Spatiotemporal organization of Ca dynamics: a modeling-based approach

Histamine activates an intracellular Ca2+ signal in normal human lung fibroblast WI-38 cells

Histamine is an inflammatory mediator that can be released from mast cells to induce airway remodeling and cause persistent airflow limitation in asthma. In addition to stimulating airway smooth muscle cell constriction and hyperplasia, histamine promotes pulmonary remodeling by inducing fibroblast proliferation, contraction, and migration. It has long been known that histamine receptor 1 (H1R) mediates the effects of histamine on human pulmonary fibroblasts through an increase in intracellular Ca2+ concentration ([Ca2+]i), but the underlying signaling mechanisms are still unknown. Herein, we exploited single-cell Ca2+ imaging to assess the signal transduction pathways whereby histamine generates intracellular Ca2+ signals in the human fetal lung fibroblast cell line, WI-38. WI-38 fibroblasts were loaded with the Ca2+-sensitive fluorophore, FURA-2/AM, and challenged with histamine in the absence and presence of specific pharmacological inhibitors to dissect the Ca2+ release/entry pathways responsible for the onset of the Ca2+ response. Histamine elicited complex intracellular Ca2+ signatures in WI-38 fibroblasts throughout a concentration range spanning between 1 µM and 1 mM. In accord, the Ca2+ response to histamine adopted four main temporal patterns, which were, respectively, termed peak, peak-oscillations, peak-plateau-oscillations, and peak-plateau. Histamine-evoked intracellular Ca2+ signals were abolished by pyrilamine, which selectively blocks H1R, and significantly reduced by ranitidine, which selectively inhibits H2R. Conversely, the pharmacological blockade of H3R and H4R did not affect the complex increase in [Ca2+]i evoked by histamine in WI-38 fibroblasts. In agreement with these findings, histamine-induced intracellular Ca2+ signals were initiated by intracellular Ca2+ release from the endoplasmic reticulum through inositol-1,4,5-trisphosphate (InsP3) receptors (InsP3R) and sustained by store-operated Ca2+ channels (SOCs). Conversely, L-type voltage-operated Ca2+ channels did not support histamine-induced extracellular Ca2+ entry. A preliminary transcriptomic analysis confirmed that WI-38 human lung fibroblasts express all the three InsP3R isoforms as well as STIM2 and Orai3, which represent the molecular components of SOCs. The pharmacological blockade of InsP3 and SOC, therefore, could represent an alternative strategy to prevent the pernicious effects of histamine on lung fibroblasts in asthmatic patients.

Reinforcing Interdisciplinary Collaborations to Unravel the Astrocyte "Calcium Code"

In this review article, we present the major insights from and challenges faced in the acquisition, analysis and modeling of astrocyte calcium activity, aiming at bridging the gap between those fields to crack the complex astrocyte "Calcium Code". We then propose strategies to reinforce interdisciplinary collaborative projects to unravel astrocyte function in health and disease.

Buffering and total calcium levels determine the presence of oscillatory regimes in cardiac cells

Calcium oscillations and waves induce depolarization in cardiac cells which are believed to cause life-threathening arrhythimas. In this work, we study the conditions for the appearance of calcium oscillations in both a detailed subcellular model of calcium dynamics and a minimal model that takes into account just the minimal ingredients of the calcium toolkit. To avoid the effects of homeostatic changes and the interaction with the action potential we consider the somewhat artificial condition of a cell without pacing and with no calcium exchange with the extracellular medium. Both the full subcellular model and the minimal model present the same scenarios depending on the calcium load: two stationary states, one with closed ryanodine receptors (RyR) and most calcium in the cell stored in the sarcoplasmic reticulum (SR), and another, with open RyRs and a depleted SR. In between, calcium oscillations may appear. The robustness of these oscillations is determined by the amount of calsequestrin (CSQ). The lack of this buffer in the SR enhances the appearance of oscillations. The minimal model allows us to relate the stability of the oscillating state to the nullcline structure of the system, and find that its range of existence is bounded by a homoclinic and a Hopf bifurcation, resulting in a sudden transition to the oscillatory regime as the cell calcium load is increased. Adding a small amount of noise to the RyR behavior increases the parameter region where oscillations appear and provides a gradual transition from the resting state to the oscillatory regime, as observed in the subcellular model and experimentally.

In cardiac cells, calcium plays a very important role. An increase in calcium levels is the trigger used by the cell to initiate contraction. Besides, calcium modulates several transmembrane currents, affecting the cell transmembrane potential. Thus, dysregulations in calcium handling have been associated with the appearance of arrhythmias. Often, this dysregulation results in the appearance of periodic calcium waves or global oscillations, providing a pro-arrhythmic substrate. In this paper, we study the onset of calcium oscillations in cardiac cells using both a detailed subcellular model of calcium dynamics and a minimal model that takes into account the essential ingredients of the calcium toolkit. Both reproduce the main experimental results and link this behavior with the presence of different steady-state solutions and bifurcations that depend on the total amount of calcium in the cell and in the level of buffering present. We expect that this work will help to clarify the conditions under which calcium oscillations appear in cardiac myocytes and, therefore, will represent a step further in the understanding of the origin of cardiac arrhythmias.

Automated Intracellular Calcium Profiles Extraction from Endothelial Cells Using Digital Fluorescence Images

Endothelial cells perform a wide variety of fundamental functions for the cardiovascular system, their proliferation and migration being strongly regulated by their intracellular calcium concentration. Hence it is extremely important to carefully measure endothelial calcium signals under different stimuli. A proposal to automate the intracellular calcium profiles extraction from fluorescence image sequences is presented. Digital image processing techniques were combined with a multi-target tracking approach supported by Kalman estimation. The system was tested with image sequences from two different stimuli. The first one was a chemical stimulus, that is, ATP, which caused small movements in the cells trajectories, thereby suggesting that the bath application of the agonist does not generate significant artifacts. The second one was a mechanical stimulus delivered by a glass microelectrode, which caused major changes in cell trajectories. The importance of the tracking block is evidenced since more accurate profiles were extracted, mainly for cells closest to the stimulated area. Two important contributions of this work are the automatic relocation of the region of interest assigned to the cells and the possibility of data extraction from big image sets in efficient and expedite way. The system may adapt to different kind of cell images and may allow the extraction of other useful features.

Diversity of Evoked Astrocyte Ca2+ Dynamics Quantified through Experimental Measurements and Mathematical Modeling

Astrocytes are a major cell type in the mammalian brain. They are not electrically excitable, but generate prominent Ca²⁺ signals related to a wide variety of critical functions. The mechanisms driving these Ca²⁺ events remain incompletely understood. In this study, we integrate Ca²⁺ imaging, quantitative data analysis, and mechanistic computational modeling to study the spatial and temporal heterogeneity of cortical astrocyte Ca²⁺ transients evoked by focal application of ATP in mouse brain slices. Based on experimental results, we tune a single-compartment mathematical model of IP₃-dependent Ca²⁺ responses in astrocytes and use that model to study response heterogeneity. Using information from the experimental data and the underlying bifurcation structure of our mathematical model, we categorize all astrocyte Ca²⁺ responses into four general types based on their temporal characteristics: Single-Peak, Multi-Peak, Plateau, and Long-Lasting responses. We find that the distribution of experimentally-recorded response types depends on the location within an astrocyte, with somatic responses dominated by Single-Peak (SP) responses and large and small processes generating more Multi-Peak responses. On the other hand, response kinetics differ more between cells and trials than with location within a given astrocyte. We use the computational model to elucidate possible sources of Ca²⁺ response variability: (1) temporal dynamics of IP₃, and (2) relative flux rates through Ca²⁺ channels and pumps. Our model also predicts the effects of blocking Ca²⁺ channels/pumps; for example, blocking store-operated Ca²⁺ (SOC) channels in the model eliminates Plateau and Long-Lasting responses (consistent with previous experimental observations). Finally, we propose that observed differences in response type distributions between astrocyte somas and processes can be attributed to systematic differences in IP₃ rise durations and Ca²⁺ flux rates.

A Bayesian approach to modelling heterogeneous calcium responses in cell populations

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding is achieved, we still lack a comprehensive theory. To achieve this goal it is necessary to reliably predict the temporal evolution of calcium spike sequences for a given stimulus. Here, we propose a modelling framework that allows us to quantitatively describe the timing of calcium spikes. Using a Bayesian approach, we show that Gaussian processes model calcium spike rates with high fidelity and perform better than standard tools such as peri-stimulus time histograms and kernel smoothing. We employ our modelling concept to analyse calcium spike sequences from dynamically-stimulated HEK293T cells. Under these conditions, different cells often experience diverse stimulus time courses, which is a situation likely to occur in vivo. This single cell variability and the concomitant small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances. Our results therefore pave the way towards a statistical description of heterogeneous calcium oscillations in a dynamic environment.

Upon stimulation a large number of cell types respond with transient increases of the intracellular calcium concentration, which often take the form of repetitive spikes. It is therefore believed that calcium spikes play a central role in cellular signal transduction. A critical feature of these calcium spikes is that they occur randomly, which raises the question of how we can predict the timing of calcium spikes. We here show that by using Bayesian ideas and concepts from stochastic processes, we can quantitatively compute the calcium spike rate for a given stimulus. Our analysis also demonstrates that traditional methods for spike rate estimation perform less favourably compared to a Bayesian approach when small numbers of cells are investigated. To test our methodology under conditions that closely mimic those experienced in vivo we challenged cells with agonist concentrations that vary both in space and time. We find that cells that experience similar stimulus profiles are described by similar calcium spike rates. This suggests that calcium spike rates may constitute a quantitative description of whole-cell calcium spiking that reflects both the randomness and the spatiotemporal organisation of the calcium signalling machinery.

Reproducibility and Comparability of Computational Models for Astrocyte Calcium Excitability

The scientific community across all disciplines faces the same challenges of ensuring accessibility, reproducibility, and efficient comparability of scientific results. Computational neuroscience is a rapidly developing field, where reproducibility and comparability of research results have gained increasing interest over the past years. As the number of computational models of brain functions is increasing, we chose to address reproducibility using four previously published computational models of astrocyte excitability as an example. Although not conventionally taken into account when modeling neuronal systems, astrocytes have been shown to take part in a variety of in vitro and in vivo phenomena including synaptic transmission. Two of the selected astrocyte models describe spontaneous calcium excitability, and the other two neurotransmitter-evoked calcium excitability. We specifically addressed how well the original simulation results can be reproduced with a reimplementation of the models. Additionally, we studied how well the selected models can be reused and whether they are comparable in other stimulation conditions and research settings. Unexpectedly, we found out that three of the model publications did not give all the necessary information required to reimplement the models. In addition, we were able to reproduce the original results of only one of the models completely based on the information given in the original publications and in the errata. We actually found errors in the equations provided by two of the model publications; after modifying the equations accordingly, the original results were reproduced more accurately. Even though the selected models were developed to describe the same biological event, namely astrocyte calcium excitability, the models behaved quite differently compared to one another. Our findings on a specific set of published astrocyte models stress the importance of proper validation of the models against experimental wet-lab data from astrocytes as well as the careful review process of models. A variety of aspects of model development could be improved, including the presentation of models in publications and databases. Specifically, all necessary mathematical equations, as well as parameter values, initial values of variables, and stimuli used should be given precisely for successful reproduction of scientific results.

Interplay Between Intracellular Ca(2+) Oscillations and Ca(2+)-stimulated Mitochondrial Metabolism

Oscillations of cytosolic Ca(2+) concentration are a widespread mode of signalling. Oscillatory spikes rely on repetitive exchanges of Ca(2+) between the endoplasmic reticulum (ER) and the cytosol, due to the regulation of inositol 1,4,5-trisphosphate receptors. Mitochondria also sequester and release Ca(2+), thus affecting Ca(2+) signalling. Mitochondrial Ca(2+) activates key enzymes involved in ATP synthesis. We propose a new integrative model for Ca(2+) signalling and mitochondrial metabolism in electrically non-excitable cells. The model accounts for (1) the phase relationship of the Ca(2+) changes in the cytosol, the ER and mitochondria, (2) the dynamics of mitochondrial metabolites in response to cytosolic Ca(2+) changes, and (3) the impacts of cytosol/mitochondria Ca(2+) exchanges and of mitochondrial metabolism on Ca(2+) oscillations. Simulations predict that as expected, oscillations are slowed down by decreasing the rate of Ca(2+) efflux from mitochondria, but also by decreasing the rate of Ca(2+) influx through the mitochondrial Ca(2+) uniporter (MCU). These predictions were experimentally validated by inhibiting MCU expression. Despite the highly non-linear character of Ca(2+) dynamics and mitochondrial metabolism, bioenergetics were found to be robust with respect to changes in frequency and amplitude of Ca(2+) oscillations.

Unifying principles of calcium wave propagation - Insights from a three-dimensional model for atrial myocytes

Atrial myocytes in a number of species lack transverse tubules. As a consequence the intracellular calcium signals occurring during each heartbeat exhibit complex spatio-temporal dynamics. These calcium patterns arise from saltatory calcium waves that propagate via successive rounds of diffusion and calcium-induced calcium release. The many parameters that impinge on calcium-induced calcium release and calcium signal propagation make it difficult to know a priori whether calcium waves will successfully travel, or be extinguished. In this study, we describe in detail a mathematical model of calcium signalling that allows the effect of such parameters to be independently assessed. A key aspect of the model is to follow the triggering and evolution of calcium signals within a realistic three-dimensional cellular volume of an atrial myocyte, but with low computational costs. This is achieved by solving the linear transport equation for calcium analytically between calcium release events and by expressing the onset of calcium liberation as a threshold process. The model makes non-intuitive predictions about calcium signal propagation. For example, our modelling illustrates that the boundary of a cell produces a wave-guiding effect that enables calcium ions to propagate further and for longer, and can subtly alter the pattern of calcium wave movement. The high spatial resolution of the modelling framework allows the study of any arrangement of calcium release sites. We demonstrate that even small variations in randomly positioned release sites cause highly heterogeneous cellular responses. This article is part of a Special Issue entitled: 13th European Symposium on Calcium.

Modulation of elementary calcium release mediates a transition from puffs to waves in an IP3R cluster model

The oscillating concentration of intracellular calcium is one of the most important examples for collective dynamics in cell biology. Localized releases of calcium through clusters of inositol 1,4,5-trisphosphate receptor channels constitute elementary signals called calcium puffs. Coupling by diffusing calcium leads to global releases and waves, but the exact mechanism of inter-cluster coupling and triggering of waves is unknown. To elucidate the relation of puffs and waves, we here model a cluster of IP3R channels using a gating scheme with variable non-equilibrium IP3 binding. Hybrid stochastic and deterministic simulations show that puffs are not stereotyped events of constant duration but are sensitive to stimulation strength and residual calcium. For increasing IP3 concentration, the release events become modulated at a timescale of minutes, with repetitive wave-like releases interspersed with several puffs. This modulation is consistent with experimental observations we present, including refractoriness and increase of puff frequency during the inter-wave interval. Our results suggest that waves are established by a random but time-modulated appearance of sustained release events, which have a high potential to trigger and synchronize activity throughout the cell.

Modelling the transition from simple to complex Ca²⁺ oscillations in pancreatic acinar cells

A mathematical model is proposed which systematically investigates complex calcium oscillations in pancreatic acinar cells. This model is based on calcium-induced calcium release via inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR) and includes calcium modulation of inositol (1,4,5) trisphosphate (IP3) levels through feedback regulation of degradation and production. In our model, the apical and the basal regions are separated by a region containing mitochondria, which is capable of restricting Ca2+ responses to the apical region. We were able to reproduce the observed oscillatory patterns, from baseline spikes to sinusoidal oscillations. The model predicts that calcium-dependent production and degradation of IP3 is a key mechanism for complex calcium oscillations in pancreatic acinar cells. A partial bifurcation analysis is performed which explores the dynamic behaviour of the model in both apical and basal regions.

Towards the Physics of Calcium Signalling in Plants

Calcium is an abundant element with a wide variety of important roles within cells. Calcium ions are inter- and intra-cellular messengers that are involved in numerous signalling pathways. Fluctuating compartment-specific calcium ion concentrations can lead to localised and even plant-wide oscillations that can regulate downstream events. Understanding the mechanisms that give rise to these complex patterns that vary both in space and time can be challenging, even in cases for which individual components have been identified. Taking a systems biology approach, mathematical and computational techniques can be employed to produce models that recapitulate experimental observations and capture our current understanding of the system. Useful models make novel predictions that can be investigated and falsified experimentally. This review brings together recent work on the modelling of calcium signalling in plants, from the scale of ion channels through to plant-wide responses to external stimuli. Some in silico results that have informed later experiments are highlighted.

Vascular endothelial growth factor stimulates endothelial colony forming cells proliferation and tubulogenesis by inducing oscillations in intracellular Ca2+ concentration

Endothelial progenitor cells (EPCs) home from the bone marrow to the site of tissue regeneration and sustain neovascularization after acute vascular injury and upon the angiogenic switch in solid tumors. Therefore, they represent a suitable tool for cell-based therapy (CBT) in regenerative medicine and provide a novel promising target in the fight against cancer. Intracellular Ca(2+) signals regulate numerous endothelial functions, such as proliferation and tubulogenesis. The growth of endothelial colony forming cells (ECFCs), which are EPCs capable of acquiring a mature endothelial phenotype, is governed by store-dependent Ca(2+) entry (SOCE). This study aimed at investigating the nature and the role of VEGF-elicited Ca(2+) signals in ECFCs. VEGF induced asynchronous Ca(2+) oscillations, whose latency, amplitude, and frequency were correlated to the growth factor dose. Removal of external Ca(2+) (0Ca(2+)) and SOCE inhibition with N-(4-[3,5-bis(trifluoromethyl)-1H-pyrazol-1-yl]phenyl)-4-methyl-1,2,3-thiadiazole-5-carboxamide (BTP-2) reduced the duration of the oscillatory signal. Blockade of phospholipase C-γ with U73122, emptying the inositol-1,4,5-trisphosphate (InsP(3))-sensitive Ca(2+) pools with cyclopiazonic acid (CPA), and inhibition of InsP(3) receptors with 2-APB prevented the Ca(2+) response to VEGF. VEGF-induced ECFC proliferation and tubulogenesis were inhibited by the Ca(2+)-chelant, BAPTA, and BTP-2. NF-κB activation by VEGF was impaired by BAPTA, BTP-2, and its selective blocker, thymoquinone. Thymoquinone, in turn, suppressed VEGF-dependent ECFC proliferation and tubulogenesis. These data indicate that VEGF-induced Ca(2+) oscillations require the interplay between InsP(3)-dependent Ca(2+) release and SOCE, and promote ECFC growth and tubulogenesis by engaging NF-κB. This novel signaling pathway might be exploited to enhance the outcome of CBT and chemotherapy.