A minimal model for the mitochondrial rapid mode of Ca²+ uptake mechanism

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.

Mg(2+) differentially regulates two modes of mitochondrial Ca(2+) uptake in isolated cardiac mitochondria: implications for mitochondrial Ca(2+) sequestration

The manner in which mitochondria take up and store Ca(2+) remains highly debated. Recent experimental and computational evidence has suggested the presence of at least two modes of Ca(2+) uptake and a complex Ca(2+) sequestration mechanism in mitochondria. But how Mg(2+) regulates these different modes of Ca(2+) uptake as well as mitochondrial Ca(2+) sequestration is not known. In this study, we investigated two different ways by which mitochondria take up and sequester Ca(2+) by using two different protocols. Isolated guinea pig cardiac mitochondria were exposed to varying concentrations of CaCl2 in the presence or absence of MgCl2. In the first protocol, A, CaCl2 was added to the respiration buffer containing isolated mitochondria, whereas in the second protocol, B, mitochondria were added to the respiration buffer with CaCl2 already present. Protocol A resulted first in a fast transitory uptake followed by a slow gradual uptake. In contrast, protocol B only revealed a slow and gradual Ca(2+) uptake, which was approximately 40 % of the slow uptake rate observed in protocol A. These two types of Ca(2+) uptake modes were differentially modulated by extra-matrix Mg(2+). That is, Mg(2+) markedly inhibited the slow mode of Ca(2+) uptake in both protocols in a concentration-dependent manner, but not the fast mode of uptake exhibited in protocol A. Mg(2+) also inhibited Na(+)-dependent Ca(2+) extrusion. The general Ca(2+) binding properties of the mitochondrial Ca(2+) sequestration system were reaffirmed and shown to be independent of the mode of Ca(2+) uptake, i.e. through the fast or slow mode of uptake. In addition, extra-matrix Mg(2+) hindered Ca(2+) sequestration. Our results indicate that mitochondria exhibit different modes of Ca(2+) uptake depending on the nature of exposure to extra-matrix Ca(2+), which are differentially sensitive to Mg(2+). The implications of these findings in cardiomyocytes are discussed.

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.

Mitochondria and arrhythmias

Mitochondria are essential to providing ATP, thereby satisfying the energy demand of the incessant electrical activity and contractile action of cardiac muscle. Emerging evidence indicates that mitochondrial dysfunction can adversely affect cardiac electrical functioning by impairing the intracellular ion homeostasis and membrane excitability through reduced ATP production and excessive reactive oxygen species (ROS) generation, resulting in increased propensity to cardiac arrhythmias. In this review, the molecular mechanisms linking mitochondrial dysfunction to cardiac arrhythmias are discussed with an emphasis on the impact of increased mitochondrial ROS on the cardiac ion channels and transporters that are critical to maintaining normal electromechanical functioning of the cardiomyocytes. The potential of using mitochondria-targeted antioxidants as a novel antiarrhythmia therapy is highlighted.

Computational analysis of Ca2+ dynamics in isolated cardiac mitochondria predicts two distinct modes of Ca2+ uptake

Cardiac mitochondria can act as a significant Ca(2+) sink and shape cytosolic Ca(2+) signals affecting various cellular processes, such as energy metabolism and excitation-contraction coupling. However, different mitochondrial Ca(2+) uptake mechanisms are still not well understood. In this study, we analysed recently published Ca(2+) uptake experiments performed on isolated guinea pig cardiac mitochondria using a computer model of mitochondrial bioenergetics and cation handling. The model analyses of the data suggest that the majority of mitochondrial Ca(2+) uptake, at physiological levels of cytosolic Ca(2+) and Mg(2+), occurs through a fast Ca(2+) uptake pathway, which is neither the Ca(2+) uniporter nor the rapid mode of Ca(2+) uptake. This fast Ca(2+) uptake component was explained by including a biophysical model of the ryanodine receptor (RyR) in the computer model. However, the Mg(2+)-dependent enhancement of the RyR adaptation was not evident in this RyR-type channel, in contrast to that of cardiac sarcoplasmic reticulum RyR. The extended computer model is corroborated by simulating an independent experimental dataset, featuring mitochondrial Ca(2+) uptake, egress and sequestration. The model analyses of the two datasets validate the existence of two classes of Ca(2+) buffers that comprise the mitochondrial Ca(2+) sequestration system. The modelling study further indicates that the Ca(2+) buffers respond differentially depending on the source of Ca(2+) uptake. In particular, it suggests that the Class 1 Ca(2+) buffering capacity is auto-regulated by the rate at which Ca(2+) is taken up by mitochondria.

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.

Extra-matrix Mg2+ limits Ca2+ uptake and modulates Ca2+ uptake-independent respiration and redox state in cardiac isolated mitochondria

Cardiac mitochondrial matrix (m) free Ca(2+) ([Ca(2+)]m) increases primarily by Ca(2+) uptake through the Ca(2+) uniporter (CU). Ca(2+) uptake via the CU is attenuated by extra-matrix (e) Mg(2+) ([Mg(2+)]e). How [Ca(2+)]m is dynamically modulated by interacting physiological levels of [Ca(2+)]e and [Mg(2+)]e and how this interaction alters bioenergetics are not well understood. We postulated that as [Mg(2+)]e modulates Ca(2+) uptake via the CU, it also alters bioenergetics in a matrix Ca(2+)-induced and matrix Ca(2+)-independent manner. To test this, we measured changes in [Ca(2+)]e, [Ca(2+)]m, [Mg(2+)]e and [Mg(2+)]m spectrofluorometrically in guinea pig cardiac mitochondria in response to added CaCl2 (0-0.6 mM; 1 mM EGTA buffer) with/without added MgCl2 (0-2 mM). In parallel, we assessed effects of added CaCl2 and MgCl2 on NADH, membrane potential (ΔΨm), and respiration. We found that ≥0.125 mM MgCl2 significantly attenuated CU-mediated Ca(2+) uptake and [Ca(2+)]m. Incremental [Mg(2+)]e did not reduce initial Ca(2+)uptake but attenuated the subsequent slower Ca(2+) uptake, so that [Ca(2+)]m remained unaltered over time. Adding CaCl2 without MgCl2 to attain a [Ca(2+)]m from 46 to 221 nM enhanced state 3 NADH oxidation and increased respiration by 15 %; up to 868 nM [Ca(2+)]m did not additionally enhance NADH oxidation or respiration. Adding MgCl2 did not increase [Mg(2+)]m but it altered bioenergetics by its direct effect to decrease Ca(2+) uptake. However, at a given [Ca(2+)]m, state 3 respiration was incrementally attenuated, and state 4 respiration enhanced, by higher [Mg(2+)]e. Thus, [Mg(2+)]e without a change in [Mg(2+)]m can modulate bioenergetics independently of CU-mediated Ca(2+) transport.

Calcium signaling in cardiac mitochondria

Mitochondrial Ca signaling contributes to the regulation of cellular energy metabolism, and mitochondria participate in cardiac excitation-contraction coupling (ECC) through their ability to store Ca, shape the cytosolic Ca signals and generate ATP required for contraction. The mitochondrial inner membrane is equipped with an elaborate system of channels and transporters for Ca uptake and extrusion that allows for the decoding of cytosolic Ca signals, and the storage of Ca in the mitochondrial matrix compartment. Controversy, however remains whether the fast cytosolic Ca transients underlying ECC in the beating heart are transmitted rapidly into the matrix compartment or slowly integrated by the mitochondrial Ca transport machinery. This review summarizes established and novel findings on cardiac mitochondrial Ca transport and buffering, and discusses the evidence either supporting or arguing against the idea that Ca can be taken up rapidly by mitochondria during ECC.

Modeling the calcium sequestration system in isolated guinea pig cardiac mitochondria

Under high Ca(2+) load conditions, Ca(2+) concentrations in the extra-mitochondrial and mitochondrial compartments do not display reciprocal dynamics. This is due to a paradoxical increase in the mitochondrial Ca(2+) buffering power as the Ca(2+) load increases. Here we develop and characterize a mechanism of the mitochondrial Ca(2+) sequestration system using an experimental data set from isolated guinea pig cardiac mitochondria. The proposed mechanism elucidates this phenomenon and others in a mathematical framework and is integrated into a previously corroborated model of oxidative phosphorylation including the Na(+)/Ca(2+) cycle. The integrated model reproduces the Ca(2+) dynamics observed in both compartments of the isolated mitochondria respiring on pyruvate after a bolus of CaCl2 followed by ruthenium red and a bolus of NaCl. The model reveals why changes in mitochondrial Ca(2+) concentration of Ca(2+) loaded mitochondria appear significantly mitigated relative to the corresponding extra-mitochondrial Ca(2+) concentration changes after Ca(2+) efflux is initiated. The integrated model was corroborated by simulating the set-point phenomenon. The computational results support the conclusion that the Ca(2+) sequestration system is composed of at least two classes of Ca(2+) buffers. The first class represents prototypical Ca(2+) buffering, and the second class encompasses the complex binding events associated with the formation of amorphous calcium phosphate. With the Ca(2+) sequestration system in mitochondria more precisely defined, computer simulations can aid in the development of innovative therapeutics aimed at addressing the myriad of complications that arise due to mitochondrial Ca(2+) overload.

A biophysical model of the mitochondrial ATP-Mg/P(i) carrier

Mitochondrial adenine nucleotide (AdN) content is regulated through the Ca(2+)-activated, electroneutral ATP-Mg/P(i) carrier (APC). The APC is a protein in the mitochondrial carrier super family that localizes to the inner mitochondrial membrane (IMM). It is known to modulate a number of processes that depend on mitochondrial AdN content, such as gluconeogenesis, protein synthesis, and citrulline synthesis. Despite this critical role, a kinetic model of the underlying mechanism has not been developed and validated. Here, a biophysical model of the APC is developed that is thermodynamically balanced and accurately reproduces a number of reported data sets from isolated rat liver and rat kidney mitochondria. The model is based on an ordered bi-bi mechanism for heteroexchange of ATP and P(i) and includes homoexchanges of ATP and P(i) to explain both the initial rate and time course data on ATP and P(i) transport via the APC. The model invokes seven kinetic parameters regarding the APC mechanism and three parameters related to matrix pH regulation by external P(i). These parameters are estimated based on 19 independent data curves; the estimated parameters are validated using six additional data curves. The model takes into account the effects of pH, Mg(2+), and Ca(2+) on ATP and P(i) transport via the APC, and supports the conclusion that the pH gradient across the IMM serves as the primary driving force for AdN uptake or efflux. Moreover, computer simulations demonstrate that extramatrix Ca(2+) modulates the turnover rate of the APC and not the binding affinity of ATP, as previously suggested.

17β-estradiol modulates mitochondrial Ca²⁺ flux in rat caudate nucleus and brain stem

The aim of this study was to examine the rapid non-genomic effect of 17β-estradiol (E2) on Ca(2+) transport in mitochondria isolated from the nerve terminals (synaptosomes) of caudate nuclei (NC) and brain stems (BS) of ovariectomised female rats. In physiological conditions no effect of E2 on Ca(2+) influx into synaptosomal mitochondria through ruthenium red (RR)-sensitive uniporter was observed. However, in the presence of uncoupling agent carbonyl cyanide4-(trifluoromethoxy)phenylhydrazone (FCCP) (1μmol/l), pre-treatment with 0.5nmol/l E2 protected mitochondrial membrane potential and consequently increased Ca(2+) influx (2.3-fold in NC and 3.1-fold in BS). At the same time, 0.5nmol/l E2 by increasing the affinity of mitochondrial Na(+)/Ca(2+) exchanger for Na(+) inhibited mitochondrial Ca(2+) efflux in NC and BS by about 40%. Also, the specific binding of physiological E2 concentrations (0.1-10nmol/l) to isolated synaptosomal mitochondria was detected. Using membrane impermeable E2 bound to bovine serum albumin and selective inhibitor of mitochondrial Na(+)/Ca(2+) exchanger, we obtained that E2's action on mitochondrial Ca(2+) efflux at least partially is due to the direct effects on the mitochondrial membrane and/or Na(+)/Ca(2+) exchanger located in inner mitochondrial membrane. Our results implicate E2 as a modulator of Ca(2+) concentration in mitochondrial matrix, and ultimately in the cytosol. Given the vital role of Ca(2+) in regulation of total nerve cells activity, especially energy metabolism, neurotransmission and directing the cells toward survival or cell death, the effects on mitochondrial Ca(2+) transport could be one of the important modes of E2 neuromodulatory action independent of the genome.

Mitochondrial calcium handling during ischemia-induced cell death in neurons

Mitochondria sense and shape cytosolic Ca(2+) signals by taking up and subsequently releasing Ca(2+) ions during physiological and pathological Ca(2+) elevations. Sustained elevations in the mitochondrial matrix Ca(2+) concentration are increasingly recognized as a defining feature of the intracellular cascade of lethal events that occur in neurons during cerebral ischemia. Here, we review the recently identified transport proteins that mediate the fluxes of Ca(2+) across mitochondria and discuss the implication of the permeability transition pore in decoding the abnormally sustained mitochondrial Ca(2+) elevations that occur during cerebral ischemia.