On the dynamical structure of calcium oscillations

A Model for the Coexistence of Competing Mechanisms for Ca 2 + Oscillations in T-lymphocytes

Ca 2 + is a ubiquitous signaling mechanism across different cell types. In T-cells, it is associated with cytokine production and immune function. Benson et al. have shown the coexistence of competing Ca 2 + oscillations during antigen stimulation of T-cell receptors, depending on the presence of extracellular Ca 2 + influx through the Ca 2 + release-activated Ca 2 + channel (Benson in J Biol Chem 29:105310, 2023). In this paper, we construct a mathematical model consisting of five ordinary differential equations and analyze the relationship between the competing oscillatory mechanisms.. We perform bifurcation analysis on two versions of our model, corresponding to the two oscillatory types, to find the defining characteristics of these two families.

Nonlinear dynamics in phosphoinositide metabolism

Phosphoinositides broadly impact membrane dynamics, signal transduction and cellular physiology. The orchestration of signaling complexity by this seemingly simple metabolic pathway remains an open question. It is increasingly evident that comprehending the complexity of the phosphoinositides metabolic network requires a systems view based on nonlinear dynamics, where the products of metabolism can either positively or negatively modulate enzymatic function. These feedback and feedforward loops may be paradoxical, leading to counterintuitive effects. In this review, we introduce the framework of nonlinear dynamics, emphasizing distinct dynamical regimes such as the excitable state, oscillations, and mixed-mode oscillations-all of which have been experimentally observed in phosphoinositide metabolisms. We delve into how these dynamical behaviors arise from one or multiple network motifs, including positive and negative feedback loops, coherent and incoherent feedforward loops. We explore the current understanding of the molecular circuits responsible for these behaviors. While mapping these circuits presents both conceptual and experimental challenges, redefining cellular behavior based on dynamical state, lipid fluxes, time delay, and network topology is likely essential for a comprehensive understanding of this fundamental metabolic network.

The CRZ1 transcription factor in plant fungi: regulation mechanism and impact on pathogenesis

Calcium (Ca2+) is a universal signaling molecule that is tightly regulated, and a fleeting elevation in cytosolic concentration triggers a signal cascade within the cell, which is crucial for several processes such as growth, tolerance to stress conditions, and virulence in fungi. The link between calcium and calcium-dependent gene regulation in cells relies on the transcription factor Calcineurin-Responsive Zinc finger 1 (CRZ1). The direct regulation of approximately 300 genes in different stress pathways makes it a hot topic in host-pathogen interactions. Notably, CRZ1 can modulate several pathways and orchestrate cellular responses to different types of environmental insults such as osmotic stress, oxidative stress, and membrane disruptors. It is our belief that CRZ1 provides the means for tightly modulating and synchronizing several pathways allowing pathogenic fungi to install into the apoplast and eventually penetrate plant cells (i.e., ROS, antimicrobials, and quick pH variation). This review discusses the structure, function, regulation of CRZ1 in fungal physiology and its role in plant pathogen virulence.

Intracellular Calcium Dynamics in Primary Human Adrenocortical Cells Deciphered with a Novel Pipeline

INTRODUCTION

The fluctuations of the intracellular Ca2+ concentration ([Ca2+]i) are key physiological signals for cell function under normal conditions and can undergo profound alterations in disease states, as high blood pressure due to endocrine disorders like primary aldosteronism (PA). However, when assessing such fluctuations several parameters in the Ca2+ signal dynamics need to be considered, which renders their assessment challenging.

AIM

Aim to develop an observer-independent custom-made pipeline to analyze Ca2+ dynamics in terms of frequency and peak parameters, as amplitude, full width at half maximum (FWHM) and area under the curve (AUC).

METHODS

We applied a custom-made methodology to aldosterone-producing adenoma (APA) and APA adjacent cells (AAC) and found this pipeline to be suitable for monitoring and processing a wide-range of [Ca2+]i events in these cell types delivering reproducible results.

CONCLUSION

The designed pipeline can provide a useful tool for [Ca2+]i signal analysis that allows comparisons of Ca2+ dynamics not only in PA, but in other cell phenotypes that are relevant for the regulation of blood pressure.

Emergence of broad cytosolic Ca2+ oscillations in the absence of CRAC channels: A model for CRAC-mediated negative feedback on PLC and Ca2+ oscillations through PKC

The role of Ca2+ release-activated Ca2+ (CRAC) channels mediated by ORAI isoforms in calcium signalling has been extensively investigated. It has been shown that the presence or absence of different isoforms has a significant effect on store-operated calcium entry (SOCE). Yoast et al. (2020) showed that, in addition to the reported narrow-spike oscillations (whereby cytosolic calcium decreases quickly after a sharp increase), ORAI1 knockout HEK293 cells were able to oscillate with broad-spike oscillations (whereby cytosolic calcium decreases in a prolonged manner after a sharp increase) when stimulated with a muscarinic agonist. This suggests that Ca2+ influx through ORAI-mediated CRAC channels negatively regulates the duration of Ca2+ oscillations. We hypothesise that, through the activation of protein kinase C (PKC), ORAI1 negatively regulates phospholipase C (PLC) activity to decrease inositol 1,4,5-trisphosphate (IP3) production and limit the duration of agonist-evoked Ca2+ oscillations. Based on this hypothesis, we construct a new mathematical model, which shows that the formation of broad-spike oscillations is highly dependent on the absence of ORAI1. Predictions of this model are consistent with the experimental results.

Ca2+ dynamics in interstitial cells: foundational mechanisms for the motor patterns in the gastrointestinal tract

The gastrointestinal (GI) tract displays multiple motor patterns that move nutrients and wastes through the body. Smooth muscle cells (SMCs) provide the forces necessary for GI motility, but interstitial cells, electrically coupled to SMCs, tune SMC excitability, transduce inputs from enteric motor neurons, and generate pacemaker activity that underlies major motor patterns, such as peristalsis and segmentation. The interstitial cells regulating SMCs are interstitial cells of Cajal (ICC) and PDGF receptor (PDGFR)α+ cells. Together these cells form the SIP syncytium. ICC and PDGFRα+ cells express signature Ca2+-dependent conductances: ICC express Ca2+-activated Cl- channels, encoded by Ano1, that generate inward current, and PDGFRα+ cells express Ca2+-activated K+ channels, encoded by Kcnn3, that generate outward current. The open probabilities of interstitial cell conductances are controlled by Ca2+ release from the endoplasmic reticulum. The resulting Ca2+ transients occur spontaneously in a stochastic manner. Ca2+ transients in ICC induce spontaneous transient inward currents and spontaneous transient depolarizations (STDs). Neurotransmission increases or decreases Ca2+ transients, and the resulting depolarizing or hyperpolarizing responses conduct to other cells in the SIP syncytium. In pacemaker ICC, STDs activate voltage-dependent Ca2+ influx, which initiates a cluster of Ca2+ transients and sustains activation of ANO1 channels and depolarization during slow waves. Regulation of GI motility has traditionally been described as neurogenic and myogenic. Recent advances in understanding Ca2+ handling mechanisms in interstitial cells and how these mechanisms influence motor patterns of the GI tract suggest that the term "myogenic" should be replaced by the term "SIPgenic," as this review discusses.

A multiple-oscillator mechanism underlies antigen-induced Ca2+ oscillations in Jurkat T-cells

T-cell receptor stimulation triggers cytosolic Ca2+ signaling by inositol-1,4,5-trisphosphate (IP3)-mediated Ca2+ release from the endoplasmic reticulum (ER) and Ca2+ entry through Ca2+ release-activated Ca2+ (CRAC) channels gated by ER-located stromal-interacting molecules (STIM1/2). Physiologically, cytosolic Ca2+ signaling manifests as regenerative Ca2+ oscillations, which are critical for nuclear factor of activated T-cells-mediated transcription. In most cells, Ca2+ oscillations are thought to originate from IP3 receptor-mediated Ca2+ release, with CRAC channels indirectly sustaining them through ER refilling. Here, experimental and computational evidence support a multiple-oscillator mechanism in Jurkat T-cells whereby both IP3 receptor and CRAC channel activities oscillate and directly fuel antigen-evoked Ca2+ oscillations, with the CRAC channel being the major contributor. KO of either STIM1 or STIM2 significantly reduces CRAC channel activity. As such, STIM1 and STIM2 synergize for optimal Ca2+ oscillations and activation of nuclear factor of activated T-cells 1 and are essential for ER refilling. The loss of both STIM proteins abrogates CRAC channel activity, drastically reduces ER Ca2+ content, severely hampers cell proliferation and enhances cell death. These results clarify the mechanism and the contribution of STIM proteins to Ca2+ oscillations in T-cells.

Structural titration reveals Ca2+-dependent conformational landscape of the IP3 receptor

Inositol 1,4,5-trisphosphate receptors (IP3Rs) are endoplasmic reticulum Ca2+ channels whose biphasic dependence on cytosolic Ca2+ gives rise to Ca2+ oscillations that regulate fertilization, cell division and cell death. Despite the critical roles of IP3R-mediated Ca2+ responses, the structural underpinnings of the biphasic Ca2+ dependence that underlies Ca2+ oscillations are incompletely understood. Here, we collect cryo-EM images of an IP3R with Ca2+ concentrations spanning five orders of magnitude. Unbiased image analysis reveals that Ca2+ binding does not explicitly induce conformational changes but rather biases a complex conformational landscape consisting of resting, preactivated, activated, and inhibited states. Using particle counts as a proxy for relative conformational free energy, we demonstrate that Ca2+ binding at a high-affinity site allows IP3Rs to activate by escaping a low-energy resting state through an ensemble of preactivated states. At high Ca2+ concentrations, IP3Rs preferentially enter an inhibited state stabilized by a second, low-affinity Ca2+ binding site. Together, these studies provide a mechanistic basis for the biphasic Ca2+-dependence of IP3R channel activity.

Neuronal actin cytoskeleton gain of function in the human brain

BACKGROUND

While advancements in imaging techniques have led to major strides in deciphering the human brain, successful interventions are elusive and represent some of the most persistent translational gaps in medicine. Human restricted CHRFAM7A has been associated with neuropsychiatric disorders.

METHODS

The physiological role of CHRFAM7A in human brain is explored using multiomics approach on 600 post mortem human brain tissue samples. The emerging pathways and mechanistic hypotheses are tested and validated in an isogenic hiPSC model of CHRFAM7A knock-in medial ganglionic eminence progenitors and neurons.

FINDINGS

CHRFAM7A is identified as a modulator of intracellular calcium dynamics and an upstream regulator of Rac1. Rac1 activation re-designs the actin cytoskeleton leading to dynamic actin driven remodeling of membrane protrusion and a switch from filopodia to lamellipodia. The reinforced cytoskeleton leads to an advantage to tolerate stiffer mechanical properties of the extracellular environment.

INTERPRETATION

CHRFAM7A modifies the actin cytoskeleton to a more dynamic and stiffness resistant state in an α7nAChR dependent manner. CHRFAM7A may facilitate neuronal adaptation to changes in the brain environment in physiological and pathological conditions contributing to risk or recovery. Understanding how CHRFAM7A affects human brain requires human studies in the areas of memory formation and erasure, cognitive reserve, and neuronal plasticity.

FUNDING

This work is supported in part by the Community Foundation for Greater Buffalo (Kinga Szigeti). Also, in part by the International Society for Neurochemistry (ISN) and The Company of Biologists (Nicolas Rosas). ROSMAP is supported by NIA grants P30AG10161, P30AG72975, R01AG15819, R01AG17917. U01AG46152, and U01AG61356.

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.

Inherent differences of small airway contraction and Ca2+ oscillations in airway smooth muscle cells between BALB/c and C57BL/6 mouse strains

BALB/c and C57BL/6 mouse strains are widely used as animal model in studies of respiratory diseases, such as asthma. Asthma is characterized by airway hyperresponsiveness, which is eventually resulted from the excessive airway smooth muscle (ASM) contraction mediated by Ca²⁺ oscillations in ASM cells. It is reported that BALB/c mice have inherently higher airway responsiveness, but show no different contractive response of tracheal ring as compared to C57BL/6 mice. However, whether the different airway responsiveness is due to the different extents of small airway contraction, and what's underlying mechanism remains unknown. Here, we assess agonist-induced small airway contraction and Ca²⁺ oscillations in ASM cells between BALB/c and C57BL/6 mice by using precision-cut lung slices (PCLS). We found that BALB/c mice showed an intrinsically stronger extent of small airway narrowing and faster Ca²⁺ oscillations in ASM cells in response to agonists. These differences were associated with a higher magnitude of Ca²⁺ influx via store-operated Ca²⁺ entry (SOCE), as a result of increased expression of SOCE components (STIM1, Orai1) in the ASM cells of small airway of BALB/c mice. An established mathematical model and experimental results suggested that the increased SOC current could result in increased agonist-induced Ca²⁺ oscillations. Therefore, the inherently higher SOC underlies the increased Ca²⁺ oscillation frequency in ASM cells and stronger small airway contraction in BALB/c mice, thus higher airway responsiveness in BALB/c than C57BL/6 mouse strain.

Too much of a good thing: The case of SOCE in cellular apoptosis

Intracellular calcium (Ca2+) is an essential second messenger in eukaryotic cells regulating numerous cellular functions such as contraction, secretion, immunity, growth, and metabolism. Ca2+ signaling is also a key signal transducer in the intrinsic apoptosis pathway. The store-operated Ca2+ entry pathway (SOCE) is ubiquitously expressed in eukaryotic cells, and is the primary Ca2+ influx pathway in non-excitable cells. SOCE is mediated by the endoplasmic reticulum Ca2+ sensing STIM proteins, and the plasma membrane Ca2+-selective Orai channels. A growing number of studies have implicated SOCE in regulating cell death primarily via the intrinsic apoptotic pathway in a variety of tissues and in response to physiological stressors such as traumatic brain injury, ischemia reperfusion injury, sepsis, and alcohol toxicity. Notably, the literature points to excessive cytosolic Ca2+ influx through SOCE in vulnerable cells as a key factor tipping the balance towards cellular apoptosis. While the literature primarily addresses the functions of STIM1 and Orai1, STIM2, Orai2 and Orai3 are also emerging as potential regulators of cell death. Here, we review the functions of STIM and Orai proteins in regulating cell death and the implications of this regulation to human pathologies.

Investigations into hydrogen sulfide-induced suppression of neuronal activity in vivo and calcium dysregulation in vitro

Acute exposure to high concentrations of hydrogen sulfide (H2S) leads to sudden death and, if survived, lingering neurological disorders. Clinical signs include seizures, loss of consciousness, and dyspnea. The proximate mechanisms underlying H2S-induced acute toxicity and death have not been clearly elucidated. We investigated electrocerebral, cardiac and respiratory activity during H2S exposure using electroencephalogram (EEG), electrocardiogram (EKG) and plethysmography. H2S suppressed electrocerebral activity and disrupted breathing. Cardiac activity was comparatively less affected. To test whether Ca2+ dysregulation contributes to H2S-induced EEG suppression, we developed an in vitro real-time rapid throughput assay measuring patterns of spontaneous synchronized Ca2+ oscillations in cultured primary cortical neuronal networks loaded with the indicator Fluo-4 using the fluorescent imaging plate reader (FLIPR-Tetra®). Sulfide >5 ppm dysregulated synchronous calcium oscillation (SCO) patterns in a dose-dependent manner. Inhibitors of NMDA and AMPA receptors magnified H2S-induced SCO suppression. Inhibitors of L-type voltage gated Ca2+ channels and transient receptor potential channels prevented H2S-induced SCO suppression. Inhibitors of T-type voltage gated Ca2+ channels, ryanodine receptors, and sodium channels had no measurable influence on H2S-induced SCO suppression. Exposures to > 5 ppm sulfide also suppressed neuronal electrical activity in primary cortical neurons measured by multi-electrode array (MEA), an effect alleviated by pretreatment with the nonselective transient receptor potential channel inhibitor, 2-APB. 2-APB also reduced primary cortical neuronal cell death from sulfide exposure. These results improve our understanding of the role of different Ca2+ channels in acute H2S-induced neurotoxicity and identify transient receptor potential channel modulators as novel structures with potential therapeutic benefits.

Calcium oscillation on homogeneous and heterogeneous networks of ryanodine receptor

Calcium oscillation is an important calcium homeostasis, imbalance of which is the key mechanism of initiation and progression of many major diseases. The formation and maintenance of calcium homeostasis are closely related to the spatial distribution of calcium channels on endoplasmic reticulum, whose complex structure was unveiled by recent observations with superresolution imaging techniques. In the current paper, a theoretical framework is established by abstracting the spatial distribution of the calcium channels as a nonlinear biological complex network with calcium channels as nodes and Ca^{2+} as edges. A dynamical model for a ryanodine receptor (RyR) is adopted to investigate the effect of spatial distribution on calcium oscillation. The mean-field model can be well reproduced from the complete graph and dense Erdös-Rényi network. The synchronization of RyRs is found important to generate a global calcium oscillation. Below a critical density of the Erdös-Rényi or BaraBási-Albert network, the amplitude and interspike interval decrease rapidly with the end of disappearance of oscillation due to the desynchronization. The clique graph with a cluster structure cannot produce a global oscillation due to the failure of synchronization between clusters. A more realistic geometric network is constructed in a two-dimensional plane based on the experimental information about the RyR arrangement of clusters and the frequency distribution of cluster sizes. Different from the clique graph, the global oscillation can be generated with reasonable parameters on the geometric network. The simulation also suggests that existence of small clusters and rogue RyRs plays an important role in the maintenance of global calcium oscillation through keeping synchronization between large clusters. Such results support the heterogeneous distribution of RyRs with different-size clusters, which is helpful to understand recent observations with superresolution nanoscale imaging techniques. The current theoretical framework can also be extent to investigate other phenomena in calcium signal transduction.

Simulation of Calcium Dynamics in Realistic Three-Dimensional Domains

The cytosolic concentration of free calcium ions ([Ca2+]) is an important intracellular messenger in most cell types, and the spatial distribution of [Ca2+] is often critical. In a salivary gland acinar cell, a polarised epithelial cell, whose principal function is to transport water and thus secrete saliva, [Ca2+] controls the secretion of primary saliva, but increases in [Ca2+] are localised to the apical regions of the cell. Hence, any quantitative explanation of how [Ca2+] controls saliva secretion must take into careful account the spatial distribution of the various Ca2+ sources, Ca2+ sinks, and Ca2+-sensitive ion channels. Based on optical slices, we have previously constructed anatomically accurate three-dimensional models of seven salivary gland acinar cells, and thus shown that a model in which Ca2+ responses are confined to the apical regions of the cell is sufficient to provide a quantitative and predictive explanation of primary saliva secretion. However, reconstruction of such anatomically accurate cells is extremely time consuming and inefficient. Here, we present an alternative, mostly automated method of constructing three-dimensional cells that are approximately anatomically accurate and show that the new construction preserves the quantitative accuracy of the model.

Dynamical behaviors of quorum sensing network mediated by combinatorial perturbation

The dynamical behaviors of the quorum sensing (QS) system are closely related to the release drugs and control the PH value in microorganisms and plants. However, the effect of the main molecules AiiA, LuxI, H$ _2 $O$ _2 $, and time delayed individual and combinatorial perturbation on the QS system dynamics and the above-mentioned biological phenomena is still unclear, which are seen as a key consideration in our paper. This paper formulates a QS computational model by incorporating these several substances. First, for the protein production time delay, a critical value is given by Hopf bifurcation theory. It is found that a larger time delay can lead to a larger amplitude and a longer period. This indicates that the length of time for protein synthesis has a regulatory effect on the release of drugs from the bacterial population. Second, hen the concentrations of AiiA, LuxI, and H$ _2 $O$ _2 $ is modulated individually, the QS system undergoes periodic oscillation and bistable state. Meanwhile, oscillatory and bistable regions can be significantly affected by simultaneously perturbing any two parameters related to AiiA, LuxI, and H$ _2 $O$ _2 $. This means that the individual or simultaneous changes of the three intrinsic molecular concentrations can effectively control the drugs release and the PH value in microorganisms and plants. Finally, the sensitivity relationship between the critical value of the delay and AiiA, LuxI, H$ _2 $O$ _2 $ parameters is analyzed.

Modelling the coupling of the M-clock and C-clock in lymphatic muscle cells

Chronic dysfunction of the lymphatic vascular system results in fluid accumulation between cells: lymphoedema. The condition is commonly acquired secondary to diseases such as cancer or the associated therapies. The primary driving force for fluid return through the lymphatic vasculature is provided by contractions of the muscularized lymphatic collecting vessels, driven by electrochemical oscillations. However, there is an incomplete understanding of the molecular and bioelectric mechanisms involved in lymphatic muscle cell excitation, hampering the development and use of pharmacological therapies. Modelling in silico has contributed greatly to understanding the contributions of specific ion channels to the cardiac action potential, but modelling of these processes in lymphatic muscle remains limited. Here, we propose a model of oscillations in the membrane voltage (M-clock) and intracellular calcium concentrations (C-clock) of lymphatic muscle cells. We modify a model by Imtiaz and colleagues to enable the M-clock to drive the C-clock oscillations. This approach differs from typical models of calcium oscillators in lymphatic and related cell types, but is required to fit recent experimental data. We include an additional voltage dependence in the gating variable control for the L-type calcium channel, enabling the M-clock to oscillate independently of the C-clock. We use phase-plane analysis to show that these M-clock oscillations are qualitatively similar to those of a generalised FitzHugh-Nagumo model. We also provide phase plane analysis to understand the interaction of the M-clock and C-clock oscillations. The model and methods have the potential to help determine mechanisms and find targets for pharmacological treatment of lymphoedema.

Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer

Targeting dysregulated Ca²⁺ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca²⁺ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca²⁺ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca²⁺ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca²⁺ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca²⁺ and cell proliferation. This intracellular Ca²⁺ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs.

Computational Approaches and Tools as Applied to the Study of Rhythms and Chaos in Biology

The temporal dynamics in biological systems displays a wide range of behaviors, from periodic oscillations, as in rhythms, bursts, long-range (fractal) correlations, chaotic dynamics up to brown and white noise. Herein, we propose a comprehensive analytical strategy for identifying, representing, and analyzing biological time series, focusing on two strongly linked dynamics: periodic (oscillatory) rhythms and chaos. Understanding the underlying temporal dynamics of a system is of fundamental importance; however, it presents methodological challenges due to intrinsic characteristics, among them the presence of noise or trends, and distinct dynamics at different time scales given by molecular, dcellular, organ, and organism levels of organization. For example, in locomotion circadian and ultradian rhythms coexist with fractal dynamics at faster time scales. We propose and describe the use of a combined approach employing different analytical methodologies to synergize their strengths and mitigate their weaknesses. Specifically, we describe advantages and caveats to consider for applying probability distribution, autocorrelation analysis, phase space reconstruction, Lyapunov exponent estimation as well as different analyses such as harmonic, namely, power spectrum; continuous wavelet transforms; synchrosqueezing transform; and wavelet coherence. Computational harmonic analysis is proposed as an analytical framework for using different types of wavelet analyses. We show that when the correct wavelet analysis is applied, the complexity in the statistical properties, including temporal scales, present in time series of signals, can be unveiled and modeled. Our chapter showcase two specific examples where an in-depth analysis of rhythms and chaos is performed: (1) locomotor and food intake rhythms over a 42-day period of mice subjected to different feeding regimes; and (2) chaotic calcium dynamics in a computational model of mitochondrial function.

Homeostatic calcium fluxes, ER calcium release, SOCE, and calcium oscillations in cultured astrocytes are interlinked by a small calcium toolkit

How homeostatic ER calcium fluxes shape cellular calcium signals is still poorly understood. Here we used dual-color calcium imaging (ER-cytosol) and transcriptome analysis to link candidates of the calcium toolkit of astrocytes with homeostatic calcium signals. We found molecular and pharmacological evidence that P/Q-type channel Cacna1a contributes to depolarization-dependent calcium entry in astrocytes. For stimulated ER calcium release, the cells express the phospholipase Cb3, IP₃ receptors Itpr1 and Itpr2, but no ryanodine receptors (Ryr1-3). After IP₃-induced calcium release, Stim1/2 - Orai1/2/3 most likely mediate SOCE. The Serca2 (Atp2a2) is the candidate for refilling of the ER calcium store. The cells highly express adenosine receptor Adora1a for IP₃-induced calcium release. Accordingly, adenosine induces fast ER calcium release and subsequent ER calcium oscillations. After stimulation, calcium refilling of the ER depends on extracellular calcium. In response to SOCE, astrocytes show calcium-induced calcium release, notably even after ER calcium was depleted by extracellular calcium removal in unstimulated cells. In contrast, spontaneous ER-cytosol calcium oscillations were not fully dependent on extracellular calcium, as ER calcium oscillations could persist over minutes in calcium-free solution. Additionally, cell-autonomous calcium oscillations show a second-long spatial and temporal delay in the signal dynamics of ER and cytosolic calcium. Our data reveal a rather strong contribution of homeostatic calcium fluxes in shaping IP₃-induced and calcium-induced calcium release as well as spatiotemporal components of intracellular calcium oscillations.

Dynamic mechanism of multiple bursting patterns in a whole-cell multiscale model with calcium oscillations

The dynamic mechanism of a whole-cell model containing electrical signalling and two-compartment Ca2+ signalling in gonadotrophs is investigated. The transition from spiking to bursting by Hopf bifurcation of the fast subsystem about the slow variable is detected via the suitable parameters. When the timescale of K+ gating variable is changed, the relaxation oscillation with locally small fluctuation, chaotic bursting and mixed-mode bursting (MMB) are revealed through chaos. In addition, the bifurcation of [Ca2+]i with regard to [IP3] is analysed, showing periodic solutions, torus, period doubling solutions and chaos. Finally, hyperpolarizations and torus canard-like behaviours of the full system under a set of specific parameters are elucidated.

Origins of oscillatory dynamics in the model of reactive oxygen species in the rhizosphere

Oscillatory processes are essential for normal functioning and survival of biological systems, and reactive oxygen species have a prominent role in many of them. A mechanism representing the dynamics of these species in the rhizosphere is analyzed using stoichiometric network analysis with the aim to determine its capabilities to simulate various dynamical states, including oscillations. A detailed analysis has shown that unstable steady states result from four destabilizing feedback cycles, among which the cycle involving hydroquinone, an electron acceptor, and its semi-reduced form is the dominant one responsible for the existence of saddle-node and Andronov-Hopf bifurcations. This requires a higher steady-state concentration for the reduced electron acceptor compared to that of the remaining species, where the level of oxygen steady-state concentration determines whether the Andronov-Hopf or saddle-node bifurcation will occur.

From spikes to intercellular waves: Tuning intercellular calcium signaling dynamics modulates organ size control

Information flow within and between cells depends significantly on calcium (Ca²⁺) signaling dynamics. However, the biophysical mechanisms that govern emergent patterns of Ca²⁺ signaling dynamics at the organ level remain elusive. Recent experimental studies in developing Drosophila wing imaginal discs demonstrate the emergence of four distinct patterns of Ca²⁺ activity: Ca²⁺ spikes, intercellular Ca²⁺ transients, tissue-level Ca²⁺ waves, and a global “fluttering” state. Here, we used a combination of computational modeling and experimental approaches to identify two different populations of cells within tissues that are connected by gap junction proteins. We term these two subpopulations “initiator cells,” defined by elevated levels of Phospholipase C (PLC) activity, and “standby cells,” which exhibit baseline activity. We found that the type and strength of hormonal stimulation and extent of gap junctional communication jointly determine the predominate class of Ca²⁺ signaling activity. Further, single-cell Ca²⁺ spikes are stimulated by insulin, while intercellular Ca²⁺ waves depend on Gαq activity. Our computational model successfully reproduces how the dynamics of Ca²⁺ transients varies during organ growth. Phenotypic analysis of perturbations to Gαq and insulin signaling support an integrated model of cytoplasmic Ca²⁺ as a dynamic reporter of overall tissue growth. Further, we show that perturbations to Ca²⁺ signaling tune the final size of organs. This work provides a platform to further study how organ size regulation emerges from the crosstalk between biochemical growth signals and heterogeneous cell signaling states.

Calcium (Ca²⁺) is a universal second messenger that regulates a myriad of cellular processes such as cell division, cell proliferation and apoptosis. Multiple patterns of Ca²⁺ signaling including single-cell spikes, multicellular Ca²⁺ transients, large-scale Ca²⁺ waves, and global “fluttering” have been observed in epithelial systems during organ development. Key molecular players and biophysical mechanisms involved in formation of these patterns during organ development are not well understood. In this work, we developed a generalized multicellular model of Ca²⁺ that captures all the key categories of Ca²⁺ activity as a function of key hormonal signals. Integration of model predictions and experiments reveals two subclasses of cell populations and demonstrates that Ca²⁺ signaling activity at the organ scale is defined by a general decrease in gap junction communication as an organ grows. Our experiments also reveal that a “goldilocks zone” of optimal Ca²⁺ activity is required to achieve optimal growth at the organ level.

The Mitochondrial Ca2+ uniporter is a central regulator of interorganellar Ca2+ transfer and NFAT activation

Mitochondrial Ca²⁺ uptake tailors the strength of stimulation of plasma membrane phospholipase C–coupled receptors to that of cellular bioenergetics. However, how Ca²⁺ uptake by the mitochondrial Ca²⁺ uniporter (MCU) shapes receptor-evoked interorganellar Ca²⁺ signaling is unknown. Here, we used CRISPR/Cas9 gene knockout, subcellular Ca²⁺ imaging, and mathematical modeling to show that MCU is a universal regulator of intracellular Ca²⁺ signaling across mammalian cell types. MCU activity sustains cytosolic Ca²⁺ signaling by preventing Ca²⁺-dependent inactivation of store-operated Ca²⁺ release–activated Ca²⁺ channels and by inhibiting Ca²⁺ extrusion. Paradoxically, MCU knockout (MCU-KO) enhanced cytosolic Ca²⁺ responses to store depletion. Physiological agonist stimulation in MCU-KO cells led to enhanced frequency of cytosolic Ca²⁺ oscillations, endoplasmic reticulum Ca²⁺ refilling, nuclear translocation of nuclear factor for activated T cells transcription factors, and cell proliferation, without altering inositol-1,4,5-trisphosphate receptor activity. Our data show that MCU has dual counterbalancing functions at the cytosol–mitochondria interface, whereby the cell-specific MCU-dependent cytosolic Ca²⁺ clearance and buffering capacity of mitochondria reciprocally regulate interorganellar Ca²⁺ transfer and nuclear factor for activated T cells nuclear translocation during receptor-evoked signaling. These findings highlight the critical dual function of the MCU not only in the acute Ca²⁺ buffering by mitochondria but also in shaping endoplasmic reticulum and cytosolic Ca²⁺ signals that regulate cellular transcription and function.

Moisture-induced autonomous surface potential oscillations for energy harvesting

A variety of autonomous oscillations in nature such as heartbeats and some biochemical reactions have been widely studied and utilized for applications in the fields of bioscience and engineering. Here, we report a unique phenomenon of moisture-induced electrical potential oscillations on polymers, poly([2-(methacryloyloxy)ethyl] dimethyl-(3-sulfopropyl) ammonium hydroxide-co-acrylic acid), during the diffusion of water molecules. Chemical reactions are modeled by kinetic simulations while system dynamic equations and the stability matrix are analyzed to show the chaotic nature of the system which oscillates with hidden attractors to induce the autonomous surface potential oscillation. Using moisture in the ambient environment as the activation source, this self-excited chemoelectrical reaction could have broad influences and usages in surface-reaction based devices and systems. As a proof-of-concept demonstration, an energy harvester is constructed and achieved the continuous energy production for more than 15,000 seconds with an energy density of 16.8 mJ/cm2. A 2-Volts output voltage has been produced to power a liquid crystal display toward practical applications with five energy harvesters connected in series.

A neurovascular-unit-on-a-chip for the evaluation of the restorative potential of stem cell therapies for ischaemic stroke

The therapeutic efficacy of stem cells transplanted into an ischaemic brain depends primarily on the responses of the neurovascular unit. Here, we report the development and applicability of a functional neurovascular unit on a microfluidic chip as a microphysiological model of ischaemic stroke that recapitulates the function of the blood-brain barrier as well as interactions between therapeutic stem cells and host cells (human brain microvascular endothelial cells, pericytes, astrocytes, microglia and neurons). We used the model to track the infiltration of a number of candidate stem cells and to characterize the expression levels of genes associated with post-stroke pathologies. We observed that each type of stem cell showed unique neurorestorative effects, primarily by supporting endogenous recovery rather than through direct cell replacement, and that the recovery of synaptic activities is correlated with the recovery of the structural and functional integrity of the neurovascular unit rather than with the regeneration of neurons.

Highly localized intracellular Ca2+ signals promote optimal salivary gland fluid secretion

Salivary fluid secretion involves an intricate choreography of membrane transporters to result in the trans-epithelial movement of NaCl and water into the acinus lumen. Current models are largely based on experimental observations in enzymatically isolated cells where the Ca²⁺ signal invariably propagates globally and thus appears ideally suited to activate spatially separated Cl and K channels, present on the apical and basolateral plasma membrane, respectively. We monitored Ca²⁺ signals and salivary secretion in live mice expressing GCamp6F, following stimulation of the nerves innervating the submandibular gland. Consistent with in vitro studies, Ca²⁺ signals were initiated in the apical endoplasmic reticulum. In marked contrast to in vitro data, highly localized trains of Ca²⁺ transients that failed to fully propagate from the apical region were observed. Following stimuli optimum for secretion, large apical-basal gradients were elicited. A new mathematical model, incorporating these data was constructed to probe how salivary secretion can be optimally stimulated by apical Ca²⁺ signals.

Improved bounds on entropy production in living systems

Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal. Here, by reformulating the problem within an optimization framework, we are able to infer improved bounds on the rate of entropy production from partial measurements of biological systems. Our approach yields provably optimal estimates given certain measurable transition statistics. In contrast to prevailing methods, the improved estimator reveals nonzero entropy production rates even when nonequilibrium processes appear time symmetric and therefore may pretend to obey detailed balance. We demonstrate the broad applicability of this framework by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, growing microtubules, and calcium oscillations within human embryonic kidney cells.

Omnitemporal choreographies of all five STIM/Orai and IP3Rs underlie the complexity of mammalian Ca2+ signaling

Stromal-interaction molecules (STIM1/2) sense endoplasmic reticulum (ER) Ca²⁺ depletion and activate Orai channels. However, the choreography of interactions between native STIM/Orai proteins under physiological agonist stimulation is unknown. We show that the five STIM1/2 and Orai1/2/3 proteins are non-redundant and function together to ensure the graded diversity of mammalian Ca²⁺ signaling. Physiological Ca²⁺ signaling requires functional interactions between STIM1/2, Orai1/2/3, and IP₃Rs, ensuring that receptor-mediated Ca²⁺ release is tailored to Ca²⁺ entry and nuclear factor of activated T cells (NFAT) activation. The N-terminal Ca²⁺-binding ER-luminal domains of unactivated STIM1/2 inhibit IP₃R-evoked Ca²⁺ release. A gradual increase in agonist intensity and STIM1/2 activation relieves IP₃R inhibition. Concomitantly, activated STIM1/2 C termini differentially interact with Orai1/2/3 as agonist intensity increases. Thus, coordinated and omnitemporal functions of all five STIM/Orai and IP₃Rs translate the strength of agonist stimulation to precise levels of Ca²⁺ signaling and NFAT induction, ensuring the fidelity of complex mammalian Ca²⁺ signaling.

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.

Calcium Dynamics and Water Transport in Salivary Acinar Cells

Saliva is secreted from the acinar cells of the salivary glands, using mechanisms that are similar to other types of water-transporting epithelial cells. Using a combination of theoretical and experimental techniques, over the past 20 years we have continually developed and modified a quantitative model of saliva secretion, and how it is controlled by the dynamics of intracellular calcium. However, over approximately the past 5 years there have been significant developments both in our understanding of the underlying mechanisms and in the way these mechanisms should best be modelled. Here, we review the traditional understanding of how saliva is secreted, and describe how our work has suggested important modifications to this traditional view. We end with a brief description of the most recent data from living animals and discuss how this is now contributing to yet another iteration of model construction and experimental investigation.

Stochastic models for single-cell data: Current challenges and the way forward

Although the quantity and quality of single-cell data have progressed rapidly, making quantitative predictions with single-cell stochastic models remains challenging. The stochastic nature of cellular processes leads to at least three challenges in building models with single-cell data: (a) because variability in single-cell data can be attributed to multiple different sources, it is difficult to rule out conflicting mechanistic models that explain the same data equally well; (b) the distinction between interesting biological variability and experimental variability is sometimes ambiguous; (c) the nonstandard distributions of single-cell data can lead to violations of the assumption of symmetric errors in least-squares fitting. In this review, we first discuss recent studies that overcome some of the challenges or set up a promising direction and then introduce some powerful statistical approaches utilized in these studies. We conclude that applying and developing statistical approaches could lead to further progress in building stochastic models for single-cell data.

Modeling of Ca2+ transients initiated by GPCR agonists in mesenchymal stromal cells

The integrative study that included experimentation and mathematical modeling was carried out to analyze dynamic aspects of transient Ca²⁺ signaling induced by brief pulses of GPCR agonists in mesenchymal stromal cells from the human adipose tissue (AD-MSCs). The experimental findings argued for IP₃/Ca²⁺-regulated Ca²⁺ release via IP₃ receptors (IP₃Rs) as a key mechanism mediating agonist-dependent Ca²⁺ transients. The consistent signaling circuit was proposed to formalize coupling of agonist binding to Ca²⁺ mobilization for mathematical modeling. The model properly simulated the basic phenomenology of agonist transduction in AD-MSCs, which mostly produced single Ca²⁺ spikes upon brief stimulation. The spike-like responses were almost invariantly shaped at different agonist doses above a threshold, while response lag markedly decreased with stimulus strength. In AD-MSCs, agonists and IP₃ uncaging elicited similar Ca²⁺ transients but IP₃ pulses released Ca²⁺ without pronounced delay. This suggested that IP₃ production was rate-limiting in agonist transduction. In a subpopulation of AD-MSCs, brief agonist pulses elicited Ca²⁺ bursts crowned by damped oscillations. With properly adjusted parameters of IP₃R inhibition by cytosolic Ca²⁺, the model reproduced such oscillatory Ca²⁺ responses as well. GEM-GECO1 and R-CEPIA1er, the genetically encoded sensors of cytosolic and reticular Ca²⁺, respectively, were co-expressed in HEK-293 cells that also responded to agonists in an "all-or-nothing" manner. The experimentally observed Ca²⁺ signals triggered by ACh in both compartments were properly simulated with the suggested signaling circuit. Thus, the performed modeling of the transduction process provides sufficient theoretical basis for deeper interpretation of experimental findings on agonist-induced Ca²⁺ signaling in AD-MSCs.

Long-Time Phase Correlations Reveal Regulation of Beating Cardiomyocytes

Spontaneous contractions of cardiomyocytes are driven by calcium oscillations due to the activity of ionic calcium channels and pumps. The beating phase is related to the time-dependent deviation of the oscillations from their average frequency, due to noise and the resulting cellular response. Here, we demonstrate experimentally that, in addition to the short-time (1-2 Hz), beat-to-beat variability, there are long-time correlations (tens of minutes) in the beating phase dynamics of isolated cardiomyocytes. Our theoretical model relates these long-time correlations to cellular regulation that restores the frequency to its average, homeostatic value in response to stochastic perturbations.

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.

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.

Calcium signaling and epigenetics: A key point to understand carcinogenesis

Calcium (Ca²⁺) signaling controls a wide range of cellular processes, including the hallmarks of cancer. The Ca²⁺ signaling system encompasses several types of proteins, such as receptors, channels, pumps, exchangers, buffers, and sensors, of which several are mutated or with altered expression in cancer cells. Since epigenetic mechanisms are disrupted in all stages of carcinogenesis, and reversibly regulate gene expression, they have been studied by different research groups to understand their role in Ca²⁺ signaling remodeling in cancer cells and the carcinogenic process. In this review, we link Ca²⁺ signaling, cancer, and epigenetics fields to generate a comprehensive landscape of this complex group of diseases.

Oscillatory Dynamics of p53-Mdm2 Circuit in Response to DNA Damage Caused by Ionizing Radiation

Although the dynamical behavior of the p53-Mdm2 loop has been extensively studied, the understanding of the mechanism underlying the regulation of this pathway still remains limited. Herein, we developed an integrated model with five basic components and three ubiquitous time delays for the p53-Mdm2 interaction in response to DNA damage following ionizing radiation (IR). We showed that a sufficient amount of activated ATM level can initiate the p53 oscillations with nearly the same amplitude over a wide range of the ATM level; a proper range of p53 level is also required for generating the oscillations, for too high or too low levels it would fail to generate the oscillations; and increased Mdm2 level leads to decreased amplitude of the p53 oscillation and reduced expression of the p53 activity. Moreover, we found that the negative feedback loop formed between p53 and nuclear Mdm2 plays a dominant role in determining the p53 dynamics, whereas when interaction strength of the negative feedback loop becomes weaker, the positive feedback loop formed between p53 and cytoplasmatic Mdm2 can induce different types of dynamics. Furthermore, we demonstrated that the total time delay required for protein production and nuclear translocation of Mdm2 can induce p53 oscillations even when the p53 level is at a certain stable high steady state or at a certain stable low steady state. In addition, the two important features of the oscillatory dynamics-amplitude and period-can be controlled by such time delay. These results are in agreement with multiple experimental observations and may enrich our understanding of the dynamics of the p53 network.

Effects of store-operated and receptor-operated calcium channels on synchronization of calcium oscillations in astrocytes

Intercellular calcium signaling allows cells to communicate with each other and to interact with adjacent cells. Gap junction is the most common and important way for cellular communication. Recently, mathematical models have been widely used to gain a precise and quantitative understanding of the dynamics of intracellular calcium ions (Ca^2＋). In this paper, we establish a mathematical model considering the gap junction permeable to Ca^2＋ and to IP₃ for describing the calcium oscillations in coupled astrocytes. Store-operated calcium entry (SOCE) is viewed as the main process which controls the non-excitable cells, hence, we focus on the effect of store-operated calcium channel (SOCC) and receptor-operated calcium channel (ROCC) on the intercellular synchronization, respectively. By employing bifurcation analysis on this model, the dynamic behaviors of the coupled system with different physiological state cells is obtained with changes in the maximum capacity of the SOCC and the ROCC. The synchronization boundaries for different conditions are gained in the two parameters space of the channel parameters and the coupling strength. The results suggest that the variation of the maximum flow for different calcium channels determines the stable oscillations of the coupled system, as well as for the frequency and amplitude of oscillations. The SOCC has an expected effect on the change of the oscillatory interval while the ROCC demonstrated the influence on the amplitude modulation. Furthermore, the coupling strength and channel parameters could induce 1:1 locking of intercellular Ca^2＋ oscillations and the synchronization region like Arnol'd tongue is found.

Ca2+ Release via IP3 Receptors Shapes the Cardiac Ca2+ Transient for Hypertrophic Signaling

Calcium (Ca²⁺) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca²⁺ channels trigger release of Ca²⁺ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca²⁺ release via inositol 1,4,5-trisphosphate receptors (IP₃Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca²⁺ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP₃Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP₃R channels on the Ca²⁺ transient and examine the sensitivity of the Ca²⁺ transient shape to properties of IP₃R activation. A key result of our study is that IP₃R activation increases Ca²⁺ transient duration for a broad range of IP₃R properties, but the effect of IP₃R activation on Ca²⁺ transient amplitude is dependent on IP₃ concentration. Furthermore we demonstrate that IP₃-mediated Ca²⁺ release in the cytosol increases the duty cycle of the Ca²⁺ transient, the fraction of the cycle for which [Ca²⁺] is elevated, across a broad range of parameter values and IP₃ concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca²⁺ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca²⁺ duty cycle as a plausible mechanism for IP₃-dependent hypertrophic signaling via Ca²⁺-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.

Laser writing of nitrogen-doped silicon carbide for biological modulation

Conducting or semiconducting materials embedded in insulating polymeric substrates can be useful in biointerface applications; however, attainment of this composite configuration by direct chemical processes is challenging. Laser-assisted synthesis has evolved as a fast and inexpensive technique to prepare various materials, but its utility in the construction of biophysical tools or biomedical devices is less explored. Here, we use laser writing to convert portions of polydimethylsiloxane (PDMS) into nitrogen-doped cubic silicon carbide (3C-SiC). The dense 3C-SiC surface layer is connected to the PDMS matrix via a spongy graphite layer, facilitating electrochemical and photoelectrochemical activity. We demonstrate the fabrication of arbitrary two-dimensional (2D) SiC-based patterns in PDMS and freestanding 3D constructs. To establish the functionality of the laser-produced composite, we apply it as flexible electrodes for pacing isolated hearts and as photoelectrodes for local peroxide delivery to smooth muscle sheets.

IP3-Dependent Ca2+ Oscillations Switch into a Dual Oscillator Mechanism in the Presence of PLC-Linked Hormones

Ca2+ oscillations that depend on inositol-1,4,5-trisphosphate (IP3) have been ascribed to biphasic Ca2+ regulation of the IP3 receptor (IP3R) or feedback mechanisms controlling IP3 levels in different cell types. IP3 uncaging in hepatocytes elicits Ca2+ transients that are often localized at the subcellular level and increase in magnitude with stimulus strength. However, this does not reproduce the broad baseline-separated global Ca2+ oscillations elicited by vasopressin. Addition of hormone to cells activated by IP3 uncaging initiates a qualitative transition from high-frequency spatially disorganized Ca2+ transients, to low-frequency, oscillatory Ca2+ waves that propagate throughout the cell. A mathematical model with dual coupled oscillators that integrates Ca2+-induced Ca2+ release at the IP3R and mutual feedback mechanisms of cross-coupling between Ca2+ and IP3 reproduces this behavior. Thus, multiple Ca2+ oscillation modes can coexist in the same cell, and hormonal stimulation can switch from the simpler to the more complex to yield robust signaling.

The native ORAI channel trio underlies the diversity of Ca2+ signaling events

The essential role of ORAI1 channels in receptor-evoked Ca2+ signaling is well understood, yet little is known about the physiological activation of the ORAI channel trio natively expressed in all cells. The roles of ORAI2 and ORAI3 have remained obscure. We show that ORAI2 and ORAI3 channels play a critical role in mediating the regenerative Ca2+ oscillations induced by physiological receptor activation, yet ORAI1 is dispensable in generation of oscillations. We reveal that ORAI2 and ORAI3 channels multimerize with ORAI1 to expand the range of sensitivity of receptor-activated Ca2+ signals, reflecting their enhanced basal STIM1-binding and heightened Ca2+-dependent inactivation. This broadened bandwidth of Ca2+ influx is translated by cells into differential activation of NFAT1 and NFAT4 isoforms. Our results uncover a long-sought role for ORAI2 and ORAI3, revealing an intricate control mechanism whereby heteromerization of ORAI channels mediates graded Ca2+ signals that extend the agonist-sensitivity to fine-tune transcriptional control.

IP3 mediated global Ca2+ signals arise through two temporally and spatially distinct modes of Ca2+ release

The 'building-block' model of inositol trisphosphate (IP3)-mediated Ca2+ liberation posits that cell-wide cytosolic Ca2+ signals arise through coordinated activation of localized Ca2+ puffs generated by stationary clusters of IP3 receptors (IP3Rs). Here, we revise this hypothesis, applying fluctuation analysis to resolve Ca2+ signals otherwise obscured during large Ca2+ elevations. We find the rising phase of global Ca2+ signals is punctuated by a flurry of puffs, which terminate before the peak by a mechanism involving partial ER Ca2+ depletion. The continuing rise in Ca2+, and persistence of global signals even when puffs are absent, reveal a second mode of spatiotemporally diffuse Ca2+ signaling. Puffs make only small, transient contributions to global Ca2+ signals, which are sustained by diffuse release of Ca2+ through a functionally distinct process. These two modes of IP3-mediated Ca2+ liberation have important implications for downstream signaling, imparting spatial and kinetic specificity to Ca2+-dependent effector functions and Ca2+ transport.

Cardiomyocyte Calcium Ion Oscillations-Lessons From Physics

We review a theoretical, coarse-grained description for cardiomyocytes calcium dynamics that is motivated by experiments on RyR channel dynamics and provides an analogy to other spontaneously oscillating systems. We show how a minimal model, that focuses on calcium channel and pump dynamics and kinetics, results in a single, easily understood equation for spontaneous calcium oscillations (the Van-der-Pol equation). We analyze experiments on isolated RyR channels to quantify how the channel dynamics depends both on the local calcium concentration, as well as its temporal behavior (“adaptation”). Our oscillator model analytically predicts the conditions for spontaneous oscillations, their frequency and amplitude, and how each of those scale with the small number of relevant parameters related to calcium channel and pump activity. The minimal model is easily extended to include the effects of noise and external pacing (electrical or mechanical). We show how our simple oscillator predicts and explains the experimental observations of synchronization, “bursting” and reduction of apparent noise in the beating dynamics of paced cells. Thus, our analogy and theoretical approach provides robust predictions for the beating dynamics, and their biochemical and mechanical modulation.

A Statistical View on Calcium Oscillations

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.

Computational Modeling Reveals Frequency Modulation of Calcium-cAMP/PKA Pathway in Dendritic Spines

Dendritic spines are the primary excitatory postsynaptic sites that act as subcompartments of signaling. Ca²⁺ is often the first and most rapid signal in spines. Downstream of calcium, the cyclic adenosine monophosphate (cAMP)/protein kinase A (PKA) pathway plays a critical role in the regulation of spine formation, morphological modifications, and ultimately, learning and memory. Although the dynamics of calcium are reasonably well-studied, calcium-induced cAMP/PKA dynamics, particularly with respect to frequency modulation, are not fully explored. In this study, we present a well-mixed model for the dynamics of calcium-induced cAMP/PKA dynamics in dendritic spines. The model is constrained using experimental observations in the literature. Further, we measured the calcium oscillation frequency in dendritic spines of cultured hippocampal CA1 neurons and used these dynamics as model inputs. Our model predicts that the various steps in this pathway act as frequency modulators for calcium, and the high frequency of calcium input is filtered by adenylyl cyclase 1 and phosphodiesterases in this pathway such that cAMP/PKA only responds to lower frequencies. This prediction has important implications for noise filtering and long-timescale signal transduction in dendritic spines. A companion manuscript presents a three-dimensional spatial model for the same pathway.

A mathematical model of calcium dynamics: Obesity and mitochondria-associated ER membranes

Multiple cellular organelles tightly orchestrate intracellular calcium (Ca²⁺) dynamics to regulate cellular activities and maintain homeostasis. The interplay between the endoplasmic reticulum (ER), a major store of intracellular Ca²⁺, and mitochondria, an important source of adenosine triphosphate (ATP), has been the subject of much research, as their dysfunction has been linked with metabolic diseases. Interestingly, throughout the cell’s cytosolic domain, these two organelles share common microdomains called mitochondria-associated ER membranes (MAMs), where their membranes are in close apposition. The role of MAMs is critical for intracellular Ca²⁺ dynamics as they provide hubs for direct Ca²⁺ exchange between the organelles. A recent experimental study reported correlation between obesity and MAM formation in mouse liver cells, and obesity-related cellular changes that are closely associated with the regulation of Ca²⁺ dynamics. We constructed a mathematical model to study the effects of MAM Ca²⁺ dynamics on global Ca²⁺ activities. Through a series of model simulations, we investigated cellular mechanisms underlying the altered Ca²⁺ dynamics in the cells under obesity. We predict that, as the dosage of stimulus gradually increases, liver cells from obese mice will reach the state of saturated cytosolic Ca²⁺ concentration at a lower stimulus concentration, compared to cells from healthy mice.

It is well known that intracellular Ca²⁺ oscillations carry encoded signals in their amplitude and frequency to regulate various cellular processes, and accumulating evidence supports the importance of the interplay between the ER and mitochondria in cellular Ca²⁺ homeostasis. Miscommunications between the organelles may be involved in the development of metabolic diseases. Based on a recent experimental study that spotlighted a correlation between obesity and physical interactions of the ER and mitochondria in mouse hepatic cells, we constructed a mathematical model as a tool to probe the effects of the cellular changes linked with obesity on global cellular Ca²⁺ dynamics. Our model successfully reproduced the experimental study that observed a positive correlation between an increase in ER-mitochondrial junctions and the magnitude of mitochondrial Ca²⁺ responses. We postulate that hepatic cells from lean animals exhibit Ca²⁺ oscillations that are more robust under higher concentrations of stimulus, compared to cells from obese animals.

Oscillatory Dynamics of p53 Genetic Network Induced by Feedback Loops and Time Delays

DNA damage caused by γ -irradiation initiates oscillatory expression of the p53 genetic network. Although many studies revealed the effects of the p53-Mdm2 circuit on p53 dynamics, a few studies explored the contribution of upstream kinases to p53 oscillation. In this paper, an integrated mathematical model of the p53 network in response to γ -irradiation is studied, which consists of five basic components, two ubiquitous time delays, and two negative feedback loops. It is found that recurrent p53 pulses are externally initiated by ataxia telangiectasia mutated (ATM), and the negative feedback loop formed between ATM and p53, via Wip1, plays a dominant role in generating p53 oscillation. In addition, p53 oscillation requires not only an appropriate Mdm2 negative strength but also a threshold level of Wip1 negative strength. Furthermore, the time delays required for transcription and translation of Mdm2 and Wip1 proteins are essential for p53 oscillation. In particular, the critical value of time delay for inducing oscillation and the properties of delay-driven Hopf bifurcation are theoretically analyzed. As expected, the results are clearly in consistence with biological experiments and observations.