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

The interplay between sodium/glucose cotransporter type 2 and mitochondrial ionic environment

Mitochondrial volume is maintained through the permeability of the inner mitochondrial membrane by a specific aquaporin and the osmotic balance between the mitochondrial matrix and cellular cytoplasm. Various electrolytes, such as calcium and hydrogen ions, potassium, and sodium, as well as other osmotic substances, affect the swelling of mitochondria. Intracellular glucose levels may also affect mitochondrial swelling, although the relationship between mitochondrial ion homeostasis and intracellular glucose is poorly understood. This article reviews what is currently known about how the Sodium-Glucose transporter (SGLT) may impact mitochondrial sodium (Na+) homeostasis. SGLTs regulate intracellular glucose and sodium levels and, therefore, interfere with mitochondrial ion homeostasis because mitochondrial Na+ is closely linked to cytoplasmic calcium and sodium dynamics. Recently, a large amount of data has been available on the effects of SGLT2 inhibitors on mitochondria in different cell types, including renal proximal tubule cells, endothelial cells, mesangial cells, podocytes, neuronal cells, and cardiac cells. The current evidence suggests that SGLT inhibitors (SGLTi) may affect mitochondrial dynamics regarding intracellular Sodium and hydrogen ions. Although the regulation of mitochondrial ion channels by SGLTs is still in its infancy, the evidence accumulated thus far of the effect of SGLTi on mitochondrial functions certainly will foster further research in this direction.

Mitochondrial Dynamics during Development

Mitochondria are dynamic membrane-bound organelles in eukaryotic cells. These are important for the generation of chemical energy needed to power various cellular functions and also support metabolic, energetic, and epigenetic regulation in various cells. These organelles are also important for communication with the nucleus and other cellular structures, to maintain developmental sequences and somatic homeostasis, and for cellular adaptation to stress. Increasing information shows mitochondrial defects as an important cause of inherited disorders in different organ systems. In this article, we provide an extensive review of ontogeny, ultrastructural morphology, biogenesis, functional dynamics, important clinical manifestations of mitochondrial dysfunction, and possibilities for clinical intervention. We present information from our own clinical and laboratory research in conjunction with information collected from an extensive search in the databases PubMed, EMBASE, and Scopus.

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.

Dynamics and stabilization mechanism of mitochondrial cristae morphofunction associated with turgor-driven cardiolipin biosynthesis under salt stress conditions

Maintaining energy production efficiency is of vital importance to plants growing under changing environments. Cardiolipin localized in the inner mitochondrial membrane plays various important roles in mitochondrial function and its activity, although the regulation of mitochondrial morphology to various stress conditions remains obscure, particularly in the context of changes in cellular water relations and metabolisms. By combining single-cell metabolomics with transmission electron microscopy, we have investigated the adaptation mechanism in tomato trichome stalk cells at moderate salt stress to determine the kinetics of cellular parameters and metabolisms. We have found that turgor loss occurred just after the stress conditions, followed by the contrasting volumetric changes in mitochondria and cells, the accumulation of TCA cycle-related metabolites at osmotic adjustment, and a temporal increase in cardiolipin concentration, resulting in a reversible topological modification in the tubulo-vesicular cristae. Because all of these cellular events were dynamically observed in the same single-cells without causing any disturbance for redox states and cytoplasmic streaming, we conclude that turgor pressure might play a regulatory role in the mitochondrial morphological switch throughout the temporal activation of cardiolipin biosynthesis, which sustains mitochondrial respiration and energy conversion even under the salt stress conditions.

Tristability in mitochondrial permeability transition pore opening

Mitochondrial permeability transition pore (PTP), a key regulator of cell life and death processes, is triggered by calcium ions (Ca²⁺) and potentiated by reactive oxygen species (ROS). Although the two modes of PTP opening, i.e., transient and persistent, have been identified for a long time, its dynamical mechanism is still not fully understood. To test a proposed hypothesis that PTP opening acts as a tristable switch, which is characterized by low, medium, and high open probability, we develop a three-variable model that focused on PTP opening caused by Ca²⁺ and ROS. For the system reduced to two differential equations for Ca²⁺ and ROS, both the stability analysis and the potential landscape feature that it exhibits tristability under standard parameters. For the full system, the bifurcation analysis suggests that it can achieve tristability over a wide range of input parameters. Furthermore, parameter sensitivity analysis demonstrates that the existence of tristability is a robust property. In addition, we show how the deterministic tristable property can be understood within a stochastic framework, which also explains the PTP dynamics at the level of a single channel. Overall, this study may yield valuable insights into the intricate regulatory mechanism of PTP opening.

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.

Mitochondrial dysfunction and beneficial effects of mitochondria-targeted small peptide SS-31 in Diabetes Mellitus and Alzheimer's disease

Diabetes and Alzheimer's disease are common chronic illnesses in the United States and lack clearly demonstrated therapeutics. Mitochondria, the "powerhouse of the cell", is involved in the homeostatic regulation of glucose, energy, and reduction/oxidation reactions. The mitochondria has been associated with the etiology of metabolic and neurological disorders through a dysfunction of regulation of reactive oxygen species. Mitochondria-targeted chemicals, such as the Szeto-Schiller-31 peptide, have advanced therapeutic potential through the inhibition of oxidative stress and the restoration of normal mitochondrial function as compared to traditional antioxidants, such as vitamin E. In this article, we summarize the pathophysiological relevance of the mitochondria and the beneficial effects of Szeto-Schiller-31 peptide in the treatment of Diabetes and Alzheimer's disease.

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.

Placental mitochondrial function as a driver of angiogenesis and placental dysfunction

The placenta is a highly vascularized and complex foetal organ that performs various tasks, crucial to a healthy pregnancy. Its dysfunction leads to complications such as stillbirth, preeclampsia, and intrauterine growth restriction. The specific cause of placental dysfunction remains unknown. Recently, the role of mitochondrial function and mitochondrial adaptations in the context of angiogenesis and placental dysfunction is getting more attention. The required energy for placental remodelling, nutrient transport, hormone synthesis, and the reactive oxygen species leads to oxidative stress, stemming from mitochondria. Mitochondria adapt to environmental changes and have been shown to adjust their oxygen and nutrient use to best support placental angiogenesis and foetal development. Angiogenesis is the process by which blood vessels form and is essential for the delivery of nutrients to the body. This process is regulated by different factors, pro-angiogenic factors and anti-angiogenic factors, such as sFlt-1. Increased circulating sFlt-1 levels have been linked to different preeclamptic phenotypes. One of many effects of increased sFlt-1 levels, is the dysregulation of mitochondrial function. This review covers mitochondrial adaptations during placentation, the importance of the anti-angiogenic factor sFlt-1in placental dysfunction and its role in the dysregulation of mitochondrial function.

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.

Increasing of malignancy of breast cancer cells after cryopreservation: molecular detection and activation of angiogenesis after CAM-xenotransplantation

Background

Ovarian tissue cryopreservation has a wide range of cancerous indications. Avoiding relapse becomes a specific concern that clinicians frequently encounter. The data about the comparative viability of cancer cells after cryopreservation are limited. This study aimed to evaluate the effect of cryopreservation on breast cancer cells.

Methods

We used in-vitro cultured ZR-75-1 and MDA-MB-231 cell lines. Cell samples of each lineage were distributed into the non-intervened and cryopreserved groups. The cryopreservation procedures comprised programmed slow freezing followed by thawing at 100 °C, 60 s. Biological phenotypes and the related protein markers were compared between the two groups. The EVOS FL Auto 2 Cell Image System was used to monitor cell morphology. Cell proliferation, motility, and penetration were characterized by CCK-8, wound-healing, and transmembrane assay, respectively. The expression of Ki-67, P53, GATA3, E-cadherin, Vimentin, and F-Actin was captured by immunofluorescent staining and western blotting as the proxy measurements of the related properties. The chorioallantoic membrane (CAM) xenotransplantation was conducted to explore angiogenesis induced by cancer cells.

Results

After 5 days in vitro culture, the cell concentration of cryopreserved and non-intervened groups was 15.7 × 10⁴ vs. 14.4 × 10⁴cells/ml, (ZR-75-1, p > 0.05), and 25.1 × 10⁴ vs. 26.6 × 10⁴ cells/ml (MDA-MB-231, p > 0.05). Some cryopreserved ZR-75-1 cells presented spindle shape with filopodia and lamellipodia and dissociated from the cell cluster after cryopreservation. Both cell lines demonstrated increased cell migrating capability and invasion after cryopreservation. The expression of Ki-67 and P53 did not differ between the cryopreserved and non-intervened groups. E-cadherin and GATA3 expression downregulated in the cryopreserved ZR-75-1 cells. Vimentin and F-actin exhibited an upregulated level in cryopreserved ZR-75-1 and MDA-MB-231 cells. The cryopreserved MDA-MB-231 cells induced significant angiogenesis around the grafts on CAM with the vascular density 0.313 ± 0.03 and 0.342 ± 0.04, compared with that of non-intervened cells of 0.238 ± 0.05 and 0.244 ± 0.03, p < 0.0001.

Conclusions

Cryopreservation promotes breast cancer cells in terms of epithelial-mesenchymal transition and angiogenesis induction, thus increasing metastasis risk.

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.

Topology-dependent, bifurcated mitochondrial quality control under starvation

Selective elimination of mitochondria by autophagy is a critical strategy for a variety of physiological processes, including development, cell-fate determination and stress response. Although several mechanisms have been identified as responsible for selective degradation of mitochondria, such as the PINK1-PRKN/PARKIN- and receptor-dependent pathways, aspects of the mechanisms and particularly the principles underlying the selection process of mitochondria remain obscure. Here, we addressed a new selection strategy in which the selective elimination of mitochondria is dependent on organellar topology. We found that populations of mitochondria undergo different topological transformations under serum starvation, either swelling or forming donut shapes. Swollen mitochondria are associated with mitochondrial membrane potential dissipation and PRKN recruitment, which promote their selective elimination, while the donut topology maintains mitochondrial membrane potential and helps mitochondria resist autophagy. Mechanistic studies show that donuts resist autophagy even after depolarization through preventing recruitment of autophagosome receptors CALCOCO2/NDP52 and OPTN even after PRKN recruitment. Our results demonstrate topology-dependent, bifurcated mitochondrial recycling under starvation, that is swollen mitochondria undergo removal by autophagy, while donut mitochondria undergo fission and fusion cycles for reintegration. This study reveals a novel morphological selection for control of mitochondrial quality and quantity under starvation.