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In our model, the simulated aging brain phenotype exhibits a distinct resting state profile of metabolite concentrations when compared with that of the young brain ( Presentation 1: Supplementary Figure S3A ). Changes in metabolite concentrations in response to stimuli also differ between the young and aging brain ( Figure 3C , Figure 4 ; Presentation 1: Supplementary Figures 3SB , S4 , S5D , S6A ), but metabolites differ in their changes in response to stimuli of varying amplitudes ( Presentation 1: Supplementary Figures S6 , S7 ). We performed uniform manifold approximation and projection (UMAP) for dimensionality reduction on relative differences in concentration traces between the two ages and observed numerous interdependencies between pathways. The pentose phosphate pathway (PPP) and tricarboxylic acid cycle (TCA) tend to form pathway-related clusters ( Presentation 1: Supplementary Figure S8 ). Moreover, the pairwise Kendall correlation between metabolic concentration temporal profiles is also affected by aging: some pairs of metabolites showed more correlated response to stimuli, while the response of other pairs either did not change or decreased ( Presentation 1: Supplementary Figure S9 ). This effect may be caused by the widely described metabolic dysregulation in aging (11). Reaction and transport fluxes are also impacted ( Presentation 1: Supplementary Figures S10 – S12 ). Aging effects on metabolite concentrations at rest and in response to stimuli are therefore metabolite-specific and largely uncorrelated, indicative of a fragmentation of the metabolic network in aging.

One of the central fueling mechanisms in brain neuroenergetics is the astrocyte-to-neuron lactate shuttle (ANLS). The intensely debated ANLS theory describes how neuronal activation drives astrocytic glycolysis and lactate export to the extracellular space, from where it can be taken up and used by neurons. Since its proposal by Magistretti and Pellerin (30–32), many studies have addressed it under various conditions [e.g., (33)]. Neuronal lactate import is lower in the aged metabolic system than the young, while astrocyte lactate export is slightly higher. This aging effect can be partially explained by reduced expression of monocarboxylate transporters (MCTs, based on RNA levels) and mitochondrial hypometabolism, which results in increased pyruvate levels and correspondingly higher levels of lactate. To examine the dependence of lactate transport directionality upon glucose levels in aged and young metabolic systems ( Presentation 1: Supplementary Figure S13 ), we simulated the effects of varying resting blood glucose levels between 1.6–13.6 mM at increments of 1 mM. We performed two experiments, one with arterial lactate scaled proportionally to arterial glucose changes (where arterial lactate in the young brain was scaled proportionally to arterial glucose levels for comparability with the aged brain) and one with a fixed scale of lactate independent of glucose in an aged brain.

In the young system with both glucose and lactate scaled, we observed the expected ANLS at all tested blood glucose levels both at rest and during neuronal activation (averaged over the time interval of 20 seconds of pre-stimulation rest state and 20 seconds upon neuronal activation); as blood glucose levels increase, lactate export from astrocytes slightly increases in the range of low-to-normal blood glucose (1.6–4.6 mM) and decreases in the range of normal-to-high blood glucose (4.6–13.6 mM), while lactate import to neurons slightly increases throughout the entire tested range following the increase in concentration gradient. This directionality is consistent with concentration gradients. In the aged metabolic system with arterial lactate scaled proportionally to arterial glucose (assumption due to sparse data), the lactate shuttle at rest and during neuronal activation (averaged over the time interval of 20 seconds of pre-stimulation rest state and 20 seconds upon neuronal activation) has the same directionality as in the young system for moderate blood glucose levels (6.6–11.6 mM), consistent with a recent publication (34). However, both neurons and astrocytes export lactate when glucose levels are low-to-normal (1.6–5.6 mM) and both neurons and astrocytes import lactate when glucose levels are high (12.6–13.6 mM). A possible explanation for this dysregulation in the aged metabolic system could involve NAD⁺/NADH and ATP/ADP ratios owing to their regulatory role over the entire metabolic network, but this counterintuitive prediction requires experimental verification.

When aging-related changes in arterial lactate are independent of those of glucose, the directionality of lactate transport depends on the scaling coefficient of lactate levels relative to blood glucose levels. For the scaling based on our default aging model, lactate was exported by both the aged neuron and astrocyte at all tested glucose concentrations (given the same fixed arterial lactate), while the young state showed ANLS at all tested concentrations. This shift in lactate supply could be one of the underlying mechanisms of brain energy disruptions in aging.

Lactate serves as an alternative fuel to cells. Its levels depend on relevant transport and pathway reaction rates, including the activity of lactate dehydrogenase (LDH), which catalyzes the reversible conversion of lactate to pyruvate with the reduction of NAD⁺ to NADH and vice versa. High glucose levels affect concentrations of glycolytic metabolites, such as lactate, pyruvate, NAD⁺, and NADH, and consequently affect LDH and MCT activities.

Kinetics of enzymes and transporters, as well as metabolite concentrations, can be cell-type specific, leading to the difference in response to high blood glucose between neurons and astrocytes. Due to these complex interactions, results of computational models can seem counterintuitive, although they open new questions and lead us to a better understanding of how the system behaves under different conditions.

We show for the first time how aging in the metabolic system leads to changes in the generation of action potentials by both synaptic input ( Figure 3 ) and current injection ( Presentation 1: Supplementary Figure S5 ). Age-related differences in neuronal firing characteristics evoked by current injection are particularly important for decomposing NGV energy use because this type of stimulation protocol excludes the metabolic demand caused by glutamate release. We found similar changes in metabolic profiles following synaptic input and current injection ( Presentation 1: Supplementary Figure S14 ), suggesting that metabolic changes mostly impact the action potential generation ability of neurons. However, the model would require a more detailed molecular coupling between the metabolic system and the entire glutamate cycle to strengthen this prediction.

We found that changes in action potential shape and size are caused by a reduction in Na⁺/K⁺-ATPase expression in the aged brain, supporting a recent theory of non-canonical control of neuronal energy status (35). To better understand whether other aspects of the metabolic system, such as reduced supply of ATP, also contribute to these changes, we increased the Na⁺/K⁺-ATPase expression levels in the aged brain model to match the young brain while leaving all other aspects of the aging metabolic system in their aged state. There were no significant differences in action potentials at low frequencies (4–8 Hz) and only slight changes at much higher frequencies (78–79 Hz), suggesting that the decreased expression of the Na⁺/K⁺-ATPase pump is the main factor impairing the ability of neurons to generate action potentials. However, it is still possible that other aspects of the NGV metabolic network become more important after sustained neuronal activity, such as those used during intense cognitive demand.

Although energy deficiency is a prominent hypothesis in brain aging (12), it is not clear if the supply is limited and/or demand is reduced; it is also unclear whether astrocytes and neurons are impacted in the same way. Adenylate energy charge (AEC), a widely used proxy for cellular energy availability (36), is higher in the young state than in the aged ( Figure 4B ). However, this value does not separate supply from demand. To separate the two factors, we first computed the total ATP cost of firing action potentials. We found that the young brain model consumes approximately 2 billion ATP molecules per second per NGV unit (where one unit is one neuron, one astrocyte, and their associated extracellular matrix and capillaries) with 8 Hz firing, while the aged brain model consumes around 1.8 billion molecules per second per unit, which aligns well with literature estimates (37–39). We found that ATP production is lower in the aged cytosol of both neurons and astrocytes and in aged neuronal mitochondria ( Presentation 1: Supplementary Figure S2 ). However, ATP consumption is also lower ( Figure 4C ) due to the lower levels of Na⁺/K⁺-ATPase (40, 41), and therefore ATP supply is not necessarily a limiting factor. Nevertheless, while reduced ATP supply does not seem to limit action potential generation in the acute state, a persistently lower ATP supply may still cause Na⁺/K⁺-ATPase expression to decrease, thereby impairing action potential generation over a longer period.

We also found that neurons and astrocytes are differentially affected by aging. Normally, astrocytic Na⁺/K⁺-ATPases consume slightly less than two-thirds as much ATP as neuronal Na⁺/K⁺-ATPases ( Figure 4D ). In astrocytes, the ATP supply is only reduced in the cytosol and not in the mitochondria, and the catalytic subunit of the Na⁺/K⁺-ATPases expression is unchanged with aging. While ATP consumption of the Na⁺/K⁺-ATPase pump in neurons decreases with aging ( Figure 4C ), it slightly increases in astrocytes—resulting in an increase in the ratio of astrocyte to neuron Na⁺/K⁺-ATPase ATP consumption from around 0.69 in the young brain to around 0.72 in the aged. Since astrocytes do not need to fire action potentials, this finding suggests that there is an increased demand on astrocytes to support the neurons to clear extracellular K⁺ in order to help neurons generate their action potentials.

The model shows that Na⁺/K⁺ pump ATP use in the astrocyte is comparable with that of the neuron ( Figure 4D ), consistent with recent evidence (42). In line with previous studies (43), mitochondrial ATP production as a share of total ATP production is higher in neurons than in astrocytes, at 84% versus 70% ( Presentation 1: Supplementary Figure S2 ).

Applying the RNAseq data (26, 27) to the respective metabolic pathways revealed that succinate dehydrogenase (SDH) is differentially affected by aging in neurons and astrocytes. SDH is a mitochondrial energy nexus and serves as complex II of the mitochondrial electron transport chain (ETC). SDH connects the tricarboxylic acid cycle (TCA) to the ETC. This result indicates that pre- and post-SDH enzymes of TCA (fumarase and succinate CoA ligase) display opposite changes in aged neurons and astrocytes. SDH itself decreases more in aged neurons than in aged astrocytes. In neurons, aging reduces both succinate CoA ligase and SDH, while increasing fumarase. Unlike in neurons, succinate CoA ligase levels rise in astrocytes during aging. SDH decreases slightly while fumarase levels decline further.

Protein dysfunction is associated with several aging hallmarks, including loss of proteostasis, oxidative damage, and impaired DNA repair (11, 26). Moreover, reduced fidelity of protein translation leads to a phenotype resembling early Alzheimer’s disease (44). To mimic molecular damage and simulate the effect on enzyme and transporter functions, we introduced one perturbation at a time for each protein’s kinetic parameters (Michaelis constant, inhibition and activation constants, and catalytic rate constant—i.e., parameters in the enzyme rate equation), increasing or decreasing its value by 20% (in separate simulations, Figure 5A ). We then calculated the changes in the response of all metabolites to measure the sensitivity of their concentrations to each perturbation. We ran 2,264 simulations with perturbed parameters, measuring metabolite sensitivities at rest and during stimulus for both the young and aged systems (see Equation 1).

where dy/dp represents sensitivity, M(1.2p)[t] and M(0.8p)[t] are the metabolite concentrations at the time point t in simulation with the parameter p value multiplied by 1.2 and 0.8 respectively, M(p)[t] is the metabolite concentration at the time point t in the original simulation (no parameter variation), and dp is the change in parameter value from its value in the original model.

The difference between the sensitivities of the resting and stimulated states ( Figure 5B ), normalized by the resting state sensitivities, yielded a rest-normalized sensitivity. A larger value for a metabolite implies that a stimulus produces a larger change in its concentration (as compared with rest) when another parameter in the system is perturbed. We therefore interpret such a change as the ability of the system to adapt to damage; we call this metric “metabolic adaptability” ( Figure 5C ).

This metric allowed us to compare the whole metabolic systems of neurons and astrocytes in the young and aged brain ( Figure 5C ). We found that the adaptability of most neuronal metabolites decreases with age, while the adaptability of the astrocyte mostly increases. This observation concurs with the literature on astrocyte reactivity, which measures a set of phenotypic characteristics, including those of metabolism, inflammatory cytokine secretion, and cytoskeleton rearrangement (45). However, in contrast to the “selfish” astrocyte hypothesis (45), it is possible that the increase in astrocytic adaptability could instead be a “self-sacrifice” in an attempt to support the declining neurons; the increased adaptability of the astrocyte might be an attempt to stabilize the already declining metabolic profile in the neuron during aging.

We visualized the adaptability of the entire NGV metabolic network in the two age states by positioning the nodes of both metabolites and enzymes using the Fruchterman-Reingold force-directed algorithm (46). The length of each of the 16,800 edges were weighted by the inverse of metabolic adaptability ( Figure 5C lower; see Presentation 1: Supplementary Information Files 1–8 ) to more intuitively reflect “metabolic fragility”. These networks displayed clustering of nodes largely by function and also revealed more evenly distributed clusters in young than in aged systems, indicative of a robust network. To quantify the network differences between young and aged systems, we calculated the centrality of nodes, which is the reciprocal of the sum of the shortest path distances between each node and all other nodes. The aged network showed longer average distances than the young network ( Figure 6A ), suggesting that the metabolic system of the aged brain is more fragile than that of the young brain.

To quantify the effect of aging on metabolic system fragility, we progressively removed edges below a given percentile and calculated the number of connected components in young and aged metabolic networks ( Figure 6B ). This revealed that the aged network is fragmented into clusters or “islands”. Both networks are fully connected at thresholds below 76% and fully disconnected at 100%, but between 76% and 93% thresholds we observed a higher number of connected islands in the aged network. We computed directed simplices, a type of all-to-all connected clique, using algebraic topology (47, 48) to quantify the topological complexity of the network (see Methods ). This showed that the dimensions (number of nodes) and number of simplices are higher in the young state ( Figures 6C–E ), indicating that the young metabolic network is more topologically complex, distributed, and robust than the aged system.

The scale of the challenge of finding new drugs for therapeutic interventions is revealed by the >16,800 possible enzyme/transporter-metabolite interaction pathways we identified in the NGV metabolic network, plus the complexity of the metabolic response when any one pathway is perturbed. The measure of metabolic adaptability can guide identification of targets within this complex dynamical system. Here, interaction pathways with the highest differences in metabolic adaptability ( Presentation 1: Supplementary Figure S16 ) are potential targets to repair the aged metabolic system ( Figure 7 ), with high-priority targets being those that improve adaptability for the highest number of pathways. The ideal drug to repair the metabolic system is one that acts like a transcription factor (TF), regulating multiple enzymes and transporters to modulate an even larger number of metabolic pathways. We therefore applied the ChIP-X Enrichment Analysis 3 (ChEA3) optimization algorithm (49), which isolates the TFs with the largest overlap between a prioritized set of genes for those enzymes and transporters that show the biggest improvement in metabolic adaptability for the largest number of interaction pathways ( Figure 8 ). We identified the ten highest-priority potential targets.

The TF with the highest score was estrogen-related receptor α (ESRRA). This TF regulates the expression of multiple metabolism-related genes, including those of mitochondrial function, biogenesis, and turnover, as well as lipid catabolism (50). It is also linked to autophagy and the nuclear factor kappa B (NF-κB)-mediated inflammatory response via silent information regulator 1 (Sirt1) signaling (51–54). Mitochondrial dysfunction and autophagy impairments are consistently among the hallmarks of aging (9–11, 55). Notably, ESRRA expression is downregulated in aging (26, 50). Altogether, therefore, ESRRA acts as a regulatory hub of multiple aging-associated pathways (outlined in Presentation 1: Supplementary Figure S19 ). The other TFs that we identified are also validated by literature reports on TFs implicated in aging and neurodegeneration (see Presentation 1: Supplementary Information Files 1–8 ).

Using the STRING database (56), we identified the following proteins most prominently associated with the top-scoring TF, ESRRA ( Figure 8 ): hypoxia inducible factor 1 (HIF1A), Sirt1, histone deacetylase 8 (HDAC8), peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PPARG1α, also called PGC1α), PPARG1β (PGC1β), myocyte enhancer factor 2C (MEF2C), nuclear receptor interacting protein 1 (NRIP1), nuclear receptor coactivator 1 (NCOA1), mitochondrial transcription factor A (TFAM), and PGC-1 and ERR-induced regulator in muscle protein 1 (PERM1). Numerous literature reports implicate these proteins in aging and neurodegeneration. The repair targets identified using our molecular model of the NGV system therefore largely align with reported experimental data on therapeutics for healthy aging (57). We additionally suggest a role for less-studied TFs in aging brain energy metabolism and provide insights into the links between molecular mechanisms implicated in aging and neurodegeneration (see Presentation 1: Supplementary Information Files 1–8 ). From a broader perspective, identified targets can be further investigated for their potential as biomarkers of aging. However, more research is needed to dissect causes from consequences and accompanying effects.

As an alternative to specifically targeting the enzymes and transporters, we investigated whether key features of the aged brain phenotype, such as energy deficiency and altered neuronal firing, could be repaired through strategic interventions. We conducted constrained optimizations (see Methods ) for (i) the interaction pathway targets identified by the differences in metabolic adaptability (same as the input for TF enrichment analysis above), (ii) the interaction pathways potentially regulated by ESRRA (above), (iii) parameters corresponding to arterial blood glucose and ketone levels (mimicking dietary factors), (iv) parameters corresponding to arterial blood lactate levels (mimicking exercise factors), and (v) total NAD-pool parameters in neurons and astrocytes (mimicking NAD-related supplementation). Surprisingly, optimization using a combination of diet (lower blood glucose and higher blood β-hydroxybutyrate), exercise (higher blood lactate), and NAD-related supplementation and modulation of the cytosol-mitochondria NAD-associated reducing equivalents shuttle (hereafter referred to as DEN therapy) increased ATP levels in both neurons and astrocytes toward values of the young metabolic system—comparable to that of the top-scoring targeted therapy ( Figure 9A ; Presentation 1: Supplementary Table S3 ). Interestingly, even though the parameter bounds for the optimization were allowed to search for increasing or decreasing values, the DEN therapy optimization converged unguided to a lower blood glucose and higher blood β-hydroxybutyrate, blood lactate, and NAD-modulation, consistent with commonly accepted benefits of calorie restriction, exercise, and NAD supplementation (58).

The DEN therapy largely, although not completely, restored the youthful state of the neuronal metabolic system but not their action potential generation. As presented, action potential amplitude and shape can only be restored in our model by increasing the levels of the Na⁺/K⁺ pump to youthful levels. We therefore additionally reversed the age-related downregulation of the Na⁺/K⁺ pump for each intervention (i.e., for the best-scored combinatorial therapy based on targeted selection of enzymes and transporters, NAD supplementation, NADH cytosol-mitochondria shuttle capacity modulation, and for the DEN therapy). This approach restored neuronal firing characteristics similar to those of a young state for each intervention ( Figure 9B ) as well as ATP levels of both neurons and astrocytes. It is reasonable to assume that changes in action potential shape could affect calcium influx into presynaptic boutons and hence the probability of vesicle release, suggesting that restoration of action potential shape may also influence release properties. Interestingly, insulin is a common factor that activates Na⁺/K⁺-ATPase and increases its expression while also lowering blood glucose, consistent with DEN therapy. A sensitivity analysis, calculating adaptabilities for the DEN therapy and top-scored therapy, showed that network fragility could not only be repaired but even improved over the young state ( Figure 9C ).

To validate predictions of the model we used publicly available data that were not used to construct the model.

First, we extensively validated the model against a corpus of data reported in the literature on how enzyme and transporter activities and metabolite concentrations change in response to stimulation ( Presentation 1: Supplementary Figure S1 , Supplementary Table S1 ). All concentration-related variables were maintained in the range of biologically plausible values by the callbacks and the “isoutofdomain” parameter to a solver, as described in the Optimization part of the Methods section. We also qualitatively compared reaction and transport fluxes to their expected response to stimuli ( Presentation 1: Supplementary Figure S2 ).

Next, we calculated the blood-oxygen-level-dependent (BOLD) signal ( Presentation 1: Supplementary Figure S1D ) and oxygen-glucose index (OGI) (ranging from 4.5–5.0 depending on stimulus, while literature data range from 4.0–5.5) using equations from Jolivet et al. to compare them with the literature (21, 24, 59). These two high-level phenomena are commonly used as benchmarks in NGV metabolism modeling papers (21, 24, 60), although these tissue-level metrics cannot be applied directly to the unitary models of NGV. We also found the lactate shuttle directionality in the aged metabolic system under moderate blood glucose levels (6.45–10.6 mM) was consistent with a recent publication (34).

Then we estimated energy use from the components of the Na⁺/K⁺-ATPase rate equation (calculated from the sum of neuron and astrocyte Na⁺/K⁺ pump ATP consumption flux in mM concentration per second with the volume of 17.8 µm³ and the literature estimate of ionic gradients sharing 31% of total energy use). Our estimates of ATP consumption rate per NGV unit at 8 Hz firing in both young and aged states align well with literature estimates (37–39). Our observations in action potential shape and size changes in aging as being caused by a reduction in Na⁺/K⁺-ATPase expression in the aged brain are in line with a recent theory of non-canonical control of neuronal energy status (35).

Furthermore, the model shows that Na⁺/K⁺ pump ATP use in the astrocyte is comparable to that of the neuron ( Figure 4C ), consistent with recent evidence (42). In line with previous studies (43), mitochondrial ATP production as a share of total ATP production is higher in neurons than in astrocytes, at 84% versus 70% ( Presentation 1: Supplementary Figure S2 ). These data emerged when the model was simulated and their consistency with a range of reported experimental data suggests that the model accurately captures the most essential elements of the brain’s metabolic system.

We further validated aging-associated effects against the literature data shown in Presentation 1: Supplementary Table S1 . TFs that we identified as regulating the most fragile enzymes and transporters are also validated by literature reports on TFs implicated in aging and neurodegeneration (see Presentation 1: Supplementary Information Files 1–8 ), and promising anti-aging therapies identified by this study are largely consistent with current understanding in the field.

Even though we strove to be as biologically detailed and unbiased as possible, we had to refine weakly constrained parameters due to limited available data and focus on the most relevant pathways and processes rather than simulating dynamics at the whole genome-scale. Additionally, owing to data sparsity, differences between in vitro and in vivo conditions, as well as sex-related differences, were not considered. Some potential refinements of the model would be to include these aspects.

Furthermore, our model specifically emphasizes the key brain energy metabolism pathways and processes involved in neuronal signal transduction. However, to gain a more comprehensive understanding of the various complementary molecular mechanisms and pathways involved in aging and disease, it would be desirable to further expand the model to a whole-cell scale and incorporate more regulatory processes. At present, this task is hindered by data limitations. As more data become available, the model can be iteratively refined and expanded.

As we mostly focused on metabolism, our model does not incorporate detailed mechanisms of cerebral blood flow regulation with neuronal activation. Changes in oxygen availability and transport with aging were also not included due to data challenges. Refinement of the blood-related part of the model would be a highly valuable improvement. More details on neuronal signaling and synaptic mechanisms would potentially widen the model applications and level of biological detail.

For the various modeled conditions, we applied literature-based scaling factors to the concentrations of enzymes and transporters, as well as initial concentrations of variable metabolites. Owing to the lack of high-quality cell-type-specific protein concentration data for young and old rodents, we relied on data on RNA levels to derive the concentrations of enzymes and transporters, with scaling in the aging group based on the assumption that changes in RNA directly affect enzyme concentrations (61). This procedure, however, is often inaccurate due to various post-translational processes and protein degradation (62). Also due to literature uncertainty and potential biological variability, the scaling of blood nutrients in aging was based on the expectation of only a mild increase in blood glucose and proportional changes in blood lactate. Ketone body β-hydroxybutyrate and glutamatergic signaling were assumed to decrease by half in aging, but better measurements would be useful. We also applied scaling to the NAD pool and synaptic glutamate release, which were literature-driven but had to be approximated, as we did not find exact numbers for their changes with aging. NADH shuttle parameters were considered to be the most flexible as they had the highest uncertainty in the sourced data, which is why we optimized these to balance the aged model.

Another potential limitation is the uncertainty surrounding the nature of molecular damage (including that which accumulates with aging) and its effects on enzyme function, which we modeled as perturbations to individual kinetic parameters. Various other modifications of the model could be designed to be consistent with experimental data, such as inhibition of glycolysis or mitochondrial respiration via specific inhibition of the ETC complex I. However, those are outside the scope of our current study.

We reconstructed and simulated a model of NGV metabolism coupled to a simple blood flow model and a Hodgkin-Huxley (HH) type of neuron model. The main concepts of electro-metabo-vascular coupling, as well as blood flow and the neuronal electrophysiology model, are based on the models available from the literature (19, 21, 24, 60). Our model specifically emphasizes the key brain energy metabolism pathways and processes involved in neuronal signal transduction. However, to gain a more comprehensive understanding of the various complementary molecular mechanisms and pathways involved in aging and disease, it is desirable to further expand the model to a whole-cell scale and incorporate more regulatory processes. At present, this task is hindered by data sparsity. As more data becomes available, the model can be iteratively refined and expanded.

Compared with the more generalized phenomenological metabolism models, our model features 183 processes: 95 enzymatic reactions; 19 processes for molecule transport across the cell and mitochondrial membranes; and 69 other processes related to ionic currents, blood flow dynamics, and some miscellaneous non-enzymatic processes, e.g., magnesium (Mg²⁺) binding to mitochondrial adenine nucleotides. Every reaction, transport, or other process is represented by a literature-derived rate equation. Changes in molecular concentrations are described by a system of 151 differential equations. Additionally, cytosolic ADP, creatine, NAD, and NADP are calculated from the conservation law and total pool of relevant molecules.

The model is based on literature data for enzyme kinetics and molecular concentrations. We meticulously collected all parameters and equations from literature sources (as referenced in Presentation 1: Supplementary Table S2 and throughout the model code) and programmatically queried the BRENDA (75) and SabioRK (76) databases. However, observed discrepancies in the parameters reported by different sources necessitated an optimization procedure to derive biologically plausible middle-ground values. These parameters with uncertainties were constrained by their lower and upper bounds, taking into account the type of the parameter (Michaelis constant of reaction, inhibition/activation constant, maximal rate of reaction, equilibrium constant, and Hill coefficient) and optimized as described in the Optimization section below.

To have the most realistic biological average for the initial values of all variables (concentrations, membrane potential, mitochondria membrane potential, venous volume, and gating variables) according to the literature, we considered not only measured and modeled literature data on the absolute values themselves but also additional constraints, such as known ratios of NADH to NAD⁺ in the neuron (22, 77–79) and astrocyte (79). One of the most important variables in the model, ATP concentration, was reported as being 2 mM in many experimental and modeling studies (20, 21, 24, 60, 80). However, more recent data report it at the 1.0–1.5 mM scale (35, 81). Assuming that more recent measurement technologies provide more precise data, we set cytosolic ATP in the neuron to approximately 1.4 mM according to Baeza-Lehnert et al. (35) and to approximately 1.3 mM in the astrocyte according to Köhler et al. (81), who reported ATP concentrations of 0.7–1.3 mM in acutely isolated cortical slices and 1.5 mM in primary cultures of cortical astrocytes.

Reported mammalian ATP to ADP ratios vary widely from 1 to >100 (82), while the ratio of ATP to adenosine monophosphate (AMP) is around 100 (80). Furthermore, metabolite ratios from Erecińska and Silver (80) were used to adjust initial concentrations of phosphocreatine and phosphate to the ATP levels. Lactate concentrations in different compartments, which is central to the ANLS debate, was set according to Mächler et al. (83). We also tested the model with all alternative literature-reported concentrations for the metabolites mentioned above.

Glucose supply from blood is of key importance to brain energy metabolism (84) and so we approached this meticulously. In our model, glucose concentrations are assigned to detailed compartments, such as arterial, capillary, endothelial, basal lamina, interstitium, neuronal cytosol, and astrocytic cytosol (85). According to the literature, hexokinase flux is split approximately equally between neuron and astrocyte (85–87), so we adjusted the maximum velocity (V_max) of hexokinase so that its flux matched the literature data at rest. Upon activation, the ratio of glucose influx to astrocyte versus neuron increases, consistent with the literature (87, 88).

Aging is a multifactor phenomenon that affects metabolism at different levels, such as transcriptome, proteome, metabolome, and potentially even kinetic properties of enzymes and transporters owing to accumulated genetic damage, lower protein synthesis fidelity, and higher chances of protein misfolding. Implementing the aging effect in our model in a fully data-driven way would require data on neuron- and astrocyte-specific proteomics, metabolomics, and enzyme kinetics. However, for the most part such data are not yet publicly available.

We modeled the aging effects using the following data:

For the above factors, which mention “approximative/approximation”, the direction of change is according to the literature, but the absolute number of scaling factors (not known/contradictory in the literature) is set with an objective for the model to be steady at rest.

We implemented the aging effects on enzyme and transporter levels in two parallel ways: (i) using cell-type specific transcriptomics data (26, 27) and (ii) using integrated proteomics data from our earlier meta-analysis (99). The first approach featured higher coverage depth for the astrocyte-specific data. To reduce bias from inferring missing data in the second method, we relied on RNA data for implementing aging effects into simulation, while we used the second data source for validation.