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WIREs Syst Biol Med
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Mitochondrial network energetics in the heart

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Abstract At the core of eukaryotic aerobic life, mitochondrial function like ‘hubs’ in the web of energetic and redox processes in cells. In the heart, these networks—extending beyond the complex connectivity of biochemical circuit diagrams and apparent morphology—exhibit collective dynamics spanning several spatiotemporal levels of organization, from the cell, to the tissue, and the organ. The network function of mitochondria, i.e., mitochondrial network energetics, represents an advantageous behavior. Its coordinated action, under normal physiology, provides robustness despite failure in a few nodes, and improves energy supply toward a swiftly changing demand. Extensive diffuse loops, encompassing mitochondrial–cytoplasmic reaction/transport networks, control and regulate energy supply and demand in the heart. Under severe energy crises, the network behavior of mitochondria and associated glycolytic and other metabolic networks collapse, thereby triggering fatal arrhythmias. WIREs Syst Biol Med 2012, 4:599–613. doi: 10.1002/wsbm.1188 This article is categorized under: Analytical and Computational Methods > Analytical Methods Models of Systems Properties and Processes > Cellular Models Physiology > Mammalian Physiology in Health and Disease

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Time course of the main variables reflecting the state of electrical, mechanical, and energetic processes during a single cardiomyocyte beat as computed by the ECME model.

When the ECME model is stimulated every 2 seconds, the depolarization and repolarization phases of the action potential (AP) take place during the first 200 ms (a). During the AP, Na+ channels are activated initiating the depolarization phase (c, left axis), which enables gating of L‐type Ca2+ channels (b, left axis) followed by Ca2+ release from internal stores in the sarcoplasmic reticulum (SR) via ryanodine receptors, Jrel (b, right axis). Ca2+ is then recaptured into the SR via SERCA activity (e, left axis) or transported out of the myocyte through the Na+Ca2+ exchanger, INaCa (b, right axis). The potassium currents IKs, IK1, and IKP (c, right axis) participate in the repolarization of the membrane potential to its resting, −80 mV (diastolic) level. The Ca2+transient in the cytoplasm (d, left axis) triggers myofibrils contraction, developing force (d, right axis), which is reflected by the ATP consumption of the ATPase activity associated with the formation of acto‐myosin cross bridges, VAM (e, left axis). In addition to VAM and SERCA activity, the other processes that contribute to the demand of ATP are the activity of the Na+, K+ ATPase (VNaKA) and the sarcolemmal Ca2+ pump (IpCa) (e, right axis). ADP in both compartments the cytoplasm, ADPi (f, left axis), and mitochondria, ADPm (f, left, axis) exhibit a transient increase which reflect the cytoplasmic increase in ATP consumption during systole and uptake by mitochondria, activating respiration and decreasing NADH levels (f, right axis). Mitochondrial Ca2+ (f, 2nd left axis) allows to recover from this transient mismatch between energy demand and supply, visualized as a restoration of NADH (f, right axis) through the tricarboxylic acid cycle activity. The shaded area in panels d–f corresponds to the same time range zoomed in panels a–c. Parameters and initial conditions of the simulation as described elsewhere.26 (Reproduced modified from Ref 69)

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Diffuse control loops in the Digitalis action on cardiac contractility.

Inhibition of the NaK ATPase converts an overall negative diffuse control loop into a positive one, i.e., inhibiting a negative controller will increase overall downstream activity of the processes negatively controlled by the pump. The primary action of Digitalis and cardiotonic glycosides (e.g., ouabain) is to inhibit the NaK pump resulting in an overall positive effect on contractility, a well‐known pharmacological action. The scheme shows the wide range of processes affected by NaK ATPase inhibition. The gray box represents the increase in cytoplasmic ATP and Ca2+resulting from the activation of the diffuse control loop by NaK ATPase inhibition, both exerting opposing effects on mitochondrial respiration, and opening the question of which will prevail (i.e., the interrogation sign in the box). See text for a detailed explanation. Key to symbols: SERCA, sarcoplasmic reticulum Ca2+ATPase; NCX (FM), Na+/Ca2+ exchanger forward mode; NCX (RM), Na+/Ca2+ exchanger reverse mode. See also the legend of Figure 3 and the text for the definition of other symbols.

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From direct to diffuse control loops in cardiomyocyte function.

This figure describes several examples of diffuse control loops exhibiting different lengths as given by the number of intermediary steps involved. Control by diffuse loops was first defined as the control that a process A exerts over process C or D without an apparent direct mechanistic link among them. Unlike in a direct loop (I), in a diffuse control loop there is at least one intermediary process between A and C (II–IV). The positive and negative signs represent the type of control (positive or negative) that each edge (e.g., calcium uniporter, Ca, adenine nucleotide translocator, ANT) in the network has on other nodes or edges in the loop (see also text). In (I) Ca exerts a negative control on cytoplasmic Ca2+, Ca, i.e., the higher the activity of the uniporter, the lower the concentration of Ca. In (II) Ca exerts an overall negative control on ATP synthesis which, mechanistically, is not direct as in (I), but indirectly mediated by the negative control of Ca upon the mitochondrial membrane potential, ΔΨm. ATP synthesis will decrease following a decrease in ΔΨm because the latter is the driving force of ADP phosphorylation by the ATP synthase. In (III) the ANT displays an overall positive control on the respiratory flux mediated by an increase in the rate of proton pumping by the ATP synthase, Vhu, which in turn control positively the rate of mitochondrial respiration, because the higher the ATP synthase activity the higher the consumption of its driving force, i.e., ΔΨm, stimulating the electron flow through the respiratory chain to reestablish the proton motive force. In (IV) the Na+K+ ATPase (NAK ATPase) overall control of respiration is negative, which is counter intuitive because one would expect the contrary from an ATP‐consuming process. The explanation resides in the extensive diffuse loop that is mediating this control as follows: the increase in Na+ pump activity lowers intracellular Na+, leading to an increased cellular extrusion of Ca via the sarcolemmal Na+/Ca2+ exchanger (NCX); this decrease in Ca lessens the extent of ΔΨm dissipation associated with mitochondrial Ca2+ transport, which results in a higher ΔΨm and a decrease of respiration.

In a complex network of reactions, the concept of control by diffuse loops is useful to interpret the changes that can be triggered by pharmacological agents among processes without direct mechanistic links between them.

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Heterarchical control and regulation in the network of energetic and electromechanical processes of the heart cell.

Heterarchical, as opposed to hierarchical, is the manner control and regulation is exerted in complex networks. In heterarchical control all edges (e.g., enzymes, channels) and nodes (e.g., metabolites, ions) control and are controlled by all other edges and nodes involved in the network of interest, e.g., energetic, mechanical, electric, and transport processes. The desired degree of detail in the description can be applied by zoom in on the network of integrated cardiomyocyte function (excitation–contraction coupling mitochondrial energetic: ECME model)72,73 according to a generalized matrix method utilized for calculating its overall structure of control and regulation. More precisely, the top panel shows a scheme of the overall network of energetic and electromechanical processes from which it is possible to zoom in the mitochondria with its own reaction network (lower left panel) or yet deeper into the tricarboxylic acid (TCA) cycle (lower right panel) with its specific biochemical circuitry. Of note is that the TCA cycle was considered as an aggregated step in the two other schemes. The ability to zoom in and out the network also reflects that heterarchical control and regulation is bidirectional, i.e., bottom‐up as well as top‐down. In the top panel, rectangular (ion or metabolites) or circular (myofibril conformations) boxes indicate state variables of the ECME network. Boxes depict a light blue background when the state variables participate in conservation relationships (ATP/ADP; creatine/creatine‐P, Cr/CrP; NAD+/NADH, tropomyosin/tropomyosin bound to Ca2+, TRPN/TRPN Ca2+, and the various conformations of myofibrils). Ionic species are indicated on a dark blue background. Hexagonal boxes denote inputs (ions or carbon substrate) that correspond to parameters in the model. Arrowheads point to the products of the numbered processes, whereas lines without arrowheads indicate inputs to those processes. In the mitochondrial energetics scheme, the TCA cycle was considered as a single step in the stoichiometric matrix. In the scheme of the TCA cycle (lower right panel) solid lines represent mass–energy transformation reactions, whereas regulatory interactions (with negative signs indicating inhibition, and positive signs activation) are denoted by dashed lines. (Reprinted with permission from Ref 69. Copyright 2012 Wiley‐VCH Verlag GmBH & Co. KGaA)

Processes accounted for by the ECME and mitochondrial energetics models are numbered according to the following key:

Number Abbreviation Name 1 TCA Tricarboxylic acid cycle2 VRCRespiratory electron transport 3 HNeRespiratory chain proton pumping 4 HFeSuccinate‐driven proton pumping 5 ATPsy Mitochondrial ATP synthase 6 HuProton pumping through ATP synthase 7 LeakProton leak 8 ANT Adenine nucleotide translocator 9 CauniMitochondrial Ca2+ uniporter 10 VNCEMitochondrial Na+ Ca2+ exchanger 11 AM‐ATP Myofibrillar ATPase 12 PMCA Sarcolemmal Ca2+ ATPase 13 SERCA Sarcoplasmic reticulum Ca2+ ATPase 14 INaKCurrent through the Na+ K+ ATPase 15 INCXCurrent through the sarcolemmal Na+ Ca2+ exchanger16 ICabBackground Ca2+ current 17 ATPasecConstitutive cytosolic ATPase 18 INaNa+ inward currents 19 LCC L‐type Ca2+ current 20 JRelCa2+ release from RyR (ryanodine receptor) 21 JxferCa2+ transport from subspace into cytoplasm 22 IKOutward potassium currents 23 Ca2+ association‐dissociation to troponin 24 CKiMitochondrial creatine kinase 25 Creatine species transport 26 CrKc Cytosolic creatine kinase 27‐35 Transitions between tropomyosin conformations

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