A phenomenological cluster-based model of Ca2+ waves and oscillations for Inositol 1,4,5-trisphosphate receptor (IP3R) channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves, and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release -- puffs, waves, and oscillations respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. We connect the termination of large-scale Ca2+ release events to IP3 unbinding or stochasticity.Comment: 18 pages, 10 figure

A comparative study of early afterdepolarization-mediated fibrillation in two mathematical models for human ventricular cells

Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two-and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model

Calcium signaling during convergent extension in Xenopus

Background: During Xenopus gastrulation, cell intercalation drives convergent extension of dorsal tissues. This process requires the coordination of motility throughout a large population of cells. The signaling mechanisms that regulate these movements in space and time remain poorly understood. Results: To investigate the potential contribution of calcium signaling to the control of morphogenetic movements, we visualized calcium dynamics during convergent extension using a calcium-sensitive fluorescent dye and a novel confocal microscopy system. We found that dramatic intercellular waves of calcium mobilization occurred in cells undergoing convergent extension in explants of gastrulating Xenopus embryos. These waves arose stochastically with respect to timing and position within the dorsal tissues. Waves propagated quickly and were often accompanied by a wave of contraction within the tissue. Calcium waves were not observed in explants of the ventral marginal zone or prospective epidermis. Pharmacological depletion of intracellular calcium stores abolished the calcium dynamics and also inhibited convergent extension without affecting cell fate. These data indicate that calcium signaling plays a direct role in the coordination of convergent extension cell movements. Conclusions: The data presented here indicate that intercellular calcium signaling plays an important role in vertebrate convergent extension. We suggest that calcium waves may represent a widely used mechanism by which large groups of cells can coordinate complex cell movements

A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During the stage II these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing $V$-gated calcium channels and hyperpolarizing $V$-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.Comment: 25 pages, 13 figures, submitte

Electroencephalographic field influence on calcium momentum waves

Macroscopic EEG fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential $\mathbf{A}$. The bottom-up process considered are $\mathrm{Ca}^{2+}$ waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of $\mathbf{A}$ on $\mathrm{Ca}^{2+}$ momentum, $\mathbf{p}$. The canonical momentum of a charged particle in an electromagnetic field, $\mathbf{\Pi} = \mathbf{p} + q \mathbf{A}$ (SI units), is calculated, where the charge of $\mathrm{Ca}^{2+}$ is $q = - 2 e$, $e$ is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG $\mathbf{A}$ can be quite influential on the momentum $\mathbf{p}$ of $\mathrm{Ca}^{2+}$ ions, in both classical and quantum mechanics. Molecular scales of $\mathrm{Ca}^{2+}$ wave dynamics are coupled with $\mathbf{A}$ fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting $\mathbf{A}$ models to EEG data as reported here, building tripartite models to develop $\mathbf{A}$ models, and studying long coherence times of $\mathrm{Ca}^{2+}$ waves in the presence of $\mathbf{A}$ due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the $\mathbf{p} + q \mathbf{A}$ interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.Comment: Final draft. http://ingber.com/smni14_eeg_ca.pdf may be updated more frequentl

Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs or sparks) from spatially localised calcium stores. The aim of this paper is to analyse how the stochastic nature of individual receptors within these stores combines to create stochastic behaviour on long timescales that may ultimately lead to waves of activity in a spatially extended cell model. Techniques from asymptotic analysis and stochastic phase-plane analysis are used to show that a large cluster of receptor channels leads to a release probability with a sigmoidal dependence on calcium density. This release probability is incorporated into a computationally inexpensive model of calcium release based upon a stochastic generalization of the Fire-Diffuse-Fire (FDF) threshold model. Numerical simulations of the model in one and two dimensions (with stores arranged on both regular and disordered lattices) illustrate that stochastic calcium release leads to the spontaneous production of calcium sparks that may merge to form saltatory waves. Illustrations of spreading circular waves, spirals and more irregular waves are presented. Furthermore, receptor noise is shown to generate a form of array enhanced coherence resonance whereby all calcium stores release periodically and simultaneously

Amyloid β-peptide directly induces spontaneous calcium transients, delayed intercellular calcium waves and gliosis in rat cortical astrocytes

The contribution of astrocytes to the pathophysiology of AD (Alzheimer's disease) and the molecular and signalling mechanisms that potentially underlie them are still very poorly understood. However, there is mounting evidence that calcium dysregulation in astrocytes may be playing a key role. Intercellular calcium waves in astrocyte networks in vitro can be mechanically induced after Aβ (amyloid β-peptide) treatment, and spontaneously forming intercellular calcium waves have recently been shown in vivo in an APP (amyloid precursor protein)/PS1 (presenilin 1) Alzheimer's transgenic mouse model. However, spontaneous intercellular calcium transients and waves have not been observed in vitro in isolated astrocyte cultures in response to direct Aβ stimulation in the absence of potentially confounding signalling from other cell types. Here, we show that Aβ alone at relatively low concentrations is directly able to induce intracellular calcium transients and spontaneous intercellular calcium waves in isolated astrocytes in purified cultures, raising the possibility of a potential direct effect of Aβ exposure on astrocytes in vivo in the Alzheimer's brain. Waves did not occur immediately after Aβ treatment, but were delayed by many minutes before spontaneously forming, suggesting that intracellular signalling mechanisms required sufficient time to activate before intercellular effects at the network level become evident. Furthermore, the dynamics of intercellular calcium waves were heterogeneous, with distinct radial or longitudinal propagation orientations. Lastly, we also show that changes in the expression levels of the intermediate filament proteins GFAP (glial fibrillary acidic protein) and S100B are affected by Aβ-induced calcium changes differently, with GFAP being more dependent on calcium levels than S100B