A model of mitochondrial Ca(2+)-induced Ca2+ release simulating the Ca2+ oscillations and spikes generated by mitochondria

Swelling and membrane potential dynamics of glial Müller cells

Presently a detailed biophysical model describing reversible and irreversible swelling dynamics of Müller cells (MC) is reported. The model includes a biophysical block of ionic and neutral species transport via MC membrane, water transport induced by osmotic pressure and pressure generated by membrane deformations, MC membrane potential and membrane mechanical properties. The model describes reversible and irreversible MC swelling (MCS) using the same set of parameters. The model was used in fitting available experimental data, and produced numerical values of previously unknown model parameters, including those describing mechanical properties of Müller cell membrane (MCM) with respect to bending and stretching. Numerical experiments simulating MC swelling showed complex oscillation dynamics of the relevant parameters in physiological initial conditions. In particular, MC membrane potential (ΔΨ_MC) demonstrated complex oscillation dynamics, which may be described by a superposition of several oscillations with their periods in the milliseconds, 100-ms and seconds time ranges. Dynamics of reversible and irreversible MCS, and the transition criteria from reversible to irreversible MCS modes were determined in model simulations.

Theoretical approaches used in the modelling of reversible and irreversible mitochondrial swelling in vitro

Existing theoretical approaches were considered that allow modelling of mitochondrial swelling (MS) dynamics. Simple phenomenological kinetic models were reviewed. Simple and extended biophysical and bioenergetic models that ignore mechanical properties of inner mitochondrial membrane (IMM), and similar models that include these mechanical properties were also reviewed. Limitations of these models we considered, as regards correct modelling of MS dynamics. It was found that simple phenomenological kinetic models have significant limitations, due to dependence of the kinetic parameter values estimated by fitting of the experimental data on the experimental conditions. Additionally, such simple models provide no understanding of the detailed mechanisms behind the MS dynamics, nor of the dynamics of various system parameters during MS. Thus, biophysical and bioenergetic models ignoring IMM mechanical properties can't be used to model the transition between reversible and irreversible MS. However, simple and extended biophysical models that include IMM mechanical properties allow modelling the transition to irreversible swelling. These latter models are still limited due to significantly simplified description of biochemistry, compared to those of bioenergetic models. Finally, a strategy of model development is proposed, towards correct interpretation of the mitochondrial life cycle, including the effects of MS dynamics.

Reversible and irreversible mitochondrial swelling: Effects of variable mitochondrial activity

An extended biophysical model was obtained by upgrading the previously reported one (Khmelinskii and Makarov, 2021). The upgraded model accommodates variations of solute transport rates through the inner mitochondrial membrane (IMM) within the mitochondrial population, described by a Gaussian distribution. However, the model may be used for any functional form of the distribution. The dynamics of system parameters as predicted by the current model differed from that predicted by the previous model in the same initial conditions (Khmelinskii and Makarov, 2021). The amount of change varied from one parameter to the other, remaining in the 1-38% range. The upgraded model fitted the available experimental data with a better accuracy (R = 0.993) compared to the previous model (R = 0.978) using the same experimental data (Khmelinskii and Makarov, 2021). The fitting procedure also estimated the Gaussian distribution parameters. The new model requires much larger computational resources, but given its higher accuracy, it may be used for better analysis of experimental data and for better prediction of MS dynamics in different initial conditions. Note that activities of individual mitochondria in mitochondrial populations should vary within biological tissues. Thus, the currently upgraded model is a better tool for biological and bio-medical applications. We believe that this model is much better adapted to the analysis of MS dynamics in vivo.

Reversible and irreversible mitochondrial swelling in vitro

Mitochondrial activity as regards ATP production strongly depends on mitochondrial swelling (MS) mode. Therefore, this work analyzes reversible and irreversible MS using a detailed biophysical model. The reported model includes mechanical properties of the inner mitochondrial membrane (IMM). The model describes MS dynamics for spherically symmetric, axisymmetric ellipsoidal and general ellipsoidal mitochondria. Mechanical stretching properties of the IMM were described by a second-rank rigidity tensor. The tensor components were estimated by fitting to the earlier reported results of in vitro experiments. The IMM rigidity constant of ca. 0.008 dyn/nm was obtained for linear deformations. The model also included membrane bending effects, which were small compared to those of membrane stretching. The model was also tested by simulation of the earlier reported experimental data and of the system dynamics at different initial conditions, predicting the system behavior. The transition criteria from reversible to irreversible swelling were determined and tested. The presently developed model is applicable directly to the analysis of in vitro experimental data, while additional improvements are necessary before it could be used to describe mitochondrial swelling in vivo. The reported theoretical model also provides an idea of physically consistent mechanism for the permeability transport pore (PTP) opening, which depends on the IMM stretching stress. In the current study, this idea is discussed briefly, but a detailed theoretical analysis of these ideas will be performed later. The currently developed model provides new understanding of the detailed MS mechanism and of the conditions for the transition between reversible and irreversible MS modes. On the other hand, the current model provides useful mathematical tools, that may be successfully used in mitochondrial biophysics research, and also in other applications, predicting the behavior of mitochondria in different conditions of the surrounding media in vitro or cellular cyto(sarco)plasm in vivo. These mathematical tools are based on real biophysical processes occurring in mitochondria. Thus, we note a significant progress in the theoretical approach, which may be used in real biological systems, compared to the earlier reported models. Significance of this study derives from inclusion of IMM mechanical properties, which directly impact the reversible and irreversible mitochondrial swelling dynamics. Reversible swelling corresponds to reversible IMM deformations, while irreversible swelling corresponds to irreversible deformations, with eventual membrane disruption. The IMM mechanical properties are directly dependent on the membrane biochemical composition and structure. The IMM deformationas are induced by osmotic pressure created by the ionic/neutral solute imbalance between the mitochondrial matrix media and the bulk solution in vitro, or cyto(sarco)plasm in vivo. The novelty of the reported model is in the biophysical mechanism detailing ionic and neutral solute transport for a large number of solutes, which were not taken into account in the earlier reported biophysical models of MS. Therefore, the reported model allows understanding response of mitochondria to the changes of initial concentration(s) of any of the solute(s) included in the model. Note that the values of all of the model parameters and kinetic constants have been estimated and the resulting complete model may be used for quantitative analysis of mitochondrial swelling dynamics in conditions of real in vitro experiments.

Stretching tension effects in permeability transition pores of inner mitochondrial membrane

Presently a mechanism of permeability transition pore (PTP) opening was proposed and discussed. This mechanism is based on mechanical stretching of inner mitochondrial membrane (IMM) caused by mitochondrial swelling (MS). The latter is induced by osmotic pressure generated by solute imbalance between the matrix and the surrounding cyto(sarco)plasm. Modelled by the Monte-Carlo method, an IMM fragment of 350 simulated biological molecules exhibited formation of micro-domains containing two protein and seven phospholipid molecules. The energies (-0.191 eV per molecule) in these micro-domains were significantly larger than those (-0.375 eV per molecule) of other parts of the IMM fragment. Stretching forces applied to such domains expanded them much more than other parts of the IMM fragment. We identify these micro-domains as the PTPs. Both linear and nonlinear functions were used for the strain-stress relation of the IMM fragment, with nonlinear effects more important at large IMM stretching strains. Thus, two main factors are incorporated into the PTP opening mechanism: (1) presence of micro-domains in the IMM structure and (2) IMM stretching stress caused by MS. Taking into account both of these factors, the equation for the probability of PTP opening was deduced, with matrix Ca²⁺ and H⁺ ionic concentrations as its parameters. Note that the equation deduced was similar to an earlier reported empirical equation describing PTP opening dynamics. This correspondence provides support to the presently proposed mechanism. Thus, a new look at the PTP opening mechanism is provided, of interest to various research areas related to mitochondrial biophysics.

Butyrate Feeding Reverses CypD-Related Mitoflash Phenotypes in Mouse Myofibers

Mitoflashes are spontaneous transients of the biosensor mt-cpYFP. In cardiomyocytes, mitoflashes are associated with the cyclophilin D (CypD) mediated opening of mitochondrial permeability transition pore (mPTP), while in skeletal muscle they are considered hallmarks of mitochondrial respiration burst under physiological conditions. Here, we evaluated the potential association between mitoflashes and the mPTP opening at different CypD levels and phosphorylation status by generating three CypD derived fusion constructs with a red shifted, pH stable Ca2+ sensor jRCaMP1b. We observed perinuclear mitochondrial Ca2+ efflux accompanying mitoflashes in CypD and CypDS42A (a phosphor-resistant mutation at Serine 42) overexpressed myofibers but not the control myofibers expressing the mitochondria-targeting sequence of CypD (CypDN30). Assisted by a newly developed analysis program, we identified shorter, more frequent mitoflash activities occurring over larger areas in CypD and CypDS42A overexpressed myofibers than the control CypDN30 myofibers. These observations provide an association between the elevated CypD expression and increased mitoflash activities in hindlimb muscles in an amyotrophic lateral sclerosis (ALS) mouse model previously observed. More importantly, feeding the mice with sodium butyrate reversed the CypD-associated mitoflash phenotypes and protected against ectopic upregulation of CypD, unveiling a novel molecular mechanism underlying butyrate mediated alleviation of ALS progression in the mouse model.

Roles of four feedback loops in mitochondrial permeability transition pore opening induced by Ca^{2+} and reactive oxygen species

Transient or sustained permeability transition pore (PTP) opening is important in normal physiology or cell death, respectively. These are closely linked to Ca^{2+} and reactive oxygen species (ROS). The entry of Ca^{2+} into mitochondria regulates ROS production, and both Ca^{2+} and ROS trigger PTP opening. In addition to this feedforward loop, there exist four feedback loops in the Ca^{2+}-ROS-PTP system. ROS promotes Ca^{2+} entering (F1) and induces further ROS generation (F2), forming two positive feedback loops. PTP opening results in the efflux of Ca^{2+} (F3) and ROS (F4) from the mitochondria, forming two negative feedback loops. Owing to these complexities, we construct a mathematical model to dissect the roles of these feedback loops in the dynamics of PTP opening. The qualitative agreement between simulation results and recent experimental observations supports our hypothesis that under physiological conditions the PTP opens in an oscillatory state, while under pathological conditions it opens in a high steady state. We clarify that the negative feedback loops are responsible for producing oscillations, wherein F3 plays a more prominent role than F4; whereas the positive feedback loops are beneficial for maintaining oscillation robustness, wherein F1 has a more dominant role than F2. Furthermore, we manifest that the proper increase in negative feedback strength or decrease in positive feedback strength not only facilitates the occurrence of oscillations and thus protects the system against a high steady state, but also assists in lowering the oscillation peak. This study may provide potential therapeutic strategies in treating neurodegenerative diseases due to PTP dysfunction.

ATP synthase c-subunit ring as the channel of mitochondrial permeability transition: Regulator of metabolism in development and degeneration

The mitochondrial permeability transition pore (mPTP) or mitochondrial megachannel is arguably one of the most mysterious phenomena in biology today. mPTP has been at the center of ongoing extensive scientific research for the last several decades. In this review we will discuss recent advances in the field that enhance our understanding of the molecular composition of mPTP, its regulatory mechanisms and its pathophysiological role. We will describe our recent findings on the role of ATP synthase c-subunit ring as a central player in mitochondrial permeability transition and as an important metabolic regulator during development and in degenerative diseases.

On the Effects of Mechanical Stress of Biological Membranes in Modeling of Swelling Dynamics of Biological Systems

We highlight mechanical stretching and bending of membranes and the importance of membrane deformations in the analysis of swelling dynamics of biological systems, including cells and subcellular organelles. Membrane deformation upon swelling generates tensile stress and internal pressure, contributing to volume changes in biological systems. Therefore, in addition to physical (internal/external) and chemical factors, mechanical properties of the membranes should be considered in modeling analysis of cellular swelling. Here we describe an approach that considers mechanical properties of the membranes in the analysis of swelling dynamics of biological systems. This approach includes membrane bending and stretching deformations into the model, producing a more realistic description of swelling. We also discuss the effects of membrane stretching on swelling dynamics. We report that additional pressure generated by membrane bending is negligible, compared to pressures generated by membrane stretching, when both membrane surface area and volume are variable parameters. Note that bending deformations are reversible, while stretching deformation may be irreversible, leading to membrane disruption when they exceed a certain threshold level. Therefore, bending deformations need only be considered in reversible physiological swelling, whereas stretching deformations should also be considered in pathological irreversible swelling. Thus, the currently proposed approach may be used to develop a detailed biophysical model describing the transition from physiological to pathological swelling mode.

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.

In silico simulation of reversible and irreversible swelling of mitochondria: The role of membrane rigidity

Mitochondria have been widely accepted as the main source of ATP in the cell. The inner mitochondrial membrane (IMM) is important for the maintenance of ATP production and other functions of mitochondria. The electron transport chain (ETC) generates an electrochemical gradient of protons known as the proton-motive force across the IMM and thus produces the mitochondrial membrane potential that is critical to ATP synthesis. One of the main factors regulating the structural and functional integrity of the IMM is the changes in the matrix volume. Mild (reversible) swelling regulates mitochondrial metabolism and function; however, excessive (irreversible) swelling causes mitochondrial dysfunction and cell death. The central mechanism of mitochondrial swelling includes the opening of non-selective channels known as permeability transition pores (PTPs) in the IMM by high mitochondrial Ca²⁺ and reactive oxygen species (ROS). The mechanisms of reversible and irreversible mitochondrial swelling and transition between these two states are still unknown. The present study elucidates an upgraded biophysical model of reversible and irreversible mitochondrial swelling dynamics. The model provides a description of the PTP regulation dynamics using an additional differential equation. The rigidity tensor was used in numerical simulations of the mitochondrial parameter dynamics with different initial conditions defined by Ca²⁺ concentration in the sarco/endoplasmic reticulum. We were able to estimate the values of the IMM rigidity tensor components by fitting the model to the previously reported experimental data. Overall, the model provides a better description of the reversible and irreversible mitochondrial swelling dynamics.

Computational Modeling of In Vitro Swelling of Mitochondria: A Biophysical Approach

Swelling of mitochondria plays an important role in the pathogenesis of human diseases by stimulating mitochondria-mediated cell death through apoptosis, necrosis, and autophagy. Changes in the permeability of the inner mitochondrial membrane (IMM) of ions and other substances induce an increase in the colloid osmotic pressure, leading to matrix swelling. Modeling of mitochondrial swelling is important for simulation and prediction of in vivo events in the cell during oxidative and energy stress. In the present study, we developed a computational model that describes the mechanism of mitochondrial swelling based on osmosis, the rigidity of the IMM, and dynamics of ionic/neutral species. The model describes a new biophysical approach to swelling dynamics, where osmotic pressure created in the matrix is compensated for by the rigidity of the IMM, i.e., osmotic pressure induces membrane deformation, which compensates for the osmotic pressure effect. Thus, the effect is linear and reversible at small membrane deformations, allowing the membrane to restore its normal form. On the other hand, the membrane rigidity drops to zero at large deformations, and the swelling becomes irreversible. As a result, an increased number of dysfunctional mitochondria can activate mitophagy and initiate cell death. Numerical modeling analysis produced results that reasonably describe the experimental data reported earlier.

Simple kinetic model of mitochondrial swelling in cardiac cells

Mitochondria play an important role in both cell survival and cell death. In response to oxidative stress, they undergo opening of non-selective permeability transition pores (PTP) in the inner mitochondrial membrane. Sustained PTP opening triggers mitochondrial swelling due to increased colloidal osmotic pressure in the matrix accompanied by mitochondrial membrane depolarization and ATP hydrolysis. Mitochondrial swelling is the major factor leading to mitochondria-mediated cell death through both apoptosis and necrosis. Hence, precise estimation of the threshold parameters of the transition of reversible swelling to irreversible swelling is important for understanding the mechanisms of PTP-mediated cell death as well as for the development of new therapeutic approaches targeting the mitochondria under pathological conditions. In this study, we designed a simple kinetic model of the Ca²⁺ -induced mitochondrial swelling that describes the mechanisms of transition from reversible to irreversible swelling in cardiac mitochondria. Values of kinetic parameters calculated using parameter estimation techniques that fit experimental data of mitochondrial swelling with minimum average differences between the experimental data and model parameters. Overall, this study provides a kinetic model verified by data simulation and model fitting that adequately describes the dynamics of mitochondrial swelling.

Different approaches to modeling analysis of mitochondrial swelling

Mitochondria are critical players involved in both cell life and death through multiple pathways. Structural integrity, metabolism and function of mitochondria are regulated by matrix volume due to physiological changes of ion homeostasis in cellular cytoplasm and mitochondria. Ca²⁺ and K⁺ presumably play a critical role in physiological and pathological swelling of mitochondria when increased uptake (influx)/decreased release (efflux) of these ions enhances osmotic pressure accompanied by high water accumulation in the matrix. Changes in the matrix volume in the physiological range have a stimulatory effect on electron transfer chain and oxidative phosphorylation to satisfy metabolic requirements of the cell. However, excessive matrix swelling associated with the sustained opening of mitochondrial permeability transition pores (PTP) and other PTP-independent mechanisms compromises mitochondrial function and integrity leading to cell death. The mechanisms of transition from reversible (physiological) to irreversible (pathological) swelling of mitochondria remain unknown. Mitochondrial swelling is involved in the pathogenesis of many human diseases such as neurodegenerative and cardiovascular diseases. Therefore, modeling analysis of the swelling process is important for understanding the mechanisms of cell dysfunction. This review attempts to describe the role of mitochondrial swelling in cell life and death and the main mechanisms involved in the maintenance of ion homeostasis and swelling. The review also summarizes and discusses different kinetic models and approaches that can be useful for the development of new models for better simulation and prediction of in vivo mitochondrial swelling.

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.

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.

Subcellular expression and neuroprotective effects of SK channels in human dopaminergic neurons

Small-conductance Ca(2+)-activated K(+) channel activation is an emerging therapeutic approach for treatment of neurological diseases, including stroke, amyotrophic lateral sclerosis and schizophrenia. Our previous studies showed that activation of SK channels exerted neuroprotective effects through inhibition of NMDAR-mediated excitotoxicity. In this study, we tested the therapeutic potential of SK channel activation of NS309 (25 μM) in cultured human postmitotic dopaminergic neurons in vitro conditionally immortalized and differentiated from human fetal mesencephalic cells. Quantitative RT-PCR and western blotting analysis showed that differentiated dopaminergic neurons expressed low levels of SK2 channels and high levels of SK1 and SK3 channels. Further, protein analysis of subcellular fractions revealed expression of SK2 channel subtype in mitochondrial-enriched fraction. Mitochondrial complex I inhibitor rotenone (0.5 μM) disrupted the dendritic network of human dopaminergic neurons and induced neuronal death. SK channel activation reduced mitochondrial membrane potential, while it preserved the dendritic network, cell viability and ATP levels after rotenone challenge. Mitochondrial dysfunction and delayed dopaminergic cell death were prevented by increasing and/or stabilizing SK channel activity. Overall, our findings show that activation of SK channels provides protective effects in human dopaminergic neurons, likely via activation of both membrane and mitochondrial SK channels. Thus, SK channels are promising therapeutic targets for neurodegenerative disorders such as Parkinson's disease, where dopaminergic cell loss is associated with progression of the disease.

Physiologic functions of cyclophilin D and the mitochondrial permeability transition pore

This review focuses on the role of cyclophilin D (CypD) as a prominent mediator of the mitochondrial permeability transition pore (MPTP) and subsequent effects on cardiovascular physiology and pathology. Although a great number of reviews have been written on the MPTP and its effects on cell death, we focus on the biology surrounding CypD itself and the non-cell death physiologic functions of the MPTP. A greater understanding of the physiologic functions of the MPTP and its regulation by CypD will likely suggest novel therapeutic approaches for cardiovascular disease, both dependent and independent of programmed necrotic cell death mechanisms.  

Multistationary and oscillatory modes of free radicals generation by the mitochondrial respiratory chain revealed by a bifurcation analysis

The mitochondrial electron transport chain transforms energy satisfying cellular demand and generates reactive oxygen species (ROS) that act as metabolic signals or destructive factors. Therefore, knowledge of the possible modes and bifurcations of electron transport that affect ROS signaling provides insight into the interrelationship of mitochondrial respiration with cellular metabolism. Here, a bifurcation analysis of a sequence of the electron transport chain models of increasing complexity was used to analyze the contribution of individual components to the modes of respiratory chain behavior. Our algorithm constructed models as large systems of ordinary differential equations describing the time evolution of the distribution of redox states of the respiratory complexes. The most complete model of the respiratory chain and linked metabolic reactions predicted that condensed mitochondria produce more ROS at low succinate concentration and less ROS at high succinate levels than swelled mitochondria. This prediction was validated by measuring ROS production under various swelling conditions. A numerical bifurcation analysis revealed qualitatively different types of multistationary behavior and sustained oscillations in the parameter space near a region that was previously found to describe the behavior of isolated mitochondria. The oscillations in transmembrane potential and ROS generation, observed in living cells were reproduced in the model that includes interaction of respiratory complexes with the reactions of TCA cycle. Whereas multistationarity is an internal characteristic of the respiratory chain, the functional link of respiration with central metabolism creates oscillations, which can be understood as a means of auto-regulation of cell metabolism.

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.

Calcium oscillations

Calcium signaling results from a complex interplay between activation and inactivation of intracellular and extracellular calcium permeable channels. This complexity is obvious from the pattern of calcium signals observed with modest, physiological concentrations of calcium-mobilizing agonists, which typically present as sequential regenerative discharges of stored calcium, a process referred to as calcium oscillations. In this review, we discuss recent advances in understanding the underlying mechanism of calcium oscillations through the power of mathematical modeling. We also summarize recent findings on the role of calcium entry through store-operated channels in sustaining calcium oscillations and in the mechanism by which calcium oscillations couple to downstream effectors.

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

Mitochondria have long been known to sequester cytosolic Ca(2+) and even to shape intracellular patterns of endoplasmic reticulum-based Ca(2+) signaling. Evidence suggests that the mitochondrial network is an excitable medium which can demonstrate independent Ca(2+) induced Ca(2+) release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca(2+) handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction that also have bioenergetic components. In this paper, we extend the modular Magnus-Keizer computational model for respiration-driven Ca(2+) handling to include a permeability transition based on a channel-like pore mechanism. We demonstrate both excitability and Ca(2+) wave propagation accompanied by depolarizations qualitatively similar to those reported in cell and isolated mitochondria preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function across the mitochondrial network. Our model provides the tools for predictions about the internal physiology that leads to this qualitatively different Ca(2+) excitability seen in mitochondria.

A bioenergetic model of the mitochondrial population undergoing permeability transition

Mitochondrial permeability transition (MPT) is a highly regulated complex phenomenon that is a type of ischemia/reperfusion injury that can lead to cell death and ultimately organ dysfunction. A novel population transition and detailed permeability transition pore regulation model were integrated with an existing bioenergetics model to describe MPT induction under a variety of conditions. The framework of the MPT induction model includes the potential states of the mitochondria (aggregated, orthodox and post-transition), their transitions from one state to another as well as their interaction with the extra-mitochondrial environment. The model encodes the three basic necessary conditions for MPT: a high calcium load, alkaline matrix pH and circumstances which favor de-energization. The MPT induction model was able to reproduce the expected bioenergetic trends observed in a population of mitochondria subjected to conditions that favor MPT. The model was corroborated and used to predict that MPT in an acidic environment is mitigated by an increase in activity of the mitochondrial potassium/hydrogen exchanger. The model was also used to present the beneficial impact of reducing the duration mitochondria spend in the orthodox state on preserving the extra-mitochondrial ATP levels. The model serves as a tool for investigators to use to understand the MPT induction phenomenon, explore alternative hypotheses for PTP regulation, as well as identify endogenous pharmacological targets and evaluate potential therapeutics for MPT mitigation.

Spatiotemporal organization of Ca dynamics: a modeling-based approach

Calcium is a ubiquitous second messenger that mediates vital physiological responses such as fertilization, secretion, gene expression, or apoptosis. Given this variety of processes mediated by Ca(2+), these signals are highly organized both in time and space to ensure reliability and specificity. This review deals with the spatiotemporal organization of the Ca(2+) signaling pathway in electrically nonexcitable cells in which InsP(3) receptors are by far the most important Ca(2+) channels. We focus on the aspects of this highly regulated dynamical system for which an interplay between experiments and modeling is particularly fruitful. In particular, the importance of the relative densities of the different InsP(3) receptor subtypes will be discussed on the basis of a modeling approach linking the steady-state behaviors of these channels in electrophysiological experiments with their behavior in a cellular environment. Also, the interplay between InsP(3) metabolism and Ca(2+) oscillations will be considered. Finally, we discuss the relationships between stochastic openings of the Ca(2+) releasing channels at the microscopic level and the coordinated, regular behavior observed at the whole cell level on the basis of a combined experimental and modeling approach.

A mathematical model of mitochondrial swelling

Background

The permeabilization of mitochondrial membranes is a decisive event in apoptosis or necrosis culminating in cell death. One fundamental mechanism by which such permeabilization events occur is the calcium-induced mitochondrial permeability transition. Upon Ca²⁺-uptake into mitochondria an increase in inner membrane permeability occurs by a yet unclear mechanism. This leads to a net water influx in the mitochondrial matrix, mitochondrial swelling, and finally the rupture of the outer membrane. Although already described more than thirty years ago, many unsolved questions surround this important biological phenomenon. Importantly, theoretical modeling of the mitochondrial permeability transition has only started recently and the existing mathematical models fail to characterize the swelling process throughout the whole time range.

Results

We propose here a new mathematical approach to the mitochondrial permeability transition introducing a specific delay equation and resulting in an optimized representation of mitochondrial swelling. Our new model is in accordance with the experimentally determined course of volume increase throughout the whole swelling process, including its initial lag phase as well as its termination. From this new model biological consequences can be deduced, such as the confirmation of a positive feedback of mitochondrial swelling which linearly depends on the Ca²⁺-concentration, or a negative exponential dependence of the average swelling time on the Ca²⁺-concentration. Finally, our model can show an initial shrinking phase of mitochondria, which is often observed experimentally before the actual swelling starts.

Conclusions

We present a model of the mitochondrial swelling kinetics. This model may be adapted and extended to diverse other inducing/inhibiting conditions or to mitochondria from other biological sources and thus may benefit a better understanding of the mitochondrial permeability transition.

The role of external and matrix pH in mitochondrial reactive oxygen species generation

Reactive oxygen species (ROS) generation in mitochondria as a side product of electron and proton transport through the inner membrane is important for normal cell operation as well as development of pathology. Matrix and cytosol alkalization stabilizes semiquinone radical, a potential superoxide producer, and we hypothesized that proton deficiency under the excess of electron donors enhances reactive oxygen species generation. We tested this hypothesis by measuring pH dependence of reactive oxygen species released by mitochondria. The experiments were performed in the media with pH varying from 6 to 8 in the presence of complex II substrate succinate or under more physiological conditions with complex I substrates glutamate and malate. Matrix pH was manipulated by inorganic phosphate, nigericine, and low concentrations of uncoupler or valinomycin. We found that high pH strongly increased the rate of free radical generation in all of the conditions studied, even when DeltapH=0 in the presence of nigericin. In the absence of inorganic phosphate, when the matrix was the most alkaline, pH shift in the medium above 7 induced permeability transition accompanied by the decrease of ROS production. ROS production increase induced by the alkalization of medium was observed with intact respiring mitochondria as well as in the presence of complex I inhibitor rotenone, which enhanced reactive oxygen species release. The phenomena revealed in this report are important for understanding mechanisms governing mitochondrial production of reactive oxygen species, in particular that related with uncoupling proteins.

Nonequilibrium statistical model of active transport of ions and ATP production in mitochondria

A model of the active transport of ions through internal membranes of mitochondria is proposed. If concentrations of ions in a cell are known, this model allows calculating concentrations of all main ions (H(+), Ca(+2), K(+), Mg(2+), Na(+), Cl(-)) in the mitochondrion matrix and the resting potential across the membrane. The theoretical values satisfactorily agree with available experimental data on the concentrations and the potentials, including different operating regimes of the adenosine triphosphate (ATP) synthetase (the main regime, short circuiting or ATP synthetase blocking). The active transport of Mg(2+) ions in exchange for protons was assumed. In accordance with the model, the ATP synthetase operation is possible only if the stoichiometric coefficient of protons is 3.

Spatio-temporal modelling explains the effect of reduced plasma membrane Ca2+ efflux on intracellular Ca2+ oscillations in hepatocytes

In many non-excitable eukaryotic cells, including hepatocytes, Ca(2+) oscillations play a key role in intra- and intercellular signalling, thus regulating many cellular processes from fertilisation to death. Therefore, understanding the mechanisms underlying these oscillations, and consequently understanding how they may be regulated, is of great interest. In this paper, we study the influence of reduced Ca(2+) plasma membrane efflux on Ca(2+) oscillations in hepatocytes. Our previous experiments with carboxyeosin show that a reduced plasma membrane Ca(2+) efflux increases the frequency of Ca(2+) oscillations, but does not affect the duration of individual transients. This phenomenon can be best explained by taking into account not only the temporal, but also the spatial dynamics underlying the generation of Ca(2+) oscillations in the cell. Here we divide the cell into a grid of elements and treat the Ca(2+) dynamics as a spatio-temporal phenomenon. By converting an existing temporal model into a spatio-temporal one, we obtain theoretical predictions that are in much better agreement with the experimental observations.

Mitochondrial permeability transition pore opening as an endpoint to initiate cell death and as a putative target for cardioprotection

In recent years, mitochondria have been recognized as regulators of cell death via both apoptosis and necrosis in addition to their essential role for cell survival. Cellular dysfunctions induced by intra- or extracellular insults converge on mitochondria and induce a sudden increase in permeability of the inner mitochondrial membrane, the so-called mitochondrial permeability transition. The mitochondrial permeability transition is caused by the opening of permeability transition pores (PTP) in the inner mitochondrial membrane with subsequent loss of ionic homeostasis, matrix swelling and outer membrane rupture. The detailed molecular mechanisms underlying the PTP-induced cellular dysfunction during cardiac pathology such as ischemia/reperfusion or post-infarction remodeling remain to be elucidated. However, a growing body of evidence supports the concept that pharmacological inhibition of the PTP is an effective and promising strategy for the protection of the heart against ischemia/reperfusion injury and for attenuation of the remodeling process which contributes to heart failure. This review summarizes and discusses current data on i) the structure and function of the PTP, ii) possible mechanisms and consequences of PTP opening and iii) the inhibition of PTP opening as a therapeutic approach for treatment of heart disease.

Mathematical model of mitochondrial ionic homeostasis: three modes of Ca2+ transport

Mitochondria play an important role in regulation of Ca2+ homeostasis in a cell. Here we present a mathematical model of mitochondrial ion transport and use this model to analyse different modes of Ca2+ uptake by mitochondria. The model includes transport of H+, Ca2+, K+, inorganic phosphate and oxidative substrates across the inner mitochondrial membrane harboring permeability transition pore (PTP). The detailed description of ion fluxes is based on the experimental ion kinetics in isolated mitochondria. Using the model we show that the kinetics of Ca2+ uptake by mitochondria is regulated by the total amount of Ca2+ in the system and the rate of Ca2+ infusion. Varying these parameters we find three different modes of ion transport. When the total amount of Ca2+ is below 140 nmol Ca2+/mg protein, all available Ca2+ is accumulated in the matrix without activation of the PTP. Between 140 and 160 nmol Ca2+/mg protein, accumulation of Ca2+ generates periodic opening and closure of the PTP and oscillations of ion fluxes. Higher levels of Ca2+ (> 160 nmol Ca2+/mg protein) result in a permanently open PTP, membrane depolarization and loss of small ions from the matrix. We show that in the intermediate range of Ca2+ concentrations the rate of Ca2+ infusion regulates the PTP state, so that slow Ca2+ infusion does not lead to PTP opening, while fast Ca2+ infusion results in an oscillatory state.

A minimal model for decoding of time-limited Ca2+ oscillations

Calcium oscillations regulate several cellular processes by activating particular proteins. Most theoretical studies focused on the idealized situation of infinitely long oscillations. Here we analyze information transfer by time-limited calcium spike trains. We show that proteins can be selectively activated in a resonance-like manner by time-limited spike trains of different frequencies, while infinitely long oscillations do not show this resonance phenomenon. We found that proteins are activated more specifically by shorter oscillatory signals with narrower spikes.

Calcium plays a key role in the effects induced by a snake venom Lys49 phospholipase A2 homologue on a lymphoblastoid cell line

A catalytically-inactive Lys49 phospholipase A2 homologue from the venom of the snake Bothrops asper induces diverse effects (necrosis, apoptosis and proliferation) in a lymphoblastoid cell line, depending on the toxin concentration. The increments in cytosolic Ca2+ levels induced by this toxin in this cell line were assessed. At high toxin concentration (100 microg/mL) the toxin induces drastic disruption of the plasma membrane, associated with a prominent Ca2+ influx and necrosis. Previous incubation of the cells with the chelating agent EGTA or with ruthenium red, an inhibitor of the uniporter mitochondrial Ca2+ transport, greatly reduced necrosis. At a toxin concentration of 12.5 microg/mL, apoptosis is the predominant response, being associated with lower increments in cytosolic Ca2+. This effect was inhibited by preincubation with ruthenium red and the cytosolic Ca2+ chelator BAPTA-AM. The proliferative response, which occurs at a low toxin concentration (0.5 microg/mL), is associated with a small and oscillatory increment in cytosolic Ca2+. It was inhibited by EGTA, ruthenium red and BAPTA-AM, by inhibitors of the endoplasmic reticulum Ca2+ -ATPase (SERCA) and by blockade of the ryanodine receptor. It is concluded that necrosis and apoptosis induced by this toxin are associated with increments in cytosolic Ca2+ levels following plasma membrane perturbation, together with the involvement of mitochondria. The cellular proliferative response depends on a limited Ca2+ influx through the plasma membrane, being associated with a concerted functional unit constituted by SERCA, the ryanodine receptor and mitochondria, which regulate the observed oscillations in cytosolic Ca2+ concentration.

Modelling of calcium handling in airway myocytes

Airway myocytes are the primary effectors of airway reactivity which modulates airway resistance and hence ventilation. Stimulation of airway myocytes results in an increase in the cytosolic Ca(2+) concentration ([Ca(2+)](i)) and the subsequent activation of the contractile apparatus. Many contractile agonists, including acetylcholine, induce [Ca(2+)](i) increase via Ca(2+) release from the sarcoplasmic reticulum through InsP(3) receptors. Several models have been developed to explain the characteristics of InsP(3)-induced [Ca(2+)](i) responses, in particular Ca(2+) oscillations. The article reviews the modelling of the major structures implicated in intracellular Ca(2+) handling, i.e., InsP(3) receptors, SERCAs, mitochondria and Ca(2+)-binding cytosolic proteins. We developed theoretical models specifically dedicated to the airway myocyte which include the major mechanisms responsible for intracellular Ca(2+) handling identified in these cells. These biocomputations pointed out the importance of the relative proportion of InsP(3) receptor isoforms and the respective role of the different mechanisms responsible for cytosolic Ca(2+) clearance in the pattern of [Ca(2+)](i) variations. We have developed a theoretical model of membrane conductances that predicts the variations in membrane potential and extracellular Ca(2+) influx. Stimulation of this model by simulated increase in [Ca(2+)](i) predicts membrane depolarisation, but not great enough to trigger a significant opening of voltage-dependant Ca(2+) channels. This may explain why airway contraction induced by cholinergic stimulation does not greatly depend on extracellular calcium. The development of such models of airway myocytes is important for the understanding of the cellular mechanisms of airway reactivity and their possible modulation by pharmacological agents.

Repetitive transient depolarizations of the inner mitochondrial membrane induced by proton pumping

Single mitochondria show the spontaneous fluctuations of DeltaPsim. In this study, to examine the mechanism of the fluctuations, we observed DeltaPsim in single isolated heart mitochondria using time-resolved fluorescence microscopy. Addition of malate, succinate, or ascorbate plus TMPD to mitochondria induced polarization of the inner membrane followed by repeated cycles of rapid depolarizations and immediate repolarizations. ADP significantly decreased the frequency of the rapid depolarizations, but the ADP effect was counteracted by oligomycin. On the other hand, the rapid depolarizations did not occur when mitochondria were polarized by the efflux of K(+) from the matrix. The rapid depolarizations became frequent with the increase in the substrate concentration or pH of the buffer. These results suggest that the rapid depolarizations depend on the net translocation of protons from the matrix. The frequency of the rapid depolarizations was not affected by ROS scavengers, Ca(2+), CsA, or BA. In addition, the obvious increase in the permeability of the inner membrane to calcein (MW 623) that was entrapped in the matrix was not observed upon the transient depolarization. The mechanisms of the spontaneous oscillations of DeltaPsim are discussed in relation to the matrix pH and the permeability transitions.

Energetic depression caused by mitochondrial dysfunction

Mitochondria, providing most of ATP needed for cell work, realizing numerous specific functions as biosyntheses or degradations, contributing to Ca2+ signalling also play a key role in the pathways to cell death. Impairment of mitochondrial functions caused by mutations of mt-genome and by acute processes are responsible for numerous diseases. The relations between changes on the level of molecules and the clinical state are rather complex, and the prediction of thresholds is difficult. Therefore investigations on different levels of an organismus (genome, metabolites, enzymes, mitochondrial function in vivo and in vitro) are necessary (multi level approach). Metabolic control theory is a valuable tool for understanding the different effects of mutations on the level of enzyme activities and mitochondrial function. Decreased concentrations of adenine nucleotides, leaky outer and inner mitochondrial membranes, decreased rates of mitochondrial linked pathways and decreased activities of respiratory chain enzymes contribute to depression of cellular energy metabolism characterized by decreased cytosolic phosphorylation potentials as one of the most important consequences of mitochondrial impairments. This review regards classical bioenergetic mechanisms of mitochondrial impairment which contribute to energetic depression.

On the encoding and decoding of calcium signals in hepatocytes

Many different agonists use calcium as a second messenger. Despite intensive research in intracellular calcium signalling it is an unsolved riddle how the different types of information represented by the different agonists, is encoded using the universal carrier calcium. It is also still not clear how the information encoded is decoded again into the intracellular specific information at the site of enzymes and genes. After the discovery of calcium oscillations, one likely mechanism is that information is encoded in the frequency, amplitude and waveform of the oscillations. This hypothesis has received some experimental support. However, the mechanism of decoding of oscillatory signals is still not known. Here, we study a mechanistic model of calcium oscillations, which is able to reproduce both spiking and bursting calcium oscillations. We use the model to study the decoding of calcium signals on the basis of co-operativity of calcium binding to various proteins. We show that this co-operativity offers a simple way to decode different calcium dynamics into different enzyme activities.

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

Participation of mitochondria in calcium signalling in the exocrine pancreas

This minireview is an attempt to put together some of the recent advances regarding the implications of mitochondria in Ca2+ homeostasis. Although the main role of this cytoplasmic organelle is ATP supply to the cell, during the past years strong evidence has been accumulated supporting an active role of these organelles in Ca2+ handling by the cell. The discovery of mitochondrial specific fluorescent dyes has permitted the study of these organelles within living cells. Due to its ubiquitous localisation within the cytosol, mitochondria would play an important role in the modulation of the subcellular patterns of Ca2+ signalling, and therefore would act as modulators of Ca2+-dependent cellular processes.

Mitochondrial modulation of intracellular Ca(2+) signaling

IP3-mediated Ca(2+) release plays a fundamental role in many cell signaling processes and has been the subject of numerous modeling studies. Only recently has the important role that mitochondria play in the dynamics of intracellular Ca(2+) signaling begun to be considered in experimental work and in computational models. Mitochondria sequester large amounts of Ca(2+) and thus have a modulatory effect on intracellular Ca(2+) signaling, and mitochondrial uptake of Ca(2+), in turn, has a regulatory effect on mitochondrial function. Here we integrate a well-established model of IP3-mediated Ca(2+) signaling with a detailed model of mitochondrial Ca(2+) handling and metabolic function. The incorporation of mitochondria results in oscillations in a bistable formulation of the IP3 model, and increasing metabolic substrate decreases the frequency of these oscillations consistent with the literature. Ca(2+) spikes from the cytosol are communicated into mitochondria and are shown to induce realistic metabolic changes. The model has been formulated using a modular approach that is easy to modify and should serve as a useful basis for the investigation of questions regarding the interaction of these two systems.

Birhythmicity, trirhythmicity and chaos in bursting calcium oscillations

We have analyzed various types of complex calcium oscillations. The oscillations are explained with a model based on calcium-induced calcium release (CICR). In addition to the endoplasmic reticulum as the main intracellular Ca2+ store, mitochondrial and cytosolic Ca2+ binding proteins are also taken into account. This model was previously proposed for the study of the physiological role of mitochondria and the cytosolic proteins in gene rating complex Ca2+ oscillations [1]. Here, we investigated the occurrence of different types of Ca2+ oscillations obtained by the model, i.e. simple oscillations, bursting, and chaos. In a bifurcation diagram, we have shown that all these various modes of oscillatory behavior are obtained by a change of only one model parameter, which corresponds to the physiological variability of an agonist. Bursting oscillations were studied in more detail because they express birhythmicity, trirhythmicity and chaotic behavior. Two different routes to chaos are observed in the model: in addition to the usual period doubling cascade, we also show intermittency. For the characterization of the chaotic behavior, we made use of return maps and Lyapunov exponents. The potential biological role of chaos in intracellular signaling is discussed.

Complex calcium oscillations and the role of mitochondria and cytosolic proteins

Intracellular calcium oscillations, which are oscillatory changes of cytosolic calcium concentration in response to agonist stimulation, are experimentally well observed in various living cells. Simple calcium oscillations represent the most common pattern and many mathematical models have been published to describe this type of oscillation. On the other hand, relatively few theoretical studies have been proposed to give an explanation of complex intracellular calcium oscillations, such as bursting and chaos. In this paper, we develop a new possible mechanism for complex calcium oscillations based on the interplay between three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosolic proteins. The majority ( approximately 80%) of calcium released from the ER is first very quickly sequestered by mitochondria. Afterwards, a much slower release of calcium from the mitochondria serves as the calcium supply for the intermediate calcium exchanges between the ER and the cytosolic proteins causing bursting calcium oscillations. Depending on the permeability of the ER channels and on the kinetic properties of calcium binding to the cytosolic proteins, different patterns of complex calcium oscillations appear. With our model, we are able to explain simple calcium oscillations, bursting and chaos. Chaos is also observed for calcium oscillations in the bursting mode.

Organophosphorus compound-induced modification of SH-SY5Y human neuroblastoma mitochondrial transmembrane potential

Organophosphorus (OP) compounds inhibit mitochondrial enzymes, respiration, and ATP generation, in addition to inducing structural changes such as matrix swelling. This implicates mitochondria as primary subcellular targets for these compounds. In this study, the health and function of cellular mitochondria following OP compound exposure were assessed by evaluating the mitochondrial transmembrane potential (DeltaPsi(m)). This was done by measuring the changes in DeltaPsi(m) in SH-SY5Y human neuroblastoma cells incubated with the cationic fluorochrome, rhodamine 123 (5 microg/ml), and the OP compounds tri-ortho-tolyl phosphate (TOTP), triphenyl phosphite (TPPi), or parathion for 7.5 to 960 minutes. OP compounds (100 microM to 1 mM) induced significant concentration-dependent mitochondrial hyperpolarization with peak maxima occurring at 60 (TOTP, TPPi) or 120 (parathion) min. Following this, the mitochondrial membranes gradually depolarized. Pretreatment with cyclosporin A (500 nM, 30 h), a mitochondrial permeability transition pore (PTP) inhibitor, decreased the hyperpolarization. In contrast, 30-h pretreatment with the muscarinic receptor agonist carbachol (1 mM) significantly increased DeltaPsi(m) and delayed subsequent depolarization. Hyperpolarization and subsequent depolarization of mitochondrial membranes occurred 16 to 24 h prior to a loss of substrate adhesion or an increase in DNA fragmentation, indicating that mitochondria were a primary target in OP compound-initiated cytotoxicity.

From calcium signaling to cell death: two conformations for the mitochondrial permeability transition pore. Switching from low- to high-conductance state

The permeability transition pore (PTP) is a channel of the inner mitochondrial membrane that appears to operate at the crossroads of two distinct physiological pathways, i.e., the Ca2+ signaling network during the life of the cell, and the effector phase of the apoptotic cascade during Ca2+-dependent cell death. Correspondingly, two open conformations of the PTP can also be observed in isolated organelles. A low-conductance state, that allows the diffusion of small ions like Ca2+, is pH-operated, promoting spontaneous closure of the channel. A high-conductance state, that allows the unselective diffusion of big molecules, stabilizes the channel in the open conformation, disrupting in turn the mitochondrial structure and causing the release of proapoptotic factors. Our current results indicate that switching from low- to high-conductance state is an irreversible process that is strictly dependent on the saturation of the internal Ca2+-binding sites of the PTP. Thus, the high-conductance state of the PTP, which was shown to play a pivotal role in the course of excitotoxic and thapsigargin-induced cell death, might result from a Ca2+-dependent conformational shift of the low-conductance state, normally participating in the regulation of cellular Ca2+ homeostasis as a pH-operated channel. These observations lead us to propose a simple biophysical model of the transition between Ca2+ signaling and Ca2+-dependent apoptosis.