Ranjan K. Pradhan

Characterization of Mg2+ Inhibition of Mitochondrial Ca2+ Uptake by a Mechanistic Model of Mitochondrial Ca2+ Uniporter

Ca(2+) is an important regulatory ion and alteration of mitochondrial Ca(2+) homeostasis can lead to cellular dysfunction and apoptosis. Ca(2+) is transported into respiring mitochondria via the Ca(2+) uniporter, which is known to be inhibited by Mg(2+). This uniporter-mediated mitochondrial Ca(2+) transport is also shown to be influenced by inorganic phosphate (Pi). Despite a large number of experimental studies, the kinetic mechanisms associated with the Mg(2+) inhibition and Pi regulation of the uniporter function are not well established. To gain a quantitative understanding of the effects of Mg(2+) and Pi on the uniporter function, we developed here a mathematical model based on known kinetic properties of the uniporter and presumed Mg(2+) 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 Eyrings free energy barrier theory for interconversion. The model satisfactorily describes a wide variety of experimental data sets on the kinetics of mitochondrial Ca(2+) uptake. The model also appropriately depicts the inhibitory effect of Mg(2+) on the uniporter function, in which Ca(2+) uptake is hyperbolic in the absence of Mg(2+) and sigmoid in the presence of Mg(2+). The model suggests a mixed-type inhibition mechanism for Mg(2+) inhibition of the uniporter function. This model is critical for building mechanistic models of mitochondrial bioenergetics and Ca(2+) handling to understand the mechanisms by which Ca(2+) mediates signaling pathways and modulates energy metabolism.

A database of thermodynamic quantities for the reactions of glycolysis and the tricarboxylic acid cycle.

Analysis of biochemical systems requires reliable and self-consistent databases of thermodynamic properties for biochemical reactions. Here a database of thermodynamic properties for the reactions of glycolysis and the tricarboxylic acid cycle is developed from measured equilibrium data. Species-level free energies of formation are estimated on the basis of comparing thermodynamic model predictions for reaction-level equilibrium constants to previously reported data obtained under different experimental conditions. Matching model predictions to the data involves applying state corrections for ionic strength, pH, and metal ion binding for each input experimental biochemical measurement. By archiving all of the raw data, documenting all model assumptions and calculations, and making the computer package and data available, this work provides a framework for extension and refinement by adding to the underlying raw experimental data in the database and/or refining the underlying model assumptions. Thus the resulting database is a refinement of preexisting databases of thermodynamics in terms of reliability, self-consistency, transparency, and extensibility.

Dynamic buffering of mitochondrial Ca2+ during Ca2+ uptake and Na+-induced Ca2+ release

In cardiac mitochondria, matrix free Ca2+ ([Ca2+]m) is primarily regulated by Ca2+ uptake and release via the Ca2+ uniporter (CU) and Na+/Ca2+ exchanger (NCE) as well as by Ca2+ buffering. Although experimental and computational studies on the CU and NCE dynamics exist, it is not well understood how matrix Ca2+ buffering affects these dynamics under various Ca2+ uptake and release conditions, and whether this influences the stoichiometry of the NCE. To elucidate the role of matrix Ca2+ buffering on the uptake and release of Ca2+, we monitored Ca2+ dynamics in isolated mitochondria by measuring both the extra-matrix free [Ca2+] ([Ca2+]e) and [Ca2+]m. A detailed protocol was developed and freshly isolated mitochondria from guinea pig hearts were exposed to five different [CaCl2] followed by ruthenium red and six different [NaCl]. By using the fluorescent probe indo-1, [Ca2+]e and [Ca2+]m were spectrofluorometrically quantified, and the stoichiometry of the NCE was determined. In addition, we measured NADH, membrane potential, matrix volume and matrix pH to monitor Ca2+-induced changes in mitochondrial bioenergetics. Our [Ca2+]e and [Ca2+]m measurements demonstrate that Ca2+ uptake and release do not show reciprocal Ca2+ dynamics in the extra-matrix and matrix compartments. This salient finding is likely caused by a dynamic Ca2+ buffering system in the matrix compartment. The Na+- induced Ca2+ release demonstrates an electrogenic exchange via the NCE by excluding an electroneutral exchange. Mitochondrial bioenergetics were only transiently affected by Ca2+ uptake in the presence of large amounts of CaCl2, but not by Na+- induced Ca2+ release.

Detailed kinetics and regulation of mammalian 2-oxoglutarate dehydrogenase

BackgroundMitochondrial 2-oxoglutarate (α-ketoglutarate) dehydrogenase complex (OGDHC), a key regulatory point of tricarboxylic acid (TCA) cycle, plays vital roles in multiple pathways of energy metabolism and biosynthesis. The catalytic mechanism and allosteric regulation of this large enzyme complex are not fully understood. Here computer simulation is used to test possible catalytic mechanisms and mechanisms of allosteric regulation of the enzyme by nucleotides (ATP, ADP), pH, and metal ion cofactors (Ca2+ and Mg2+).ResultsA model was developed based on an ordered ter-ter enzyme kinetic mechanism combined with con-formational changes that involve rotation of one lipoic acid between three catalytic sites inside the enzyme complex. The model was parameterized using a large number of kinetic data sets on the activity of OGDHC, and validated by comparison of model predictions to independent data.ConclusionsThe developed model suggests a hybrid rapid-equilibrium ping-pong random mechanism for the kinetics of OGDHC, consistent with previously reported mechanisms, and accurately describes the experimentally observed regulatory effects of cofactors on the OGDHC activity. This analysis provides a single consistent theoretical explanation for a number of apparently contradictory results on the roles of phosphorylation potential, NAD (H) oxidation-reduction state ratio, as well as the regulatory effects of metal ions on ODGHC function.

Characterization of Membrane Potential Dependency of Mitochondrial Ca2+ Uptake by an Improved Biophysical Model of Mitochondrial Ca2+ Uniporter

Mitochondrial Ca2+ uniporter is the primary influx pathway for Ca2+ into respiring mitochondria, and hence plays a key role in mitochondrial Ca2+ homeostasis. Though the mechanism of extra-matrix Ca2+ dependency of mitochondrial Ca2+ uptake has been well characterized both experimentally and mathematically, the mechanism of membrane potential (ΔΨ) dependency of mitochondrial Ca2+ uptake has not been completely characterized. In this paper, we perform a quantitative reevaluation of a previous biophysical model of mitochondrial Ca2+ uniporter that characterized the possible mechanism of ΔΨ dependency of mitochondrial Ca2+ uptake. Based on a model simulation analysis, we show that model predictions with a variant assumption (Case 2: external and internal Ca2+ binding constants for the uniporter are distinct), that provides the best possible description of the ΔΨ dependency, are highly sensitive to variation in matrix [Ca2+], indicating limitations in the variant assumption (Case 2) in providing physiologically plausible description of the observed ΔΨ dependency. This sensitivity is attributed to negative estimate of a biophysical parameter that characterizes binding of internal Ca2+ to the uniporter. Reparameterization of the model with additional nonnengativity constraints on the biophysical parameters showed that the two variant assumptions (Case 1 and Case 2) are indistinguishable, indicating that the external and internal Ca2+ binding constants for the uniporter may be equal (Case 1). The model predictions in this case are insensitive to variation in matrix [Ca2+] but do not match the ΔΨ dependent data in the domain ΔΨ≤120 mV. To effectively characterize this ΔΨ dependency, we reformulate the ΔΨ dependencies of the rate constants of Ca2+ translocation via the uniporter by exclusively redefining the biophysical parameters associated with the free-energy barrier of Ca2+ translocation based on a generalized, non-linear Goldman-Hodgkin-Katz formulation. This alternate uniporter model has all the characteristics of the previous uniporter model and is also able to characterize the possible mechanisms of both the extra-matrix Ca2+ and ΔΨ dependencies of mitochondrial Ca2+ uptake. In addition, the model is insensitive to variation in matrix [Ca2+], predicting relatively stable physiological operation. The model is critical in developing mechanistic, integrated models of mitochondrial bioenergetics and Ca2+ handling.

Modeling the calcium sequestration system in isolated guinea pig cardiac mitochondria.

Under high Ca2+ load conditions, Ca2+ concentrations in the extra-mitochondrial and mitochondrial compartments do not display reciprocal dynamics. This is due to a paradoxical increase in the mitochondrial Ca2+ buffering power as the Ca2+ load increases. Here we develop and characterize a mechanism of the mitochondrial Ca2+ 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+/Ca2+ cycle. The integrated model reproduces the Ca2+ 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 Ca2+ concentration of Ca2+ loaded mitochondria appear significantly mitigated relative to the corresponding extra-mitochondrial Ca2+ concentration changes after Ca2+ efflux is initiated. The integrated model was corroborated by simulating the set-point phenomenon. The computational results support the conclusion that the Ca2+ sequestration system is composed of at least two classes of Ca2+ buffers. The first class represents prototypical Ca2+ buffering, and the second class encompasses the complex binding events associated with the formation of amorphous calcium phosphate. With the Ca2+ 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 Ca2+ overload.

Carrier-Mediated Transport Through Biomembranes

In living cells, the uptake and extrusion of hydrophilic molecules are generally governed by specialized membrane proteins known as transporters or carriers. Unlike pores or channels, they undergo enzyme-like binding and conformational changes to promote energetically downhill transport of their specific molecules. Elucidation of the catalytic properties of carriers by a combination of experimental measurements of carrier fluxes and analysis of those data by kinetic models is a fundamental endeavor in this field. This chapter provides a systematic guideline towards the formulation and analysis of kinetic models of carrier-mediated transport across biomembranes. Detailed analyses are provided for the transport of Ca 2+ Ca 2 + ions into the mitochondrial matrix via the Ca 2+ Ca 2 + uniporter located in the inner mitochondrial membrane. A brief introduction is also given for the kinetic treatment of cotransporters and antiporters. The analyses presented in this chapter can be easily extended to study the kinetics of carrier-mediated ion and metabolite transport in general.

A model of indispensability of a large glial layer in cerebrovascular circulation

We formulate the problem of oxygen delivery to neural tissue as a problem of association. Input to a pool of neurons in one brain area must be matched in space and time with metabolic inputs from the vascular network via the glial network. We thus have a model in which neural, glial, and vascular layers are connected bidirectionally, in that order. Connections between neuro-glial and glial-vascular stages are trained by an unsupervised learning mechanism such that input to the neural layer is sustained by the precisely patterned delivery of metabolic inputs from the vascular layer via the glial layer. Simulations show that the capacity of such a system to sustain patterns is weak when the glial layer is absent. Capacity is higher when a glial layer is present and increases with the layer size. The proposed formulation of neurovascular interactions raises many intriguing questions about the role of glial cells in cerebral circulation.

Modeling the Paradoxical Increase in Mitochondrial Calcium Buffering Power as Matrix Calcium Increases

Mitochondria possess the remarkable ability to take up a massive, but finite, amount of Ca2+ before their primary function is compromised. Surprisingly, there has been very little progress in mathematically characterizing this phenomenon. We propose here a novel approach that implicitly models the known matrix Ca2+ buffering proteins and resultant Ca2+ sequestration in order to explain our recent experimental data from isolated guinea pig mitochondria. The model consists of our corroborated models of the TCA cycle and oxidative phosphorylation integrated with our previous models of the Na+/Ca2+ cycle, a unique model of the Ca2+ uniporter coupled to the putative rapid-mode of Ca2+ uptake, and a Ca2+-matrix buffering system. The model reproduces both the mitochondrial matrix and the extra-mitochondrial [Ca2+] dynamics observed when a bolus of Ca2+ is administered to the mitochondria followed by a bolus of Na+. These results help elucidate why the reported change in matrix [Ca2+] of Ca2+-loaded mitochondria appears significantly mitigated relative to the corresponding extra-mitochondrial [Ca2+] dynamics when Ca2+ efflux is initiated. Future work entails using the model to propose novel experiments in order to dissect the current model into components that explicitly describes these phenomena in a biophysically detailed manner. With the mitochondrial Ca2+-sequestration system mathematically defined, computer simulations can then be used to design innovative therapeutics aimed at addressing the myriad of complications that arise due to cytosolic Ca2+ overload.

Increases in Extra-Matrix Mg2+ Inhibit Ca2+ Uptake via the Ca2+-Uniporter but do not Acutely Alter State 3 Respiration

Magnesium is essential for all energy-dependent transport systems, glycolysis, and oxidative energy metabolism. In addition, Mg2+ binds to ADP and ATP, regulating their availability. It also controls matrix free Ca2+ concentration (m[Ca2+]) through its inhibitory effect on the mitochondrial Ca2+-uniporter. Here we investigated the interplay between Ca2+ and Mg2+ and their roles in regulating mitochondrial bioenergetics. Mitochondria from guinea pig hearts were isolated by differential centrifugation, incubated with fluorescent dyes indo-1-AM for m[Ca2+], furaptra-AM for m[Mg2+], or DMSO. Ca2+-uptake in mitochondria, which were suspended in respiration buffer containing EGTA, 0, 0.5 or 2 mM MgCl2, and 0.5 mM pyruvic acid, was measured in response to 0, 0.25 and 0.50 mM CaCl2. In separate experiments Mg2+ uptake was measured after adding 0, 0.5 and 2 mM MgCl2. O2 consumption was measured using a Clark-2 O2-electrode during states 2 through 4 respiration, i.e. before, during and after adding 250 µM ADP. Addition of MgCl2 to the buffer inhibited Ca2+-uptake in a dose-dependent manner. 0.25 mM CaCl2 increased m[Ca2+] from 59 nM to 325, 131 and 93 nM Ca2+ in the 0, 0.5 and 2 mM MgCl2 groups, respectively, whereas 0.50 mM CaCl2 increased m[Ca2+] to 1045, 360 and 279 nM, respectively. Adding 0.5 mM MgCl2 did not increase m[Mg2+], but 2 mM MgCl2 increased m[Mg2+] slowly from 0.35 to 0.55 mM over ten minutes. State 3 respiration was not different among the three MgCl2 groups, but state 4 was faster with MgCl2 present. We conclude that the inhibitory effect of extra-matrix Mg2+ on Ca2+-uptake is close to maximum in the low range of normal cytosolic [Mg2+], and that mitochondrial Mg2+ influx by itself is not fast enough to acutely modulate state 3 respiration.