Ca2+-activation kinetics modulate successive puff/spark amplitude, duration and inter-event-interval correlations in a Langevin model of stochastic Ca2+ release

An integrate-and-fire approach to Ca2+ signaling. Part I: Renewal model

In computational neuroscience integrate-and-fire models capture the spike generation by a subthreshold dynamics supplemented by a simple fire-and-reset rule; they allow for a numerically efficient and analytically tractable description of stochastic single cell as well as network dynamics. Stochastic spiking is also a prominent feature of Ca2+ signaling which suggests to adopt the integrate-and-fire approach for this fundamental biophysical process. The model introduced here consists of two components describing 1) activity of clusters of inositol-trisphosphate receptor channels and 2) dynamics of the global Ca2+ concentrations in the cytosol. The cluster dynamics is given in terms of a cyclic Markov chain, capturing the puff, i.e., the punctuated release of Ca2+ from intracellular stores. The cytosolic Ca2+ concentration is described by an integrate-and-fire dynamics driven by the puff current. For the cyclic Markov chain we derive expressions for the statistics of the interpuff interval, the single-puff strength and the puff current assuming constant cytosolic Ca2+. The latter condition is often well approximated because cytosolic Ca2+ varies much slower than the cluster activity does. Furthermore, because the detailed two-component model is numerically expensive to simulate and difficult to treat analytically, we develop an analytical framework to approximate the driving puff current of the stochastic cytosolic Ca2+ dynamics by a temporally uncorrelated Gaussian noise. This approximation reduces our two-component system to an integrate-and-fire model with a nonlinear drift function and a multiplicative Gaussian white noise, a model that is known to generate a renewal spike train, i.e., a point process with statistically independent interspike intervals. The model allows for fast numerical simulations, permits to derive analytical expressions for the rate of Ca2+ spiking and the coefficient of variation of the interspike interval, and to approximate the interspike interval density and the spike train power spectrum. Comparison of these statistics to experimental data is discussed.

Anti-cross-correlation between the adjacent open and closed durations of Markovian channels

We show that a non-Markovian behavior can appear in a type of Markovian multimeric channel. Such a channel consists of N independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as M out of N subunits in the open state with N>M>0. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can show a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.

Memory in a fractional-order cardiomyocyte model alters properties of alternans and spontaneous activity

Cardiac memory is the dependence of electrical activity on the prior history of one or more system state variables, including transmembrane potential (V_m), ionic current gating, and ion concentrations. While prior work has represented memory either phenomenologically or with biophysical detail, in this study, we consider an intermediate approach of a minimal three-variable cardiomyocyte model, modified with fractional-order dynamics, i.e., a differential equation of order between 0 and 1, to account for history-dependence. Memory is represented via both capacitive memory, due to fractional-order V_m dynamics, that arises due to non-ideal behavior of membrane capacitance; and ionic current gating memory, due to fractional-order gating variable dynamics, that arises due to gating history-dependence. We perform simulations for varying V_m and gating variable fractional-orders and pacing cycle length and measure action potential duration (APD) and incidence of alternans, loss of capture, and spontaneous activity. In the absence of ionic current gating memory, we find that capacitive memory, i.e., decreased V_m fractional-order, typically shortens APD, suppresses alternans, and decreases the minimum cycle length (MCL) for loss of capture. However, in the presence of ionic current gating memory, capacitive memory can prolong APD, promote alternans, and increase MCL. Further, we find that reduced V_m fractional order (typically less than 0.75) can drive phase 4 depolarizations that promote spontaneous activity. Collectively, our results demonstrate that memory reproduced by a fractional-order model can play a role in alternans formation and pacemaking, and in general, can greatly increase the range of electrophysiological characteristics exhibited by a minimal model.

Role of Cytosolic Calcium Diffusion in Murine Cardiac Purkinje Cells

Cardiac Purkinje cells (PCs) are morphologically and electrophysiologically different from ventricular myocytes and, importantly, exhibit distinct calcium (Ca²⁺) homeostasis. Recent studies suggest that PCs are more susceptible to action potential (AP) abnormalities than ventricular myocytes; however, the exact mechanisms are poorly understood. In this study, we utilized a detailed biophysical mathematical model of a murine PC to systematically examine the role of cytosolic Ca²⁺ diffusion in shaping the AP in PCs. A biphasic spatiotemporal Ca²⁺ diffusion process, as recorded experimentally, was implemented in the model. In this study, we investigated the role of cytosolic Ca²⁺ dynamics on AP and ionic current properties by varying the effective Ca²⁺ diffusion rate. It was observed that AP morphology, specifically the plateau, was affected due to changes in the intracellular Ca²⁺ dynamics. Elevated Ca²⁺ concentration in the sarcolemmal region activated inward sodium–Ca²⁺ exchanger (NCX) current, resulting in a prolongation of the AP plateau at faster diffusion rates. Artificially clamping the NCX current to control values completely reversed the alterations in the AP plateau, thus confirming the role of NCX in modifying the AP morphology. Our results demonstrate that cytosolic Ca²⁺ diffusion waves play a significant role in shaping APs of PCs and could provide mechanistic insights in the increased arrhythmogeneity of PCs.