Computational Model of Cellular Metabolic Dynamics in Skeletal Muscle Fibers during Moderate Intensity Exercise

Kinetic Mathematical Modeling of Oxidative Phosphorylation in Cardiomyocyte Mitochondria

Oxidative phosphorylation (OXPHOS) is an oxygen-dependent process that consumes catabolized nutrients to produce adenosine triphosphate (ATP) to drive energy-dependent biological processes such as excitation-contraction coupling in cardiomyocytes. In addition to in vivo and in vitro experiments, in silico models are valuable for investigating the underlying mechanisms of OXPHOS and predicting its consequences in both physiological and pathological conditions. Here, we compare several prominent kinetic models of OXPHOS in cardiomyocytes. We examine how their mathematical expressions were derived, how their parameters were obtained, the conditions of their experimental counterparts, and the predictions they generated. We aim to explore the general landscape of energy production mechanisms in cardiomyocytes for future in silico models.

A Modular Mathematical Model of Exercise-Induced Changes in Metabolism, Signaling, and Gene Expression in Human Skeletal Muscle

Skeletal muscle is the principal contributor to exercise-induced changes in human metabolism. Strikingly, although it has been demonstrated that a lot of metabolites accumulating in blood and human skeletal muscle during an exercise activate different signaling pathways and induce the expression of many genes in working muscle fibres, the systematic understanding of signaling-metabolic pathway interrelations with downstream genetic regulation in the skeletal muscle is still elusive. Herein, a physiologically based computational model of skeletal muscle comprising energy metabolism, Ca2+, and AMPK (AMP-dependent protein kinase) signaling pathways and the expression regulation of genes with early and delayed responses was developed based on a modular modeling approach and included 171 differential equations and more than 640 parameters. The integrated modular model validated on diverse including original experimental data and different exercise modes provides a comprehensive in silico platform in order to decipher and track cause-effect relationships between metabolic, signaling, and gene expression levels in skeletal muscle.

A dynamical system for the IGF1-AKT signaling pathway in skeletal muscle adaptation

Physical activity produces a change in skeletal-muscle size by activating synthesis or degradation of protein, which are outcomes of stimulating the IGF1-AKT signaling pathway. In this work, we propose a mathematical model that predicts the variation in muscle size under different activity conditions. The IGF1-AKT pathway was modeled using its 4 main molecules as variables in a dynamical system. We checked the stability of the system; we defined exercise training as a function of intensity, duration, and frequency; and we tested the model under four scenarios: first, we considered the daily low-intensity activity that should not promote atrophy nor hypertrophy (steady state); second, we simulated the effects of physical therapy in spinal cord injury patients (atrophy); third, we simulated exercise training in healthy subjects (hypertrophy); and fourth, we considered the effects of suspending a training program in healthy subjects (recovery after hypertrophy). Results showed that: protein synthesis and degradation are inactive, thus the size of the muscle stays stable in the first scenario; the muscle decreases only 10% of its initial size after 84 days of therapy every two days in the second scenario; training frequency produces rapid hypertrophy (11% after 25 days) when training every day, to no hypertrophy when training every 5 days in the third scenario; and a reduction of 50% the gain of the training program in the fourth scenario. By comparing our results to experimental reports, we found a remarkable agreement; therefore, our model is suitable for the development of training and therapeutic protocols.

Mitochondrial Utilization of Competing Fuels Is Altered in Insulin Resistant Skeletal Muscle of Non-obese Rats (Goto-Kakizaki)

Aim

Insulin-resistant skeletal muscle is characterized by metabolic inflexibility with associated alterations in substrate selection, mediated by peroxisome-proliferator activated receptor δ (PPARδ). Although it is established that PPARδ contributes to the alteration of energy metabolism, it is not clear whether it plays a role in mitochondrial fuel competition. While nutrient overload may impair metabolic flexibility by fuel congestion within mitochondria, in absence of obesity defects at a mitochondrial level have not yet been excluded. We sought to determine whether reduced PPARδ content in insulin-resistant rat skeletal muscle of a non-obese rat model of T2DM (Goto-Kakizaki, GK) ameliorate the inhibitory effect of fatty acid (i.e., palmitoylcarnitine) on mitochondrial carbohydrate oxidization (i.e., pyruvate) in muscle fibers.

Methods

Bioenergetic function was characterized in oxidative soleus (S) and glycolytic white gastrocnemius (WG) muscles with measurement of respiration rates in permeabilized fibers in the presence of complex I, II, IV, and fatty acid substrates. Mitochondrial content was measured by citrate synthase (CS) and succinate dehydrogenase activity (SDH). Western blot was used to determine protein expression of PPARδ, PDK isoform 2 and 4.

Results

CS and SDH activity, key markers of mitochondrial content, were reduced by ∼10-30% in diabetic vs. control, and the effect was evident in both oxidative and glycolytic muscles. PPARδ (p < 0.01), PDK2 (p < 0.01), and PDK4 (p = 0.06) protein content was reduced in GK animals compared to Wistar rats (N = 6 per group). Ex vivo respiration rates in permeabilized muscle fibers determined in the presence of complex I, II, IV, and fatty acid substrates, suggested unaltered mitochondrial bioenergetic function in T2DM muscle. Respiration in the presence of pyruvate was higher compared to palmitoylcarnitine in both animal groups and fiber types. Moreover, respiration rates in the presence of both palmitoylcarnitine and pyruvate were reduced by 25 ± 6% (S), 37 ± 6% (WG) and 63 ± 6% (S), 57 ± 8% (WG) compared to pyruvate for both controls and GK, respectively. The inhibitory effect of palmitoylcarnitine on respiration was significantly greater in GK than controls (p < 10^-3).

Conclusion

With competing fuels, the presence of fatty acids diminishes mitochondria ability to utilize carbohydrate derived substrates in insulin-resistant muscle despite reduced PPARδ content.

Integrated approach for data acquisition, visualization and processing of analog polarographic systems for bioenergetics studies

Bioenergetic function is characterized with assays obtained by polarographic systems. Analog systems without data acquisition, visualization, and processing tools are used but require cumbersome operations to derive respiration rate and ADP to oxygen stoichiometry of oxidative phosphorylation (ADP/O ratio). The analog signal of a polarograhic system (YSI-5300) was digitized and a graphical user interface (GUI) was developed in MATLAB to integrate visualization, recording, calibration and processing of bioenergetic data. With the GUI, the signal is continuously visualized during the experiment and respiratory rates and ADP/O ratios can be determined. The integrated system was tested to evaluate bioenergetic function of subpopulations of mitochondria isolated from rat skeletal muscle (n = 10). Signal processing was applied to denoise data recorded at the sampling rate of 1000Hz, and maximize data decimation for computational applications. The error in calculating the bioenergetic outputs using decimated data is negligible when data are denoised. The estimate of respiration rate, ADP/O ratio and RCR obtained with denoised data at sampling rate as low as 5Hz was similar to that obtained with raw data recorded at sampling rate of 1000Hz. In summary, the integrated tools of the GUI overcome the limitations of data processing, accuracy, and utilization of analog polarographic systems.

Mechanistic inferences on metabolic dysfunction in posttraumatic stress disorder from an integrated model and multiomic analysis: role of glucocorticoid receptor sensitivity

Posttraumatic stress disorder (PTSD) is associated with neuroendocrine alterations and metabolic abnormalities; however, how metabolism is affected by neuroendocrine disturbances is unclear. The data from combat-exposed veterans with PTSD show increased glycolysis to lactate flux, reduced TCA cycle flux, impaired amino acid and lipid metabolism, insulin resistance, inflammation, and hypersensitive hypothalamic-pituitary-adrenal (HPA) axis. To analyze whether the co-occurrence of multiple metabolic abnormalities is independent or arises from an underlying regulatory defect, we employed a systems biological approach using an integrated mathematical model and multiomic analysis. The models for hepatic metabolism, HPA axis, inflammation, and regulatory signaling were integrated to perform metabolic control analysis (MCA) with respect to the observations from our clinical data. We combined the metabolomics, neuroendocrine, clinical laboratory, and cytokine data from combat-exposed veterans with and without PTSD to characterize the differences in regulatory effects. MCA revealed mechanistic association of the HPA axis and inflammation with metabolic dysfunction consistent with PTSD. This was supported by the data using correlational and causal analysis that revealed significant associations between cortisol suppression, high-sensitivity C-reactive protein, homeostatic model assessment of insulin resistance, γ-glutamyltransferase, hypoxanthine, and several metabolites. Causal mediation analysis indicates that the effects of enhanced glucocorticoid receptor sensitivity (GRS) on glycolytic pathway, gluconeogenic and branched-chain amino acids, triglycerides, and hepatic function are jointly mediated by inflammation, insulin resistance, oxidative stress, and energy deficit. Our analysis suggests that the interventions to normalize GRS and inflammation may help to manage features of metabolic dysfunction in PTSD.

Cardiopulmonary responses to maximal aerobic exercise in patients with cystic fibrosis

Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients’ data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework. The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient’s treatment therapies.

Muscle V˙O2-power output nonlinearity in constant-power, step-incremental, and ramp-incremental exercise: magnitude and underlying mechanisms

A computer model of the skeletal muscle bioenergetic system was used to simulate time courses of muscle oxygen consumption (V˙O2), cytosolic metabolite (ADP, PCr, P_i, and ATP) concentrations, and pH during whole‐body constant‐power exercise (CPE) (6 min), step‐incremental exercise (SIE) (30 W/3 min), and slow (10 W/min), medium (30 W/min), and fast (50 W/min) ramp‐incremental exercise (RIE). Different ESA (each‐step activation) of oxidative phosphorylation (OXPHOS) intensity‐ATP usage activity relationships, representing different muscle fibers recruitment patterns, gave best agreement with experimental data for CPE, and for SIE and RIE. It was assumed that the muscle V˙O2‐power output (PO) nonlinearity is related to a time‐ and PO‐dependent increase in the additional ATP usage underlying the slow component of the V˙O2 on‐kinetics minus the increase in ATP supply by anaerobic glycolysis leading to a decrease in V˙O2. The muscle V˙O2‐PO relationship deviated upward (+) or downward (−) from linearity above critical power (CP), and the nonlinearity equaled +16% (CPE),+12% (SIE), +8% (slow RIE), +1% (moderate RIE), and −2% (fast RIE) at the end of exercise, in agreement with experimental data. During SIE and RIE, changes in PCr and P_i accelerated moderately above CP, while changes in ADP and pH accelerated significantly with time and PO. It is postulated that the intensity of the additional ATP usage minus ATP supply by anaerobic glycolysis determines the size of the muscle V˙O2‐PO nonlinearity. It is proposed that the extent of the additional ATP usage is proportional to the time integral of PO ‐ CP above CP.

Integrated computational model of the bioenergetics of isolated lung mitochondria

Integrated computational modeling provides a mechanistic and quantitative framework for describing lung mitochondrial bioenergetics. Thus, the objective of this study was to develop and validate a thermodynamically-constrained integrated computational model of the bioenergetics of isolated lung mitochondria. The model incorporates the major biochemical reactions and transport processes in lung mitochondria. A general framework was developed to model those biochemical reactions and transport processes. Intrinsic model parameters such as binding constants were estimated using previously published isolated enzymes and transporters kinetic data. Extrinsic model parameters such as maximal reaction and transport velocities were estimated by fitting the integrated bioenergetics model to published and new tricarboxylic acid cycle and respirometry data measured in isolated rat lung mitochondria. The integrated model was then validated by assessing its ability to predict experimental data not used for the estimation of the extrinsic model parameters. For example, the model was able to predict reasonably well the substrate and temperature dependency of mitochondrial oxygen consumption, kinetics of NADH redox status, and the kinetics of mitochondrial accumulation of the cationic dye rhodamine 123, driven by mitochondrial membrane potential, under different respiratory states. The latter required the coupling of the integrated bioenergetics model to a pharmacokinetic model for the mitochondrial uptake of rhodamine 123 from buffer. The integrated bioenergetics model provides a mechanistic and quantitative framework for 1) integrating experimental data from isolated lung mitochondria under diverse experimental conditions, and 2) assessing the impact of a change in one or more mitochondrial processes on overall lung mitochondrial bioenergetics. In addition, the model provides important insights into the bioenergetics and respiration of lung mitochondria and how they differ from those of mitochondria from other organs. To the best of our knowledge, this model is the first for the bioenergetics of isolated lung mitochondria.

Regulation of oxidative phosphorylation is different in electrically- and cortically-stimulated skeletal muscle

A computer model of the skeletal muscle bioenergetic system was used to study the regulation of oxidative phosphorylation (OXPHOS) in electrically-stimulated and cortically-stimulated skeletal muscle. Two types of the dependence of the intensity of each-step activation (ESA) of OXPHOS complexes on ATP usage activity were tested: power-type dependence and saturating-type dependence. The dependence of muscle oxygen consumption ([Formula: see text]), phosphocreatine (PCr), cytosolic ADP, ATP, inorganic phosphate (Pi), pH and τp (characteristic transition time) of the principal component of the muscle [Formula: see text] on-kinetics on the ATP usage activity was simulated for both types of the ESA intensity-ATP usage activity dependence. Computer simulations involving the power-type dependence predict system properties that agree well with experimental data for electrically-stimulated muscle. On the other hand, model predictions for the saturating-type dependence in the presence of the 'additional' ATP usage (postulated previously to underlie the slow component of the VO2 on-kinetics) reproduce well system properties encountered in human skeletal muscle during voluntary exercise. It is postulated that the difference between the regulation and kinetic properties of the system in electrically- and cortically-stimulated muscle is mostly due to the different muscle fibers recruitment pattern. In the former, all fiber types are recruited in parallel already at low power output (PO) values, while in the latter type I fibers (with higher ESA intensity) are stimulated at low PO values, while type II fibers (especially type II b and IIx fibers) with low ESA intensity are recruited predominantly at high PO values.

'Idealized' state 4 and state 3 in mitochondria vs. rest and work in skeletal muscle

A computer model of oxidative phosphorylation (OXPHOS) in skeletal muscle is used to compare state 3, intermediate state and state 4 in mitochondria with rest and work in skeletal muscle. 'Idealized' state 4 and 3 in relation to various 'experimental' states 4 and 3 are defined. Theoretical simulations show, in accordance with experimental data, that oxygen consumption (V'O2), ADP and Pi are higher, while ATP/ADP and Δp are lower in rest than in state 4, because of the presence of basal ATP consuming reactions in the former. It is postulated that moderate and intensive work in skeletal muscle is very different from state 3 in isolated mitochondria. V'O2, ATP/ADP, Δp and the control of ATP usage over V'O2 are much higher, while ADP and Pi are much lower in the former. The slope of the phenomenological V'O2-ADP relationship is much steeper during the rest-work transition than during the state 4-state 3 transition. The work state in intact muscle is much more similar to intermediate state than to state 3 in isolated mitochondria in terms of ADP, ATP/ADP, Δp and metabolic control pattern, but not in terms of V'O2. The huge differences between intact muscle and isolated mitochondria are proposed to be caused by the presence of the each-step activation (ESA) mechanism of the regulation of OXPHOS in intact skeletal muscle. Generally, the present study suggests that isolated mitochondria (at least in the absence of Ca2+) cannot serve as a good model of OXPHOS regulation in intact skeletal muscle.

Model analysis of the relationship between intracellular PO2 and energy demand in skeletal muscle

On the basis of experimental studies, the intracellular O(2) (iPo(2))-work rate (WR) relationship in skeletal muscle is not unique. One study found that iPo(2) reached a plateau at 60% of maximal WR, while another found that iPo(2) decreased linearly at higher WR, inferring capillary permeability-surface area (PS) and blood-tissue O(2) gradient, respectively, as alternative dominant factors for determining O(2) diffusion changes during exercise. This relationship is affected by several factors, including O(2) delivery and oxidative and glycolytic capacities of the muscle. In this study, these factors are examined using a mechanistic, mathematical model to analyze experimental data from contracting skeletal muscle and predict the effects of muscle contraction on O(2) transport, glycogenolysis, and iPo(2). The model describes convection, O(2) diffusion, and cellular metabolism, including anaerobic glycogenolysis. Consequently, the model simulates iPo(2) in response to muscle contraction under a variety of experimental conditions. The model was validated by comparison of simulations of O(2) uptake with corresponding experimental responses of electrically stimulated canine muscle under different O(2) content, blood flow, and contraction intensities. The model allows hypothetical variation of PS, glycogenolytic capacity, and blood flow and predictions of the distinctive effects of these factors on the iPo(2)-contraction intensity relationship in canine muscle. Although PS is the main factor regulating O(2) diffusion rate, model simulations indicate that PS and O(2) gradient have essential roles, depending on the specific conditions. Furthermore, the model predicts that different convection and diffusion patterns and metabolic factors may be responsible for different iPo(2)-WR relationships in humans.