A Statistical View on Calcium Oscillations

T cell Ca2+ microdomains through the lens of computational modeling

Cellular Ca2+ signaling is highly organized in time and space. Locally restricted and short-lived regions of Ca2+ increase, called Ca2+ microdomains, constitute building blocks that are differentially arranged to create cellular Ca2+ signatures controlling physiological responses. Here, we focus on Ca2+ microdomains occurring in restricted cytosolic spaces between the plasma membrane and the endoplasmic reticulum, called endoplasmic reticulum-plasma membrane junctions. In T cells, these microdomains have been finely characterized. Enough quantitative data are thus available to develop detailed computational models of junctional Ca2+ dynamics. Simulations are able to predict the characteristics of Ca2+ increases at the level of single channels and in junctions of different spatial configurations, in response to various signaling molecules. Thanks to the synergy between experimental observations and computational modeling, a unified description of the molecular mechanisms that create Ca2+ microdomains in the first seconds of T cell stimulation is emerging.

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.

A Tale of two receptors

Calcium (Ca²⁺) oscillations in hepatocytes have a wide dynamic range. In particular, recent experimental evidence shows that agonist stimulation of the P2Y family of receptors leads to qualitatively diverse Ca²⁺ oscillations. We present a new model of Ca²⁺ oscillations in hepatocytes based on these experiments to investigate the mechanisms controlling P2Y-activated Ca²⁺ oscillations. The model accounts for Ca²⁺ regulation of the IP₃ receptor (IP₃R), the positive feedback from Ca²⁺ on phospholipase C (PLC) and the P2Y receptor phosphorylation by protein kinase C (PKC). Furthermore, PKC is shown to control multiple cellular substrates. Utilising the model, we suggest the activity and intensity of PLC and PKC necessary to explain the qualitatively diverse Ca²⁺ oscillations in response to P2Y receptor activation.

The Oscillation Amplitude, Not the Frequency of Cytosolic Calcium, Regulates Apoptosis Induction

Although a rising concentration of cytosolic Ca²⁺ has long been recognized as an essential signal for apoptosis, the dynamical mechanisms by which Ca²⁺ regulates apoptosis are not clear yet. To address this, we constructed a computational model that integrates known biochemical reactions and can reproduce the dynamical behaviors of Ca²⁺-induced apoptosis as observed in experiments. Model analysis shows that oscillating Ca²⁺ signals first convert into gradual signals and eventually transform into a switch-like apoptotic response. Via the two processes, the apoptotic signaling pathway filters the frequency of Ca²⁺ oscillations effectively but instead responds acutely to their amplitude. Collectively, our results suggest that Ca²⁺ regulates apoptosis mainly via oscillation amplitude, rather than frequency, modulation. This study not only provides a comprehensive understanding of how oscillatory Ca²⁺ dynamically regulates the complex apoptotic signaling network but also presents a typical example of how Ca²⁺ controls cellular responses through amplitude modulation.

GPCR mediated control of calcium dynamics: A systems perspective

G-protein coupled receptor (GPCR) mediated calcium (Ca²⁺)-signaling transduction remains crucial in designing drugs for various complex diseases including neurodegeneration, chronic heart failure as well as respiratory diseases. Although there are several reviews detailing various aspects of Ca²⁺-signaling such as the role of IP₃ receptors and Ca²⁺-induced-Ca²⁺-release, none of them provide an integrated view of the mathematical descriptions of GPCR signal transduction and investigations on dose-response curves. This article is the first study in reviewing the network structures underlying GPCR signal transduction that control downstream [Ca_c²⁺]-oscillations. The central theme of this paper is to present the biochemical pathways, as well as molecular mechanisms underlying the GPCR-mediated Ca²⁺-dynamics in order to facilitate a better understanding of how agonist concentration is encoded in Ca²⁺-signals for G_αq, G_αs, and G_αi/o signaling pathways. Moreover, we present the GPCR targeting drugs that are relevant for treating cardiac, respiratory, and neuro-diseases. The current paper presents the ODE formulation for various models along with the detailed schematics of signaling networks. To provide a systems perspective, we present the network motifs that can provide readers an insight into the complex and intriguing science of agonist-mediated Ca²⁺-dynamics. One of the features of this review is to pinpoint the interplay between positive and negative feedback loops that are involved in controlling intracellular [Ca_c²⁺]-oscillations. Furthermore, we review several examples of dose-response curves obtained from [Ca_c²⁺]-spiking for various GPCR pathways. This paper is expected to be useful for pharmacologists and computational biologists for designing clinical applications of GPCR targeting drugs through modulation of Ca²⁺-dynamics.