dependent activation rate show that the duration of LCC opening helps modulate its effects on the APD restitution at different diastolic intervals. Ultimately, a longer duration of calcium sparks was observed in relation to the SR Ca2+ loading at high pacing rates. Overall, this study demonstrates the spontaneous Ca2+ release events and ion channel responses throughout various stimuli.

Understanding Calmodulin Variants Affecting Calcium-Dependent Inactivation of L-Type Calcium Channels through Whole-Cell Simulation of the Cardiac Ventricular Myocyte

Mutations in the calcium-sensing protein calmodulin (CaM) have been linked to two cardiac arrhythmia diseases, Long QT Syndrome 14 (LQT14) and Catecholaminergic Polymorphic Ventricular Tachycardia Type 4 (CPVT4), with varying degrees of severity. Functional characterization of the CaM mutants most strongly associated with LQT14 show a clear disruption of the calcium-dependent inactivation (CDI) of the L-Type calcium channel (LCC). CPVT4 mutants on the other hand are associated with changes in their affinity to the ryanodine receptor. In clinical studies, some variants have been associated with both CPVT4 and LQT15. This study uses simulations in a model for excitation-contraction coupling in the rat ventricular myocytes to understand how LQT14 variant might give the functional phenotype similar to CPVT4. Changing the CaM-dependent transition rate by a factor of 0.75 corresponding to the D96V variant and by a factor of 0.90 corresponding to the F142L or N98S variants, in a physiologically based stochastic model of the LCC prolonger, the action potential duration changed by a small amount in a cardiac myocyte but did not disrupt CICR at 1, 2, and 4 Hz. Under beta-adrenergic simulation abnormal excitation-contraction coupling was observed above 2 Hz pacing for the mutant CaM. The same conditions applied under beta-adrenergic stimulation led to the rapid onset of arrhythmia in the mutant CaM simulations. Simulations with the LQT14 mutations under the conditions of rapid pacing with beta-adrenergic stimulation drives the cardiac myocyte toward an arrhythmic state known as Ca2+ overload. These simulations provide a mechanistic link to a disease state for LQT14-associated mutations in CaM to yield a CPVT4 phenotype. The results show that small changes to the CaM-regulated inactivation of LCC promote arrhythmia and underscore the significance of CDI in proper heart function.

Pacing Dynamics Determines the Arrhythmogenic Mechanism of the CPVT2-Causing CASQ2G112+5X Mutation in a Guinea Pig Ventricular Myocyte Computational Model

Calsequestrin Type 2 (CASQ2) is a high-capacity, low-affinity, Ca2+-binding protein expressed in the sarcoplasmic reticulum (SR) of the cardiac myocyte. Mutations in CASQ2 have been linked to the arrhythmia catecholaminergic polymorphic ventricular tachycardia (CPVT2) that occurs with acute emotional stress or exercise can result in sudden cardiac death (SCD). CASQ2G112+5X is a 16 bp (339-354) deletion CASQ2 mutation that prevents the protein expression due to premature stop codon. Understanding the subcellular mechanisms of CPVT2 is experimentally challenging because the occurrence of arrhythmia is rare. To obtain an insight into the characteristics of this rare disease, simulation studies using a local control stochastic computational model of the Guinea pig ventricular myocyte investigated how the mutant CASQ2s may be responsible for the development of an arrhythmogenic episode under the condition of β-adrenergic stimulation or in the slowing of heart rate afterward once β-adrenergic stimulation ceases. Adjustment of the computational model parameters based upon recent experiments explore the functional changes caused by the CASQ2 mutation. In the simulation studies under rapid pacing (6 Hz), electromechanically concordant cellular alternans appeared under β-adrenergic stimulation in the CPVT mutant but not in the wild-type nor in the non-β-stimulated mutant. Similarly, the simulations of accelerating pacing from slow to rapid and back to the slow pacing did not display alternans but did generate early afterdepolarizations (EADs) during the period of second slow pacing subsequent acceleration of rapid pacing.

Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges

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.

The Role of Ca2+ Sparks in Force Frequency Relationships in Guinea Pig Ventricular Myocytes

Calcium sparks are the elementary Ca2+ release events in excitation-contraction coupling that underlie the Ca2+ transient. The frequency-dependent contractile force generated by cardiac myocytes depends upon the characteristics of the Ca2+ transients. A stochastic computational local control model of a guinea pig ventricular cardiomyocyte was developed, to gain insight into mechanisms of force-frequency relationship (FFR). This required the creation of a new three-state RyR2 model that reproduced the adaptive behavior of RyR2, in which the RyR2 channels transition into a different state when exposed to prolonged elevated subspace [Ca2+]. The model simulations agree with previous experimental and modeling studies on interval-force relations. Unlike previous common pool models, this local control model displayed stable action potential trains at 7 Hz. The duration and the amplitude of the [Ca2+]myo transients increase in pacing rates consistent with the experiments. The [Ca2+]myo transient reaches its peak value at 4 Hz and decreases afterward, consistent with experimental force-frequency curves. The model predicts, in agreement with previous modeling studies of Jafri and co-workers, diastolic sarcoplasmic reticulum, [Ca2+]sr, and RyR2 adaptation increase with the increased stimulation frequency, producing rising, rather than falling, amplitude of the myoplasmic [Ca2+] transients. However, the local control model also suggests that the reduction of the L-type Ca2+ current, with an increase in pacing frequency due to Ca2+-dependent inactivation, also plays a role in the negative slope of the FFR. In the simulations, the peak Ca2+ transient in the FFR correlated with the highest numbers of SR Ca2+ sparks: the larger average amplitudes of those sparks, and the longer duration of the Ca2+ sparks.

Critical Requirements for the Initiation of a Cardiac Arrhythmia in Rat Ventricle: How Many Myocytes?

Cardiovascular disease is the leading cause of death worldwide due in a large part to arrhythmia. In order to understand how calcium dynamics play a role in arrhythmogenesis, normal and dysfunctional Ca²⁺ signaling in a subcellular, cellular, and tissued level is examined using cardiac ventricular myocytes at a high temporal and spatial resolution using multiscale computational modeling. Ca²⁺ sparks underlie normal excitation-contraction coupling. However, under pathological conditions, Ca²⁺ sparks can combine to form Ca²⁺ waves. These propagating elevations of (Ca²⁺)_i can activate an inward Na⁺-Ca²⁺ exchanger current (I_NCX) that contributes to early after-depolarization (EADs) and delayed after-depolarizations (DADs). However, how cellular currents lead to full depolarization of the myocardium and how they initiate extra systoles is still not fully understood. This study explores how many myocytes must be entrained to initiate arrhythmogenic depolarizations in biophysically detailed computational models. The model presented here suggests that only a small number of myocytes must activate in order to trigger an arrhythmogenic propagating action potential. These conditions were examined in 1-D, 2-D, and 3-D considering heart geometry. The depolarization of only a few hundred ventricular myocytes is required to trigger an ectopic depolarization. The number decreases under disease conditions such as heart failure. Furthermore, in geometrically restricted parts of the heart such as the thin muscle strands found in the trabeculae and papillary muscle, the number of cells needed to trigger a propagating depolarization falls even further to less than ten myocytes.

Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives

Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.