A tribute to Leif Hertz: The historical context of his pioneering studies of the roles of astrocytes in brain energy metabolism, neurotransmission, cognitive functions, and pharmacology identifies important, unresolved topics for future studies

Leif Hertz, M.D., D.Sc. (honōris causā) (1930–2018), was one of the original and noteworthy participants in the International Conference on Brain Energy Metabolism (ICBEM) series since its inception in 1993. The biennial ICBEM conferences are organized by neuroscientists interested in energetics and metabolism underlying neural functions; they have had a high impact on conceptual and experimental advances in these fields and on promoting collaborative interactions among neuroscientists. Leif made major contributions to ICBEM discussions and understanding of metabolic and signaling characteristics of astrocytes and their roles in brain function. His studies ranged from uptake of K+ from extracellular fluid and its stimulation of astrocytic respiration, identification, and regulation of enzymes specifically or preferentially expressed in astrocytes in the glutamate–glutamine cycle of excitatory neurotransmission, a requirement for astrocytic glycogenolysis for fueling K+ uptake, involvement of glycogen in memory consolidation in the chick, and pharmacology of astrocytes. This tribute to Leif Hertz highlights his major discoveries, the high impact of his work on astrocyte–neuron interactions, and his unparalleled influence on understanding the cellular basis of brain energy metabolism. His work over six decades has helped integrate the roles of astrocytes into neurotransmission where oxidative and glycogenolytic metabolism during neurotransmitter glutamate turnover are key aspects of astrocytic energetics. Leif recognized that brain astrocytic metabolism is greatly underestimated unless the volume fraction of astrocytes is taken into account. Adjustment for pathway rates expressed per gram tissue for volume fraction indicates that astrocytes have much higher oxidative rates than neurons and astrocytic glycogen concentrations and glycogenolytic rates during sensory stimulation in vivo are similar to those in resting and exercising muscle, respectively. These novel insights are typical of Leif's astute contributions to the energy metabolism field, and his publications have identified unresolved topics that provide the neuroscience community with challenges and opportunities for future research.


| INTRODUC TI ON
The biennial International Conference on Brain Energy Metabolism (ICBEM) is a cutting-edge conference series that focuses on themes of timely importance in brain energetics and neural metabolism underlying brain functions.Each ICBEM conference is unique, consisting of talks by invited speakers and poster sessions that together foster intense, informal discussions of debated scientific issues, and each has had a highly cited journal special issue.The 14th ICBEM Special Issue in the Journal of Neurochemistry includes this tribute to Leif Hertz, M.D., D.Sc.(honōris causā) .Leif is one of the key founding members and invaluable participants in the ICBEM conference series, who has contributed manuscripts to 8 of 11 special issues between 1993 and 2014.Leif is widely recognized for his detailed, insightful knowledge of the cellular basis of functional metabolism, for having passionate discussions of unresolved topics and encouraging novel approaches to experimentally examine and ultimately understand these issues.Leif was not one to back away from inaccurate, incomplete, or wrong information or incorrect conclusions, and he held that one should always "call a spade a spade," that is, tell it like it is.Many of his scientific contributions illustrate how key experiments and long-term pursuit of their implications can have a high impact on the field.This synopsis of Leif's work by colleagues who have worked with him embodies a historical perspective of his interests in and contributions to elucidating the roles of astrocytes in brain energetics, neurotransmission, higher brain functions, and pharmacological treatments of various brain disorders.Some of the topics in which Leif was an active participant are still debated and are, therefore, described in sufficient detail to illustrate the basis for the unresolved issues.Discussion of earlier work and future directions for key topics in this article is important because many younger neuroscientists are not familiar with much of the earlier work that led to current thinking about critical and debated roles of astrocytes in many important brain functions and energetics.Therefore, a second major objective of this commentary is to stimulate more experimental work in these areas, and also to emphasize the high impact of ICBEM conferences on multidisciplinary progress in brain energy metabolism.
Leif Hertz was a truly visionary scientist who had a profound influence on the fields of neurochemistry and brain metabolism (Schousboe & Dienel, 2018).His research and papers from his early studies developed and pioneered using cultures of brain cells to study and understand the unique properties and metabolism of astrocytes, glutamatergic, and γ-aminobutyric acid-ergic (GABAergic) neurons (e.g., Hertz et al., 1988;Schousboe & Hertz, 1987).His most recent, insightful reviews analyzing and integrating glycolysis, glycogen formation and degradation, the glutamate (Glu)-glutamine (Gln) cycle, and the role(s) of lactate in brain and in learning/memory have inspired, pushed, and challenged others in the field to figure out how to address these important questions (Hertz & Chen, 2016a, 2017, 2018a, 2018b).While many investigators can synthesize and integrate the information from specific focused areas of research, Leif Hertz had the unique ability to see farther, understand brain metabolism more clearly, and, importantly, communicate his synthesis of this integrated information to others in the field so that we might better understand the intricacies and nuances of neuronal and glial metabolism in brain.Leif was always engaged in a critical review of the literature on brain metabolism and function and was delighted and, perhaps astonished, when new findings helped to explain phenomena that had confounded researchers for years (Hertz & Chen, 2018b).Leif was not shackled by long-held dogmas.
He embraced new concepts that were based on rigorous experimental evidence and he had little regard for concepts based on poor experimental design, challenging those with imprecise, inaccurate, or experimentally unsupported interpretations and conclusions.He continuously reassessed brain metabolism in the light of important new findings, and, unlike many scientists, would point out limitations in earlier studies from his own lab as well as from others in the field.
In addition, he would encourage others to develop and perform additional experiments and measurements necessary to directly resolve controversies and, therefore, advance the field.His goal was not fame or recognition, but rather it was to gain a better understanding of the links between metabolism, neuron-astrocyte interactions, neurotransmission, and learning so that even more exciting, focused, and clinically relevant questions related to the cellular basis of brain functions could be addressed.We should all aspire to meet his standards.This tribute to Leif Hertz highlights his seminal contributions to brain energy metabolism within the historical context of elucidation of roles of astrocytes in brain function that have strongly influenced his colleagues, including the present authors.His rigorous development and evaluation of cell culture procedures are presented first, than neurons and astrocytic glycogen concentrations and glycogenolytic rates during sensory stimulation in vivo are similar to those in resting and exercising muscle, respectively.These novel insights are typical of Leif's astute contributions to the energy metabolism field, and his publications have identified unresolved topics that provide the neuroscience community with challenges and opportunities for future research.

K E Y W O R D S
astrocyte and neuron cell culture, astrocytic metabolism and energetics, astrocytic pharmacology, cellular maturation in vitro, Glu/GABA-Gln cycle, glycogen followed by his assessment of astrocytic and neuronal maturation in vitro in comparison to brain development in vivo, and quantitative analyses of glycolytic and oxidative metabolism in astrocytes, GABAergic neurons, and glutamatergic neurons.Then, his work on unique roles of glycogen and its utilization during memory consolidation is discussed.The paper concludes with his contributions to understanding how astroglia couple energy metabolism to neuronal signaling in vivo, and his studies of pharmacology of astrocytes.
Selected topics that still have discordant experimental results and interpretations are presented as examples that require more work.
Although this commentary specifically recognizes the contributions of Leif Hertz, we emphasize that many other scientists, especially his long-term collaborator, Arne Schousboe, made very important contributions to the studies, concepts, and topics discussed herein.

| K + exposure stimulates respiration: Studies at the cellular level
This section emphasizes Leif's early studies of effects of K + on astrocytic metabolism, a theme that remained a passionate interest throughout his entire career.Dissection of the cellular basis of effects of K + required development and characterization of astrocytic and neuronal cultures, and these in vitro preparations facilitated many types of studies that helped clarify the cellular specialization of metabolism related to energetics and excitatory and inhibitory neurotransmission (Figure 1).
In order to be able to study effects of depolarizing concentrations of K + in brain tissue at the cellular level, Leif Hertz, very early in his career (1970s), set out to establish methods to prepare cultures of glial cells and neurons separately.Using the Rose chamber technique (Rose, 1954), astrocytes were cultured from chick embryo spinal cord and neurons from chick embryo dorsal root ganglia or cerebral hemispheres dissected from 7-day-old chick embryos.The oxygen consumption as well as the ATP content of the cells was measured during and after incubation in physiological media (3.7-4 mM K + ) and in media containing 54 mM K + .The cultured neurons exhibited a high rate of oxygen consumption as well as a high ATP content.
Neuronal exposure to a high potassium concentration had no effect on the cellular content of ATP, whereas exposure of astrocytes to high potassium led to a dramatic decrease in the ATP content (Dittmann, Hertz, et al., 1973;Schousboe et al., 1970).Notably, astrocytes and neurons had similar respiration rates on a per-cell basis (Dittmann, Sensenbrenner, et al., 1973) and the rate of astrocytic oxygen consumption (CMR O2 ) was stimulated by 55 mM K + (Hertz et al., 1973;Hertz & Hertz, 1979).These studies demonstrated that cultured brain cells could be used to study brain metabolism at the cellular level and subsequently, methods were developed to prepare separate astrocyte and neuron cell cultures from dissociated brain tissue from rats or mice (Hertz et al., 1982(Hertz et al., , 1984).Leif's interest in the energetics of K + uptake into brain cells was a life-long pursuit that culminated with demonstration of involvement of K + with glycogenolysis and complex signaling pathways in astrocytes.These pathways involve K + transport and Na + ,K + -ATPase activity (Hertz et al., 2017;Hertz, Song, et al., 2015;Xu et al., 2013), as described in more detail below.

| Primary cultures of astrocytes
In order to obtain highly morphologically differentiated astrocytes, the newly developed method for preparation of cultured astrocytes from dissociated brain hemispheres from newborn rats or mice (Booher & Sensenbrenner, 1972) was used.To achieve morphological and functional differentiation of the cells, the newly discovered ability of dibutyryl-cyclic AMP (dBcAMP) to induce stellation of astrocytes in culture (Moonen et al., 1975) was utilized.To investigate the effects of dBcAMP on astrocyte function, a series of studies leading to development of astrocyte cultures that mimic astrocyte functions in the brain in vivo were performed over the following years, and one example is the study published by Hertz, Bock, and Schousboe (1978).This study clearly demonstrated that astrocytes treated with dBcAMP during the last week of a culture period of 3 weeks exhibited a high expression level of glial fibrillary acidic protein (GFAP), as well as high activities of Gln synthetase (GS) that increased by ~3-fold from weeks 1 to 2 in vitro and by another 50% from weeks 2 to 3, and the high-affinity Glu transporter, three major hallmarks of astrocytic function (Eng et al., 1971;Hertz, Schousboe, et al., 1978;Martinez-Hernandez et al., 1977;Schousboe et al., 1977).
Throughout his career, Leif worked together with his wife Elna (Figure 2a), and together they set a very high standard for cell culture models.Their scientific collaboration included co-authorship of at least 19 publications.When contrasting results were reported by another laboratory that used a different culture method, the other procedure was evaluated, and Elna noted, "when we used his culture method, we got the same results as he did."Elna's testimony underscores the critical importance of reporting exact procedures and culture medium components that are frequently omitted in publications thereby preventing meaningful comparisons of different cell culture studies and identification of testable reasons for discrepant results.
The basic biochemical and morphological properties of these astrocyte cultures (Figure 1) are summarized by Hertz et al. (1982), and a detailed discussion of the validity of the astrocyte culture system to study the functional roles of this cell type in the brain can be found in a review paper (Lange et al., 2012) in the special issue of Neurochemical Research (37:11, 2295Research (37:11, -2626Research (37:11, , 2012) ) containing 26 manuscripts published in the honor of Leif Hertz.Hertz also subsequently reviewed the correspondence between his and other cultured astrocyte preparations and astrocytes in living adult brain (Hertz et al., 2017).Key elements of astrocyte culture preparation were addition of dBcAMP to evoke differentiation, inclusion of low [K + ] concentrations in the medium, ~3-4 weeks culture duration to permit maturation of important enzymes, and use of lower glucose levels (5-6 mM) to minimize consequences of chronic hyperglycemia (see below, Section 2.4).Hertz emphasized that astrocytes in culture have pronounced capacity for plasticity that can be influenced by seemingly minor differences in culture techniques, and careful attention must be given to culture procedures and conditions.

GABAergic neurons
Two publications describing the methods for preparation of neuronal cultures from cerebellum and cerebral cortex (Dichter, 1978;Messer, 1977;Messer et al., 1980) prompted Leif Hertz and coworkers to refine and utilize neuronal cell culture systems for in vitro investigations of the mechanisms, regulation, and metabolism supporting glutamatergic and GABAergic neurotransmission responsible for the vast majority of excitatory and inhibitory neurotransmission in the brain (Curtis et al., 1959a(Curtis et al., , 1959b;;Curtis & Johnston, 1974).
In a series of publications in the early part of the 1980s, cultures of neurons from either dissociated cerebellum from 7-day-old mice or dissociated cerebral cortical hemispheres from gestational day 15 mouse embryos were characterized and shown to be reliable model systems for the study of glutamatergic and GABAergic neurotransmission, respectively.Investigations of the uptake and evoked release of Glu and GABA, as well as the activities of enzymes pertinent F I G U R E 1 Some of the major research interests of Leif Hertz.Leif Hertz made major contributions to properties of cultured astrocytes and neurons and their functions, including energy metabolism, neurotransmitter receptors, and signaling pathways, the glutamateglutamine cycle and related metabolic pathways, the validity of the notion of astrocyte-neuron lactate shuttling versus rapid and substantial lactate release from activated brain tissue, and roles of glycogen in brain functions.Abbreviations: Glc, glucose; DG, deoxyglucose; FDG, fluorodeoxyglucose; HK, hexokinase; Glycogen shunt, incorporation of Glc-6-phosphate (Glc-6-P) into glycogen followed by release of a glucosyl unit from glycogen and generation of Glc-6-P that can re-enter the glycolytic or pentose phosphate pathway (PPP); V PC , rate of pyruvate carboxylation; V PDH-a , rate of the pyruvate dehydrogenase (PDH) reaction in astrocytes; TCA cycle, tricarboxylic acid cycle; AAT, aspartate aminotransferase; αKG, α-ketoglutarate; OAA, oxaloacetic acid; Asp, aspartate; Glu, glutamate; Glu-Gln cycle, glutamateglutamine (Gln) cycle; GS, Gln synthetase; GDH, Glu dehydrogenase; V NTcycle , rate of neurotransmission (NT) cycle involving Glu and Gln; MCT, monocarboxylic acid transporter, with numbers identifying different isoforms of the MCTs; Lac, lactate; V PDH-n-Glu , rate of the PDH reaction in glutamatergic neurons; V TCA-a , rate of the TCA cycle in astrocytes; V PDH-n-postsyn , rate of the PDH reaction in post-synaptic neuronal structures.
to the metabolic pathways involving Glu and GABA as a function of development in culture, demonstrated that the cultured cerebellar and cortical neurons to a considerable extent reflected properties of mature glutamatergic and GABAergic neurons, respectively (Drejer et al., 1982(Drejer et al., , 1983(Drejer et al., , 1985;;Larsson et al., 1985;Yu et al., 1984;Yu & Hertz, 1982).
As will be explained in subsequent sections, these preparations of cultures of astrocytes (Hertz, Juurlink, et al., 1989), glutamatergic (Schousboe et al., 1989), and GABAergic (Hertz, Yu, et al., 1989) neurons have been used in a large number of studies in many laboratories aimed at delineating the basic properties of astrocytic and neuronal metabolic processes involved in glutamatergic and GABAergic neurotransmission as well as in neuron-astroglial interactions in these processes.Additionally, these culture systems (for further details of the cultures, see Hertz et al., 1984) have provided important knowledge about the relative contributions of neurons and astrocytes to overall brain energy metabolism, a field in which the impact of studies performed by Leif Hertz and colleagues is unparalleled.

| Summary and future directions
Hertz, Schousboe, and their colleagues carried out detailed, quantitative studies to characterize maturation of cultured neurons and astrocytes in vitro, compared to the in vitro enzyme, receptor, and transporter developmental profiles to those in brain in vivo; established metabolic and other characteristics of cultured cells, for example, receptors and responses to neurotransmitters and neuromodulators; and assessed the effects of components of the culture medium (Figure 1).For example, the culture medium for astrocytes used by various laboratories may contain ~5-25 mM glucose, with culture for up to about a month, whereas neurons are generally cultured in 25-50 mM glucose (because neurons die after complete medium change) for about 7-10 days.Diabetic rat brain has twice the normal glucose levels which are ~2-3 μmol/g (Gandhi et al., 2010), and complications of diabetes can be expected to become manifest in high-glucose cultures.Takahashi and colleagues established that medium-glucose concentration has a high impact on astrocytic rates of glucose phosphorylation, oxidation, and pentose phosphate shunt fluxes, for example, those grown in 2 mM glucose are more dependent on glucose oxidation than those grown in 22 mM glucose (Abe et al., 2006;Takahashi et al., 2012).Clearly, the impact of culture conditions on cellular phenotypes must be an essential component for future work.Also, unless experimentally verified, as done by Hertz-Schousboe and colleagues, cultured cells, particularly neurons, may be immature compared with adult brain.This is important because the largest incremental increases in enzyme and transporter activities during neonatal brain development occur between post-natal (P) ages P10-P30 days (Baquer et al., 1977;Cremer et al., 1975;Leong & Clark, 1984b, 1984c;Nehlig, 1997;Vannucci & Simpson, 2003), including glutamatergic and GABAergic fluxes between P10 and P30 (Chowdhury et al., 2007) and Glu loading into synaptic vesicles (Kish et al., 1989).The culture medium components and culture duration are critical, and interpretation of data from immature neuronal and astrocytic cultures must, therefore, be based on extent of maturation in vitro.These caveats underscore the importance of careful, detailed characterization of brain cell cultures and quantitative comparison to brain in vivo for both past and future studies.Investigators who do not characterize cellular and functional maturation in vitro cannot claim relevance to brain activity in vivo.In fact, the application of data from tissue culture studies to the in vivo state was a long-term concern of Leif Hertz, Arne Schousboe, and their colleagues.From the earliest stages of and throughout Leif's career, he published detailed comparisons of tissue culture and in vivo measurements, using the latter as the guide for culture studies and as the "gold standard" for metabolic and developmental measurements (e.g., for early references, Hertz, 1969Hertz, , 1977aHertz, , 1977b;;Hertz & Schousboe, 1975, 1980;Hertz, Schousboe, et al., 1978;Hertz, Yu, et al., 1980;Schousboe et al., 1977Schousboe et al., , 1980;;Schousboe & Hertz, 1981).

| Cellular specialization
Astrocytes and neurons have highly specialized roles in brain energy metabolism and in excitatory and inhibitory neurotransmission.Of particular interest are the cellular contributions to major pathways of glucose metabolism, to the de novo synthesis of neurotransmitters and their degradation, and to processes involved in neurotransmission itself.This knowledge base is necessary for understanding brain function, interpretation of [ 18 F]fluorodeoxyglucose ([ 18 F]FDG) positron-emission (PET) metabolic brain images, and interpretation of 13 C-magnetic resonance spectroscopic (MRS) metabolic-labeling data, as discussed in more detail below.
Astrocytes have an essential role in the de novo synthesis of the carbon skeletons of Glu, aspartate (Asp), Gln, and GABA because they, not neurons, contain the enzymatic machinery to convert glucose into these amino acids via the oxidative pathways (Figure 1; see section 3.6).Astrocytes also have a major role in amino acid homeostasis because they can carry out partial (to a 4-carbon compound) or complete (to CO 2 ) oxidation of Glu as an ATP source at the time and site of increased energy demand (Figure 1; see section 3.4 and 3.5).Temporal-spatial energetics is critical because astrocytes have a complex architecture, with their endfeet surrounding the vasculature, the soma and large processes containing glial fibrillary acidic protein (GFAP) that delineates only about 15% of the cellular volume, and the small peripheral astrocytic processes (PAPs) that surround and interact with synapses (Bushong et al., 2002).PAPs are mobile (Reichenbach et al., 2010), they contain mitochondria, Gln synthetase, and Glu transporters (Anlauf & Derouiche, 2013;Derouiche et al., 2015;Lavialle et al., 2011), and they are packed with glycogen (Oe et al., 2016).These attributes indicate that oxidation of some Glu taken up from the synaptic cleft, conversion of Glu to Gln for transfer back to neurons as Glu precursor, ion pumping, and metabolism of glycogen are important aspects of energetics of neurotransmission carried out in the PAPs.With this background, the following sections discuss quantitative studies by Hertz, Schousboe, and colleagues of the major metabolic pathways in cultured astrocytes that have made major contributions to establishing roles of astrocytes in overall brain energetics and neurotransmission.

| Astrocytic glycolytic versus oxidative metabolism
The concept of a high level of oxidative metabolism of astrocytes that was advocated early on by Leif Hertz has for years been controversial and at odds with the more prevailing notion that neurons are primarily responsible for oxidative metabolism.As stated above (Section 2.1), astrocytes cultured from chick embryo spinal cord exhibited a large decrease in the ATP content subsequent to exposure to a high concentration of potassium (Schousboe et al., 1970).In keeping with this finding, it was later shown, using cultures of astrocytes from dissociated cerebral cortical hemispheres from newborn mice, that exposure of these cells to a high-potassium concentration led to a transient increase in the oxygen consumption of approximately 100% of the basal oxygen consumption (Hertz & Hertz, 1979).
This result reflects the previous demonstration by Hertz (1966) that the potassium-stimulated oxygen uptake in the brain can best be explained by an effect on astrocytic oxidative metabolism of glucose (and glycogen) during activation (see also Hertz & Schousboe, 1975).

| The debate over validity of the astrocyteneuron lactate shuttle model
The extreme version of the concept that astrocytes have no increase in oxidative metabolism of glucose, only with enhanced glycolytic activity during activation coupled with the oxidative metabolism of astrocytic lactate in neurons, was proposed in the astrocyte-neuron-lactate shuttle (ANLS) hypothesis by Pellerin and Magistretti (1994).This model, which remains unproven and is still debated in the literature, proposed that Na + -dependent Glu uptake into astrocytes stimulates glycolysis to fuel Na + extrusion and Gln synthesis from Glu and that the lactate is shuttled to neurons for oxidation.This notion is in keeping with the controversial report (Ramos et al., 2003) that astrocytes expressed only low levels of the Asp-Glu carrier, Aralar, a component of the malate-Asp shuttle (MAS) without which NADH generated in the cytosol by the glycolytic pathway cannot be oxidized.This finding suggested that there may be little or no oxidative glucose metabolism in astrocytes and that NAD + is regenerated by conversion of pyruvate to lactate, with lactate released from the cell.
In sharp contrast to these results, transcriptomic analysis of freshly isolated adult brain cells, as well as by protein analyses, demonstrated that Aralar is indeed expressed in astrocytes in adult brain in vivo at levels comparable to that in neurons (Li et al., 2012;Lovatt et al., 2007).Furthermore, metabolic assays in astrocytes freshly isolated from adult mice with [ 13 C]glucose clearly demonstrated oxidation of glucose, consistent with the presence of Aralar and the MAS to produce 13 C-labeled pyruvate that then labeled tricarboxylic acid cycle (TCA)-derived metabolites (Lovatt et al., 2007).As discussed below (see Section 3.6), de novo synthesis of Glu from glucose as a precursor for neurotransmitter Glu and GABA occurs only in astrocytes and requires pyruvate carboxylase, the MAS, and active oxidative metabolism that generates almost as much ATP per Glu synthesized (i.e., 31 ATP) as does oxidation of one molecule of glucose (32 ATP) (Hertz et al., 2007).There is, however, some evidence for the presence of the glycerol phosphate redox shuttle in brain cells (Brancati et al., 2021;McKenna et al., 2006), and the quantitative contributions of these two redox shuttles in neurons and astrocytes at different stages of development in culture and in brain in vivo remain to be carefully examined.
As pointed out by Leif Hertz and others, astrocytes do have a high capacity for oxidative glucose metabolism.When in vivo 13 C MRS measurements of the glial TCA cycle in the awake cerebral cortex are normalized by the fractional astrocytic volume of brain tissue of at most 25% (Hertz et al., 2007), the rates are similar to that in neurons (Hertz & Zielke, 2004;Hyder et al., 2006;Lovatt et al., 2007;Riera et al., 2008;Yu et al., 2018).However, a smaller astrocyte volume fraction of 5%-10% was reported by Gundersen et al. (2015), as well as meta-analysis of data from 31 studies (Dienel & Rothman, 2020), revealed regional differences in the astrocytic volume fraction within the range 6%-15%.Using these data, the volume fraction-corrected in vivo rates of astrocytic oxidative metabolism ranges from similar to neurons (maximum volume fraction estimate of 25%) to fourfold higher than neurons (minimum volume fraction estimate of 6%).Volume fraction-adjusted resting brain glycogen concentrations and rates of glycogenolysis during activation approach those in muscle (Dienel & Rothman, 2020). 1 These calculations suggest that energy demands in astrocytes may be considerably higher than generally recognized and that physiological roles of astrocytic ATP-requiring reactions are incompletely understood.
These are important topics for future quantitative studies.
The controversy related to astrocytes being primarily glycolytic is derived, in large part, from tissue culture studies in which astrocytes typically release more lactate to the medium than neurons (Figure 1).
However, the true basis for this difference between responses of various culture preparations remains to be established: is it because of in vitro developmental differences in glycolytic and oxidative enzyme activities in neurons and astrocytes?; does it arise from different numbers of monocarboxylic acid transporters (MCT) in the two cell types?; and do the kinetic differences of astrocytic MCT1 and MCT4 (Km for MCT1 = 3-5 mM; Km for MCT4 = 15-30 mM) compared with neuronal MCT2 (Km = 0.7 mM) influence the amounts of lactate released?Based on MCT Km differences, neuronal lactate efflux would be restricted when intracellular lactate increased compared with astrocytic lactate efflux, which would be expected to help maximize neuronal oxidative metabolism (Chih & Roberts Jr, 2003;Hertz & Dienel, 2005).Lactate release from cultured cells is also highly dependent upon the specific experimental conditions, and the two cell types can release similar amounts of lactate under strongly activating conditions (Walz & Mukerji, 1988a, 1988b).Indeed, the fact that cultured neurons release lactate to the medium in amounts equivalent to about half of the glucose consumed (Gebril et al., 2016;Jekabsons et al., 2017;Waagepetersen et al., 2000) is frequently ignored in the literature.For this reason, statements that increases in brain lactate concentration during activation are derived from astrocytes (e.g., Gao et al., 2016;Suzuki et al., 2011) are simply speculative with no experimental basis; these authors and the studies they cited in support of their beliefs did not test nor establish the cellular source(s) and fates of the lactate.In fact, when carefully assessed, activated neurons were shown to up-regulate glycolysis, not lactate import (Ashrafi et al., 2017;Ashrafi & Ryan, 2017;Diaz-Garcia et al., 2017;Diaz-Garcia & Yellen, 2019;Yellen, 2018).

| Impact of culture conditions on metabolic assays
An important, related point recognized by Leif Hertz is that tissue culture assays are not useful for evaluating glycolytic versus oxidative rates since the lactate dehydrogenase (LDH) reaction (pyruvate ↔ lactate) and the plasma membrane MCTs are equilibrative, concentration-driven reactions.Because the enormous volume of the extracellular medium of cultured cells greatly exceeds the intracellular volume, the intracellular lactate will be "pulled" into the medium by its dilution (Dienel & Hertz, 2001;Hertz & Dienel, 2005).
This phenomenon greatly exaggerates glycolytic fluxes in comparison to oxidative rates.As a result of these and other experimental constraints in cultured cells, the preferential use of ATP derived from glycolytic or oxidative pathways for various processes, such as the plasma membrane-bound Na + ,K + -ATPase, is an important, unresolved issue that requires more work.
Another critical issue relevant to metabolic assays in vitro is that when the assays are typically carried out, the cultured neurons have been in vitro for 7-10 days after culture in high, supra-diabetic levels of glucose (25-50 mM) in the media and they are probably much more immature than cultured astrocytes that are generally assayed at ~21-30 days in vitro.Neurons are commonly derived from embryonic day 15 (cerebral cortical cultures) or post-natal day 7 (cerebellar cultures) rodents.Pups are weaned at about post-natal day 21 prior to which time their nutrients are derived from mothers' milk and their brain cells metabolize more ketone bodies, lactate, and perhaps fatty acids compared with glucose which becomes the predominant brain fuel after weaning (Cremer, 1982;Nehlig & Pereira de Vasconcelos, 1993;Vannucci & Simpson, 2003).Large changes in development of enzymes involved in metabolism and excitatory/inhibitory neurotransmission occur between post-natal days 15-30 (e.g., Chowdhury et al., 2007;Land et al., 1977;Leong & Clark, 1984a, 1984b, 1984c).Therefore, the use of immature cells would provide information discordant with in vivo studies in adult subjects.For this reason, Hertz and colleagues treated their astrocyte cultures with dBcAMP to induce differentiation and maturation to more closely resemble astrocytes in mature brain (see Section 2.2), and they specified other culture conditions (e.g., medium contents, including serum type and concentration) that can influence astrocytic plasticity in culture (e.g., Hertz, Peng, & Lai, 1998;Juurlink & Hertz, 1985).
In relation to the above-mentioned ANLS, it should be pointed out that Hertz and colleagues were among the first to question the methodology which led to the ANLS proposal (Hertz, 2004a;Hertz, Swanson, et al., 1998).The original study (Pellerin & Magistretti, 1994) utilized an astrocyte culture preparation grown in 25 mM glucose (vs.1.5-3 mM in rat brain in vivo or ~20% of arterial plasma glucose concentration) that was not treated with dBcAMP.These cells do not represent mature, well-differentiated astrocytes and the metabolic assays used experimental conditions that could lead to a significant overestimation of the 2-deoxy[ 14 C]glucose (DG) phosphorylation (Hertz, Swanson, et al., 1998).Studies using a preparation of more welldifferentiated astrocytes and rigorous experimental conditions showed that Glu uptake in astrocytes is indeed driven by oxidative metabolism of Glu and other substrates, not by aerobic glycolysis (Peng et al., 2001).

| Fate of lactate in vivo versus in vitro: A wealth of evidence against lactate shuttling
Direct measurement of lactate transfer among brain cells in adult rat brain slices demonstrated that lactate shuttling among gap junctioncoupled astrocytes (Figure 1) was two-to fourfold faster and higher capacity than lactate transfer from an astrocyte to neuron over a wide range of 2-40 mM lactate (Gandhi et al., 2009).Of interest, metabolic modeling and simulation studies provide strong evidence for lactate trafficking in the opposite direction, an in vivo neuron-toastrocyte shuttle (DiNuzzo et al., 2010a;Mangia et al., 2009Mangia et al., , 2011)).
Subsequent, detailed analysis of the Pellerin and Magistretti (1994) report revealed that the stoichiometry between glucose consumption and lactate production by their cultured astrocytes during Glu exposure does not support the required predictions of the ANLS (Dienel, 2017).Indeed, it should have been evident upon publication of the ANLS hypothesis (Pellerin & Magistretti, 1994) that the model could not be valid in activated brain.Pellerin and Magistretti (1994) cited the Fox and Raichle (1986) report in which there was only a 5% increase in CMR O2 compared with a 50% rise in CMR glc during visual stimulation of awake humans.This small increase in respiration rate cannot support neuronal oxidation of nearly all of the lactate produced from the increased rate of glucose consumption.Even when the numbers from recent studies using advanced PET and fMRI technology are used, in which total glucose consumption increases by twofold (as opposed to 10-fold) relative to glucose oxidation, the predicted mechanistic stoichiometry of the ANLS model fails to match the data (for a more extensive comparison see Rothman, Dienel, et al., 2022).To summarize, if all glucose-derived lactate were oxidized during activation, CMR O2 would increase in parallel with CMR glc , and if glycogen plus glucose-derived lactate were oxidized, then CMR O2 would exceed CMR glc , which is never the case in brain in vivo (Dienel, 2019a;Dienel & Cruz, 2016).
Among the in vivo studies of brain energy metabolism that support the conclusions of the studies by Hertz et al. (e.g., Hertz, 2004a;Hertz, Swanson, et al., 1998;Peng et al., 2001) that the ANLS is not valid include the following.In vivo FDG-MRS studies demonstrated that neuronal synaptic endings (synaptosomes) phosphorylated FDG (i.e., glucose) in proportion to that in whole brain during activation (Patel et al., 2014), demonstrating that glycolysis was not preferentially and specifically up-regulated in astrocytes during activation, as required by the ANLS model.Also, parallel in vivo studies of brain activation with [ 14 C]glucose and [ 14 C]DG demonstrated that calculated CMR glc based on [ 14 C]DG phosphorylation rate and corrected for the appropriate value of the lumped constant (the value that converts DG phosphorylation rate to glucose utilization rate) was about twice that determined with [ 14 C]glucose (Ackermann & Lear, 1989;Adachi et al., 1995;Collins et al., 1987;Cruz et al., 1999Cruz et al., , 2007Cruz et al., , 2013;;Dienel et al., 2002;Dienel & Cruz, 2004;Lear & Ackermann, 1988, 1989).This means that metabolites of [ 14 C]glucose were not retained within the brain, with [ 14 C]lactate being the most mobile metabolite that is quickly released into blood (Adachi et al., 1995;Cruz et al., 1999).Furthermore, arteriovenous differences and the calculated oxygen-glucose index (OGI = CMR O2 /CMR glc ) determined in rodents during alerting-activating situations (Linde et al., 1999(Linde et al., , 2006;;Madsen et al., 1998Madsen et al., , 1999)), in human subjects during mental testing (Madsen et al., 1992(Madsen et al., , 1995)), and during human exercise to exhaustion revealed that the ratios of oxygen-to-carbohydrate utilization fell during activation, whereas if lactate were oxidized, the OGI and oxygen-carbohydrate index (OCI = CMR O2 /(CMR glc + CMR glycogen )) would be stable, or increase if glycogen utilization (that was not measured in these studies) were included in the calculations (e.g., Dalsgaard, 2006;Dalsgaard, Quistorff, et al., 2004;Dalsgaard & Secher, 2007;Dalsgaard, Volianitis, et al., 2004;Quistorff et al., 2008).
In addition, in vivo microdialysis studies in rat brain do not support the ANLS as they showed that equal amounts of lactate were oxidized in astrocytes and neurons, whereas oxidation of glucose was twice as high in neurons as in astrocytes (Zielke et al., 2009).Finally, comparison of fits of currently available in vivo metabolic rate data with predictions of the glucose sparing by glycogenolysis (GSG) model and the ANLS model clearly demonstrated that the ANLS model did not fit the data (Rothman, Dienel, et al., 2022).Thus, there is a wide range of in vivo studies under very different experimental and physiological systems involving activation of different brain regions that negate the notion that lactate shuttling coupled with its oxidation during activation is a viable model.

| Intracellular lactate shuttling via endoplasmic reticulum is not viable
A derivative of the ANLS was proposed by Müller et al. (2018) and highlighted by Pellerin (2018) to suggest intracellular trafficking of glucose in astrocytes with delivery of glucose or metabolites to neurons.In brief, this model states that glucose taken up by perivascular endfeet is phosphorylated by hexokinase, transported into the endoplasmic reticulum (ER) where it is dephosphorylated by glucose-6-phosphatase, followed by glucose diffusion through the ER to peri-synaptic processes where it exits the ER to cytosol, and metabolized to lactate, neurotransmitter precursors, or remains as glucose for shuttling to neurons.However, analysis of this model revealed that the rate-limiting step, transport of glucose-6-phosphate into the ER, is 550-3300 times slower than glucose consumption (Dienel, 2019c), so this model is not feasible.Furthermore, recent cutting-edge imaging studies clearly show that astrocytes do not act as a diffusion barrier for glucose (Eleftheriou et al., 2023), strongly supporting the conclusion that blood-borne glucose is readily available to neurons.A more likely function for astrocytic glucose-6-phosphatase is elimination of a toxic metabolite, anhydroglucitol-6-phosphate, derived from a glucose analog, anhydroglucitol, that is present in food, competes with glucose for transport into brain, is phosphorylated by hexokinase, and can inhibit hexokinase as a result of competition with ATP (Dienel, 2020).The critical function of removal of this toxic metabolite from neutrophils by the phosphatase was elegantly demonstrated in great detail by Veiga-da-Cunha et al. (2019).

| Summary and future directions
In strong support of Leif's initial objections to the ANLS, the overwhelming preponderance of evidence from in vivo and in vitro metabolic studies demonstrates that the ANLS cannot be a major flux because the oxygen consumed is too small to support the total amount of glucose and glycogen consumed during activation.
Instead, most lactate generated during brain activation is quickly released directly to cerebral venous blood or indirectly via the perivascular drainage systems (Dienel, 2017(Dienel, , 2019a(Dienel, , 2019b;;Dienel & Rothman, 2019;Rothman, Dienel, et al., 2022).The cellular basis of lactate production, routes of lactate efflux, and pathways of metabolite and fuel trafficking during activation in vivo remain important, unresolved issues that are necessary to fully understand activationinduced shifts in brain energetics and pathway fluxes in neurons and astrocytes.
Importantly, lactate efflux has recently been shown to be accurately predicted by the requirement for astroglial glycogenolysis to spare glucose metabolism during intense activation (Rothman, Dienel, et al., 2022).The available evidence suggests that the lactate generated from glycogen and glucose by astrocytes is quickly released from activated tissue, whereas the lactate retained in the brain during activation may, in fact, be derived from activated neurons.This conclusion is based on (i) the extensive lactate trafficking through astrocytic gap junctions with its rapid release to blood and perivascular fluid via their endfeet, potentially without mixing with neuronal pyruvate/lactate (Dienel, 2012a(Dienel, , 2012c)), (ii) astrocytic glycogenolysis does not reduce the specific activity of brain lactate during activation, indicating compartmentation of glycolytic metabolism of unlabeled glycogen and 14 C-labeled blood-borne glucose (Dienel & Rothman, 2019), and (iii) the oxygen-carbohydrate index (OCI = CMR O2 /(CMR glc + CMR glycogen )) falls to a lower value than the oxygen-glucose index (OGI = CMR O2 / CMR glc ) when glycogen is included in the calculation (2.80 vs. 4.95, respectively), demonstrating that oxygen is not used to metabolize glycogen, strongly supporting rapid release of glycogen-derived lactate from brain (Dienel & Rothman, 2019).Taken together, these in vivo studies demonstrate that astrocyte-neuron lactate shuttling is not a major flux and the ANLS model is not correct.Compartmentation of lactate production, trafficking, and glucose/glycogen metabolism, as well as glucose delivery, to activated cells are still important, poorly understood issues that require further study.

| Proportion of exogenous Glu oxidized versus converted to Gln:
A key controversy at the first ICBEM meeting in Carcassonne, France, 1993 Developmental aspects of Glu-metabolizing enzymes in cultures of astrocytes had been used as an indicator of the functional state of the cells and hence, as a means to validate the concept that these cells in culture would have a potential to reflect the functional capability of mature astrocytes in the brain (Hertz et al., 2017;Lange et al., 2012;Schousboe et al., 1977).This prompted studies of Glu and GABA metabolism to be performed with an emphasis on Glu since this amino acid, being present in brain at a high concentration (for references, see Erecinska & Silver, 1990), could be considered a substrate for oxidative metabolism.As discussed above with respect to Glu-evoked astrocyte-neuron lactate shuttling, many examples of treatment of cultured astrocytes with various concentrations of Glu either did not stimulate or reduce glycolysis, in contrast to other reports where glycolysis and lactate release were stimulated.These findings also suggested that oxidation of Glu taken up from the medium may contribute to the energetics of its Na + -dependent uptake and its ATP-dependent conversion to Gln (Figure 1).
One of the first studies on Glu metabolism in astrocytes by Yu, Schousboe, and Hertz et al. (1982) using 14 C-labeled Glu demonstrated considerable oxidation of Glu to 14 CO 2 in the presence of glucose in the medium, with similar findings reported by other laboratories.Farinelli and Nicklas (1992) later showed that most of the [ 14 C]Glu was converted to [ 14 C]Gln, along with some oxidation.In contrast, Sonnewald, Schousboe et al. (1993) reported that more [U- 13 C 5 ]Glu was oxidized than was converted to Gln.Later studies showed that Glu alone can support astrocyte metabolism when no glucose is present (Hertz & Hertz, 2003;McKenna, Tildon, et al., 1996) and that Glu oxidation by undifferentiated astrocytes is not reduced by the presence of other substrates (McKenna, 2012).
Discordant results in studies of the metabolic fate of Glu in astrocytes, that is, oxidation or conversion to Gln, were hotly debated in the first ICBEM conference in Carcassonne which was a satellite to ISN meeting in Montpelier, France.The controversy stemmed from 13 C-MRS results showing higher oxidation of 0.5 mM medium Glu compared with conversion to Gln (Sonnewald et al., 1993), contrasting data from several groups showing that most of the 0.05 mM medium [ 14 C]Glu was converted to [ 14 C]Gln (e.g., Farinelli & Nicklas, 1992).
Two of the present authors (M.C.M. and A.S.) note that part of the concern was the potential for differences in astrocytes cultured from rat or mouse brain, which would have been extremely problematic since various groups were using either species.The outcome of the discussion was considerable concern, with no consensus reached after much debate.During the meeting, Mary McKenna and Ursula Sonnewald planned a 13 C-MRS study to incubate astrocytes with different concentrations of Glu, with the goal of resolving the conflicting results by using assays with 0.05 to 0.5 mM exogenous Glu in the same astrocyte preparation.They found that the metabolic fate of Glu was concentration dependent, and the fraction oxidized progressively rose from 15.3% at 0.1 mM Glu to 42.7% at 0.5 mM, whereas that converted to Gln fell from 84.7% to 57.3% (McKenna, Sonnewald, et al., 1996).This study resolved the most debated issue at this ICBEM meeting, underscoring the importance of these highly interactive conferences to identify and discuss timely issues and facilitate collaborative studies to carry out critical experiments.

| Roles for AAT and GDH in oxidation of exogenous Glu: An on-going controversy
Glu oxidation for energy obviously requires exogenous Glu to gain access to the mitochondrial oxidative metabolic machinery involving the TCA cycle (Figure 1), and two major enzymatic reactions could be involved, Asp aminotransferase (AAT also known as glutamic oxaloacetic transaminase, GOT) and/or Glu dehydrogenase (GDH), both of which have high activity in astrocytes (Schousboe et al., 1977).Since pyridoxal phosphate-requiring enzymes, such as the aminotransferases, can be inhibited by the carbonyl-trapping agent aminooxyacetic acid (AOAA; for references, see McKenna et al., 2006), this drug was used to distinguish between the AAT and GDH metabolic pathways by Yu et al. (1982), who found that AOAA had almost no effect on the production of CO 2 from 50 μM [1-14 C]Glu.These results strongly indicated that GDH was the most important enzyme for mitochondrial oxidative Glu metabolism, with much lower rates of transaminase activity to produce labeled Asp from [U-14 C]Glu.This finding was subsequently challenged by a similar study by Farinelli and Nicklas (1992), who observed about 70% inhibition of 14 CO 2 production from oxidation of 50 μM [1-14 C]Glu by AOAA, with the majority of the [U-14 C]Glu being incorporated into Gln and some into Asp and other compounds.
However, subsequent studies of astrocytic Glu metabolism by others who used AOAA to inhibit the aminotransferases showed about 50% inhibition at low concentrations of Glu (≤0.1 mM) in the assay medium and relatively small inhibition (~20%) at 0.2-1 mM Glu, pointing toward an important role of GDH in metabolism of Glu (McKenna et al., 1993, 2006;McKenna, Tildon, et al., 1996).
This was consistent with the finding by Westergaard et al. (1996) that labeling of lactate from metabolism of [U- 13 C 5 ]Glu was decreased by only 20% in the presence of AOAA.In contrast, earlier studies of Glu metabolism in brain mitochondria by Haslam and Krebs (1963) and Balazs (1965) had concluded that initial transamination (AAT) was more important than oxidative deamination (GDH).However, the use of parapyruvate in the former study makes interpretation difficult, as this compound may inhibit AAT (discussed in McKenna et al., 2016).In a recent review, Leif Hertz also proposed that AAT would be likely to play an important role in Glu oxidation (Hertz, 2013), and, as discussed below, the review by Hertz and Rothman (2017) supported the importance of AAT in Glu metabolism.However, data from a key study (McKenna, Tildon, et al., 1996) showed that at closer to physiological levels of 0.01-0.05mM Glu, without Gln in the assay medium, AAT and These authors also suggested that it is likely that AAT and GDH may work together in brain, as in other tissues, and that astrocytes in particular may utilize AAT more when very low concentrations of Glu are present, on the order of 0.005 mM or less (Qin et al., 2013) and utilize GDH immediately after depolarization of neurons when the extracellular concentration of Glu is transiently quite high (0.2-1.0 mM), with the possibility of transient shifts in the relative amount of Glu metabolized by AAT and/or GDH (McKenna, 2013;McKenna et al., 2016).This possibility was discussed in Hertz and Rothman (2017) but within the context of an intense train of neuronal depolarizations, such as induced in sensory stimulation, as opposed to individual temporally wellseparated depolarization events.
Later, Hertz reevaluated his and other studies that established a primary role for GDH (Hertz & Rothman, 2017).In this study, it was pointed out that a key, subtle difference between these two studies is that Yu et al. grew and incubated their astrocytes in 2 mM Gln, whereas those of Farinelli and Nicklas had 0.5 mM Gln in the medium.Hertz attributed the more prominent role of GDH versus AAT in the Yu et al. study to the higher-medium-Gln levels (Hertz & Rothman, 2017), underscoring the potential influence of the exact composition of the culture medium on experimental outcome.Based on a meta-analysis, a relationship was found between the higher concentration of Gln (and Glu) in the medium and the lower effectiveness of AOAA inhibition on Glu metabolism (Hertz & Rothman, 2017).
In contrast to the conclusion that AAT predominates at low exogenous Glu concentrations, a major role for GDH in both Glu uptake and decarboxylation is evident when assayed at 0.5-1 μM extracellular Glu (Bauer et al., 2012;Whitelaw & Robinson, 2013).In a series of studies, Mike Robinson's group showed a close association of a high-affinity Na + -dependent Glu transporter with GDH and mitochondria in astrocytic processes close to synapses, suggesting that this relationship may facilitate delivery of exogenous Glu to mitochondrial GDH for oxidation (Bauer et al., 2012;Genda et al., 2011;Robinson & Jackson, 2016;Whitelaw & Robinson, 2013).Bauer et al. (2012) showed that inhibition of GDH impaired both uptake of 1 μM [1-14 C]Glu and its decarboxylation (corresponding to ~9% of the transported Glu within 15 min) in cerebral cortical astrocyte cultures.Whitelaw & Robinson (2013) extended this work with 0.5 μM Glu uptake assays in crude P2 membranes (P2 contains mitochondria, myelin, synaptosomes, and astroglial fragments) prepared from cerebral cortex and cerebellum of adult rats.Inhibition of GDH blocked Glu uptake into cerebral cortical P2 membranes mediated mainly by the GLT-1 (EAAT2) isoform, but not cerebellar P2 fractions mediated mainly by GLAST (EAAT1), suggesting preferential GDH involvement in Glu uptake in the forebrain versus cerebellum.They did not examine the effects of AAT inhibition or the extent of Glu conversion to Gln.
The relative importance of AAT and GDH in Glu oxidation is still unresolved (see Section 6.3 for further discussion and effects of GDH knockout) and it remains an important topic because Glu/Gln metabolism is an essential aspect of excitatory neurotransmission, amino acid metabolism, and cellular ammonia homeostasis, as well as in neurological disorders.The importance of the role of GDH is underscored by association of gain-of-function mutations with epilepsy (Stanley, 2011) and hyperexcitability (Raizen et al., 2005) and loss of activity with neurological disorders (Plaitakis et al., 1984).
Glu-evoked excitotoxicity is a causative factor in cell death after stroke, and overexpression of AAT reduced the lesion volume, whereas knockdown exacerbated the severity of brain damage (Khanna et al., 2015).

| Methodological limitations of metabolic studies of Glu metabolism
As described above, a major focus of Leif Hertz's work was in improving the methodology for in vitro studies of metabolism.Metabolic studies in cultured brain cells, subcellular fractions, brain slices, and living brain have greatly improved our understanding of the roles of Glu in brain metabolism, functions, and neurotransmission.It is widely recognized that radiolabeled substrates (e.g., 3 H, 14 C, 18 F) can be used in tracer amounts (i.e., they do not alter the molar concentrations of endogenous compounds) because of high sensitivity of scintillation counting, autoradiography, and PET assays, but identification of specific labeled carbons and labeled compounds is laborious.On the other hand, MRS assays with 13 C or other stable isotopes are less sensitive and require higher substrate/product levels but can provide much more information about labeled carbons and compounds.
In this regard, the use of high intravenous doses of [ 13 C]glucose to achieve and maintain constant arterial plasma glucose levels required for analysis of data using metabolic models and steady-state conditions (reviewed by Hyder & Rothman, 2017) does not disrupt glucose utilization.Glucose metabolism is regulated at the first irreversible step, hexokinase, and CMR glc determined with [ 14 C]DG is essentially constant over a wide range of arterial plasma glucose concentrations (7-31 mM) until brain glucose level falls sufficiently low so that hexokinase becomes unsaturated and CMR glc decreases (e.g., by 14% at plasma glucose of 2.4 mM vs. 6 mM) (Orzi et al., 1988;Schuier et al., 1990;Suda et al., 1990).In contrast, infusion or injection of large quantities of lactate or other substrates that are transported by equilibrative, concentration-driven reactions will cause flooding of the cells and can alter metabolic reactions in many pathways by various mechanisms.
A limitation of biochemical assays of Glu metabolism is the sensitivity of the assay methodology that secondarily influences the duration of the experimental interval required to detect labeled products.ies are 15, 750-3000, 1500, 6000-60 000, and 60 000 (nmol/mL) min.In brain, the resting extracellular Glu concentration is ~25 nM (Bauer et al., 2012), with brief (on the order of milliseconds) peak at 1-3 mM Glu concentration transients in the synaptic cleft (Bergles et al., 1999).To make a very rough comparison between in vivo Glu time-concentration integrals estimated from microelectrode assays during synaptic activity and the above in vitro biochemical assays of Glu metabolism, assume a peak of 3 mM Glu that lasts for 1 ms then decays to 0.5 mM Glu for 100 ms before cleared to give respective time-concentration integrals of 0.5 and 0.8 (nmol/mL)min for a total of 1.3 (nmol/mL)min.This is an order of magnitude below the shortest biochemical assay with the lowest Glu concentration that exposed the entire dorsal surface area of the cultured astrocyte to Glu, not just the astrocytic processes surrounding active synaptic clefts.
Thus, although in vitro models have provided great insight into the pathways and concentration dependencies of astroglial Glu metabolism, additional work is needed to further match in vivo conditions.Glu exposure in all of the above in vitro biochemical assays, the time integral of Glu concentration, greatly exceeds that as a result of glutamatergic neurotransmission in vivo, perhaps putting "stresses" on ion pumping and energetics, secondarily influencing the metabolic pathways involved in Glu disposal, as well as the experimental outcomes related to roles of AAT and GDH.Similar limitations are expected to apply to studies of the fates of GABA, Gln, and other compounds.Because Na + -Glu uptake creates an energy demand for the astrocytes, longer exposure and use of higher concentrations could be expected to result in channeling Glu into the oxidative pathways to produce ATP and dispose of the excess carbon taken up in excess of that converted to Gln that can be released from cells to the medium.The fates of exogenous and endogenous Glu in brain cells and mechanisms that control its metabolism are long-standing, complex issues that have been of considerable interest to neurochemists for at least 50 years (e.g., Benjamin & Quastel, 1972, 1974;Dennis et al., 1977;Dennis & Clark, 1977).We point out the limitations and concerns related to these studies to encourage investigators to develop novel methods to determine rapid changes in brain metabolism in ex vivo preparations under physiological conditions.New approaches are required to evaluate the metabolism of compounds involved in neurotransmission and as fuels for brain cells.
Another interpretive complication is the influence on in vitro maturation of astrocyte source (cerebral cortex, cerebellum, species, age, etc.), culture methods, medium, and duration.Studies of the developmental profiles of Glu-metabolizing enzymes in welldifferentiated astrocytes showed that AAT activity greatly exceeds (by about 17-fold) that of GDH for 3 weeks in culture and that GDH activity falls by about 60% between weeks 2 and 3, depending on the amounts of serum and dBcAMP in the medium (Hertz, Bock, & Schousboe, 1978;Schousboe et al., 1980) 2012) study were not stated, but cited methods used by that laboratory (Garlin et al., 1995;Robinson et al., 1993) suggest that the assays were carried out at 10-14 days in vitro using astrocytes grown in high glucose without use of dBcAMP.Thus, assay and culture conditions differ among the studies with apparently discordant results, and experimental resolution of the quantitative roles of AAT and GDH in astrocytic Glu metabolism requires parallel studies in the same culture preparations generated by the different methods cited above.

| Summary and future directions
To non-specialist readers the above discussions may seem to be technical discourses relevant only to experts in brain metabolism.However, a major take-home message is that important, but seemingly inconsequential differences among assays (substrate concentration, assay duration, culture medium composition, age, cellular maturation, etc.) can have a high but unrecognized impact on experimental outcome and apply to all types of investigations, not just metabolism.Despite this concern, it should be emphasized that important information about the regulation of metabolism has resulted from cell cultures studies.
A key underlying issue is the fate of the neurotransmitter Glu molecule, which is important for all neuroscientists to understand at a basic level.If transamination occurs, the ammonia is transferred from Glu to oxaloacetate to produce Asp that can subsequently donate the ammonia back to α-ketoglutarate for re-synthesis of transmitter Glu.If GDH predominates, ammonia is released, and an ammonia donor is required for re-synthesis of Glu.In both cases, the α-ketoglutarate produced by AAT or GDH can be partially or completely oxidized in the TCA cycle to produce ATP during excitatory neurotransmission.
A clear understanding of the metabolic fate of transmitter Glu is central to understanding the overall energetics of excitatory neurotransmission, the roles of astrocytes in processing the neurotransmitter, and ammonia homeostasis during brain activation, and this is a very important topic for future studies.

| Astrocytic Gln, GABA, and Asp oxidation
Since astrocytes express phosphate-activated glutaminase (Schousboe et al., 1979), they are able to metabolize the amino acid Gln to CO 2 and the rate of oxidation is only marginally lower than that of Glu (Yu & Hertz, 1983).It should be noted that the metabolism of Gln and Glu in astrocytes has been shown to be compartmentalized, that is, the metabolic pattern of Glu taken up from the medium is different from Glu generated intracellularly from Gln taken up from the medium (Schousboe et al., 1993).This conclusion is based on the finding that following incubation with radioactively labeled Gln, the product, that is, labeled Glu, had a higher specific radioactivity than the precursor, Gln.This can only occur if separate Gln pools exist and these pools have different turnover rates.Entry of endogenous Glu formed from Gln into the TCA cycle may be predominantly via AAT, in contrast to entry of exogenous Glu, which is predominantly via GDH (McKenna et al., 1993;McKenna, Tildon, et al., 1996;Westergaard et al., 1996), but the above apparently contradictory results need to be sorted out.
In addition to Glu, astrocytes have been shown to oxidatively metabolize Asp and GABA but the rate of CO 2 production, particularly from GABA, is lower than that generated from Glu oxidation (Rao & Murthy, 1992;Yu & Hertz, 1983).Notably, norepinephrine stimulates oxidation of Asp in cultured cortical astrocytes but not in cultured cortical or cerebellar neurons, linking noradrenergic neurotransmission to astrocytic TCA cycle activity (Subbarao & Hertz, 1990b), as well as to glycogenolysis (see below Section 5).
Asp oxidation requires that the carbon skeleton enters the TCA cycle subsequent to transamination to oxaloacetate (Schousboe et al., 2014).Therefore, it may be somewhat surprising that malate is oxidized to a much less extent than Asp (Hertz et al., 1992;Rao & Murthy, 1992;Yu & Hertz, 1983).However, this may be explained by the fact that Asp is transported into astrocytes much more effectively than malate (Drejer et al., 1983;Hertz et al., 1992), and that many metabolites modulate the activity of enzymes involved in malate metabolism (Malik et al., 1993;McKenna et al., 1995).Astrocytes are very flexible metabolically and can oxidize many other substrates for energy including 3-hydroxybutyrate, lactate, Gln, and fatty acids (Auestad et al., 1991;Edmond et al., 1987;McKenna, 2012;Panov et al., 2014).Indeed, they are poised to utilize or release these substrates depending on their metabolic requirements and the substrates in the extracellular milieu (McKenna, 2012).

| Cataplerosis: Pyruvate recycling and the complete oxidation of Glu
Complete oxidation/degradation of the carbon skeleton of Glu (Figure 1) mentioned above requires that Glu be metabolized in the TCA cycle to malate, which can leave the cycle and be metabolized by malic enzyme to pyruvate, which can subsequently be converted to acetyl CoA and re-enter the cycle for oxidation (complete pyruvate recycling) or be converted to lactate (partial recycling) (McKenna, 2013).This pyruvate recycling pathway which was first identified in brain by Cerdan (Cerdan et al., 1990;Künnecke et al., 1993) may have an important role in balancing formation of Glu, which involves anaplerosis (discussed below) with Glu degradation (cataplerosis) (Figure 1), as any lactate formed can be released and exit the brain (Olsen & Sonnewald, 2015;Sonnewald, 2014).Studies support the localization of the pyruvate recycling pathway in astrocytes as well as in cortical synaptosomes and cerebellar neurons (Amaral et al., 2011;Cerdan, 2017;Cerdan et al., 1990;Cruz et al., 1998;Haberg et al., 1998;Künnecke et al., 1993;McKenna et al., 2000;Olstad et al., 2007;Sonnewald et al., 1996).Neurons contain most of the Glu in brain (Ottersen & Storm-Mathisen, 1984;Storm-Mathisen et al., 1983), and on the other hand, astrocytes are the cells that synthesize Glu de novo and take up most of the neurotransmitter from the synaptic cleft.As shown quantitatively by McKenna (2013) in a paper in which Leif Hertz is acknowledged for his encouragement, oxidation of one Glu molecule leads to net production of approximately 23-26 ATP molecules (also see similar caculations in Hertz et al., 2007 andDienel, 2013), which can be used to help support astroglial energy demands primarily for associated K + uptake, as well as neurotransmitter uptake and Gln synthesis (DiNuzzo et al., 2017;Rothman, Dienel, et al., 2022).However, it is important to take into account the temporal nature of this process as pointed out by Hertz and Rothman (2017).In vivo, the ATP initially generated by partial or total Glu oxidation is ultimately balanced by the ATP required for Glu re-synthesis.However, excess ATP is made in the re-synthesis process, primarily as a result of glucose oxidation, which can be used to support other processes (for a calculation of the stoichiometry of both the oxidation and re-synthesis processes, see Rothman, Dienel, et al., 2022).Therefore, the initial large ATP generation from Glu oxidation likely plays an important role in supporting the high energetic demands on astroglia caused by neuronal K + release associated with excitatory neurotransmission.

| Anaplerosis in astrocytes via pyruvate carboxylase
Based on the classical studies that found high rates of in vivo radiolabeling of Glu from [ 14 C]glucose (e.g., Cremer, 1964;Gaitonde et al., 1965;O'Neal & Koeppe, 1966;Van den Berg et al., 1969), it was believed that neurons had a very rapid rate of Glu synthesis.
Although this interpretation was incorrect, owing to the rapid exchange by cytosolic and mitochondrial AAT causing labeling by exchange rather than net synthesis, it led to investigation of what is the source of net neuronal Glu synthesis (Schousboe, 2012).Since the carbon skeleton of Glu can only originate from α-ketoglutarate, such a net synthesis obviously leads to a depletion of TCA cycle intermediates.Hence, a mechanism must exist by which a de novo synthesis (anaplerosis) of TCA cycle intermediates can take place.The enzymatic reaction involved in this process in the brain is catalyzed by pyruvate carboxylase (PC), the primary enzyme responsible for carbon dioxide fixation in the brain (Patel, 1974) (Figure 1).In the early 1980s, Leif Hertz and co-workers set out to investigate the activity of PC in cultured neurons and astrocytes and found that only astrocytes express this enzyme, the activity of which was found to be below the detection limit of the assay in both cultured cortical and cerebellar neurons (Yu et al., 1983).This finding was confirmed by immunocytochemical labeling (Cesar & Hamprecht, 1995;Shank et al., 1985).Thus, it is now generally accepted that de novo, net synthesis of Glu and, more importantly, Gln from glucose is an astrocytic feature since both PC and Gln synthetase (GS) are highly, but not exclusively, enriched in astrocytes (Martinez-Hernandez et al., 1977;Norenberg & Martinez-Hernandez, 1979;Yu et al., 1983).There is evidence from subsequent studies that both PC (Amaral et al., 2013(Amaral et al., , 2016;;Murin et al., 2009) and GS (Bernstein et al., 2014

| Neuronal conversion of Gln to transmitter Glu
While discussing the role of newly synthesized Gln as precursor for synthesis of neurotransmitter Glu in neurons (Figure 1), it should be mentioned that, based on experiments using phenylsuccinate and AOAA to inhibit different entities of the malate-Asp shuttle (MAS; see, McKenna et al., 2006), a model explaining the involvement of the neuronal MAS for conversion of astrocyte-derived Gln to neurotransmitter Glu was proposed by Hertz and coworkers (Palaiologos et al., 1988).Most of the experimental work had been performed in Copenhagen and during the yearly 2-week visit by me (AS) in the laboratory of Leif in Saskatoon during January, Leif and I sat down analyzing the results.We realized that a schematic model had to be made to explain the results and obviously this model was based on the MAS.Our original sketchy drawings were refined by a local artist and this refined model was submitted to Journal of Neurochemistry and subsequently published (Palaiologos et al., 1988).According to this model (Figure 3a), called the pseudo-MAS, Gln deamidated by the action of phosphate-activated glutaminase (PAG) would generate Glu that would be released in the mitochondrial matrix.This mechanism was controversial at the time since PAG had been associated with the outer part of the inner mitochondrial membrane, and Glu was thought to be directly released to the cytosol (Kvamme et al., 2001;Roberg et al., 1995).However, subsequent experiments using [ 13 C] Gln and histidine to inhibit its transport through the inner mitochondrial membrane demonstrated that Glu formed in the PAG-catalyzed reaction did indeed get access to the mitochondrial matrix (Bak et al., 2008;Ziemińska et al., 2004).The Glu generated by this mechanism in the mitochondrial matrix would be transaminated by AAT to form Asp and α-ketoglutarate, both of which would be transported out of the mitochondria by the Glu-Asp exchanger and the dicarboxylate carrier, respectively (Palaiologos et al., 1988).In the cytosol, Asp and α-ketoglutarate would undergo a transamination catalyzed by cytosolic AAT forming oxaloacetate (OAA) and Glu (Figure 3a).The latter would be available for incorporation into synaptic vesicles and OAA would be reduced to malate by cytosolic malate dehydrogenase and would subsequently be transported into the mitochondria by the dicarboxylate carrier (Palaiologos et al., 1988).It was subsequently shown by Kihara and Kubo (1989) and Chen (2017) revisited the importance of the neuronal MAS in generation of neurotransmitter Glu from extracellular Gln (Figure 3a) and its quantitative relationship with Glu-Gln cycle rates (Figure 3b) but they did not include data related to PAG localization and Gln transport across the inner membrane into the matrix.Limitations of the pseudo-MAS model (Figure 3a) and alternative models for Gln conversion to neurotransmitter Glu that satisfy the 1:1 mechanistic stoichiometry between neurotransmitter cycling and glucose oxidation rates, and maintain carbon, nitrogen, proton, and redox balance across the neuronal mitochondrial and cell membranes are described by Rothman, Behar, and Dienel (2022).More work is required to understand the biochemical basis for the 1:1 stoichiometry between rates of neuronal oxidation of glucose and excitatory glutamatergic neurotransmission and the exact mechanisms for conversion of Gln to neurotransmitter Glu (Rothman, Behar, & Dienel, 2022;Sibson, Dhankhar, et al., 1998;Yu et al., 2018).

| Summary and future directions
Studies in cultures of astrocytes and neurons by Leif Hertz and many other neuroscientists have made critically important contributions to understanding metabolism of Glu, Gln, GABA, and related compounds.Due, in part, to technical aspects of culture procedures and assays, these studies have also generated controversial topics that have persisted for decades and require further work.Among these topics are fuels for activation of astrocytes and neurons; differential roles of glucose, glycogen, lactate, and minor substrates in astrocytes and neurons; specific functions of AAT and GDH in neurotransmitter cycling and oxidative metabolism; and mechanisms for conversion of Gln to neurotransmitter Glu.

| Influence of K + on metabolism
Many studies have shown that increases in extracellular K + concentration stimulate specific metabolic enzymes and pathway fluxes.
For example, Outlaw Jr. and Lowry (1979) showed that pyruvate kinase required K + and that the in vitro activity could be used as a quantitative assay to determine K + concentration.K + also stimulates the activity of the astrocyte-enriched enzyme pyruvate carboxylase in a concentration-dependent manner, enhancing CO 2 fixation by about 50% when [K + ] is increased from 2 to 10 mM, and by twofold at 25 mM (Kaufman & Driscoll, 1992, 1993).Importantly, K + uptake from extracellular fluid during activation triggers astrocytic glycogenolysis in a concentration-dependent manner (Hof et al., 1988;Rothman, Dienel, et al., 2022).In astrocytes, these three reactions can act in concert to increase pyruvate formation and carboxylation to provide precursors for the TCA cycle and for neurotransmitter synthesis (Figure 1).
Early studies in Leif Hertz' career demonstrated that high levels of K + enhanced respiration in cultured astrocytes and acute brain slices, indicating a primary metabolic effect on respiration in astrocytes, not neurons, in living brain tissue (Hertz et al., 1973;Hertz & Kjeldsen, 1985).Peng, Hertz, and colleagues (Peng et al., 1994;Peng & Hertz, 1993) subsequently reported that increased extracellular [K + ] stimulated oxidative metabolism of glucose in glutamatergic neuronal cultures and astrocytic cultures and enhanced glucose utilization (measured as [ 14 C]DG phosphorylation) in cultured astrocytes.This finding was not replicated by Takahashi et al. (1995), a report that initiated considerable discussion in the field because Takahashi et al. reported that increased extracellular [K + ] did not stimulate DG phosphorylation, whereas exogenous Glu did.These findings contrast the Hertz-Peng data (cited above) where glucose utilization was stimulated by exogenous K + but not Glu.However, the K + effects were confirmed in a subsequent pharmacological and developmental study in the Peng-Hertz lab (Peng et al., 1996).DG phosphorylation rate at low (5.4 mM) K + was inhibited by about 50% by ouabain, indicating a substantial role for Na + ,K + -ATPase (Figure 1) in astrocytic glucose consumption, and increasing [K + ] to 12 mM stimulated DG phosphorylation in mature, well-differentiated astrocytes, but not in immature cells; this effect developed after long time in culture.Takahashi and colleagues (Abe et al., 2006) subsequently did observe increased astrocytic DG phosphorylation with increased [K + ] but did not identify the cause(s) for the previously discrepant results that could conceivably have arisen from culture differences and maturation.

| Modeling the energetics of K + pumping
The above series of studies were very important because they linked astrocytic glucose utilization to ATP demands for ion pumping after exposure to K + , a conclusion strongly supported by the flux-balance analysis by DiNuzzo et al. (2017).In contrast, uptake of Na + plus Glu did not stimulate DG phosphorylation in the Hertz astrocyte preparation, presumably because oxidation of Glu (see Sections 3.2 and 3.3) and metabolism of glycogen to support energetics of K + pumping (see Section 5.2), not glycolytic metabolism of extracellular or blood-borne glucose, supplied the ATP required for Na + extrusion and Gln synthesis after Na + -Glu uptake into the astrocyte.In fact, stimulation by Glu is not a robust phenotype of cultured astrocytes, and many laboratories have reported either no effect of Glu or a decrease in glucose utilization (Dienel & Cruz, 2004).
The insightful studies and reviews by DiNuzzo, Mangia, and colleagues (DiNuzzo, 2019;DiNuzzo et al., 2010bDiNuzzo et al., , 2011DiNuzzo et al., , 2012DiNuzzo et al., , 2013) ) linked need for glycogenolysis to support astrocytic metabolism during K + uptake and to spare blood-borne glucose for neuronal consumption (see Section 5).In fact, the 2012 report by DiNuzzo et al. ( 2012) was the stimulus for further studies by Hertz, Peng, and colleagues to assess the role of K + in glycogenolysis (Xu et al., 2013).
Magistretti's group (Hof et al., 1988) previously showed that Ca 2+dependent glycogen mobilization in brain slices increased in direct proportion to extracellular [K + ] over the physiological range, but did not determine the signaling mechanism.Xu et al. (2013) elucidated signaling pathways involved in the requirement for glycogenolysis in uptake of K + , including L-channel-mediated Ca 2+ uptake after exposure to 10 mM K + , ERK1/2 phosphorylation, Na + ,K + ,2Cl − (NKCC1) cotransporter activity, and other processes.The complexity of this process indicates that consumption of glycogen to help maintain K + homeostasis during brain activation is governed by many processes, not only by allosteric regulation by energy-related metabolites or neurotransmitters, for example, AMP and norepinephrine.

| Summary and future directions
Leif Hertz's major contributions to the metabolic influence of K + on cultured astrocytes include its stimulation of both glucose utilization and glycogenolysis and elucidation of signaling pathways through which K + exerts its influence on astrocytic metabolism.He also had important contributions to regulation of astrocytic glycogen by neurotransmitters and neuromodulators, as well as roles of glycogen in gliotransmitter release.Details of these mechanisms are important topics for future experimentation in mature, differentiated astrocytes, and in brain of developing and adult subjects.

| Early studies demonstrating the presence and lability of glycogen in brain
Brain glycogen has a very long history, but roadblocks to continuous progress in understanding its roles in brain function include technical/analytical limitations that include the high lability of glycogen to physiological conditions and sampling/extraction procedures and lack of methods to easily measure glycogen responses to activation in living brain.Up-to-date reviews of the history and major aspects of brain glycogen metabolism are in recent mini-reviews in the Journal of Biological Chemistry (Bak et al., 2018;Carlson et al., 2018;Gentry et al., 2018;Nadeau et al., 2018;Prats et al., 2018) and in the compendium entitled, "Brain glycogen metabolism" (DiNuzzo & Schousboe, 2019) to which interested readers are referred.
Early quantitative studies of glycogen were carried out by Stanley Kerr in the 1930s.He established the requirement for rapid inactivation of brain enzymes to preserve glycogen levels, carefully characterized brain glycogen, and showed that it is present in relatively high amounts (Kerr, 1936(Kerr, , 1938)).Unfortunately, many researchers today still do not appreciate the rapid activation of glycogen phosphorylase during anoxia or ischemia that accompanies tissue harvest (Breckenridge & Norman, 1962, 1965;Kerr & Ghantus, 1937) and the absolute requirement for immediate inactivation of enzymes that degrade glycogen in vivo and in vitro.In fact, phosphorylase activation occurs within seconds in vivo (Breckenridge & Norman, 1965;Lust et al., 1973), and glycogen levels are not valid unless special precautions are taken to inactivate enzymes, for example, in situ freezing (Kerr & Ghantus, 1937;Pontén et al., 1973), microwave fixation (Medina et al., 1975), or freeze blowing (Veech et al., 1973), and to minimize sensory stimulation and any stress that could activate norepinephrine release from the locus coeruleus throughout the brain (Cruz & Dienel, 2002;Dienel & Cruz, 2016).Post-mortem consumption of glycogen is not the only consequence of improper brain tissue harvest.For example, within 5 s after decapitation, 65% of the ATP is consumed, AMP, inorganic phosphate, and ammonia levels rise 16-, 3.4-, and 1.6-fold, respectively, followed by other progressive changes in metabolite levels including metabolism of glucose and glycogen with lactate accumulation (Lowry, Passonneau, et al., 1964;Ogushi et al., 1990).The above studies validated rapid enzyme inactivation methods for brain tissue, with caveats raised by Lust et al. (1973).

| Glycogenolysis is activated during brain activity
Since the early in vivo studies of glycogen level, labeling, and turnover in brain, the conceptual role of brain glycogen has transitioned from that of a static energy reserve to an active participant in many critical brain functions, ranging from ion homeostasis to memory consolidation.Swanson et al. (1992) were the first to demonstrate localized consumption of glycogen labeled in vivo with [ 14 C]glucose only in brain structures activated by whisker stimulation, and Swanson (1992) suggested that glycogen may spare glucose during brain activation.It is long known that most brain glycogen is localized in astrocytes (Figure 1) (e.g., Shimizu & Kumamoto, 1952), but small amounts are present in neurons (Saez et al., 2014), and both total (Duran et al., 2013) and neuronal (Duran et al., 2019) glycogen have important roles in long-term potentiation and memory consolidation.
Studies in cultured astrocytes have been essential to establishing the relationships between glycogenolysis and neurotransmitters and neuromodulators.However, there appear to be far fewer quantitative studies to establish the precise methods required to fully preserve glycogen in cultured astrocytes.A cautionary note is issued because muscle phosphorylase activity is readily measurable at 0°C (Lowry, Schulz, & Passonneau, 1964), and Lowry and Passonneau (1972) noted that at 0°C some enzymes have 20% of the activity at 38°C (Lowry & Passonneau, 1972, p. 112), and that enzyme action causes differential rates of loss of various metabolites within minutes at −5 and −10°C (Lowry & Passonneau, 1972, pp. 122 and 224).Incomplete inactivation of enzymes will also affect levels of other labile metabolites besides glycogen, for example, glucose, lactate, and phosphocreatine.In addition, the wash procedure will remove intracellular metabolites that are transported by equilibrative carriers (e.g., glucose and lactate) unless transport inhibitors are included in the wash solution (Dienel et al., 2017).To sum up, unknown amounts of glycogen and other compounds can be metabolized and/or washed out of the cells during routine cold-wash procedures prior to cell harvest and extraction.This limitation notwithstanding, studies of glycogen metabolism in cultured astrocytes and brain slices have made major advances in understanding neuron-astrocyte interactions and responses of astrocytes to neuronal signaling.

| Glycogenolysis is activated by many signaling compounds
Many laboratories contributed to identification of compounds that influence glycogen metabolism, for example, β-adrenergic agonists, norepinephrine, histamine, serotonin, amphetamine-like compounds, vasoactive intestinal compound, adenosine, K + , Ca 2+ , and receptor subtype agonists and antagonists (e.g., Hof et al., 1988;Magistretti et al., 1981Magistretti et al., , 1986;;Quach et al., 1978Quach et al., , 1980Quach et al., , 1981Quach et al., , 1982Quach et al., , 1988;;Subbarao et al., 1995;Subbarao & Hertz, 1990a;Zhang et al., 1993).These findings clearly linked astrocytic glycogen metabolism to neurotransmission.Leif Hertz's more than 40 papers related to glycogen include the role of glycogenolysis in K + clearance and homeostasis, the requirement for glycogenolysis in gliotransmitter ATP release, and the obligatory role of glycogenolysis in specific stages of memory consolidation in the 1-day-old chick.Subbarao et al. (1995) investigated the basis for large K + -evoked stimulation in astrocytic glycogenolysis that they previously observed (Subbarao & Hertz, 1990a) compared with a marginal, if any, K + stimulation reported by Magistretti et al. (1983).The Subbarao-Hertz studies demonstrated that the effect of K + was robust only in cultures treated with dBcAMP to trigger biochemical differentiation that included induction of expression of voltage-dependent L-channels for calcium and its uptake that was essential for glycogenolysis.The Magistretti study did not use dB-cAMP, once again emphasizing the critical importance for all studies of detailed characterization of the exact culture conditions and maturation in vitro.Subbarao et al. (1995) also calculated initial rates of glycogenolysis when stimulated by 10 mM K + and found that it was about twice the rate of glycolysis, indicating that glycogen mobilization is fast source of glycolytic ATP.This conclusion is consistent with in vivo comparisons of these rates during sensory stimulation: glycogenolysis is about 60% of CMR glc by all cells but if this rate is adjusted for an assumed maximal astrocytic volume fraction of 25% (Hertz et al., 2007), CMR glycogen is 2.4-fold higher than CMR glc (Dienel & Rothman, 2019).In our subsequent meta-analysis of the impact of correction of astrocytic rates for lower (i.e., 6%-15%) regional volume fractions, glucose oxidation rates were 4-to 10-fold higher than neuronal rates, and volume-adjusted glycogen concentrations and utilization rates were similar to or higher than in exercising muscle (Dienel & Rothman, 2020).Importantly, the ATP yield per glucosyl unit from glycogen is 3 ATP versus 2 ATP from blood-borne glucose because the hexokinase step is bypassed during glycogen degradation.These calculations indicate that astrocytes have much higher energy demands than generally recognized, as exemplified by ion pumping requires four times more ATP than Glu-Gln cycling that has been emphasized in the ANLS model (DiNuzzo et al., 2017) even during the resting-awake state, and even more so during activation (Rothman, Dienel, et al., 2022).
As discussed above, Hertz, Peng, and colleagues made substantial contributions to understanding the signaling pathways involved in K + -mediated increases in glycogenolysis (Xu et al., 2013), and this group also reported that glycogenolysis is required for release of the gliotransmitter ATP (Xu, Song, Bai, Zhou, et al., 2014).In related studies by others, glycogenolysis was shown to fuel the ATPase that pumps Ca 2+ into the astrocytic endoplasmic reticulum (Müller et al., 2014).These studies indicate that glycogen has unanticipated, critically important functions in astrocytes, including sparing bloodborne glucose for neuronal consumption (DiNuzzo et al., 2010b).

| Glycogenolysis supports higher brain functions
A series of studies on mechanisms of consolidation of adverse-taste memory in the 1-day-old chick was carried out by Marie Gibbs and colleagues in collaboration with Leif Hertz.Their report in 1994 was the first to reveal that inhibition of glycogenolysis impaired memory (O'Dowd et al., 1994).Subsequent studies provided strong circumstantial evidence that carbon derived from glycogen was required to synthesize Glu during memory consolidation (Gibbs et al., 2007).
Detailed analyses of the sequential events involved in the consolidation process identified specific intervals during which glycogen was a key substrate for learning (reviewed by Chen et al., 2016;Hertz et al., 2013;Hertz & Gibbs, 2009).Studies by other laboratories have also demonstrated the requirement for glycogenolysis in foot-shock avoidance learning (Suzuki et al., 2011), spatial working memory (Newman et al., 2011), and drug of abuse-paired memories (Zhang et al., 2016).These investigators concluded that glycogen-derived lactate is shuttled to neurons for oxidation to fulfill energy demands of memory consolidation.However, none of these studies identified the cellular or pathway source(s) of the rise in extracellular lactate concentration after the triggering event, nor did they measure cell-cell lactate transport or lactate oxidation.These lactate shuttle conclusions are based on unproven assumptions with no supporting data.In fact, comparison of in vivo consumption of oxygen with that of glucose plus glycogen during sensory stimulation shows that respiration is too low to support oxidation of the amount of carbohydrate consumed.In addition, the amount of lactate retained in tissue was much less than the equivalents of carbohydrate consumed in excess of oxygen, indicating rapid release of lactate, not shuttling coupled with oxidation (Dienel, 2019a(Dienel, , 2019b;;Dienel & Rothman, 2019).

| Summary and future directions
Leif Hertz's studies of glycogen provided details of the complex signaling mechanisms initiated by uptake K + to stimulate glycogenolysis that was a higher flux than glycolytic metabolism of glucose.He also linked glycogen mobilization as a requirement for release of a gliotransmitter, and was instrumental in dissection of the temporal stages of aversion memory formation in the 1-day-old chick that required glycogen, in part, for synthesis of transmitter Glu.Talks by Douglas Rothman, Jordi Duran, and Matthew Gentry at the 14th ICBEM in 2022 reported strong evidence for glucose sparing for neurons by astrocytic glycogenolysis during activation, differential roles for glycogen in neurons and astrocytes in memory consolidation and epilepsy, and that glucosamine is a component of glycogen used for synthesis of glycoproteins.These topics are important directions for future work in roles of glycogen in brain.In addition, development of in vivo methods to measure glycogen concentrations in serial assays in the same subject is critically important for studies of physiological and cognitive functions of brain glycogen.

| Roles of astrocytes in neurotransmission
Although the majority of Leif Hertz's experimental studies were in cell culture preparations, he strongly believed that in vitro systems did not intrinsically reconstitute in vivo mechanisms because of the strong interactions between neurons, astroglia, and the neurovascular system (Hertz, 2004b).As a consequence, by the mid-1990s, despite extensive progress on in vitro models and potential regulatory mechanisms, there was little progress in understanding the quantitative contributions of astroglial Glu metabolism to maintaining the neuronal GABA and Glu neurotransmitter pools (Figure 1) relative to the uncertain status in the late 1970s (Shank & Aprison, 1979).
Therefore, when the first in vivo 13 C MRS measurements of neuronal and astroglial Glu metabolism became available in the late 1990s, Hertz embraced them and during the latter part of his career he spent a substantial effort in evaluating mechanisms and relative fluxes derived from in vitro studies compared to the in vivo results from stable isotope methods.These efforts included formal and informal collaborations with scientists who worked primarily with in vivo systems (including two of the authors of this article, GD and DLR).In this section, we briefly review Leif Hertz's contributions to in vivo studies of brain energy metabolism and neurotransmitter cycles.

| A watershed at Waterville Valley, New Hampshire
The importance of astroglia metabolism for brain function is now widely accepted.However, when the first measurements obtained in vivo of astroglial metabolic fluxes were presented in the late 1990s, the significance of these pathways was largely neglected in the broader field of neuroscience.The historical bases for this neglect have not to date been reviewed, but Leif Hertz was acutely aware of the uphill battle the field of astroglial metabolism, and brain metabolism in general, faced.One of the authors (DLR) speculates that among the critical factors leading to this neglect were the near cessation of in vivo studies of cerebral metabolic pathways by the late 1970s and the uncertain status of the in vivo contribution of astroglial Glu and GABA metabolism at the time (Shank & Aprison, 1979), early PET and later fMRI findings that were interpreted as neuronal signaling only requiring a minimal amount of energy of ATP from non-oxidative glycolysis (Fox et al., 1988), and microscopy studies that found "neurotransmitter" Glu was stored in small vesicles (e.g., Ottersen & Storm-Mathisen, 1985;Storm-Mathisen et al., 1983).
The latter studies, and findings of low in vitro labeling, were interpreted by other groups as showing that there could not be a metabolically significant Glu/GABA-Gln cycle flux.(For a contemporary explanation of this view, see Erecinska and Silver (1990).)These beliefs became codified in the terms "neurotransmitter" and "metabolic" Glu and GABA pools with the connotation that neurotransmitter fluxes were only a very minor part of Glu and GABA metabolism.
(We note here that the flaw in the reasoning that small pool = low flux was already known based on the pathways in the brain with the highest metabolic flux, glycolysis, and the TCA cycle, having several extremely low-concentration intermediates that also show very low total levels of label incorporation.) A watershed moment for the study of functional astroglial metabolism was the 3rd ICBEM entitled "Energy Metabolism in Brain Function and Neuroprotection" in Waterville Valley, N.H., in 1997, for which one of the co-authors (MCM) was the primary organizer and co-editor of the conference special issue in Developmental Neuroscience (McKenna & Edmond, 1998).This was the first meeting in which in vivo 13 C MRS studies of in vivo astroglial metabolism and neurotransmitter cycling (including in human brain) were presented at a meeting with a large contingent of neurochemists studying brain energy metabolism at the in vitro and isolated enzyme level.In addition, studies in which brain metabolites were labeled by 13 C isotopes in vivo and then analyzed in extracts of fast-frozen brain tissue were presented.A key presentation at the meeting, by Robert Shulman of the Yale group, was the results of the first in vivo 13 C MRS studies of the relationship between the Glu/GABA-Gln cycle and cerebral cortex energy metabolism (Sibson, Dhankhar, et al., 1998;Sibson, Shen, et al., 1998).The study, which used variable anesthesia and pharmacological stimulation to modulate brain electrical activity in the rat cerebral cortex, found a close to 1:1 relationship between cerebral cortex glucose oxidation and the Glu/GABA-Gln cycle flux (Figure 3b).Or, in other words, the astroglial metabolic fluxes that converted neurotransmitter Glu and GABA to Gln (Figure 3a) were quantitatively almost as large as the brain oxidative glucose metabolism rate (Figure 3b)-far from almost negligible scavenging pathways (Sibson, Dhankhar, et al., 1998).
Even among neurochemists at the meeting, there was no consensus about the flux values of the pathways of astroglial neurotransmitter Glu and GABA metabolism, with many holding to the view that they were minor scavenging pathways.Therefore, the reports of in vivo high flux rates of the Glu/GABA-Gln cycle and other astroglial metabolic pathways presented at the meeting were largely unexpected.An eminent neurochemist at the meeting told one of the authors (DLR) that he would rather retire than see the field accept that there could be any significant contribution of astroglia to support the energetics and neurotransmitter requirements of normal brain signaling (fortunately he did not retire and continued to make important contributions to the field).Leif Hertz had already weathered many similar criticisms for decades.He realized that the only way to definitively address them was to have in vivo measurements of astroglial pathways that would allow the results of in vitro studies to be scaled up and directly compared.Having already worked on this approach, he was one of the few neurochemists at the meeting not surprised by the magnitude of the reported fluxes.
Furthermore, he saw the ability of in vivo 13 C MRS and MRS studies to distinguish neuronal and astroglial metabolic pathways as a direct link from understanding at the level of in vitro systems to the functioning intact brain (Hertz, 2004b).
Although in retrospect, the Sibson, Dhankhar, et al. (1998) and Sibson, Shen, et al. (1998) study clearly showed the importance of astroglial Glu metabolism for in vivo brain function, at the meeting it was poorly received by many and ignited several sometimes heated debates.Part of the controversy was over the magnitude of the reported fluxes based on issues of metabolic modeling, which have largely been worked out and the current consensus values are in agreement with the original finding as well as measurements of the astroglial glucose oxidation flux by Rolf Gruetter's group presented at the meeting (Gruetter et al., 1998(Gruetter et al., , 2001) (see Rothman, Dienel, et al., 2022 for an updated meta-analysis of all in vivo measurements).However, the major debate among neurochemists at the meeting was over the mechanistic interpretation of the findings.The mechanistic stoichiometry (for discussion of the definition of this term, see Endnote 2 and Supplementary Information in Rothman, Behar, & Dienel, 2022) of the model, which incorporates the ANLS and the finding in cell culture by Pellerin and Magistretti (1994) that Glu transport in astroglia cell cultures (see Section 3.2 for a critical discussion of these findings) depends on glycolytic ATP, matched the experimental findings.However, the ANLS model does not include astroglial oxidative metabolism or Glu metabolic pathways other than Gln synthesis, which Hertz and many others had studied in cell culture.
As shown in Figure 2b,c, Leif Hertz was actively involved in the ensuing debates at meeting sessions and many of the informal discussions in between.His contributions at the meeting, and afterward, played an important role in clarifying the key scientific questions being debated on how to integrate in vivo and in vitro results to derive a mechanistic understanding of how astroglia metabolically support brain function.Furthermore, for the remainder of his career, he made important theoretical and experimental contributions to all of these areas (e.g., Dienel & Hertz, 2001;Hertz, 2004bHertz, , 2013;;Hertz et al., 2007;Hertz & Dienel, 2002;Hertz & Robinson, 1999;Hertz & Rodrigues, 2014;Hertz & Rothman, 2016;Hertz & Zielke, 2004).The following sections are organized around Leif Hertz's contributions to addressing the major questions (and controversies) that arose at the Waterville Valley ICBEM meeting.Many of the disagreements that took place at the Waterville Valley meeting, and long after, were as a result of neither the neurochemistry groups, who mainly worked in cell culture, nor in vivo groups, fully understanding what the other was measuring.Hertz played a major role, informally and formally, in his reviews of the field, in reconciling these differences in order to focus both fields on answering the actual key mechanistic questions about functional astroglial metabolism.The largest misunderstanding was over the absence of anaplerosis in the model in Sibson, Dhankhar, et al. (1998), which was interpreted among neurochemists at the meeting that the anaplerosis flux and related Glu catabolic fluxes were considered negligible.In fact, the Yale group had spent extensive effort measuring and modeling anaplerosis including studies presented at the meeting (Shen et al., 1998;Sibson, Shen, et al., 1998), as had Rolf Gruetter's group (Gruetter et al., 1998(Gruetter et al., , 2001;;Öz et al., 2004) and others, with the reported measurements being similar to presently accepted values (Lanz et al., 2013(Lanz et al., , 2014;;Rothman, Dienel, et al., 2022).However, most of the workers in the in vivo field were not familiar with neurotransmitter Glu oxidation, and therefore assumed, based on in vivo single-pass brain ammonia uptake and whole brain arteriovenous (AV) difference studies of brain ammonia balance and hyperammonemia (e.g., Cooper et al., 1981Cooper et al., , 1985;;Cooper & Lai, 1987;Cooper & Plum, 1987;Tsukada et al., 1998) as well as in vivo MRS studies (Shen et al., 1998), that even during normoammonemia anaplerosis was used primarily for removal of ammonia in the brain as Gln.Conversely, the role of anaplerosis in whole-brain nitrogen balance was largely neglected by neurochemists who worked on in vitro systems.This divide in assumptions of the function of anaplerosis led some investigators in both camps to mistakenly believe that their fields were being criticized regarding their measurements of anaplerosis.
Leif Hertz, while always passionate about his work, was not concerned about the in vivo work threatening his field.Instead, he saw the ability to perform in vivo metabolic measurements as an opportunity (Hertz, 2004b) to resolve the long-standing question of the quantitative role of astroglial Glu metabolism, and spent extensive time at the meeting and afterward discussing with members of the in vivo groups how they performed their measurements and metabolic modeling so that he could better understand how to integrate them with in vitro work.His efforts at resolving the differences in interpretation between the fields led to the first in vivo MRS paper that incorporated in its metabolic modeling the alternate uses of anaplerosis for replacing oxidized neurotransmitter Glu (Lebon et al., 2002).It also led to in vivo studies focusing on the relationships between the anaplerosis flux and the fluxes of astroglial and neuronal glucose oxidation and the Glu/GABA-Gln cycle (for reviews, see Lanz et al., 2013Lanz et al., , 2014;;McNair et al., 2022).As shown in the meta-analysis by Lanz et al. (2013), these studies have found a linear relationship between the rate of anaplerosis and the rates of the Glu/GABA-Gln cycle as predicted from in vitro studies (see above).The slope of anaplerosis with the Glu/GABA-Gln cycle is approximately 0.15, which is highly significant flux.In the undisturbed awake state, approximately 80% of the anaplerotic flux is devoted to supporting the Glu/GABA/Gln cycle with the remainder being used for ammonia detoxification (Mason et al., 2007;McNair et al., 2022).
However, several important questions remain.Foremost, among them are the pathways of Glu oxidation taken in vivo.As described above, Hertz already at the time of the Waterville Valley meeting was questioning the role of GDH in Glu oxidation, but he believed the ultimate arbiter would be in vivo studies.Results of quantitative in vivo studies of 13 C labeling in GDH-knockout mice were not available at the time of the 2017 paper (Hertz & Rothman, 2017), although earlier in vivo studies had concluded in slices that there was no impact on the Glu cycle (Frigerio et al., 2012;Karaca et al., 2015;Karaca & Maechler, 2014).Results from in vivo labeling studies were published soon after (Hohnholt et al., 2018) and showed under resting-awake conditions, no differences in 13 C labeling, consistent with the paper's prediction that GDH was not the major pathway of Glu oxidation under "normal" activity conditions.However, in vivo studies (Frigerio et al., 2012;Hohnholt et al., 2018) also found evidence of disruption of homeostasis of Asp and total Asp plus Glu levels which requires GDH activity (AAT cannot change the total level of Asp plus Glu, just redistribute the amino groups).These findings can be reconciled by GDH being active primarily during short periods of high neuronal signaling activity and resultant Glu/GABA-Gln cycle flux, while AAT or a combination of AAT and GDH is used during the longer periods of lower activity closer to average signaling rates (Smith et al., 2002).
As a result, the short periods of high GDH activity would be time averaged out in the 13 C NMR measurements which require a minimum of 20 min to determine fluxes even in small animal models.Another limitation of the in vivo studies is that knockout mice undergo major metabolic adaptations to compensate for the knocked-out enzyme.
Therefore, it would be of great utility to redo these types of studies using methods that allow rapid modulation of GDH activity so that the animals studied start in the wild-type state.
Another important remaining question is the degree of pyruvate recycling in vivo (see above, Section 3.5).A limitation of in vivo studies to date in measuring pyruvate recycling is that the predicted labeling patterns are subtle and easily overwhelmed by scrambling of 13 C label in plasma glucose and lactate by liver pyruvate recycling and gluconeogenesis (Duarte et al., 2011;Lebon et al., 2002).
Furthermore, partial Glu oxidation does not require pyruvate recycling (Maciejewski & Rothman, 2008;Sonnewald, 2014) and still generates ATP.To reconcile the apparently larger anaplerosis flux than pyruvate cycling flux, Sonnewald (2014) proposed that the combination of anaplerosis by PC and malic enzyme activity can be used for lactate synthesis, thereby explaining oxidative lactate production.The development of in vivo 13 C MRS measurements and labeling strategies more sensitive to pyruvate recycling will be of utmost importance for further understanding of the relationship between anaplerosis, pyruvate recycling, and Glu oxidation.

| What are the functional neuroenergetic components of astroglial metabolism?
The ANLS and lactate metabolism in general played a prominent role at Waterville Valley (see https://www.karger.com/Journal/Issue/ 225541) with both in vivo and in vitro groups using it for interpreting their results.Even before the meeting, Hertz had strong objections to the ANLS theory, including functional astroglial energetics being exclusively assigned to Glu transport, thereby ignoring the in vitro studies by him and others showing the main functional energy cost was likely to be uptake of released K + and return to the extracellular fluid via the Na + , K + -ATPase activity (Figure 1).During the meeting, Hertz challenged presenters of in vivo and in vitro results who interpreted them using the ANLS to reconcile their interpretations with the full body of in vitro work.Afterward, Hertz continued to encourage and guide in vivo and in vitro researchers and also published several important papers in which he worked toward developing a synthesis of in vivo and in vitro findings (Dienel & Hertz, 2001;Hertz, 2004bHertz, , 2013;;Hertz et al., 2007;Hertz & Dienel, 2002;Hertz & Rodrigues, 2014;Hertz & Rothman, 2016, 2017;Hertz & Zielke, 2004).Through these papers and his encouragement to both in vitro and in vivo researchers to work together on reconciling their results, the present consensus emerged that astroglia account for approximately one-third of the ATP consumption associated with brain signaling activity as measured by the Glu/GABA-Gln cycle (Lanz et al., 2013(Lanz et al., , 2014;;Rothman, Dienel, et al., 2022;Yu et al., 2018).Although beyond the scope of this paper, it recently has been shown that the 1:3 relationship is likely determined by the shift during high activity to ATP from astroglial glycogenolysis required to fuel astroglial K + buffering (DiNuzzo et al., 2017;Rothman, Dienel, et al., 2022) as Hertz predicted in his in vitro and in vivo studies of glycogenolysis (e.g., Hertz et al., 2013;Hertz & Chen, 2016b, 2018b;Hertz, Xu, et al., 2015;Xu et al., 2013) (also see Section 5).

| The pseudo-MAS model predicts neuronal glycolysis and a 1:1 measured flux ratio of neuronal glucose oxidation and the Glu/GABA-Gln cycle rates: A mechanistic alternative to the ANLS
The criticisms of the ANLS model by Hertz and other attendees at Waterville Valley (e.g., Hertz, Swanson, et al., 1998) led advocates and skeptics of the model to perform experiments to test its prediction.Hertz's studies and contributions to the debate are described in Section 3.2.By 2003, a range of in vitro and in vivo studies that disagreed with predictions by the ANLS had been published (e.g., Chih & Roberts Jr, 2003; Section 3.2), as well as studies interpreted to support it (Pellerin & Magistretti, 2003).
However, in the opening article of a point-counterpoint debate in the Journal of Cerebral Blood Flow and Metabolism that year, the originators of the ANLS theory adopted an unprecedented position that their theory could not be disproven by disagreement with experiments because it was already shown to be "heuristically valid": "The important point here is not so much to decide, based upon the actual pieces of evidence, whether an hypothesis is right or  (Pellerin & Magistretti, 2003).
Therefore, they concluded that any apparently contradictory experimental findings were due to still-to-be-discovered neurochemical mechanisms as opposed to a failure of the theory (Pellerin & Magistretti, 2003).Hertz, who privately considered this claim an epistemological "free pass," acknowledged their view at the beginning of his contribution to the debate, and then proceeded anyway to give a point-by-point refutation based on experimental evidence (Hertz, 2004a).Hertz's critiques of the ANLS are an example of his contrasting scientific philosophy that theories (including his own as shown by his re-evaluation of the relative roles of AAT and GDH) need to be constantly re-evaluated based on how well they explain the full range of scientific findings.While Hertz remained a major critic of the ANLS, he did not see the failure of the ANLS as a mechanism to invalidate the possibility that there is a mechanistic basis that explained the ~1:1 relationship of glucose oxidation and the Glu/GABA-Gln cycle, and other near-integer flux ratios between neuronal and astroglial functional glucose and glycogen metabolism later found by in vivo studies.However, he was concerned about the objection originally proposed and developed by one of the co-authors (MCM) that as a result of many metabolic fates of Glu in the astrocyte, no one astroglial pathway could regulate the approximate 1:1 coupling of neuronal glucose oxidation and the Glu/GABA-Gln cycle, (McKenna, 2007) (Figure 3).These pathways are illustrated in Figure 1, and in more detail in McKenna (2007).Hertz recognized that while neuronal Glu metabolism is also complex, under physiological conditions, there is minimal net oxidation or synthesis in these cells, and it is in the same compartment as functional neuronal glucose oxidation.Therefore, it is likely that there is an important neuronal component in the regulation of the Glu/ GABA/Gln cycle flux.He spent years working on how an alternate neuronal mechanism could explain the findings, and in 2017, came up with an ingenious solution based on his earlier in vitro work (Hertz & Chen, 2017).Using the pseudo-MAS model that he developed with Georgios Palaiologos and Arne Schousboe (Palaiologos et al., 1988), these investigators showed that the model predicted a 1:2 flux ratio in which glycolytic metabolism of one glucose molecule would support conversion of two Gln to two transmitter Glu molecules.He also proposed that this mechanism explained the brain's obligatory requirement for glucose metabolism in neurons based on two mechanisms: (i) neuronal glycolysis produces NADH (Figure 3a) and pyruvate as mitochondrial oxidative substrates, linking neuronal glucose oxidation to the mechanism for conversion of astrocyte-derived Gln into transmitter Glu (Figure 3b); and (ii) neuronal glycolysis supports Glu/GABA neurotransmission via generation of glycolytic ATP to fuel vesicular transmitter packaging (Takeda & Ueda, 2017;Ueda, 2016).Lactate metabolism can provide cytoplasmic NADH but not cytosolic ATP and it does not adequately support V cycle .
Chowdhury, Behar, and colleagues later showed in a study in which beta-hydroxybutyrate was used to displace glucose oxidation in vivo at different metabolic activities, approximately half of the functional component of neuronal energetics depended on glucose (Chowdhury et al., 2014).When this factor of ½ is assigned to the fraction of neurons using the pseudo-MAS, a flux ratio of ~1:1 is predicted, consistent with in vivo findings (Chowdhury et al., 2014;Rothman, Behar, & Dienel, 2022) (Figure 3).We emphasize the importance of conceptual merging of results and models based on in vivo and in vitro studies, as illustrated in Figure 3, because the mechanism(s) of fueling neurotransmission; shuttling, metabolism, and re-synthesis of the molecules involved in the Glu/GABA-Gln cycle; and coupling of V cycle with glucose oxidation over a wide range of activity remain as important, unresolved topics in neuroenergetics (Rothman, Behar, & Dienel, 2022).
A limitation of the Hertz and Chen (2017) model is that while it successfully integrated the pseudo-MAS model developed in vitro with in vivo findings, it did not update the original pseudo-MAS mechanism.As described in Section 3.7, this mechanism has been criticized based on the proposal that Glu synthesized by PAG on the outer mitochondrial membrane has to be channeled to the Asp-Glu carrier (AGC), as opposed to directly diffusing out to the cytosol.Furthermore, subsequent extensive studies of mitochondria in other organs (e.g., heart) and cancer cells support localization of PAG inside the mitochondrial matrix.However, recently, it was shown that there are multiple ways in which the original pseudo-MAS mechanistic stoichiometry can be maintained with PAG inside the mitochondria (Rothman, Behar, & Dienel, 2022).While this finding supports the conceptual pseudo-MAS proposal, extensive studies are needed to determine the activity and regulation of the specific mitochondrial membrane transporters, and mitochondrial enzymes in order to definitively identify how the very high net Glu flux to the cytosol is supported.

| The role of brain energy and neurotransmitter metabolism in development
The majority of focus of in vitro and in vivo metabolic studies looking at functional energetic and neurotransmitter pathway relationships (Figure 1) have been on adult animal models and humans.Leif Hertz felt that an important area these studies could also contribute to is in understanding the establishment of metabolic relationships during development needed for adult synaptic function.In his 2013 review paper (Hertz, 2013) entitled "The glutamate-glutamine (GABA) cycle: importance for late postnatal development and potential reciprocal interactions between biosynthesis and degradation," he challenged the dogma that the main factor in synaptic maturation was the morphology of the pre-and post-synaptic nerve terminals, with astroglia mainly playing a structural role.By integrating the results of in vivo 13 C-MRS, [ 14 C]DG, and conventional biochemical studies with synaptic physiology and behavioral studies of brain maturation (e.g., Chowdhury et al., 2007;Cremer, 1982;Nehlig, 1997;Nehlig et al., 1988;Nehlig & Pereira de Vasconcelos, 1993), he showed that the establishment of the Glu/GABA-Gln cycle and its relationship with neuronal and astroglial glucose metabolism was critical for adult synaptic function (Hertz, 2013).Maturation of glutamatergic neurotransmission involves parallel increases in key astrocytic enzymes, Gln synthetase, and pyruvate carboxylase (reviewed by Brekke et al., 2015), and these pathways have robust activities in cerebral cortex and cerebellum of 18-day-old rats (Ferreira et al., 2021), supporting the importance of astrocytic metabolism.
Hertz also suggested specific integrated experimental approaches to further understand the relationship, but, unfortunately, there has been little funding to pursue this direction, possibly because of what he believed was the neuron-centric bias of the development field.
Hertz's contention that this is a critical area that needs continuing research holds even more so now that increasing evidence for alterations in Glu and GABA metabolism are being found in childhood developmental disorders such as autism (Horder et al., 2018), dyslexia (Del Tufo et al., 2018), and neonatal brain injury (McKenna et al., 2015;Morken et al., 2014;Scafidi et al., 2009).

| Summary and future directions
Leif Hertz made crucial contributions, both behind the scenes and in the literature, to our present understanding of how mechanisms established in vitro determine in vivo functional metabolic relationships between astroglia and neurons and vice versa.A simple way to assess his impact on the field of not just brain metabolism but neuroscience in general is by looking at papers over the last decade on Glu and GABA neurotransmission and neuromodulation.A large fraction will have overview figures directly showing the role of astroglia in neurotransmitter and K + cycling.In contrast, even a couple of decades ago astroglia would rarely be illustrated except for specific studies of them.However, Leif was never satisfied with the current understanding and continuously made key contributions to defining and setting the research agenda, several of which are currently actively pursued, as described in this article.
Important areas for future work based on the above discussion include the regulation and roles of AAT, GDH, and PC in neurotransmitter Glu turnover and neurotransmission, the extent and functional occurrence of pyruvate recycling, identification and quantification of the major energy demands of astrocytes (e.g., K + pumping costs more than Glu uptake and involves glycogenolysis; DiNuzzo et al., 2017;Rothman, Dienel, et al., 2022), the molecular mechanisms that regulate the astrocyte-neuron metabolic coupling to obtain a 1:1 stoichiometry between neuronal glucose oxidation and the Glu/GABA-Gln cycle, the molecular mechanisms that regulate the coupling during functional activation of non-oxidative glycogenolysis and glucose metabolism to neuronal signaling and the Glu/GABA-Gln cycle, and establishing the details required for the pseudo-MAS model to convert astrocyte-derived Gln to neurotransmitter Glu (see discussion in Rothman, Behar, & Dienel, 2022).at the Institute of Psychiatry in Arhus, Denmark.However, even at that time, the focus of molecular neuropharmacology was shifting to the dominant view that psychiatric disorders, and therefore treatments, were caused by alterations in neuronal neurotransmitter receptor-binding kinetics (Johnstone et al., 1978;Reynolds, 2004).
Hertz's work challenged this dogma by showing a potentially critical role in neuropharmacological action of astroglial receptor binding (Figure 1), and perhaps even more so in the subsequent large changes in the levels and isoforms of enzymes and proteins that regulated astrocytic glycogen and Glu metabolism as well as K + and Ca ++ regulation, was well outside the accepted school of thought (Johnstone et al., 1978;Reynolds, 2004).As one of the author's witnessed directly (DLR), challenging the main dogma in the field made it exceptionally difficult for his work in this area to get published.However, Leif Hertz persevered, and his work both directly and by inspiring in vivo studies of changes in astrocytic Glu metabolism in psychiatric disorders helped lead to a paradigm shift in which astroglial and other "downstream" metabolic and ion-trafficking consequences are being directly incorporated into studies of drug action (Duman, 2009;Mei et al., 2018;Sanacora & Banasr, 2013).
Although rarely discussed in the psychiatric medical literature, astrocytes have receptors and transporters for the monoamine neurotransmitters, such as dopamine, norepinephrine, and serotonin, that have been the major targets of psychiatric drug development (Hertz, Song, et al., 2014).Hertz was one of the first researchers to question the standard paradigms of neurological and psychiatric drug mechanisms, by studying their binding, transport, and metabolic sequelae on astroglia.His initial publication in this field was in 1979 (Hertz et al., 1979), and he continued to make important contributions to this area for the remainder of his scientific career.
Particular emphasis is put on his studies of astroglial selective serotonin reuptake inhibitor (SSRI) mechanisms, which was a major focus of his research in this area.(Stahl, 1998).Although this mechanism is conceptually appealing in its simplicity, it has failed to explain findings that SSRIs require several weeks to have a clinical effect on anxiety and depression.There are similar discordant clinical findings on drugs targeting the dopamine system and the accepted mechanisms of action.
In 2015, Leif Hertz published a comprehensive synthesis of the work by his and other groups working at the in vitro level with in vivo studies which proposed a paradigm shift in which what had been dismissed as "off target" effects of SSRI treatment on a myriad of glial (and neuronal) metabolic and ion cycling pathways were in fact a major factor in their clinical efficacy (Hertz, Rothman, et al., 2015).
His synthesis was based on a number of data sets: (i) glial 5-HT 2B receptor stimulation is needed for the in vivo anti-depressant action (Diaz et al., 2012); (ii) extensive findings in in vivo models of a key role of astroglial Glu metabolism and transport in the mechanism of action of anti-depression therapies (e.g., Sanacora & Banasr, 2013); (iii) the findings of Hertz's group that the main SSRIs in clinical use had equipotential binding to the 5-HT 2B receptor despite large differences in their inhibition of SERT (Zhang et al., 2010); (iv) additional findings from his group that 5-HT 2B inhibition led to a myriad of long-term changes in the regulation of glial glycogen and Glu metabolism and Ca 2+ levels (e.g., Li et al., 2008Li et al., , 2011;;Xu, Song, Bai, Cai, et al., 2014;Zhang et al., 1993Zhang et al., , 2010)); and (v) increased mRNA levels encoding for key enzymes and signaling pathways involved in the regulation of astroglial metabolism (Li et al., 2013).The findings of Hertz and Gibbs on the importance of glycogenolysis in learning and synaptic plasticity (see Section 5) were particularly emphasized as a result of the findings that successful depression treatment in animal models by ketamine, electrical convulsion therapy, and other interventions was associated with a long-term increase in structural and functional measures of neuroplasticity (Duman, 2009;Sanacora & Banasr, 2013).

| Contributions to understanding astroglial mechanisms of anti-epileptic drugs
Benzodiazepines are a class of psychoactive drugs that modulate the effects of GABA and have sedative-like, calming, and anti-convulsant effects.One of the more commonly used drugs in this class, diazepam (valium), acts on astrocytes via specific receptors and can reduce the concentration of cGMP and other actions (Hertz & Mukerji, 1980 and cited references).Ketamine is another anti-convulsant drug that acts via the GABA system, and it impairs GABA uptake into cultured astrocytes (Wood & Hertz, 1980).Barbiturates also have various effects on astrocytes, including GABA and K + transport, and diazepam binding (Hertz, 1979;Hertz & Sastry, 1978).

| Contributions to understanding astroglial mechanisms of non-SSRI anti-depressant drugs
Doxepin is a tricyclic anti-depressant that inhibits the rise in cAMP evoked by isoproterenol, a β-adrenergic agonist, but does not by itself alter cAMP levels (Hertz, Richardson, & Mukerji, 1980).In a series of studies over a 10-year interval, Hertz and colleagues showed that midazolam, a water-soluble benzodiazepine, enhances the K +evoked rise in intracellular [Ca 2+ ] in cultured astrocytes via its action on diazepam receptors and it enhances K + -stimulated glycogenolysis (Bender & Hertz, 1987;Code et al., 1990;Subbarao et al., 1995;Zhao et al., 1996).This latter effect probably contributed to the higher levels of lactate in astrocytes compared with neurons in mice anesthetized with the unusual drug cocktail comprised of midazolam, fentanyl, and medetomidine (Mächler et al., 2016; for further discussion of the cellular effects of these three drugs, see Dienel & Cruz, 2016).
Lithium is a classical drug for treatment of manic-depressive disorder, and Hertz and colleagues have shown that astrocytes are targets of the drug.Chronic and acute treatment with therapeutic levels of lithium affect astrocytic K + uptake (Walz et al., 1983;Walz & Hertz, 1982), it interferes with noradrenaline-induced changes in intracellular [Ca 2+ ] ( Chen & Hertz, 1996), reduces inositol pool size and uptake (Wolfson et al., 1998(Wolfson et al., , 2000)), and it alters astrocytic gene expression of the kainate receptor GluK2 (Peng et al., 2012).

| Summary and future directions
Through his group's findings and review papers synthesizing the results of multiple in vitro and in vivo studies including of patients, Leif Hertz made important contributions to the role of astroglial Glu and GABA metabolism, and neuronal-glial ion and neurotransmitter trafficking, in neuropharmacological mechanism of action.His work, directly and indirectly by inspiring an overall renewed interest in the Glu/GABA-Gln cycle, has had a highly significant impact on neuropharmacology.For example, a simple PubMed search on "Glu" and "depression" shows an increase in publications per year from 28 in 1980 to approximately 400 per year in the last decade, and for a search on "Glu" and "schizophrenia," an increase from 5 in 1980 to an average of approximately 300 per year over the last decade.Although this renewed interest is highly encouraging, many

F
I G U R E 2 Leif Hertz with family and discussions with colleagues.(a) Elna Hertz and Dr. Leif Hertz with Spot (photo courtesy of Leif Hertz, reproduced from Dienel (2012b) Copyright © 2012, Springer Science Business Media, LLC, with permission).(b) Left to right: Mary McKenna, Arne Schousboe, and Leif Hertz in a discussion at the 3rd ICBEM meeting in Waterville Valley, New Hampshire, USA, 1997 (photo courtesy of Mary McKenna).(c) Discussion after an invited talk at the ICBEM conference in Waterville Valley.In line for questions for the speaker, left to right: Leif Hertz, Mary McKenna, Robert Shulman, and Arthur Cooper.In the foreground lower right, Sebastian Cerdan (photo courtesy of Mary McKenna).

.
Controversial topics related to glucose, lactate, and Glu metabolism, lactate shuttling, and astrocytic responses to applications of Glu or K + were intensively discussed during the 3rd ICBEM conference in Waterville Valley, New Hampshire, USA, in 1997, the 5th in Trondheim, Norway, in 2001, the 6th in Heraklion, Crete, Greece in 2004, the 7th in Lausanne, Switzerland, in 2006, and the 11th in Helsinge, Denmark, in 2014, as well as in other ICBEM meetings.Lactate shuttling and roles of astrocytes in brain energetics have evoked long-standing debates at the ICBEM meetings and in papers published in the conference special issues that have stimulated many studies by conferees and other researchers.
GDH are responsible for approximately equal fractions of Glu conversion to α-ketoglutarate.The controversial aspects of the relative role of AAT and GDH in Glu oxidation were recently reviewed by McKenna et al. (2016), with the conclusion that the two different enzymatic pathways responsible for entry of Glu into the TCA cycle are likely to play different roles depending on the purpose of Glu metabolism, i.e. either complete oxidation, increased capacity for acetyl CoA oxidation, or a role in a truncated TCA cycle (McKenna et al., 2016).

.
As noted above, the culture medium differed in the Yu et al. and Farinelli-Nicklas studies, and Yu et al. reported GDH flux was four times higher than AAT flux despite the much higher AAT activity.Because of their interest in developing brain, the McKenna (2012) study used methods similar to their previous studies that used newborn rats, a culture medium containing 5 mM glucose, no dBcAMP to evoke differentiation, and assays carried out at days 10-11 in vitro.Detailed procedures used in the Bauer et al. ( ; D'Amelio et al., 1990; Tansey et al., 1991; Xin et al., 2019) are present in oligodendroglia, and their role in overall anaplerosis requires further work.
,Shank et al. (1989), andPeng et al. (1991) that α-ketoglutarate did indeed serve as precursor for releasable transmitter Glu albeit to a less extent than Gln.It should be noted, however, that GDH may also have a role in oxidation of Gln for energy since AOAA did not inhibit Gln oxidation in freshly isolated synaptosomes from rat brain(McKenna et al., 1993).Hertz F I G U R E 3 Mechanistic linkage of glutamatergic neurotransmission with neuronal glycolysis and glucose oxidation.(a) The pseudomalate-aspartate shuttle model in which astrocyte-derived glutamine (Gln) is converted to neurotransmitter glutamate (Glu) by phosphateactivated glutaminase (PAG) located on the outer face of the inner mitochondrial membrane (MEM).This Glu enters the matrix via the aspartate (Asp)-Glu carrier (1) where it is transaminated to produce α-ketoglutarate (αKG) that exits to the cytosol via the ketodicarboxylate carrier (2) for transamination to form Glu that is packaged into synaptic vesicles.Components of the transamination reactions are oxaloacetate (OAA) and Asp.Conversion of OAA to malate (Mal) enables transfer of cytosolic reducing equivalents (NADH) produced by neuronal glycolysis to the matrix for oxidation by the electron transport chain.From figure 5 of Hertz and Chen (2017), Copyright © 2017 Hertz and Chen.This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) that is modified from Palaiologos et al. (1988) Copyright © International Society for Neurochemistry, with permission.(b) Rate of neuronal glucose oxidation (CMR glc(ox)N ) versus the rate of the Glu-Gln (V cycle(tot) ).Values are the results of a meta-analysis of [ 13 C]glucose studies in rat and human cerebral cortex, showing a near-linear relationship with a slope of approximately 1. From figure 2 of Hertz and Chen (2017), which is modified from Hertz and Rothman (2016) Copyright © 2016, Springer International Publishing Switzerland, with permission.The figure in Hertz and Rothman is figure 2a of Hyder et al. (2013).© 2013 The Authors.With permission of D. L. Rothman, co-author of both the original and present publications.

6. 3 |
What is the in vivo activity dependence of anaplerosis, and what are the relative contributions of AAT and GDH to Glu oxidation, and PC to re-synthesis?
area of Leif Hertz's research was the study of the role of astrocytes in the etiology of neurological psychiatric diseases and as targets in their treatment.Hertz's interest in what is now called molecular neuropharmacology began in the late 1950s during his clinical training and experimental work in pharmacology Perhaps the major contribution Leif Hertz made to understanding the role of glia in psychopharmacology was in vitro studies of the effect of chronic SSRI stimulation of the 5-HT 2B receptor on glial metabolism.SSRI action has been long considered a triumph of the orthodox neuronal receptor model of neuropharmacology.The dominant view of the mechanism of SSRIs has largely been their blockage of the neuronal reuptake of serotonin by the serotonin transporter (SERT).The blockage then leads to an increase in the synaptic level of 5-HT, which increases neuronal binding of serotonin to multiple neuronal receptors