Calcium spikes: Chance or necessity?

Modeling IP3-induced Ca2+ signaling based on its interspike interval statistics

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. Recent research demonstrated randomness of Ca2+ signaling on all structural levels. We compile eight general properties of Ca2+ spiking common to all cell types investigated and suggest a theory of Ca2+ spiking starting from the random behavior of IP3 receptor channel clusters mediating the release of Ca2+ from the endoplasmic reticulum capturing all general properties and pathway-specific behavior. Spike generation begins after the absolute refractory period of the previous spike. According to its hierarchical spreading from initiating channel openings to cell level, we describe it as a first passage process from none to all clusters open while the cell recovers from the inhibition which terminated the previous spike. Our theory reproduces the exponential stimulation response relation of the average interspike interval Tav and its robustness properties, random spike timing with a linear moment relation between Tav and the interspike interval SD and its robustness properties, sensitive dependency of Tav on diffusion properties, and nonoscillatory local dynamics. We explain large cell variability of Tav observed in experiments by variability of channel cluster coupling by Ca2+-induced Ca2+ release, the number of clusters, and IP3 pathway component expression levels. We predict the relation between puff probability and agonist concentration and [IP3] and agonist concentration. Differences of spike behavior between cell types and stimulating agonists are explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the identified general properties.

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.

Deterministic Limit of Intracellular Calcium Spikes

In nonexcitable cells, global Ca^{2+} spikes emerge from the collective dynamics of clusters of Ca^{2+} channels that are coupled by diffusion. Current modeling approaches have opposed stochastic descriptions of these systems to purely deterministic models, while both paradoxically appear compatible with experimental data. Combining fully stochastic simulations and mean-field analyses, we demonstrate that these two approaches can be reconciled. Our fully stochastic model generates spike sequences that can be seen as noise-perturbed oscillations of deterministic origin, while displaying statistical properties in agreement with experimental data. These underlying deterministic oscillations arise from a phenomenological spike nucleation mechanism.

Stochastic contribution for the coding of agonist induced calcium oscillation in hepatocytes

The influence of stochastic inositol-1,4,5-trisphosphate receptor (IP₃R) dynamics and their clustering have been extensively investigated to explore the mechanism through which the stochastic molecular event finally shape the intracellular calcium signaling. Most of the previous works employed simplified models which take the concentration of IP₃ instead of that of the agonist as the stimulation intensity. However, the IP₃ level is not linearly dependent on the agonist concentration in stimulus induced signaling systems because there are feedback links in the transduction network. In this work, we include both the IP₃R dynamics and the typical agonist induced signaling transduction cascade in the model to investigate the essential influence of stochastic IP₃R dynamics on the coding of the stimulus induced calcium signal. Simulation results reveal two distinct oscillation areas under different stimulation levels. The signal is optimally modulate by the IP₃R cluster number in the weak stimulated area while affected by the stimulus intensity in the strong stimulated area. Different dependences of coefficient of variance (CV) on the number of clusters are obtained in these two areas, which explains the disagreement in the previous reported results. Besides, the transition between these areas explains the significant CV reduction observed in experiments.

Timescales of IP(3)-evoked Ca(2+) spikes emerge from Ca(2+) puffs only at the cellular level

The behavior of biological systems is determined by the properties of their component molecules, but the interactions are usually too complex to understand fully how molecular behavior generates cellular behavior. Ca(2+) signaling by inositol trisphosphate receptors (IP(3)R) offers an opportunity to understand this relationship because the cellular behavior is defined largely by Ca(2+)-mediated interactions between IP(3)R. Ca(2+) released by a cluster of IP(3)R (giving a local Ca(2+) puff) diffuses and ignites the behavior of neighboring clusters (to give repetitive global Ca(2+) spikes). We use total internal reflection fluorescence microscopy of two mammalian cell lines to define the temporal relationships between Ca(2+) puffs (interpuff intervals, IPI) and Ca(2+) spikes (interspike intervals) evoked by flash photolysis of caged IP(3). We find that IPI are much shorter than interspike intervals, that puff activity is stochastic with a recovery time that is much shorter than the refractory period of the cell, and that IPI are not periodic. We conclude that Ca(2+) spikes do not arise from oscillatory dynamics of IP(3)R clusters, but that repetitive Ca(2+) spiking with its longer timescales is an emergent property of the dynamics of the whole cluster array.

Quantifying the uncertainty of spontaneous Ca2+ oscillations in astrocytes: particulars of Alzheimer's disease

The quantification of spontaneous calcium (Ca(2+)) oscillations (SCOs) in astrocytes presents a challenge because of the large irregularities in the amplitudes, durations, and initiation times of the underlying events. In this article, we use a stochastic context to account for such SCO variability, which is based on previous models for cellular Ca(2+) signaling. First, we found that passive Ca(2+) influx from the extracellular space determine the basal concentration of this ion in the cytosol. Second, we demonstrated the feasibility of estimating both the inositol 1,4,5-trisphosphate (IP(3)) production levels and the average number of IP(3) receptor channels in the somatic clusters from epifluorescent Ca(2+) imaging through the combination of a filtering strategy and a maximum-likelihood criterion. We estimated these two biophysical parameters using data from wild-type adult mice and age-matched transgenic mice overexpressing the 695-amino-acid isoform of human Alzheimer β-amyloid precursor protein. We found that, together with an increase in the passive Ca(2+) influx, a significant reduction in the sensitivity of G protein-coupled receptors might lie beneath the abnormalities in the astrocytic Ca(2+) signaling, as was observed in rodent models of Alzheimer's disease. This study provides new, to our knowledge, indices for a quantitative analysis of SCOs in normal and pathological astrocytes.