Fig 1.
Central pathways of glucose and fatty acid catabolism and transport.
Glucose and FA are oxidized via the cytosolic reactions of glycolysis and the mitochondrial reactions of β-oxidation, respectively. The mitochondrial outer membrane (OM), inner membrane space (IMS), inner membrane (IM), and matrix are labeled. Transport fluxes for glucose (GLUT4), FA (CD36), O2, CO2, and lactate considered by the constraint-based modeling approach are indicated by a red asterisk. Metabolic demand, or ATP demand, in the model is determined by the ATP hydrolysis rate. All model reactions are explicitly defined in S1 Table.
Fig 2.
Metabolic transport fluxes for HCR and LCR rats.
Transport fluxes were obtained during a previously published graded treadmill experiment [30] and converted to molar quantities. In this experiment, HCR and LCR rats were ran at an increasing treadmill speed (every 2 minutes) until exhaustion. (A) O2 uptake fluxes for HCR (blue) and LCR (red) rats. (B) CO2 output fluxes for HCR (blue) and LCR (red) rats. (C) Estimated carbohydrate uptake flux for HCR (blue) and LCR (red) rats. (D) Estimated FA uptake fluxes for HCR (blue) and LCR (red) rats.
Fig 3.
HCR and LCR metabolic constraint-based solutions.
(A) HCR constraint-based solution: Eq 1 (in Methods) was solved at each time point for internal reaction fluxes using given carbohydrate, FA, O2, and CO2 transport fluxes. Transport fluxes were derived from HCR O2 and CO2 flux data [30] shown in Fig 2. (Inset) Zoomed in view of HCR mitochondrial FA transport and beta-oxidation enzyme fluxes. (B) LCR constraint-based solution: Eq 1 (in Methods) was solved at each time point for internal reaction fluxes using given carbohydrate, FA, O2, and CO2 fluxes [30] shown in Fig 2. (Inset) Zoomed in view of LCR mitochondrial FA transport and beta-oxidation enzyme fluxes. (C) The ATPase (ATP → ADP + Pi) flux (circles) from the HCR constraint-based solution in panel A was used to estimate the ATPase rate with time for subsequent simulations.
Fig 4.
Simulation of HCR and minimal simulation of LCR rat exercise data.
HCR (blue circles) and LCR (red circles) rat data were collected previously [30] during a graded treadmill experiment. Major pathways (87 reactions) of glucose, FA transport, oxidation, and bioenergetics (Fig 1) were simulated using an ordinary differential equation system (98 state variables). Enzyme activities (X, Eq 4) were adjusted to fit the HCR data (blue circles), while a change in HCR enzyme activities were used to fit the LCR data (red circles). Simulations are represented by lines for HCR (blue) and LCR (red). LCR: solid lines were simulated by decreasing HCR total mitochondrial and FAO activities (error function value = 2.68), red dash-dot lines were simulated by decreasing total HCR mitochondrial enzyme activities only (error function value = 2.89), and dashed lines were simulated by decreasing HCR FAO enzyme activities only (error function value = 4.03). Total acyl-carnitine concentrations shown in panels (E-J) were derived from HCR and LCR gastrocnemius muscle [30]. Error bars represent standard error of the mean, while error bars in panel D were calculated from the propagation of error using errors in JCO2 and JO2 fluxes shown in panel A and B, respectively. (A) HCR and LCR rat carbon dioxide flux (JCO2). (B) HCR and LCR rat molecular oxygen flux (JO2). (C) Plasma lactate from HCR and LCR. (D) Respiratory quotient (JCO2/JO2) for HCR and LCR. (E) Total C16-carnitine muscle concentration for HCR and LCR rats. (F) Total C14-carnitine muscle concentration for HCR and LCR rats. (G) Total C8-carnitine muscle concentration for HCR and LCR rats. (H) Total C4-carnitine muscle concentration for HCR and LCR rats. (I) Total Acetyl-carnitine muscle concentration for HCR and LCR. (J) Total Carnitine muscle concentration for HCR and LCR rats.
Fig 5.
Ratios of HCR/LCR enzyme activities for minimal LCR simulation.
The enzyme activities used to fit the HCR and LCR data in Fig 4 were used to create the ratio XHCR/XLCR. Enzyme activities are labeled by shortened identifiers, described in S1 Table, and further grouped with brackets into major pathways defined in Fig 1.
Fig 6.
Simulation of HCR and LCR metabolism during exercise.
In all panels, HCR and LCR simulations are represented by blue and red lines, respectively. Simulations were performed using the minimal difference parameter set between HCR and LCR (Figs 4 and 5). (A) Cytosolic ATP with time. (B) Gibbs free energy potential (Eq 2, Methods) for cytosolic ATP hydrolysis with time. (C) Cytosolic ratio of oxidized (NAD+) over reduced (NADH) NAD with time. (D) Time-dependent average flux from glycolytic enzymes. (E) Time-dependent average flux of glycerol-3-phosphate (G3P) shuttle enzymes. (F) Lactate dehydrogenase flux with time. (G) Pyruvate dehydrogenase (PDH) complex flux with time. (H) Cytosolic pyruvate with time. (I) Mitochondrial pyruvate with time. (J) Time-dependent mitochondrial membrane potential. (K) Mitochondrial NAD ratio for oxidized (NAD+) over reduced (NADH) NAD with time. Inset is a zoomed-out view of the main panel. (L) Mitochondrial Acetyl-CoA to CoA ratio with time. (M) Time-dependent average flux of TCA cycle enzymes. (N) Time-dependent average flux of FA β-oxidation enzymes. (O) Adenine nucleotide transporter (ANT) flux with time.
Fig 7.
Simulation families of HCR and LCR data.
HCR (blue circles) and LCR (red circles) rat exercise data [30] are as described in Fig 4. Several independent attempts were made to simulate the HCR and LCR data by independently adjusting the enzyme activities yielding 10 families of fits. All simulations are depicted by lines of the corresponding color (HCR (blue) and LCR (red)). Error bars represent standard error of the mean, while error bars in panel D were calculated from the propagation of error formula using errors in JCO2 and JO2 fluxes shown in panel A and B, respectively. LCR simulations (red lines) are truncated at 18 minutes in panels E-J for clarity. (A) HCR and LCR rat carbon dioxide flux (JCO2). (B) HCR and LCR rat molecular oxygen flux (JO2). (C) Plasma lactate from HCR and LCR. (D) Respiratory quotient (JCO2/JO2) for HCR and LCR. (E) Total C16-carnitine muscle concentration for HCR and LCR rats. (F) Total C14-carnitine muscle concentration for HCR and LCR rats. (G) Total C8-carnitine muscle concentration for HCR and LCR rats. (H) Total C4-carnitine muscle concentration for HCR and LCR rats. (I) Total acetyl-carnitine muscle concentration for HCR and LCR rats. (J) Total carnitine muscle concentration for HCR and LCR rats.
Fig 8.
Histograms of HCR and LCR enzyme activity ratios (XHCR/XLCR) from multiple parameter sets.
A 103 parameter sets, each composed of 86 enzyme activities, individually fitted to HCR and LCR data were used to obtain a multitude of enzyme activity ratios (XHCR/XLCR). All combinations of each of the 103 parameter sets for HCR and LCR were used yielding 106 ratios for each of the 86 enzyme activities. Each histogram panel in the figure represents one of the 86 enzyme activity ratios and are annotated per the shortened enzyme identifier defined in S1 Table. In each histogram panel, the y-axis represents the frequency of ratio (XHCR/XLCR) occurrence and the x-axis represents the value of the ratio.
Fig 9.
Histograms of HCR enzyme activity (XHCR) sensitivities to fuel selection ranked from multiple HCR parameter sets.
A 103 parameter sets, each composed of 86 enzyme activities, individually fitted to HCR were used to obtain 103 sensitivity coefficients for each activity. Each histogram panel in the figure represents a distribution of one of the 86 enzyme activity sensitivity coefficients. Each panel is annotated per the shortened enzyme identifier defined in S1 Table. In each histogram panel, the y-axis represents the observed occurrence, or frequency, of a sensitivity coefficient and the x-axis represents the rank, or order of sensitivity coefficient magnitude out of 86. For instance, rank 1 is the most sensitive activity (XHCR) whereas as rank 86 is the least sensitive activity. Histogram panels are ordered per their median rank value from top left to bottom right in the figure. Thus, the most sensitive activities are ordered from top left to bottom right in the figure.
Fig 10.
Histograms of LCR enzyme activity (XLCR) sensitivities to fuel selection ranked from multiple LCR parameter sets.
A 103 parameter sets, each composed of 86 enzyme activities, individually fitted to LCR were used to obtain 103 sensitivity coefficients for each activity. Each histogram panel in the figure represents a distribution of one of the 86 enzyme activity sensitivity coefficients. Each panel is annotated per the shortened enzyme identifier defined in S1 Table. In each histogram panel, the y-axis represents the observed occurrence, or frequency, of a sensitivity coefficient and the x-axis represents the rank, or order of sensitivity coefficient magnitude out of 86. For instance, rank 1 is the most sensitive activity (XLCR) whereas as rank 86 is the least sensitive activity. Histogram panels are ordered per their median rank value from top left to bottom right in the figure. Thus, the most sensitive activities are ordered from top left to bottom right in the figure.
Fig 11.
Median HCR and LCR normalized enzyme activity scores.
HCR and LCR enzyme activities, each from 103 parameter sets, and their corresponding sensitivity coefficients, were used to calculate a median enzyme activity score to assess each enzyme’s importance in fuel selection. HCR scores are depicted by blue bars and LCR by red bars. Enzyme activity scores are labeled by shortened identifiers, described in S1 Table, and further grouped with brackets into major pathways defined in Fig 1. (Inset) Zoomed in view of certain beta-oxidation enzyme activity scores. Error bars represent standard deviations.
Fig 12.
Simulated estimation of HCR and LCR fatty acid oxidation capacity.
To theoretically assess FA utilization capacity in HCR (blue) and LCR (red), glycolytic enzyme activities were decreased by several orders of magnitude to eliminate ATP synthesis from glucose. (A) Average ATP concentration at increasing ATPase rates. (B) Average mitochondrial adenine nucleotide transporter (ANT) flux at increasing ATPase rates. (C) Average of β-oxidation enzyme fluxes at increasing ATPase rates. The error bars represent standard deviations from 10 families of HCR and LCR activity parameter sets (Fig 7).
Fig 13.
HCR and LCR transient and steady-state fuel utilization with normalized exercise.
(A) Data only: Transient respiratory quotient (JCO2/JO2) data obtained from HCR (blue connected circles) and LCR (red connected circles) rats during the previously described treadmill exercise protocol [30] are plotted as a function of %VO2max. Steady-state respiratory quotient HCR (blue diamond) and LCR (red diamond) data obtained at 75% VO2max are also plotted in panel A. (B) Transient data with transient simulations: HCR and LCR parameter set families, transitioned from a resting state parameter set, were used to simulate transient normalized exercise intensity (described in Methods), as a function of %VO2max. HCR data are shown as blue circles (as in panel A) while the simulations are shown as blue lines. LCR data are shown as red circles (as in panel A) while the simulations are shown as red lines. Transient simulations were conducted by simulating exercise for 2 min at each %VO2max, as is the case with HCR and LCR transient data. (C) Steady-state data with steady-state simulation: Lines are simulated as in panel B except with 60 minutes of simulation time to mimic steady-state exercise data. HCR data are shown as blue diamonds while the HCR simulations are shown as blue lines. LCR data are shown as red diamonds while the LCR simulations are shown as red lines. LCR was also simulated without an additional reduction in FAO enzyme and FA transport activities (red dashed line), to better match the LCR steady-state data. (D) Simulated HCR % fuel utilization: HCR fuel utilization percentages with both transient (dashed lines) and steady-state (solid lines), normalized exercise intensity. FA (Fatty acid) percentages are shown as circles and carbohydrate are shown as squares. (E) Simulated LCR % fuel utilization: LCR fuel utilization percentages with both transient (dashed lines) and steady-state exercise (solid lines). FA percentages are shown as circles and carbohydrate are shown as squares. (F) Simulated steady-state HCR and LCR %fuel utilization only: Steady-state fuel utilization percentage estimates from panel D and E for HCR (blue) and LCR (red) are re-plotted in this panel for comparison.