In vivo calibration of genetically encoded metabolite biosensors must account for metabolite metabolism during calibration and cellular volume

Isotopic assays of brain glucose utilization rates have been used for more than four decades to establish relationships between energetics, functional activity, and neurotransmitter cycling. Limitations of these methods include the relatively long time (1–60 min) for the determination of labeled metabolite levels and the lack of cellular resolution. Identification and quantification of fuels for neurons and astrocytes that support activation and higher brain functions are a major, unresolved issues. Glycolysis is preferentially up‐regulated during activation even though oxygen level and supply are adequate, causing lactate concentrations to quickly rise during alerting, sensory processing, cognitive tasks, and memory consolidation. However, the fate of lactate (rapid release from brain or cell–cell shuttling coupled with local oxidation) is long disputed. Genetically encoded biosensors can determine intracellular metabolite concentrations and report real‐time lactate level responses to sensory, behavioral, and biochemical challenges at the cellular level. Kinetics and time courses of cellular lactate concentration changes are informative, but accurate biosensor calibration is required for quantitative comparisons of lactate levels in astrocytes and neurons. An in vivo calibration procedure for the Laconic lactate biosensor involves intracellular lactate depletion by intravenous pyruvate‐mediated trans‐acceleration of lactate efflux followed by sensor saturation by intravenous infusion of high doses of lactate plus ammonium chloride. In the present paper, the validity of this procedure is questioned because rapid lactate–pyruvate interconversion in blood, preferential neuronal oxidation of both monocarboxylates, on‐going glycolytic metabolism, and cellular volumes were not taken into account. Calibration pitfalls for the Laconic lactate biosensor also apply to other metabolite biosensors that are standardized in vivo by infusion of substrates that can be metabolized in peripheral tissues. We discuss how technical shortcomings negate the conclusion that Laconic sensor calibrations support the existence of an in vivo astrocyte–neuron lactate concentration gradient linked to lactate shuttling from astrocytes to neurons to fuel neuronal activity.


| INTRODUC TI ON
Glucose is the obligatory fuel for brain, and its utilization is an essential component of brain function because metabolism of glucose provides most of the ATP to support brain energetics and supplies the carbon required for other essential pathways, including excitatory (glutamate) and inhibitory γ-aminobutyric acid (GABA) amino acid neurotransmitter synthesis (Dienel, 2019a).Glucose utilization rates (CMR glc ) measured at the hexokinase step with [ 14 C]deoxyglucose (DG) and autoradiography or with [ 18 F]fluorodeoxyglucose (FDG)positron emission tomography (PET) have, therefore, been widely used as surrogates to localize and quantify local changes in functional activity throughout the living brain (Sokoloff, 1981).Magnetic resonance spectroscopic (MRS) assays in vivo in conjunction with metabolic modeling enabled quantitative assays of pathway fluxes in neurons and astrocytes using 13 C-labeled glucose and other substrates (Yu et al., 2018).
Limitations of these methods include the relatively long time (from 1 to 60 min) required for accurate quantification of metabolic rates, lack of cellular resolution, metabolic modeling assumptions (e.g., sizes and cellular distributions of metabolic pools), and infusion of high concentrations of 13 C-labeled compounds compared to use of tracer amounts of 14 C-and 18 F-labeled compounds.Similar limitations apply to cell culture studies that typically grow cells in high glucose (5-25 mM) media thereby subjecting them to diabetic complications (e.g., glycation reactions, sorbitol accumulation).Primary cultures can differ substantially from those in vivo with respect to morphological, molecular, and developmental/maturational characteristics due, in part, to harvest from immature brains, lack of signals from other cell types, and short culture durations.Biochemical assays in extracts of brain or cell culture to evaluate metabolite levels and temporal responses to challenges are limited by analytical sensitivity and cannot carry out serial assays on the same subjects or cultures.
Quantification of fluxes in pathways of metabolic up-regulation during brief brain activation, the fates of glucose carbon, and neuronal and astrocytic fuels during activation are topics of long-standing interest to neuroscientists (e.g., see Rothman et al., 2022 and references cited therein).Glycolysis is preferentially up-regulated during activation even though oxygen levels and delivery to brain are adequate (Dienel, 2019a;Dienel & Cruz, 2016), leading to increased lactate production due to the conversion of pyruvate to lactate to sustain glycolytic flux by regeneration of NAD + from the NADH produced at the glyceraldehyde-3-phosphate step.For this reason, quantification of time courses and quantities of lactate produced by neurons and astrocytes are important aspects of understanding how glycolytic metabolism supports processing of sensory information, cognitive function, and other aspects of brain function and disease.
Use of genetically encoded optical sensors that enable real-time assays of intracellular metabolite concentrations at the cellular and subcellular levels in cultured cells and in living brain is a major technological advance (Chandris et al., 2022;Koveal et al., 2020;Koveal et al., 2022;San Martín et al., 2022).The toolbox includes biosensors for glucose, lactate, pyruvate, NADH, citrate, glutamate, glutamine, α-ketoglutarate, and other compounds.Optical biosensor technology is widely used in multiple fields, but usually qualitatively to look at the spatial distribution of large changes such as during physiological challenge and pathology.Quantitative comparisons of cellular responses to sensory, behavioral, and biochemical challenges require accurate sensor calibration, which is challenging as an intracellular standard is needed.
In this paper, we focus on methodology used for vivo calibrations of a representative genetically encoded lactate sensor, Laconic (San Martin et al., 2013).Application of this sensor by Mächler et al. (2016) led to claims of an astrocyte-to-neuron lactate concentration gradient in brain of anesthetized mice; this putative cell-cell concentration difference is an essential pre-requisite for astrocyteto-neuron lactate shuttling (ANLS) down its concentration gradient.
In their follow-up study in awake mice, Zuend et al. (2020) reported that an arousal-evoked decrease in intracellular lactate concentration in astrocytes was accompanied by an increase in lactate level in extracellular fluid, followed by a slower rise in neuronal intracellular lactate level; these sequential changes were interpreted as evidence supporting ANLS (Pellerin & Magistretti, 1994).The notion of neuronal oxidation of astrocyte-derived lactate as preferred fuel during activation has been a controversial topic for decades (e.g., Chih et al., 2001;Chih & Roberts Jr, 2003;Dienel, 2012;Dienel, 2019a;Dienel, 2019b;Hertz, 2004) in large part because data claimed to support ANLS are circumstantial and predictions based on the shuttle model are not consistent with the results of in vivo studies (e.g., Dienel, 2017;Rothman et al., 2022).These issues raise the question whether conclusions related to lactate shuttling drawn from Laconic biosensor signals are correct, or the result of improper calibration or its interpretation.
Recognized limitations of the Laconic lactate sensor include (i) the relationship between the signal emitted by the sensor and lactate concentration is nonlinear (large concentration changes lead to small signal changes) requiring highly accurate and precise lactate measurements by an independent method for calibration even for quantification of relative lactate differences or changes; (ii) absolute lactate levels may not be as accurate as required for detecting small differences in a lactate gradient between cells or cells and extracellular fluid; and (iii) concentration changes do not report metabolic or transport rates.In the present study, evaluation of procedures previously used by others to calibrate their Laconic sensors in vivo reveals four serious concerns that can invalidate sensor baseline and calibration, genetically encoded biosensor, Laconic, pyruvate-lactate metabolism, sensor saturation, trans-acceleration saturation calibrations and confound their interpretation: (i) Rapid pyruvate-lactate equilibration and net interconversion in blood and via peripheral tissues during pyruvate infusion used to deplete intracellular lactate levels via trans-acceleration and during lactate infusion to saturate the sensor confounds interpretation of calibration signals.(ii) Evidence suggests that both lactate and pyruvate are preferentially oxidized in neurons, and the extent of delivery of these monocarboxylates to neurons and astrocytes is not established.(iii) Glycolytic metabolism is on-going during the calibration procedure.(iv) The volume fraction and estimated cellular volume of astrocytes are smaller than those of neurons, and as a consequence, astrocytic lactate pool size changes are most readily achieved.As a consequence of these confounds, the available evidence derived from Laconic signals is not sufficient to conclude that there is an astrocyte-to-neuron lactate concentration gradient coupled with extensive lactate shuttling and substantial neuronal lactate oxidation in living brain.
In vivo calibration of any genetically encoded biosensor is essential for quantitative determination of absolute metabolite concentration, and metabolism in blood and peripheral tissues of compounds used for biosensor standardization can invalidate the calibration, as evident for the Laconic lactate biosensor.Major issues relevant to in vivo biosensor calibrations are, therefore, presented in detail in the following sections.First, the properties and calibration procedures for the Laconic sensor are reviewed.Second, technical complications and pitfalls of calibration and the impact of cellular volume fraction are evaluated.Third, alternative interpretations of calibration data and context for the magnitude of lactate "surges" are explained.

| L ACONI C S EN SOR C ALIB R ATI ON CURVE S
The Laconic FRET (Förster or Fluorescence Resonance Energy Transfer) ratio signal is approximately proportional to the logarithm of lactate concentration and is characterized by small FRET signal responses to large concentration changes (Figure 1A).An approximately 15-20% increase in the FRET signal was observed over four to five orders of magnitude of lactate concentration, i.e., 10 −6 to 10 −2 M when calibrated in vitro or in cultured HEK293 cells (Mächler et al., 2016;San Martin et al., 2013).In the physiological range, in vitro calibrations exhibit about a 10% increase in the FRET signal over the 50-fold range of 0.1 to 5 mM lactate, whereas calibrations in cultured HEK293 cells obtained about a 25% signal increase over the 100-fold range from 0.1 to 10 mM lactate (San Martin et al., 2013).
In contrast, in vivo studies in which brain lactate levels were measured during intense physiological sensory stimulation find increases from 1.3-to 2-fold (e.g., Bednarik et al., 2015;Bednarik et al., 2018;Dienel et al., 2002;Dienel et al., 2007;Rothman et al., 2022), which as we describe below may be well below the accuracy and precision of the method.Importantly, San Martin et al. (2013) stated that the change in all of the Laconic ratio signals determined in HEK293 cells was about twice all of those observed in vitro, indicating that in vitro calibrations are not appropriate for use in cell culture or in vivo studies.Also, the small alkaline pH sensitivity of the in vitro FRET signal (San Martin et al., 2013) was not reproduced in their subsequent study (Mächler et al., 2016), a discordance ascribed to in vitro artifacts arising from Laconic protein instability at room temperature in a non-cellular milieu (Sotelo-Hitschfeld et al., 2015).
The Laconic sensor has been an important tool to evaluate rapid changes in intracellular lactate concentration and to monitor lactate responses to a variety of experimental conditions in cultured cells and in living brain (e.g., Diaz-Garcia et al., 2017;Mächler et al., 2016;San Martin et al., 2013;Sotelo-Hitschfeld et al., 2015;Zuend et al., 2020).However, conversion of FRET ratio signals to actual lactate concentrations requires calibration of the sensor in all cells of interest under the specific experimental conditions.Calibration accuracy is important because increases in lactate level that typically occur during brain activation correspond to a less-sensitive region of the calibration curve compared with dips in concentration (Figure 1A,Ba).Although the Laconic sensor is very useful to track dynamic changes in lactate concentration, accurate quantification of the magnitude of these changes is a critical aspect of metabolic studies.Absolute values are required for the comparison of lactate responses in neurons and astrocytes or other cell types.

| Cultured cells
Baseline Laconic sensor calibration was carried out by superfusion of cultured cells with high concentrations of a monocarboxylic acid transporter (MCT) substrate (either pyruvate or monochloroacetate) to enhance efflux of lactate from the cells and reduce the intracellular Laconic lactate signal to a stable minimum (San Martin et al., 2013;Sotelo-Hitschfeld et al., 2015).This phenomenon, called trans-acceleration, is illustrated in Figure 1Ba for cultured astrocytes in which 10 mM pyruvate was used to reduce the baselinenormalized Laconic signal from 1.0 to ~0.84.Intracellular substrate depletion is based on faster movement of a substrate-loaded MCT carrier (denoted by MCT-S, Figure 1Ce) across the membrane, while noting that the fractional enhancement of efflux rate of the internal substrate is smaller than the percent increase in the concentration of the external substrate (Brown & Brooks, 1994;Juel, 1996).Critical aspects of this calibration are the absence of lactate in the external medium and a high external substrate level to enhance efflux and to dilute the lactate released to the medium and prevent its re-entry into the cells.
Saturation calibration assays of the Laconic sensor in cultured astrocytes used superfusion with 5 mM sodium lactate and 2 mM glucose.These assays revealed a peak-normalized signal of ~1.03 compared with the resting normalized value of 1.0 with 1 mM lactate in the medium (Figure 1Ba).Based on these calibrations, cultured astrocytes were stated to have a calculated resting intracellular lactate concentration of 1.4 mM (Sotelo-Hitschfeld et al., 2015), with a control lactate level of 80 nmol/mg protein in astrocyte extracts (see Figure S2B in San Martin et al., 2013).Thus, the magnitude of the Laconic signal decrement when intracellular lactate was depleted (~1.4 mM → ~0 mM) is larger (16%) than the increment (3%) at saturation at an undefined intracellular lactate concentration (Figure 1Ba).
Resting lactate levels in cultured astrocytes (Figure 1Bb) were estimated by Sotelo-Hitschfeld et al. (2015) using the protocol in Figure 1Ba.The x-axis scale above the bar graph in Figure 1Bb gives their calculated intracellular lactate concentrations plotted against sensor saturation on the lower x-axis.Note that there is a very wide range of cells having >75% saturation with intracellular lactate concentrations between ~1 and 10 mM.The 100% saturation level corresponds to >10 mM, which seems very high, given the culture conditions.Blocking the MCTs to trap lactate in the astrocytes caused the normalized Laconic signal to rise to 1.1, exceeding apparent sensor saturation of 1.03 (compare Figures 1B-D in Sotelo-Hitschfeld et al., 2015).The calculated intracellular lactate levels in cultured astrocytes varied over more than a 10-fold range under resting conditions, perhaps reflecting inaccurate determination of absolute levels and/or high variability of intracellular lactate levels in these cells.
Normal physiological lactate levels in cultured brain cells and in brain are similar and close to the concentration that produces Laconic sensor saturation.Walz and Mukerji (1988b) reported control intracellular lactate levels in cultured astrocytes and neurons are 157 and 148 nmol/mg protein, respectively, about twice those of San Martin et al. (2013).Total brain lactate concentration is 1.35 μmol/g intracellular water (similar to 1.4 mM in cultured astrocytes), with a pyruvate concentration of 0.10 μmol/g water (Veech et al., 1979).During activation, brain lactate concentrations typically rise from ~1 μmol/g wet weight (~80% water) at rest to ~2 μmol/g (Cruz & Dienel, 2002;Dienel, 2012), i.e., they shift toward the Laconic saturation level (see discussion below, noting that saturation depends on sensor expression and metabolite binding and could conceivably influence metabolic rates).Further evidence of in vivo lactate concentrations being at the Laconic sensor saturation levels is from in vivo studies of human brain during sensory stimulation which have found that lactate increases (all cellular compartments) to approximately 1.2-1.3mM from a non-stimulated concentration of 0.9 mM (Bednarik et al., 2015;Bednarik et al., 2018;Rothman et al., 2022).Mächler et al. (2016) used baseline and saturation calibrations in anesthetized mice to evaluate the relative lactate levels in astrocytes and neurons and concluded that there is an astrocyteneuron lactate concentration gradient.They and Sotelo-Hitschfeld et al. (2015) used an unusual mixture of anesthetics (fentanyl, midazolam, and medetomidine) to avoid volatile halogenated anesthetics known to increase brain lactate levels (Boretius et al., 2013;Horn & Klein, 2010).However, this mixture is likely to have differential effects on neurons and astrocytes, with identified effects on astrocytes (see discussion p.30-32 in Dienel & Cruz, 2016), and its influence on cellular lactate concentration differences was not ruled out.

| Living brain-Anesthetized mice
The goal of the trans-acceleration saturation experiments was to eliminate (or greatly reduce) the concentration of cellular lactate via an intravenous infusion of sodium pyruvate (4 mmol/kg, 500 mM solution for 3 min).The high level of plasma pyruvate competes with lactate transport into the cell and hypothetically will reduce lactate levels to near zero through enhanced lactate efflux.
During the infusion, the baseline-normalized Laconic signal in astrocytes was reduced by 4.7%, with little change in neurons (0.6%) (Figure 1Ca).Simultaneous assays with the intracellular pyruvate sensor, Pyronic, showed a signal increase in astrocytes but not in neurons (Figure 1Ca).Extracellular lactate concentration measured with a pre-calibrated probe increased during and peaked after the pyruvate infusion interval, with a net rise of 0.084 mM lactate (absolute baseline concentrations were not reported) (Figure 1Cb).This increase was considered by the authors to be consistent with lactate efflux resulting from trans-acceleration.
In separate experiments, intravenous sodium lactate infusion (4 mmol/kg, 500 mM solution for 3 min) increased plasma lactate level to 17 mM, caused a net rise of extracellular lactate level of 0.27 mM, and increased the neuronal lactate signal more than that in astrocytes, 5.7 versus 4.3%, respectively (Mächler et al., 2016).
Notably, intravenous infusion of smaller sodium lactate loads (0.5, 1, or 2 mmol/kg, 500 mM solutions) increased lactate signals in both cell types to the same extent and same time course, demonstrating that differential effects in astrocytes and neurons are dependent on lactate infusion amount.
Intravenous infusions of high doses of NH 4 Cl (4 mmol/kg, 500 mM solution) + sodium lactate (8 mmol/kg, 1 M solution) for 15 min followed by sodium lactate infusion (4 mmol/kg, 500 mM solution for 3 min) were used to saturate the Laconic sensor in the anesthetized mice.As discussed in more detail below (see section 4.3, "Saturation of Laconic sensor signal"), these near-neurotoxic levels of ammonia will stimulate astrocytic synthesis of glutamine to detoxify the ammonia (neurons do not express glutamine synthetase), thereby consuming ATP and altering astrocytic energy demands and metabolism.
Normalization of the Laconic signals to the saturation value revealed a lower mean baseline signal in neurons than in astrocytes (0.90 and 0.93, respectively; see Figure 4 in Mächler et al., 2016), similar to the single-experiment baseline differences illustrated in Figure 1Cc.
Repeated sodium pyruvate infusions increased the Laconic signal in astrocytes and neurons, and subsequent pyruvate infusion reduced the signal in both cell types (Figure 1Cd), suggesting that high intracellular lactate levels (caused by conversion of pyruvate to lactate, see section 4.1 "Rapid pyruvate-lactate interconversion") are necessary to observe the effects of trans-acceleration.
To summarize, the larger reduction in Laconic signal in astrocytes during sodium pyruvate infusions and the higher astrocytic signal when normalized to saturation levels were interpreted by Mächler et al. (2016) as evidence for higher resting lactate levels in astrocytes than in neurons.The graphical abstract in their article and the illustration of astrocyte-neuron lactate fluxes (see Figure 6 in Mächler et al., 2016) emphasize lactate shuttling.However, shuttling was not measured, and the illustrations do not reflect the complexity of brain lactate dynamics, as discussed below.were based on Laconic signal dips, peaks, slopes, and areas under the curve during arousal, but signals were not calibrated to quantify lactate concentrations.A major finding was that the astrocytic lactate signal dip coincided with a rise in extracellular lactate level, both of which preceded the rise in the neuronal signal.Treatment with the non-specific β-adrenergic blocker, propranolol, revealed that adrenergic signaling triggered the lactate increases that involved glycogenolysis and were prevented in glycogen synthase 1 knockout mice.Lactate signal increments, called "surges" by Zuend et al., were interpreted as glycogen-derived lactate production in astrocytes, lactate release to extracellular space, and neuronal uptake.

| Living brain-Awake mice
However, the fate of the extracellular lactate and astrocyte-neuron lactate shuttling were not determined.Furthermore, the source(s) of neuronal lactate is unknown and the lactate is likely to be derived from neuronal glycolysis, as shown by Diaz-Garcia and Yellen (2019) for activated neurons.
Trans-acceleration experiments with sodium pyruvate infusion (4 μmol/kg, 500 mM solutions for 3 min) revealed similar kinetics in awake control and glycogen-synthase knockout mice for neurons (a slow progressive signal increase) and for astrocytes (a dip within ~1 min followed by an overshoot and slow decline) (see Extended Data Figures 8 and 9 in Zuend et al., 2020).However, the Laconic signals were not calibrated, and the concentrations of lactate in the "surges" in astrocytes and neurons remain unknown.Normalization of lactate signals to the respective baselines enables comparison of temporal dynamics, but it prevents the assessment of quantitative changes that are necessary to understand the role of lactate in brain energetics.As noted above in the Mächler et al. (2016) study, their summary graphic emphasizes astrocyte-to-neuron lactate shuttling (see Figure 5 in Zuend et al., 2020) without any direct proof of shuttling and omits key aspects of lactate dynamics in brain.

| TECHNI C AL COMPLI C ATI ON S C AN INVALIDATE L ACONIC C ALIB R ATIONS
Influx of pyruvate and lactate from blood into brain increases with arterial plasma lactate concentration in anesthetized rats (Cremer et al., 1979), and both lactate uptake and lactate oxidation increase with plasma lactate level in brain of awake humans (Boumezbeur et al., 2010;van Hall et al., 2009).However, the influence of plasma lactate concentration on brain lactate level may vary with species or experimental conditions.In studies that used intravenous infusions of [ 13 C]lactate in humans to raise plasma lactate levels about threeto five-fold from 0.7-1 mM to 3-5 mM, brain lactate concentration was linearly related to that in plasma (Boumezbeur et al., 2010).In contrast, an increase in plasma lactate in the anesthetized rats to approximately 4-5 mM did not increase brain levels, although only one level of plasma lactate was examined (Duarte et al., 2015).
Determination of actual brain lactate concentrations during transacceleration and lactate flooding experiments is, therefore, important for the interpretation of sensor responses.
Insertion of the genetically encoded biosensors into brain cells may have a heterogeneous distribution among cells in the brain region of interest, as well as within the cells of interest.Although the sensor is reported to be cytoplasmic and be expressed throughout astrocytes and neurons (Mächler et al., 2016), it is not clear whether the numbers of sensors are the same per unit cytoplasm in all subcellular compartments.In addition, cellular and intracellular heterogeneity of metabolic enzyme and lactate transporter distributions and of metabolic pools in subcellular structures can also influence local sensor responses.This is important because when a small, limited class of objects was examined in the hippocampus, axons, dendrites, and glia accounted for about 50%, 40%, and 8% of neuropil volume, respectively (Mishchenko et al., 2010).A more complete analysis of neuronal structures by Chklovskii et al. (2002) revealed that axons, dendrites, boutons, spines, and soma of neurons corresponded to 30-35%, 20-30%, ~12%, ~5%, ~12%, and glia 4-10%, respectively, of total neuropil in visual and piriform cortex and hippocampus, suggesting that specific structures or cell types may contribute differentially to sensor signals.
In vivo baseline calibration of the Laconic lactate sensor used intravenous sodium pyruvate-evoked trans-acceleration of lactate to reduce Laconic signals in brain cells of anesthetized mice.However, these data cannot be simply interpreted in terms of lactate depletion for four major reasons: (i) Lactate-pyruvate interconversion and net conversion in blood and via peripheral tissues are fast, producing large amounts of lactate in blood that will enter the brain from blood and brain cells from extracellular fluid in competition with pyruvate.
(ii) Lactate and pyruvate are rapidly and preferentially metabolized in neurons, suggesting a favored neuronal uptake.(iii) The overall astrocytic volume fraction in cerebral cortex is ~10% with ~80% for neurons, and the estimated volume per neuron is 2.6 times that of the volume of an astrocyte in layer II/III of visual cortex.This means that the amount of lactate that must be removed from an astrocyte to bring the intracellular concentration to zero or the amount added to saturate the astrocytic Laconic sensor is smaller than for neurons.(iv) In addition, glycolytic lactate production continues to be highly active in brain during pyruvate infusion, leading to high lactate levels, as shown by hyperpolarized [ 13 C]pyruvate MR imaging studies (Grist et al., 2019;Miloushev et al., 2018).Furthermore, metabolic studies have shown that even maximum lactate levels in blood cannot displace the majority of brain glycolytic glucose consumption (Boumezbeur et al., 2010;Quistorff et al., 2008;van Hall et al., 2009).Therefore, the determination of brain lactate depends on knowing glucose (and glycogen) metabolic rates as well as lactate blood levels and transport kinetics.Furthermore, as discussed below, the relative metabolism of lactate and pyruvate differs between neurons and astrocytes and will also be concentration dependent.In contrast, in cellular calibration studies using the trans-displacement method, it is assumed (due to the high MCT activity of the astroglial membranes) that the maximum transport rate is many times greater than metabolic lactate and pyruvate production.However, in vivo the blood-brain barrier is the limiting step in lactate and pyruvate transport, and the key assumption of the displacement method does not hold.Proper calibration, therefore, requires the calculation of lactate concentration using a sophisticated kinetic model taking all these factors into account as well as the relative volumes of neurons, astrocytes, and the extracellular space (see below).
On the other hand, sensor saturation assays used high intravenous loads of ammonium chloride plus sodium lactate that are close to the neurotoxic level for ammonia and are likely to have differential metabolic effects on astrocytes and neurons.Rapid lactate-pyruvate interconversion, extensive net interconversion, potentially-different effects of increased blood osmolarity on astrocytes and neurons, and preferential neuronal metabolism also complicate the interpretation of saturation levels.The actual concentrations of lactate in astrocytes and neurons at Laconic saturation were not established as identical, so if cellular saturation concentrations differ, normalization to the saturation signal will produce artifacts.The intracellular environment in HEK293 cells doubled the Laconic signal compared with in vitro calibration, raising the possibility that the neuronal and astrocytic environments may differentially alter the Laconic signal response to intracellular lactate.These and related issues are discussed in more detail in the following sections because they apply to in vivo calibration of any lactate biosensor, as well as to other metabolite biosensors calibrated with compounds that can be metabolized by peripheral tissues.

| Rapid pyruvate-lactate interconversion in blood influences lactate depletion and saturation
The trans-acceleration method for lactate depletion depends on the assumption of a very large excess of pyruvate to lactate ratio be maintained in the blood for an extended period of time required for lactate to be lost from the brain.However, this assumption is challenged by findings by Wolfe and colleagues who demonstrated that intravenous infusions of [ 13 C]pyruvate or [ 13 C]lactate are characterized by rapid and extensive isotopic equilibration between pyruvate and lactate, regardless of which compound was infused.When [ 13 C] lactate was infused into anesthetized dogs (Wolfe et al., 1988), pyruvate enrichment rapidly equaled that of lactate (within 6 min), and the average ratio of pyruvate to lactate enrichment (92 ± 2.4%) persisted throughout the 240-min infusion interval.Furthermore, this pattern of pyruvate-lactate enrichment ratio was maintained during hypoxia when blood lactate levels rose 17-fold from ~0.5 to 8.7 mM within 10 min and during infusion of dichloroacetate to stimulate pyruvate oxidation in peripheral tissues, thereby reducing blood lactate level by about 50%.Thus, rapid pyruvate-lactate equilibration occurred even when altered by metabolism in peripheral tissues that changed the circulating lactate level over the range from about half to nine times the basal level.
To identify the source of lactate-pyruvate interconversion, Romijn et al. (1994) tested human whole-blood samples in vitro.A bolus of either [ 13 C]pyruvate or [ 13 C]lactate was injected, and isotopic equilibration occurred almost completely within 3-4 min with both precursors.In contrast, there was no equilibration in plasma, indicating that red cells carried out the interconversion at a rate three to four times faster than endogenous net lactate production, i.e., from red cell glycolysis.
In a follow-up study, Zhang et al. (1993) simultaneously infused  2 and Table 1).Fast production of lactate within the brain from both tracer and loading doses of pyruvate will interfere with the trans-acceleration calibration procedure.At 1, 2, and 5 min after the injection, the mean serum [ 13 C]pyruvate concentrations were 6.7, 3.2, and 1.3 mM, respectively, and serum [ 13 C]lactate concentration increased from 2.1 at 2 min (80% enrichment) to 8 mM at 5 min (27% enrichment) (Table 1, Gonzalez et al., 2005), consistent with rapid, substantial net pyruvate-lactate interconversion.Presumably the blood lactate concentration increased from 2 to 5 min after the injection due to the uptake of infused pyruvate into body tissues and its conversion to lactate with release of lactate back to the circulation, as in the above studies by Wolfe et al.
This rapid and extensive pyruvate-lactate interconversion is expected to substantially increase blood and brain lactate levels during and after the sodium pyruvate infusion to produce transacceleration in the Zuend et al. and Mächler et al. studies, as well as pyruvate formation during sodium lactate infusions to fill brain intracellular lactate pools.This leads to uptake of both pyruvate and lactate into brain cells, confounding the interpretation of cellular Laconic signals measured during the 3-to 5-min intervals of pyruvate or lactate infusions and longer time intervals after cessation of lactate or pyruvate infusions (see figures 2-5 in Mächler et al., 2016 and Extended Data figures 8 and 9 in Zuend et al., 2020).
The above prediction of rapid production of large amounts of lactate in blood from infused sodium pyruvate (4 mmol/kg, 500 mM solution for 3 min) was confirmed by data from Zuend et al. (2020).
Figure 2a illustrates their experimental paradigm for pyruvateevoked trans-acceleration in awake mice.Neurons had an increase in the Laconic signal (i.e., toward sensor saturation) during the infusion interval, and it remained elevated for >10 min thereafter (Figure 2b).
In contrast, pyruvate infusion caused a dip in the astrocytic Laconic signal at ~1 min after infusion onset, followed by an overshoot and gradual decline over time (Figure 2c). Figure 2e shows that blood lactate concentrations were about 3.3, 13.3, and 8.3 mM at times T2, T6, and T7, respectively, revealing a four-fold rise in blood lactate level within ~1 min of starting the pyruvate infusion (i.e., time T6).This increase must have contributed to the rise in neuronal Laconic signal and to the astrocytic overshoot following the brief dip (Figure 2a,b).
For comparison to pyruvate, infusion of lactate (4 mmol/kg, 500 mM solution for 3 min), which should also raise blood pyruvate levels due to net interconversion, increased mean blood lactate level to 17 mM, raising extracellular brain lactate level by 0.27 mM (see fig- Mächler et al., 2016).This small increment is in contrast to in vivo MRS studies of human cerebral cortex, in which an increase in plasma lactate to 2.6 mM (from approximately 1.0 mM) increased tissue levels by 0.6 mM (Boumezbeur et al., 2010), whereas in rats infused with [ 13 C]lactate, the brain lactate concentrations were similar before and 150 min after the infusion (Duarte et al., 2015).Either modest increases or no changes in cisternal fluid or whole brain lactate levels were also reported in primates and rats after intravenous infusion of 500-1 M lactate (Coplan et al., 1992;Dager et al., 1990;Dager et al., 1992).Furthermore, brain lactate (and pyruvate) uptake was shown to increase approximately linearly with plasma concentration in anesthetized rats (Cremer et al., 1979) so that an increase to 17 mM in plasma lactate is predicted to increase brain lactate in short experiments.Thus, the rise in extracellular lactate of 0.084 mM during pyruvate infusion in the Mächler study (Figure 1Cb) was probably mainly due to lactate influx from blood rather than to lactate efflux arising from trans-acceleration, as suggested by the authors.In addition, in vivo studies suggest a much greater rise in cellular lactate, and likely extracellular lactate, than reported using the sensor.
To summarize, the interpretation of in vivo sodium pyruvatemediated trans-acceleration and sodium lactate infusion-mediated Laconic saturation experiments is complicated, perhaps fatally compromised, by rapid and substantial pyruvate-lactate interconversion in blood, competitive transport of both monocarboxylates into the brain, and their competitive uptake from extracellular fluid into brain cells.For lactate infusion, the results of lactate measurements give a much lower level of extracellular lactate determined in anesthetized mice with a pre-calibrated lactate biosensor in the Mächler et al. ( 2016) report (i.e., a 0.27 mM net increase, see their Figure 3b) than measured net uptake rates or brain concentrations during lactate infusion or exhaustive exercise by in vivo MRS which has been established as a quantitative method, as well as quantitative biochemical assays (Boumezbeur et al., 2010;Dager et al., 1992;Quistorff et al., 2008;van Hall et al., 2009), questioning the overall sensor calibration procedure.Thus, the pyruvate trans-acceleration assays must account for lactate uptake, and lactate saturation assays need to address pyruvate uptake and potential suppression of low lactate Laconic signals by 1 and 10 mM pyruvate (see figure 2g in San Martin et al., 2013), as well as the high rate of glycolytic lactate production which continues during either lactate or pyruvate infusion.In vivo calibration procedures are much more complex than in cultured cells where the composition of the superfusate is readily controlled.
In adult rats, the rates of lactate and pyruvate influx into brain from blood at 5 mM substrate are similar when assayed separately, but since these monocarboxylic acids share the same blood-brain barrier carrier (MCT1), they will compete with each other for uptake into brain and brain cells (Cremer, 1982;Cremer et al., 1979).The infused compound will initially and briefly have the highest concentration in blood, with rapid, time-dependent changes in blood composition as the lactate and pyruvate equilibrate and are taken up into brain and peripheral tissues, thereby confounding interpretation of Laconic and Pyronic sensor signals.

| Preferential oxidation of lactate and pyruvate in neurons: Cellular supply-metabolism
Studies of metabolic compartmentation in brain in the 1960s to 1970s identified precursors that are preferentially metabolized in neurons and astrocytes.The experimental paradigm for these assays involved the injection of a tracer amount of a 14 C-labeled precursor, purification of glutamate, glutamine, and other metabolites from brain extracts, the determination of the specific activities (SA = dpm/μmol) of the compounds of interest, and the calculation of the ratio of SA-glutamine/SA glutamate.When administered by intravenous or intracarotid routes, the SA of glutamine was less than that of glutamate (i.e., SA-glutamine/SA-glutamate <1) for 14 C-labeled glucose, lactate, and pyruvate (Table 1).In other words, more label from these precursors was metabolized to α-ketoglutarate via the TCA cycle and entered the glutamate pool than entered the glutamine pool to give a higher glutamate SA even though the total tissue glutamate level exceeds glutamine (12.5 and 5.5 μmol/g, respectively) in cerebral cortex (e.g., Dienel et al., 2002).In contrast, the SA-glutamine/SA-glutamate ratio was >1 for 14 C-labeled acetate and butyrate (Table 1), as well as bicarbonate, glutamate, and glutamine (not shown).In this case, glutamate is the precursor of glutamine, but more label entered the product compared with the precursor to give a higher SA for glutamine.This appeared to violate precursor-product relationships (product would have a lower SA than precursor due to dilution of label in the unlabeled product pool), and the data were interpreted as evidence for compartmentation, with a small glutamate pool used for glutamine synthesis from TCA cycle substrates, as opposed to via the glutamine synthetase reaction that converts glutamate directly to glutamine.Of interest, intracisternal injection has a different outcome for pyruvate and glucose, producing SA-glutamine/SA-glutamate >1 at 2-4 min whereas the ratio is <1 after intravenous or intracarotid injections (Table 1).These findings suggest greater access of glucose and pyruvate to astrocytic metabolism when transport across the blood-brain barrier is circumvented.
Preferential labeling of glutamate by lactate, pyruvate, and glucose has been widely interpreted by neurochemists as revealing metabolism via the "large" neuronal glutamate pool, whereas carbon from butyrate and acetate preferentially enters the "small" astrocytic glutamate pool that is the precursor for glutamine (reviewed in Balázs & Cremer, 1972, Berl et al., 1975, Fonnum, 1978, Duarte et al., 2015).Intracarotid injections of tracer amounts of [ 14 C] pyruvate were used by Cremer et al. (1978) to minimize its uptake into liver after intravenous or intraperitoneal injection and conversion to labeled glucose by gluconeogenesis (Koeppe & Hahn, 1962;McMillan & Mortensen, 1963) Metabolic compartmentation of glutamate and glutamine was subsequently confirmed by quantitative immunocytochemical studies (e.g., Gundersen et al., 1991;Ottersen et al., 1992;Ottersen & Storm-Mathisen, 1984;Storm-Mathisen et al., 1983).Glutamate-like immunoreactivity was highly localized in neurons, including soma, nerve terminals, and synaptic vesicles.In the cerebellum, glutamatelike immunoreactivity was highest in excitatory neurons and their processes, whereas glutamine-like labeling was highest in astrocytes (Ottersen et al., 1992).Glutamatergic terminals were calculated to contain four-to five-fold more glutamate than glutamine, whereas the average astrocyte contained about five-fold more glutamine relative to glutamate.Taken together, the metabolic and immunolabeling data indicate that metabolic labeling of the large glutamate pool by glucose, lactate, and pyruvate to obtain a higher glutamatespecific activity than that for glutamine strongly supports the rapid, preferential oxidative metabolism of these substrates by neurons.
Although a detailed discussion is beyond the scope of the present substrate preference discussion, there is evidence for "metabolic" and "neurotransmitter" pools glutamate and glutamine.
Through diffusion and mixing via the glutamate/GABA-glutamine cycle, these pools will rapidly achieve similar steady state labeling in the awake animal due to the approximately 1:1 stoichiometry with neuronal glucose oxidation (Rothman et al., 2022;Yu et al., 2018).
However, the time required for labeling of the nerve terminal/neurotransmitter pool may be delayed by several minutes or more under anesthetized conditions, as found in a recent study looking at the time course of labeling in synaptosomes extracted from the cerebral cortex of anesthetized rats during a [1-13 C]glucose infusion (Patel et al., 2017).
In MRS studies in mice by Gonzalez et al. (2005)  pyruvate (Gonzalez et al., 2005), with the caveat that fluoroacetate disrupts brain metabolism in a time and dose-dependent manner (e.g., Fonnum et al., 1997;Hassel et al., 1997).In contrast to the data obtained with [ 13 C]pyruvate, fluoroacetate substantially reduced labeling by [1,2-13 C 2 ]acetate (that is primarily oxidized in astrocytes), e.g., labeling of Glu C 4 fell by about 85% and labeling of GABA C 4 and Gln C 4 by [ 13 C]pyruvate (via the "metabolic" TCA cycle pools) was eliminated (Gonzalez et al., 2005).
We note that intravenous [1-13 C]pyruvate infusion has recently been extensively studied since it is used as a tracer for detecting tumors with 13 C hyperpolarized magnetic resonance imaging (HP-13 C MR).In these studies, it has been shown that in tumors and healthy tissue, including the brain, the pyruvate is converted to lactate rapidly in the tissue by lactate dehydrogenase.This conversion depends initially on the pre-established lactate pool providing NADH, but continues subsequently with additional glycolytic (and potentially mitochondrial via the malate-aspartate shuttle) NADH production being trapped in the large pyruvate pool (Xu et al., 2016).
Due to these factors, the interpretation of a change in lactate concentration due to pyruvate infusion is fraught with uncertainty unless both are measured or modeled and the impact of transacceleration isolated.
Metabolism of [3-13 C]lactate in human brain after programmed intravenous infusions to achieve resting physiological levels of 1.5 or 2.5 mM in blood preferentially labeled [4- 3 min) was used to saturate the Laconic signal in neurons and astrocytes in brain of anesthetized mice (Figure 1Cc).These procedures should increase plasma osmolarity, as reported for rats infused with 1 M sodium lactate for 20 min (Dager et al., 1992), and perhaps alter brain water content.Normalization of the cellular Laconic signals to saturation revealed a higher signal in astrocytes than in neurons, interpreted by the authors as evidence for an astrocyte-neuron lactate gradient.
The blood and brain ammonia and lactate levels achieved in the above saturation experiments were not reported, but intraperitoneal injections of coma-or lethargy-producing doses of ammonium acetate (7.8 or 5 mmol/kg, respectively) increased blood and brain ammonia levels from 0.13 and 0.2 mM, respectively, to approximately 1.5-3 mM and 1 mM, respectively, at 15 min after the injections (Ehrlich et al., 1980).Higher brain ammonia levels could be expected after intravenous injections in anesthetized mice used by Mächler et al. (2016).The neurotoxic threshold dose of ammonium acetate (5 mmol/kg, intraperitoneally) given to awake rats caused hyperventilation and reduced spontaneous activity, whereas 7.8 mmol/kg also caused drowsiness, hyperreactivity to stimulation, and seizures and death or coma.These symptoms would be blunted or undetectable in anesthetized mice (Mächler et al., 2016), whereas if similar ammonia infusions into awake mice were used by Zuend et al. (2020), the procedure may stimulate body movements and interfere with sensor imaging (see their paradigm in Figure 2a).
In addition to behavioral effects, neurotoxic levels of ammonia have metabolic consequences in brain cells.Programmed intravenous infusion of ammonium acetate to raise blood ammonia from ~45 μM to ~0.5 mM reduced brain glutamate level by ~20%, increased brain glutamine level 1.7-fold, and doubled brain lactate level by 50 min of infusion (Fitzpatrick et al., 1989).Acute exposure of cultured astrocytes and neurons to 3 mM ammonium chloride did not alter 14 CO 2 production from [U-14 C]glucose in either cell type, whereas it reduced astrocytic, not neuronal, 14 CO 2 production from [2-14 C]pyruvate by ~55% (Fitzpatrick et al., 1988).These findings suggest predominant metabolic effects of ammonia on astrocytes (Kala & Hertz, 2005) that contain glutamine synthetase (Martinez-Hernandez et al., 1977) and detoxify ammonia by its ATP-dependent conversion of glutamate to glutamine (Cooper & Plum, 1987).This process increases astrocytic ATP demand and would enhance metabolism in astrocytes.
Graded levels of ammonia given to cultured astrocytes (0.2, 0.5, and 5 mM), brain slices (0.05, 0.1, and 0.2 mM), or brain in vivo (intravenous 2.5 mmol/kg) increased intracellular lactate levels in all three models (Lerchundi et al., 2015).Ammonia also stimulated lactate release from cultured astrocytes that were shown to accumulate lactate when its efflux is blocked; these two findings were taken to indicate that astrocytes are net lactate producers (Lerchundi et al., 2015;Sotelo-Hitschfeld et al., 2015).However, both unstimulated cultured astrocytes and cultured neurons are long-known to be net lactate exporters in amounts corresponding to ~80% and 45% of glucose consumed, respectively (Jekabsons et al., 2017;Waagepetersen et al., 2000).Lactate release from both cell types varies with experimental condition (Walz & Mukerji, 1988a;Walz & Mukerji, 1988b), and in fact, cultured cells are not useful model systems to evaluate glycolysis, lactate production, and lactate release.
A major reason for substantial lactate export from cultured cells is the immense medium volume compared to intracellular volume.
Lactate production and trans-membrane transport are lactate concentration and pH gradient-driven, equilibrative reactions, and lactate dilution in the culture medium "pulls" lactate out of the cells (Hertz & Dienel, 2005).
To summarize, the intracellular concentrations of lactate in astrocytes and neurons that achieve Laconic saturation have not been  2016) on astrocytic lactate levels is likely (Dienel & Cruz, 2016) and needs to be resolved.

| INFLUEN CE OF CELLUL AR VOLUME ON S EN SOR C ALIB R ATI ON S AND S I G NAL S
Another potential source of influence in comparisons of estimated absolute values for astroglial and neuronal lactate concentrations using the Laconic sensor is due to the impact on calibration and evoked signals of the relative volumes of neurons and astrocytes.
A Laconic sensor binds one molecule of lactate per sensor to emit a signal (S).The baseline (b) signal (S b ′) per unit volume will rise with increasing intracellular lactate concentration until the sensor is saturated (S sat ).Because the volume of a cell or tissue compartment is constant, relative cellular or compartmental concentration changes within that cell or compartment with condition can be reliably compared.
The baseline signal from a cellular compartment c of volume V c within the microscopy measurement volume V (which is in units such as ml or g-wet weight) is given by where K is a measured function that describes the relationship be- If a quantity of Lac (Q 1 ) is added to or taken from the compartment, the new concentration is given by and the new signal from the compartment is given by Note that unless V c is known neither S 2 nor S b can be converted to concentration.Altering the baseline quantity of lactate by an amount Q 1 will change the intracellular concentration by a value that depends on V c .As discussed below in section 5.2.2 and shown in Table 2, at present there is considerable uncertainty in the relative astrocytic and neuronal volume fractions.
However, based on the full range of literature reports, the astrocytic volume is several fold smaller, and therefore subject to larger percentage errors which then propagates to the lactate concentration calculation.
Both the rate of change and magnitude of the resulting uncalibrated signal derived from the new concentration can be influenced by the volume of the compartment and the rates of lactate influx, efflux, and metabolism in each cell type, as well as glycolytic metabolism of glucose in each cell type and glycolytic metabolism of glycogen in astrocytes.The smaller the volume of the cell or compartment, the greater the concentration change caused by Q 1 .
However, if the new concentration of lactate is saturating, then the signal becomes independent of concentration: Division of any signal S x by S sat cancels out the V c component and gives: Because, at concentrations of lactate more than 2-fold above the Michaelis-Menten binding constant of the sensor, Ssat becomes independent of lactate concentration, and the compartmental concentration under baseline conditions can be determined from an in vitro calibration curve, provided that in vivo conditions are accurately simulated, which need not be the case (San Martin et al., 2013).
Normalization of S x to either S b or S sat in the same compartment or cell type gives the ratio of the quantities of intracellular lactate in the two conditions and, in principle, can remove the requirement of knowing the volume: and However, based on the studies reviewed below, even at very high plasma lactate concentrations, the increase in cellular and extracellular concentration in brain is relatively small and well below the levels required for complete sensor lactate binding site occupancy.In addition, due to the high fluorescence signal from the sensor even in the absence of intravenously infused lactate, it is necessary to also (1) (2) determine the fluorescence when lactate concentration is at zero, which also cannot be achieved in vivo.
Therefore, the differences reported in the literature between neurons and astroglia can only be interpreted as relative changes in fluorescence between a baseline condition and a condition in which intracellular lactate is elevated by either infusing high levels of sodium lactate or alternatively altering cell metabolism to raise intracellular lactate levels (e.g., hypoxia, chemical inhibitors of oxidation, increase metabolic demand and glycolytic flux, or lactate transport).Although the percent change in the compartment fluorescence can be determined, as for example reported in Mächler et al. ( 2016)), Diaz-Garcia et al. ( 2017)), Zuend et al. (2020)), the total concentration as well as the actual percent change in lactate concentration cannot be established.This limitation can be explained by comparing two cells or compartments that have the same concentration but different volumes.Then, the quantity of lactate in the cell, and therefore amplitude of the fluorescence signal, with larger volume exceeds that of the cell with smaller volume.Normalized values report relative changes in the quantities of lactate in that compartment but do not allow comparisons of absolute concentrations between compartments unless the saturation and zero lactate calibrations can be used.
Regarding achieving sensor saturation, it has not been demonstrated in humans or animal models under awake resting, exercise to exhaustion, or anesthetized conditions that the brain lactate levels achieved during lactate infusion or strenuous muscular activity are sufficient to saturate the Laconic sensor, even at very high blood lactate concentrations.For example, figure 3 in Mächler et al. (2016) shows that intravenous infusion of 500 mM sodium lactate raised blood lactate level from 0.81 to 17 mM within ~3 min, whereas the net rise in brain extracellular brain lactate level was only 0.27 mM.
Their Figure 4 reported that simultaneous infusion of 500 mM ammonium chloride plus 1 M sodium lactate for 15 min followed by 500 mM sodium lactate for 3 min increased extracellular lactate by a net of 0.87 mM.Assuming a normal resting brain lactate level of ~1 mM, then the elevated brain lactate levels under these two conditions would be ~1.3 or ~1.9 mM, respectively, too low to saturate the Laconic sensor, based on in vitro studies in cultured astrocytes (see Figure 1 and Sotelo-Hitschfeld et al., 2015).
In studies of exercise to exhaustion in rats, blood lactate rose from <1 mM at rest to ~5 mM at 120 min of exercise, and over that time interval, the regional brain lactate levels rose from ~1.1 μmol/g up to at most 2.7 μmol/g (Matsui et al., 2011).In exercising humans, arterial blood lactate rose from the resting value of 1 mM to a peak of ~14.5 mM at ~2 min after completion of exhaustive arm and leg exercise for 10 min, whereas CSF lactate level after exercise (1.2 mM) was essentially the same as before exercise (1.4 mM) (Dalsgaard et al., 2004).
Intravenous infusion for 20 min of 1 M sodium dl-lactate into 1% halothane-anesthetized primates increased the cisternal fluid total lactate level (d-and l-lactate were measured enzymatically and summed) from ~1.4 mM to ~2.1 mM at 5 min and to ~4.2 mM at 20 min when the respective arterial blood lactate levels were 0.6, 5.5, and 13 mM, respectively (Dager et al., 1990).In contrast, infusion of 0.5 M racemic lactate for 40 min into ketamine-anesthetized primates (Coplan et al., 1992) increased venous blood L-lactate from 0.76 to 8 mM after 40 min, but did not change cisternal fluid L-lactate level, a difference from the above study that was ascribed, in part to higher total (dl-) lactate concentrations and use of halothane that increases brain lactate level (Boretius et al., 2013).Infusion of 1 M L-lactate into ketamine-xylazine-anesthetized rats for 20 min increased venous blood lactate from 2.3 to 43 mM, whereas wholebrain lactate rose from 1 mM to 1.5 mM at 5 min and to 3.2 mM at 20 min; serum osmolality rose from 327 to 385 mOsm/kg over 20 min (Dager et al., 1992).
Another caveat is that the infusion of a hypertonic solution (e.g., 500 mM mannitol or 500 mM sodium L-lactate) is used to reduce brain swelling and intracranial pressure in patients with traumatic brain injury (Bajamal et al., 2021;Gantner et al., 2014;Ichai et al., 2009;Ichai et al., 2013;van Gemert et al., 2022).Hypertonic sodium lactate (1 M) infusion increased serum osmolality (Dager et al., 1992), and infusions of hypertonic 0.5 or 1 M solutions of pyruvate, lactate, and ammonium chloride alone or in combination may reduce brain water content and differentially alter the volumes of brain cells since astrocytes contain aquaporin-4, whereas neurons do not (Nagelhus & Ottersen, 2013), conceivably altering astrocytic intracellular lactate concentration more than in neurons.
Therefore, the assumption of Laconic sensor saturation being achieved without a direct measurement by non-optical methods is not valid.Furthermore, even if the total level of brain lactate is at a saturating level, it cannot be automatically inferred that it is saturating in both compartments due to the difference in the relationship between extracellular lactate concentration and intracellular lactate concentration between astroglia and neurons as a consequence of different transporter kinetic constants and differences in their rates of lactate, glucose, and glycogen metabolism.Once again, knowledge of the astroglial and neuronal volume fractions are essential for the interpretation unless independent non-optical measurements of each compartment during high plasma lactate levels are performed to validate the saturation assumption.
In the sections below, we review evidence for differences between volumes of brain compartments, astrocytes, neurons, and interstitial fluid (ISF) and how they can impact the rate of increase of astrocytic, neuronal, and ISF compartment lactate concentrations.We note that although at steady state the volume fractions will not matter, the time to achieve steady state can be considerable.However, even at steady state, differences in the relationships between lactate transport kinetics (V lac-max , K T ) and lactate/glucose/glycogen metabolism in each cell type can confound the assumption that saturation is reached in all compartments, which also will be described.

| Impact of cellular volume differences
In the Mächler et al. (2016) and Zuend et al. (2020) studies, the viral vectors for the Laconic sensors were injected into adjacent, nonoverlapping regions of somatosensory cortex of the mouse, and an extracellular lactate biosensor probe was separately inserted into somatosensory cortex.Intravenous flooding doses of pyruvate or lactate plus ammonia were used to calibrate the biosensors, and sensor signals were recorded from physically separated sensor-expressing neurons and sensor-expressing astrocytes in laminae II/III.The cellular concentration changes were interpreted with the implicit assumption that all neurons and all astrocytes in the physically-separated regions respond in aggregate to calibration procedures and to challenges, as portrayed in their summary graphical depictions of an astrocyte-interstitial fluidneuron lactate concentration gradient.
In order to properly interpret the signals from an astrocytic and neuronal Laconic lactate sensor quantitatively in terms of concentration requires accurate knowledge of the respective volumes of cells containing the biosensors.This is important because if the resting lactate concentrations in both cell types are equal but one cell type has a smaller volume, then its quantity of lactate is smaller and the rate of change to new concentration is faster.Thus, the concentration changes in astrocytes in response to a pyruvate-lactate flooding protocol may overestimate the fraction of the total flux due to their smaller volume.Although there is considerable uncertainty in the local cellular volume fractions throughout the brain, the astroglial volume fraction is no more than 30% of the neuronal fraction; it is generally much smaller and it influences interpretation of aggregate metabolic rates (Dienel & Rothman, 2020).We previously applied the results in our meta-analysis of astrocyte volume fraction to re-evaluate the calculated aggregate glucose utilization rates in MRS studies (Dienel & Rothman, 2020).Blood-borne glucose fuels neurons at higher calculated glucose oxidation rates compared with astrocytes (Rothman et al., 2022;Yu et al., 2018), but when in vivo metabolic rates were re-calculated to take into account the much smaller volume fraction of astrocytes (mean for cerebral cortex = 9.6%, see below), the aggregate rates of glucose oxidation in astrocytes per unit cellular volume greatly exceed those of neurons, and astrocytic glycogen levels and glycogenolysis rates are similar to those in muscle (Dienel & Rothman, 2020).
For these calculations, we emphasize that adjustments for aggregate volume fraction (i.e., multiplication by 1/volume fraction) are valid for conversion of metabolic rates or glycogen concentration from measured values reported in units per gram tissue to units per cellular volume and for assignment of the amount of a metabolite contained within that volume fraction.On the other hand, the volume fraction adjustments cannot be made for diffusible brain metabolites, the concentrations of which are the net result of influx and efflux across the blood brain barrier, reversible transport across cellular membranes, and intracellular metabolism.For example, brain glucose concentration is about 20% that of arterial plasma, brain glucose and lactate are evenly distributed between intra-and extracellular space (Pfeuffer et al., 2000), and there is no diffusion barrier for glucose (Eleftheriou et al., 2023).Autoradiographic and PET studies with the labeled nonmetabolizable glucose analog, 3-O-methylglucose, also reveal the homogeneous concentrations of glucose throughout the rat and human brain (Dienel et al., 1997;Gjedde et al., 1985;Gjedde & Diemer, 1983;Sokoloff et al., 1977).Therefore, if brain glucose level of 2 μmol/g were partitioned with a 10% astrocyte volume fraction, then 10% of the total would be contained in astrocytes.However, an adjustment by multiplying 1/0.1 gives a calculated level per unit astrocyte volume of 20 μmol/g.This approach cannot be correct for glucose, lactate, and other metabolites that traverse membranes in a passive, concentration-driven manner and equilibrate among brain compartments.In contrast, glycogen is synthesized and stored as a large polymer in astrocytes; it cannot cross cell membranes and the volume fraction adjustment factor can be appropriately applied.Similarly, aggregate glucose utilization rates measured in tissue can be adjusted by volume fraction because the glucose is delivered from blood to brain at or close to a rate that matches utilization rate so that the intracellular concentration remains relatively stable under steady state conditions.The following discussions evaluate the impact of volume fraction on Laconic sensor responses, first in the aggregate, then on the basis of single cells.

| Aggregate cellular concentration changes estimated from volume fractions
Figure 3a portrays an astrocyte and a neuron with similar cellular volumes denoted by equal areas as in the graphical illustrations presented in the Mächler and Zuend studies.However, the increased complexity in Figure 3a comes from the fact that astrocytes take up lactate from extracellular fluid and disperse lactate among gap junction-coupled astrocytes at two-to four-fold faster rates and higher capacity than both neuronal lactate uptake and astrocytic lactate shuttling to neurons; astrocytes are poised to release lactate to interstitial and perivascular fluids and blood (Ball et al., 2010;Cruz et al., 1999;Cruz et al., 2007;Gandhi et al., 2009).Astrocytes have close apposition to the brain vasculature and readily, bidirectionally exchange metabolites with perivascular fluid and blood (Abbott et al., 2006;Hladky & Barrand, 2014;Hösli et al., 2022;Mathiisen et al., 2010).When brain lactate level exceeds that in blood (i.e., with minimal muscular activity), the large total blood volume compared with brain volume (Herculano-Houzel et al., 2006;Lee & Blaufox, 1985) and high blood flow rate (Jay et al., 1988;Sakurada et al., 1978) along with lactate metabolism in peripheral organs (Romijn et al., 1994;Wolfe et al., 1988;Zhang et al., 1993) create an infinite sink for brain lactate (Figure 3a).Quantification of lactate efflux from brain to blood is, therefore, essential for interpretation of the magnitudes of lactate fluxes and release, and lactate shuttling among brain cells.
The intravenous injections of large amounts of pyruvate or lactate plus ammonia in the Mächler and Zuend Laconic calibration studies will flood the entire brain with pyruvate-lactate so that even though lactate can more rapidly enter or leave astrocytes or be dispersed among coupled astrocytes, all astrocytes are subjected to the flooding conditions via the entire brain vasculature, thereby reducing or eliminating local gradients.In brief flooding experiments, local distributions of lactate or pyruvate will be influenced by MCT transporter isoform, number, subcellular locations, and transport half-saturation level and capacities (K T and V Tmax ), as well as metabolism.However, as long as sufficient time is allowed to reach the maximal and minimal intracellular concentrations, then basal pool size and transporter characteristics should not be determinants in outcome but rates of change will be influenced by cellular volume that influences intracellular quantity at a given concentration.Figure 3b illustrates three major factors that can influence Laconic sensor calibration: cellular volume, lactate-pyruvate metabolism in blood, and preferential neuronal metabolism of lactate and pyruvate; the latter two were discussed above, along with on-going glucose/glycogen metabolism as a source for lactate and pyruvate.Astrocytes have a much smaller brain volume fraction than neurons with a mean value of 9.5 ± 3.8% for three major brain regions that are statistically significantly different from each other: cerebellum (15.0 ± 2.2%, n = 5), hippocampus (6.1 ± 1.7%, n = 9), and cerebral cortex (9.6 ± 2.8%, n = 14) (see table 2 in Dienel & Rothman, 2020).This contrasts with neuronal volume fractions of 75-90% (soma, axons, dendrites, boutons, and spines) in different brain structures (for references, see Footnote c in table 4 in Dienel & Rothman, 2020).Extracellular space is also small (~20%) and contains ISF, extracellular matrix, and other molecules (Hrabetova et al., 2018).These data are from studies in different species and regions within larger brain structures, and they are considered to be approximations for evaluation of aggregate responses of neurons and astrocytes.Due to compilation of many data sets, these mean percentages do not add to 100% and they do not include the small volume fractions for the vasculature, microglia, and oligodendroglia.
F I G U R E 3 Impact of astrocyte, neuron, and blood compartments on interpretation of Laconic lactate sensor calibrations in brain in vivo.(a) Graphical illustration of lactate movements among gap junction-coupled astrocytes, lactate release to extracellular fluid, perivascular fluid, and blood, and lactate shuttling to and from astrocytes and neurons.Note that blood volume greatly exceeds brain volume, blood flow rate to brain is high, and blood represents an infinite sink for brain lactate when muscular activity and blood lactate levels are low.(b) Technical issues complicate Laconic sensor calibration in vivo, and interpretation of calibration data must take into account the following: (i) the volume fraction of astrocytes is much smaller than of neurons, (ii) rapid equilibration of lactate and pyruvate in blood when either monocarboxylate is infused intravenously, and (iii) preferential metabolism of lactate and pyruvate in neurons.See text for details.(c) Influence of lactate amount on pool depletion or filling.For hypothetical calculations, the amount of lactate in resting astrocytes and neurons was taken as equal (1 mM) or 50% higher in astrocytes (1.2 vs. 0.8 mM); depleted pool = 0 mM and pool filling/saturation as an arbitrary 5 mM.When cellular volume fractions and lactate concentrations are equal in both cell types, the same amount of lactate is needed to deplete or fill the pool, whereas when the concentration in astrocytes is 50% higher, more lactate must be removed from the astrocyte to deplete the pool, and more inserted into the neuron to fill the pool.When the amounts of lactate are adjusted for cellular volume fraction of ~10% in astrocytes and ~80% in neurons (Dienel & Rothman, 2020), the astrocytic lactate pools are much smaller than those in neurons and are more readily depleted and filled.In contrast, pool depletion in neurons involves removal of larger amount compared with astrocytes, and much larger amounts must enter neurons to fill the pool and saturate the Laconic sensor.Se text for details.Abbreviations: ANL, astrocyte-neuron lactate; ECF, extracellular fluid; Glu, glutamate; Lac, lactate; Pyr, pyruvate; TCA, tricarboxylic acid.
To illustrate the potential impact of cellular and extracellular volume fractions on aggregate biosensor calibrations in astrocytes, neurons, and ISF in the rat cerebral cortex, these compartments were assumed to have the same resting lactate concentrations of 1 mM (Figure 3b), a value that falls within the range of ~0.5-1 μmol/g brain in normal, resting, carefully handled rats (Cruz & Dienel, 2002;Dienel et al., 2007).For the hypothetical calculations illustrated in Figure 3b,c, cerebral cortical volume fractions were approximated as 10% for astrocytes (Dienel & Rothman, 2020), 80% for neurons (not including their soma that are about 10-13%) (Chklovskii et al., 2002;Foh et al., 1973), and 20% for ISF (Hrabetova et al., 2018).Using these values, the relative amounts (i.e., concentration times overall volume fraction) of lactate in astrocytes, ISF, and neurons are 0.1, 0.2, and 0.8 μmol, respectively.Because the approximate quantities of lactate in astrocytes and ISF are on the order of 1/8th and 1/4th, respectively, that of neurons, depletion or filling the lactate pools is, therefore, most readily achieved in astrocytes and ISF, i.e., smaller changes in the intracellular quantity can cause faster and larger concentration changes, as illustrated in the following examples: (i) Equal aggregate cellular volumes: When intracellular lactate levels are assumed to be 1 mM and equal in neurons and astrocytes, the same amount of lactate (0.5 μmol, Figure 3c) must be removed from each cell type to reduce intracellular lactate to zero.Similarly, the same amount must be added to raise the intracellular concentration to 5 mM and achieve putative Laconic sensor saturation, i.e., add 2 μmol lactate (Figure 3c), calculated as follows: assume saturation at 5 μmoL/mL × 0.5 volume fraction = 2.5 μmol minus the resting value of 0.5 μmol = 2 μmol to add.Mächler et al. (2016) claimed, based on their Laconic calibrations, that astrocytes had significantly higher lactate levels than neurons, but they did not provide numerical values for cellular lactate concentrations.Nevertheless, for the purpose of illustration, assume that the aggregate astrocytic lactate level is 50% higher than that in neurons (1.2 and 0.8 mM, respectively, so the intracellular amounts are 0.6 and 0.4 μmol, respectively, Figure 3c).In this case, 0.2 μmol more lactate must be removed from astrocytes to reach baseline compared with neurons, and 0.2 μmol more lactate must be added to neurons compared to astrocytes to saturate the Laconic signal (Figure 3c).Thus, when cellular volume fractions are equal, the hypothetical amounts of lactate that must be removed from or added to neurons and astrocytes to achieve the same baseline and saturation concentrations for Laconic sensor calibration are similar.This is not the case when the actual cellular volume fractions are not equal.
(ii) ~8-Fold smaller volume fraction in cerebral cortical astrocytes than neurons: The smaller cortical volume fraction of astrocytes (10%) compared with neurons (80%) means that aggregate lactate depletion and pool filling are more readily achieved than from neurons even with a 50% (or more) higher concentration in astrocytes (Figure 3c), and the rates of concentration change in response to global, extracellular flooding and to experimental challenges can be faster for cells with smaller volumes.For example, if the resting cells have the same lactate concentration of 1 mM, the astrocytes and neurons contain 0.1 and 0.8 μmol lactate, respectively.Total lactate depletion is achieved in astrocytes when only ~12% of the lactate (0.1 μmol) is removed from neurons (Figure 3c).If astrocytes have 50% higher resting lactate levels, baseline zero lactate is achieved by removal of 0.12 μmol lactate, whereas neurons must export 0.64 μmol (Figure 3c).On the other hand, saturation of the neuronal lactate sensor requires much more lactate than that needed to fill astrocytic pools (3.2 vs. 0.4 μmol, respectively), with similar discordance when the baseline lactate level is 50% higher than in neurons (Figure 3c).
In arousal studies in awake mice, the time courses of normalized lactate levels in astrocytes, ISF, and neurons were superimposed (see figure 2e,f in Zuend et al., 2020), giving the impression that lactate was directly transferred from astrocytes through extracellular fluid to neurons even though these sensor-containing cell populations and probe-containing ISF were physically separated, i.e., depiction of an aggregate response.However, the amounts of lactate in the astrocytic and ISF compartments are very small compared with that in neurons (Figure 3c), suggesting that neuronal glycolysis may have increased more slowly but to a greater extent than in astrocytes during and after arousal.The importance of inclusion of compartmental volume fractions in data interpretation is further underscored by the ISF volume fraction being twice that of astrocytes and one-fourth that of neurons.Without knowledge of the true magnitudes of the evoked dip in astrocytic lactate concentration compared with the rapid rise in lactate level in ISF and delayed increase in astrocytes and neurons (see figure 2 in Zuend et al., 2020), the amounts of lactate transferred among these three compartments cannot be evaluated (note that the assignment of cellular origin requires additional proof, e.g., specific inhibition of cellular transporters).For example, Figure 3c shows that release of only 12% (0.1 μmol) of the intracellular neuronal lactate (0.8 μmol) at the early stage of arousal would increase the ISF lactate concentration by 50% (0.2 → 0.3 μmol) and would correspond to release of all of the astrocytic lactate, which is very unlikely during activation that involves stimulation of glycogenolysis in astrocytes.
Signaling properties of lactate may also influence intracellular lactate levels during lactate or pyruvate calibration infusions.Increased global influx of lactate from blood into brain during trans-acceleration assays raises extracellular lactate level (Figure 1Cb) and isoflurane-evoked increases extracellular lactate levels of 1.1 mM (see figure 2b in Zuend et al., 2020) are expected to stimulate norepinephrine release throughout the brain, secondarily enhancing glycogenolysis and astrocytic lactate production.Tang et al. (2014) discovered that receptor-mediated L-lactate signaling with an EC 50 of 0.68 mM excited locus coeruleus neurons and triggered norepinephrine release.Additionally, L-lactate is a neuromodulator that reduces neuronal activity with an IC 50 of 4.2 mM (Bozzo et al., 2013).Depending on local lactate levels, astrocytes may be activated and neurons inhibited by lactate TA B L E 2 Astrocyte and neuron volume fractions, ratios of cell type numbers and somatic volumes, cell and territorial volumes, and estimated cell volumes in laminae of cerebral cortex.Volumes are either cellular/subcellular volumes or territorial volumes.The territory represents the volume of neuropil occupied or monitored by a single astrocyte (Grosche et al., 2013), e.g., the volume occupied by one dye-filled astrocyte.The territory is on the order of 10-fold larger than the cellular volume (Chao et al., 2002, Wolff & Chao, 2004).None of the cited studies reported neuronal cellular volumes.

Species
b The mean numbers of astrocytes/mm 3 tissue volume are 17,600 and 29,800 for parieto-occipital cortex and visual cortex, respectively.The cell volumes and cell numbers for parieto-occipital cortex are for layers V and VI. c Cell volumes were estimated from the data of Gabbott and Stewart (1987) by multiplying 1/(number of cells/mm 3 ) by the volume fraction approximated as 9% for astrocytes in laminae II/III, IV, and V (average of 5 values, excluding layer I of piriform cortex), and 90% for neurons based on the tabulated values from separate studies.

TA B L E 2 (Continued)
signaling mechanisms.These mechanisms further complicate interpretation of procedures used to calibrate a lactate biosensor in vivo.

| Single-cell responses-Influence of different cellular volumes
A limitation of the above discussion of aggregate responses is that Laconic sensors report concentration changes per cell, and the overall, aggregate response involves the number of cells and volumes of each cell type in the region of interest, i.e., laminae II/III of somatosensory cortex in the Mächler-Zuend studies.We are not aware of any literature data for both astrocyte and neuron cell volumes for this lamina, but limited information is available for the rat area 17 visual cortex where the astrocyte volume fraction is 9.9% in layer II/III.This value is similar to that in other cortical structures and laminae in rats and mice, with a mean of 9% for laminae II-V (Table 2).Pyramidal cells account for >87% of the neurons in all lamina but they vary in size, with lamina II/III having medium-sized pyramidal neurons and deeper layers having larger pyramidal neurons (Peters et al., 1985;Peters & Kara, 1985).In rats, the ratio of the number of neurons to astrocytes per mm 3 varies with lamina ranging from 0.1 in the astrocyte-rich layer I to 1.9-5.3 in the other layers (Table 2; Gabbott & Stewart, 1987).In rat somatosensory cortex, the ratios of the numbers of neurons to astrocytes are 0.45 and 5 in lamina I and II/III, respectively, compared with 0.1 and 3.8 in the same laminae of rat visual cortex (Table 2).Neuronal soma are 2.5-7.4 times larger than those of astrocytes in laminae I-VI of visual cortex (Table 2), consistent with the need for bigger soma to support larger neuronal cellular volumes.In another study of the rat somatosensory cortex, neurons also outnumber total non-neuronal cells (most of which are astrocytes) in all lamina except layer I (Bass et al., 1971).
Territorial volumes reported in studies using different experimental procedures vary over an eight-fold range (10 000-83 200 μm 3 ) but generally appear to be smaller in cortex compared with hippocampus and larger in older rodents (Table 2).These territorial volume differences can arise from methodology (e.g., perfusion method and shrinkage correction, potential cellular volume changes in brain slices (i.e., during recovery from decapitation ischemia), electron microscopy, Golgi impregnation, dye filling), species and age of the animals, and genetic backgrounds (see discussion by Grosche et al., 2013).Whole-cell neuronal volume measurements in the literature, if any, were not found.
The Gabbott-Stewart study (1987) measured cell numbers per mm 3 in the 6 laminae of rat visual cortex (   2).These calculated values for astrocytic volume (Table 2: 3640-5490 μm 3 ) are similar to that reported by Wolff and Chao (5700 μm 3 ), both of which are lower than that of Chvátal et al.
(14 700 μm 3 ) (see Table 2).Nevertheless, any systematic methodological issues in the Gabbott-Stewart data (Table 2) should similarly affect the volume density of both neurons and astrocytes and calculated cellular volumes.The neuron-astrocyte volume ratio was 2.6 in lamina II/III, and this value was used to calculate the relative cellular amounts of lactate per unit volume of an astrocyte and a neuron (Table 2).
On a per cell basis, when astrocytes are fully depleted of lactate (0.41 × 10 −5 nmol), about 62% of the basal level of lactate would remain in neurons (Table 2).On the other hand, about half as much lactate would be required to saturate the astrocyte sensor compared with neuronal saturation (Table 2).Importantly, increasing the lactate concentration from the basal level in the astrocyte by the same amount as in a neuron within the same time interval will yield a higher rate of response of astrocytic intracellular concentration and larger concentration change.For example, increasing the amount in the astrocyte by about 0.2 × 10 −5 nmol raises the relative concentration by 50%, whereas in neuron, it increases the relative neuronal concentration by 18%.The impact of lactate amount applies to a physiological or experimental challenge, as well as to global flooding calibration procedures, all of which would be influenced by the intracellular lactate amounts.
To sum up, the calculated estimates of neuron and astrocyte cellular volumes are not as accurate as desired, but in the absence of any data for neurons and limited data for cellular volumes of astrocytes (Table 2), they are a first step toward cell-cell volume comparisons.
Nevertheless, the overall conclusions regarding the relative amounts of lactate that must be displaced or added to the basal amounts in neurons, and astrocytes are in the same direction for the aggregate (Figure 3c) and single-cell approach (Table 2).The change in amount per cell is smaller in the single-cell analysis than for the aggregate Different amounts of lactate must be removed from astrocytes and neurons to deplete their respective pools (Figure 3c, Table 2), and rapid interconversion and net conversion of pyruvate and lactate in blood and peripheral tissues generate lactate that will be taken up into brain cells, confounding interpretation of baseline lactate levels.For example, Figure 1Ca shows that astrocytes in brain of anesthetized mice attain a minimal Laconic signal shortly after cessation of the 3-min pyruvate infusion.The neuronal lactate signal is relatively constant during pyruvate infusion and then rises as the extracellular lactate level peaks (Figure 1Cb), whereas the astrocytic signal returns to the resting level (Figure 1Ca).
These observations can be explained by the smaller amount of lactate in astrocytes compared with neurons, whether calculated in aggregate or single cells.Less lactate must be removed to deplete the pool and less added to restore or exceed the resting concentration.The larger partial volume of the neurons contains a greater quantity of lactate at the same concentration as astrocytes and can "buffer" concentration changes and magnitude of the Laconic signals when small amounts of lactate are added to or removed from the neuronal pool.
The relative stability and larger rise in neuronal lactate levels in anesthetized mice (Figure 1Ca) may arise from pyruvatederived lactate preferentially entering neurons from blood (Figure 3b).In pyruvate-evoked trans-acceleration calibration in awake mice, Zuend et al. (2020) 2b,c).Lactate influx into brain from blood probably accounted for most of the rise in extracellular lactate concentration (Figure 1Cb), rather than efflux from brain cells, as suggested by Zuend et al. (2020).
To sum up, pyruvate-lactate equilibration, net interconversion, and intracellular lactate amount were not taken into account during baseline calibrations.The smaller amounts of lactate in astrocytes than those in neurons enhance their responses to concentration change during pyruvate infusions that produce large amounts of lactate in blood.

| Influence of volume and intracellular lactate amount on saturation Laconic calibration
The consequences of intravenous infusions of ammonium chloride plus lactate to saturate the Laconic sensor would also be subjected to uncertainties arising from rapid interconversion and net interconversion of lactate and pyruvate in blood, followed by competitive entry of both monocarboxylates into brain and brain cells, with preferential metabolism of lactate and pyruvate in neurons.The initial rise in intracellular lactate in astrocytes appeared to be faster than that in neurons during the saturation assay (Figure 1Cc), probably reflecting the smaller astrocytic pool size.Importantly, the actual lactate concentrations in neurons and astrocytes at sensor saturation were not proven to be identical.1Bb).When the saturation protocol was used, a wide range of intracellular levels was observed, with most cells not reaching saturation (Figure 1Bb).If the same equilibration calculation as above is used for 5 mM extracellular lactate and assuming no intracellular acidification due to lactate-H + co-transport, calculated intracellular level would be 3.15 mM, suggesting that lactate must also be generated by glycolysis and retained intracellularly to approach saturation levels of at least 10 mM (Figure 1Bb).If intracellular acidification takes place, then the calculated intracellular lactate level would be lower.The reason for the very high intracellular lactate (≥10 mM) levels in the presence of 5 mM lactate plus

| MAG NITUDE OF INTR ACELLUL AR L AC TATE " SURG E" DURING AROUSAL
The actual intracellular lactate concentrations in astrocytes and neurons that were described as "surges" during arousal were not determined.However, the "surge" size may be similar to the net ~1.1 mM rise in extracellular lactate reported by Zuend et al. (2020).
It is widely recognized that total brain lactate levels in tissue extracts and extracellular lactate levels in microdialysis assays approximately double during intense physiological sensory activation, rising from ~1 to ~2 μmol/g (Dienel, 2012).This is a large percentage change from baseline (100%), but, as discussed below, it is a quite small fraction of glucose plus glycogen consumed.Veech (1991) emphasized that lactate concentration alone only reports lactate concentration and more information is required to understand metabolic changes.
The following sections provide context for lactate "surges" by considering in vivo lactate concentration changes, first from studies of glycogenolysis, lactate specific activity, and the oxygen-glucose/ carbohydrate index, and second from assays of CMR glc during brain activation.to that of [1-or 6-14 C]glucose was close to the theoretical maximum of 0.5 (Dienel & Cruz, 2009).The SA ratio of 0.5 comes from production of one labeled lactate and one unlabeled lactate from one [1-or 6-14 C]glucose, and two moles of lactate reduce its SA to half that of glucose.These findings are consistent with (i) blood-borne The lactate equivalents of glycogen consumed during 5-min sensory stimulation of awake rats (2.7 μmol/g glucosyl units consumed × 2 lactate/glucosyl unit = 5.4 lactate equivalents) greatly exceed net accumulation of lactate (1.1 μmol/g) in brain (Cruz & Dienel, 2002;Dienel et al., 2002).Lactate retained in brain regardless of its metabolic origin corresponded to ~20% of the lactate equivalents of glycogen consumed, strongly supporting the conclusion that there must be rapid and substantial lactate release from activated brain.Thus, the lactate concentration in brain cells is not a fuel "reservoir" as claimed by others; instead, it is a small pool with high through flux.

| Glycogenolysis reveals lactate compartmentation and lactate release
Inclusion of glycogen utilized in the calculation of the oxygenglucose index (i.e., OGI = CMR O2 /CMR glc versus oxygen-carbohydrate index, OCI = CMR O2 /(CMR glc + CMR lac + CMR glycogen )) reduced the ratio from 5.5 to 2.8 (see table 4 in Dienel & Rothman, 2019).This is strong evidence that most glycogen-derived lactate is not oxidized (otherwise oxygen and total carbohydrate use would be stoichiometrically matched) and, therefore, not shuttled to neurons and oxidized.
Instead, most of this glycogen-derived lactate must have been released from brain, accounting for lack of effects on lactate SA in tissue extracts that would contain glycogen-derived lactate and would dilute the SA below 0.5 in the above experiments.These findings extend the calculations demonstrating the fall in global OGI calculated from arteriovenous differences for oxygen and glucose during arousal and brain activation in awake rats and humans (Madsen et al., 1995;Madsen et al., 1998;Madsen et al., 1999;Schmalbruch et al., 2002).The values for glycogen included in the above OCI calculation for rats are the net reduction in glycogen concentration per minute during the 5-min experimental interval, assuming a linear decrease in glycogen level with time during activation.In fact, metaanalysis of available data from rodent and human brain strongly supports the model in which astrocytic glycogenolysis spares bloodborne glucose for glycolytic and oxidative metabolism by neurons during activation, sharply contrasting the predictions of the lactate shuttle model that are discordant with measured data from in vivo studies (Rothman et al., 2022).
Previous studies suggested that glycogenolysis provided lactate to neurons to fuel memory consolidation in rodents (Newman et al., 2011;Suzuki et al., 2011) and claimed that β 2 -adrenergic receptor activity was required for this process (Gao et al., 2016).However, mammalian glycogenolysis is stimulated by β 1 , not β 2 , adrenergic receptors (Hertz et al., 2015;Quach et al., 1988;Xu et al., 2014), whereas in the day-old chick, β 2 receptors trigger glycogenolysis and are involved in taste-aversion memory (Gibbs, 2016).There is no question that glycogen is required for rodent memory consolidation (Duran et al., 2013;Duran et al., 2019), but its actual functions remain to be established.Alternative explanations for putative roles for glycogen-derived lactate in neurotransmission and memory formation were evaluated in detail by Dienel (2019b).
To sum up, the non-specific β-adrenergic receptor antagonist, propranolol, reduced glycogenolysis and lactate production (Zuend et al., 2020), but assays of lactate level itself do not quantify contributions of different pathways and nor account for lactate efflux to blood.When evaluating lactate responses to arousal in glycogen synthase 1 knockout mice, it is important to recognize that impairment of glycogenolysis causes large compensatory increases in utilization of blood-borne glucose (Dienel et al., 2007).Since astrocytes use glycogen to fuel their activities during activation, it is reasonable to assign a large fraction of this compensatory CMR glc response to astrocytes that in the absence of glycogen compete with neurons for blood-borne glucose.

| Comparison of rise in lactate level with glucose utilization
In order to interpret lactate level changes in the astrocyte as a quantitative increase in glycolysis from glucose or glycogen requires the relationship between lactate concentration and non-oxidative astrocytic glycolysis be known.However, based on two in vivo studies, the steady-state elevation of total lactate is only a small fraction of the increase in total glucose/glycogen metabolism over the same time period.Therefore, the pathways of lactate transport away from the activated region need to be known.For a quantitative example illustrating the problem, the net increases in brain lactate level of ~1 μmol/g during a 5 min of sensory stimulation interval were associated with a modest increase in CMR glc of ~20% (Dienel et al., 2002).In that study, calculated cortical CMR glc rose from 1 to ~1.2 μmol/g/min, and in 5 min consumed 6 μmol glucose/g or 12 pyruvate-lactate equivalents.Glycogen consumed during this interval was equivalent to 2.7 μmol glucose or 5.4 lactate-pyruvate, for a total of 17.4 lactate-pyruvate from glucose and glycogen.The net accumulation of ~1 μmol/g lactate during this 5-min experimental interval and retained in the tissue corresponds to 1/17.4 or only ~6% of the blood-borne glucose plus endogenous glycogen consumed.
Similar analyses drew the same conclusion that metabolite concentration changes do not report pathway fluxes (see figure 5 in Dienel et al., 2007).
Separate, independent studies of activation in different laboratories using parallel CMR glc assays with [ 14 C]DG or [ 18 F]FDG and [ 14 C] glucose showed that labeled glucose, products of which are trapped via the oxidative pathways, underestimated CMR glc determined at the hexokinase step with labeled DG or FDG by ~50% (reviewed in Dienel & Cruz, 2016).We note that if brain glucose concentrations fall below ~0.5 μmol/g, the value of the lumped constant of the DG method, the factor used to convert DG phosphorylation rate to glucose utilization rate (Sokoloff et al., 1977), must be adjusted upwards to account for reduced competition of DG with glucose for transport and phosphorylation (i.e., more DG is phosphorylate with lower glucose levels); in contrast, the lumped constant is relatively stable with increases in brain and plasma glucose concentration (Dienel et al., 1991;Schuier et al., 1990;Suda et al., 1990).In the major studies in which incomplete trapping of products of labeled glucose was identified by comparison with parallel DG assays, brain glucose levels were measured and demonstrated to be stable in extracellular fluid and brain tissue (e.g., Adachi et al., 1995;Collins et al., 1987;Cruz et al., 1999;Cruz et al., 2007).Ackermann and Lear (1989) did not measure the glucose level but adjusted the value for the FDG lumped constant upwards to account for the presumed fall in brain glucose level in hippocampus to ~1 μmol/g, based on the previous study by Cremer et al. (1988) on the effects of kainate on glucose transport, phosphorylation, and concentrations.In other words, a change in the value of lumped constant is not a confounding issue in conclusions drawn from the above studies, and label corresponding to about half of the glucose consumed was released from the brain within about 5 min.Phosphorylated glycolytic intermediates are retained in cells, whereas pyruvate and lactate are diffusible.Lactate levels are about 10-13 times higher than pyruvate (Siesjö, 1978;Veech et al., 1979), so lactate efflux from brain is the major cause for underestimation of CMR glc with labeled glucose.
Studies in cultured neurons and brain slices also support increased neuronal glucose uptake, glycolysis, and lactate production, not lactate uptake, under activating conditions (Ashrafi et al., 2017;Ashrafi & Ryan, 2017;Diaz-Garcia et al., 2017;Diaz-Garcia & Yellen, 2019;Yellen, 2018).The bottom line is that the amount of lactate retained in the tissue is a very small fraction of glucose consumed and most lactate generated from glucose and glycogen rapidly leaves the brain.Thus, the lactate "surge" described by Zuend et al. (2020) represents about 6% of the carbohydrate metabolized.
If lactate were oxidized, then the label would accumulate in amino acids, and oxygen consumption would stoichiometrically match glucose utilization, neither of which occur.

| CON CLUDING COMMENTS
The genetically encoded Laconic lactate biosensor has been used to evaluate lactate concentration changes under a wide variety of experimental conditions in cultured astrocytes and in living brain.
These are important, valuable advances based on real-time, cellular metabolite assays.However, they have the limitations that concentration changes are qualitative, they report a single glycolytic metabolite, and data interpretation is very limited in scope and context.
In vivo calibrations of the baseline and saturation levels of the sensor led to the conclusion that resting lactate levels in astrocytes are higher than those in neurons.However, calibration studies did not account for four critical aspects of the procedure: metabolism and

F
I G U R E 1 Laconic FRET signals and two-point calibration procedures.(A) Semilogarithmic plot of net change in FRET ratio as function of lactate (Lac) concentration in vitro.From figure 2b in San Martin et al. (2013) Copyright © 2013, the authors reproduced with permission for open-access article.(B, a) Calibration of the Laconic sensor.Intracellular lactate level in cultured astrocytes was first depleted by superfusion with 10 mM pyruvate (pyr) for 3 min (shaded area), followed by superfusion with 5 mM lactate ([lac]o, lactate in superfusate) plus 2 mM glucose, then 1 mM lactate.Note the apparent sensor saturation at 5 M lactate.Values are normalized to baseline ratio.(b) Resting cultured astrocytes were subjected to the two-point calibration protocol illustrated in panel 1Ba, and intracellular lactate concentrations (top x-axis) were calculated and plotted against sensor saturation (bottom x-axis).The equilibrium lactate level, MCT eq , of 0.63 mM was calculated from intracellular pH and medium lactate and pH levels.From figure 1b,c in Sotelo-Hitschfeld et al. (2015), where details describing these results are provided.Copyright © 2015, the authors reproduced with permission of JNeurosci.Creative Commons Attribution 4.0 International License.(C, a) Comparison of Laconic lactate sensor and Pyronic pyruvate sensor ratio changes in astrocytes and neurons during intravenous infusion of pyruvate (Pyr) (4 mmol/kg body weight in 3 min).Normalized to corresponding baseline signal.(b) Increase in extracellular lactate concentration determined with calibrated biosensor probe inserted into the tissue.(c) Laconic sensor saturation procedure.Laconic and Pyronic responses to intravenous infusion for 15 min of NH 4 Cl (4 mmol/kg body weight) + Lac (8 mmol/kg), followed by Lac (4 mmol/ kg for 3 min), then by Pyr (4 mmol/kg for 3 min).Normalized to saturation levels.(d) Intracellular lactate concentration changes due to intravenous infusions of Pyr (4 mmol/kg for 3 min) to deplete intracellular lactate by trans-acceleration of lactate efflux via monocarboxylic acid transporters (MCT).(e) Illustration of trans-acceleration in which substrate (S) outside (out) the cell binds to the MCT (MCT-S) and is carried more quickly (rate k 2 ) across the plasma membrane compared with MCT without substrate (k 1 ), enhancing efflux of the intracellular substrate.Reproduced from figure 5 in Mächler et al. (2016), Copyright © 2016, Elsevier Inc., with permission.
Zuend et al. (2020) assessed the temporal changes in Laconic signals under different arousal paradigms in awake mice, thereby overcoming the limitations arising from the use of anesthesia in the Mächler et al. (2016) study.Comparisons of astrocytic and neuronal responses

[ 1 -
13 C]lactate and [U-13 C 3 ]pyruvate into anesthetized dogs and compared [1-13 C]-and [U-13 C 3 ]lactate enrichments under basal and hyper-insulinemic conditions.The enrichments of [1-13 C]-and [U-13 C 3 ]lactate had similar temporal profiles, and the 1-13 C/U-13 C ratios were not significantly different.These data along with the 10-to 15-fold larger lactate pool compared with that of pyruvate in blood support their conclusion that circulating lactate and pyruvate are functionally represented as a single pool with most of the label in the lactate pool regardless of the tracer infused.Romijn et al. (1994) calculated that the half-life of labeled lactate in human blood was 6 min at rest versus 2.5 and 7 min during heavy and light exercise, respectively. 13C equilibration occurred rapidly regardless of changes in blood lactate level, consistent with corresponding adjustments in the concentrations of circulating unlabeled blood lactate and pyruvate arising from tissue metabolism.Consistent with the above studies, Gonzalez et al. (2005) reported that at 1 min after intravenous bolus injection of 9 mmol/kg of [3-13 C]pyruvate into anesthetized mice, [3-13 C]pyruvate predominated in serum with little labeled lactate and alanine and no labeled glucose.However, the amount of [3-13 C]lactate in brain extracts exceeded that of [3-13 C]pyruvate, indicating a rapid pyruvate-to-lactate metabolism in brain, as observed by Cremer et al. (1978) who used intracarotid injection of tracer doses of [ 14 C]pyruvate (see below Section 4.

F
Intravenous pyruvate infusion rapidly and substantially elevates blood lactate concentration.(a) Schematic of experimental paradigm for intravenous pyruvate infusion-evoked trans-acceleration of lactate efflux to deplete intracellular lactate levels.(b, c) Dynamic responses of intracellular lactate level during and after pyruvate infusion (4 mmol/kg body weight in 3 min) in neurons (b) and astrocytes (c).(d) Stability of intracellular lactate level during and after saline infusion.(e, f) Blood glucose and lactate levels during and after pyruvate (e) or saline infusion (f).Note the rise in blood lactate concentration from a baseline level of ~3.3 mM at time T2 to ~13.3 mM at time T6 (about 1 min after onset of pyruvate infusion), with a decline to ~8.3 mM at time T7 (panel e).The red arrows superimposed on the figure connect the time T6 in neurons, astrocytes, and blood, linking the beginning of the increase in neuronal lactate level (b), the dip in astrocytes (c), and the elevated blood lactate level (e).Reproduced from Extended Data figure 9 in Zuend et al. (2020), Copyright © 2020, Springer Nature with permission.Abbreviations: [Lac] I , intracellular lactate concentration; [Pyr] E , extracellular pyruvate concentration; T, time.
established as identical and normalization to the saturation signal at different lactate concentrations would cause artifacts.Additional concerns related to saturation signals arise from use of near-toxic doses of ammonia, stimulation of astrocytic energy demand by ammonia, lactate-pyruvate isotopic interconversion and substantial net conversion in blood and peripheral tissues within the time frame of the Laconic sensor calibration procedure, and preferential oxidation of lactate and pyruvate in neurons.The influence of the anesthetic mixture (fentanyl, midazolam, and medetomidine) used by Mächler et al. ( tween optical signal intensity per unit volume and lactate concentration in that cell type and experimental condition (e.g., in vitro vs. in vivo calibrations in different cell types in which K could be influenced by the expression of the sensor (the number of sensors in the compartment of interest), laser power that influences signal intensity, interactions of the sensor with nearby proteins, and by local conditions including pH and levels of interfering compounds; see Yellen & Mongeon, 2015, Koveal et al., 2020).[Lac] b is the baseline intracellular lactate concentration in the cellular compartment, and Q b is the quantity of lactate (number of molecules) in the compartment, [Lac] b Due to lack of neuronal volume data, the Gabbott-Steward cell density values were used to estimate the cellular volumes of neurons and astrocytes as follows: [average volume fraction for astrocytes (9%) or neurons (90%)] times [1/number of respective cells per mm 3 ] (Table analysis, but taking into consideration the smaller cellular volume and lower number of astrocytes per unit volume to convert single-cell sensor signals to aggregate signals would yield more-comparable data for the two approaches.These findings emphasize the importance in biosensor studies in any tissue or cell culture of measuring the volumes or relative volumes of cells of interest in order to better understand intracellular concentration changes.If not determined, challenges designed to evoke cell-type specific changes in metabolism and lactate concentration may give misleading data when comparisons of relative or normalized signal changes are made between cell types and cells with different volumes.In addition, the subcellular number and location of biosensors in each cell type are important to determine, since smaller magnitude of responses would be anticipated for lower numbers of sensors.

2
mM glucose followed by 1 mM lactate has not been established, and the basis for large signal variability among the astrocytes is not known.Of related interest,Bekdash et al. (2021) reported that the Laconic sensor protein expressed in NIH3T3 cells also shows a wide range of responses to 10 mM lactate, and protein analysis of cell extracts revealed two bands on western blot suggesting that Laconic may be degraded or truncated and/or cleaved, perhaps influencing the fluorescence change (see figure4cinBekdash et al., 2021).In other words, degradative inactivation of some of the sensors may influence the signal response and contribute to variability among cells.To sum up, unresolved issues with Laconic sensor calibration in astrocytes and neurons prevent accurate comparisons of actual concentrations in these cell types.Rapid metabolism of lactate and pyruvate in blood and rapid, preferential metabolism of both monocarboxylates in neurons, and the impact of cellular volume per cell or in aggregate provide alternative explanations for observed Laconic signals, and the existence of an astrocyte-neuron gradient is challenged.

[
14 C]glucose being the predominant source of the lactate recovered from brain extracts and (ii) rapid release of glycogen-derived lactate from brain.The lactate SAs were assayed in extracts, so retention of unlabeled, glycogen-derived lactate would reduce the SA in the extracts that combine all lactate pools.The basis for apparent lactate compartmentation is not established, but it could arise from separate glycolytic pathways that metabolize unlabeled glycogen in astrocytes and blood-borne labeled glucose in neurons.

Injection route Labeling time Ratio of SA-glutamine / SA-glutamate after labeling by tracer amounts of different 14 C-labeled precursors
Rapid labeling of the large neuronal glutamate pool by labeled lactate and pyruvate.
The blood lactate was more highly enriched with 13 C at 2 min than at 5 min, and at 1 min the brain [ 13 C] lactate peak height exceeded that of [ 13 C]pyruvate.These findings suggest uptake of [ 13 C]pyruvate into peripheral tissue followed by its conversion to [ 13 C]lactate and release to blood followed by its uptake into brain, as well as rapid conversion of [ 13 C]pyruvate to [ 13 C]lactate in the brain (as evident in the intracarotid injections of Cremer et al. (1978)enous dose of [3-13 C]pyruvate (9 mmol/kg), the blood [ 13 C]pyruvate level peaked within 0.5 min, then declined while blood [ 13 C] lactate level increased (Table1).traceramounts of [ 14 C]pyruvate in theCremer et al. (1978)study (Table1)), based on higher [ 13 C]pyruvate blood levels at 0.5-1 min.Labeling of [4-13 C]glutamate by [3-13 C]pyruvate was not affected by pre-treatment with the gliotoxin, fluoroacetate, whereas label incorporation into [4-13 C]glutamine was reduced by half, consistent with predominant neuronal metabolism of the blood-borne [ 13 C]

of the Laconic sensor signal: Are cellular lactate concentrations equal?
(Mathiisen et al., 2010)r and large, loading doses of pyruvate are rapidly converted to lactate in blood and brain, and both pyruvate and lactate are predominantly metabolized in neurons to label the "large," neuronal glutamate pool regardless of dose.Rapid, substantial pyruvate-lactate interconversion confounds interpretation of trans-acceleration studies using pyruvate to deplete intracellular lactate levels.High coverage of the brain vasculature by astrocytic endfeet(Mathiisen et al., 2010)may lead to the inference that astrocytes have preferential access to substrates that traverse blood-brain barrier, but the actual route(s) of lactate-pyruvate entry into brain and ultimately to neurons is unknown.A large fraction of blood-borne pyruvate is reduced to lactate in brain within seconds, then predominantly metabolized via the neuronal oxidative pathways with high label incorporation into glutamate.In electrically stimulated neurons in acute hippocampal slices and in brain of awake mice, the intra- Lerchundi et al. (2015)17)ared with [4-13 C]glutamine (GlnC4), giving a fractional enrichment ratio of [GlnC4]/[GluC4] similar to that for [1-13 C]glucose (0.78 and 0.87, respectively,Boumezbeur et al., 2010).(AlsoseeDuarteetal., 2015and their cited references for studies of lactate infusion in rodents that provide evidence for preferential metabolism of lactate in neurons.)Theseratioscontrast the glutamine/glutamate fractional enrichment ratio of 2.9 obtained in human brain with [2-13 C]acetate that is preferentially oxidized in astrocytes(Boumezbeur et al., 2010).As described above, these infusions also increased brain cellular lactate substantially more than calculated from the Laconic sensor in mice.celularlactateconcentrationassayed with the Laconic biosensor quickly increased with and without inhibition of monocarboxylic acid transporters, indicating that the rise in lactate level is due to neuronal glycolysis; it is not due to lactate import, a finding consistent with the rapid stimulus-evoked rise in neuronal NADH concentration (i.e., the NADH/NAD + ratio increased) that was assayed with the Peredox biosensor(Diaz-Garcia et al., 2017).Thus, greater uptake of lactate and pyruvate into neurons followed by neuronal metabolism is anticipated during in vivo Laconic calibrations, slowing or preventing neuronal lactate depletion.In addition, pyruvate flooding during trans-acceleration assays may artifactually reduce Laconic signals due to pyruvate interference with the lactate signal, especially at lactate concentrations less than about 0.5 mM (see figure2gin SanMartin et al., 2013).Two issues can influence baseline calibrations, rapid conversion of pyruvate to lactate and pyruvate interference with the lactate Laconic signal.4.3 | SaturationLerchundi et al. (2015), intravenous infusion of NH 4 Cl (4 mmol/kg, 500 mM solution) plus sodium lactate (8 mmol/kg, 1 M solution) for 15 min followed by sodium lactate (4 mmol/kg, 500 mM solution for Abbreviations: A, astrocyte; Cx, cortex; GFAP, glial fibrillary acidic protein; ML molecular layer; N, neuron; N/A, ratio of value for neuron to value for astrocyte; SM, stratum moleculare; SR, stratum radiatum. a

Table 2 )
Takata and Hirase (2008)3)reported a similar number of astrocytes, 15 696 astrocytes/mm 3 , in somatosensory cortex laminae II-IV.Using this value and the neuron/astrocyte ratio of 5 for somatosensory cortex layer II/III byTakata and Hirase (2008), the neuronal number is 78 480/mm 3 , similar to that of Gabbott-Steward in Table2.
If not, then normalization to the peak signal would not provide accurate relative values for baseline lactate levels in neurons and astrocytes.