Open-loop (feed-forward) and feedback control of coronary blood flow during exercise, cardiac pacing, and pressure changes.

A control system model was developed to analyze data on in vivo coronary blood flow regulation and to probe how different mechanisms work together to control coronary flow from rest to exercise, and under a variety of experimental conditions, including cardiac pacing and with changes in coronary arterial pressure (autoregulation). In the model coronary flow is determined by the combined action of a feedback pathway signal that is determined by the level of plasma ATP in coronary venous blood, an adrenergic open-loop (feed-forward) signal that increases with exercise, and a contribution of pressure-mediated myogenic control. The model was identified based on data from exercise experiments where myocardial oxygen extraction, coronary flow, cardiac interstitial norepinephrine concentration, and arterial and coronary venous plasma ATP concentrations were measured during control and during adrenergic and purinergic receptor blockade conditions. The identified model was used to quantify the relative contributions of open-loop and feedback pathways and to illustrate the degree of redundancy in the control of coronary flow. The results indicate that the adrenergic open-loop control component is responsible for most of the increase in coronary blood flow that occurs during high levels of exercise. However, the adenine nucleotide-mediated metabolic feedback control component is essential. The model was evaluated by predicting coronary flow in cardiac pacing and autoregulation experiments with reasonable fits to the data. The analysis shows that a model in which coronary venous plasma adenine nucleotides are a signal in local metabolic feedback control of coronary flow is consistent with the available data.

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

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

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

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

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

In cardiac mitochondria, matrix free Ca(2+) ([Ca(2+)]m) is primarily regulated by Ca(2+) uptake and release via the Ca(2+) uniporter (CU) and Na(+)/Ca(2+) exchanger (NCE) as well as by Ca(2+) buffering. Although experimental and computational studies on the CU and NCE dynamics exist, it is not well understood how matrix Ca(2+) buffering affects these dynamics under various Ca(2+) uptake and release conditions, and whether this influences the stoichiometry of the NCE. To elucidate the role of matrix Ca(2+) buffering on the uptake and release of Ca(2+), we monitored Ca(2+) dynamics in isolated mitochondria by measuring both the extra-matrix free [Ca(2+)] ([Ca(2+)]e) and [Ca(2+)]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, [Ca(2+)]e and [Ca(2+)]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 Ca(2+)-induced changes in mitochondrial bioenergetics. Our [Ca(2+)]e and [Ca(2+)]m measurements demonstrate that Ca(2+) uptake and release do not show reciprocal Ca(2+) dynamics in the extra-matrix and matrix compartments. This salient finding is likely caused by a dynamic Ca(2+) buffering system in the matrix compartment. The Na(+)- induced Ca(2+) release demonstrates an electrogenic exchange via the NCE by excluding an electroneutral exchange. Mitochondrial bioenergetics were only transiently affected by Ca(2+) uptake in the presence of large amounts of CaCl2, but not by Na(+)- induced Ca(2+) release.

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 Eyring's 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.

Detailed kinetics and regulation of mammalian 2-oxoglutarate dehydrogenase.

BACKGROUND: Mitochondrial 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 (Ca(2+) and Mg(2+)). RESULTS: A 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. CONCLUSIONS: The 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 Ca(2+) uniporter is the primary influx pathway for Ca(2+) into respiring mitochondria, and hence plays a key role in mitochondrial Ca(2+) homeostasis. Though the mechanism of extra-matrix Ca(2+) dependency of mitochondrial Ca(2+) uptake has been well characterized both experimentally and mathematically, the mechanism of membrane potential (ΔΨ) dependency of mitochondrial Ca(2+) uptake has not been completely characterized. In this paper, we perform a quantitative reevaluation of a previous biophysical model of mitochondrial Ca(2+) uniporter that characterized the possible mechanism of ΔΨ dependency of mitochondrial Ca(2+) uptake. Based on a model simulation analysis, we show that model predictions with a variant assumption (Case 2: external and internal Ca(2+) binding constants for the uniporter are distinct), that provides the best possible description of the ΔΨ dependency, are highly sensitive to variation in matrix [Ca(2+)], 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 Ca(2+) 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 Ca(2+) binding constants for the uniporter may be equal (Case 1). The model predictions in this case are insensitive to variation in matrix [Ca(2+)] 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 Ca(2+) translocation via the uniporter by exclusively redefining the biophysical parameters associated with the free-energy barrier of Ca(2+) 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 Ca(2+) and ΔΨ dependencies of mitochondrial Ca(2+) uptake. In addition, the model is insensitive to variation in matrix [Ca(2+)], predicting relatively stable physiological operation. The model is critical in developing mechanistic, integrated models of mitochondrial bioenergetics and Ca(2+) handling.

A biophysically based mathematical model for the kinetics of mitochondrial Na+-Ca2+ antiporter.

Sodium-calcium antiporter is the primary efflux pathway for Ca(2+) in respiring mitochondria, and hence plays an important role in mitochondrial Ca(2+) homeostasis. Although experimental data on the kinetics of Na(+)-Ca(2+) antiporter are available, the structure and composition of its functional unit and kinetic mechanisms associated with the Na(+)-Ca(2+) exchange (including the stoichiometry) remains unclear. To gain a quantitative understanding of mitochondrial Ca(2+) homeostasis, a biophysical model of Na(+)-Ca(2+) 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(+):1Ca(2+) 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 Ca(2+) handling and bioenergetics to understand the mechanisms by which Ca(2+) plays a role in mitochondrial signaling pathways and energy metabolism.

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.

Desynchronized vasomotion and desynchronized fiber activation pattern enhance oxygenation in a model of skeletal muscle.

Although the full physiological significance of vasomotion is still debated, it is generally thought to have a role in optimizing tissue oxygenation parameters. We study the effect of vasomotion rhythm in skeletal muscle on oxygen transport using a computational model. The model is used: (i) to test a novel hypothesis that "vasomotors" form a chemical network in which the rhythm adapts to meet oxygen demand in skeletal muscle and (ii) to study the contribution of desynchronized/chaotic vasomotion in optimizing oxygen delivery to skeletal muscle. We formulate a 2D grid model of skeletal muscle consisting of an interleaved arrangement of vessels and muscle fibers fired by a motor neuronal network. The vasomotors too form a network interacting by chemical means. When positive (negative) synapses dominate, the neuronal network exhibits synchronized (desynchronized) activity. Similarly, when positive (negative) chemical interactions dominate, the vessels exhibit synchronized (desynchronized) activity. Optimal oxygenation is observed when both neuronal network and vasomotor network exhibit desynchronous activity. Muscle oxygenation is thought to result by interactions between the fiber/neuron network and the vessel network; optimal oxygenation depends on precise rhythm-related conditions on the two networks. The model provides interesting insights into the phenomenon of muscle fatigue.

A computational model that links non-periodic vasomotion to enhanced oxygenation in skeletal muscle.

We propose a model of a capillary network in which chaotic capillary activity is crucial for efficient oxygenation of a muscle fiber. Tissue oxygenation by microcirculation is controlled by a complex pattern of opening and closing of precapillary sphincters, a phenomenon known as vasomotion. We model the individual precapillary sphincter as a non-linear oscillator that exhibits perfectly periodic vasomotion in isolation. The precapillary sphincters surrounding an active fiber are considered as a network; specific modes of interaction within this network result in complex patterns of vasomotion. In our model, efficient oxygenation of the fiber depends crucially on the mode of interaction among the vasomotions of the individual capillaries. Network interactions that lead to chaotic vasomotion are found to be essential for meeting the tissue oxygen demands precisely. Interactions that cause regular rhythmic patterns of vasomotion fail to meet oxygenation demands accurately.

Effect of chaotic vasomotion in skeletal muscle on tissue oxygenation.

Vasomotion refers to spontaneous variations in the lumen size of small vessels, with a plausible role in regulation of various aspects of microcirculation. We propose a computational model of vasomotion in skeletal muscle in which the pattern of vasomotion is shown to critically determine the efficiency of oxygenation of a muscle fiber. In this model, precapillary sphincters are modeled as nonlinear oscillators. We hypothesize that these sphincters interact via exchange of vasoactive substances. As a consequence, vasomotion is described as a phenomenon associated with a network of nonlinear oscillators. As a specific instance, we model the vasomotion of precapillary sphincters surrounding an active fiber. The sphincters coordinate their rhythms so as to minimize oxygen deficit in the fiber. Our modeling studies indicate that efficient oxygenation of the fiber depends crucially on the mode of interaction among the vasomotions of individual sphincters. While chaotic forms of vasomotion enhanced oxygenation, regular patterns of vasomotion failed to meet the oxygenation demand accurately.