Computational Modeling of Substrate-Dependent Mitochondrial Respiration and Bioenergetics in the Heart and Kidney Cortex and Outer Medulla

Abstract Integrated computational modeling provides a mechanistic and quantitative framework to characterize alterations in mitochondrial respiration and bioenergetics in response to different metabolic substrates in-silico. These alterations play critical roles in the pathogenesis of diseases affecting metabolically active organs such as heart and kidney. Therefore, the present study aimed to develop and validate thermodynamically constrained integrated computational models of mitochondrial respiration and bioenergetics in the heart and kidney cortex and outer medulla (OM). The models incorporated the kinetics of major biochemical reactions and transport processes as well as regulatory mechanisms in the mitochondria of these tissues. Intrinsic model parameters such as Michaelis–Menten constants were fixed at previously estimated values, while extrinsic model parameters such as maximal reaction and transport velocities were estimated separately for each tissue. This was achieved by fitting the model solutions to our recently published respirometry data measured in isolated rat heart and kidney cortex and OM mitochondria utilizing various NADH- and FADH2-linked metabolic substrates. The models were validated by predicting additional respirometry and bioenergetics data, which were not used for estimating the extrinsic model parameters. The models were able to predict tissue-specific and substrate-dependent mitochondrial emergent metabolic system properties such as redox states, enzyme and transporter fluxes, metabolite concentrations, membrane potential, and respiratory control index under diverse physiological and pathological conditions. The models were also able to quantitatively characterize differential regulations of NADH- and FADH2-linked metabolic pathways, which contribute differently toward regulations of oxidative phosphorylation and ATP synthesis in the heart and kidney cortex and OM mitochondria.


Introduction
Heart and kidney are the most meta bolicall y acti v e organs with the highest mitochondrial contents, metabolic rates, and oxygen consumptions in the human body. [1][2][3][4][5] They carry out distinct metabolic functions essential for the survival of the organism. Consequentl y, meta bolic d ysfunctions in these or gans can lead to an array of car dio vascular and renal diseases, including saltsensiti v e (SS) hypertension. [6][7][8][9][10][11][12][13][14] Considering the r elati v el y large energy demand in these organs and their dependency of energy production upon mitochondrial respiration and bioenergetics, it is v er y important to systematicall y c har acterize mitoc hondrial respiration and bioenergetics in these organs and identify potential differences and underlying mechanisms. 1 Such information is highly essential for computational modeling, needed for a mechanistic and quantitati v e understanding of the role of mitoc hondrial respir ation and bioenergetics in the pathogenesis of metabolic diseases.
Both the heart and kidney deri v e nearl y 95% of their energy adenosine triphosphate (ATP) form mitochondrial oxidati v e phosphor ylation (OxPhos). 1 , 3 , 4 , 8 The primary substrate for energy production in the heart is free fatty acids. 8 , 15-17 On the other hand, both free fatty acids and ketone bodies are primarily utilized for energy production in the proximal tubules (PT) of the kidney cortex, whereas glucose is primarily utilized for energy production in the medullary thick ascending limbs (mTAL) of the kidney outer medulla (OM). 2 , 3 , 6 , 14 , 18 , 19 For a gi v en tissue, alteration in the primary substrate(s) can result in changes in the kinetics and efficiencies of mitochondrial energy production. 1 , 20 Mechanistic and quantitati v e c har acterization of how different substr ates re gulate mitoc hondrial respir ation and bioenergetics in the selected tissues is an important ste p tow ard understanding how changes in the kinetics and efficiencies of mitochondrial energy production may contribute to tissue/organ dysfunctions and disease processes. 1 Significant differences have been found in mitochondrial enzyme activities, substrate utilization, respiration, and bioenergetics between the heart and kidney cortex and OM under physiolo gical and patholo gical conditions. 1 , 6 , 10 , 14 Using 3D optical fluorescence cryoimaging tec hnique , Salehpour et al. 21 found that kidney OM, but not kidney cortex, exhibits a decreased N ADH/FAD redox r atio in the Dahl SS hypertensi v e rat fed a high salt diet. The same study also indicated that kidney cortex and OM must be treated as 2 distinct tissues and that their mitoc hondrial respir ation and bioenergetics be studied se paratel y. In a recent study, 1 we have found that different metabolic substrates produce significantly different respiratory and bioenergetic responses in isolated mitochondria from the normal Sprague-Da wle y (SD) rat heart and kidne y cortex and OM, which signify substrate-dependent distinct kinetics and efficiency of OxPhos for ATP production in these tissues. Data from that study have enabled the development and validation of inte gr ated computational models of mitochondrial respiration and bioenergetics to elucidate the distinct emergent metabolic system properties of mitochondria in these tissues, which is the focus of the present study.
Tissue-specific changes in mitochondrial respiration, bioenergetics, redox states, and substrate utilization have been observed in the progression of both cardiac and renal diseases. 5 , 6 , 8 , 10 , 15-17 , 21 , 22 Although impaired mitochondrial substrate and energy metabolism has been directly linked to the deterioration of heart and kidney functions, the exact substratedependent network of transporters and enzymes r esponsib le for the metabolic dysfunctions remains unclear. Moreover, a systematic tissue-specific and substrate-dependent characterization is lac king, whic h is r equir ed for a mechanistic and quantitati v e understanding of the relationships between altered substrate oxidation, altered mitochondrial metabolism, and the pr ogr ession of cardiac and renal diseases.
Inte gr ated computational modeling provides a mechanistic and quantitati v e fr amew ork for c har acterizing in-silico c hanges within a gi v en meta bolic network to better understand complex interactions and r egulations r esulting fr om mitochondrial metabolic alterations under physiological and pathological conditions. [23][24][25] Computational models of mitochondrial respiration and bioenergetics have been developed for different levels of biolo gical comple xity by v arious gr oups (eg, see r ef. [24][25][26][27][28][29][30][31][32][33][34][35][36] and the "Discussion" section for an extensi v e r e vie w of existing models and their r elev ance). Those models have enabled modelers to zoom in and out of a gi v en network of processes and quantitati v el y understand mitochondrial meta bolic r esponses at levels ranging from single proteins (enzymes and transporters) to a network of interacting proteins. Although several models of mitochondrial electron transport chain (ETC), tricarboxylic acid (TC A) c ycle , and metabolite and cation tr ansporters re gulating OxPhos and ATP synthesis have been developed, integrated models comparing mitochondrial r espirator y and bioenergetic responses to different metabolic substrates in different tissues/organs such as the heart vs. kidney are lacking. As such, none of the existing models can describe tissue-specific and substrate-de pendent r esponses of mitochondrial r espiration and bioenergetics observed in our recent experimental study. 1 In addition, although there are several such models for the heart and skeletal muscle mitochondria, 24-27 , 29-36 there is a scarcity of such models for the kidney mitochondria.
Efforts to war d this end wer e made r ecentl y b y Ed wards et al. 37 by modifying a pr eviousl y dev eloped cardiac mitochondrial respiration and bioenergetics model 35 by adjusting several model parameters r elev ant to kidney anatomy and physiology. Although their modified model can simulate kidney mitochondrial oxygen consumption (respiration) and ATP generation in the rat PT cells, model simulations were not fitted to any experimental data nor the mitochondrial r espirator y and bioenergetic responses to different metabolic substrates were studied. Previously, we have developed a thermodynamically constrained inte gr ated computational model of rat lung tissue mitochondrial respiration and bioenergetics, which was parameterized and validated using in-house and published data using different metabolic substrates, 28 and hence providing the foundation for the present computational modeling work.
Starting with our recent rat lung tissue mitochondrial model, 28 in the present study, we have developed and validated 3 parallel computational models to study in-silico respiration and bioenergetics of mitochondria isolated from normal SD rat heart and kidney cortex and OM. These models account for the kinetics of mitochondrial metabolites and phosphates transporters, adenine nucleotide translocase (ANT) for ATP/ADP exc hange , proton (H + ) leak, TC A c ycle reactions, ETC reactions and OxPhos, and tissue-specific regulations of NADH-and FADH 2 -linked meta bolic pathw ays ( Figur e 1 ). The models w ere par ameterized based on a systematic and well-controlled dataset obtained r ecentl y in our la borator y, 1 ena b ling us to study in-silico mitoc hondrial respir ation and bioenergetics in the presence of NADH-linked metabolic substrates including pyruvate + malate, glutamate + malate, and alpha-ketoglutarate + malate, and FADH 2 -linked metabolic substrate succinate in the absence or pr esence of r otenone (complex I inhibitor) in these tissues. To the best of our knowledge, the present models represent the first data-dri v en attempts to c har acterize in-silico the r espirator y and bioenergetic responses of the heart and kidney cortex and OM mitochondria to both NADH-and FADH 2 -linked metabolic substrates. These models serve as valuable tools for identifying new therapeutic targets and modifying mitochondrial substrate and energy metabolism that affects the development of metabolic disorders in meta bolicall y acti v e organs such as the heart and kidney.

Experimental Data
The mitochondrial models were parametrized by fitting the model solutions to mitochondrial oxygen consumption rate (OCR or J O2 flux; respiration) data acquired using the experimental protocol of Figure S1A and validated by predicting the mitochondrial OCR and membrane potential ( m ) data acquired using the experimental protocol of Figure S1B . Mitoc hondria w er e isolated fr om normal SD rat heart and kidney cortex and OM tissues by differential centrifugation. The mitoc hondrial OCR w er e measur ed via an Oxygraph-2k (O2k) r espir ometer (Or obor os Instrument, Innsbruck, Austria) at 37 • C, and m were measured via a Photon Technology International (PTI) spectr ofluor ometer (Horiba Scientific Inc.) using the cationic fluorescent dye rhodamine-123 (R123) at 37 • C and calibrated, as detailed in Tomar et al. 1 In Figure S1A experimental protocol (used for fitting), 0.05 mg/mL of heart mitochondria or 0.2 mg/mL of kidney cortex or OM mitochondria were added to the O2k chamber. Then, one of the following substrate combinations: pyruvate + malate (PYR + MAL or PM; 5:2.5 m m ), glutamate + malate (GLU + MAL or GM; 5:2.5 m m ), alpha-ketoglutarate + malate (AKG + MAL or AM; 5:2.5 m m ), and succinate in the absence or presence of rotenone (SUC ± ROT; 10 m m ± 0.5 μm ) was added followed by the sequential addition of increasing ADP concentrations of 25, 50, 75, 100, 150, and 250 μm . In Figure S1B experimental protocol (used for model validation), 0.1 mg/mL of heart mitochondria or 0.2 mg/mL of kidney cortex or OM mitochondria were added to the O2k chamber. Then, one of the following substrate combinations: PM (5:2.5 m m ), GM (5:2.5 m m ), AM (5:2.5 m m ), and SUC ± ROT (10 m m ± 0.5 μm ) was added followed by the addition of 200 μm ADP to the heart mitochondria and 100 μm ADP to the kidney cortex and OM mitochondria.

Computational Model
The present computational models of mitochondrial respiration and bioenergetics for the heart and kidney cortex and OM wer e dev eloped starting with our pr eviousl y dev eloped thermodynamically constr ained mec hanistic modeling fr amew ork and computational model of isolated lung tissue mitochondrial respiration and bioenergetics. 28 The lung tissue mitochondrial model was modified by adding multiple regulation mechanisms specific to the heart and kidney mitoc hondrial respir ation and bioenergetics (eg, see the "Modeling SUC-pathway mediated regulations" section) based on our r ecentl y pub lished experimental data. 1 As shown in Figure 1 , each of the 3 proposed models consists of 3 different re gions: extr a-mitoc hondrial buffer re gion, mitoc hondria matrix re gion, and intermembr ane space (IMS) region. In addition, each model includes the kinetics of 24 reaction and transport fluxes and the dynamics of 37 state varia b les (36 meta bolite concentr ations and mitoc hondrial membrane potential). The outer mitochondrial membrane (OMM) has porins, and hence, it is assumed to be fr eel y permea b le to most of the meta bolites, exce pt cytochr ome c, which has a r elati v el y high molecular weight. In addition, cytochrome c is assumed to exist in the IMS along the inner mitoc hondrial membr ane (IMM). The model does not account for the dynamics of cations (eg, H + , K + , Na + , Mg 2 + , and Ca 2 + ). Rather, cations are assumed to be fixed at their stipulated values in the different regions of the model, based on the well-controlled experimental conditions of Tomar et al. 1 The r elati v e v olumes of differ ent r egions of the model are determined based on the amount of mitochondrial protein used in an experiment, which are provided in Table 1 , along with the levels of conserved metabolite pools within the mitochondrial matrix. The details of the model state v aria b les, enzymatic reactions and transporters, flux expressions and the associated kinetic parameters, and mass balance-based ordinar y differ ential equations (ODEs) and the associated initial conditions for the state v aria b les ar e pr ovided in Supplementary Material S1 .

Mitochondrial TCA Cycle and ETC Reactions
The model accounts for 9 TC A c ycle reaction fluxes responsib le for meta bolite oxidation and NADH and/or FADH 2 generation, which subsequently provide electrons for the ETC reactions r esponsib le for OxPhos and ultimately ATP production. A general form of multisubstrate m ultipr oduct enzymatic reaction is described as: where S i is the i th substrate; P j is the j th product; Ns and Np are the number of substrates and products, respectively; α i and β j ar e the stoichiometr y coefficients corr esponding to the substrate S i and product P j , respectively. The corresponding reaction flux ( J RXN ) is described by the following general Michaelis-Menten equation, which is based on a generalized randomordered rapid-equilibrium kinetic mechanism 28 : where V maxf is the maximum forward reaction rate; C Si and C Pi are the concentrations of the substrate S i and product P j , respecti v el y; and K Si and K Pj are the binding constants corresponding to the substrate S i and product P j , r especti v el y; K eq is the apparent equilibrium constant of the reaction at specified thermodynamic conditions (ie, temperature, ionic strength, and pH), which is the ratio of the forward and reverse rate constants of the reaction and is equal to the mass action ratio at equilibrium. The corresponding equilibrium constant at pH = 7, K 0 eq , is related to the transformed Gibb's free energy r G 0 of the reaction at pH = 7, and is defined as: K eq for a proton producing and consuming reaction at a specified pH can be calculated using eqns ( 4 ) and ( 5 ), respecti v el y: where R is the ideal gas constant (8.314 J/mole/Kelvin), T is the a bsolute temperatur e (310.15 K elvin), nH is the n umber of pr otons produced or consumed in the reaction, and pH m is the mitochondrial matrix pH = 7.6. The flux expressions and the associated kinetic parameter values for individual enzymatic reactions in the inte gr ated mitoc hondrial model are defined in the Supplementary Material S2 .

Mitochondrial Metabolite Transporters
The model accounts for 10 metabolites and phosphates transporters r esponsib le for the transport of TC A c ycle metabolites, adenine nucleotides, and inorganic phosphate between the IMS [assumed to be equilibrated with the extra-mitochondrial (buffer) region] and mitochondrial matrix. We used the following general equations to describe the fluxes of different types of transporters including uniporters (eqn 7 ), symporters or cotransporters (eqn 9 ), and antiporters or exchangers (eqn 11 ) involving neutral compounds. For transport of charged compounds (e g, ATP/ADP exc hange) and pumps (e g, ETC complexes), the effect of mitochondrial membrane potential is appr opriatel y incorporated into the equations (see Supplementary Material S 3 ).
Symporter : Antiporter : where e and m subscripts are for the extr a-mitoc hondrial re gion and mitochondrial matrix, r especti v el y; A and B are the different species being transported between the extra-mitochondrial region and mitochondrial matrix; K 's are the Michaelis-Menten or binding constants of the species for the transporters at the external (e) or internal (m) side; T maxf 's are the maximal forward tr ansport r ates. Species are assumed to be r apidly equilibr ating between the extra-mitochondrial and IMS regions, and ther efor e their concentrations are assumed to be equal in these 2 regions.

Model Governing ODEs
The model includes 37 state v aria b les in differ ent r egions r e pr esenting TC A c ycle meta bolites, adenine n ucleotides, inorganic phosphate, redox variables, oxygen, and membrane potential. The dynamics of the state v aria b les in a region is governed by ODEs-based mass balance of the state v aria b les in that region: where subscripts m , i , and e denote the mitochondrial matrix, IMS, and extra-mitochondrial (buffer) regions; C x, j is the concentration of j th species in the region x ; V x is the volume of the region x ; β x, k, j is the stoichiometric coefficient of j th species in k th reaction in the region x (positive or negative depending on the species is a reactant or a product); J x,,k, j is the k th reaction flux involving j th species in the region x ; and J e↔ m,k, j is the k th transporter flux involving j th species between the regions e and m . Detailed mass balance equations and the associated initial conditions for metabolites are included in the Supplementary Mat erial S4 .

Modeling SUC-Pathway Mediated Regulations
To describe potential differences between mitochondrial metabolism in the heart and kidney cortex and OM, we added specific regulations to several metabolic enzyme and metabolite transporter models. These regulations helped us to uncover the hidden differences in underlying mechanisms of substr ate-dependent mitoc hondrial respir ation and bioenergetics between the heart and kidney cortex and OM mitochondria, as observed by Tomar et al. 1 The dicarboxylate carrier (DCC; gene name SLC25A10) transports both malate (MAL) and succinate (SUC) in exchange for inorganic phosphate (Pi) across the IMM, as studied extensi v el y by Palmieri and coworkers. [38][39][40][41][42][43] Accordingly, both MAL and SUC compete for the binding and transport by the DCC, and hence, one can inhibit the transport of the other. Different kinetic models of this transporter have been developed by Bazil et al. 31 and Zhang et al. 28 accounting for the competiti v e binding and inhibition by each other during their transport via the DCC. We have distinguished the transport of MAL and SUC by the DCC as DCCM and DCCS, r especti v el y, having similar kinetic mechanisms (ie, inhibition of the transport of cytosolic MAL by mitochondrial SUC and inhibition of the transport of cytosolic SUC by mitochondrial MAL). However, the regulation of these 2 transport processes (DCCM and DCCS) and the associated kinetic parameters have not been evaluated and compared in different tissues, for example, heart and kidney. Gi v en the different respiratory responses of isolated mitochondria from the heart and kidney cortex and OM to SUC substr ate , 1 w e hypothesized that SUC and MAL transport and their oxidations must be differ entiall y r egulated in the heart and kidney cortex and OM.
Similarly, it is well-known that oxaloacetate (OXA) is a potent inhibitor and malate (MAL) is a potent acti v ator of the succinate dehydr ogenase (SDH) r eaction. 44 In addition, in several recent studies including that of Fink and coworkers, 45 , 46 the inhibitor y r ole of OXA on SUC-dri v en mitochondrial r espiration/OxPhos has been firml y esta b lished. Howev er, the differ ential SUC-dri v en r espiration/OxPhos inhibition by OXA and activation by MAL in the mitochondria from different tissues such as the heart and kidney cortex and OM have not been well established or compared. Hence, given different respiratory responses of isolated mitochondrial from the heart and kidney cortex and OM to SUC substr ate , 1 w e h ypothesized that SUC oxidation b y SDH/complex II must be differentially regulated in the heart and kidney cortex and OM by OXA and MAL.
Ther efor e, to sim ulate the observ ed differ ences in mitochondrial meta bolic r esponses between SUC vs. SUC + R OT in the 3 tissues, 1 we modified SUC-dependent transporters and enzymes in the mitochondria including DCCS, DCCM, and SDH, as described below.
The SUC-Pi antiporter (DCCS) flux expression in eqn ( 15 ) was modified to account for the inhibitory effect of mitochondrial MAL on the DCCS transporter by scaling the intrinsic SUC binding constant for DCCS, K SUC , as follows: where C MALm is the MAL concentration in the mitochondrial matrix; K MAL is the r egulator y MAL binding constant for DCCS to compete for SUC binding; K SU C is the apparent SUC binding constant accounting for the inhibitory effect of MAL accumulation in the mitochondrial matrix on DCCS (MAL is assumed to inhibit the influx of SUC into the mitochondrial matrix). Hence, an increase in MAL concentration in the mitochondrial matrix inhibits SUC binding to DCCS, which in turn inhibits SUC influx into the mitochondrial matrix. Similarly, we modified the MAL-Pi antiporter (DCCM) flux expression in eqn ( 17 ) to account for the inhibitory effect of mitochondrial SUC on the DCCM transporter by modifying the intrinsic MAL binding constant for DCCM, K MAL , as follows: where C SUCm is the SUC concentration in the mitochondrial matrix region; K SUC is the r egulator y SUC binding constant for DCCM to compete for MAL binding; K MAL is the apparent MAL binding constant after the inhibitory effect of SUC accumulation in the mitochondrial matrix on DCCM accounted for. Hence, as the SUC concentration in the mitochondrial matrix increases, MAL binding to DCCM is inhibited and ther efor e MAL outflux to the buffer region is inhibited (reverse mode of DCCM). The postulated mechanism of DCCM inhibition by SUC is via its competition with MAL for binding to DCCM.
To account for the inhibitory effect of OXA and stim ulator y effect of MAL on the SDH reaction flux, we modified the intrinsic SUC binding constant for the SDH enzyme, K SUC , as follows: where C OXAm is the OXA concentration in the mitochondrial matrix; K OXA is the r egulator y OXA binding constant for SDH; C MALm is the MAL concentration in the mitochondrial matrix; K MAL is the r egulator y MAL binding constant for SDH; K SU C is the apparent SUC binding constant after the inhibitory effect of OXA accumulation in the mitochondrial matrix on SDH is accounted for; K SU C is the apparent SUC binding constant after the stim ulator y effect of MAL accum ulation in the mitochondrial matrix on SDH is accounted for. As a result of SUC addition, OXA is produced at a high rate and accumulates in the mitoc hondrial matrix, whic h then inhibits SDH by reducing SUC binding affinity (ie, increasing SUC binding constant) for SDH. This results in an increase in SUC concentration in the mitoc hondrial matrix, whic h in turn inhibits DCCM stalling outflux of MAL. Inhibition of DCCM leads to MAL accumulation in the mitochondrial matrix, which in turn stimulates SDH by increasing SUC binding affinity (ie, decreasing SUC binding constant). Accumulation of MAL in the mitochondrial matrix also inhibits DCCS stalling SUC influx. As a result of these re gulations, SUC concentr ation in the mitoc hondrial matrix is reduced, which leads to reversing DCCM inhibition, increasing MAL outflux, and decreasing MAL concentration in the mitochondrial matrix. Reduced MAL concentration in the mitochondrial matrix also r ev erses DCCS inhibition and enhances SUC influx.

Par ameter Estima tion
Intrinsic model parameters such as Michaelis-Menten constants ( K m 's) c har acterizing the binding of metabolites (reactants and products) to the enzymes and transporters are set to values from our previous studies based on isolated enzymes and transporters kinetics. 28 , 31 , 35 The assumption is that differences in the K m values between different tissues are ne gligible . The tissuespecific unknown extrinsic model parameters such as maxim um r eaction v elocities ( V max 's and T max 's) of different enzymatic and transporter r eactions wer e estimated as described below.
The extrinsic model parameters V max 's and T max 's are tissuespecific, because of differ ential expr essions of enzymes and transporters and their catalytic activities and regulations in different tissues to perform distinct metabolic functions. Therefore, these parameters were estimated separately for each tissue based on tissue-specific experimental data, including mitochondrial O 2 consumption rate (peak OCR or J O2 flux) with different metabolic substrates at different respiratory states by ADP. This was achie ved b y minimizing the objecti v e function defined below using the optimization functions " ga " (genetic algorithm) and/or " fmincon " (constrained minimization algorithm) in MATLAB (Mathworks Inc.). The objecti v e function E ( P ) is defined as the normalized sum of squared errors (SSE) between model simulations and experimental data: where X i, j and x i, j are the model solutions (peak OCR or J O 2 flux as functions of added ADP concentration, which depend Table 2. Estimated values of tissue-specific V max and T max parameters (unit: nmol/min/mg mitochondrial protein at 37 • C) and computed normalized sensitivity coefficients. on the parameter values P ) and the corresponding experimental data at the i th data point in the j th data set, r especti v el y; N j is the number of data points in a given data set (ADP variation); and M is the number of data sets (different substrates) used for the parameter estimation. The estimated V max and T max values for the heart and kidney cortex and OM mitochondria ar e pr esented in Ta b le 2 and in Figur e S2 of the Supple mentary Material S5 . The general model parameters including temper ature , buffer volume , mitoc hondrial matrix volume , and IMS volume were fixed at 37 • C, 2 mL (respirometry) or 1 mL (spectr ofluor ometr y), 1 μL/mg pr otein, and 0.1 μL/mg pr otein, r especti v el y, based on experimental setup and literatur e ( Ta b le 1 ).

Parameter Sensitivity Analysis and Correlation Coefficient Matrix
Model parameter sensitivity analysis was performed in 2 ways after parameter estimation. First, the variation in E / E 0 as a function of P j / P j, 0 was c har acterized for eac h par ameter P j in the range 0.5 P j, 0 ≤ P j ≤ 1.5 P j, 0 , where P j, 0 is the estimated optimal value of P j and E 0 is the corresponding optimal value of E . Second, the normalized sensitivity coefficients for the optimal par ameter estimates w ere calculated using the following equation: A central difference method with 1% change in P j, 0 is used to accurately compute the normalized parameter sensitivity coeffi-cients. A r elati v el y high sensiti vity v alue indicates that changing a gi v en parameter v alue would r esult in a significant change in the model simulations and the SSE objecti v e function ( E ). The sensiti vity anal ysis r esults for the heart and kidney cortex and OM mitochondria are presented in Table 2 and Figures S3 and S4 in the Supplementary Material S5 .
The correlation coefficients ( CC i j ) between the model parameters that best fit the model solutions to the experimental data were obtained from eqn 24 : where Np is the number of model parameters and HM is the inverse of the product of the Jacobian matrix ( JM ) of the model solution and its transpose ( JM' ). The model solution for mitochondrial OCR ( J O2 flux) as a function of added ADP concentrations for 5 different substrates was fitted to corresponding experimental data. Thus, where A high correlation coefficient between 2 estimated model parameter values indicates their dependency on each other, suggesting the nonidentifiability and nonestimability of the 2 model parameters. The correlation coefficient matrices for the heart and kidney cortex and OM mitochondria ar e pr esented in Figure S5 in the Supplementary Material S5 .

Results
The computational models of the heart and kidney cortex and OM mitoc hondrial respir ation and bioenergetics w er e dev eloped and parameterized by indi viduall y fitting them to the OCR data obtained from isolated mitochondria oxidizing 5 different metabolic substrate combinations, followed by sequential additions of increasing ADP concentrations. These parameterized models were then validated by predicting the OCR and m data in the presence of the same 5 substrate combinations followed by single dose of ADP addition. Using these validated models, key mitochondrial bioenergetic state v aria b les and emergent metabolic system properties, such as NADH ratio, UQH 2 ratio, CytCred ratio, m , and r espirator y contr ol index (RCI; state 3 OCR/state 2 OCR) were predicted under physiological and pathological conditions. In particular, the mitochondrial proton leak (UCP2) activity was increased to simulate a pathological condition induced by mitochondrial uncoupling of OxPhos in each of the 3 tissues, and to predict alterations of emergent metabolic system properties. The validated models were also used to develop hypotheses that may explain the differences observed in the oxidation of SUC vs. SUC + ROT in the 3 tissues. The heart mitochondria showed r elati v el y large differ ences in metabolite concentrations and metabolic fluxes in the presence of SUC vs. SUC + ROT while the differences were relatively small in the kidney OM mitochondria and non in the kidney cortex mitochondria.

Model Fittings and Par ametriza tion Using Mitochondrial Respir a tion Da ta With Sequential and Incremental ADP Additions
Figur e 2 A-C de pict the time courses of measur ed OCR ( J O2 flux) in isolated mitochondria from the SD rat heart and kidney cortex and OM, as r e ported fr om our la borator y by Tomar et al., 1 based on the experimental protocol described in Figure S1A . In this protocol, increasing concentrations of ADP were sequentially added to isolated mitochondria in the presence of 5 different substrate combinations. Across substrates, the heart mitochondria had significantly higher OCRs than the kidney cortex and OM mitochondria, and the kidney cortex mitochondria had significantly higher OCRs than the kidney OM mitochondria. Furthermor e, ther e wer e distinct differ ences in the OCR profiles for different substrates in each tissue and between tissues. For instance, the dynamics of OCR while utilizing SUC vs. SUC + R OT wer e distinctl y differ ent in the heart mitochondria but were similar in the kidney cortex and OM mitochondria. Additionally, for all 5 substrate combinations and for all 3 tissues studied, the state 3 OCR increased with increasing ADP concentr ations, reac hing maximal values at satur ating ADP concentrations. These maximal OCR values also differed significantly betw een different substr ates and different tissues. All descriptions of significance are based on the statistical analyses in the studies of Tomar et al. 1 The mitochondrial models were tailored to capture the distincti v e featur es of the OCR data for v arious substrates. To achieve this, for each tissue, the solution of the corresponding model equation (ie, J O2 or J CIV flux) was concurrently fitted to the av era ge of state 2 OCR data after each substrate addition and the peaks of state 3 OCR data after each ADP addition for each substr ate ( F igure 2 G-I). By using the values of the model parameters estimated from the OCR data in Figure 2 G-I, the models were then a b le to sim ulate the time courses of OCR data in Figure 2 A-C with corresponding state 3 durations in the heart and kidney cortex and OM mitochondria as well as the substrate-dependent differences in the 3 tissues ( Figure 2 D-F). In line with the experimental findings, the model simulations of OCR w ere low est for GM and SUC in the heart mitochondria and GM and AM in the kidney cortex and OM mitochondria, and highest while oxidizing SUC + ROT in the heart mitochondria, SUC ± ROT in the kidney cortex mitochondria, and SUC ± ROT and PM in the kidney OM mitochondria. Thus, in all 3 tissues, GM had the lowest respiration while SUC + ROT had the highest respiration. Moreover, the model was able to predict the distinct responses to the addition of ADP between PM and SUC( ±ROT) in the kidney cortex and OM mitochondria, as shown in Figure 2 E, F, H, I.
Based on the optimal estimates of the extrinsic model parameter values ( Table 2 and Figure S2 ), it was observed that the V max and T max values for the heart mitochondria were consistently higher than those for the kidney cortex ( > 2 times) and OM mitochondria ( > 4 times), which is consistent with the differences in the measured OCRs in these tissues. This suggests that differ ential expr essions of the enzymes and transporters and their catalytic activities and regulations in different tissues are r equir ed for distinct metabolic functions. For a specific tissue, the estimated V max and T max values were also widely variable among themselves, indicating differential expressions, activities, and regulations in the tissue to optimally perform their indi vidual functions. Inter estingl y, exce pt for complex I (CI), for other membrane potential ( m )-dependent transporters and pumps (eg, CIII-CV, ATP/ADP exchange, and H + leak), the estimates of V max 's and T max 's were small, indicating that the high acti vity of CI w as a consequence of its high abundance. Furthermor e, the acti vity of AKGDH was found to be several orders of magnitude lower in the kidney cortex and OM mitochondria than the heart mitochondria, consistent with the observed lower OCR with the AKG substrate in the kidney cortex and OM mitochondria than the heart mitochondria. These results suggest that the activities of various enzymes and transporters are critical determinants of mitoc hondrial respir ation and bioenergetics in different tissues.
The parameter sensitivity analyses ( Figures S3 -S4 ) and the computed parameter correlation coefficient matrices ( Figure S5 A -C ) r ev ealed that most of the V max and T max par ameters w ere r obustl y estimated for the heart and kidney cortex and OM mitochondrial models. As depicted in Figure S3 , most of the normalized sensitivity coefficients for the SSE objective function, E ( P ), computed using the optimal parameter estimates P 0 (eqn 23 ), were small and on the same order of magnitude for all 3 tissues. This was further verified in the parameter sensitivity plots in Figure S4 in which E/E 0 did not v ar y appr ecia b l y fr om one in the neighborhood of P j /P j, 0 = 1 for most parameters ( P j ) and for all 3 tissues. Small changes in some parameters ( P j /P j, 0 ), such as the activities of the ETC complexes and phosphate transporters, r esulted in pr ominent changes in E/E 0 showing high sensitivity of the model solutions for the measur ed v aria b le ( J O2 ) to those parameters. Both Figures S3 and S4 show that in the heart model, the SSE objecti v e function, E ( P ), was highly sensitive to the activities of DCCS, DCCM, ANT GOT (glutamate-oxaloacetate transaminase), CII, and CIII, while in the kidney cortex and OM models, the SSE objecti v e function w as most sensiti v e to the activities of ANT, H + leak, CII, CIII, and CV. This is conceivable as these transporters and enzymes are directly associated with the measur ed v aria b les ( J O2 ) and perturbations (ie, substrate transport and ATP/ADP exchange). There were also several parameters for which the model solutions ( J O2 ) were not v er y sensiti v e to large changes in the parameter values (0.5 P j, 0 ≤ P j ≤ 1.5 P j, 0 ), suggesting that any values for those parameters within the specified range provide as good a fit to the data as the optimal fit.
The correlation coefficient matrices in Figure S5A -C show the direction and amplitude of correlations between every 2 parameters in each of the 3 models. Usually, a small correlation coefficient (eg, | CC | < 0.8) between 2 parameters indicates a weak dependency between those parameters, and a high confidence in the estimability of those parameters. This was noted for many pairs of parameters in all 3 models. On the other hand, r elati v el y high correlation coefficients (ie, | CC | > 0.8) were also obtained between few of the parameters. For example, in the heart mitochondrial model, the highest correlation coefficients (ie, | CC | > 0.9) were obtained between H + leak and CII, CIII, and CIV activities, and between malate dehydrogenase (MDH) and citrate synthase (CITS) activities. Similarly, high correlation coefficients were obtained between few of the estimated parameters in the other 2 models. For example, in the kidney OM mitochondrial model, the activity of tricarboxylic carrier (TCC) was highly correlated with the activities of p yruvate deh ydrogenase (PDH) and pyruvate-H + cotransporter (PYRH). In addition, the activity of PYRH was negatively correlated with the activity of isocitrate dehydrogenase (IDH) and positively correlated with the activities of PDH and glutamate-aspartate exchanger (GAE); the activity of GAE was negatively correlated with the activities of IDH and glutamate-H + cotransporter (GLUH); the activity of CII was negati v el y corr elated with the acti vity of CIII.

Model Validation and Corroboration of Mitochondrial Respir a tion and Membrane Potential With the Addition of a Single Dose of ADP
The parameterized models were validated by predicting the OCR and m dynamics and comparing them with the corresponding experimental data 1 collected from isolated heart and kidney cortex and OM mitoc hondria ( F igure 3 ). Those datasets were not used for the parameterization of the models. As described in Figure S1B, the heart mitochondria wer e stim ulated with 200 μm ADP and the kidney cortex and OM mitochondria were stimulated with 100 μm ADP. All were energized in the pres-

Model Predictions of Mitochondrial Bioenergetics Under Sequential and Incremental ADP Additions (Physiological Perturbations)
The validated models were used to simulate the time courses of differ ent meta bolic fluxes ( Figur e S6A -F ) and meta bolite concentr ations ( F igure S7A -F ) in isolated heart and kidney cortex and OM mitochondria with sequential and incremental additions of ADP in the presence of 5 different metabolic substrate combinations. These predictions show how different substrate combinations differ entiall y acti v ated NADH and FADH 2 -linked meta bolic pathw ays including meta bolite and phosphate transporters, TC A c ycle , ETC, and OxPhos in the mitoc hondria of the 3 tissues leading to differ ent meta bolic fluxes and metabolite concentr ations re gulating redox states, m , and O 2 consumption during proton leak-mediated respiration (state 2) and ADP concentration-de pendent r espiration (state 3) and ATP synthesis c har acterizing OxPhos.
The dynamic sim ulation r esults fr om Figur es S6 and S7 wer e used to deri v e key bioenergetic state v aria b les and physiological emergent metabolic system properties including N ADH r atio, UQH 2 r atio, CytCred r atio, m , and RCI (state 3 J O2 /state 2 J O2 ) as functions of added ADP concentrations in isolated heart and kidney cortex and OM mitochondria ( Figure 4 ). The redox ratio is defined as the ratio of the concentration of a reduced metabolite to the total (reduced + oxidized) concentration of that metabolite [eg, NADH ratio is defined as C NADH /( C NAD + C NADH )]. These r esults pr ovide a quantitati v e and mechanistic understanding of how mitochondrial redox and bioenergetic states are differentiall y r egulated in r esponse to sequential and incremental ADP additions in the presence of different substrate combinations, leading to differential OCR and ATP synthesis in a particular tissue. These results show that the redox and bioenergetic states v ar y distinctl y in r esponse to ADP in a tissue-specific and substrate-dependent manner.
The sim ulation r esults in Figur e 4 showed that the NADH ratio decreased in response to ADP for all substrates in all 3 tissues, while the UQH 2 and CytCred ratios increased with N ADH-linked substr ates and decreased with FADH 2 -linked substrates. Although the redox responses were similar across all 3 tissues, the a bsolute v alues and r elati v e changes in these ratios varied. The most prominent differences in the redox ratios between tissues occurred in the presence of AM or SUC, where the redox changes were similar to those with PM in the heart mitochondria and to those with GM in the kidney cortex and OM mitochondria. Inter estingl y, the NAD pool became drastically oxidized in response to ADP in the presence of SUC for both the heart and kidney OM mitochondria while it remained reduced in the mitochondria of the kidney cortex. Similarly, the changes in UQH 2 and CytCred ratios were similar in the kidney cortex and OM mitochondria but different in the heart mitochondria. These distinct redox responses can be attributed to v ariations in meta bolic fluxes in the 3 tissues, as predicted in Figure S6 .
The sim ulation r esults fr om Figur e 4 A to C showed that the N ADH r atio varied among the 3 tissues in the presence of different substrates. In the presence of SUC + ROT, the N ADH r atio was ∼100% in all 3 tissues due to inhibition of CI. In the presence of PM, it was > 70%, and in the presence of GM, it was < 10% in response to ADP in all 3 tissues. In the presence of AM, the N ADH r atio was ∼90% in the heart mitochondria but only ∼10% in the kidney cortex and OM mitochondria in response to ADP. Furthermore, in the presence of SUC, after addition of only 75 μm ADP, the NAD pool was fully oxidized (ie, NADH ratio was 0%) in the heart mitochondria, ∼10% oxidized in the kidney cortex mitochondria, and ∼90% oxidized in the kidney OM mitochondria. These distinct NADH redox states are attributed to differential acti vities (maxim um v elocities) of the NADH pr oducing TCA cycle enzymes in different tissues ( Ta b le 2 and Figure S2 ) and differ ential acti v ation of the TC A c ycle enzymes with different substrate combinations at saturated concentrations.
Model simulations showed that the UQ pool was less reduced in response to ADP compared to the NAD pool in all 3 tissues. In the heart mitochondria, the UQ pool w as r educed to ∼5%, ∼18%, and ∼25% in response to ADP in the presence of GM, PM, and AM, r especti v el y ( Figur e 4 D). The incr ease in UQ pool r eduction at saturated ADP was less than 10% for NADH-linked substrates.
In the presence of SUC and SUC + ROT, the UQ pool was oxidized by more than 30%, decreasing from ∼40% (at state 2) to ∼10% and ∼1% (at saturated ADP), r especti v el y ( Figur e 4 D). In the kidney cortex mitochondria, the UQ pool w as r educed to ∼25% in the presence of GM and AM, ∼50% in the presence of PM, and ∼70% in the presence of SUC ± ROT in response to ADP ( Figure 4 E). In the kidney OM mitochondria, the UQ pool was reduced to ∼20% for PM, ∼10% for AM, ∼5% for GM, and ∼5% for SUC ± ROT in response to ADP. In the kidney cortex mitochondria, the UQ pool w as mor e r educed compar ed to the heart and kidney OM mitoc hondria ( F igure 4 D-F). The c hanges in UQH 2 oxidation in SUC vs. SUC + ROT in response to ADP were the same in the kidney cortex and OM mitochondria despite their differences in the heart mitochondria ( Figure 4 D-F). The UQ pool in response to ADP in the presence of SUC was oxidized to ∼1%, ∼70%, and ∼5% in the heart, cortex, and OM mitochondria, r especti v el y ( Figur e 4 D-F).
Model simulations predicted that the CytC pool was less r educed compar ed to the NAD and UQ pools in response to ADP in all 3 tissues. In the heart mitochondria, the CytC pool was reduced to ∼10% for PM and AM, ∼5% for GM and SUC + ROT, and ∼1% for SUC in response to ADP ( Figure 4 G). In the kidney cortex mitochondria, the CytC pool was reduced to ∼15% for PM and SUC ± ROT and ∼10% for GM and AM in response to ADP ( Figure  4 H). In the kidney OM mitochondria, the CytC pool was reduced to ∼15% for PM, ∼10% for AM, and ∼8% for GM and SUC ± ROT in response to ADP ( Figure 4 I). In all 3 tissues, the CytC pool c hanged betw een 5% and 20% ( F igure 4 G-I). These distinct UQ and CytC redox states are attributed to differential activities of the ETC complexes in different tissues ( Table 2 and Figure S2 ) and differential activation of the ETC complexes with different substrate combinations at saturated concentrations.
In all 3 tissues, m decreased after addition of ADP due to OxPhos and pumping of H + from IMS to the mitochondrial matrix ( Figure 4 J-L). In the heart mitochondria, m was ∼170 mV for AM, ∼165 mV for PM, ∼145 mV for GM and SUC + ROT, and ∼130 mV for SUC in state 3 ( Figure 4 J). In the kidney cortex mitochondria, m was ∼160 mV for PM and SUC ± ROT and ∼140 mV for AM and GM ( Figure 4 K). In the kidney OM mitochondria, m was ∼170 mV for PM and ∼140 mV for AM, GM, and SUC ± R OT ( Figur e 4 L). These distinct m are attributed to differential activities of the ETC complexes in differ ent tissues ( Ta b le 2 and Figur e S2 ) in the pr esence of different substrate combinations at saturated concentrations, leading to differential redox states and proton pumping, as predicted in Figures S6 and S7 .
Model simulations predicted that the RCI values (state 3 J O2 /state 2 J O2 ) were highest in the heart mitochondria compared to the kidney cortex and OM mitochondria, which had similar RCIs ( Figure 4 M-O). In the heart mitochondria, the RCI values were ∼11 for PM, ∼9 for AM, ∼7 for GM, ∼3 for SUC + ROT, and ∼2 for SUC at saturated ADP ( Figure 4 M). In the kidney cortex mitochondria, the corresponding RCI values were ∼6 for PM, ∼5 for AM and GM, and ∼3 for SUC ± R OT ( Figur e 4 N), while in the kidney OM mitochondria, the RCI values were ∼5 for PM, AM, and GM, and ∼2 for SUC ± R OT ( Figur e 4 O). These modelpr edicted RCI v alues ar e consistent with our r ecent experimental study 1 and signify how OxPhos has differential efficiency for ATP pr oduction for differ ent meta bolic substrates in differ ent tissues.

Model Predictions of Mitochondrial Bioenergetics Under Pathological Conditions of Increased Proton Leak (UCP Activity) and Mitochondrial Uncoupling
The validated models were also used to simulate alterations of key bioenergetic state v aria b les and emergent metabolic system properties in response to increased H + leak (UCP2) activity, which can uncouple OxPhos and lead to a pathological condition in isolated heart and kidney cortex and OM mitochondria ( Figure  5 ). The key model predictions included N ADH r atio, UQH 2 r atio, CytCred ratio, m , and RCI (state 3 J O2 /state 2 J O2 ). The pathological condition was simulated by increasing the maximal H + leak activity parameter ( T max ) from 100% to 900%, where 100% T max r e pr esents the normal physiological condition as r e pr esented in Figures 2 -4 , and 200% to 900% T max represent the progressive pathological condition of increased H + leak and uncoupling of OxPhos. Mitoc hondrial respir atory and bioenergetic responses to a single dose of ADP (200 μm for the heart mitochondria and 100 μm for the kidney cortex and OM mitochondria) were simulated in the presence of different substrates as in Figure 3 (experimental protocol of Figure S1B). For all 3 tissues, model sim ulations pr edicted that in the pr esence of NADH-linked substrates, the state 2 NADH ratio, UQH 2 ratio, and CytCred ratio following substrate addition did not change appr ecia b l y despite r elati v el y larg e chang es in the presence of FADH 2 -linked substrates.
In state 2, the NAD pool was majorly oxidized in the presence of SUC in the heart and kidney OM mitochondria despite minor oxidation in the kidney cortex mitoc hondria ( F igure 5 A-C). In the presence of SUC + ROT, the state 2 NAD pool was only slightly oxidized in the heart and kidney cortex mitochondria, despite major oxidation in the kidney OM mitochondria ( Figure  5 A-C). In state 2, the UQ and CytC pools were majorly oxidized in the presence of SUC despite their minor oxidation in the presence of SUC + ROT in the heart mitochondria ( Figure 5 D and G ). In the kidney cortex and OM mitochondria, the state 2 UQ and CytC pools were slightly oxidized in the presence of SUC with or without ROT ( Figure 5 E-F, H-I).
The state 2 reduction of m with increased H + leak activity was minor in the presence of NADH-linked substrates and SUC + ROT in all 3 tissues, consistent with minor changes in the redox ratios ( Figure 5 J-L). However, the state 2 m was apprecia b l y r educed (120 mV) with incr eased H + leak acti vity in the presence of SUC in the heart mitochondria despite minor reduction in the kidney cortex and OM mitochondria ( Figure 5 J-L).
In the control condition (100% T max for H + leak), the RCI values were highest in the heart mitoc hondria follow ed by the kidney cortex and OM mitochondria. In addition, the RCI values wer e appr ecia b l y higher for NADH-linked substrates compared to FADH 2 -linked substrates. These results are consistent with our recent experimental study. 1 In all 3 tissues, the RCI values pr ogr essi v el y decr eased with incr eased H + leak acti vity in the presence of both NADH-linked and FADH 2 -linked substrates, albeit appr ecia b le decr ease in the heart and kidney cortex mitochondria compared to the kidney OM mitochondria. The reduction in the RCI values in the presence of SUC ± R OT w as minor in all 3 tissues ( Figure 5 M-O).

Model Predictions of Differential Tissue-Specific Mitochondrial Bioenergetics Responses to SUC vs. SUC + ROT
To explore the mechanisms underlying the differential oxidation of SUC vs. SUC + ROT in the 3 tissues, model simulations were conducted and analyzed as shown in Figures 6 and 7 . These simulations r ev eal major differ ences in the FADH 2 -linked ETC r eactions, TC A c ycle enzymes, and metabolite transporters in the heart mitochondria, but not in the kidney cortical or OM mitoc hondria ( F igures 6 , 7 , S6B, D, F , and S7B, D, F ).
In the heart mitochondria, the comparison of SUC vs. SUC + R OT pr ofiles showed appr ecia b le differ ences in m dynamics and in the dynamics of metabolites involved in the FADH 2 -linked pathway including SUC m , MAL m , OXA m , and Pi m ( Figure 6 ). However, in the kidney cortex and OM mitochondria, all metabolites and m dynamics were similar except for OXA m . The heart and kidney cortex and OM mitochondria did not produce OXA in the presence of SUC + ROT due to fully reduced N AD pool (ie , N ADH r atio is ∼100%). In the heart and kidney cortex and OM mitochondria before substrate addition, OXA is produced by GOT reaction of indigenous AKG and ASP in the mitochondrial matrix ( Figures S6 and S7 ). In the heart and kidney OM mitochondria, the concentration of OXA is r elati v el y higher after SUC and ADP additions compared to that before SUC addition due to highly oxidized N AD pool, whic h suppresses the initial OXA concentr ation ( F igure 6 G, I). In contr ast, in the kidney cortex mitochondria, after additions of SUC and ADP, NADH is onl y minimall y oxidized to NAD + at CI, compar ed to that in the heart and kidney OM mitochondria. Ther efor e, despite of the high MAL av aila bility, OXA pr oduction is limited by r educed NAD pool, and hence OXA concentration after SUC addition is smaller than OXA concentration before SUC addition. In the presence of SUC, the OXA concentration was ∼10 4 times higher in the heart mitochondria than in the kidney OM mitochondria and w as negligib le in the kidney cortex mitochondria ( Figure 6 G-I).
The MAL produced after each ADP addition is accumulated in the mitochondrial matrix for all tissues, but this MAL accumulation w as gr eater in the heart mitochondria than in the kidney cortex mitochondria, which in turn was higher than that in the kidney OM mitochondria ( Figure 6 D-F). In the heart mitochondria, m was lower in the presence of SUC compared to SUC + ROT. However, m in the presence of SUC with or without R OT wer e similar in the kidney cortex and OM mitochondria ( Figure 6 N, O).
The model analysis revealed appreciable differences in metabolic fluxes related to the FADH 2 pathway, including ETC SDH/CII and CIV complexes and DCCM, DCCS, and phosphate carrier (PiC) transporters, in the heart mitochondria between SUC vs. SUC + ROT, but not in the kidney cortex and OM mitoc hondria ( F igure 7 ). In the heart mitochondria oxidizing SUC, the influx rate of SUC e and efflux rate of MAL m to and from the mitochondrial matrix were reduced after the second dose of ADP (75 μm ), indicting inhibition of SUC e influx and MAL m efflux ( Figure 7 A, D). In addition, the rate of SUC oxidation by SDH was decr eased, which w as due to inhibition of SDH by OXA m ( Figure  7 G). Our model also pr edicts r eduction in the rate of Pi influx to the mitochondrial matrix by PiC in response to high concentration of Pi m and decreased O 2 reduction rate by CIV ( Figure  7 J, M). These r esponses wer e not evident in simulations of the heart mitochondria oxidizing SUC + ROT. In addition, the modelpr edicted r esponses of the kidney cortex and OM mitochondria were identical for SUC and SUC + ROT ( Figure 7 , the middle and right columns).

Discussion
There is ample evidence that the kinetics and efficiency of mitochondrial O 2 consumption (respiration) for ATP production depend on the choice of metabolic substrates being utilized. 1 , 20 Differ ent substrates differ entiall y generate the r educing equi valents NADH and FADH 2 via the TC A c ycle , whic h feed electrons to the ETC that dri v e OxPhos and ATP synthesis. However, the precise contributions of these substrates have not been systematicall y and quantitati v el y c har acterized in mitoc hondria of the heart or the kidney, the 2 major energy consuming organs in our body. [1][2][3][4][5] The present modeling study aimed to fill this knowledge gap, gi v en the critical r ole that mitochondrial r espirator y and bioener getic d ysfunctions play in these organs in the context of car dio vascular and renal diseases such as hypertension. [6][7][8][9][10][11][12][13][14] The pathogenesis of a cardiac disease contributes to the pathogenesis of a renal disease and vice versa due to the interconnections among pr ocesses dri ving car dio v ascular and r enal diseases. [47][48][49][50][51] In our recent experimental study, 1 we r e ported appr ecia b le differences in substr ate-dependent respir ation and bioenergetics between isolated mitochondria from normal SD rat heart and kidney cortex and OM. Specifically, heart mitochondria showed pr edominantl y higher r espirator y rates (OCR) and membrane potential ( m ) for both NADH-and FADH 2 -linked substrates compared to the kidney cortex and OM mitochondria. Additionally, OxPhos efficiency in the heart mitochondria was higher for NADH-linked substrates and lower for FADH 2 -linked substrates compared to the kidney cortex and OM mitochondria. We also observed major differences in mitochondrial respiration and R OS pr oduction in the presence of SUC with and without ROT (complex I inhibitor) in the heart, whereas only minor differ ences wer e observ ed in the kidney OM and no differences wer e observ ed in the kidney cortex. 1 When SUC is used as substr ate , heart mitoc hondria pr oduce excess R OS under states 2 and 4 via r ev erse electr on transfer (RET) at complex I (CI) and e xcess o xaloacetate (OXA) in state 3 via TC A c ycle , whic h subsequentl y inhibits SDH r eaction and alters r espiration, OxPhos, and R OS pr oduction. 1 , 45 , 46 , 52 Inhibition of CI by ROT stalls the RET-mediated R OS pr oduction and impr ov es mitochondrial r espiration and OxPhos. 1 However, why that is not the case for kidney cortex and OM mitochondria is not well known. To investigate these di v erse kinetic data and begin to elucidate differences in underlying mechanisms, we developed computational models of mitochondrial respiration and bioenergetics. These models and resulting simulations provided a deeper quantitati v e understanding of the mechanisms r esponsib le for the differ ential r esponses of substrate-de pendent mitochondrial r espiration and bioenergetics in the heart and kidney cortex and OM.

Pre vious Computa tional Mitochondrial Models and T heir Limita tions
Other groups have also developed models of mitochondrial respiration and bioenergetics at different levels of complexity, depending on the questions being addressed. As such, models hav e impr ov ed ov er the y ears to incorpor ate our expanding knowledge of mitochondrial function and dysfunction in health and diseases. K orzenie wski and colleagues 53 de veloped one of the first mitochondrial OxPhos models which included simple mass action kinetics for complexes I, III, IV, and V, proton leak, inorganic PiC, and ANT for ATP/ADP exchange in skeletal muscle. Subsequently, they conducted a series of theoretical studies to understand various potential re gulation mec hanisms of OxPhos and ATP production in skeletal muscle during different types of exer cises (e g, see [54][55][56] ). Saito et al. 57 expanded upon the model de veloped b y K orzenie wski and colleagues 53 b y integrating the kinetics of TC A c ycle reactions and cation transporters. They then used this model to investigate how Ca 2 + ions r egulate r espiration and OxPhos in isolated cardiac mitochondria, specifically in the presence of glutamate and malate substrates. They also used the model to understand the mechanisms that maintain cardiac levels of energy metabolites constant during changes in workload in vi v o. Cortassa et al. 26 , 27 developed a detailed inte gr ated model of cardiac mitochondrial energy metabolism and Ca 2 + dynamics that included the mechanistic enzymatic kinetics of TC A c ycle, ETC and OxPhos, and Ca 2 + handling, with a goal of understanding different regulation mechanisms of OxPhos and ATP synthesis in the heart during excitation-contraction coupling.
Beard et al. 36 developed a thermodynamically constrained mitochondrial OxPhos model including complexes I, III, IV, and V, proton leak, potassium transport, PiC, and ANT using simple mass action kinetics but accounting for Gibb's free energy of reactions. Heiske et al. 58 then developed a hybrid OxPhos model based on Beard's 36 and K orzenie wski's 59 models using Michaelis-Menten kinetics instead of mass action kinetics for reactions and transporters. Dash and coworkers 32-34 further extended Beard's OxPhos model 36 and developed inte gr ated models of cardiac mitochondria that accounted for mitochondrial Na + and Ca 2 + transports and Ca 2 + sequestration. Bazil et al. 30 r ecentl y modified Beard's OxPhos model 36 to develop a hybrid model of isolated rat heart mitochondria that included the kinetics of ETC and OxPhos, PiC, ANT, H + leak, and K + transport to study regulation of mitochondrial OxPhos and ROS production under physiological conditions with imposed workloads. However, these models did not include TC A c ycle reactions. In separate studies, Wu et al. 35 integrated Beard's OxPhos model 36 with the kinetics of TC A c ycle reactions (including SDH/complex II) using data from rat heart and skeletal muscle mitochondria, and studied the effects of NADH-linked substrates including pyruvate, malate, and glutamate on mitochondrial respiration and bioenergetics. However, their model 35 did not consider the effects of other N ADH-linked substr ates suc h as alpha-ketoglutarate and FADH 2 -linked substrate such as succinate. Wu et al. 60 , 61 later extended their model 35 to study regulations of phosphate and energetic metabolites during ischemia and exercise in the heart and skeletal muscle in vi v o. Bazil et al. 31 later extended Wu et al. model 35 to include cation handling from Dash and Beard 34 and study the regulation of mitochondrial bioenergetics and volume dynamics.
Despite n umer ous computational studies on heart mitochondria, existing models have limited applicability in describing mitochondrial respiration and bioenergetics of other organs such as kidneys. Edwards et al. 37 recently modified Wu et al. model 35 to study oxygen consumption and ATP production of kidney proximal tubular (PT) cells. However, their model cannot account for the differential mitoc hondrial respir ation and bioenergetics between the kidney cortex and OM and their distinct responses to different metabolic substrates 1 . It is known that different segments of ne phr on (eg, PT and mTAL) and differ ent r e gions of kidney (e g, cortex and OM) hav e v ar ying mitochondrial contents, energy r equir ements, meta bolic rates, and oxygen consumptions. Our present computational modeling focuses on the PT and mTAL segments and cortex and OM regions of the kidney, which are metabolically active segments and r egions inv olv ed in r ea bsorption of filter ed sodium and r e present an important step forward in the field.

Important Aspects of the Current Computational Mitochondrial Models: Rele v ance to Tissue/Organ Bioenergetic Functions
The present models of mitochondrial respiration and bioenergetics in the heart and kidney cortex and OM were developed based on the lung tissue mitoc hondrial respir ation and bioenergetics model that we pr eviousl y dev eloped. 28 To account for potential differences in mitochondrial bioenergetics between these organs, w e incorpor ated tissue-specific and substratede pendent r e gulations of enzymatic and tr ansporter reactions into the model. The intrinsic model parameters such as Michaelis-Menten constants ( K m 's) characterizing the binding of metabolites to enzymes and transporters wer e ke pt constant and set to the same values as in our previous model 28 for all enzymatic reactions and metabolite transporters unless otherwise mentioned. The extrinsic model par ameters suc h as maximal reaction and transporter velocities ( V max 's and T max 's) were estimated to account for possible differences in tissue-specific enzyme and transporter activities.
The present models of mitochondrial respiration and bioenergetics were parameterized and validated ( Figures 2 and 3 ) using a di v erse set of experimental data r ecentl y pub lished by our la borator y. 1 The models wer e parameterized se paratel y for each tissue by fitting the model solutions for J O2 or J CIV fluxes to the OCR data obtained using 5 differ ent meta bolic substrate combinations with sequential and incremental ADP additions to the isolated heart and kidney cortex and OM mitoc hondria ( F igure 2 ). The substr ate combinations included those which acti v ate both NADH and FADH 2 -linked metabolic pathwa ys. F or a gi v en tissue, the ability of the corresponding model simulations to fit well all the substrate-dependent experimental data suggests that the model accounts for the dominant processes that affect mitochondrial respiration and bioenergetics for the different substrate combinations studied. The optimal estimates of the tissue-specific V max and T max parameters ar e gi v en in Ta b le 2 and Figur e S2 . The quality contr ol measures performed on the optimal parameter estimates (ie , par ameter sensitivity analyses and correlation coefficient matrices; Figures S3 -S5 ) suggest robustness and high confidence in the estimated values of most of the model parameters.
As postulated, the estimated V max and T max values were largel y differ ent fr om each other in a specific tissue, indicating differ ential expr essions, acti vities, and r egulations of differ ent enzymes and transporters in that tissue to optimally perform the indi vidual meta bolic functions. In addition, the estimated V max and T max v alues wer e sev eral folds higher in heart mitochondria than in kidney cortex mitochondria, and several folds higher in kidney cortex mitochondria than in kidney OM mitochondria, consistent with the measured OCR data. 1 These findings are also consistent with the general notion that differential expressions of enzymes and transporters and their catalytic activities and regulations in different tissues ( viz. , heart and kidney cortex and OM) are required for those tissues to optimally perform their distinct metabolic functions.
The present models were further validated and strengthened by their abilities to predict isolated heart and kidney cortex and OM mitochondrial OCR and m responses to the same 5 metabolic substrate combinations activating both NADH and FADH 2 -linked pathways followed by stimulation of single dose of ADP addition, 1 which were not used for the estimation of tissuespecific V max and T max par ameters ( F igur e 3 ). Fairl y good corr espondence between model simulations and experimental data signifies robust model validation and corroboration.
The present models not only adequately captured the tissuespecific and substrate-dependent experimental data on mitoc hondrial respir ation and m ( F igures 2 and 3 ), but also allowed for prediction of emergent metabolic system properties such as mitochondrial redox states, enzyme and transporter fluxes, metabolite concentrations, respiratory control index (RCI = state 3 OCR/state 2 OCR), and m under di v erse physiological and pathological perturbations ( Figures 4 , 5 , S6 , and S7 ). This enabled prediction of changes in various metabolic fluxes and metabolite concentrations that are difficult to measure experimentally, which helped in elucidating the underlying mechanisms correlating observed changes of mitochondrial respiration and bioenergetics in the heart and kidney cortex and OM. Overall, the validated models and their predictions of emergent metabolic system properties further our understanding of mitochondrial metabolism, OxPhos, and bioenergetics in the heart and kidney cortex and OM under physiological and pathological conditions.
Inter estingl y, the model simulations predicted that the heart and kidney cortex and OM mitochondrial redox states and bioenergetics are not very prone to mild increases in proton leak in the presence of N ADH-linked substr ates ( F igure 5 ). The same was also predicted to be the case in the kidney cortex mitochondria in the presence of FADH 2 -linked substrates (SUC ± ROT). However, the heart and kidney OM mitochondria were predicted to be v er y sensiti v e to mild incr eases in pr oton leak in the pr esence of the FADH 2 -linked substrate SUC, resulting in apprecia b le changes in their emergent metabolic system properties. These results indicate that mitochondrial SUC accumulation combined with increased uncoupling of OxPhos is detrimental to the bioenergetic function of the heart and kidney OM mitochondria due to considera b le changes in their emergent metabolic system properties, including redox states. Additionally, the model simulations revealed that the low r espirator y r esponses of GM in all 3 tissues could be attributed to high concentrations of ASP in the mitochondrial matrix. The simulations demonstrated that these higher concentrations caused the electro genic GLU/ASP e xchanger (GAE) to utilize ASP m in exchange for GLU e , and the GLUH cotransporter to work in the opposite direction resulting in extrusion of H + m and GLU m from the mitochondrial matrix ( Figures S6 and S7 ). Consequently, GLU e influx was limited only to the GAE antiporter rather than the GLUH cotransporter. Additionally, the model predictions showed that the activity of AKGDH was several orders of magnitude lower in kidney cortex and OM mitochondria than in heart mitochondria ( Ta b le 2 and Figure S2 ). These findings provide v alua b le insights into the differences in mitochondrial respiration and bioenergetics among different tissues, which could have significant implications in our understanding of various pathological states associated with metabolic dysfunctions of the heart and kidney.
The model simulations not only revealed major differences in mitochondrial r espirator y and bioenergetics responses among different tissues, but also provided insights into the likely mechanisms underlying differences in metabolic fluxes and metabolite concentrations associated with SUC vs. SUC + ROT oxidation in the heart mitochondria vs. kidney cortex and OM mitoc hondria ( F igures 6 and 7 ). Specifically, the high concentration of SUC in the heart mitochondria w as pr edicted to inhibit the DCCM resulting in MAL m accumulation, which then lead to mor e OXA m pr oduction and SDH inhibition by OXA m ( Figur e 8 B). Excess MAL m accumulation also inhibited the DCCS reducing the influx of SUC e to the mitochondrial matrix and r ev ersing OXA m and MAL m accum ulation ( Figur e 8 B). This mechanism was found highl y pr ominent in the heart mitochondria and not in the kidney cortex or OM mitochondria, due to the lower affinity of MAL m binding to DCCS in the kidney cortex and OM mitochondria.

Model Predictions of the Differences in NADH-linked Pathway Fluxes and Metabolite Profiles Among the Heart and Kidney Cortex and OM Mitochondria
In the presence of N ADH-linked substr ates (ie , during FET), the NAD pool is majorl y r educed followed by reduced UQ pool and CytC pool leading to OxPhos and ATP production ( Figure 8 A). For N ADH-linked substr ates, the mitoc hondrial OCR, ATP synthesis r ate , and other intermediate metabolic fluxes were highest in the presence of PM and lowest in the presence of GM in all 3 tissues studied. This is consistent with the estimated higher V max values for PDH and lower V max values for GO T sho wn in Figure S2 . Interestingly, metabolic fluxes in the presence of AM were as high as those in the presence of PM in the heart mitochondria but as low as those in the presence of GM in the kidney cortex and OM mitochondria as demonstrated in Figures 2 and S6 -S7 . This can be explained by the higher value of V max for AKGDH in the heart mitochondria compared to the kidney cortex and OM mitochondria ( Figure S2 ).
Mor eov er, mitochondria utilizing GM yielded the lowest OCR in all 3 tissues ( Figure 2 ), and the model predicts that this can be attributed to the limitations of GLU influx via the GAE antiporter and GLUH cotransporter, as well as limitations of oxidations by GOT and AKGDH ( Figures S6 and S7 ). GLU transport is limited to the electrogenic GAE antiporter rather than the GLUH cotransporter due to high ASP concentrations which are produced when mitochondria are energized with GLU. This phenomenon has been r e ported in pr evious studies, 62 whic h demonstr ated that GAE antiporter plays a vital role in controlling mitochondrial respiration. Other studies have suggested that reduction of the GLUH cotransporter activity for GLU transport could be explained by a decrease in matrix pH. 63 Our model predictions support this idea, as evidence by the reduced m during state 3 respiration in the presence of GM compared to other substrates as shown in Figures 3 and 4 . In addition, the model predicts a considera b l y oxidized NAD pool (ie, low NADH) in mitochondria utilizing GM for all 3 tissues.
Considering all things together regarding GM substrate, our model analyses and supporting data indicate that protons are transferred to the mitochondrial matrix via GAE. The addition of ADP and mitochondrial ATP synthesis leads to an imbalance of the proton gradient across the IMM, resulting in the GLUH cotr ansporter w orking in the opposite direction and extruding Figure 8. Schematics of the NADH vs. FADH 2 pathway differences and regulations between the heart and kidney cortex and OM mitochondria. The diagram includes metabolites, transporters, and TC A c ycle enzymes involved in (A) forward electron transfer (FET) through NADH pathway for the heart and kidney cortex and OM mitochondria in brown and (B) reverse electron transfer (RET) through FADH 2 pathway for the kidney cortex and OM mitochondria in yellow and heart mitochondria in green. The black arrows show the control addition or production of metabolites, the red arrows show considera b l y high incr ease in concentration of meta bolites, and b lue arr o ws sho w decrease in concentration of metabolites. The solid blue stars show that ATP is produced, and the solid blue multiplication sign show that ATP is not produced. The blue striped stars show that an enzyme or transporter is stimulated, and the black striped stars show that an enzyme or transporter is acti v ated.
protons, which reduces the proton gradient along with GLU. This negati v e transport of protons and GLU is negligible in all tissues, as shown in Figure S6 .

Model Predictions of the Differences in FADH 2 -linked Pathway Fluxes and Metabolite Profiles Among the Heart and Kidney Cortex and OM Mitochondria
Alterations in SDH activity associated with pathological conditions can significantly affect mitochondrial OxPhos and R OS pr oduction by affecting SUC oxidation, as r e ported by pr evious studies. 52 , 64 , 65 In the heart, increased oxidation of SUC (via SDH) and the associated elevation in mitoc hondrial membr ane potential ( m ) have also been shown to drive mitochondrial ROS production. 52 In addition, we have recently shown that there are significant differences in mitoc hondrial respir ation and ROS production between the heart and kidney cortex and OM in the presence of SUC ± ROT. 1 In the present study, computational modeling was used to develop hypotheses that may explain the differences observed in the oxidation of SUC vs. SUC + ROT in these 3 tissues ( Figure 8 B).
In contrast to the heart, in the kidney cortex and OM, the mitochondrial OCR dynamics during the sequential and incremental ADP additions were similar when utilizing SUC or SUC + R OT ( Figur e 2 ). These differences appear to be explained by excess OXA production and accumulation in the heart mitochondria compared to the kidney cortex and OM mitochondria in the presence of SUC which inhibits SDH and electron transfer to the ETC resulting in changes in the OCR and ATP synthesis rate ( Figure 8 B), consistent with previous differential results in different tissues . 45 , 46 , 66 As shown in Figures 6 and 7 , the model also predicts oscillating O XA d ynamics in the heart and kidney OM mitochondria with sequential and incremental ADP additions in the presence of SUC, during which ascending and descending of OXA concentrations ar e synchr onized with similar oscillations in the SDH flux and OCR. It w as observ ed that in the presence of SUC, the DCCS flux w as positi v e (SUC entering mitochondria and Pi exiting) while DCCM flux was negati v e (MAL exiting mitochondria and Pi entering). The model suggests that with SUC influx to the mitochondrial matrix and SDH inhibition by OXA accumulation, there is an accumulation of SUC, which inhibits DCCM slowing the outflow of MAL. This results in accumulation of MAL in the mitochondrial matrix which inhibits DCCS reducing SUC influx and stimulates SDH increasing SUC oxidation. This results in reduction in SUC concentration in the mitochondrial matrix which r ev erses DCCM inhibition and increases MAL outflux. This leads to a reduction of OXA in the mitochondrial matrix which r ev erses the SDH inhibition. Thus, r ev ersing SDH inhibition and stimulating SDH facilitates the transfer of electrons to the ETC and increases the OCR. This mechanism results in synchronized oscillating dynamics in OXA concentration, ATP synthesis, SDH flux, and OCR. Our studies found that this phenomenon is considera b l y less prominent in the kidney cortex and OM mitochondria.
Inter estingl y, in the heart mitochondria, the concentrations of accumulated FUM and MAL with sequential and incremental ADP additions in the presence of the FADH 2 -linked substrates SUC ± ROT were predicted to be several folds higher than those in the presence of NADH-linked substrates. However, in the kidney cortex and OM mitochondria, the concentrations of accumulated FUM and MAL with the same sequential and incremental ADP additions in the presence of the FADH 2 -linked substrates SUC ± R OT wer e pr edicted to be considera b l y lower than those in the presence of NADH-linked substrates ( Figure S7 ). Moreover, the dynamics of DCCM flux in the heart mitochondria were predicted to be considera b l y differ ent fr om that in the kidney cortex and OM mitochondria with sequential and incremental ADP additions ( Figures 7 and S6 ). These findings are consistent with our proposed hypothesis that the inhibitory binding constants of MAL and SUC for the DCCS and DCCM transporters are different between the heart and kidney cortex and OM ( Figure 8 B). SUC has the highest binding affinity for DCCM in the heart mitochondria, resulting in more potent inhibition of DCCM by SUC and accumulation of MAL. In contrast, the binding affinity of MAL for DCCS in the heart mitochondria is the lowest, resulting in less potent inhibition of DCCS by MAL and more influx of SUC. This in turn leads to more MAL m being r equir ed to inhibit DCCS to slow the SUC influx. In the kidney cortex and OM mitochondria, SUC binding affinity for DCCM is lower, inhibiting DCCM to a lesser extent and allowing for more efflux of MAL m . Also, the higher binding affinity of MAL for DCCS inhibits DCCS to a greater extent and stalls the influx of SUC.

Model Predictions of the Differences in Redox Ratios and Bioenergetics Among the Heart and Kidney Cortex and OM Mitochondria in Physiological Conditions
The model predicts that when N ADH-linked substr ates are added to the mitochondria leading to H + leak state respiration (state 2), the NAD pool is reduced due to NADH production via the dehydrogenase enzymes in the TC A c ycle. Ho wever, in mitochondria stimulated by ADP (state 3), the NAD pool is oxidized by complex I due to OxPhos. It is worth noting that, among the N ADH-linked substr ates, GM sho ws the lo w est reduced N AD pool in the heart mitochondria, and GM and AM produce the lowest reduced NAD pool in the kidney cortex and OM mitochondria. Additionally, the UQ pool and CytC pool are reduced in the H + leak state and further reduced by complexes I and III during OxPhos ( Figures 4 and S7 ). Similarly, the model predicts that when the FADH 2 -linked substrate SUC is added to the mitochondria, the NAD pool is full y r educed by complex I via RET in the H + leak state, while the UQ pool and CytC pool ar e onl y partiall y r educed by complexes II and III, r especti v el y. During OxPhos state (state 3), the NAD pool, UQ pool, and CytC pool are all oxidized. Inhibition of complex I by R OT b loc ks N ADH oxidation and ther efor e the N ADH r atio remains at its initial value. In the OxPhos state, the UQ pool and CytC pool are oxidized in manner similar to SUC ( Figures 4 and S7 ).
Our model analyses suggest that when SUC is present in response to ADP addition (state 3), the NAD pool is 100% oxidized via FET by complex I in the heart mitochondria, only ∼20% in the kidney cortex mitochondria, and > 90% in the kidney OM mitochondria. Mor eov er, we found that RET exists in the heart mitochondria to a greater extent than the kidney OM mitochondria while the kidney cortex mitochondria exhibit intermediate levels of RET ( Figure S7). Additionally, during OxPhos (state 3) in the presence of SUC, the UQ and CytC pools are the same in the kidney cortex and OM mitochondria, indicating that RET is not a dominant mechanism in these mitochondria compared to heart mitoc hondria ( F igure S7 ).
Mitochondrial RCI (state 3 OCR/state 2 OCR) was higher in the presence of N ADH-linked substr ates compared to FADH 2linked substrates ( Figure 4 M-O). This indicates greater efficiency of mitochondrial OxPhos for ATP production via the NADH pathway. Among NADH-linked substrates, PM had the highest m and GM had the lowest m in all r espirator y states, similar to the OCR trend ( Figure 4 J-L). The m in the presence of SUC + R OT w as determined to be ∼150 mV in the 3 tissues during OxPhos, and with SUC alone in the kidney cortex and OM. In contrast, the heart mitochondria in the presence of SUC, m was found to be as low as ∼130 mV during OxPhos with enhancement of the pr oton moti v e force thereby contributing to the RET.

Model Predictions of the Differences in Mitochondrial Redox Ratios and Bioenergetics in the Heart and Kidney Cortex and OM in Pathological Conditions
Multiple studies have found that the development and progression of heart 67 and kidney 68 failure is associated with mitochondrial uncoupling of OxPhos, which diminishes the production of ATP, enhances oxidati v e str ess, and facilitates organ failure. The pathological condition of mitochondrial OxPhos uncoupling was simulated by increasing the proton leak (UCP2 activity) in the model and predicted tissue-specific and substrate-dependent changes in the mitochondrial emergent metabolic system properties ( Figure 5 ). Interestingly, it was found that the redox ratios including N ADH r atio, UQH 2 r atio, and CytCred r atio did not change appr ecia b l y in the pr esence of N ADH-linked substr ates despite their considera b le changes in the presence of FADH 2linked substrates in the 3 tissues. This indicates that in the presence of NADH-linked substrates with increased influx of protons into the mitochondrial matrix, the ETC complexes I, III, and IV compensate by pumping protons across the IMM at a higher capacity resulting in minimal changes in m in these 3 tissues. However, the RCI values were considerably reduced after tripling (3 ×) the proton leak in the presence of all substrates in all 3 tissues, demonstrating that increasing proton leak considera b l y affects mitochondrial respiration at state 2 rather than state 3. The redox ratios obtained at state 2, as shown in Figure  5 , did not change with increase in the proton leak. Therefore, we concluded that the reductions in the RCI values were due to incr eased r espiration at state 2. These model predictions provide important mechanistic insights explaining such observations as found in diabetic rats, which have increased mitochondrial UCP2 expression in the renal PT cells with mitochondrial uncoupling and increased O 2 consumption, which appears to lead to progr essi v e kidney damage. 68 Similarly, mechanistic insights from the model predict that with greater oxidation of SUC by the heart, the resulting reduction of the proton motive force would reduce ATP synthesis and contribute to bioenergetic dysfunctions. 45 , 46 , 52 Specifically, the model predicted that oxidation of SUC in the heart mitochondria with 3 × incr eased pr oton leak led to considera b le decr eases in the redox ratios, indicating that the redox pools are oxidized. The excess OXA production by MDH inhibits SDH, which blocks electr on flow upstr eam in the ETC. Consequentl y, complexes III and IV cannot pump protons across the IMM resulting in reduction of m . However, when complex I is blocked by ROT electrons can move upstream ETC to complexes III and IV, pumping pr otons acr oss IMM and resulting in a balanced H + concentrations across the IMM with minimal changes in m . Additionally, since NAD pool is fully reduced, NAD + is not available for MDH to produce OXA, which does not inhibit SDH. In the kidney cortex and OM, the redox ratios and m did not change in the presence of SUC with or without ROT, indicating that SDH is not inhibited by OXA. Ther efor e, electr ons can flow upstr eam of the ETC and complexes III and IV can pump protons across the IMM keeping H + concentrations balanced across the IMM. Hence, the role of mitochondrial proton leak in metabolism and OxPhos alteration is more prominent in the heart than kidney cortex and OM particularly in the presence of SUC, supported by previous findings. 69

Overall Summary, Model Limitations, and Futur e Dir ections
In this study, we developed computational models of how the mitochondria of the heart and kidney cortex and outer medullary cells produce energy. We used kinetic data from our previous studies to build these models. The models were calibrated by comparing their results to the measurements of oxygen consumption in isolated mitochondria. We tested the models by predicting how mitochondria would function when exposed to different combinations of energy sources. The validated models were then used to make predictions about how mitochondria behave in normal and stressed (eg, disease) conditions. We looked at various aspects of mitochondrial function, suc h as bioc hemical reactions, substr ate tr ansporters, and the lev els of differ ent molecules. By using these methods, we gained insights into why mitochondrial in the heart and kidney cortex and outer medulla behav e differ entl y when they oxidize different energy sources.
Consistent with the experimental data, the models developed in this stud y allo wed us to simulate how the mitochondria in the heart and kidney cortex and outer medullary cells respond to different food substances and different conditions. It was found that the responses of the mitochondria were considera b l y differ ent de pending on the type of tissue and energy source they were using. Interestingly, the heart mitochondria energized with succinate without rotenone (a complex I inhibitor) failed to produce a robust state 3 response after we added a high concentration of ADP. However, the mitochondria of the kidney cortex and outer medulla showed similar responses to succinate with or without rotenone, suggesting that a different regulatory mechanism is at play in these tissues. Our model simulations also r ev ealed that oxaloacetate, an intermediate of the citric acid cycle , whic h inhibits the oxidation of succinate, accum ulated mor e quickl y in the heart mitochondria comparing to the kidney cortex and outer medullary mitochondria. Overall, these models helped to elucidate how different combinations of energy sources affect the way mitochondria produce ATP, the ener gy currenc y of cells, in the heart and kidney cortex and outer medulla.
As with all models, the 3 models have limitations. One major limitations of the current models is the exclusion of the regulator y r oles of R OS , suc h as O 2 •− and H 2 O 2 , on mitochondrial bioenergetics. It was assumed in the models that cation concentr ations w er e constant as w as the case in all the experimental data 1 utilized in the present study. The extr a-mitoc hondrial buffer was maintained at a physiological pH of 7.15 and had ne gligible concentr ations of Ca 2 + due to the presence of 1 m m EGTA (a Ca 2 + chelator). In addition, the concentrations of K + and Na + in the buffer wer e ke pt at physiological levels of 140 and 10 m m , r especti v el y. The experiments with isolated mitoc hondria w ere performed in the absence of Mg 2 + . The pH of the mitochondrial matrix was fixed at a physiological level of 7.55 to maintain an appropriate pH gradient and pr oton moti v e force across the mitochondrial inner membr ane . Similarl y, R OS concentr ations w ere assumed to be within the ph ysiological le vels, meaning they were negligib l y small and had no impact on mitoc hondrial respir ation and bioenergetics.
In futur e v ersions of the model, the dynamics of pH, K + , Na + , Ca 2 + , and Mg 2 + ions will be included 26 , 27 , 31-34 , 57 to understand the differential regulatory roles of cations (eg, Ca 2 + ) on mitoc hondrial respir ation and bioenergetics in v arious meta bolicall y acti v e tissues, as we have shown r ecentl y in another experimental study. 70 The kinetics of R OS pr oduction via the ETC 71 , 72 and R OS scav enging via the glutathione and thioredoxin systems [73][74][75][76] will also be included to model mitochondrial ROS homeostasis [77][78][79] and better understand alternations in mitochondrial respiration and bioenergetics during the pr ogr ession of cardiac and renal diseases such as SS hypertension.

Authors Contribution
S .S .: conceptualization; computational model development and parameterization; data anal ysis; inv estigation; writing-original draft; and writing-re vie w and editing; X.Z.: conceptualization, computational model development and parameterization; data analysis; and investigation; S.H.A.: investigation; and writingre vie w and editing; A.W.C.: conceptualization; investigation; supervision; writing-re vie w and editing; and funding acquisition; R.K.D.: Conceptualization; computational model development and parameterization; data analysis; investigation; supervision; writing-re vie w and editing; project administration; and funding acquisition.

Supplementary Material
Supplementary material is av aila b le at the APS Function online.

Funding
This work was supported by the NIH grant R01-HL151587 (to R.K.D. and A.W.C.) and NSF grant DMS 2153387 (to R.K.D.). The content is solely the responsibility of the authors and does not necessaril y r e pr esent the official views of the NIH or NSF. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Conflict of Interest
A.W.C. holds the position of an Executi v e Editor for FUNCTION and is blinded from re vie wing or making decisions for the manuscript. All the other authors declare that the y ha ve no known competing financial interests or personal relationships that could have appeared to influence the work r e ported in this manuscript.

Da ta Av ailability
The model is developed in MatLab. The MatLab codes and the associated data files used to generate all the results in this manuscript can be found at https://github.com/MCWComputat ionalBiologyLab/Sadri Function 2023 . The MatLab codes and the datasets analyzed during the current study can also be obtained from the corresponding authors on request.