Membrane associated complexes in calcium dynamics modelling

Temporal multiscale modeling of biochemical regulatory networks: Calcium-regulated hepatocyte lipid and glucose metabolism

Hepatocyte lipid and glucose metabolism is regulated not only by major hormones like insulin and glucagon but also by many other factors, including calcium ions. Recently, mitochondria-associated membrane (MAM) dysfunction combined with incorrect IP3-receptor regulation has been shown to result in abnormal calcium signaling in hepatocytes. This dysfunction could further lead to hepatic metabolism pathology. However, the exact contribution of MAM dysfunction, incorrect IP3-receptor regulation and insulin resistance to the calcium-insulin-glucagon interplay is not understood yet. In this work, we analyze the role of abnormal calcium signaling and insulin dysfunction in hepatocytes by proposing a model of hepatocyte metabolic regulatory network with a detailed focus on the model construction details besides the biological aspect. In this work, we analyze the role of abnormal calcium signaling and insulin dysfunction in hepatocytes by proposing a model of hepatocyte metabolic regulatory network. We focus on the model construction details, model validation, and predictions. We describe the dynamic regulation of signaling processes by sigmoid Hill function. In particular, we study the effect of both the Hill function slope and the distance between Hill function extremes on metabolic processes in hepatocytes as a model of nonspecific insulin dysfunction. We also address the significant time difference between characteristic time of glucose hepatic processing and a typical calcium oscillation period in hepatocytes. Our modeling results show that calcium signaling dysfunction results in an abnormal increase in postprandial glucose levels, an abnormal glucose decrease in fasting, and a decreased amount of stored glycogen. An insulin dysfunction of glucose phosphorylation, glucose dephosphorylation, and glycogen breakdown also cause a noticeable effect. We also get some insight into the so-called hepatic insulin resistance paradox, confirming the hypothesis regarding indirect insulin action on hepatocytes via dysfunctional adipocyte lipolysis.

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.

Calcium-dependent insulin resistance in hepatocytes: mathematical model

Hepatocyte insulin resistance is one of the early factors of developing type II diabetes. If insulin resistance is treated early, type II diabetes could be prevented. In recent years, scientists have been conducting extensive research on the underlying issues on a cellular and molecular level. It was found that the modulation of IP₃-receptors, the mitochondrial ability to form the mitochondria-associated membranes (MAMs) and the endoplasmic reticulum stress during Ca²⁺ signaling play a key role in hepatocyte being able to maintain euglycemia and provide metabolic flexibility. However, researchers cannot agree on what factor is the key one in resulting in insulin resistance. In this work, we propose a mathematical model of Ca²⁺ signaling. We included in the model all the major contributors of a proper Ca²⁺ signaling during both the fasting and the postprandial state. Our modeling results are in good agreement with available experimental data. The analysis of modeling results suggests that MAMs dysfunction alone cannot result in abnormal Ca²⁺ signaling and the wrong modulation of IP₃-receptors is a more definite reason. However, both the MAMs dysfunction and the IP₃ signaling dysregulation combined can lead to a robust Ca²⁺ signal and improper glucose release. In addition, our model results suggest a strong dependence of Ca²⁺ oscillations pattern on morphological characteristics of the ER and the mitochondria.

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.

Modeling the role of endoplasmic reticulum-mitochondria microdomains in calcium dynamics

Upon inositol trisphosphate (IP₃) stimulation of non-excitable cells, including vascular endothelial cells, calcium (Ca²⁺) shuttling between the endoplasmic reticulum (ER) and mitochondria, facilitated by complexes called Mitochondria-Associated ER Membranes (MAMs), is known to play an important role in the occurrence of cytosolic Ca²⁺ concentration ([Ca²⁺]_Cyt) oscillations. A mathematical compartmental closed-cell model of Ca²⁺ dynamics was developed that accounts for ER-mitochondria Ca²⁺ microdomains as the µd compartment (besides the cytosol, ER and mitochondria), Ca²⁺ influx to/efflux from each compartment and Ca²⁺ buffering. Varying the distribution of functional receptors in MAMs vs. the rest of ER/mitochondrial membranes, a parameter called the channel connectivity coefficient (to the µd), allowed for generation of [Ca²⁺]_Cytoscillations driven by distinct mechanisms at various levels of IP₃ stimulation. Oscillations could be initiated by the transient opening of IP₃ receptors facing either the cytosol or the µd, and subsequent refilling of the respective compartment by Ca²⁺ efflux from the ER and/or the mitochondria. Only under conditions where the µd became the oscillation-driving compartment, silencing the Mitochondrial Ca²⁺ Uniporter led to oscillation inhibition. Thus, the model predicts that alternative mechanisms can yield [Ca²⁺]_Cyt oscillations in non-excitable cells, and, under certain conditions, the ER-mitochondria µd can play a regulatory role.

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.

The role of S-nitrosylation of kainate-type of ionotropic glutamate receptor 2 in epilepsy induced by kainic acid

Epilepsy is a chronic brain disease affecting millions of individuals. Kainate receptors, especially kainate-type of ionotropic glutamate receptor 2 (GluK2), play an important role in epileptogenesis. Recent data showed that GluK2 could undergo post-translational modifications in terms of S-nitrosylation (SNO), and affect the signaling pathway of cell death in cerebral ischemia-reperfusion. However, it is unclear whether S-nitrosylation of GluK2 (SNO-GluK2) contributes to cell death induced by epilepsy. Here, we report that kainic acid-induced SNO-GluK2 is mediated by GluK2 itself, regulated by neuronal nitric oxide synthase (nNOS) and the level of cytoplasmic calcium in vivo and in vitro hippocampus neurons. The whole-cell patch clamp recordings showed the influence of SNO-GluK2 on ion channel characterization of GluK2-Kainate receptors. Moreover, immunohistochemistry staining results showed that inhibition of SNO-GluK2 by blocking nNOS or GluK2 or by reducing the level of cytoplasmic calcium-protected hippocampal neurons from kainic acid-induced injury. Finally, immunoprecipitation and western blotting data revealed the involvement of assembly of a GluK2-PSD95-nNOS signaling complex in epilepsy. Taken together, our results showed that the SNO-GluK2 plays an important role in neuronal injury of epileptic rats by forming GluK2-PSD95-nNOS signaling module in a cytoplasmic calcium-dependent way, suggesting a potential therapeutic target site for epilepsy.

Dynamic analysis on the calcium oscillation model considering the influences of mitochondria

Based on the model considering the influences of mitochondria, a further theoretical study on the dynamic behaviors of calcium signals is made. First of all, the reason for the generation and disappearance of calcium oscillations is verified in theory. Second, an analysis on the model considering the influences of mitochondria and the model neglecting the influences of mitochondria is carried out. Third, β (representing calcium leak) is introduced and it can be found that with the increase of β, the Hopf bifurcation points of system move towards the decreasing direction of μ (representing stimulus intensity) and calcium oscillations region gradually decreases. Forth, the study on τ_h (representing relaxation time) indicates that with the increase of τ_h, the second Hopf bifurcation point of system moves towards the increasing direction of μ and calcium oscillations region gradually increases. Under certain stimulus intensity, when relaxation time increases, calcium oscillation peak rises rapidly and the period increases obviously. Fifth, two-parameter bifurcation diagram of V_m1 (representing mitochondria activity) and μ contains three regions: stable region, oscillation region and unstable region. When the parameters fall in the unstable region Ca²⁺ gather towards mitochondria and further lead to cell apoptosis. With the increase of V_m1, calcium oscillations region shrinks gradually. V_m1 and μ both play a key role in regulating cell apoptosis. Only when V_m1 and μ are high enough can cells enter into programmed cell death and the higher V_m1 is, the lower the stimulus intensity required by cell apoptosis is.

Capturing intracellular Ca2+ dynamics in computational models of neurodegenerative diseases

Many signaling pathways crucial for homeostatic regulation, synaptic plasticity, apoptosis and immune response depend on Ca²⁺. Ca²⁺ dysregulation disrupts normal function of neurons and neuronal networks. This causes severe motor and cognitive disabilities. Understanding how Ca²⁺ dysregulation triggers disease onset and progression, and affects downstream processes, can help identify targets for treatments. Because of intermingling of molecular pathways, dissecting the role of individual mechanisms and establishing causality is very challenging. Computational models provide a way to decipher these processes. I review some computational models with Ca²⁺ dynamics to illustrate their predictive power, and note where extending those models to capture multiscale interaction of Ca²⁺ dependent molecular pathways can be useful for therapeutic and drug discovery purposes.

Mitochondrial Ca2+ handling in Huntington's and Alzheimer's diseases - Role of ER-mitochondria crosstalk

Mitochondria play a relevant role in Ca²⁺ buffering, governing energy metabolism and neuronal function. Huntington's disease (HD) and Alzheimer's disease (AD) are two neurodegenerative disorders that, although clinically distinct, share pathological features linked to selective brain damage. These include mitochondrial dysfunction, intracellular Ca²⁺ deregulation and mitochondrial Ca²⁺ handling deficits. Both diseases are associated with misfolding and aggregation of specific proteins that physically interact with mitochondria and interfere with endoplasmic reticulum (ER)/mitochondria-contact sites. Cumulating evidences indicate that impairment of mitochondrial Ca²⁺ homeostasis underlies the susceptibility to selective neuronal death observed in HD and AD; however data obtained with different models and experimental approaches are not always consistent. In this review, we explore the recent literature on deregulation of mitochondrial Ca²⁺ handling underlying the interplay between mitochondria and ER in HD and AD-associated neurodegeneration.

Impaired mitochondrial function due to familial Alzheimer's disease-causing presenilins mutants via Ca(2+) disruptions

Mutants in presenilins (PS1 or PS2) is the major cause of familial Alzheimer's disease (FAD). FAD causing PS mutants affect intracellular Ca(2+) homeostasis by enhancing the gating of inositol trisphosphate (IP3) receptor (IP3R) Ca(2+) release channel on the endoplasmic reticulum, leading to exaggerated Ca(2+) release into the cytoplasm. Using experimental IP3R-mediated Ca(2+) release data, in conjunction with a computational model of cell bioenergetics, we explore how the differences in mitochondrial Ca(2+) uptake in control cells and cells expressing FAD-causing PS mutants affect key variables such as ATP, reactive oxygen species (ROS), NADH, and mitochondrial Ca(2+). We find that as a result of exaggerated cytosolic Ca(2+) in FAD-causing mutant PS-expressing cells, the rate of oxygen consumption increases dramatically and overcomes the Ca(2+) dependent enzymes that stimulate NADH production. This leads to decreased rates in proton pumping due to diminished membrane potential along with less ATP and enhanced ROS production. These results show that through Ca(2+) signaling disruption, mutant PS leads to mitochondrial dysfunction and potentially to cell death.

Optimal microdomain crosstalk between endoplasmic reticulum and mitochondria for Ca2+ oscillations

A Ca²⁺ signaling model is proposed to consider the crosstalk of Ca²⁺ ions between endoplasmic reticulum (ER) and mitochondria within microdomains around inositol 1, 4, 5-trisphosphate receptors (IP₃R) and the mitochondrial Ca²⁺ uniporter (MCU). Our model predicts that there is a critical IP₃R-MCU distance at which 50% of the ER-released Ca²⁺ is taken up by mitochondria and that mitochondria modulate Ca²⁺ signals differently when outside of this critical distance. This study highlights the importance of the IP₃R-MCU distance on Ca²⁺ signaling dynamics. The model predicts that when MCU are too closely associated with IP₃Rs, the enhanced mitochondrial Ca²⁺ uptake will produce an increase of cytosolic Ca²⁺ spike amplitude. Notably, the model demonstrates the existence of an optimal IP₃R-MCU distance (30–85 nm) for effective Ca²⁺ transfer and the successful generation of Ca²⁺ signals in healthy cells. We suggest that the space between the inner and outer mitochondria membranes provides a defense mechanism against occurrences of high [Ca²⁺]_Cyt. Our results also hint at a possible pathological mechanism in which abnormally high [Ca²⁺]_Cyt arises when the IP₃R-MCU distance is in excess of the optimal range.