The low conductance mitochondrial permeability transition pore confers excitability and CICR wave propagation in a computational model

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.

Dual dynamics of mitochondrial permeability transition pore opening

Mitochondria play an essential role in bioenergetics and cellular Ca\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{2+}$$\end{document}2+ handling. The mitochondrial permeability transition pore (mPTP) is a non-specific channel located in the inner mitochondrial membrane. Long-lasting openings of the pore allow the rapid passage of ions and large molecules, which can result in cell death. The mPTP also exhibits transient, low conductance openings that contribute to Ca\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{2+}$$\end{document}2+ homeostasis. Although many regulators of the pore have been identified, none of them uniquely governs the passage between the two operating modes, which thus probably relies on a still unidentified network of interactions. By developing a core computational model for mPTP opening under the control of mitochondrial voltage and Ca\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{2+}$$\end{document}2+, we uncovered the existence of a positive feedback loop leading to bistability. The characteristics of the two stable steady-states correspond to those of the two opening states. When inserted in a full model of Ca\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{2+}$$\end{document}2+ handling by mitochondria, our description of the pore reproduces observations in mitochondrial suspensions. Moreover, the model predicted the occurrence of hysteresis in the switching between the two modes, upon addition and removal of free Ca\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{2+}$$\end{document}2+ in the extra-mitochondrial medium. Stochastic simulations then confirmed that the pore can undergo transient openings resembling those observed in intact cells.

Cytoplasmic and Mitochondrial Calcium Signaling: A Two-Way Relationship

Intracellular Ca²⁺ signals are well organized in all cell types, and trigger a variety of vital physiological processes. The temporal and spatial characteristics of cytosolic Ca²⁺ increases are mainly governed by the fluxes of this ion across the membrane of the endoplasmic/sarcoplasmic reticulum and the plasma membrane. However, various Ca²⁺ transporters also allow for Ca²⁺ exchanges between the cytoplasm and mitochondria. Increases in mitochondrial Ca²⁺ stimulate the production of ATP, which allows the cells to cope with the increased energy demand created by the stimulus. Less widely appreciated is the fact that Ca²⁺ handling by mitochondria also shapes cytosolic Ca²⁺ signals. Indeed, the frequency, amplitude, and duration of cytosolic Ca²⁺ increases can be altered by modifying the rates of Ca²⁺ transport into, or from, mitochondria. In this review, we focus on the interplay between mitochondria and Ca²⁺ signaling, highlighting not only the consequences of cytosolic Ca²⁺ changes on mitochondrial Ca²⁺, but also how cytosolic Ca²⁺ dynamics is controlled by modifications of the Ca²⁺-handling properties and the metabolism of mitochondria.

Data-driven modeling of mitochondrial dysfunction in Alzheimer's disease

Intracellular accumulation of oligomeric forms of β amyloid (Aβ) are now believed to play a key role in the earliest phase of Alzheimer's disease (AD) as their rise correlates well with the early symptoms of the disease. Extensive evidence points to impaired neuronal Ca²⁺ homeostasis as a direct consequence of the intracellular Aβ oligomers. However, little is known about the downstream effects of the resulting Ca²⁺ rise on the many intracellular Ca²⁺-dependent pathways. Here we use multiscale modeling in conjunction with patch-clamp electrophysiology of single inositol 1,4,5-trisphosphate (IP₃) receptor (IP₃R) and fluorescence imaging of whole-cell Ca²⁺ response, induced by exogenously applied intracellular Aβ₄₂ oligomers to show that Aβ₄₂ inflicts cytotoxicity by impairing mitochondrial function. Driven by patch-clamp experiments, we first model the kinetics of IP₃R, which is then extended to build a model for the whole-cell Ca²⁺ signals. The whole-cell model is then fitted to fluorescence signals to quantify the overall Ca²⁺ release from the endoplasmic reticulum by intracellular Aβ₄₂ oligomers through G-protein-mediated stimulation of IP₃ production. The estimated IP₃ concentration as a function of intracellular Aβ₄₂ content together with the whole-cell model allows us to show that Aβ₄₂ oligomers impair mitochondrial function through pathological Ca²⁺ uptake and the resulting reduced mitochondrial inner membrane potential, leading to an overall lower ATP and increased production of reactive oxygen species and H₂O₂. We further show that mitochondrial function can be restored by the addition of Ca²⁺ buffer EGTA, in accordance with the observed abrogation of Aβ₄₂ cytotoxicity by EGTA in our live cells experiments.

Composite mathematical modeling of calcium signaling behind neuronal cell death in Alzheimer's disease

Background

Alzheimer’s disease (AD) is a progressive neurological disorder, recognized as the most common cause of dementia affecting people aged 65 and above. AD is characterized by an increase in amyloid metabolism, and by the misfolding and deposition of β-amyloid oligomers in and around neurons in the brain. These processes remodel the calcium signaling mechanism in neurons, leading to cell death via apoptosis. Despite accumulating knowledge about the biological processes underlying AD, mathematical models to date are restricted to depicting only a small portion of the pathology.

Results

Here, we integrated multiple mathematical models to analyze and understand the relationship among amyloid depositions, calcium signaling and mitochondrial permeability transition pore (PTP) related cell apoptosis in AD. The model was used to simulate calcium dynamics in the absence and presence of AD. In the absence of AD, i.e. without β-amyloid deposition, mitochondrial and cytosolic calcium level remains in the low resting concentration. However, our in silico simulation of the presence of AD with the β-amyloid deposition, shows an increase in the entry of calcium ions into the cell and dysregulation of Ca ²⁺ channel receptors on the Endoplasmic Reticulum. This composite model enabled us to make simulation that is not possible to measure experimentally.

Conclusions

Our mathematical model depicting the mechanisms affecting calcium signaling in neurons can help understand AD at the systems level and has potential for diagnostic and therapeutic applications.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0529-2) contains supplementary material, which is available to authorized users.

The gain-of-function enhancement of IP3-receptor channel gating by familial Alzheimer's disease-linked presenilin mutants increases the open probability of mitochondrial permeability transition pore

Mutants in presenilins (PS1 or PS2) are the major cause of familial Alzheimer's disease (FAD). They affect intracellular Ca(2+) homeostasis by increasing the open probability (Po) of inositol 1,4,5-trisposphate (IP3) receptor (IP3R) Ca(2+) release channel located on the endoplasmic reticulum (ER) leading to exaggerated Ca(2+) release into a cytoplasmic microdomain formed by neighboring cluster of a few IP3R channels and mitochondrial Ca(2+) uniporter (MCU). Ca(2+) concentration in the microdomain ( [Formula: see text] ) depends on the distance between the cluster and MCU (r); the number of IP3R in the cluster releasing Ca(2+) to the cytoplasm ( [Formula: see text] ), and Po of IP3R. Using experimental whole-cell IP3R-mediated cytosolic Ca(2+) data, in conjunction with a computational model of cell bioenergetics, a data-driven Markov chain model for IP3R gating, and a model for the dynamics of the mitochondrial permeability transition pore (PTP), we explore differences in mitochondrial Ca(2+) uptake in cells expressing wild type (PS1-WT) and FAD-causing mutant (PS1-M146L) PS. We find that increased mitochondrial [Formula: see text] due to the gain-of-function enhancement of IP3R channels in the cells expressing PS1-M146L leads to the opening of PTP in high conductance state (PTPh), where the latency of opening is inversely correlated with r and proportional to [Formula: see text] . Furthermore, we observe diminished inner mitochondrial membrane potential (ΔΨm), [NADH], [Formula: see text] , and [ATP] when PTP opens. Additionally, we explore how parameters such as the pH gradient, inorganic phosphate concentration, and the rate of the Na(+)/Ca(2+)-exchanger affect the latency of PTP to open in PTPh.

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.

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

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

Characterization of the effect of the mitochondrial protein Hint2 on intracellular Ca(2+) dynamics

Hint2, one of the five members of the superfamily of the histidine triad AMP-lysine hydrolase proteins, is expressed in mitochondria of various cell types. In human adrenocarcinoma cells, Hint2 modulates Ca(2+) handling by mitochondria. As Hint2 is highly expressed in hepatocytes, we investigated if this protein affects Ca(2+) dynamics in this cell type. We found that in hepatocytes isolated from Hint2(-/-) mice, the frequency of Ca(2+) oscillations induced by 1 μM noradrenaline was 150% higher than in the wild-type. Using spectrophotometry, we analyzed the rates of Ca(2+) pumping in suspensions of mitochondria prepared from hepatocytes of either wild-type or Hint2(-/-) mice; we found that Hint2 accelerates Ca(2+) pumping into mitochondria. We then resorted to computational modeling to elucidate the possible molecular target of Hint2 that could explain both observations. On the basis of a detailed model for mitochondrial metabolism proposed in another study, we identified the respiratory chain as the most probable target of Hint2. We then used the model to predict that the absence of Hint2 leads to a premature opening of the mitochondrial permeability transition pore in response to repetitive additions of Ca(2+) in suspensions of mitochondria. This prediction was then confirmed experimentally.

Modeling the intracellular organization of calcium signaling

Calcium (Ca²⁺) is a key signaling ion that plays a fundamental role in many cellular processes in most types of tissues and organisms. The versatility of this signaling pathway is remarkable. Depending on the cell type and the stimulus, intracellular Ca²⁺ increases can last over different periods, as short spikes or more sustained signals. From a spatial point of view, they can be localized or invade the whole cell. Such a richness of behaviors is possible thanks to numerous exchange processes with the external medium or internal Ca²⁺ pools, mainly the endoplasmic or sarcoplasmic reticulum and mitochondria. These fluxes are also highly regulated. In order to get an accurate description of the spatiotemporal organization of Ca²⁺ signaling, it is useful to resort to modeling. Thus, each flux can be described by an appropriate kinetic expression. Ca²⁺ dynamics in a given cell type can then be simulated by a modular approach, consisting of the assembly of computational descriptions of the appropriate fluxes and regulations. Modeling can also be used to get insight into the mechanisms of decoding of the Ca²⁺ signals responsible for cellular responses. Cells can use frequency or amplitude coding, as well as take profit of Ca²⁺ oscillations to increase their sensitivity to small average Ca²⁺ increases.

Modeling molecular pathways of neuronal ischemia

Neuronal ischemia, the consequence of a stroke (cerebrovascular accident), is a condition of reduced delivery of nutrients to brain neurons. The brain consumes more energy per gram of tissue than any other organ, making continuous blood flow critical. Loss of nutrients, most critically glucose and O2, triggers a large number of interacting molecular pathways in neurons and astrocytes. The dynamics of these pathways take place over multiple temporal scales and occur in multiple interacting cytosolic and organelle compartments: in mitochondria, endoplasmic reticulum, and nucleus. The complexity of these relationships suggests the use of computer simulation to understand the interplay between pathways leading to reversible or irreversible damage, the forms of damage, and interventions that could reduce damage at different stages of stroke. We describe a number of models and simulation methods that can be used to further our understanding of ischemia.

Modeling the neuroprotective role of enhanced astrocyte mitochondrial metabolism during stroke

A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and endoplasmic reticulum Ca(2+) handling, IP3 production, and GTP-binding protein-coupled receptor signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GTP-binding protein-coupled receptor (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca(2+) release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting variables in P2Y1R-enhanced astrocyte protection after cerebral ischemic stroke.

Membrane associated complexes in calcium dynamics modelling

Mitochondria not only govern energy production, but are also involved in crucial cellular signalling processes. They are one of the most important organelles determining the Ca(2+) regulatory pathway in the cell. Several mathematical models explaining these mechanisms were constructed, but only few of them describe interplay between calcium concentrations in endoplasmic reticulum (ER), cytoplasm and mitochondria. Experiments measuring calcium concentrations in mitochondria and ER suggested the existence of cytosolic microdomains with locally elevated calcium concentration in the nearest vicinity of the outer mitochondrial membrane. These intermediate physical connections between ER and mitochondria are called MAM (mitochondria-associated ER membrane) complexes. We propose a model with a direct calcium flow from ER to mitochondria, which may be justified by the existence of MAMs, and perform detailed numerical analysis of the effect of this flow on the type and shape of calcium oscillations. The model is partially based on the Marhl et al model. We have numerically found that the stable oscillations exist for a considerable set of parameter values. However, for some parameter sets the oscillations disappear and the trajectories of the model tend to a steady state with very high calcium level in mitochondria. This can be interpreted as an early step in an apoptotic pathway.

Cardiac mitochondrial network excitability: insights from computational analysis

In the heart, mitochondria form a regular lattice and function as a coordinated, nonlinear network to continuously produce ATP to meet the high-energy demand of the cardiomyocytes. Cardiac mitochondria also exhibit properties of an excitable system: electrical or chemical signals can spread within or among cells in the syncytium. The detailed mechanisms by which signals pass among individual elements (mitochondria) across the network are still not completely understood, although emerging studies suggest that network excitability might be mediated by the local diffusion and autocatalytic release of messenger molecules such as reactive oxygen species and/or Ca(2+). In this short review, we have attempted to described recent advances in the field of cardiac mitochondrial network excitability. Specifically, we have focused on how mitochondria communicate with each other through the diffusion and regeneration of messenger molecules to initiate and propagate waves or oscillations, as revealed by computational models of mitochondrial network.

Villous trophoblast apoptosis is elevated and restricted to cytotrophoblasts in pregnancies complicated by preeclampsia, IUGR, or preeclampsia with IUGR

Human placental villi are surfaced by an outer multinucleated syncytiotrophoblast and underlying mononucleated cytotrophoblasts. Conflicting data have attributed one, or the other, of these villous trophoblast phenotypes to undergo enhanced apoptosis in complicated pregnancies, compared to term, normotensive pregnancies. We use high-resolution confocal microscopy after co-staining for E-cadherin, as a trophoblast plasma membrane marker, and for the cleavage products of cytokeratin 18 and PARP1, as markers for caspase-mediated apoptosis, to distinguish between apoptotic cytotrophoblasts and apoptosis within the syncytiotrophoblast. We test the hypothesis that increased caspase-mediated apoptosis occurs in villi of placentas derived from pregnancies complicated by preeclampsia, intrauterine growth restriction (IUGR), or both. We find significantly elevated apoptosis in villous cytotrophoblasts from women with preeclampsia and/or IUGR, compared to term, normotensive pregnancies. Apoptosis of cytotrophoblasts in villi from complicated pregnancies appears to progress similarly to what we found previously for apoptotic cytotrophoblasts in villi from in term, normotensive pregnancies. Notably, caspase-mediated apoptosis was not detectable in regions with intact syncytiotrophoblast, suggesting strong repression of apoptosis in this trophoblast phenotype in vivo. We suggest that the elevated apoptosis in cytotrophoblasts in preeclampsia contributes to the placental dysfunction characteristic of this disorder. We also propose that repression of apoptosis in the syncytiotrophoblast is important to prevent apoptosis sweeping throughout the syncytium, which would result in widespread death of this essential interface for maternal-fetal exchange.