Comprehensive mathematical model of oxidative phosphorylation valid for physiological and pathological conditions

Mitochondrial morphology governs ATP production rate

Life is based on energy conversion. In particular, in the nervous system, significant amounts of energy are needed to maintain synaptic transmission and homeostasis. To a large extent, neurons depend on oxidative phosphorylation in mitochondria to meet their high energy demand. For a comprehensive understanding of the metabolic demands in neuronal signaling, accurate models of ATP production in mitochondria are required. Here, we present a thermodynamically consistent model of ATP production in mitochondria based on previous work. The significant improvement of the model is that the reaction rate constants are set such that detailed balance is satisfied. Moreover, using thermodynamic considerations, the dependence of the reaction rate constants on membrane potential, pH, and substrate concentrations are explicitly provided. These constraints assure that the model is physically plausible. Furthermore, we explore different parameter regimes to understand in which conditions ATP production or its export are the limiting steps in making ATP available in the cytosol. The outcomes reveal that, under the conditions used in our simulations, ATP production is the limiting step and not its export. Finally, we performed spatial simulations with nine 3-D realistic mitochondrial reconstructions and linked the ATP production rate in the cytosol with morphological features of the organelles.

AW, Dash RK. Computational Modeling of Substrate-Dependent Mitochondrial Respiration and Bioenergetics in the Heart and Kidney Cortex and Outer Medulla

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.

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.

Computational modeling of complex bioenergetic mechanisms that modulate CD4+ T cell effector and regulatory functions

We built a computational model of complex mechanisms at the intersection of immunity and metabolism that regulate CD4+ T cell effector and regulatory functions by using coupled ordinary differential equations. The model provides an improved understanding of how CD4+ T cells are shaping the immune response during Clostridioides difficile infection (CDI), and how they may be targeted pharmacologically to produce a more robust regulatory (Treg) response, which is associated with improved disease outcomes during CDI and other diseases. LANCL2 activation during CDI decreased the effector response, increased regulatory response, and elicited metabolic changes that favored Treg. Interestingly, LANCL2 activation provided greater immune and metabolic modulation compared to the addition of exogenous IL-2. Additionally, we identified gluconeogenesis via PEPCK-M as potentially responsible for increased immunosuppressive behavior in Treg cells. The model can perturb immune signaling and metabolism within a CD4+ T cell and obtain clinically relevant outcomes that help identify novel drug targets for infectious, autoimmune, metabolic, and neurodegenerative diseases.

MITODYN: An Open Source Software for Quantitative Modeling of Mitochondrial and Cellular Energy Metabolic Flux Dynamics in Health and Disease

Mitochondrial respiratory chain (RC) transforms the reductive power of NADH or FADH2 oxidation into a proton gradient between the matrix and cytosolic sides of the inner mitochondrial membrane, that ATP synthase uses to generate ATP. This process constitutes a bridge between carbohydrates' central metabolism and ATP-consuming cellular functions. Moreover, the RC is responsible for a large part of reactive oxygen species (ROS) generation that play signaling and oxidizing roles in cells. Mathematical methods and computational analysis are required to understand and predict the possible behavior of this metabolic system. Here we propose a software tool that helps to analyze individual steps of respiratory electron transport in their dynamics, thus deepening understanding of the mechanism of energy transformation and ROS generation in the RC. This software's core is a kinetic model of the RC represented by a system of ordinary differential equations (ODEs). This model enables the analysis of complex dynamic behavior of the RC, including multistationarity and oscillations. The proposed RC modeling method can be applied to study respiration and ROS generation in various organisms and naturally extended to explore carbohydrates' metabolism and linked metabolic processes.

Tools and approaches for analyzing the role of mitochondria in health, development and disease using human cerebral organoids

Mitochondria are cellular organelles involved in generating energy to power various processes in the cell. Although the pivotal role of mitochondria in neurogenesis was demonstrated (first in animal models), very little is known about their role in human embryonic neurodevelopment and its pathology. In this respect human-induced pluripotent stem cells (hiPSC)-derived cerebral organoids provide a tractable, alternative model system of the early neural development and disease that is responsive to pharmacological and genetic manipulations, not possible to apply in humans. Although the involvement of mitochondria in the pathogenesis and progression of neurodegenerative diseases and brain dysfunction has been demonstrated, the precise role they play in cell life and death remains unknown, compromising the development of new mitochondria-targeted approaches to treat human diseases. The cerebral organoid model of neurogenesis and disease in vitro provides an unprecedented opportunity to answer some of the most fundamental questions about mitochondrial function in early human neurodevelopment and neural pathology. Largely an unexplored territory due to the lack of tools and approaches, this review focuses on recent technological advancements in fluorescent and molecular tools, imaging systems, and computational approaches for quantitative and qualitative analyses of mitochondrial structure and function in three-dimensional cellular assemblies-cerebral organoids. Future developments in this direction will further facilitate our understanding of the important role or mitochondrial dynamics and energy requirements during early embryonic development. This in turn will provide a further understanding of how dysfunctional mitochondria contribute to disease processes.

A mathematical model for persistent post-CSD vasoconstriction

Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.

A model of mitochondrial O2 consumption and ATP generation in rat proximal tubule cells

Oxygen tension in the kidney is mostly determined by O₂ consumption (Qo₂), which is, in turn, closely linked to tubular Na⁺ reabsorption. The objective of the present study was to develop a model of mitochondrial function in the proximal tubule (PT) cells of the rat renal cortex to gain more insight into the coupling between Qo₂, ATP formation (G_ATP), ATP hydrolysis (Q_ATP), and Na⁺ transport in the PT. The present model correctly predicts in vitro and in vivo measurements of Qo₂, G_ATP, and ATP and P_i concentrations in PT cells. Our simulations suggest that O₂ levels are not rate limiting in the proximal convoluted tubule, absent large metabolic perturbations. The model predicts that the rate of ATP hydrolysis and cytoplasmic pH each substantially regulate the G_ATP-to-Qo₂ ratio, a key determinant of the number of Na⁺ moles actively reabsorbed per mole of O₂ consumed. An isolated increase in Q_ATP or in cytoplasmic pH raises the G_ATP-to-Qo₂ ratio. Thus, variations in Na⁺ reabsorption and pH along the PT may, per se, generate axial heterogeneities in the efficiency of mitochondrial metabolism and Na⁺ transport. Our results also indicate that the G_ATP-to-Qo₂ ratio is strongly impacted not only by H⁺ leak permeability, which reflects mitochondrial uncoupling, but also by K⁺ leak pathways. Simulations suggest that the negative impact of increased uncoupling in the diabetic kidney on mitochondrial metabolic efficiency is partly counterbalanced by increased rates of Na⁺ transport and ATP consumption. This model provides a framework to investigate the role of mitochondrial dysfunction in acute and chronic renal diseases.

ROS and pentose phosphate pathway: mathematical modelling of the metabolic regulation in response to xenobiotic-induced oxidative stress and the proposed Impact of the gluconate shunt

Elevated intracellular levels of reactive oxygen species (ROS), e.g. resulting from exposure to xenobiotics, can cause severe damages. Antioxidant defence mechanisms, which involve regulation of enzyme activities, protect cells to a certain extent. Nevertheless, continuous or increased exposure can overwhelm this system resulting in an adverse cellular state. To simulate exposure scenarios and to investigate the transition to an adverse cellular state, a mathematical model for the dynamics of ROS in response to xenobiotic-induced oxidative stress has been developed. It is based on exposure experiments of human urothelial cells (RT4) to the nitrated polycyclic aromatic hydrocarbon 3-nitrobenzanthrone (3-NBA), a component of diesel engine exhaust, and takes into account the following metabolic pathways of the antioxidant defence system: glutathione redox cycle scavenging directly ROS, the pentose phosphate pathway and the gluconate shunt as NADPH supplier and the beginning of glycolysis. In addition, ROS generation due to the bioactivation of 3-NBA has been implemented. The regulation of enzyme activities plays an important role in the presented mathematical model. The in silico model consists of ordinary differential equations on the basis of enzyme kinetics and mass action for the metabolism of 3-NBA. Parameters are either estimated from performed in vitro experiments via least-squares fitting or obtained from the literature. The results underline the importance of the pentose phosphate pathway to cope with oxidative stress and suggest an important role of the gluconate shunt during low-dose exposure.

Cyclosporin A Protected Cardiomyocytes Against Oxidative Stress Injury by Inhibition of NF-κB Signaling Pathway

PURPOSE

This study aims to investigate the effects and the molecular mechanism of cyclosporin A (CsA) against oxidative stress injury in cultured neonatal rat cardiomyocytes.

METHODS

Bax/Bcl-2, cl-casp-9/casp-9, cl-casp-3/casp-3, and iNOS/β-actin ratios and p-IκB and IκB levels were analyzed by western blot. IL-1β and TNF-α levels were analyzed by ELISA.

RESULTS

CsA effectively improved the cell viability and reduced the extracellular lactate dehydrogenase release in cardiomyocytes after H₂O₂-induced oxidative damage. CsA significantly increased the superoxide dismutase activity, glutathione production, and catalase activity but decreased the malonaldehyde level. CsA treatment considerably reduced the H₂O₂-induced intracellular generation of reactive oxygen species, mitochondrial dysfunction, and release of cytochrome c. CsA could act against H₂O₂-induced ATP reduction, TCA cycle enzymes, mitochondrial complex I enzyme, and complex V enzyme in cardiomyocytes. CsA significantly decreased the Bax/Bcl-2 ratio, cl-casp-9/casp-9, and cl-casp-3/casp-3 in a concentration-dependent manner. CsA also remarkably reduced the cleaved PARP level and DNA fragmentation. NF-κB was closely related to oxidative stress injury. CsA inhibited NF-κB activation, thereby preventing the upregulation of IL-1β, TNF-α, iNOS, and intracellular NO release.

CONCLUSIONS

CsA protected cardiomyocytes against H₂O₂-induced cell injury. Hence, CsA may be developed as a candidate drug to prevent or treat myocardial ischemia reperfusion injury.

A physical model of cell metabolism

Cell metabolism is characterized by three fundamental energy demands: to sustain cell maintenance, to trigger aerobic fermentation and to achieve maximum metabolic rate. The transition to aerobic fermentation and the maximum metabolic rate are currently understood based on enzymatic cost constraints. Yet, we are lacking a theory explaining the maintenance energy demand. Here we report a physical model of cell metabolism that explains the origin of these three energy scales. Our key hypothesis is that the maintenance energy demand is rooted on the energy expended by molecular motors to fluidize the cytoplasm and counteract molecular crowding. Using this model and independent parameter estimates we make predictions for the three energy scales that are in quantitative agreement with experimental values. The model also recapitulates the dependencies of cell growth with extracellular osmolarity and temperature. This theory brings together biophysics and cell biology in a tractable model that can be applied to understand key principles of cell metabolism.