A simulation study on the constancy of cardiac energy metabolites during workload transition

Abstract

Key points: The cardiac energy metabolites such as ATP, phosphocreatine, ADP and NADH are kept relatively constant during physiological cardiac workload transition. How this is accomplished is not yet clarified, though Ca²⁺ has been suggested to be one of the possible mechanisms. We constructed a detailed mathematical model of cardiac mitochondria based on experimental data and studied whether known Ca²⁺ -dependent regulation mechanisms play roles in the metabolite constancy. Model simulations revealed that the Ca²⁺ -dependent regulation mechanisms have important roles under the in vitro condition of isolated mitochondria where malate and glutamate were mitochondrial substrates, while they have only a minor role and the composition of substrates has marked influence on the metabolite constancy during workload transition under the simulated in vivo condition where many substrates exist. These results help us understand the regulation mechanisms of cardiac energy metabolism during physiological cardiac workload transition.

Abstract: The cardiac energy metabolites such as ATP, phosphocreatine, ADP and NADH are kept relatively constant over a wide range of cardiac workload, though the mechanisms are not yet clarified. One possible regulator of mitochondrial metabolism is Ca²⁺ , because it activates several mitochondrial enzymes and transporters. Here we constructed a mathematical model of cardiac mitochondria, including oxidative phosphorylation, substrate metabolism and ion/substrate transporters, based on experimental data, and studied whether the Ca²⁺ -dependent activation mechanisms play roles in metabolite constancy. Under the in vitro condition of isolated mitochondria, where malate and glutamate were used as mitochondrial substrates, the model well reproduced the Ca²⁺ and inorganic phosphate (P_i ) dependences of oxygen consumption, NADH level and mitochondrial membrane potential. The Ca²⁺ -dependent activations of the aspartate/glutamate carrier and the F₁ F_o -ATPase, and the P_i -dependent activation of Complex III were key factors in reproducing the experimental data. When the mitochondrial model was implemented in a simple cardiac cell model, simulation of workload transition revealed that cytoplasmic Ca²⁺ concentration ([Ca²⁺ ]_cyt ) within the physiological range markedly increased NADH level. However, the addition of pyruvate or citrate attenuated the Ca²⁺ dependence of NADH during the workload transition. Under the simulated in vivo condition where malate, glutamate, pyruvate, citrate and 2-oxoglutarate were used as mitochondrial substrates, the energy metabolites were more stable during the workload transition and NADH level was almost insensitive to [Ca²⁺ ]_cyt . It was revealed that mitochondrial substrates have a significant influence on metabolite constancy during cardiac workload transition, and Ca²⁺ has only a minor role under physiological conditions.

Keywords: heart; mathematical modelling; mitochondria.

Figure 1. A scheme of the mitochondrial model

Allosteric regulation by Ca²⁺ and P_i is indicated by red and blue arrows, respectively. Shown inside the dotted box are additional cytoplasmic and plasmalemmal components to simulate an in vivo workload change of cardiomyocytes with mitochondria incorporated. AcCoA, acetyl‐CoA; ALA, alanine; ANT, adenine nucleotide translocase; ASP^–, aspartate; C1, Complex I of the respiratory chain; C3, Complex III of the respiratory chain; C4, Complex IV of the respiratory chain; CS, citrate synthase; Cytco, oxidized form of cytochrome c; Cytcr, reduced form of cytochrome c; FH, fumarate hydratase; FUM^2–, fumarate; GLU^–, glutamate; HCIT^2–, citrate; MAL^2–, malate; NDK, nucleoside diphosphate kinase; OAA^2–, oxaloacetate; OG^2–, 2‐oxoglutarate; PYR^–, pyruvate; SDH, succinate dehydrogenase; SUC^2–, succinate; UQH2; ubiquinol; ScCoA, succinyl‐CoA.

Figure 2. Dependences of mV˙O2 , NADH and ΔΨ on [Ca²⁺]_cyt and [P_i]_cyt

Simulations were performed using the model of isolated mitochondria with the experimental conditions of Territo et al. (2000) (A) and Bose et al. (2003) (B). A, [Ca²⁺]_cyt dependence. Experimental data (exp; open circles) are from Territo et al. (2000). Simulation data (model; filled circles) were normalized to those at 10^–6 μm [Ca²⁺]_cyt. B, [P_i]_cyt dependence. Simulation data (model) were in state III (with ADP, filled circles) and state IV (without ADP, filled triangles). Experimental data (exp; open circles and triangles) were from Bose et al. (2003).

Figure 3. Sensitivity analysis of the isolated mitochondrial model

The simulation conditions were the same as those of Fig. 2 A, with [Ca²⁺]_cyt = 1.0 μm. Sensitivity (S) for parameter X (X = $\mathrm{m}\dot{V}{}_{{\mathrm{O}}_2}$, NADH and ΔΨ) was calculated as the relative change by ±5% change of the expression level of each component: $S=\frac{|X_{+5\%}-X_{-5\%}|}{0.1X_{\mathrm{original}}}$.

Figure 4. Contribution of the Ca²⁺‐ and P_i‐dependent activation mechanisms to the [Ca²⁺]_cyt dependences in the isolated mitochondrial model

The basic simulation condition was the same as that of Fig. 2 A. The Ca²⁺‐dependent activation terms of PDHC, ICDH, OGDH, AGC and SN, that is, PDHC A_Ca, ICDH A_Ca, OGDH A_Ca, AGC A_Ca and SN A_Ca, were removed from the mathematical formula individually or at the same time. In addition, the P_i‐dependent activation terms of Complex III and OGDH, that is, C3 A_Pi and OGDH A_Pi, were removed individually or at the same time. A, removal of AGC A_Ca, SN A_Ca and C3 A_Pi. Open circles represent the control model, and filled symbols represent the absence of AGC A_Ca, SN A_Ca and C3 A_Pi. B, summary of the simulation results. Ratios of $\mathrm{m}\dot{V}{}_{{\mathrm{O}}_2}$, NADH and ΔΨ at 10^–6 μm [Ca²⁺]_cyt to those at 0.535 μm [Ca²⁺]_cyt were plotted. Dotted lines indicate the ratios obtained from the control model. –All A_Ca: Ca²⁺‐dependent activation terms were removed from all components; –All A_Pi: P_i‐dependent activation terms were removed from all components.

Figure 5. Contribution of the Ca²⁺‐ and P_i‐dependent activation mechanisms to the [P_i]_cyt dependences in the isolated mitochondrial model

The basic simulation conditions were the same as those of Fig. 2 B. Removal of the Ca²⁺‐dependent activation term and P_i‐dependent activation term was the same as in Fig 4. A, removal of AGC A_Ca, SN A_Ca and C3 A_Pi under the condition of state III (with [P_i]_cyt and ADP in addition to malate/glutamate). Open circles represent the control model, and filled symbols represent the absence of AGC A_Ca, SN A_Ca and C3 A_Pi. B, summary. Values of $\mathrm{m}\dot{V}{}_{{\mathrm{O}}_2}$, NADH and ΔΨ at 2 mm [P_i]_cyt were expressed as percentage difference from the control model. Data are from state III (black) and state IV (with only [P_i]_cyt in addition to malate/glutamate; grey).

Figure 6. Workload and [Ca²⁺]_cyt dependences of energy metabolites in the simple cardiac cell model

The coefficient of ATP usage, k _ATPuse, was changed from 1.5 × 10^–5 to 1.88 × 10^–4 mm ms⁻¹, and [Ca²⁺]_cyt was changed from 0.001 to 10 μm. A, total cytoplasmic ATP. B, cytoplasmic PCr, ADP and P_i, and mitochondrial NADH. Data at 0.1 to 2.0 μm [Ca²⁺]_cyt are shown.

Figure 7. Effects of additional substrate on the workload and [Ca²⁺]_cyt dependences of NADH in the simple cardiac cell model

Pyruvate (A), citrate (B), 2‐oxoglutarate (C) and aspartate (D) were added to the cytoplasm of the simple cardiac cell model, in addition to malate/glutamate. The middle and right panels show the results of simulations at 0.1 and 0.3 μm [Ca²⁺]_cyt, respectively. Unit for $\mathrm{m}\dot{V}{}_{{\mathrm{O}}_2}$ is mm min^–1.

Figure 8. Activities of representative enzymes and substrate transporters at different combinations of substrates in the simple cardiac cell model

A, 5 mm malate and 5 mm glutamate. B, 5 mm malate, 5 mm glutamate and 0.3 mm pyruvate. C, 5 mm malate, 5 mm glutamate and 0.3 mm citrate. D, 5 mm malate, 5 mm glutamate and 0.1 mm 2‐oxoglutarate. E, 5 mm malate, 5 mm glutamate and 3 mm aspartate. F, full substrates; 1 mm malate, 5 mm glutamate, 0.3 mm pyruvate, 0.3 mm citrate, 0.1 mm 2‐oxoglutarate and 3 mm aspartate. All the simulations were done at 0.3 μm [Ca²⁺]_cyt and 1.5 × 10^–4 mm ms⁻¹ k _ATPuse ($\mathrm{m}\dot{V}{}_{{\mathrm{O}}_2}$ = 8.8 mm min⁻¹ except for E, 3.2 mm min⁻¹).

Figure 9. Workload and [Ca²⁺]_cyt dependences of energy metabolites in the simple cardiac cell model with multiple mitochondrial substrates: 1 mm malate, 5 mm glutamate, 0.3 mm pyruvate, 0.3 mm citrate, 0.1 mm 2‐oxoglutarate and 3 mm aspartate

The same protocols as in Fig. 6 were used. A, total cytoplasmic ATP. B, cytoplasmic PCr, ADP, P_i and mitochondrial NADH.

Figure 10. [Ca²⁺]_cyt dependence of four dehydrogenases, AGC and OGC

A, 5 mm malate and 5 mm glutamate condition. B, full substrates condition: 1 mm malate, 5 mm glutamate, 0.3 mm pyruvate, 0.3 mm citrate, 0.1 mm 2‐oxoglutarate and 3 mm aspartate. k _ATPuse = 1.5 × 10^–4 mm ms⁻¹ ($\mathrm{m}\dot{V}{}_{{\mathrm{O}}_2}$ = 9.4 – 9.8 mm min⁻¹ in A, 8.8 – 8.9 mm min⁻¹ in B).

Figure 11. Substrate dependence of NADH in the simple cardiac cell model

The basic combination of substrates was the same as in Fig. 9. Pyruvate (A), malate (B), glutamate (C), aspartate (D), 2‐oxoglutarate (E) and citrate (F) were systematically increased in the presence of 0.3 μm [Ca²⁺]_cyt. k _ATPuse was set to 1.5 × 10^–4 mm ms⁻¹ ($\mathrm{m}\dot{V}{}_{{\mathrm{O}}_2}$ = 8.6–8.9 mm min⁻¹). Shaded areas show physiological range of each substrate (Albe et al. 1990; Kato et al. 2010).