Dietary Mg2+ Intake and the Na+/Mg2+ Exchanger SLC41A1 Influence Components of Mitochondrial Energetics in Murine Cardiomyocytes

Cardiomyocytes are among the most energy-intensive cell types. Interplay between the components of cellular magnesium (Mg) homeostasis and energy metabolism in cardiomyocytes is poorly understood. We have investigated the effects of dietary Mg content and presence/functionality of the Na+/Mg2+ exchanger SLC41A1 on enzymatic functions of selected constituents of the Krebs cycle and complexes of the electron transport chain (ETC). The activities of aconitate hydratase (ACON), isocitrate dehydrogenase (ICDH), α-ketoglutarate dehydrogenase (KGDH), and ETC complexes CI–CV have been determined in vitro in mitochondria isolated from hearts of wild-type (WT) and Slc41a1−/− mice fed a diet with either normal or low Mg content. Our data demonstrate that both, the type of Mg diet and the Slc41a1 genotype largely impact on the activities of enzymes of the Krebs cycle and ETC. Moreover, a compensatory effect of Slc41a1−/− genotype on the effect of low Mg diet on activities of the tested Krebs cycle enzymes has been identified. A machine-learning analysis identified activities of ICDH, CI, CIV, and CV as common predictors of the type of Mg diet and of CII as suitable predictor of Slc41a1 genotype. Thus, our data delineate the effect of dietary Mg content and of SLC41A1 functionality on the energy-production in cardiac mitochondria.


Introduction
Cardiovascular diseases (CVD) account for~31% of all estimated deaths worldwide (www.who.int). Ageing per se is the major intrinsic risk factor for heart failure and CVD [1]. An unhealthy diet including ETC in cardiac mitochondria isolated from hearts of knock-out (KO; Slc41a1 − / − ) and wild-type (WT; Slc41a1 + / + ) mice have been evaluated.

Effect of Dietary Mg Content and Slc41a1 Genotype on Activities of ACON, ICDH, and KGDH in Lysates of Mitochondria of Murine Cardiac Cells
First, we examined the impact of LMgD on the activity of ACON in lysates of murine Slc41a1 +/+ and Slc41a1 −/− heart mitochondria. ACON is an enzyme that catalyzes the reversible 2-step (de)hydration conversion between citrate as a substrate and the final product isocitrate via the intermediate, cis-aconitate [41]. Two-factorial ANOVA (2F-ANOVA) indicated that low dietary Mg decreased ACON activity (p < 0.01); whereas absence of the Slc41a1 gene (Slc41a1 −/− cf. Slc41a1 +/+ animals) increased ACON activity (p < 0.01) in heart cell mitochondria ( Figure 1A,B). There was no statistically significant interaction (p = 0.50), indicating that both factors superimposed on each other independently. The eROC (receiver operating characteristic) curve analyses revealed 76.7% and 85.6% ability to discriminate ACON activities based on the type of Mg diet and Slc41a1 genotype, respectively ( Figure 1C,D); the uncertainty of the ROC curve estimate was considered, as shown in Figure 1C,D.  Next, we examined the effect of LMgD on the activity of mitochondrial NAD + -dependent ICDH, an enzyme that catalyzes the regulated conversion (oxidative decarboxylation) of isocitrate to α-ketoglutarate and CO 2 . This is the first of four oxidative steps within the Krebs cycle and is the key rate-limiting step of this cycle [42]. The results were qualitatively comparable to those obtained for ACON. 2F-ANOVA revealed a significant decrease (p < 0.001) of ICDH activity in cardiac mitochondria of animals fed LMgD compared with animals fed NMgD; whereas the Slc41 −/− genotype tended to increase the activity of ICDH in cardiac mitochondria (p = 0.059; Figure 2A,B). Again, no significant interaction (p = 0.31) was detected between dietary Mg content and Slc41a1 genotype, indicating that the type of response for one factor was not dependent on the type of response for the other factor. The utilization of eROC curve analyses revealed 100% and 64.4% ability to discriminate ICDH activities based on the type of Mg diet and on Slc41a1 genotype, respectively ( Figure 2C,D); the uncertainty of the ROC curve estimate was considered ( Figure 2C,D). Next, we examined the effect of LMgD on the activity of mitochondrial NAD + -dependent ICDH, an enzyme that catalyzes the regulated conversion (oxidative decarboxylation) of isocitrate to α-ketoglutarate and CO2. This is the first of four oxidative steps within the Krebs cycle and is the key rate-limiting step of this cycle [42]. The results were qualitatively comparable to those obtained for ACON. 2F-ANOVA revealed a significant decrease (p < 0.001) of ICDH activity in cardiac mitochondria of animals fed LMgD compared with animals fed NMgD; whereas the Slc41 −/− genotype tended to increase the activity of ICDH in cardiac mitochondria (p = 0.059; Figure 2A,B). Again, no significant interaction (p = 0.31) was detected between dietary Mg content and Slc41a1 genotype, indicating that the type of response for one factor was not dependent on the type of response for the other factor. The utilization of eROC curve analyses revealed 100% and 64.4% ability to discriminate ICDH activities based on the type of Mg diet and on Slc41a1 genotype, respectively ( Figure 2C,D); the uncertainty of the ROC curve estimate was considered ( Figure 2C,D). KGDH mediates the tightly regulated conversion of α-ketoglutarate to succinyl-CoA while reducing NAD + to NADH and thereby supplying electrons for the respiratory chain. It represents a key control point in the Krebs cycle. It is inhibited by its products succinyl-CoA and NADH; a positive total energy balance in the cell has also an inhibitory effect on the enzymatic activity of KGDH [43]. ADP and Ca 2+ play a role as allosteric activators of KGDH [44]. Also for KGDH, 2F-ANOVA revealed a significantly decreased activity (p < 0.05) in cardiac mitochondria of animals fed with LMgD; however, in this case, no significant effect (p = 0.36) of the Slc41a1 −/− genotype was detected ( Figure 3A,B). A trend for interaction (p = 0.077) between Mg diet and Slc41a1 genotype existed with regard to KGDH activity. The eROC curve analyses revealed 74.4% and 62.2% ability to KGDH mediates the tightly regulated conversion of α-ketoglutarate to succinyl-CoA while reducing NAD + to NADH and thereby supplying electrons for the respiratory chain. It represents a key control point in the Krebs cycle. It is inhibited by its products succinyl-CoA and NADH; a positive total energy balance in the cell has also an inhibitory effect on the enzymatic activity of KGDH [43]. ADP and Ca 2+ play a role as allosteric activators of KGDH [44]. Also for KGDH, 2F-ANOVA revealed a significantly decreased activity (p < 0.05) in cardiac mitochondria of animals fed with LMgD; however, in this case, no significant effect (p = 0.36) of the Slc41a1 −/− genotype was detected ( Figure 3A,B). A trend for interaction (p = 0.077) between Mg diet and Slc41a1 genotype existed with regard to KGDH activity. The eROC curve analyses revealed 74.4% and 62.2% ability to discriminate KGDH activities according to type of Mg diet and Slc41a1 genotype, respectively ( Figure 3C,D); the considered uncertainties of the ROC curve estimates are given in Figure 3C,D.  Figure 3C,D); the considered uncertainties of the ROC curve estimates are given in Figure 3C,D.

Effect of Dietary Mg Content and A1 Genotype on Activities of ETC Complexes (Including F1Fo-ATPase) in Lysates of Murine Mitochondria of Cardiac Cells
ETC is a redox cascade, downstream of Krebs cycle, consisting of protein complexes enabling the transport of electrons (to their final acceptor O2) coupled with the transport of H + from matrix to inter-membrane space, resulting in build-up of a large inside-negative membrane potential on the inner mitochondrial membrane and in the production of ATP by CV/F1Fo-ATPase. Only a paucity of information is available regarding any possible interference between mitochondrial Mg homeostasis, ETC, and consequent energy production and metabolism.
The 2F-ANOVA revealed a significant increasing effect (p < 0.001) of dietary Mg starvation on CI activity in cardiac mitochondria when the animals on LMgD and the animals on NMgD were compared balanced for Slc41a1 genotype ( Figure 4A). Irrespective of dietary regime, a significantly higher (p < 0.05) activity of CI was measured in cardiac mitochondria of Slc41a −/− animals when compared with the CI activity in mitochondria of Slc41a1 +/+ animals ( Figure 4B). No significant interaction (p = 0.74) between dietary Mg content and Slc41a1 genotype was detected for CI activity. Based on eROC curve analyses, the type of Mg diet and Slc41a1 genotype had 91.1% and 75.6%

Effect of Dietary Mg Content and A1 Genotype on Activities of ETC Complexes (Including F 1 F o -ATPase) in Lysates of Murine Mitochondria of Cardiac Cells
ETC is a redox cascade, downstream of Krebs cycle, consisting of protein complexes enabling the transport of electrons (to their final acceptor O 2 ) coupled with the transport of H + from matrix to inter-membrane space, resulting in build-up of a large inside-negative membrane potential on the inner mitochondrial membrane and in the production of ATP by CV/F 1 F o -ATPase. Only a paucity of information is available regarding any possible interference between mitochondrial Mg homeostasis, ETC, and consequent energy production and metabolism.
The 2F-ANOVA revealed a significant increasing effect (p < 0.001) of dietary Mg starvation on CI activity in cardiac mitochondria when the animals on LMgD and the animals on NMgD were compared balanced for Slc41a1 genotype ( Figure 4A). Irrespective of dietary regime, a significantly higher (p < 0.05) activity of CI was measured in cardiac mitochondria of Slc41a −/− animals when compared with the CI activity in mitochondria of Slc41a1 +/+ animals ( Figure 4B). No significant interaction (p = 0.74) between dietary Mg content and Slc41a1 genotype was detected for CI activity.
Based on eROC curve analyses, the type of Mg diet and Slc41a1 genotype had 91.1% and 75.6% ability to serve as discriminants/predictors of CI activities, respectively ( Figure 4C,D); the uncertainties of the ROC curve estimates were considered and are given in Figure 4C,D.  The 2F-ANOVA data analysis revealed no significant effect (p = 0.18) of the diet on CII activity in cardiac mitochondria when animals on LMgD and NMgD were compared ( Figure 5A). A significant decreasing effect (p < 0.001) of the Slc41a1 −/− genotype on the CII activity was seen in cardiac mitochondria when compared with CII activity in mitochondria of Slc41a1 +/+ animals ( Figure  5B). No significant interaction (p = 0.32) between dietary Mg content and Slc41a1 genotype was detected for CII activity. The eROC curve analyses revealed 64.4% and 94.4% ability of type of Mg diet and Slc41a1 genotype to serve as discriminants/predictors of CII activities, respectively ( Figure  5C,D); the uncertainties of the ROC curve estimates are given in Figure 5C,D. The 2F-ANOVA data analysis revealed no significant effect (p = 0.18) of the diet on CII activity in cardiac mitochondria when animals on LMgD and NMgD were compared ( Figure 5A). A significant decreasing effect (p < 0.001) of the Slc41a1 −/− genotype on the CII activity was seen in cardiac mitochondria when compared with CII activity in mitochondria of Slc41a1 +/+ animals ( Figure 5B). No significant interaction (p = 0.32) between dietary Mg content and Slc41a1 genotype was detected for CII activity. The eROC curve analyses revealed 64.4% and 94.4% ability of type of Mg diet and Slc41a1 genotype to serve as discriminants/predictors of CII activities, respectively ( Figure 5C,D); the uncertainties of the ROC curve estimates are given in Figure 5C,D.
The statistical analysis with 2F-ANOVA revealed no significant effect (p = 0.60) of the diet on CIII activity in heart mitochondria when the animals on LMgD and the animals on NMgD were compared balanced for genotype ( Figure 6A). Irrespective of the type of Mg diet, a significant increasing effect (p < 0.001) of the Slc41a1 −/− genotype on the activity of CIII was measured in cardiac mitochondria when compared with the CIII activity in mitochondria of Slc41a1 +/+ animals ( Figure 6B). No significant (p = 0.66) interaction between Mg diet and Slc41a1 genotype was determined for CIII activity. The 54.4% and 94.4% ability of the type of Mg diet and of Slc41a1 genotype to discriminate/predict CIII activities The statistical analysis with 2F-ANOVA revealed no significant effect (p = 0.60) of the diet on CIII activity in heart mitochondria when the animals on LMgD and the animals on NMgD were compared balanced for genotype ( Figure 6A). Irrespective of the type of Mg diet, a significant increasing effect (p < 0.001) of the Slc41a1 /-genotype on the activity of CIII was measured in cardiac mitochondria when compared with the CIII activity in mitochondria of Slc41a1 +/+ animals ( Figure  6B). No significant (p = 0.66) interaction between Mg diet and Slc41a1 genotype was determined for CIII activity. The 54.4% and 94.4% ability of the type of Mg diet and of Slc41a1 genotype to discriminate/predict CIII activities were determined by eROC curve analyses, respectively ( Figure  6C,D); the uncertainties of the ROC curve estimates are given in Figure 6C,D. For CIV (cytochrome c oxidase) activity, significant increasing effects of LMgD vs. NMgD (p < 0.001; Figure 7A) and Slc41a1 −/− vs. Slc41a1 +/+ genotype (p < 0.05; Figure 7B) were detected in cardiac mitochondria. However, a highly significant interaction (p < 0.001) between dietary Mg content and Slc41a1 genotype indicated a strong interdependence of the two factors. As such, no significant difference (p = 0.064) of CIV activity was detected in cardiac mitochondria when Slc41a1 +/+ animals on LMgD were compared with Slc41a1 +/+ animals on NMgD (LMgD 745 ± 20 nmol/min/mg protein vs. NMgD 597 ± 25 nmol/min/mg protein; Figure A1). By contrast, the CIV activity was increased in cardiac mitochondria by 186.1% (p < 0.001) in Slc41a1 −/− animals on LMgD when compared to Slc41a1 −/− animals on NMgD (LMgD 1070 ± 22 nmol/min/mg protein vs. NMgD 374 ± 20 nmol/min/mg protein; Figure A1). Moreover, cardiac mitochondria of Slc41a1 −/− animals had 37.4% lower CIV activity on NMgD (p < 0.01) and 43.6% higher CIV activity on LMgD (p < 0.001) when compared with cardiac mitochondria from A1 +/+ animals ( Figure A1).
The eROC analyses revealed 97.8% and 44.4% ability of the type of Mg diet and of Slc41a1 genotype to serve as discriminants/predictors of CIV activities, respectively ( Figure 7C,D); the uncertainties of the ROC curve estimates are given in Figure 7C,D.
The eROC analyses revealed 96.7% and 78.9% ability of the type of Mg diet and of Slc41a1 genotype to discriminate/predict activities of CV, respectively ( Figure 8C,D); the uncertainties of the ROC curve estimates are given in Figure 8C,D.

Random Forest Machine-Learning (RFM-L) Analysis of the Activities of Selected Krebs Cycle Enzymes and ETC Complexes as Potential Predictors/Discriminators between LMgD and NMgD and between Slc41a1 −/− and Slc41a1 +/+ Genotypes
In order to analyze the activities of ACON, ICDH, KGDH, CI, CII, CIII, CIV, and CV/F 1 F o -ATPase as potential predictors/discriminators between the types of Mg diet fed to MK-1 mice (LMgD vs. NMgD) and between the Slc41a1 genotypes of the animals (Slc41a1 −/− vs. Slc41a1 +/+ ), we trained the RFM-L algorithm using our data. The algorithm evaluated the discriminative importance of individual activities of the tested Krebs cycle enzymes and ETC complexes by a technical construct known as graph depth [45]. The predictive ability of these enzymes/enzyme complexes was visualized by ROC curves and quantified by AUC. A perfect discriminative ability of predictors is associated with 100% AUC; 50% AUC (or less) corresponds to no discriminative ability [45]. The best discriminative ability between mitochondria isolated from the hearts of animals fed with LMgD and mitochondria isolated from the hearts of animals fed with NMgD (irrespective of their Slc41a1 genotype) were computed for the activity of ICDH followed by the activities of CIV > CV > CI ( Figure 9A). The importance plot revealed the activity of CII ( Figure 9B) as the only suitable individual discriminator between mitochondria isolated from hearts of Slc41a1 −/− mice and the mitochondria from hearts of Slc41a1 +/+ mice (irrespective of the content of Mg in their diet). The RFM-L algorithm trained in the mode in which the activities of ICDH, CI, CIV, and CV served as joined predictors led to an ROC curve with 100% AUC; thus, the joint activities of ICDH, CI, CIV, and CV can serve as a perfect predictor/discriminator between LMgD and NMgD ( Figure 9C). Training of the RFM-L algorithm in the mode in which the activity of CII served as a predictor led to an ROC curve with 96.7% AUC; thus, the activity of CII could be considered as a near perfect predictor/discriminator between the Slc41a1 −/− and Slc41a1 +/+ genotypes ( Figure 9D).

A brief Summary of the Results
The results are briefly summarized in Table 1. The upper part of the table compiles outcome of 2F-ANOVA, while the bottom part (on gray background) summarizes outcomes of post-hoc Tukey

A Brief Summary of the Results
The results are briefly summarized in Table 1. The upper part of the table compiles outcome of 2F-ANOVA, while the bottom part (on gray background) summarizes outcomes of post-hoc Tukey multiple comparisons of group means. For CIV and CV the significant interaction between Slc41a1 genotype and Mg diet has been identified and for both also the data resulting from post-hoc Tukey test were previously provided. To obtain the complex information carried in post-hoc analyze, they were performed also for each enzyme/complex, for which no significant interaction between Slc41a1 genotype and Mg diet has been identified (ACON, ICDH, KGDH, CI, CII and CIII). The outcomes of these analyzes are provided in Appendix A (Figures A3-A8).

Discussion
Disturbed intracellular Mg homeostasis and chronic systemic Mg deficiency have been linked with cardiovascular complications [29]. CVD have further been associated with disturbed functions of mitochondria in cardiac cells [46]. Only recently, Mg has been revealed to play an essential role in the maintenance of mitochondrial homeostasis [20,32,47]. However, the molecular background behind the network between Mg homeostasis, mitochondrial function, and CVD is not as yet fully understood.
Here, we demonstrate that the Na + /Mg 2+ exchanger SLC41A1 and dietary Mg intake are essential regulators of mitochondrial function in mice. Low Mg 2+ diets were associated with reduced Krebs cycle activity and a compensatory increase in activity of ETC components in mitochondrial lysates form mouse hearts. Moreover, the effect of SLC41A1 on mitochondrial function was shown, indicating a close relationship between plasma membrane Mg 2+ transport and energy metabolism.
A plethora of molecular components of the energy-producing machinery in mitochondria are dependent on Mg 2+ [31][32][33][34][35][36][37][38]48,49]. Our data show that the type of Mg diet, i.e., Mg per se, influences the activities of ACON, ICDH, KGDH, CI, CIV, and CV in cardiomyocytes (Table 1). Indeed, Mg 2+ is required for the enzymatic activity of ICDH and of KGDH [34,42]. Panov and Scarpa [34] showed that either Ca 2+ or Mg 2+ increase the activity of KGDH, and that the effects are additive if the [Ca 2+ ] and [Mg 2+ ] are below 0.1 mM and 1 mM, respectively. Moreover, Garfinkel and Garfinkel [31], as early as 1985, demonstrated that Mg is an important coherent controller of glycolysis and the Krebs cycle. Therefore, we assumed that a longer-lasting (2-week) Mg-starvation would negatively impact ICDH and KGDH activity in the mitochondria of cardiac cells, i.e., that it would negatively influence the direct energetic outcome and the production of ETC substrates in the Krebs cycle.
In our experimental setting, the depletion of dietary Mg led to decreases of the activities of all Krebs cycle enzymes measured (i.e., ACON, ICDH and KGDH) in cardiac mitochondria of both Slc41a1 −/− and Slc41a1 +/+ animals ( Table 1). The lower activities of ACON, ICDH and KGDH can be explained by lower [Mg] in the mitochondrial matrix as it conforms with the reduction of most Krebs cycle metabolites in mitochondria observed after abolishing the influx of Mg into mitochondria via Mrs2 [20,39]. The new finding of the present study was that this can be reversed by knock-out of Slc41a1. When balanced for the Mg content of diet, the lack of functional Na + /Mg 2+ exchanger SLC41A1 in cardiac cells had obvious positive effects on ACON, ICDH and KGDH. In the case of KGDH, this effect was only evident with NMgD, though there was a trend for interaction between the type of Mg diet and the Slc41a1 genotype. For ACON and ICDH, however, no interaction was identified between type of Mg diet and the Slc41a1 genotype, indicating that these factors superimpose on each other independently. Therefore, our data show clearly that the chronic lack of dietary Mg has obvious negative effects on ACON, and ICDH and KGDH, the key rate-limiting and regulatory components of Krebs cycle [42,43]. For the understanding of the present results, it is important to note that they represent the outcome of chronic dietary depletion of Mg on enzyme activity and not an effect of acute depletion of Mg 2+ as cofactor during the actual measurement of enzyme activity. Enzyme activity measurements were done with the sufficient Mg concentration (as indicated in Material and Methods). Thus a decrease in enzyme activity measured with our assay could be aggravated further by an actual decrease of intracellular Mg 2+ concentration in vivo. Vice versa, our results further show that knock-out of Slc41a1 can at least partially rescue the negative effects of Mg starvation on Krebs cycle enzymes in cardiac mitochondria.
Yamanaka and colleagues [20] have proposed that the lack of intra-mitochondrial Mg 2+ suppresses the efflux of ATP from the mitochondria (most probably conducted via the ATP-Mg/P i carrier [21]) resulting in ATP accumulation in the mitochondrial matrix. Excess ATP in mitochondria is well known to inhibit ICDH and KGDH in Krebs cycle; thus, a lack of Mg 2+ might indirectly contribute to the suspension of ATP production by mitochondria [20,50]. This mechanism is poorly researched but would give Mg 2+ the role of a central coordinator of the key mitochondrial processes, namely Krebs cycle, ETC, and ADP/ATP translocation [20]. Our data seem to fully support Yamanaka's hypothesis [20].
In our experiments, the chronic lack of dietary Mg evidently led to increased activity of CI, CIV, and CV in lysates of cardiac mitochondria ( Table 1). The latter applied to both genotypes for CI and CV; whereas, it applied to only Slc41a1 −/− animals in the case of CIV. These data are generally compatible with data from male broiler chickens fed with LMgD (Mg = 1.2 g/kg dry matter) or control diet (Mg = 2.4 g/kg dry matter) for 6 weeks [51]. Compared with the control, the muscle [Mg] of broiler chickens from the LMgD group decreased by 9.5%. In parallel, activities of CII and CIII of ETC increased by 23% and 35% in the broilers on LMgD, respectively. Based on these findings, the authors concluded that the feeding of broilers with LMgD induced higher activities of mitochondrial ETC [51]. It remains to be answered by further studies why the ETC complexes CI, CIV, and CV were more active in mice fed with LMgD in our study, whereas CII and CIII were more active in the previous study of Liu and coworkers [51]. Possible factors include origin/species (mouse vs. chicken), target organ (heart vs. skeletal muscle), and duration of starvation (2 weeks vs. 6 weeks). Another important factor might be the content of Mg in the LMgD, which was, in our case, six times lower than that in the study of Liu and colleagues [51].
Teleologically, the increased activity of the ETC could represent an attempt to compensate for the reduced activity of the Krebs cycle in order to maintain energy provision during Mg-deficiency. It has to be considered that our data (and also of Liu and coworkers [51]) have been acquired in vitro, when substrate availability is not limiting the reactions. If we see increasing activities of certain ETC complexes in our in vitro experimental settings after Mg starvation, but in the presence of sufficient Mg and substrates, this may not similarly apply in vivo where Mg and substrates are limiting. As such, we hypothesize that cells overexpress ETC complexes, to compensate for decreased performance caused by the lack of substrates and Mg 2+ . For example, Mg 2+ -depleted cytochrome c oxidase retains only 40% activity of the native, Mg 2+ -containing enzyme [48] and would thus require overexpression during Mg 2+ deficiency to secure near to normal performance of ETC. Upon our experimental conditions, when above physiological amounts of Mg 2+ [39,52] and excessive amounts of substrates are provided, the overexpression of particular ETC complexes then reflects as gain of their activities above those in controls.
The role of SLC41A1 for ETC is less clear because in most instances the knock-out of Slc41a1 did not counteract the stimulation of ETC by LMgD but rather co-stimulated the activity of certain ETC complexes. The activities of CIII, CIV, and CV were increased in the cardiac mitochondria of Slc41a1 −/− animals fed with LMgD ( Table 1). The heart mitochondria of Slc41a1 −/− animals fed with NMgD exhibit significantly increased activities of CIII and decreased activities of CII and CIV when compared with Slc41a1 +/+ animals ( Table 1). Irrespective of the type of Mg diet, we have observed increased activities of CI, CIII, CIV, and CV and the decreased activity of CII in Slc41a1 −/− compared with Slc41a1 +/+ animals (Table 1). These data make it clear that the presence or absence, and thus the functionality, of SLC41A1 influences mitochondrial processes involved in energy production.
Finally, we utilized RFM-L with the aim of identifying, among the tested enzymes and ETC complexes, those that might reliably distinguish between the type of Mg diet or the Slc41a1 genetic background. Following the priority pre-analysis, the activities of ICDH, CI, CIV, and CV jointly qualified as perfect markers able to distinguish between samples from LMgD-fed and NMgD-fed animals with 100% reliability. Importantly, the outcomes of the RFM-L analysis and of the standard frequentist statistics approach overlap. RFM-L analysis further identified the activity of CII as a 96.7% reliable marker able to distinguish between Slc41a1 −/− and Slc41a1 +/+ animals. In this case, the outcome is once again in agreement with the results of the 2F-ANOVA.
The present study provided several lines of molecular and biochemical proof that dietary Mg content and SLC41A1 functionality are crucial for the energy-production in cardiac mitochondria. To extrapolate more clearly on their physiological and disease relevance, future studies on the effects of dietary Mg and SLC41A1 function on cellular energy metabolism in cardiac cells (or any other tissues) should extend investigations to monitoring of additional parameters such as oxygen consumption/mitochondrial respiration, ATP production, ROS production and expression of markers of the mitochondrial oxidative stress, as well as measurement of the mitochondrial membrane potential (∆Ψ m ). Structural changes of mitochondrial architecture related to changed activities of the energy metabolism constituents are also possible and should be examined [53].

Development of Slc41a1 Knock-Out Mouse
Constitutive KO Slc41a1 −/− mice (strain MK-1), derived from the C57BL/6 mouse strain, were developed in cooperation with GenOway (Lyon, France). The exon/intron organization of the gene was established based on the Slc41a1 cDNA sequence AK154819. The mouse Slc41a1 is located on chromosome 1 and extends over 20. protein. Splicing of exons 2 to 7 led to a frame shift, which resulted in a premature stop codon in exon 8. Via the stage of recombinant ES cells, blastocyst injection, and generation of chimeras, we developed a floxed mouse line suitable for the generation of a conditional KO model for Slc41a1. This mouse line was further mated with deleter mice, which constitutively express the Cre recombinase, to generate a constitutive Slc41a1 −/− KO model in which the genetic manipulation is present in all cells of the animal.

Animal Breeding, Housing, and Euthanization
The study was approved by the Animal Ethics Board of the Radboud University Nijmegen (RU DEC 2015-0112; 22-02-2016) and by the Dutch Central Commission for Animal Experiments (AVD103002016382; 22-02-2016). In total, ten Slc41a1 +/+ and ten Slc41a1 −/− male mice aged between 8-12 weeks were selected for this study. The animals were individually housed in metabolic cages for 48 h (24 h adaptation, 24 h sampling) prior to the collection of urine and feces. Subsequently, the mice were randomly divided into two groups of five animals and fed with a normal (0.23% (w/w)) or with a low (0.02% (w/w)) Mg 2+ synthetic diet (Ssniff Spezialdiäten, Soest, Germany; n = 5 per group per genotype) for two weeks. Researcher and animal caretakers were blinded for the Mg 2+ content of

Animal Breeding, Housing, and Euthanization
The study was approved by the Animal Ethics Board of the Radboud University Nijmegen (RU DEC 2015-0112; 22-02-2016) and by the Dutch Central Commission for Animal Experiments (AVD103002016382; 22-02-2016). In total, ten Slc41a1 +/+ and ten Slc41a1 −/− male mice aged between 8-12 weeks were selected for this study. The animals were individually housed in metabolic cages for 48 h (24 h adaptation, 24 h sampling) prior to the collection of urine and feces. Subsequently, the mice were randomly divided into two groups of five animals and fed with a normal (0.23% (w/w)) or with a low (0.02% (w/w)) Mg 2+ synthetic diet (Ssniff Spezialdiäten, Soest, Germany; n = 5 per group per genotype) for two weeks. Researcher and animal caretakers were blinded for the Mg 2+ content of the experimental diets throughout the experiment. Animals were sacrificed via exsanguination under isoflurane anesthesia. The heart and other organs were collected for further analyses. One Slc41a1 −/− mouse from NMgD group died prematurely before completion of the experiments.

Isolation of Cardiac Mitochondria
Frozen powdered tissue of the whole murine heart (about 150 mg) was thawed in 10 volumes of ice-cold homogenization buffer (30 mM KH 2 PO 4 , 5 mM EDTA, 0.3 M sucrose; pH 7.0), with 0.3 mM phenylmethylsulfonyl fluoride as a protease inhibitor, and homogenized 5× at 1200 rpm in 25 s/20 s intervals with a polytetrafluoroethylene pestle in a Potter-Elvehjem homogenizer. The mitochondrial fraction was isolated from individual tissue homogenates (1 mL aliquots) by differential centrifugation at 3200× g for 10 min at 4 • C, and the supernatant obtained was further centrifuged at 10,000× g for 40 min at 4 • C. The resulting mitochondrial fraction was resuspended in 0.2 mL standard solution (30 mM imidazole, 60 mM KCl, and 2 mM MgCl 2 ) and stored at −70 • C for further experiments.
The purity of the mitochondrial fraction was estimated by immunodetection (anti-mitochondria fraction Western blot cocktail antibody, ab139416, Abcam, Cambridge, UK) involving the positive detection of ATP5A (mitochondrial marker) and the minimal/no presence of cytosolic GAPDH or nuclear marker histone H3 ( Figure A9).
Protein concentrations were determined with a DC Protein assay (Bio-Rad Laboratories, Hercules, CA, USA). Bovine serum albumin was used as a standard.

Determination of Krebs Cycle Enzymes Activities
Activities of Krebs cycle enzymes were evaluated after exposure of cardiac mitochondria (diluted in 25.0 mM KH 2 PO 4 and 0.5 mM EDTA, pH 7.25; containing 0.01% Triton X-100) to sonication for 30 s in a water bath. All assays were performed at room temperature, and enzyme activities were determined at 340 nm (ε = 6.2 mM −1 ·cm −1 ) according to the modified methods of Nulton-Persson and Szweda [54]. ACON activity was assayed as the rate of NADP + reduction by ICDH upon the addition of 5.0 mM sodium citrate, 0.6 mM MgCl 2 , 0.2 mM NADP + , and 1.0 unit/mL ICDH to sonicated mitochondria (0.03 mg/mL protein). ICDH activity was assayed as the rate of NAD + reduction upon the addition of 5.0 mM MgCl 2 , 0.04 mM rotenone, 2.5 mM isocitrate, and 1.0 mM NAD + to 0.05 mg/mL mitochondrial protein. KGDH activity was assayed as the rate of NAD + reduction upon the addition of 5.0 mM MgCl 2 , 0.04 mM rotenone, 2.5 mM α-ketoglutarate, 0.1 mM coenzyme A, 0.2 mM thiamine pyrophosphate, and 1.0 mM NAD + to sonicated mitochondria (0.03 mg/mL protein).

Statistics and Bioinformatics
The data were explored and analyzed by R [ (1) A boxplot overlaid with swarmplot (2) was used for data visualization. A 2F-ANOVA with an interaction term was used to test the null hypothesis of the equality of population means among the factors, followed by the Tukey HSD post-hoc test with the adjusted p-values. Results with the p-value below 0.05 were considered statistically significant. The predictive power of diet or genotype was assessed by the empirical eROC curve (3) and quantified by the area under ROC. Uncertainty of the ROC curve estimate was quantified by the 95% confidence band. In addition to the above statistical analyses, the data were subjected to machine-learning predictive modeling by the random forest algorithm (4). Enzyme activities were used as predictors of either the Slc41a1 genotype or the diet. Important predictors (enzymes) were identified by means of the nested cross-validation algorithm with the minimum graph depth criterion (4). The predictive performance of the resulting subset of selected important enzymes was visualized by the ROC curve (5), based on the out-of-bag data, thus providing a realistic estimate of the predictive performance of the algorithm on future data.
Where applicable, data are presented as a mean ± SEM; p-values below 0.05 were considered significant.

Conclusions
In summary, our findings demonstrate a prominent impact of dietary Mg on the functional capacity of key components of the energy-producing machinery in cardiac mitochondria. Dietary Mg depletion quenched the activity of Krebs cycle components (ACON, ICDH and KGDH), and consequently production of ETC substrates (reducing equivalents transporting molecules NAD + and FAD). Our analyses also suggest a compensatory effect of functional SLC41A1 disruption on the effect of LMgD on activities of Krebs cycle enzymes ACON, ICDH and KGDH. Thus, for the first time, our data suggest a link between the presence of intact Slc41a1, thus the functionality of Na + /Mg 2+ exchanger SLC41A1, and mitochondrial energy production. Furthermore, we hypothesize that insufficient supply of dietary Mg leads to decreased activities of particular ETC complexes in vivo, perhaps compensated by overexpression of these complexes aiming to sustain ETC efficiency. This assumption is supported by our findings in vitro where excessive amounts of Mg and substrates revealed increased activities of particular ETC complexes in mitochondria from Mg-deprived animals. Dysfunction of SLC41A1 had mostly similar effects on ETC as Mg starvation. The latter may point towards other functions of SLC41A1 in cellular physiology (e.g., in cellular signaling) that may prevail its function in Mg homeostasis in respect to ETC. It might also be possible that the activation of yet unknown transport mechanism, with similar modus operandi to SLC41A1 in respect to Mg 2+ transport, substitutes SLC41A1 functionally.
Overall, our pivotal data further support that hypothesis that other Mg 2+ transporting systems or Mg homeostatic factors of the cytoplasmic membrane (e.g., TRPM6/7, CNNM2, CNNM4) may equally impact on energy production in mitochondria. It remains to be tested whether the communication between SLC41A1 (or other Mg transporters/homeostatic factors) and the mitochondrial energy-producing machinery is simply dependent on their effects on cytoplasmic [Mg 2+ ] and matrix [Mg 2+ ], or whether a more intricate network of various signaling cascades is involved.
Magnesium is increasingly shown to play important roles in the molecular physiology of the cardiovascular system. Our work clearly indicates that a longer-lasting lack of dietary Mg and/or a lack of the functional Na + /Mg 2+ exchanger SLC41A1 influence Krebs cycle and ETC and thus modulate mitochondrial energy production in heart mitochondria and probably global heart physiology. The effect of Slc41a1 knock-out on integrative heart physiology should now be particular subject of further studies.

Acknowledgments:
We are grateful to Martin Marak (JFM CU), Maria Martincekova (JFM CU) Anique ter Braake (RUMC), and Lisanne Gommers (RUMC) for their competent technical support of the project. We would like to extend our thanks to the team lead by Jean Cozzi (GenOway SA., France) for their cooperation on the development of MK-1 (Slc41a1 −/− ) mice, and also to Theresa Jones for the language editing of the manuscript.