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Regulation of Cardiac Muscle Contraction

Modular regulation analysis of heart contraction: application to in situ demonstration of a direct mitochondrial activation by calcium in beating heart

¹Résonance Magnétique des Systèmes Biologiques, UMR5536 Centre National de la Recherche Scientifique- Université Victor Segalen Bordeaux 2, Bordeaux, France; and ²U441, Athérosclérose, Pessac, France

Submitted 16 March 2006 ; accepted in final form 22 May 2006

	ABSTRACT

TOP ABSTRACT EXPERIMENTAL PROCEDURES RESULTS AND DISCUSSION GRANTS REFERENCES

 
Heart contraction is characterized by the absence of changes in energetic intermediates in response to a large increase of activity. Until now no experimental approach could address this question concerning the intact beating heart. Ca²⁺ plays a crucial role in the excitation-contraction coupling, and in vitro studies have evidenced that Ca²⁺ may also directly activate mitochondrial oxidative phosphorylation. We applied our new in situ modular control and regulation analysis on isolated beating rat heart perfused under two different calcium concentrations with pyruvate or glucose as the substrate. Modular control analysis demonstrated experimentally that, although control by energy production was slightly higher under glucose conditions compared with pyruvate, most of the control of heart contraction resides in energy utilization. This behavior is the direct consequence of the high sensitivity (elasticity) of the energy producer processes to ATP utilization. Interestingly, the increase in heart metabolic rate by Ca²⁺ did not significantly change the pattern of control distribution. The regulation analysis performed under the two calcium conditions demonstrated a balanced activation of myofibrils ATPases, and mitochondrial ATP synthesis in response to Ca²⁺ increase. This first study demonstrates in situ the hypothesis that the energetic adequation in heart contraction is mediated by a parallel activation of both processes of energy production and utilization by Ca²⁺. The results presented here show that modular control and regulation analyses allow in situ study of internal regulations in intact beating heart energetics and function and may now be applied to heart dysfunctions and therapeutic effects.

rat perfused heart; ³¹P-labeled magnetic resonance spectroscopy; calcium signaling; metabolic control analysis; systems biology

The essential role of calcium in the coupling process from electrical excitation of the myocyte to contraction in heart is now well established and appears as a good lead to a better understanding of excitation-contraction coupling (3, 5, 27). Ca²⁺ is the direct activator of the myofilaments, and therefore contraction depends on free intracellular calcium concentration ([Ca²⁺]_i). Indeed, myocyte mishandling of Ca²⁺ is a central cause of contractile dysfunctions (7). In heart, rhythmic contraction is the consequence of transient changes in [Ca²⁺]_i. Furthermore, there is now increasing evidence that Ca²⁺ has multiple effects on other intracellular processes and particularly on several mitochondrial functions (19, 23, 32), including dehydrogenases, ATP synthase, and, more recently, the binding of PCr-kinase with mitochondrial membranes (34). Thus, activation of mitochondrial oxidative phosphorylation during Ca²⁺ transient may now also be considered as an important mechanism in excitation-contraction coupling in heart (25–27) (Fig. 1). Therefore, in heart, the electrical excitation of the myocyte may result in a parallel activation by Ca²⁺ of both energy-producing and energy-consuming processes (3, 5, 12, 13, 25–27). This mechanism would be fundamental in the capacity for the heart to dramatically increase contraction without any change in energetic intermediates. Until now, while theoretical studies have demonstrated the necessity for such parallel activation to occur in heart contraction (25–27), no experimental evidence could be obtained. One of the challenges for the future is to develop integrated in situ experimental approaches to evaluate such complex biological processes and to lead to a comprehensive understanding of basic cellular properties (3).

View larger version (37K): [in this window] [in a new window]   Fig. 1. Parallel activation of mitochondrial oxidative phosphorylation and myofilaments by Ca2+. Ca2+ activates not only myofibrils ATPases but also key mitochondrial dehydrogenases, ATP synthase, and promotes association of the mitochondrial creatine-kinase with the ATP/ADP translocator. PCr, phosphocreatine; Cr, creatine.

Experimentally, the full analysis requires the measurement of all fluxes and intermediates involved. Since our main objective was to develop potential therapeutic applications, we decided to address this crucial point in situ and noninvasively on intact beating heart: the Langendorff-perfused rat heart (see EXPERIMENTAL PROCEDURES). We previously described the first application to intact heart (12) in which we defined two modules: the producer and the consumer of the energetic intermediates (Fig. 2). Energetic intermediates in heart and muscle are phosphorylated molecules (PCr, ATP, ADP, and P_i) that could be kinetically studied using ³¹P-labeled NMR (12), whereas energy flux could be estimated by measuring heart contractile activity (see EXPERIMENTAL PROCEDURES) and/or total heart oxygen consumption (12). In working heart, the ATP consumer module comprises all the ATP consuming processes occurring during contraction (mainly myosin ATPases and calcium reuptake by sarcoplasmic reticulum and cell membrane). As for the producer, we used two different substrates (glucose and pyruvate) with the consequence of studying two different modules, including glycolysis enzymes and mitochondria (with glucose in the absence of pyruvate) or only mitochondria (in the presence of pyruvate, directly oxidizable by mitochondria).

View larger version (10K): [in this window] [in a new window]   Fig. 2. System definition for modular control analysis (MoCA) of perfused rat heart. We defined the system of contraction as two modules connected by the pool of energetic intermediates. The producer module comprises all the metabolic steps included from substrate supply (including oxygen supply) to mitochondrial production of PCr. The producer is therefore different when pyruvate (feeds directly to mitochondria) or glucose (includes glycolysis) is used as substrate. The consumer module comprises all the steps consuming ATP/PCr linked to contractile activity (contraction of myofilaments and ATP used for Ca2+ recapture). The elasticities of each module toward the intermediates (PCr as representative) are calculated after inducing slight changes in steady-state contraction induced by alteration of the other module. Cyanide (KCN) was chosen to specifically inhibit mitochondrial cytochrome oxidase and measure consumer elasticity (PCrC) as the response of the system to the relative PCr concentration change observed. On the other hand, change in internal balloon pressure was used to increase contractility and measure producer elasticity (PCrP).

	EXPERIMENTAL PROCEDURES

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Langendorff Perfusion and NMR Measurements

Male Sprague-Dawley rats (350–400 g) were used. Rats were anesthetized with 40 mg of pentobarbital injected intraperitoneally. The thorax was opened, and hearts were rapidly excised, immediately cooled in iced Krebs buffer, and perfused by an aortic cannula at constant pressure (100 mmHg) with Krebs-Henseleit solution (95% O₂-5% CO₂, pH 7.35, temperature 37°C) perfused using a solution containing 10 mmol/l Na-pyruvate or 16.7 mmol/l glucose as substrate, as described previously (14). Depending on the experiments, actual free calcium concentration was set to 2.0 or 3.5 mmol/l. Left ventricle systolic pressure of unpaced heart was measured under isovolumic conditions of contraction by a latex balloon inserted into the left ventricle and connected to a pressure transducer. Mechanical performance was evaluated as the product of heart frequency and developed pressure [rate-ventricular pressure product (RPP) in mmHg·beat·min^–1]. The perfused heart was placed into a 20-mm NMR tube inserted into a 9.4-T super-conducting magnet equipped with a 20-mm bore (Bruker DPX400 Avance) for ³¹P-labeled NMR spectroscopy. To eliminate endogenous substrates and remaining anesthetics, 20 min were allowed for stabilization of heart activity before any measurement was carried out (28, 29). Except for specific modifications for MoCA application (see below), all experimental procedures have been described previously (14).

For the study of steady-state modifications in the framework of MoCA, four NMR spectra (5-min duration time for each spectrum) were acquired before modulation was applied, then after a transition time equivalent to one spectrum (5 min) four new spectra (20 min) were recorded. Each steady state (before and after modulation) was characterized by the mean values of the four spectra for RPP and phosphorylated compounds.

MoCA

We previously described our new approach of intact perfused heart energetics using MoCA (12). By using this approach, complex systems may be simplified by grouping reactions and reactants into large modules connected by a small number of explicit intermediates (10). We applied this to the study of energy transfer during contraction in heart (or muscle) by defining two modules (so-called producer and consumer) linked by several obligatory energetic intermediates (see Fig. 2). In working heart, as ATP concentration was unchanged under all physiological conditions, PCr was chosen as the representative intermediate between energy production and consumption (12). The producer module is then defined as all the steps from substrate and oxygen supply to mitochondrial PCr production through the PCr-CK system (Fig. 1), therefore it includes glycolysis when glucose is used as substrate instead of pyruvate directly oxidized by mitochondria. The consumer module comprises all the ATP consuming processes occurring during contraction (myosin ATPases and calcium reuptake by sarcoplasmic reticulum and cell membrane) (12). Control and regulation of our modular system can be analyzed using MoCA, as long as intermediate concentrations and module activities (flux) can be studied. Continuous ³¹P-labeled NMR spectroscopy gives access to all energetic intermediates, including our intermediate PCr. The energetic flux through the system was simultaneously assessed as the contractile activity measured by heart RPP (see above).

Control analysis. Following the principles of top-down analysis, control coefficients over the energy flux in heart contraction were calculated from the overall elasticities of the producer and consumer modules toward the intermediate PCr (9). In this study, the elasticity (_PCr^Module) of each module toward the intermediate may be calculated from the changes in flux (RPP) and PCr concentration ([PCr]) induced by any slight modulation of the other module (see Ref. 12 for details). Experimentally, to measure consumer elasticity (_PCr^C), two low concentrations of cyanide (0.1 and 0.2 mM KCN) were used to progressively inhibit mitochondrial cytochrome oxidase. Then the evolution in RPP was plotted as a function of [PCr], and _PCr^C was calculated from the relative slope of this curve

Producer elasticity (_PCr^P) was measured the same way, but changes in [PCr] and RPP were induced by increasing internal balloon volume (from 100 to 150 µl) to trigger increased heart contractility. The elasticity was calculated by using the previous equation.

Elasticities were calculated for each heart, and results are expressed as the mean value of all experiments (see Table 2). The control coefficients of both modules (C_P^Flux and C_C^Flux) were thus calculated from experimentally measured _PCr^C and _PCr^P, according to summation and connectivity theorems (21).

As for any effector, data required for the complete regulation analysis of the effect of increasing calcium concentration from 2.0 to 3.5 mM are 1) the complete control analysis at low calcium concentration (elasticities toward the intermediates and flux control coefficients) corresponding to the starting conditions; and 2) the global effect of calcium increase on the flux and the intermediates expressed as relative changes in RPP and [PCr].

The direct effect of calcium increase on each Module is different from the total measured effect in that module activity is also affected by indirect changes in the intermediate PCr due to concomitant modification of the activity of the other module. For each module, the indirect effect due to this relative change in PCr may be easily deduced from elasticity analysis; it is the product of the relative change in PCr and the module's elasticity toward PCr.

Therefore, the direct effect of calcium on each module [defined as the integrated elasticity (IE)] (2, 8) is calculated as the difference between the total measured effect of the calcium increase on contraction /RPP) and the previously calculated indirect effect.

The final important parameter for the description of the regulation of heart contraction by calcium is the global response [or integrated response (IR)] (2, 8), which describes quantitatively how activation of each module by calcium influences total heart inotropic response. By definition, the control coefficient links the change in module activity to the change in the flux. Therefore, the integrated response for each module is the product of the control coefficient and the direct effect on this very module.

Statistical Analysis

Experimental values are reported as means ± SD for the number of independent rat hearts. Statistical comparisons between groups (glucose vs. pyruvate, high vs. low calcium concentrations) were performed by ANOVA. The error associated with calculated control coefficients (C), IE, and responses coefficients (IR) was determined by using Monte Carlo simulations (1). Experimental values of PCr/PCr and RPP/RPP were simulated from observed means and SDs. Simulations were based on a normal distribution with a mean equal to the mean of the experimental points and an SD equal to the SD of the experimental points. , C, IE, and IR were calculated as described in above sections from simulated values.

	RESULTS AND DISCUSSION

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MoCA

There are two ways of modulating the strength of cardiac contraction: by altering the amplitude or duration of the cytosolic Ca²⁺ transient, and by altering the sensitivity of the myofilaments to calcium (7). Experimentally, the classical way to modulate cytosolic Ca²⁺ transients is to change the calcium concentration in the perfusate, which induces different contractile activities of isolated perfused heart. It has also been shown that myocardial oxygen consumption and contractile activity are proportional to cytosolic Ca²⁺ concentration (3, 35). We have previously shown that under our experimental conditions (2 mM and 3.5 mM Ca²⁺) the contractile activity was proportional to the oxygen consumption of the heart, suggesting a constant energetic efficiency of heart contraction over a large range of activity (12). Therefore, there is a linear relationship between Ca²⁺ concentration in the perfusate and cytosolic [Ca²⁺] (3), and by using these two different Ca²⁺ concentrations, we determined two different steady-state levels of heart activities characterized by two cytosolic [Ca²⁺]. The comparison of these two conditions by applying MoCA allows the quantitative description of the effect of cytosolic Ca²⁺ on heart contraction.

Table 1 presents the physiological state of the perfused rat hearts under the four conditions studied here. Main observations deal with the classical decreased PCr concentration when glucose was used as substrate associated with an increase in free P_i concentration (not shown). The first step in the analysis is the determination of the kinetic interactions (elasticities) of the two modules to PCr concentration or, in other words, how each module responds to small changes in PCr (see EXPERIMENTAL PROCEDURES). These changes (not physiologically occurring in heart) were artificially provoked by inhibiting or activating the other module (see Fig. 2). To determine producer response to PCr changes, myofilament Ca²⁺ sensitivity (consumer) was enhanced dynamically by stretching slightly the myofilaments (7) (Fig. 3A). This was carried out by increasing the volume of the balloon inserted in the left ventricle (as when the heart fills with blood) otherwise used to continuously measure heart contractile activity. The resulting stronger contraction is mainly due to the transverse filament lattice compression that occurs on stretch, which enhances the actin-myosin interaction (7, 17). This is the mechanism by which the heart adjusts to diastolic filling, i.e., the Frank-Starling response. It has been shown that the rapid increase in twitch force after muscle stretch was not associated with a rise in calcium transient (24, 31) or a modification of calcium recirculation (33). In this study, the experiment was started under low pressure conditions, and the balloon was further inflated to normal pressure. This increase in balloon pressure induced a small but measurable change in PCr concentration (Fig. 3A) associated with an increase in heart contractile activity, reflecting the response of the producer module to the induced change in PCr (Table 2). As to the producer, as any specific mitochondrial inhibitor will do, cyanide (at very low concentration) was chosen for this study to determine consumer elasticity to PCr (Fig. 3B). Under all PCr modulation experiments, the absence of any shift of P_i peak indicated the absence of pH change.

View larger version (23K): [in this window] [in a new window]   Fig. 3. Typical changes in 31P-labeled NMR spectra of perfused rat liver induced by increase in balloon pressure from low to normal (A) and addition of 0.1 mM KCN to perfusate (B). On this representative experiment, isolated rat hearts were perfused using pyruvate as substrate and in the presence of 3.5 mM calcium. NTP, nucleoside triphosphate (essentially ATP); , , and , position of the three phosphate atoms; Pcr, phosphocreatine; Pi, inorganic phosphate.

These experimental data were used to calculate the MoCA coefficients (see EXPERIMENTAL PROCEDURES) reported in Table 3. The high sensitivity of the producer is now expressed as an important absolute value of the elasticity coefficient, and the converse is true for the consumer. The constraint introduced by using glucose as substrate instead of pyruvate resulted in a significant decrease in the elasticity (sensitivity) of the producer to changes in PCr.

Regulation Analysis

Taking into account that Ca²⁺ may possibly directly activate both the producer and the consumer of PCr/ATP, we need to discriminate these specific effects from indirect effects induced by internal changes in metabolites (i.e., PCr). All of the information is available from the MoCA carried out under two different Ca²⁺ conditions. These indirect effects may be deduced from the total measured effect induced by Ca²⁺ activation (RPP and PCr concentration changes) and calculated elasticities of each module toward PCr (see EXPERIMENTAL PROCEDURES, results are presented in Fig. 4). Then direct effect of Ca²⁺ on each module (integrated elasticity) may be calculated as the total effect observed on contraction minus the indirect effects. As seen before, the paradigm of heart contraction is that only slight changes in PCr are associated with activity increase (30). Therefore, very small indirect effects of Ca²⁺ are involved. The results presented in Fig. 4 clearly show that a direct mitochondrial activation occurs in heart in response to calcium increase. With pyruvate as respiratory substrate, this direct mitochondrial activation by Ca²⁺ is equivalent to myofilament activation itself (Fig. 4A). However, with glucose as substrate, producer activation is significantly lower than myofilaments activation (Fig. 4B). These results may be explained by an absence of activation of glycolysis by Ca²⁺, since under these conditions glycolysis is part of the producer as pyruvate supplier to mitochondria.

View larger version (32K): [in this window] [in a new window]   Fig. 4. MoCA of the effects of calcium concentration changes in the perfusion medium on heart bioenergetics under pyruvate and glucose conditions. Calcium effects on both PCr producer and consumer modules were calculated as described in EXPERIMENTAL PROCEDURES. Direct effect refers to the Integrated elasticity (total effect minus indirect effect), and global response refers to the response coefficient of each module on the increase in contraction induced by calcium increase. The size of the arrows is proportional to calcium effect, and the figures represent the effect expressed as %change from starting condition (2.0 mM Ca2+). Pyruvate: (actual values ± error calculated from 500 Monte-Carlo simulations). Direct effect 41.4 ± 21.3 and 36.4 ± 1.8, global effect 3.2 ± 1.7 and 33.6 ± 1.7, and indirect effect –4.7 ± 0.2 and 0.4 ± 0.02. Glucose: direct effect 11.4 ± 3.0 and 21.5 ± 3.0, global effect 2.4 ± 0.6 and 17.0 ± 2.3, and indirect effect 8.0 ± 0.6 and –2.2 ± 0. 2.

In conclusion, this study illustrates the potential use of the modular control and regulation analyses in combination with noninvasive techniques like ³¹P-labeled NMR for the study of in situ energetics in beating heart. The low control by mitochondria on contraction is due to its high sensitivity to changes in energetic intermediates. In other words, these results show that heart contraction should not be sensitive to modulations of mitochondrial activity, but will be highly sensitive to any modulation of the contraction system. Energy flux in rat heart contraction is therefore mostly controlled by Ca²⁺ activation of myofilament ATPases. Regulation analysis not only demonstrated that a parallel activation of both energy producer and consumer occurs during calcium activation (direct effect), but also that the inotropic effect is the consequence of myofilament activation and not to the direct effect of calcium on mitochondria (global effect). The direct mitochondrial activation by Ca²⁺ is, however, crucial for the homeostasis of energetic intermediates and for heart physiologic response to Ca²⁺ increase (27).

MoCA is currently the only approach applicable to intact beating heart that gives information on the quantitative internal controls and regulations of integrated organ function. We show here that regulation analysis (8, 10) has the potential to provide a quantitative description of how an effector leads the system to move from a steady state to a new one. This approach should be fruitfully applied to the diagnosis of heart dysfunctions or drug effect. It will give two levels of information: the quantitative description of the effect on each module (direct effect) and the consequences of these modulations on heart contraction (global effect).

	GRANTS

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This work was supported by the Centre National de la Recherche Scientifique, the Université Victor Segalen (Bordeaux 2) and the Conseil Régional de la Région Aquitaine, France.

	FOOTNOTES

 

Address for reprint requests and other correspondence: P. Diolez, Résonance Magnétique des Systèmes Biologiques, UMR5536 CNRS-Université Victor Segalen Bordeaux 2, 146 rue Léo-Saignat, 33076 Bordeaux cedex, France (e-mail: Diolez{at}rmsb.u-bordeaux2.fr)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

	REFERENCES

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1. Ainscow EK, Brand MD. Errors associated with metabolic control analysis. Application of Monte-Carlo simulation of experimental data. J Theor Biol 194: 223–233, 1998.[CrossRef][ISI][Medline]
2. Ainscow EK, Brand MD. Quantifying elasticity analysis: how external effectors cause changes to metabolic systems. BioSystems 49: 151–159, 1999.[CrossRef][ISI][Medline]
3. Balaban RS. Cardiac energy metabolism homeostasis: role of cytosolic calcium. J Mol Cell Cardiol 34: 1259–1271, 2002.[CrossRef][ISI][Medline]
4. Balaban RS, Bose S, French SA, Territo PR. Role of calcium in metabolic signaling between cardiac sarcoplasmic reticulum and mitochondria in vitro. Am J Physiol Cell Physiol 284: C285–C293, 2003.[Abstract/Free Full Text]
5. Balaban RS, Bose S, French SA, Territo PR. Role of calcium in metabolic signaling between cardiac sarcoplasmic reticulum and mitochondria in vitro. Am J Physiol Cell Physiol 284: C285–C293, 2003.[Abstract/Free Full Text]
6. Balaban RS, Kantor HL, Katz LA, Briggs RW. Relation between work and phosphate metabolite in the in vivo paced mammalian heart. Science 232: 1121–1123, 1986.[Abstract/Free Full Text]
7. Bers DM. Cardiac excitation-contraction coupling. Nature 415: 198–205, 2002.[CrossRef][Medline]
8. Brand MD. Regulation analysis of energy metabolism. J Exp Biol 200: 193–202, 1997.[Abstract]
9. Brand MD. Top down metabolic control analysis. J Theor Biol 182: 351–360, 1996.[CrossRef][ISI][Medline]
10. Brand MD, Curtis RK. Simplifying metabolic complexity. Biochem Soc Trans 30: 25–30, 2002.[CrossRef][ISI][Medline]
11. Brown GC, Hafner RP, Brand MD. A top down approach to the determination of control coefficients in metabolic control theory. Eur J Biochem 188: 321–325, 1990.[ISI][Medline]
12. Diolez P, Raffard G, Simon C, Leducq N, Dos Santos P, Canioni P. Mitochondria do not control heart bioenergetics. Mol Biol Rep 29: 193–196, 2002.[CrossRef][ISI][Medline]
13. Diolez P, Simon C, Leducq N, Canioni P, Dos Santos P. Top down analysis of heart bioenergetics. In: BTK2000: Animating the Cellular Map, edited by Hofmeyr J-HS, Rohwer M, and Snoep JL. Stellenbosch, South Africa: Stellenbosch University Press, 2000, p. 101–106.
14. Dos Santos P, Aliev MK, Diolez P, Duclos F, Besse P, Bonoron-Adele S, Sikk P, Canioni P, Saks VA. Metabolic control of contractile performance in isolated perfused rat heart. Analysis of experimental data by Reaction: diffusion mathematical model. J Mol Cell Cardiol 32: 1703–1734, 2000.[CrossRef][ISI][Medline]
15. Dufour S, Rousse N, Canioni P, Diolez P. Top-down control analysis of temperature effect on oxidative phosphorylation. Biochem J 314: 743–751, 1996.[ISI][Medline]
16. Fell DA. Metabolic control analysis: a survey of its theoretical and experimental development. Biochem J 286: 313–330, 1992.[ISI][Medline]
17. Fukuda N, Sasaki D, Ishiwata S, Kurihara S. Length dependence of tension generation in rat skinned cardiac muscle: role of titin in the Frank-Starling mechanism of the heart. Circulation 104: 1639–1645, 2001.[Abstract/Free Full Text]
18. Hafner RP, Brown GC, Brand MD. Analysis of the control of respiration rate, phosphorylation rate, proton leak rate and protonmotive force in isolated mitochondria using the ‘top-down’ approach of metabolic control theory. Eur J Biochem 188: 313–319, 1990.[ISI][Medline]
19. Harris DA, Das AM. Control of mitochondrial ATP synthesis in the heart. Biochem J 280: 561–573, 1991.[ISI][Medline]
20. Heinrich R, Rapoport TA. A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. Eur J Biochem 42: 89–95, 1974.[ISI][Medline]
21. Kacser H, Burns JA. The control of flux. Symp Soc Exp Biol 27: 65–104, 1973.[Medline]
22. Kacser H, Burns JA. The control of flux. Biochem Soc Trans 23: 341–366, 1995.[ISI][Medline]
23. Kavanagh NI, Ainscow EK, Brand MD. Calcium regulation of oxidative phosphorylation in rat skeletal muscle mitochondria. Biochim Biophys Acta 1457: 57–70, 2000.[Medline]
24. Kentish JC, Wrzosek A. Changes in force and cytosolic Ca²⁺ concentration after length changes in isolated rat ventricular trabeculae. J Physiol 506: 431–444, 1998.[Abstract/Free Full Text]
25. Korzeniewski B. Regulation of ATP supply during muscle contraction: theoretical studies. Biochem J 330: 1189–1195, 1998.[ISI][Medline]
26. Korzeniewski B, Harper ME, Brand MD. Proportional activation coefficients during stimulation of oxidative phosphorylation by lactate and pyruvate or by vasopressin. Biochim Biophys Acta 1229: 315–322, 1995.[Medline]
27. Korzeniewski B, Noma A, Matsuoka S. Regulation of oxidative phosphorylation in intact mammalian heart in vivo. Biophys Chem 116: 145–157, 2005.[CrossRef][ISI][Medline]
28. Kupriyanov VV, Lakomkin VL, Korchazhkina OV, Steinschneider A, Kapelko VI, Saks VA. Control of cardiac energy turnover by cytoplasmic phosphates: 31P-NMR study. Am J Physiol 261, Suppl 4: 45–53, 1991.[ISI][Medline]
29. Kupriyanov VV, Lakomkin VL, Korchazhkina OV, Stepanov VA, Steinschneider A, Kapelko VI. Cardiac contractile function, oxygen consumption rate and cytosolic phosphates during inhibition of electron flux by amytal–a 31P-NMR study. Biochim Biophys Acta 1058: 386–399, 1991.[Medline]
30. Kushmerick MJ. Skeletal muscle: a paradigm for testing principles of bioenergetics. J Bioenerg Biomembr 27: 555–569, 1995.[CrossRef][ISI][Medline]
31. Macgowan GA, Kirk JA, Evans C, Shroff SG. Pressure-calcium relationships in the perfused mouse heart. Am J Physiol Heart Circ Physiol 290: H2614–H2624, 2006.[Abstract/Free Full Text]
32. Mildaziene V, Baniene R, Nauciene Z, Marcinkeviciute A, Morkuniene R, Borutaite V, Kholodenko B, Brown GC. Ca²⁺ stimulates both the respiratory and phosphorylation subsystems in rat heart mitochondria. Biochem J 320: 329–334, 1996.[ISI][Medline]
33. Mizuno J, Araki J, Mohri S, Minami H, Doi Y, Fujinaka W, Miyaji K, Kiyooka T, Oshima Y, Iribe G, Hirakawa M, Suga H. Frank-Starling mechanism retains recirculation fraction of myocardial Ca²⁺ in the beating heart. Jpn J Physiol 51: 733–743, 2001.[CrossRef][ISI][Medline]
34. Schlattner U, Dolder M, Wallimann T, Tokarska-Schlattner M. Mitochondrial creatine kinase and mitochondrial outer membrane porin show a direct interaction that is modulated by calcium. J Biol Chem 276: 48027–48030, 2001.[Abstract/Free Full Text]
35. Wu ST, Kojima S, Parmley WW, Wikman-Coffelt J. Relationship between cytosolic calcium and oxygen consumption in isolated rat hearts. Cell Calcium 13: 235–247, 1992.[CrossRef][ISI][Medline]

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