Application of the principles of systems biology and Wiener's cybernetics for analysis of regulation of energy fluxes in muscle cells in vivo

Abstract

The mechanisms of regulation of respiration and energy fluxes in the cells are analyzed based on the concepts of systems biology, non-equilibrium steady state kinetics and applications of Wiener's cybernetic principles of feedback regulation. Under physiological conditions cardiac function is governed by the Frank-Starling law and the main metabolic characteristic of cardiac muscle cells is metabolic homeostasis, when both workload and respiration rate can be changed manifold at constant intracellular level of phosphocreatine and ATP in the cells. This is not observed in skeletal muscles. Controversies in theoretical explanations of these observations are analyzed. Experimental studies of permeabilized fibers from human skeletal muscle vastus lateralis and adult rat cardiomyocytes showed that the respiration rate is always an apparent hyperbolic but not a sigmoid function of ADP concentration. It is our conclusion that realistic explanations of regulation of energy fluxes in muscle cells require systemic approaches including application of the feedback theory of Wiener's cybernetics in combination with detailed experimental research. Such an analysis reveals the importance of limited permeability of mitochondrial outer membrane for ADP due to interactions of mitochondria with cytoskeleton resulting in quasi-linear dependence of respiration rate on amplitude of cyclic changes in cytoplasmic ADP concentrations. The system of compartmentalized creatine kinase (CK) isoenzymes functionally coupled to ANT and ATPases, and mitochondrial-cytoskeletal interactions separate energy fluxes (mass and energy transfer) from signalling (information transfer) within dissipative metabolic structures - intracellular energetic units (ICEU). Due to the non-equilibrium state of CK reactions, intracellular ATP utilization and mitochondrial ATP regeneration are interconnected by the PCr flux from mitochondria. The feedback regulation of respiration occurring via cyclic fluctuations of cytosolic ADP, Pi and Cr/PCr ensures metabolic stability necessary for normal function of cardiac cells.

Keywords: cytoskeleton; metabolic homeostasis; mitochondria; muscle cells; phosphotransfer networks; regulation; respiration; systems biology.

Figure 1.

Kinetic analysis of respiration regulation by ADP in permeabilized fibres from human vastus lateralis muscle. Biopsy samples were taken from healthy volunteers and permeabilized fibers prepared as described by Kuznetsov et al. [88]. (A) Oxygraph recording of respiration rates during stepwise stimulation by increasing amounts of ADP in the presence of 5 mM glutamate and 2 mM malate. Cytochrome c and atractyloside are used to test the integrity of mitochondria outer and inner membranes. (B) Henri-Michelis-Menten type hyperbolic function of dependence of oxygen consumption rate on ADP concentrations. (C) Linearization of data from Figure 1B in double reciprocal plot gives the value of apparent Km for free ADP equal to 182.9 μM (n = 10). This value corresponds to mixed fibre muscle content (for comparison: in glycolytic gastrocnemius rats’ muscle the Kmapp for free ADP is about 20 μM and for highly oxidative cardiac muscle is about 300–400 μM). Reproduced from [92] with permission.

Figure 2.

Demonstration of the central role of mitochondrial creatine kinase, MtCK, in regulation of respiration of permeabilized muscle cells. (A) Scheme shows the principles of the method used to study interaction between mitochondrial and glycolytic systems in competition for endogenous ADP. This Scheme shows mitochondrion in situ within intracellular energetic units, ICEUs [93] surrounded by cytoskeleton proteins (depicted as “x” factor) and myofibrils. Exogenous ATP is hydrolyzed by cellular ATPases into endogenous extramitochondrial ADP and inorganic phosphate (Pi). Mitochondrial (MtCK) and non-mitochondrial creatine kinases in myofibrils and at membrane of sarcoplasmic reticulum in the presence of creatine and ATP produce endogenous intra-and extramitochondrial ADP. Phosphoenolpyruvate (PEP) and pyruvate kinase (PK) system removes extramitochondrial ADP produced by intracellular ATP consuming reactions and continuously regenerate extramitochondrial ATP. Endogenous intramitochondrial ADP produced by MtCK forms microcompartments within the mitochondrial intermembrane space (IMS) and is re-imported into the matrix via adenine nucleotide translocase (ANT) due to its functional coupling with MtCK. Reproduced from [29] with permission. (B,C) Oxygraph recording of respiration of permeabilized cardiomyocytes (B) and fibers from human skeletal m. vastus lateralis (C) prepared from biopsy samples of healthy volunteers as described in Figure 1 in the presence of 2 mM malate and 5 mM glutamate as substrates. Addition of 2 mM MgATP activates respiration due to production of endogenous MgADP in ATPase reaction. Pyruvate kinase (PK) in the presence of 5 mM phosphoenolpyruvate (PEP) decreases respiration rate due to removal of extramitochondrial MgADP. Creatine in the presence of MgATP activates mitochondrial creatine kinase (MtCK) reaction of production of endogenous intramitochondrial MgADP which rapidly activates respiration up to the maximal rate (see Figure 1A), that showing that mitochondrial ADP is not accessible for PK-PEP system due to the limited permeability of mitochondrial outer membrane in the cells in situ. Right panels in B and C show confocal images of isolated cardiomyocytes and fibers from m. vastus lateralis, correspondingly. Reproduced from [92] with permission.

Figure 2.

Demonstration of the central role of mitochondrial creatine kinase, MtCK, in regulation of respiration of permeabilized muscle cells. (A) Scheme shows the principles of the method used to study interaction between mitochondrial and glycolytic systems in competition for endogenous ADP. This Scheme shows mitochondrion in situ within intracellular energetic units, ICEUs [93] surrounded by cytoskeleton proteins (depicted as “x” factor) and myofibrils. Exogenous ATP is hydrolyzed by cellular ATPases into endogenous extramitochondrial ADP and inorganic phosphate (Pi). Mitochondrial (MtCK) and non-mitochondrial creatine kinases in myofibrils and at membrane of sarcoplasmic reticulum in the presence of creatine and ATP produce endogenous intra-and extramitochondrial ADP. Phosphoenolpyruvate (PEP) and pyruvate kinase (PK) system removes extramitochondrial ADP produced by intracellular ATP consuming reactions and continuously regenerate extramitochondrial ATP. Endogenous intramitochondrial ADP produced by MtCK forms microcompartments within the mitochondrial intermembrane space (IMS) and is re-imported into the matrix via adenine nucleotide translocase (ANT) due to its functional coupling with MtCK. Reproduced from [29] with permission. (B,C) Oxygraph recording of respiration of permeabilized cardiomyocytes (B) and fibers from human skeletal m. vastus lateralis (C) prepared from biopsy samples of healthy volunteers as described in Figure 1 in the presence of 2 mM malate and 5 mM glutamate as substrates. Addition of 2 mM MgATP activates respiration due to production of endogenous MgADP in ATPase reaction. Pyruvate kinase (PK) in the presence of 5 mM phosphoenolpyruvate (PEP) decreases respiration rate due to removal of extramitochondrial MgADP. Creatine in the presence of MgATP activates mitochondrial creatine kinase (MtCK) reaction of production of endogenous intramitochondrial MgADP which rapidly activates respiration up to the maximal rate (see Figure 1A), that showing that mitochondrial ADP is not accessible for PK-PEP system due to the limited permeability of mitochondrial outer membrane in the cells in situ. Right panels in B and C show confocal images of isolated cardiomyocytes and fibers from m. vastus lateralis, correspondingly. Reproduced from [92] with permission.

Figure 3.

Mitochondrial Interactosome (MI) in cardiac, oxidative skeletal muscle and brain cells. Mitochondrial interactosome consists of ATP Synthasome (formed by ATP synthase, adenine nucleotide carrier (ANC) as proposed by Pedersen [152]), and inorganic phosphate carrier (PIC)), mitochondrial creatine kinase (MtCK) functionally coupled to ATP synthasome and voltage dependent anion channel (VDAC) with regulatory proteins (tubulin and linker proteins (LP)). ATP regenerated by ATP synthase is transferred to MtCK due to its functional coupling with ATP syntasome. MtCK catalyses transfer of phosphate group from ATP to creatine producing phosphocreatine (PCr) which leaves mitochondria as a main energy carrier due to highly selective permeability of VDAC. ADP is returned to and recycled in ATP Synthasome. Small signaling amounts of cytosolic ADP enter the intermembrane space (see the text) and increase the ADP recycling rate within MI maintaining increased production of the PCr. In this way coupled MtCK amplifies cytosolic ADP signal. MOM, mitochondrial outer membrane; MIM, mitochondrial inner membrane; IMS, mitochondrial intermembrane space. Reproduced from [32] with permission.

Figure 4.

Role of endogenous ADP produced in MgATPase reactions at different added MgATP concentration in regulation of respiration of permeabilized cardiomyocytes under different conditions: (▪) – without ADP trapping system (PEP-PK) and in the absence of creatine; (•) – without PEP-PK system but in the presence of 20 mM creatine (i.e., activated MtCK); () – in the presence of both trapping system for free ADP and 20 mM creatine. Reproduced from [32] with permission.

Figure 5.

Important role of limited and selective permeability of the mitochondrial outer membrane and nonequilibrium MtCK reaction coupled to ANT in feedback metabolic signaling by cytoplasmic ADP between MgATPases and mitochondria in cardiac cells. (A) Dependence of respiration rate on the ADP concentration in the medium. Results of 17–29 experiments with isolated mitochondria and permeabilized cardiomyocytes are summarized. The gray area delimits physiologic range of changes in cytosolic [ADP] calculated by the model of compartmentalized energy transfer in B. In isolated mitochondria (curve (○)), no regulation of respiration is possible because of the saturating [ADP]c for the minimal workload. When the ADP diffusion is restricted as in mitochondria in situ in permeabilized cardiomyocytes [curve (•)], the respiration rates become linearly dependent on ADP concentrations in their physiological range. In this interval of quasi-linear dependence under physiological conditions the activating effect of ADP can be amplified by creatine [curve (▪)], due to activation of coupled MtCK. The resulting apparent Km for cytoplasmic ADP is significantly decreased and respiration rate increased. Reproduced from [92] with permission. (B) Calculated fluctuations of ADP concentrations in myofibrillar core corresponding to different heart workloads. Reproduced from [–160] with permission.

Figure 6.

Four principal characteristics of heart energy metabolism. (A) Summary of data from different laboratories on metabolic homeostasis in heart cells. Very similar stable average intracellular PCr concentrations corresponding to different increasing respiration rates are always observed. (B) shows oscillations of relative PCr content during cardiac cycle in perfused rat’s heart under conditions of metabolic stability. The curve marked by empty circles (○) is refitted using experimental data received by Honda et al., 2002 in gate-pacing in [165] (with permission), only the mean values of metabolites are shown. (C) The origin of the problem of the compartmentalization of adenine nucleotides and metabolic energy sensing in cardiac cells. The data show metabolic changes in the totally ischemic dog hearts. Data are redrawn from [10] (with permission). (D) Peak systolic pressure P_syst of isolated isometric hypoxic rat hearts is independent from free energy of ATP hydrolysis, dG/dξ calculated from creatine kinase equilibrium and total tissue contents of creatine, phosphocreatine and ATP. Reproduced from [167] with permission.

Figure 6.

Four principal characteristics of heart energy metabolism. (A) Summary of data from different laboratories on metabolic homeostasis in heart cells. Very similar stable average intracellular PCr concentrations corresponding to different increasing respiration rates are always observed. (B) shows oscillations of relative PCr content during cardiac cycle in perfused rat’s heart under conditions of metabolic stability. The curve marked by empty circles (○) is refitted using experimental data received by Honda et al., 2002 in gate-pacing in [165] (with permission), only the mean values of metabolites are shown. (C) The origin of the problem of the compartmentalization of adenine nucleotides and metabolic energy sensing in cardiac cells. The data show metabolic changes in the totally ischemic dog hearts. Data are redrawn from [10] (with permission). (D) Peak systolic pressure P_syst of isolated isometric hypoxic rat hearts is independent from free energy of ATP hydrolysis, dG/dξ calculated from creatine kinase equilibrium and total tissue contents of creatine, phosphocreatine and ATP. Reproduced from [167] with permission.

Figure 7.

Separation of energy transfer by PCr flux and information transfer by low amplitude metabolites’ concentrations in cardiomyocytes: realization of cybernetics principle of feedback regulation. (A) Scheme represents intracellular energy unit (ICEU) consisting of ATP production sites (mitochondrion, glycolysis), ATP consumption sites (myosin ATPase, SERCA, ions-pumping-ATPase) communicating via the system of compartmentalized creatine kinase (CK) isoforms and PCr/CK phosphotransfer network. (B) Non-equilibrium state of MtCK in mitochondria and MM-creatine kinase reactions at sites of ATP utilization functioning in mitochondria opposite directions. (a) In mitochondria the constant rate of net PCr production in non- equilibrium steady state of coupled MtCK reaction is established for any workload to meet the cellular energy requirements [colored lines correspond to different workloads depicted in Figures 5B and 7B(b)]. (b) The cyclic changes in rates of ATP regeneration in non-equilibrium myofibrillar MMCK reaction during contraction cycles at different workloads correspond to oscillations of [ADP]c described in Figure 5B (colored lines in both figures show the amplitudes of ADP and ATP productions to different heart workloads, Figure 5B). Reproduced from [–160] with permission.

Scheme 1.

General scheme of intracellular reactions of energy metabolism in heart and skeletal muscle cells.

Scheme 2.

The original scheme of the general principle of feedback regulation proposed by Norbert Wiener, adapted from [21]. For explanations see the text.

Scheme 3.

General presentation of the nature of the mechanism of feedback metabolic signaling in regulation of energy metabolism within intracellular energy units. Due to the non-equilibrium steady-state MtCK and MMCK reactions intracellular ATP utilization (marked as output) and mitochondrial ATP regeneration (marked as input) are interconnected via the cyclic fluctuations of cytosolic ADP, Pi and Cr/PCr.