### Animals

Hearts were isolated from male C57BL/6J male mice (~20–25 g) (Charles River JAXTM stock number 000664) or from WT and PLM3SA knock-in mice18. This investigation complied with all the relevant ethical regulations for animal testing and research: UK Home Office Guidance on the Operation of the Animals (Scientific Procedures) Act, 1986.

PLM3SA knock-in mice were backcrossed with C57BL/6J mice (Charles River, UK) for >5 generations and were generated by heterozygous pair mating. The PLM3SA mouse expresses a non-phosphorylatable form of PLM in which Ser 63, 68, and 69 have been mutated to alanine and exhibits a Na/K ATPase that is unresponsive to kinase regulation and hence shows chronically elevated Nai15. Unless otherwise stated, littermates were used as the appropriate wild-type controls (PLMWT). Animals were kept under pathogen-free conditions, 12-h light–dark cycle, controlled humidity (~40%), temperature (20–22 °C), and fed chow and water ad libitum. All animals used in studies were male. For pharmacologically induced acute Nai elevation studies, 6-week-old C57BL/6J male mice (~25 g body weight) were purchased from Charles River (UK). Myocardial hypertrophy was induced in 6-week-old C57BL/6J mice (20–22 g) (Charles River, UK). For cellular compartmentation of the 23Na TQF NMR signal experiment, Male Wistar rats (250 g) were purchased from Charles River, UK.

### Glucose tolerance test

Oral glucose tolerance test40 was performed after 5 h fast (n = 8/group), (50 mg glucose, oral gavage).

### Tissue and plasma collection

After an overnight fast, blood was collected from vena cava from terminally anaesthetized mice (PLM3SA and PLMWT) by heparinized 1 ml syringe and immediately centrifuged in pre-cooled vials (3000 rpm, 4 °C, 10 min) to obtain plasma. Skeletal muscles (gastrocnemius and soleus) were dissected and snap frozen by Wollenberger tongs for 1H NMR metabolic profiling. Concentrations of adiponectin, alanine aminotransferase, alkaline phosphatase, creatine kinase, free fatty acids, glucose, high density lipoprotein, insulin, lactate, lactate dehydrogenase, triacylglycerols, adrenaline and noradrenaline were measured by the Mouse Biochemistry Laboratory, Addenbrooke’s Hospital, Cambridge University Hospitals NHS Trust. In a separate cohort of non-fasted terminally anaesthetized animals (n = 5/group), the heart, and skeletal muscle (mixed soleus and gastrocnemius) were excised, snap frozen in liquid nitrogen and stored at −80 °C for 1H NMR metabolomic profiling, western blotting assessment of protein expression and messenger RNA qRT- PCR. RNA was isolated using RNeasy Fibrous Tissue Kit (Qiagen) according to the manufacturer’s instructions. RNA quantity and quality was assessed using Nanodrop (ThermoFisher) and only RNA with 260/280 > 1.8 was used for downstream analyses.

500 ng total RNA was reverse transcribed using Superscript VILO cDNA synthesis kit (ThermoFisher). For quantitative PCR, gene specific primer sequences (Supplementary Table 1: glut1, glut4, cd36, caspase 3, pdk 4, ucp3, cpt1, atg3, mte-1) were obtained from PrimerBank (https://pga.mgh.harvard.edu/primerbank/).

PCR specificity and efficiency were confirmed for each primer pair prior to use. 2.5 ng of cDNA was used per qPCR reaction in triplicates using Power SYBR Green PCR Master Mix (ThermoFisher) according to the manufacturer’s instructions with the following cycling conditions: 95 C for 10 min, 40 cycles of 95 C for 15 s and 60 C for 1 min using AB 7900HT (Applied Biosystems) qPCR cycler (SDS software v 2.4).

The relative quantity of each gene was calculated using ΔΔCT method with gapdh as endogenous control. Myocardial protein expression of IDH3 and pyruvate dehydrogenase (PDH) was examined using manufacturer supplied methods for extraction and detection (Abcam). The following antibodies were for the western blotting experiments: rabbit-anti-IDH3A, Abcam,ab58641 (1.25 μg ml−1), anti-rabbit, GE Healthcare NA934V (1:5000 dilution), rabbit -anti-α/β Tubulin, Cell Signalling, 2148-S / 7 (1:2000), anti-rabbit, GE Healthcare,NA934V (1:2000 dilution), mouse-anti-PDH, Abcam, ab110333 (1 μg ml−1),anti-mouse, GE Healthcare, NA931V (1:2000 dilution). Blots were scanned and analysed using Biorad Gel 800 scanner and Image Lab software (v 6.1).

### Cardiac hypertrophy

Myocardial hypertrophy was induced by pressure overload following supra-renal aortic constriction (banding) in 6-week-old C57BL/6J mice (20–22 g)18. Cardiac function and morphometry was measured in vivo in anaesthetized mice 5-weeks post-surgery using 2D echocardiography (Visualsonics Vevo 770).

### Langendorff-heart perfusions

Mice were terminally anesthetized, hearts rapidly excised, cannulated and perfused as a standard Langendorff preparation41 or using a custom-built NMR-compatible perfusion system in which hearts were beating spontaneously17. Mice were terminally anesthetized using pentobarbitone (~140 mg kg−1 i.p.), hearts rapidly excised, cannulated and perfused as a standard Langendorff preparation41 or using a custom-built NMR-compatible perfusion system in which hearts were beating spontaneously17. To study substrate preference and metabolic flux rates using 13C-labelled substrates, we adapted the standard perfusion system to utilise a counter-current membrane oxygenator41. At the end of each experiment, hearts were immediately freeze-clamped using Wollenberger tongs for metabolic profiling by 1H NMR, 13C NMR and GC-, LC-MS/MS.

### Blebbistatin and CGP 37157 Krebs-Henseleit (KH) buffer

Pilot studies were performed in C57BL6/J perfused mouse hearts in order to determine the working concentrations of pharamacological agents used in the study: Na/K ATPase inhibitor ouabain (Sigma Aldrich,UK), myosin II inhibitor 1-phenyl-1,2,3,4-tetrahydro-4-hydroxypyrrolo[2.3-b]-7-methylquinolin-4-one (blebbistatin, Sigma Aldrich, UK) and mitochondrial Na/Ca exchanger inhibitor 7-chloro-5-(2-chlorophenyl)-1,5-dihydro-4,1-benzothiazepin-2(3H)-one (CGP13757, Sigma-Aldrich UK). In order to avoid precipitation of the blebbistatin in the vasculature and resultant ischaemia, 3.42 mmol/l blebbistatin stock solution (DMSO-diluted, aliquoted, frozen) was dissolved in KH buffer according to the previously described protocol42. To eliminate the possibility that any direct interaction between blebbistatin (DMSO) and ouabain mixed together in aqueous solution leads to the production of new chemical entities or binding between the two drugs, buffer samples [5 µmol/l blebbistatin (0.029% v/v DMSO), 50 µmol/l ouabain and 5 µmol/l blebbistatin (0.029% v/v DMSO) + 50 µmol/l ouabain] were analysed by mass spectrometry (Agilent 1200 LC and Agilent 6510 Q-TOF). No new chemical entities (peaks) were formed by mixing of the two pharmacological agents, thus blebbistatin did not sequester ouabain in KH. Furthermore, there was no impact of the added blebbistatin on the KH [Na+], [K+] and [Ca2+] as analysed by Vetscan i-STAT1 analyser (CG8 + cartridge, Abaxis, UK).

Administration of ouabain causes immediate Na/K ATPase inhibition resulting in immediate rise in Nai accompanied by positive inotropy. The final concentration of ouabain (75 μmol l−1) chosen for the acute Nai elevation study protocols caused significant Nai elevation which, when combined with 100 nM blebbistatin eliminated ouabain-induced inotropy (Fig. 3b).

CGP13757 was re-suspended in DMSO (1 mg/ml), aliquoted and stored at 4 °C. Final concentration used in KH (1 μmol/l) and the duration of administration was based on previously published protocols in mitochondria, cells and perfused hearts32,33,34. KH buffers containing pharmacological agents were prepared in amber glassware immediately prior to the experiment.

### Metabolic KH buffer and perfusion protocols

For the assessment of the relative contributions of exogenous metabolic substrates (glucose and palmitate) to myocardial oxidative metabolism (n = 7/group) substrate-enriched metabolic KH Buffer (KHmetab) was used. In KHmetab the glucose concentration was 5 mmol l−1 and the following additional substrates and compounds included (in mmol/l): 1 sodium L-lactate; 0.1 sodium pyruvate; 0.5 L-glutamic acid monosodium salt monohydrate; 5 mU l−1 insulin (NovoRapid insulin, Novo Nordisk, Denmark) and 0.3 sodium palmitate with 3% (w/v) bovine serum albumin (BSA, Proliant Biologicals, USA)43. Prior to inclusion, BSA was dissolved and purified as previously described43. KHmetab of identical composition (in terms of components and their concentrations) but containing [U-13C] palmitate and [1,6-13C] glucose (Cambridge Isotopes, Goss Scientific, UK) was used for 13C NMR substrate selection/metabolic flux assessment (13C-KHmetab).

After a 20-min functional equilibration period with KH, hearts were randomly assigned to treatment groups for perfusion:

#### C57BL6/J hearts

1. (i)

KH buffer plus vehicle (0.029% v/v DMSO).

2. (ii)

KH buffer plus 75 μM ouabain.

3. (iii)

KH buffer plus 100 nM blebbistatin.

4. (iv)

KH buffer plus 75 μM ouabain and 100 nM blebbistatin.

5. (v)

KH buffer plus 1 μM CGP13757.

6. (vi)

KH buffer plus 1 μM CGP13757, 75 μM ouabain and 100 nM blebbistatin.

7. (vii)

Metabolic K-H plus 75 μM ouabain and 100 nM blebbistatin.

#### PLM3SA and PLMWT hearts

1. i.

KH buffer perfusion, paced at 550 beats min−1 via epicardial silver wire electrodes placed at the apex of the left ventricle and the right atrium.

2. ii.

KH buffer perfusion unpaced.

#### Banded and sham control hearts

1. i.

KH buffer perfusion.

2. ii.

For 13C NMR substrate selection/metabolic flux analysis, PLM3SA, PLMWT, banded and sham control hearts were functionally equilibrated for 30 min with KHmetab and switched to a 40 min perfusion with 13C-KHmetab. Separate cohorts of PLM3SA, PLMWT, banded and sham control hearts after equilibration were perfused for 40 min with 13C- KHmetab buffer with added 1 μmol l−1 CGP13757.

### In situ 23Na and 31P NMR Langendorff perfusion protocols

All in situ NMR Langendorff mouse heart perfusion experiments were carried out on a Bruker Avance III 9.4 T 400 MHz vertical wide-bore spectrometer (Bruker, Karlsruhe, Germany) equipped with triple-axis gradients, a microimaging probe and exchangeable RF coil inserts (10 mm 23Na coil or 10 mm 1H/31P dual tune coil). Following cannulation on an MR-compatible umbilical perfusion rig, hearts were perfused with phosphate free KH buffer (11 mM glucose) and subsequently lowered into the center of the magnet for real-time multiple quantum filtered 23Na NMR (triple quantum filtered TQF and double quantum filtered DQF) quantification of Nai and 31P NMR assessment of cardiac energetics as previously described17,41. The hardware setup required changing between coils so that fully relaxed 31P data were acquired at baseline prior to any elevation in Nai and at the end of 30 min treatment protocol, while 23Na acquisitions were acquired throughout the functional equilibration period and during the 30 min Nai elevation/drug treatment protocols. Fully relaxed 31P experiments were acquired with a 60° flip angle, 256 scans, a repetition time of 3.8 s and a total experiment duration of 16 min. Nai quantification, the assessment of cardiac energetics and pH were performed as previously described17,41. MQF 23Na experiments were acquired with 192 scans, 2048 data points, sweep width of 50 ppm, an acquisition time of 200 ms, pre-scan delay of 200 ms and a total acquisition time of 1.24 min. The mixing time (τm = 3.6 ms) was calibrated for the maximumTQF signal and set to be the same for the DQF experiments. An exponential line broadening factor of 10 Hz was applied prior to Fourier transformation and subsequent baseline correction. Peak integrals were measured using Bruker Top Spin version 2.1 software.

The TQF Nai signal is a composite signal arising from the sum of various compartments each with varying electrostatic interactions, Na concentrations, and the volume occupied. The mechanism by which a TQF signal is produced is through slow rotational reorientation of the Na ion giving rise to quadrupolar relaxation when it is bound to macromolecules, and therefore largely from the intracellular compartment although there is also a contribution from the extracellular interstitial compartment. We have performed a series of in situ multiple quantum filtered 23Na NMR spectroscopy experiments in order to assess the cellular compartmentation of the 23Na TQF signal. In brief, this has involved following the TQF signal while sequentially washing out

1. (i)

the extracellular compartment (with a Na-free solution)

2. (ii)

the cytosolic compartment (with a Na-free solution plus saponin). Saponin should selectively permeabilise the cholesterol containing sarcolemma.

3. (iii)

the mitochondrial compartment (with a Na-free solution plus Triton X-100). Triton should permeabilise all other non-cholesterol-containing membrane such as the mitochondria.

### High resolution 1H NMR of tissue extracts

Frozen, weighed and pulverized hearts were subject to methanol/ water/ chloroform dual phase extraction adapted from Chung et al.44 The upper aqueous phase was separated from the chloroform and protein fractions. 20–30 mg chelex-100 was added to chelate paramagnetic ions, vortexed and centrifuged at 3600 RPM for 1 min at 4 °C. The supernatant was then added to a fresh Falcon tube containing 10 µL universal pH indicator solution followed by vortexing and lyophilisation. Dual-phase-extracted metabolites were reconstituted in 600 µL deuterium oxide (containing 8 g L−1 NaCl, 0.2 g L−1 KCl, 1.15 g L−1 Na2HPO4, 0.2 g L−1 KH2PO4 and 0.0075% w/v trimethylsilyl propanoic acid (TSP)) and adjusted to pH ≈ 6.5 using 1 M hydrochloric acid and/or 1 M sodium hydroxide (<5 µL of each) prior to vortexing. The solution was transferred to a 5 mm NMR tube (Norel Inc., USA) and then analysed using a Bruker Avance III 400 MHz (9.4 T) wide-bore spectrometer (Bruker, Germany) with a high-resolution broadband spectroscopy probe at 298 K. A NOESY 1D pulse sequence was used with 128 scans, 2 dummy scans, total repetition time 6.92 s, sweep width of 14 ppm and an acquisition duration of 15 min. Data were analysed using TopSpin software version 2.1 (Bruker, Germany), FIDs were multiplied by a line broadening factor of 0.3 Hz and Fourier-transformed, phase and automatic baseline-correction were applied. Chemical shifts were normalised by setting the TSP signal to 0 ppm. Peaks of interest were initially integrated automatically using a pre-written integration region text file and then manually adjusted where required. Assignment of metabolites to their respective peaks was carried out based on previously obtained in-house data, confirmed by chemical shift, NMR spectra of standards acquired under the same conditions and confirmed using Chenomx NMR Profiler Version 8.1 (Chenomx, Canada). Peak areas were normalized to the TSP peaks and metabolite concentrations quantified per gram tissue wet weight42,44. Intracellular concentration of NADH, ATP + ADP, phosphocreatine, creatine, lactate, succinate, fumarate, carnitine, phosphocholine, choline, acetyl carnitine, acetate, aspartate, glutamine, glycine, alanine was analysed. The fold change with respect to the control group was then calculated for each metabolite.

### LC-MS/MS

Lyophilised aqueous metabolite extracts were reconstituted in 350 µL ultrapure water (Millipore Corporation, USA). A series of mixed standards were prepared in ultrapure water containing 0.0025–50 µM of each metabolite. An Agilent 1100 HPLC system (Agilent Technologies, USA) consisting of an autosampler, a binary pump, a degasser unit and a column oven coupled to an Applied Biosystems Sciex API 3000 mass spectrometer with Turbo Ionspray interface (MDS Sciex, Canada). Chromatograpic separation was achieved using a Supelcogel C610-H column (300 mm × 7.7 mm) with a Supelcogel H guard column (50 mm × 4.6 mm) (Supelco, USA) with an isocratic flow (0.4 mL min−1) of mobile phase consisting of 0.01% v/v formic acid and methanol (90:10) and an injection volume of 100 µL.

The HPLC eluate was split (4:1) just before the Turbo Ionspray interface resulting in a flow of 0.1 mL/min into the mass spectrometer. In order to eliminate peak to peak interference, two separate acquisitions were performed for each sample and standard. Acquisition 1 included α-ketoglutarate (145 > 101 m/z), citrate (191 > 87 m/z), isocitrate (191 > 155 m/z), fumarate (115 > 71 m/z) and lactate (89 > 43 m/z) whilst Acquisition 2 included pyruvate (87 > 43 m/z), malate (133 > 115 m/z) and succinate (117 > 73 m/z). Data were acquired using Analyst software (version 1.4.2) and metabolite concentrations in the samples were interpolated using calibration curves of each metabolite.

### GC-MS/MS

Polar metabolites were extracted from the frozen pulverized cardiac tissue (50 mg) using the modified Folch method involving methanol water and chloroform with some modifications. Namely, a 200 µl of ice-cold distilled water with 1 mcg Norvalin as internal standard was added to the samples and 1 h sonication was performed in cold conditions. This was followed by addition of 500 µl HPLC grade methanol (ice cold) to each samples with 1 h sonication in ice cold conditions. Subsequently, the methanol: water extract was transferred using glass Pasteur pipette to a new labelled high grade Eppendorf tube and 500 µl chloroform was added to each tube, vortexed for 1 min followed by 15 min shaking on the shaker at high speed. Subsequently, the Eppendorf tubes were centrifuged at 13,000 rpm, 4 C for 15 min and the top polar layer was aspirated to a clean Eppendorf tubes. The polar extract was dried using a speedvac and stored in −80 freezer for subsequent derivatization.

### Derivatization method

All derivatization steps were carried out in a fume hood. In order to derivatize proteinogenic amino acids, organic acids and glycolytic intermediates for GC-MS analysis, the dried extract was incubated at 95 °C in open tubes in order to remove any residual moisture in the samples. The dried extract was solubilized in 40 μl of 2% methoxyamine HCL in pyridine (Sigma-Aldrich, Dorset,UK) followed by 60 min incubation at 60 °C and subsequently 60 μl N-tertbutyldimethylsilyl-N-methyltrifluoroacetamide (MTBSTFA) with 1% (w/v) tertbutyldimethyl-chlorosilane (TBDMSCI) (Sigma-Aldrich, Dorset, UK) derivatization reagent was added. The suspension was incubated for an hour at 60 °C in a well-sealed tube to prevent evaporation. Finally the samples were centrifuged at 13,000 rpm for 5 min and the clear supernatant was transferred to a chromatography vial with a glass insert (Thermo Fisher, Scientific, Chromacol, Hertfordshire, UK) and proceeded immediately to GC-MS analysis.

### GC-MS/MS analysis

For analysis of the derivatized samples an Agilent 7890B Series GC/MSD gas chromatograph with a polydimethylsiloxane GC column coupled, with a mass spectrometer (GC-MS) (Agilent Technologies UK Limited, Stockport, UK) was used. Prior to sample analysis the GC-MS was tuned to a full width at half maximum (FWHM) peak width of 0.60 a.m.u. in the mass range of 50 to 650 mass to charge ratio (m/z) using PFTBA tuning solution.

One microlitre of sample was injected into the GC-MS in splitless mode with helium carrier gas at a rate of 1.0 ml min−1. The inlet liner containing glass wool was set to a temperature of 270 °C. Oven temperature was set at 100 °C for 1 min before ramping to 280 °C at a rate of 5 °C min−1. Temperature was further ramped to 320 °C at a rate of 10 °C min−1 held at 320 °C for 5 mins. Compound detection was carried out in full scan mode in the mass range 50–650 m/z, with 2–4 scans s−1, a source temperature of 250 °C, a transfer line temperature of 280 °C and a solvent delay time of 6.5 min. The injector needle was cleaned with acetonitrile three times before measurement commencement and three times following every measurement thereafter. The raw GC-MS data were converted to common data format (CDF) using the acquisition software and further processing of the isotope data including isotope correction and mass isotopomer analysis /batch quantification was performed on metabolite detector software. To determine absolute concentration, a 7 point calibration series covering the mass range of 0–8.46 µM was prepared in triplicates with 100 µl of 8.5 µM of internal standard added to each sample of the calibration series and were extracted as the method outlined above. The dried extract were then derivatised followed by GCMS analysis. For absolute quantification, the ratio of peak area of each concentration to the peak area of internal standard was calculated and plotted against the ratio of the concentration of analyte with respect to the concentration of internal standard to generate the equation and estimate the linear dynamic range. Subsequently, the raw peak area for each analyte of interest was calculated using the metabolite detector software followed by normalizing the response to the internal standard peak area.

### Tissue extraction for 13C NMR

Frozen hearts were weighed and ground to a fine powder under liquid nitrogen and extracted at 4 °C with 6% perchloric acid (PCA) in a ration 5:1. The suspension was centrifuged at 4000 RPM, 4 °C for 10 min and a known volume of supernatant decanted and neutralised with 6 M KOH to pH7.0 at 4 °C. The mixture was centrifuged and the supernatant lyophilised at −40 °C. Lyophilised tissue extracts were reconstituted in 0.6 ml of 50 mM deuterated phosphate (KH2PO4) buffer pH 7.0 lyophilised and resuspended in D2O. A small amount of chelating resin (Chelex-100) was added to samples to remove any paramagnetic ions and filtered through a 0.22 μm syringe filter into 3 mm NMR tube.

### High resolution 13C NMR of tissue extracts

High-resolution 1H-decoupled 13C NMR spectra were acquired under automation at 298 K on a Bruker Avance III 700 (16.4 T) NMR spectrometer (Bruker Biospin, Coventry, UK) equipped with a 5 mm TCI helium-cooled cryoprobe and a refrigerated SampleJet sample changer. The temperature was allowed to stabilise for 3 min after insertion into the magnet. Tuning, matching and shimming was performed automatically for each sample and the 1H pulse length was calibrated on each sample and was typically around 8 µs. 1D 1H-decoupled 13C spectra (zgpg60) were acquired with 8192 transients, a spectral width of 200 ppm, 64 K data points, a mixing time of 10 ms, relaxation delay of 1 s and repetition time of 2 s. 1H-decoupling was achieved using a WALTZ65 sequence during the relaxation delay and acquisition. Spectra were processed in the manufacturer’s software (Topspin 3.2.6). Free induction decays were multiplied with an exponential function (line broadening of 0.25 Hz), Fourier transformed, phase correction was performed manually and automatic baseline correction was applied. Representative spectra are shown in Fig. 1b. The relative contributions of exogenous 13C substrates (palmitate vs glucose) to oxidative phosphorylation were determined from 13C glutamate isotopomer labelling patterns (Fig. 1b) using tcaCALCtm software (v2.07)22,24.

### In silico modelling

In silico simulations were performed using the metabolic network of the cardiomyocyte CardioNet21,22,45. Mathematical modelling has previously been used to study the dynamics of cardiac metabolism in response to stress20,21,46, and CardioNet has been successfully applied to identify limiting metabolic processes and estimate flux distributions20,22. Flux balance analysis (FBA) allows to estimate flux rates in a cellular model based on metabolic constraints that are defined by the extracellular environment (e.g. oxygen and nutrient supply), cellular demands (e.g. proliferation, contraction) and tissue type (e.g. heart vs. liver). This modelling approach combines biochemical network models with optimality problems, which describe different cost or benefit functions and allow us to include experimental data, for example metabolite levels, enzyme levels or flux rates.

The advantage of flux balance analysis is that it considers system-wide effects of processes and allows us to assess metabolic limitations in an unbiased approach. We applied flux balance analysis to identify which reactions are involved in myocardial metabolic adaptations to high levels of Nai.

### Mathematical modelling of myocardial metabolic adaptations to Nai elevation

Metabolic flux distributions were calculated using constrained based modelling. To calculate flux rate changes (vi), we constrained the model for each metabolite using experimentally determined metabolite concentrations (1H NMR, LC-MS/MS, effluent lactate production, 13C substrate utilization measurements) to maximize cardiac work reflected by ATP hydrolysis (vATPase). The decision to optimize steady-state ATP production was not arbitrary. Our data show that while Na elevation re-programs metabolism, it does so while not compromising energetics—as demonstrated by our 31P-NMR measurements showing maintained ATP, PCr, PCr/ATP ratios and pHi. ATP and PCr concentrations are clearly a product of both production and consumption, however, our wet-biology experimental design tries to keep consumption as constant as possible (by the titration of contractility with blebbistatin) thereby keeping steady-state ATP consumption constant. Simulations were run with boundary conditions reflecting the metabolite composition of the perfusion buffer and experimentally measured uptake and release rates of substrates. At the same time, various metabolites, including amino acids and lipids, were set to previously reported values21,47,48,49, in order to mimic the ex vivo experimental conditions. Based on these constrains we first determined flux distributions ($$v_m^{}$$) under baseline control conditions. We then calculated fold-changes (FC) for experimentally measured metabolite concentrations between baseline controls and treatment groups (acute and chronic Nai elevation), and used these FC to further constrain fluxes ($$v_m^{}$$) for the synthesis and/or degradation of intracellular metabolites. We included FC based on the assumption that changes in metabolite concentrations under experimental conditions are accompanied by a proportional increase or decrease in the respective flux for the metabolite pool. By using metabolite level changes (fold changes) to estimate flux rate changes (vFC), we imply that the altered steady-state concentrations of metabolites are reflected in the newly evolved flux state and potentially limit metabolic functions.

The following flux balance analysis was applied to identify steady-state flux distributions that are in agreement with applied substrate uptake and release rates, and changes in metabolite pools:

$${\mathrm{max}}\,v_{\mathrm{ATPase}}$$

(1)

subject to (1)

$$S \cdot v = 0,$$

(2)

$$v_i^{( – )} \le v_i \le v_i^{\left( + \right)},$$

(3)

$$L_j^{( – )} \le v_j \le L_j^{\left( + \right)}\left( {j = j_1,\,j_2,\, \ldots } \right),$$

(4)

$$v_m \le FC_m \cdot v_m^0\left( {m = m_1,\,m_2,\, \ldots } \right),$$

(5)

where $$v_i$$ denotes the flux rate change through reaction $$i$$, $$v_j$$ denotes the measured uptake or secretion rate through reaction $$j$$, S is the stoichiometric matrix, and $$v_i^{( – )}$$ and $$v_i^{( + )}$$ are flux constraints. The CPLEX LP solver was used to find the solution to the FBA problems. The logarithm of the metabolic flux rate values is presented in the form of heatmaps. Metabolic reactions are clustered according to their association to metabolic pathways and plot colours indicate estimated flux rates for each metabolic reaction. All reactions and their metabolic subsystems, classified in the Kyoto Encyclopedia of Genes and Genomes database50.

### Data statistics and reproducibility

Data are presented as mean ± SEM and analysed blind to phenotype or treatment. Statistical analysis was conducted using GraphPad Prism (v 8.3) and Microsoft Excel (v.16.16.15). All data were obtained from a minimum of two independent experiments. Comparison between groups was by Student’s t-test (Gaussian data distribution), two-way analysis of variance (ANOVA) with Bonferroni’s correction for multiple comparison and one-way ANOVA using Bonferroni’s correction for multiple comparisons where applicable. After pharmacological agent treatment (ouabain, blebbistatin, CGP13757), hearts were compared to baseline control values for the same genotype. Metabolite fold changes of the ratio of treated (T) vs control (C) groups were calculated and the fold change. Propagated standard error (SEM) of the ratio was calculated using the formula $${\mathrm{SEM}}_{(T/C)} = (T/C)\sqrt {(\mathrm{SEM}_T/T)^2 + (\mathrm{SEM}_C/C)^2}$$, assuming the covariance between the two groups is zero, i.e., C and T are uncorrelated. Metabolic differences between the flux distributions were analysed by R Statistics (version 1.2.1335 for Fedora/RatHat 7 64-bit, R version 3.0.1, Boston Massachusetts, USA, www.rstudio.com)51. Datasets were tested for normal distribution using the Shapiro–Wilk test. Groups were compared using non-parametric (Kruskal–Wallis) test methods. Unsupervised hierarchical clustering and PCA were conducted using R-Studio. Heat maps and z-scores were generated using R-Studio with the heatmap.2 function and viridis colour palettes from the R-package gplots (version 3.0.1.1)

Z-scores were calculated as follows:

$$z = \frac{{(X – \mu )}}{\sigma }$$

(6)

where z denotes the z-score, X is the average flux rate for a given reaction within an experimental group (control, acute and chronic Na elevation), μ is the population mean, σ and is the standard deviation. Z-scores were calculated for each reaction (each row in the heat map) including all control, acute and chronic Na elevation values. Each calculated z-score was assigned a colour as depicted in the heat map. The similarity between groups was assessed using a Euclidean distance and the number of clusters was determined using the k-means algorithm. We applied the Elbow method to determine optimal numbers of clusters. Columns (experimental groups) were clustered hierarchically according to dissimilarities between clusters with the squared Euclidean distances between cluster means calculated.

Differences were considered significant when P < 0.05.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Source