A quantitative kinetic model for ATP-induced intracellular Ca2+ oscillations

Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell

Calcium is a ubiquitous molecule and second messenger that regulates many cellular functions ranging from exocytosis to cell proliferation at different time scales. In the vasculature, a constant adenosine triphosphate (ATP) concentration is maintained because of ATP released by red blood cells (RBCs). These ATP molecules continuously react with purinergic receptors on the surface of endothelial cells (ECs). Consequently, a cascade of chemical reactions are triggered that result in a transient cytoplasmic calcium (Ca[Formula: see text]), followed by return to its basal concentration. The mathematical models proposed in the literature are able to reproduce the transient peak. However, the trailing concentration is always higher than the basal cytoplasmic Ca[Formula: see text] concentrations, and the Ca[Formula: see text] concentration in endoplasmic reticulum (ER) remains lower than its initial concentration. This means that the intracellular homeostasis is not recovered. We propose, herein, a minimal model of calcium kinetics. We find that the desensitization of EC surface receptors due to phosphorylation and recycling plays a vital role in maintaining calcium homeostasis in the presence of a constant stimulus (ATP). The model is able to capture several experimental observations such as refilling of Ca[Formula: see text] in the ER, variation of cytoplasmic Ca[Formula: see text] transient peak in ECs, the resting cytoplasmic Ca[Formula: see text] concentration, the effect of removing ATP from the plasma on Ca[Formula: see text] homeostasis, and the saturation of cytoplasmic Ca[Formula: see text] transient peak with increase in ATP concentration. Direct confrontation with several experimental results is conducted. This work paves the way for systematic studies on coupling between blood flow and chemical signaling, and should contribute to a better understanding of the relation between (patho)physiological conditions and Ca[Formula: see text] kinetics.

Modeling of Endothelial Calcium Responses within a Microfluidic Generator of Spatio-Temporal ATP and Shear Stress Signals

Intracellular calcium dynamics play essential roles in the proper functioning of cellular activities. It is a well known important chemosensing and mechanosensing process regulated by the spatio-temporal microenvironment. Nevertheless, how spatio-temporal biochemical and biomechanical stimuli affect calcium dynamics is not fully understood and the underlying regulation mechanism remains missing. Herein, based on a developed microfluidic generator of biochemical and biomechanical signals, we theoretically analyzed the generation of spatio-temporal ATP and shear stress signals within the microfluidic platform and investigated the effect of spatial combination of ATP and shear stress stimuli on the intracellular calcium dynamics. The simulation results demonstrate the capacity and flexibility of the microfluidic system in generating spatio-temporal ATP and shear stress. Along the transverse direction of the microchannel, dynamic ATP signals of distinct amplitudes coupled with identical shear stress are created, which induce the spatio-temporal diversity in calcium responses. Interestingly, to the multiple combinations of stimuli, the intracellular calcium dynamics reveal two main modes: unimodal and oscillatory modes, showing significant dependence on the features of the spatio-temporal ATP and shear stress stimuli. The present study provides essential information for controlling calcium dynamics by regulating spatio-temporal biochemical and biomechanical stimuli, which shows the potential in directing cellular activities and understanding the occurrence and development of disease.

Multiple calcium patterns of rat osteoblasts under fluidic shear stress

The intracellular calcium ([Ca²⁺ ]_i ) response induced by external forces can be diverse and complex. Using primary osteoblasts from Wistar rats, we found multiple patterns of [Ca²⁺ ]_i responses induced by fluidic shear stress (Fss), including homogeneous non-oscillation and heterogeneous oscillations. These multiple-patterned [Ca²⁺ ]_i responses could be influenced by Fss intensity, cell density, and cell differentiation. Our real-time measurements with free calcium, ATP, ATP without calcium, suramin, apyrase, and thapsigargin confirmed homogeneous [Ca²⁺ ]_i patterns and/or heterogeneous [Ca²⁺ ]_i oscillations with respect to the combined degree of external Ca²⁺ influx, and intracellular Ca²⁺ release. Our theoretical model supported diverse Fss-induced calcium activities as well. We concluded that a singular factor of Ca²⁺ influx or release dominated to produce smooth homogeneous patterns, but combined factors produced oscillatory heterogeneous patterns. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:2039-2051, 2018.

Computational Model of Ca2+ Wave Propagation in Human Retinal Pigment Epithelial ARPE-19 Cells

Objective

Computational models of calcium (Ca²⁺) signaling have been constructed for several cell types. There are, however, no such models for retinal pigment epithelium (RPE). Our aim was to construct a Ca²⁺ signaling model for RPE based on our experimental data of mechanically induced Ca²⁺ wave in the in vitro model of RPE, the ARPE-19 monolayer.

Methods

We combined six essential Ca²⁺ signaling components into a model: stretch-sensitive Ca²⁺ channels (SSCCs), P₂Y₂ receptors, IP₃ receptors, ryanodine receptors, Ca²⁺ pumps, and gap junctions. The cells in our epithelial model are connected to each other to enable transport of signaling molecules. Parameterization was done by tuning the above model components so that the simulated Ca²⁺ waves reproduced our control experimental data and data where gap junctions were blocked.

Results

Our model was able to explain Ca²⁺ signaling in ARPE-19 cells, and the basic mechanism was found to be as follows: 1) Cells near the stimulus site are likely to conduct Ca²⁺ through plasma membrane SSCCs and gap junctions conduct the Ca²⁺ and IP³ between cells further away. 2) Most likely the stimulated cell secretes ligand to the extracellular space where the ligand diffusion mediates the Ca²⁺ signal so that the ligand concentration decreases with distance. 3) The phosphorylation of the IP₃ receptor defines the cell’s sensitivity to the extracellular ligand attenuating the Ca²⁺ signal in the distance.

Conclusions

The developed model was able to simulate an array of experimental data including drug effects. Furthermore, our simulations predict that suramin may interfere ligand binding on P₂Y₂ receptors or accelerate P₂Y₂ receptor phosphorylation, which may partially be the reason for Ca²⁺ wave attenuation by suramin. Being the first RPE Ca²⁺ signaling model created based on experimental data on ARPE-19 cell line, the model offers a platform for further modeling of native RPE functions.

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.

A dynamic model for intracellular calcium response in fibroblasts induced by electrical stimulation

Regulation of intracellular calcium ion concentration ([Ca(2+)]in) in fibroblasts induced by exogenous electrical stimulation could be applied to control gene expressions selectively which in turn modulate the function of the fibroblasts. Regarding the mechanism for electric-field-induced Ca(2+) influx via voltage-gated Ca(2+) channels and/or stretch-activated cation channels in the fibroblasts, a dynamic mathematical model is proposed to quantify the [Ca(2+)]in dynamics in response to direct current or alternating current electric fields. Simulation results demonstrate that the changes in [Ca(2+)]in predicted by our dynamic model are consistent with the experimental data in the literature. The proposed dynamic model could provide not only more insights into the electric-field-induced intracellular Ca(2+) response but also a quantitative way to regulate the [Ca(2+)]in dynamics by controlling the external electrical stimulation.

Fluid flow induced calcium response in osteoblasts: mathematical modeling

Fluid flow in the bone lacuno-canalicular network can induce dynamic fluctuation of intracellular calcium concentration ([Ca(2+)](i)) in osteoblasts, which plays an important role in bone remodeling. There has been limited progress in the mathematical modeling of this process probably due to its complexity, which is controlled by various factors such as Ca(2+) channels and extracellular messengers. In this study we developed a mathematical model to describe [Ca(2+)](i) response induced by fluid shear stress (SS) by integrating the major factors involved and analyzed the effects of different experimental setups (e.g. [Ca(2+)](i) baseline, pretreatment with ATP). In this model we considered the ATP release process and the activities of multiple ion channels and purinergic receptors. The model was further verified quantitatively by comparing the simulation results with experimental data reported in literature. The results showed that: (i) extracellular ATP concentration has more significant effect on [Ca(2+)](i) baseline (73% increase in [Ca(2+)](i) with extracellular ATP concentration varying between 0 and 10 μM), as compared to that induced by SS (25% variation in [Ca(2+)](i) with SS varying from 0 to 3.5 Pa); (ii) Pretreatment with ATP-medium results in different [Ca(2+)](i) response as compared to the control group (ATP-free medium) under SS; (iii) Relative [Ca(2+)](i) fluctuation over baseline is more reliable to show the [Ca(2+)](i) response process than the absolute [Ca(2+)](i) response peak. The developed model may improve the experimental design and facilitate our understanding of the mechanotransduction process in osteoblasts.

Phase-locked signals elucidate circuit architecture of an oscillatory pathway

This paper introduces the concept of phase-locking analysis of oscillatory cellular signaling systems to elucidate biochemical circuit architecture. Phase-locking is a physical phenomenon that refers to a response mode in which system output is synchronized to a periodic stimulus; in some instances, the number of responses can be fewer than the number of inputs, indicative of skipped beats. While the observation of phase-locking alone is largely independent of detailed mechanism, we find that the properties of phase-locking are useful for discriminating circuit architectures because they reflect not only the activation but also the recovery characteristics of biochemical circuits. Here, this principle is demonstrated for analysis of a G-protein coupled receptor system, the M3 muscarinic receptor-calcium signaling pathway, using microfluidic-mediated periodic chemical stimulation of the M3 receptor with carbachol and real-time imaging of resulting calcium transients. Using this approach we uncovered the potential importance of basal IP3 production, a finding that has important implications on calcium response fidelity to periodic stimulation. Based upon our analysis, we also negated the notion that the Gq-PLC interaction is switch-like, which has a strong influence upon how extracellular signals are filtered and interpreted downstream. Phase-locking analysis is a new and useful tool for model revision and mechanism elucidation; the method complements conventional genetic and chemical tools for analysis of cellular signaling circuitry and should be broadly applicable to other oscillatory pathways.

Key to robust discernment of cell circuit architecture is to have as many distinct response features as possible for comparison and evaluation. One under-appreciated characteristic of oscillatory circuits is that under periodic stimulation, these systems will exhibit responses synchronized to this stimulatory input, a phenomenon termed phase-locking. We demonstrate that phase-locked response characteristics vary noticeably depending on circuit activation and recovery properties; these response characteristics thereby provide a unique set of criteria for oscillatory circuit architecture analysis. The concept is validated through experiments on an oscillatory calcium pathway in mammalian cells; the experimental setup allowed us to explore, for the first time, the properties of chemically induced phase-locking of intracellular signals. Observations of this phenomenon were then used to test the predictions of several existing mathematical models of calcium signaling. Most of the models we evaluated were unable to match all our experimental observations, suggesting that current models are missing mechanistic elements in the context of calcium signaling for the cell type and receptor/stimulant tested. The observations of phase-locking further led us to identify one simple mechanistic modification that would account for all the experimental observations. The techniques and methodology presented should be broadly applicable to a variety of biological oscillators.