A Biophysically Based Mathematical Model for the Kinetics of Mitochondrial Na-Ca Antiporter

Sodium-calcium antiporter is the primary efflux pathway for Ca²⁺ in respiring mitochondria, and hence plays an important role in mitochondrial Ca²⁺ homeostasis. Although experimental data on the kinetics of Na⁺-Ca²⁺ antiporter are available, the structure and composition of its functional unit and kinetic mechanisms associated with the Na⁺-Ca²⁺ exchange (including the stoichiometry) remains unclear. To gain a quantitative understanding of mitochondrial Ca²⁺ homeostasis, a biophysical model of Na⁺-Ca²⁺ antiporter is introduced that is thermodynamically balanced and satisfactorily describes a number of independent data sets under a variety of experimental conditions. The model is based on a multistate catalytic binding mechanism for carrier-mediated facilitated transport and Eyring's free energy barrier theory for interconversion and electrodiffusion. The model predicts the activating effect of membrane potential on the antiporter function for a 3Na⁺:1Ca²⁺ electrogenic exchange as well as the inhibitory effects of both high and low pH seen experimentally. The model is useful for further development of mechanistic integrated models of mitochondrial Ca²⁺ handling and bioenergetics to understand the mechanisms by which Ca²⁺ plays a role in mitochondrial signaling pathways and energy metabolism.     

线粒体钙单向转运体和线粒体应激关系的研究进展

钙离子(calcium ion,Ca~(2+))在线粒体功能障碍及细胞损伤凋亡过程中发挥重要的细胞信号作用。近些年来关于Ca~(2+)通道以及其调控蛋白的研究越来越多,其中,线粒体单向转运体(uniporter)复合物的结构组成及其相关蛋白的分布特点成为主要研究热点。作为uniporter复合物中关键的通道蛋白,线粒体钙单向转运蛋白(mitochondrial calcium uniporter,MCU)可顺电化学梯度摄入Ca~(2+),将Ca~(2+)从胞质转运到线粒体基质并控制转运速率,其在胞内Ca~(2+)信号转导、Ca~(2+)稳态、线粒体能量代谢以及细胞凋亡方面具有重要意义。识别调控线粒体内Ca~(2+)信号的MCU及其相关蛋白可深入阐明线粒体应激在相关疾病中的发生发展,并为进一步的疾病治疗提供理论依据。     

Mitochondrial Calcium Uniporter Activity Is Dispensable for MDA-MB-231 Breast Carcinoma Cell Survival

Calcium uptake through the mitochondrial Ca²⁺ uniporter (MCU) is thought to be essential in regulating cellular signaling events, energy status, and survival. Functional dissection of the uniporter is now possible through the recent identification of the genes encoding for MCU protein complex subunits. Cancer cells exhibit many aspects of mitochondrial dysfunction associated with altered mitochondrial Ca²⁺ levels including resistance to apoptosis, increased reactive oxygen species production and decreased oxidative metabolism. We used a publically available database to determine that breast cancer patient outcomes negatively correlated with increased MCU Ca²⁺ conducting pore subunit expression and decreased MICU1 regulatory subunit expression. We hypothesized breast cancer cells may therefore be sensitive to MCU channel manipulation. We used the widely studied MDA-MB-231 breast cancer cell line to investigate whether disruption or increased activation of mitochondrial Ca²⁺ uptake with specific siRNAs and adenoviral overexpression constructs would sensitize these cells to therapy-related stress. MDA-MB-231 cells were found to contain functional MCU channels that readily respond to cellular stimulation and elicit robust AMPK phosphorylation responses to nutrient withdrawal. Surprisingly, knockdown of MCU or MICU1 did not affect reactive oxygen species production or cause significant effects on clonogenic cell survival of MDA-MB-231 cells exposed to irradiation, chemotherapeutic agents, or nutrient deprivation. Overexpression of wild type or a dominant negative mutant MCU did not affect basal cloning efficiency or ceramide-induced cell killing. In contrast, non-cancerous breast epithelial HMEC cells showed reduced survival after MCU or MICU1 knockdown. These results support the conclusion that MDA-MB-231 breast cancer cells do not rely on MCU or MICU1 activity for survival in contrast to previous findings in cells derived from cervical, colon, and prostate cancers and suggest that not all carcinomas will be sensitive to therapies targeting mitochondrial Ca²⁺ uptake mechanisms.     

Different Subunit Location of the Inhibition and Transport Sites in the Mitochondrial Calcium Uniporter

The mitochondrial calcium uniporter behaves as a cooperative mechanism, where the velocity is dependent on [Ca2+]ex. Transport kinetics follows a sigmoidal behavior with a Hill coefficient near 2.0, indicating the binding of at least two calcium molecules. Calcium transport in mitochondria is dependent on a negative inner membrane potential and is inhibited by policationic ruthenium compounds. In this study, calcium uptake activity was reconstituted into cytochrome oxidase vesicles by incorporating solubilized mitochondrial proteins. Calcium accumulation plotted against increasing Ca2+ concentrations followed a sigmoidal behavior with a Hill coefficient of 1.53. The uptake was sensitive to ruthenium policationic inhibitors, e.g. ruthenium red and Ru360. After mitochondrial proteins were separated by preparative isoelectrofocusing and incorporated into cytochrome oxidase vesicles, two peaks of calcium uptake activity were recovered. One of the activities was inhibited by Ru360, while the second activity was insensitive to Ru360 and was associated with proteins focused at very acidic isoelectric points. By using a thiol-group crosslinker and radiolabeled Ru360, we proposed a scheme of partial dissociation of the uniporter inhibitor-binding subunit under acidic conditions.     

A Mathematical Model for the Regulation of Tumor Dormancy Based on Enzyme Kinetics

In this paper we present a two-compartment model for tumor dormancy based on an idea of Zetter [1998, Ann. Rev. Med. 49, 407–422] to wit: The vascularization of a secondary (daughter) tumor can be suppressed by an inhibitor originating from a larger primary (mother) tumor. We apply this idea at the avascular level to develop a model for the remote suppression of secondary avascular tumors via the secretion of primary avascular tumor inhibitors. The model gives good agreement with the observations of [De Giorgi et al., 2003, Derm. Surgery 29, 664–667]. These authors reported on the emergence of a polypoid melanoma at a site remote from a primary polypoid melanoma after excision of the latter. The authors observed no recurrence of the melanoma at the primary site, but did observe secondary tumors at secondary sites 5–7 cm from the primary site within a period of 1 month after the excision of the primary site. We attempt to provide a reasonable biochemical/cell biological model for this phenomenon. We show that when the tumors are sufficiently remote, the primary tumor will not influence the secondary tumor while, if they are too close together, the primary tumor can effectively prevent the growth of the secondary tumor, even after it is removed. It should be possible to use the model as the basis for a testable hypothesis.     

Characterization of Mg Inhibition of Mitochondrial Ca Uptake by a Mechanistic Model of Mitochondrial Ca Uniporter

Ca²⁺ is an important regulatory ion and alteration of mitochondrial Ca²⁺ homeostasis can lead to cellular dysfunction and apoptosis. Ca²⁺ is transported into respiring mitochondria via the Ca²⁺ uniporter, which is known to be inhibited by Mg²⁺. This uniporter-mediated mitochondrial Ca²⁺ transport is also shown to be influenced by inorganic phosphate (Pi). Despite a large number of experimental studies, the kinetic mechanisms associated with the Mg²⁺ inhibition and Pi regulation of the uniporter function are not well established. To gain a quantitative understanding of the effects of Mg²⁺ and Pi on the uniporter function, we developed here a mathematical model based on known kinetic properties of the uniporter and presumed Mg²⁺ inhibition and Pi regulation mechanisms. The model is extended from our previous model of the uniporter that is based on a multistate catalytic binding and interconversion mechanism and Eyring's free energy barrier theory for interconversion. The model satisfactorily describes a wide variety of experimental data sets on the kinetics of mitochondrial Ca²⁺ uptake. The model also appropriately depicts the inhibitory effect of Mg²⁺ on the uniporter function, in which Ca²⁺ uptake is hyperbolic in the absence of Mg²⁺ and sigmoid in the presence of Mg²⁺. The model suggests a mixed-type inhibition mechanism for Mg²⁺ inhibition of the uniporter function. This model is critical for building mechanistic models of mitochondrial bioenergetics and Ca²⁺ handling to understand the mechanisms by which Ca²⁺ mediates signaling pathways and modulates energy metabolism.     

Cardiolipin Regulates the Activity of the Reconstituted Mitochondrial Calcium Uniporter by Modifying the Structure of the Liposome Bilayer

Reconstitution of mitochondrial calcium transport activity requires the incorporation of membrane proteins into a lipidic ambient. Calcium uptake has been measured previously using Cytochrome oxidase vesicles. The enrichment of these vesicles with cardiolipin, an acidic phospholipid that is found only in the inner mitochondrial membrane of eukaryotic cells, strongly inhibits calcium transport, in remarkable contrast with the activation effect that cardiolipin exerts upon other mitochondrial transporters and enzymes. The relation of the inactivation of calcium transport to the physical state of the bilayer was studied by following the polarization changes of 1,6-diphenyl-1,3,5-hexatriene (DPH) and by flow cytometry in the cardiolipin-enriched liposomes with incorporated mitochondrial solubilized proteins. Non-bilayer molecular arrangements in the cardiolipin-supplemented liposomes, detected by flow cytometry, may produce the fluidity changes observed by fluorescence polarization of DPH. Fluidity changes correlate with the abolition of calcium uptake, but have no effect on the establishment of a membrane potential in the vesicles required for calcium transport activity. Changes in the membrane structure and uniporter function are observed in the combined presence of cardiolipin and calcium leading to a modified lipid configuration.     

Probing Novel Roles of the Mitochondrial Uniporter in Ovarian Cancer Cells Using Nanoparticles

Nanoparticles provide a potent tool for targeting and understanding disease mechanisms. In this regard, cancer cells are surprisingly resistant to the expected toxic effects of positively charged gold nanoparticles (⁺AuNPs). Our investigations led to the identification of MICU1, regulator of mitochondrial calcium uniporter, as a key molecule conferring cancer cells with resistance to ⁺AuNPs. The increase in cytosolic [Ca²⁺]_cyto in malignant cells induced by ⁺AuNPs is counteracted by MICU1, preventing cell death. Pharmacological or siRNA-mediated inhibition of mitochondrial Ca⁺² entry leads to endoplasmic reticulum stress and sensitizes cancer cells to ⁺AuNP-induced cytotoxicity. Silencing MICU1 decreases Bcl-2 expression and increases caspase-3 activity and cytosolic cytochrome c levels, thus initiating the mitochondrial pathway for apoptosis: effects further enhanced by ⁺AuNPs. This study highlights the potential of nanomaterials as a tool to broaden our understanding of cellular processes, establishes MICU1 as a novel regulator of the machinery in cancer cells that prevents apoptosis, and emphasizes the need to synergize nanoparticle design with understanding of mitochondrial machinery for enhancing targeted cellular toxicity.     

Essential Role of Mitochondrial Ca2+ Uniporter in the Generation of Mitochondrial pH Gradient and Metabolism-Secretion Coupling in Insulin-releasing Cells

In pancreatic β-cells, ATP acts as a signaling molecule initiating plasma membrane electrical activity linked to Ca²⁺ influx, which triggers insulin exocytosis. The mitochondrial Ca²⁺ uniporter (MCU) mediates Ca²⁺ uptake into the organelle, where energy metabolism is further stimulated for sustained second phase insulin secretion. Here, we have studied the contribution of the MCU to the regulation of oxidative phosphorylation and metabolism-secretion coupling in intact and permeabilized clonal β-cells as well as rat pancreatic islets. Knockdown of MCU with siRNA transfection blunted matrix Ca²⁺ rises, decreased nutrient-stimulated ATP production as well as insulin secretion. Furthermore, MCU knockdown lowered the expression of respiratory chain complexes, mitochondrial metabolic activity, and oxygen consumption. The pH gradient formed across the inner mitochondrial membrane following nutrient stimulation was markedly lowered in MCU-silenced cells. In contrast, nutrient-induced hyperpolarization of the electrical gradient was not altered. In permeabilized cells, knockdown of MCU ablated matrix acidification in response to extramitochondrial Ca²⁺. Suppression of the putative Ca²⁺/H⁺ antiporter leucine zipper-EF hand-containing transmembrane protein 1 (LETM1) also abolished Ca²⁺-induced matrix acidification. These results demonstrate that MCU-mediated Ca²⁺ uptake is essential to establish a nutrient-induced mitochondrial pH gradient which is critical for sustained ATP synthesis and metabolism-secretion coupling in insulin-releasing cells.     

Molecular Tuning of the Axonal Mitochondrial Ca2+ Uniporter Ensures Metabolic Flexibility of Neurotransmission

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Biophysically Based Mathematical Modeling of Interstitial Cells of Cajal Slow Wave Activity Generated from a Discrete Unitary Potential Basis

Spontaneously rhythmic pacemaker activity produced by interstitial cells of Cajal (ICC) is the result of the entrainment of unitary potential depolarizations generated at intracellular sites termed pacemaker units. In this study, we present a mathematical modeling framework that quantitatively represents the transmembrane ion flows and intracellular Ca²⁺ dynamics from a single ICC operating over the physiological membrane potential range. The mathematical model presented here extends our recently developed biophysically based pacemaker unit modeling framework by including mechanisms necessary for coordinating unitary potential events, such as a T-Type Ca²⁺ current, V_m-dependent K⁺ currents, and global Ca²⁺ diffusion. Model simulations produce spontaneously rhythmic slow wave depolarizations with an amplitude of 65 mV at a frequency of 17.4 cpm. Our model predicts that activity at the spatial scale of the pacemaker unit is fundamental for ICC slow wave generation, and Ca²⁺ influx from activation of the T-Type Ca²⁺ current is required for unitary potential entrainment. These results suggest that intracellular Ca²⁺ levels, particularly in the region local to the mitochondria and endoplasmic reticulum, significantly influence pacing frequency and synchronization of pacemaker unit discharge. Moreover, numerical investigations show that our ICC model is capable of qualitatively replicating a wide range of experimental observations.     

MICU1 Controls Both the Threshold and Cooperative Activation of the Mitochondrial Ca2+ Uniporter

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Dimerization of MICU Proteins Controls Ca2+ Influx through the Mitochondrial Ca2+ Uniporter

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A Mathematical Model for Extrachromosomal Heredity

During embryogeny the components of the cytoplasm of a zygote are subject to certain irregularities. This has been investigated with the aid of some probability models and distribution functions. For mitochondria, which are the most important cell components with respect to extra-chromosomal heredity, a four-phase model with computer programs was developed. The complete arithmetical results total 15,000 pages from a fast printer. For the jobs a CPU-time of 500 hours, using a SIEMENS 4004 system, was required.     

A Mathematical Model for Bacterial Chemotaxis

A differential equation describing the chemotactic migration of a bacterial population in a fixed exponential gradient of attractant has been integrated using the appropriate boundary conditions. The solution predicts an initial bacterial accumulation at the concentration “knee” with the final distribution of bacteria approaching a time-independent state. Specific additional experiments to obtain further data for a rigorous test of the theory are suggested.     

一个人体运动的数学模型

本文采用L-E法和铰分解法研究了人体运动的数学模型问题,给出了一种人体运动的规范建模方法。该方法适用于多种拓扑结构形式的人体运动（如空翻、步行、滑行等）,所得方程具有适合于计算机程式求解的特点。     

Kinetics of Mitochondrial Complementation

Mitochondrial complementation (enhancement of oxidative activity of mitochondrial occured when mitochondria of some inbrveds of eron were mixed in vitro. It was found that mixtures composed of various proportions of mitochondria of inbreds exhibited complementation. Extracts of mitochondria of one inbred did not promote complementation when they were added to infact mitochondria of inbreds exhihited complententation. Extracts of mitochondria of on einbred did not promote complementation when they were added to infact mitochondria of the second inbred. Serial dillutions of mixtures resulted in a rapid reduction of mitochondrial oxidation (QO₂ N) suggesting that intimale association between mitochondria was minimized by the dilution and that this decreased complementation. Similar dilutions of mitochondria from inbreds did not decrease their specific activity. Kinetics of mitochondrial oxidation were measured polarographically and it was found that complementation was measurable immediately (1 min) following the mixing. This suggested that physical contact between mitochondria was necessary for complementation.