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

Mitochondrial Volume Regulation and Swelling Mechanisms in Cardiomyocytes

Mitochondrion, known as the "powerhouse" of the cell, regulates ion homeostasis, redox state, cell proliferation and differentiation, and lipid synthesis. The inner mitochondrial membrane (IMM) controls mitochondrial metabolism and function. It possesses high levels of proteins that account for ~70% of the membrane mass and are involved in the electron transport chain, oxidative phosphorylation, energy transfer, and ion transport, among others. The mitochondrial matrix volume plays a crucial role in IMM remodeling. Several ion transport mechanisms, particularly K+ and Ca2+, regulate matrix volume. Small increases in matrix volume through IMM alterations can activate mitochondrial respiration, whereas excessive swelling can impair the IMM topology and initiates mitochondria-mediated cell death. The opening of mitochondrial permeability transition pores, the well-characterized phenomenon with unknown molecular identity, in low- and high-conductance modes are involved in physiological and pathological increases of matrix volume. Despite extensive studies, the precise mechanisms underlying changes in matrix volume and IMM structural remodeling in response to energy and oxidative stressors remain unknown. This review summarizes and discusses previous studies on the mechanisms involved in regulating mitochondrial matrix volume, IMM remodeling, and the crosstalk between these processes.

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.

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.

Modulation and pre-amplification of PAR1 signaling by ADP acting via the P2Y12 receptor during platelet subpopulation formation

BACKGROUND

Two major soluble blood platelet activators are thrombin and ADP. Of these two, only thrombin can induce mitochondrial collapse and programmed cell death leading to phosphatidylserine (PS) exposure required for blood clotting reactions acceleration. Thrombin can also greatly potentiate collagen-induced PS exposure. However, ADP acting through the P2Y12 receptor was shown to increase the PS-exposing (PS+) platelets fraction produced by thrombin or thrombin-plus-collagen via an unknown mechanism.

METHODS

We developed a comprehensive multicompartmental computational model of platelet PAR1-and-P2Y12 calcium signal transduction that included cytoplasmic signaling, dense tubular system and mitochondria. To test model predictions, flow cytometry experiments with washed, annexin V-labeled platelets were performed.

RESULTS

Stimulation of thrombin receptor PAR1 in the model induced cytoplasmic calcium oscillations, calcium uptake by mitochondria, opening of the permeability transition pore and collapse of the mitochondrial membrane potential. ADP stimulation of P2Y12 led to cAMP decrease that, in turn, caused changes in phospholipase C phosphorylation by protein kinase A, increase in cytoplasmic calcium level and, consequently, PS+ platelet formation. ADP addition before stimulation of PAR1 produced much greater increase of the PS+ fraction because cAMP concentration had time to go down prior to calcium oscillations; this prediction was also tested and confirmed experimentally.

CONCLUSION

These results suggest a mechanism of ADP-dependent PS exposure regulation and show a likely mode of action that could be important for the PS exposure regulation in thrombi, where ADP is released before thrombin formation.

Compartmentalized calcium signaling triggers subpopulation formation upon platelet activation through PAR1

A computational model of PAR1-stimulated platelet calcium signaling is developed to analyze the formation of platelet subpopulations. This occurs via a mitochondria-dependent decision-making mechanism. This is a stochastic phenomenon caused by a small number of PARs.

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.

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.

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.

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.

Ionic storm in hypoxic/ischemic stress: can opioid receptors subside it?

Neurons in the mammalian central nervous system are extremely vulnerable to oxygen deprivation and blood supply insufficiency. Indeed, hypoxic/ischemic stress triggers multiple pathophysiological changes in the brain, forming the basis of hypoxic/ischemic encephalopathy. One of the initial and crucial events induced by hypoxia/ischemia is the disruption of ionic homeostasis characterized by enhanced K(+) efflux and Na(+)-, Ca(2+)- and Cl(-)-influx, which causes neuronal injury or even death. Recent data from our laboratory and those of others have shown that activation of opioid receptors, particularly delta-opioid receptors (DOR), is neuroprotective against hypoxic/ischemic insult. This protective mechanism may be one of the key factors that determine neuronal survival under hypoxic/ischemic condition. An important aspect of the DOR-mediated neuroprotection is its action against hypoxic/ischemic disruption of ionic homeostasis. Specially, DOR signal inhibits Na(+) influx through the membrane and reduces the increase in intracellular Ca(2+), thus decreasing the excessive leakage of intracellular K(+). Such protection is dependent on a PKC-dependent and PKA-independent signaling pathway. Furthermore, our novel exploration shows that DOR attenuates hypoxic/ischemic disruption of ionic homeostasis through the inhibitory regulation of Na(+) channels. In this review, we will first update current information regarding the process and features of hypoxic/ischemic disruption of ionic homeostasis and then discuss the opioid-mediated regulation of ionic homeostasis, especially in hypoxic/ischemic condition, and the underlying mechanisms.

Acidic lipids, H(+)-ATPases, and mechanism of oxidative phosphorylation. Physico-chemical ideas 30 years after P. Mitchell's Nobel Prize award

Peter D. Mitchell, who was awarded the Nobel Prize in Chemistry 30 years ago, in 1978, formulated the chemiosmotic theory of oxidative phosphorylation. This review initially analyzes the major aspects of this theory, its unresolved problems, and its modifications. A new physico-chemical mechanism of energy transformation and coupling of oxidation and phosphorylation is then suggested based on recent concepts regarding proteins, including ATPases that work as molecular motors, and acidic lipids that act as hydrogen ion (H(+)) carriers. According to this proposed mechanism, the chemical energy of a redox substrate is transformed into nonequilibrium states of electron-transporting chain (ETC) coupling proteins. This leads to nonequilibrium pumping of H(+) into the membrane. An acidic lipid, cardiolipin, binds with this H(+) and carries it to the ATP-synthase along the membrane surface. This transport generates gradients of surface tension or electric field along the membrane surface. Hydrodynamic effects on a nanolevel lead to rotation of ATP-synthase and finally to the release of ATP into aqueous solution. This model also explains the generation of a transmembrane protonmotive force that is used for regulation of transmembrane transport, but is not necessary for the coupling of electron transport and ATP synthesis.

Calcium influx into phospholipid vesicles caused by dynorphin neuropeptides

Dynorphins, endogeneous opioid peptides, function as ligands to the opioid kappa receptors but also induce non-opioid excitotoxic effects. Dynorphin A can increase the intra-neuronal calcium concentration through a non-opioid and non-NMDA mechanism. In this investigation, we show that big dynorphin, dynorphin A and to some extent dynorphin A (1-13), but not dynorphin B, allow calcium to enter into large unilamellar phospholipid vesicles with partly negative headgroups. The effects parallel the previously studied potency of dynorphins to translocate through biological membranes and to cause calcein leakage from large unilamellar phospholipid vesicles. There is no calcium ion influx into vesicles with zwitterionic headgroups. We have also investigated if the dynorphins can translocate through the vesicle membranes and estimated the relative strength of interaction of the peptides with the vesicles by fluorescence resonance energy transfer. The results show that dynorphins do not translocate in this membrane model system. There is a strong electrostatic contribution to the interaction of the peptides with the membrane model system.

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.

Kinetic model for Ca2+-induced permeability transition in energized liver mitochondria discriminates between inhibitor mechanisms

Cytotoxicity associated with pathophysiological Ca(2+) overload (e.g. in stroke) appears mediated by an event termed the mitochondrial permeability transition (mPT). We built and solved a kinetic model of the mPT in populations of isolated rat liver mitochondria that quantitatively describes Ca(2+)-induced mPT as a two-step sequence of pre-swelling induction followed by Ca(2+)-driven, positive feedback, autocatalytic propagation. The model was formulated as two differential equations, each directly related to experimental parameters (Ca(2+) flux/mitochondrial swelling). These parameters were simultaneously assessed using a spectroscopic approach to monitor multiple mitochondrial properties. The derived kinetic model correctly identifies a correlation between initial Ca(2+) concentration and delay interval prior to mPT induction. Within the model's framework, Ru-360 (a ruthenium complex) and Mg(2+) were shown to compete with the Ca(2+)-stimulated initiation phase of mPT induction, consistent with known inhibition at the phenomenological level of the Ca(2+) uniporter. The model further reveals that Mg(2+), but not Ru-360, inhibits Ca(2+)-induced effects on a downstream stage of mPT induction at a site distinct from the uniporter. The analytical approach was then applied to promethazine, an FDA-approved drug previously shown to inhibit both mPT and ischemia-reperfusion injury. Kinetic analysis revealed that promethazine delayed mPT induction in a manner qualitatively distinct from that of lower concentrations of Mg(2+). In summary, we have developed a kinetic model to aid in the quantitative characterization of mPT induction. This model is consistent with/informative about the biochemistry of several mPT inhibitors, and its success suggests that this kinetic approach can aid in the classification of agents or targets that modulate mPT induction.