Glucose sparing by glycogenolysis (GSG) determines the relationship between brain metabolism and neurotransmission

Abstract

Over the last two decades, it has been established that glucose metabolic fluxes in neurons and astrocytes are proportional to the rates of the glutamate/GABA-glutamine neurotransmitter cycles in close to 1:1 stoichiometries across a wide range of functional energy demands. However, there is presently no mechanistic explanation for these relationships. We present here a theoretical meta-analysis that tests whether the brain’s unique compartmentation of glycogen metabolism in the astrocyte and the requirement for neuronal glucose homeostasis lead to the observed stoichiometries. We found that blood-brain barrier glucose transport can be limiting during activation and that the energy demand could only be met if glycogenolysis supports neuronal glucose metabolism by replacing the glucose consumed by astrocytes, a mechanism we call Glucose Sparing by Glycogenolysis (GSG). The predictions of the GSG model are in excellent agreement with a wide range of experimental results from rats, mice, tree shrews, and humans, which were previously unexplained. Glycogenolysis and glucose sparing dictate the energy available to support neuronal activity, thus playing a fundamental role in brain function in health and disease.

Introduction

Despite intense research about the energetic requirements of neuronal signaling, it is still not known why the brain has an obligatory need for glucose (Glc) to fuel functional processes. ¹ Similarly, we do not have yet a fundamental understanding of how during increased neurotransmission, i.e., glutamate/GABA-glutamine (Glu/GABA-Gln) cycle (that we refer to as ${\text{V}}_{\text{NTcycle}}$ ), there is a large increase in nonoxidative glucose and glycogen metabolism despite the 16- and 10-fold lower energy yields, respectively, than is produced by complete glucose oxidation. ² Thus far, models of brain energetics have been mostly based on the astrocyte-to-neuron lactate shuttle (ANLS) hypothesis, in which the reuptake of neuronally-released glutamate by astrocytes is assumed to trigger glucose and glycogen metabolism in these cells followed by lactate transfer to neurons for fueling signaling processes.^3,4 However, a range of studies has found that several essential stoichiometric predictions of the ANLS model cannot be reconciled with experiments (for a review see ⁵ ).

An alternative to glycogen providing fuel to the neurons as lactate ⁶ is for glycogenolysis to replace astrocytic glucose consumption, thereby making more glucose available for neurons.^7–13 In this study, we introduce a novel comprehensive model of brain metabolism that incorporates the concepts of the glycogen shunt, ¹⁴ glucose sparing,^7,9 astrocytic active K⁺ uptake and buffering, ¹⁵ and neuronal coupling between neurotransmitter glutamate oxidation and glutamate synthesis, ¹⁶ which we collectively refer to as the Glucose Sparing by Glycogenolysis (GSG) mechanism (Figure 1). We show that the GSG model accounts for the experimental outcomes of enhanced signaling during brain activation. The derivations of the main quantitative relationships used for the analysis are presented below, while the full model is detailed in the supplementary information (SI).

Figure 1.

Schematics of the major metabolic pathways of the GSG model. (a) shows a schematic of the fluxes of neuronal and astrocytic glucose metabolism for Glu-/GABA/-Gln cycle rates at or below the resting awake (RA) state, identified by ${\text{V}}_{\text{NTcycle}-\text{RA}}$ . Under the RA condition the net rate of glycogenolysis ( ${\text{V}}_{\text{Gnet}}$ ) is equal to 0. The pseudo-MAS (PMAS) is a mechanism that couples glycolytic production of NADH in neuronal cytoplasm with NADH shuttling to and oxidation in mitochondria during the conversion of astrocyte-derived glutamine into neurotransmitter glutamate (see SI Section 6 and Fig. SI-3 for details); both the MAS and PMAS involve oxidation-reduction and transamination reactions. The dotted lines from Lac to the plasma membranes of astrocytes and neurons represent lactate release that corresponds to a small fraction (about 5%) of the glucose metabolized from the cells and from brain at or below the RA state.

(b) shows the incremental fluxes of glucose and glycogen, as well as ATP synthesis, due to an increase in ${\text{V}}_{\text{NTcycle}}$ above RA state ( $\Delta {\text{V}}_{\text{NTcycle}}>0$ ). The flux values and predicted stoichiometries are derived in SI Sections 2-5. The majority of pyruvate from glycogenolysis leaves the astrocyte as lactate with a small fraction being oxidized as part of the glutamate and GABA oxidation and resynthesis pathways. Major pathways of ATP synthesis ( $\Delta {\text{V}}_{\text{ATP}}$ ) coupled to the rates of glucose and glycogen metabolism are indicated in green. Major pathways of ATP consumption are indicated in red, the largest being assigned to the neuronal and astrocytic Na⁺,K⁺-ATPase (see SI Section 5). For the derivation of the coefficients for ATP synthesis rates see SI Section 2, Eqs. SI-25 and SI-26. For derivation of the coefficients for astrocytic and neuronal ATP consumption by the Na⁺, K⁺-ATPase, see SI Section 5 and Eq. SI-64. The solid lines from Lac to the plasma membranes of astrocytes and neurons represent release of larger amounts of lactate from the activated cells and from brain.

Abbreviations: Glc-6-P, glucose-6-phosphate; HK, hexokinase; Pyr, pyruvate; Lac, lactate; Mito, mitochondria; Glu, glutamate; GABA, γ-aminobutyric acid; Gln, glutamine; MAS, malate-aspartate shuttle; CMR, cerebral metabolic rate; V denotes rates for different pathways identified by subscripts and are defined in the ‘Theory and Calculations' within the main text.

Theory and calculations

Main assumptions underlying the GSG model

1) We assume that the maximum rate of glucose transport ( ${\text{V}}_{\text{GT}-\text{max}}$ ) for plasma glucose concentrations under fed and physiological fasting conditions can be calculated using the well-established reversible two state Michaelis-Menten model with transport parameters obtained from in vivo MRS measurements. ¹⁷ When the ratio of plasma glucose ( ${\text{G}}_0$ ) to intracellular glucose ( ${\text{G}}_{\text{i}}$ ) concentration is very high, backward transport of glucose can be neglected, whereby net glucose transport becomes equal to the unidirectional inflow rate, ${\text{V}}_{\text{GT}-\text{max}}={\text{CMR}}_{\text{glc}-\text{max}}{\text{=T}}_{\text{max}}\text{/}[({\text{K}}_{\text{t}}/{\text{G}}_0)+1]$ where ${\text{CMR}}_{\text{glc}-\text{max}}$ is the maximal rate of glucose utilization ( ${\text{CMR}}_{\text{glc}}$ ), ${\text{T}}_{\text{max}}$ is the maximum glucose transport capacity and ${\text{K}}_{\text{t}}$ is the transporter affinity for glucose. In absence of additional descriptive subscripts, CMR_glc refers to the total glucose consumption rate of both astrocytes (A) and neurons (N), from both oxidative (CMR_glc-ox) and nonoxidative (CMR_glc-nonox) pathways.

2) We assume that net glycogenolysis ( ${\text{V}}_{\text{Gnet}}$ ) is negligible ( ${\text{V}}_{\text{Gnet}}=0$ ) for neural activity levels at or below the resting awake (RA) state (Figure 1(a)), as supported by measurements of glycogen turnover in rat and human brains,^18,19 while it increases above RA during physiological stimulation ²⁰ or during non-physiological states such as seizure. ²¹ We define net glycogenolysis as ${\text{V}}_{\text{Gnet}}={\text{V}}_{\text{GPhos}}-{\text{V}}_{\text{GSyn}}$ where V_GPhos and V_GSyn are rates of glycogen breakdown and synthesis respectively, and incremental neurotransmission as $\Delta {\text{V}}_{\text{NTcycle}}={\text{V}}_{\text{NTcycle}}-{\text{V}}_{\text{NTcycle}-\text{RA}}$ , and because ${\text{V}}_{\text{Gnet}-\text{RA}}=0$ then $\Delta {\text{V}}_{\text{Gnet}}={\text{V}}_{\text{Gnet}}-{\text{V}}_{\text{Gnet}}{\hspace{0.17em}}_{-\text{RA}}={\text{V}}_{\text{Gnet}}$ . Glycogen concentration and rates of glycogenolysis are expressed in terms of glucose units.

3) We assume that astrocytes completely support their additional ATP needs above the RA state (i.e., for $\Delta {\text{V}}_{\text{NTcycle}}>0$ ) by switching from oxidation of glucose to utilization of glycogen (nonoxidative and oxidative glycogenolysis), i.e., during stimulation there is no incremental astrocytic glucose consumption: $\Delta {\text{CMR}}_{\text{glc}-\text{A}}={\text{CMR}}_{\text{glc}-\text{A}}-{\text{CMR}}_{\text{glc}-\text{A}-\text{RA}}=0$ , and $\Delta {\text{V}}_{\text{Gnet}}>0$ (Figure 1(b)).

4) We assume that when glycogen is not available above the RA state, for example during pharmacological inhibition of glycogen degradation or prior complete glycogen depletion, astrocytes use nonoxidative (i.e., glycolytic) glucose metabolism to meet their ATP needs. We can express this situation as $\Delta {\text{CMR}}_{\text{glc-}\hspace{0.17em}\text{A}}>0$ and $\Delta {\text{V}}_{\text{Gnet}}=0$ . Notably, in the case of inactive glycogenolysis the compensatory increase in astrocytic glucose consumption can be expressed as $\Delta {\text{CMR}}_{\text{glc}-\text{A}|\Delta \text{VGnet}=0}=(3/2)\times \Delta {\text{V}}_{\text{Gnet}|\Delta \text{VGnet}>0}$ where the factor of (3/2) takes into account that more glucose is needed to produce the same amount of ATP normally generated by glycogenolysis, as supported by the compensatory increase in glucose utilization reported in rat cerebral cortex upon inhibition of glycogenolysis.^22,23 In the following, unless explicitly specified, we will generally refer to the variable of interest ${\text{X}}_{\text{i}}$ during conditions of active glycogenolysis (i.e., ${\text{X}}_{\text{i}}={\text{X}}_{\text{i}}{\hspace{0.17em}}_{|\Delta \text{V}\text{Gnet}>0}$ ).

5) We assume that neuronal glutamate (and GABA) synthesis for neurotransmission is linearly proportional to neuronal glucose oxidation, in agreement with extensive experimental findings, ²⁴ as well as the extended meta-analysis we performed (see Figure 5 and Tables SI-3, SI-4, and SI-5). There are several neuronal mechanisms that could explain this proportionality, such as the pseudo-malate-aspartate shuttle (PMAS),^16,25 which we address in the Discussion.

Figure 5.

Plots of meta-analysis data for ${\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ versus ${\text{V}}_{\text{NTcycle}}$ . Plots of (a) ${\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ versus ${\text{V}}_{\text{NTcycle}}$ , (b) ${\text{CMR}}_{\text{glc}-\text{ox}-\text{N}-\text{Glu}}$ versus ${\text{V}}_{\text{NTcycle}-\text{Glu}}$ , (c) ${\text{CMR}}_{\text{glc}-\text{ox}-\text{GABA}}$ versus ${\text{V}}_{\text{NTcycle-GABA}}$ and (d) ${\text{CMR}}_{\text{glc}-\text{ox}-\text{N}-(\text{Glu}+\text{GABA})}$ versus ${\text{V}}_{\text{NTcycle}}{\hspace{0.17em}}_{-(\text{Glu}+\text{GABA})}$ . Best fit slopes and CI_95% are shown by solid and dashed black lines, respectively. See Tables SI-3, SI-4, and SI-5 for values and references. All oxidation rates are expressed in glucose units. The best fit lines and statistics were calculated from rat cerebral cortex data only (black dots). In panel a, data from mouse (blue), tree shrew (green) and human (orange) (Table SI-9) are plotted along with the rat data.

Main predictions of the GSG model

In this section we derive the main predictions of the GSG model, which are summarized in Table SI-1. From Assumption (5) we have a linear relationship between neuronal glucose oxidation and ${\text{V}}_{\text{NTcycle}}$ with a slope ${\text{C}}_{\text{VNTcycle}}$ :

$$\Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}={\text{C}}_{\text{VNTcycle}}\times \Delta {\text{V}}_{\text{NTcycle}}$$ (1)

Experimental measurements obtained when ${\text{V}}_{\text{NTcycle}}$ was above the resting awake state show that the rates of oxidative and nonoxidative glucose metabolism are approximately equal (Tables SI-2, SI-6, and SI-7, and SI Section 7.3). Note that both rates of oxidative and nonoxidative glucose metabolism are here expressed in units of glucose to avoid potential confusion arising from expression of glucose oxidation in triose units (i.e., the pyruvate dehydrogenase complex rate that is twice the hexokinase rate). Based on assumption 3 we assign these increases to the neuron, which gives $\Delta {\text{CMR}}_{\text{glc}-\text{N}}=\Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}+\Delta {\text{CMR}}_{\text{glc}-\text{nonox}-\text{N}}=\text{2}\times \Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ , which, taking equation (1) into account, gives the following linear relationship:

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}}=2\times \Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}=2\times {\text{C}}_{\text{VNTcycle}}\times \Delta {\text{V}}_{\text{NTcycle}}$$ (2)

Since in our model $\Delta {\text{CMR}}_{\text{glc}-\text{A}}=0$ (Assumption (3)), this gives a linear dependence between total incremental glucose consumption and neurotransmission (i.e., $\Delta {\text{CMR}}_{\text{glc}}=2\times {\text{C}}_{\text{VNTcycle}}\times \Delta {\text{V}}_{\text{NTcycle}}$ ). Neurons have minimal glycogen reserves, ²⁶ so their maximum rate of signaling is limited by the maximum rate at which glucose can be transported and phosphorylated by hexokinase. As stated above, under conditions of complete glucose sparing, glycogenolysis replaces incremental astrocytic glucose metabolism (i.e., $\Delta {\text{CMR}}_{\text{glc}-\text{A}}=0$ ), thus the maximum rate and incremental rate of neuronal glucose consumption are respectively given by:

$${\text{CMR}}_{\text{glc}-\text{N}-\text{max}}={\text{CMR}}_{\text{glc}-\text{N}-\text{RA}}+\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}={\text{V}}_{\text{GT}-\text{max}}-{\text{CMR}}_{\text{glc}-\text{A}-\text{RA}}-\Delta {\text{CMR}}_{\text{glc}-\text{A}}={\text{V}}_{\text{GT}-\text{max}}-{\text{CMR}}_{\text{glc}-\text{A}-\text{RA}}$$ (3)

and

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}={\text{V}}_{\text{GT}-\text{max}}-{\text{CMR}}_{\text{glc}-\text{RA}}$$ (4)

The value of ${\text{V}}_{\text{GT}-\text{max}}$ is usually measured as the ratio ${\text{V}}_{\text{GT}-\text{max}}{\text{/ CMR}}_{\text{glc}-\text{RA}}$ . Therefore, to allow direct comparison with measured values we multiplied the terms on the right side of equation (4) by $\text{1}={\text{CMR}}_{\text{glc}-\text{RA}}{\text{/CMR}}_{\text{glc}-\text{RA}}$ and rearranged to give:

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}=({\text{V′}}_{\text{GT}-\text{max}}-\text{1})\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (5)

In equation (5) the terms divided by ${\text{CMR}}_{\text{glc}-\text{RA}}$ are denoted by ′ (for example, ${\text{CMR′}}_{\text{glc}-\text{RA}}$ ). Based on experimental measurements and transport modeling (see Results) the value of ${\text{V′}}_{\text{GT}-\text{max}}$ in the rat cerebral cortex at normoglycemia (7.0 mM) is 1.57. Therefore, when the glucose transport maximum rate is reached, equation (5) gives:

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}=0.57\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (6)

To calculate the maximum increment in signaling ( $\Delta {\text{V}}_{\text{NTcycle}-\text{max}}$ ) relative to the RA state we used equations (1), (2) and (6), obtaining:

$$\Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}-\text{max}}=0.5\times 0.57\times {\text{CMR}}_{\text{glc}-\text{RA}}=0.29\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (7)

and

$$\Delta {\text{V}}_{\text{NTcycle}-\text{max}}={\text{(1/C}}_{\text{VNTcycle}}\text{)}\times 0.29\times {\text{CMR}}_{\text{glc}-\text{RA}}=0.37\times {\text{CMR}}_{\text{glc}-\text{RA}}=0.57\times {\text{V}}_{\text{NTcycle}-\text{RA}}$$ (8)

where the value of ${\text{C}}_{\text{VNTcycle}}=0.784$ was determined from a meta-analysis of ¹³C MRS results from the rat cerebral cortex (Figure 5(a) and Table SI-5; see also ‘Results’).

Therefore, the sparing of glucose for neurons due to glycogenolysis augments the attainable increment in neuronal glucose phosphorylation and ${\text{V}}_{\text{NTcycle}}$ until the glucose transport limit is reached (SI Section 13 and Fig. SI-4). At this point a further increase in the rate of neuronal glucose uptake has to be balanced by an equal decrease in the rate of astrocytic glucose uptake ( $\Delta {\text{CMR}}_{\text{glc}-\text{A}}$ ,which is now negative) eventually replacing baseline (RA) astrocytic glucose consumption, which corresponds to $\Delta {\text{V}}_{\text{Gnet}}=-{\text{CMR}}_{\text{glc}-\text{A}-\text{RA}}>\Delta {\text{CMR}}_{\text{glc}-\text{N}}$ and the minimum value of $\Delta {\text{V}}_{\text{Gnet}}$ that meets this condition is given by:

$$\Delta {\text{V}}_{\text{Gnet}}=\Delta {\text{CMR}}_{\text{glc}-\text{N}}=\Delta {\text{CMR}}_{\text{glc}}$$ (9)

In other words, when total glucose metabolism reaches ${\text{V}}_{\text{GT}-\text{max}}$ , the rate of astrocytic glucose metabolism decreases at the same rate as net glycogenolysis increases. To estimate the maximum increment in ${\text{V}}_{\text{NTcycle}}$ ( $\Delta {\text{V}}_{\text{NTcycle}-\text{max}}$ ) we used equations (1) and (2).

This reciprocal relationship is illustrated in Fig. SI-4. Combining equations (2) and (9) the value of $\Delta {\text{V}}_{\text{Gnet}}$ is given by the following linear relationship:

$$\Delta {\text{V}}_{\text{Gnet}}=\text{2}\times \Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}=\text{2}\times {\text{C}}_{\text{VNTcycle}}\times \Delta {\text{V}}_{\text{NTcycle}}$$ (10)

In order to maintain a constant astrocytic and neuronal ATP cost for signaling, the relationship in equation (10) must hold throughout the full activity range above the RA state.

Under the above conditions of total glucose sparing $\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}$ can be calculated from the following relationship:

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}=({\text{V′}}_{\text{GT}-\text{max}}-\text{1}+{\text{CMR′}}_{\text{glc}-\text{A}-\text{RA}})\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (11)

To calculate $\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}$ from equation (11) requires experimental measurements of ${\text{CMR}}_{\text{glc}-\text{A}-\text{RA}}$ and ${\text{CMR}}_{\text{glc}-\text{N}-\text{RA}}$ . We calculated these values from the best linear fits from the meta-analyses of ¹³C′MRS studies and the average value of V_NTcycle-RA = $\text{0}\text{.57}{\text{μmol\hspace{0.17em}g}}^{-1}{\text{min}}^{-1}$ (Figure 5(a) and Table SI-5; see also ‘Results’), which gives ${\text{CMR}}_{\text{glc}-\text{A}-\text{RA}}=0.32{\text{μmol\hspace{0.17em}g}}^{-1}{\text{min}}^{-1}$ and CMR_glc-N-RA= 0.56  μmol g⁻¹min⁻¹. Substituting these in equation (11) and using the relationships in equations (6) and (7) gives:

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}=0.94\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (12)

and

$$\Delta {\text{V}}_{\text{NTcycle}-\text{max}}=0.6\times {\text{CMR}}_{\text{glc}-\text{RA}}=0.92\times {\text{V}}_{\text{NTcycle}-\text{RA}}$$ (13)

The effect of glucose sparing by glycogenolysis on increasing the maximum range of neuronal signaling can be seen by calculating $\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}$ under conditions of no glycogenolysis, that is:

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}=({\text{V′}}_{\text{GT}-\text{max}}-1-\Delta {\text{CMR′}}_{\text{glc}-\text{A}})\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (14)

where $\Delta {\text{CMR}}_{\text{glc}-\text{A}}$ can be calculated from equations (9) and (10) corrected for the increased efficiency of glycolytic ATP production from glycogen (3 ATP per glucosyl moiety) versus glucose (2 ATP per glucose molecule). When expressed in terms of $\Delta {\text{CMR}}_{\text{glc}}$ we have:

$$\Delta {\text{CMR′}}_{\text{glc}|\Delta \text{VGnet}=0}=(5/2)\times \Delta {\text{CMR′}}_{\text{glc}|\Delta \text{VGnet}>0}$$ (15)

Equation (15) summarizes the fact that above the RA state, under conditions of inactive glycogenolysis $\Delta {\text{CMR}}_{\text{glc}}$ is predicted to be 2.5-fold larger than when glycogen is available. Under this condition $\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}$ and $\Delta {\text{V}}_{\text{NTcycle}-\text{max}}$ are given by:

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}=[{\text{V′}}_{\text{GT}-\text{max}}-1-(\text{3/2})\mathrm{\hspace{0.17em}\times \hspace{0.17em}\Delta }{\text{CMR′}}_{\text{glc}-\text{N}-\text{max}}]\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (16)

$$\Delta {\text{CMR}}_{\text{glc}-\text{N}-\text{max}}=0.24\times {\text{CMR}}_{\text{glc}-\text{RA}}$$ (17)

$$\Delta {\text{V}}_{\text{NTcycle}-\text{max}}=0.23\times {\text{V}}_{\text{NTcycle}-\text{RA}}$$ (18)

We also calculated the slopes for neuronal and astrocytic ATP production versus $\Delta {\text{V}}_{\text{NTcycle}}$ during stimulation using the known stoichiometries between glucose and glycogen metabolism and ATP production. For nonoxidative glycogenolysis we should have a stoichiometry of 3 ATP molecules per glucosyl moiety, but as shown in Figure 1 and described in SI Section 2, astrocytes also produce ATP from oxidation of a small fraction of the glycogenolysis flux (glycogen-derived pyruvate) in order to support oxidation and resynthesis of GABA and glutamate.^27,28 When ATP from nonoxidative and oxidative glycogenolysis is considered, we have:

$$\Delta {\text{V}}_{\text{ATP}-\text{A}}=3\times \Delta {\text{V}}_{\text{Gnet}}+4.8\times \Delta {\text{V}}_{\text{NTcycle}}=(6\times {\text{C}}_{\text{VNTcycle}}+4.78)\times \Delta {\text{V}}_{\text{NTcycle}}=9.48\times \Delta {\text{V}}_{\text{NTcycle}}$$ (19)

where we have used equatiuons (1) and (10) for expressing $\Delta {\text{V}}_{\text{Gnet}}$ and $\Delta {\text{V}}_{\text{NTcycle}}$ in terms of $\Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ . The astrocytic oxidative term is directly proportional to $\Delta {\text{V}}_{\text{NTcycle}}$ due to the need for resynthesis of neurotransmitter GABA and a fraction of glutamate neurotransmitter flux (SI Section 2) oxidized in the astrocyte. The ATP for resynthesis derives from a fraction of the glycogenolytic flux undergoing oxidative phosphorylation, which additionally provides excess ATP to support functional astrocytic processes at a rate of $4.8\times \Delta {\text{V}}_{\text{NTcycle}}$ .

Under stimulated conditions, the incremental neuronal glucose metabolism is approximately evenly divided between oxidative and nonoxidative glycolysis (see above). Using the stoichiometries of ATP production versus oxidative and nonoxidative glucose metabolism gives:

$$\Delta {\text{V}}_{\text{ATP}-\text{ox}-\text{N}}=30\times \Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}=23.52\times \Delta {\text{V}}_{\text{NTcycle}}$$ (20)

$$\Delta {\text{V}}_{\text{ATP}-\text{N}}=32\times \Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}+2\times \Delta {\text{CMR}}_{\text{glc}-\text{nonox}-\text{N}}=34\times \Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}=26.65\times \Delta {\text{V}}_{\text{NTcycle}}$$ (21)

Comparison of the GSG predicted relationship between $\Delta {\text{V}}_{\text{ATP}-\text{A}}$ and $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ versus ¹³C MRS measurements at or below the resting awake state

To test our hypothesis that the GSG determines the functional energetic relationship between neurons and astrocytes we used equations (19) and (21) to determine the relationship between signaling related astrocytic and neuronal ATP production rates:

$$\Delta {\text{V}}_{\text{ATP}-\text{A}}/\Delta {\text{V}}_{\text{ATP}-\text{N}}=9.48/26.65=0.356$$ (22)

We also independently calculated the theoretical $\Delta {\text{V}}_{\text{ATP}-\text{A}}/\Delta {\text{V}}_{\text{ATP}-\text{N}}$ (see SI Section 4), taking only ion pumping ATP costs into account, based on our previous approach of applying mass balance constraints required to maintain homeostasis of K⁺ and Na ⁺ concentrations in neurons, astrocytes, and the extracellular space during signaling. ¹⁵ The ratio predicted based on ionic flux balance consideration (0.33) is similar to that calculated from glucose sparing (0.34).

In order to calculate the relationship between $\Delta {\text{V}}_{\text{ATP}-\text{A}}$ and $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ below the resting awake state from ¹³C MRS data we used the following formula (SI Section 3, Eq. [SI-55]):

$${\text{V}}_{\text{ATP}-\text{A}}={\text{V}}_{\text{ATP}-\text{A}-\text{nonsignaling}}+\Delta {\text{V}}_{\text{ATP}-\text{A}}=15.83\times {\text{V}}_{\text{g}}+28.5\times ({\text{V}}_{\text{PC}}-0.035)+8.5\times 0.035$$ (23)

In this formula ${\text{V}}_{\text{PC}}$ is the flux through pyruvate carboxylase, and ${\text{V}}_{\text{g}}$ is the flux through the TCA cycle after α-ketoglutarate. The value 0.035 subtracted from ${\text{V}}_{\text{PC}}$ is the pyruvate carboxylase flux that is used for de novo glutamine synthesis for ammonia detoxification and is not coupled to neuronal signaling (see SI Section 3.9). The calculation of energetics in equation (23) is based on previous work and the derivation is presented in the SI Section 3. The values of ${\text{V}}_{\text{g}}$ and ${\text{V}}_{\text{PC}}$ used in the analysis are given in Table SI-4. It is assumed in the formula that the pyruvate represented by the activity dependent flux through PC (or the equivalent glutamate oxidation flux) is completely oxidized by pyruvate recycling (SI Sections 2–3). To calculate $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ below the resting awake state we used equation (23) with the value of ${\text{C}}_{\text{VNTcycle}}$ set to 0.784 from the meta-analysis best-fit line:

$$\Delta {\text{V}}_{\text{ATP}-\text{N}}={\text{V}}_{\text{ATP}-\text{N}}-{\text{V}}_{\text{ATP}-\text{N}-\text{nonsignaling}}=32\times {\text{C}}_{\text{VNTcycle}}\times {\text{V}}_{\text{NTcycle}}=25\times {\text{V}}_{\text{NTcycle}}$$ (24)

Predicted values of $\text{d}[\text{Lac}]/\text{dt}$ versus ${\text{CMR}}_{\text{glc}-\text{ox}}$ and comparison with human functional MRS studies

We finally calculated the rate of lactate formation versus ${\text{V}}_{\text{NTcycle}}$ based on the GSG model. At signaling rates above ${\text{V}}_{\text{NTcycle}-\text{RA}}$ , lactate will be produced from both neuronal nonoxidative glucose metabolism and astrocytic glycogenolysis. Based on the predictions of the model and measurement of the ratio of nonoxidative to total incremental glucose consumption, the rate of change of lactate concentration as a function of time is given by $\text{d}[\text{Lac}]/\text{dt}=0.915\times \Delta {\text{V}}_{\text{Gnet}}+0.47\times \Delta {\text{CMR}}_{\text{glc}}-{\text{Y}}_{\text{Lac}}\times ([\text{Lac}]-{[\text{Lac}]}_{\text{o}})$ where ${\text{Y}}_{\text{Lac}}$ is the rate constant for lactate clearance and ${[\text{Lac}]}_{\text{o}}$ is the concentration of brain lactate in the resting awake state when lactate inflow from the blood approximately matches lactate efflux from the brain. The 0.915 coefficient is due to a fraction (0.085) of the glycogen degraded being oxidized to support glutamate and GABA oxidation and resynthesis in the astrocyte. The difference $([\text{Lac}]-{[\text{Lac}]}_{\text{o}})$ is used because in the resting awake state there is minimal net lactate efflux. ²⁹ If the measurement is made before there is time for significant lactate clearance, or ${\text{Y}}_{\text{Lac}}\times ([\text{Lac}]-{[\text{Lac}]}_{\text{o}})\approx 0$ , the previous equation for $\text{d}[\text{Lac}]/\text{dt}$ can be approximated by:

$$\text{d}[\text{Lac}]/\text{dt}={\text{V}}_{\text{Lac}}=0.915\times \Delta {\text{CMR}}_{\text{glc}}+0.47\times \Delta {\text{CMR}}_{\text{glc}}=1.38\times \Delta {\text{CMR}}_{\text{glc}}=2.76\times \Delta {\text{CMR}}_{\text{glc-ox}}$$ (25)

In contrast, the difference of the incremental rates of total and oxidative glucose metabolism predicts the rate of change of lactate concentration under conditions of inactive glycogenolysis:

$$\text{d}[\text{Lac}]/\text{dt}={\text{V}}_{\text{Lac}}=\Delta {\text{CMR}}_{\text{glc}}-\Delta {\text{CMR}}_{\text{glc-ox}}=\Delta {\text{CMR}}_{\text{glc}-\text{nonox}}\mathrm{\hspace{0.17em}=\hspace{0.17em}}\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$$ (26)

Summary of major predictions of the GSG model that are tested

The GSG model predicts a number of quantitative relationships among the incremental increases in rates of neuronal signaling ( $\Delta {\text{V}}_{\text{NTcycle}}$ ), glucose utilization ( $\Delta {\text{CMR}}_{\text{glc}-\text{N}}$ and $\Delta {\text{CMR}}_{\text{glc}}$ ), glycogenolysis ( $\Delta {\text{V}}_{\text{Gnet}}$ ), and neuronal ( $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ ) and astrocytic ( $\Delta {\text{V}}_{\text{ATP}-\text{A}}$ ) ATP production that were evaluated and compared with experimental data. In addition, we assessed the (i) extent to which glycogenolysis supports the energy demands of astrocytic Na⁺,K⁺-ATPase, (ii) magnitude of compensatory changes in ${\text{CMR}}_{\text{glc}}$ when glycogenolysis is blocked, (iii) rates of lactate production with and without glycogen mobilization, and (iv) linearity predictions, glucose transport limitations, and applicability of the model to glutamatergic and GABAergic neurons.

Main predictions of the ANLS model

We also tested how well the ANLS model predicted the experimental results used to evaluate the GSG model. In the ANLS model, glucose uptake coupled to ${\text{V}}_{\text{NTcycle}}$ takes place in the astrocyte and provides glycolytic ATP needed to fuel glutamate transport and glutamine synthesis. We note that the ANLS model is incomplete because it omits the energetics of astrocytic glutamate/GABA oxidation and Na⁺/K⁺ pumping. The predicted stoichiometry of this process in the astrocyte has been shown to be 1 glucose per 1 glutamate cycled,^4,30 which can be equivalently expressed as $\Delta {\text{CMR}}_{\text{glc}-\text{A}}^{\text{ANLS}}=\Delta {\text{V}}_{\text{NTcycle}}$ . The lactate generated by glycolysis in astrocytes is then shuttled to the neurons for oxidation. Due to the (3/2) greater yield of ATP production when glycogen is the source of glycolytic ATP, the corresponding slope is given by:

$$\Delta {\text{V}}_{\text{Gnet}}^{\text{ANLS}}=(2/3)\times \Delta {\text{V}}_{\text{NTcycle}}$$ (27)

In the ANLS model, by definition, there is no neuronal glucose uptake coupled to ${\text{V}}_{\text{NTcycle}}$ under stimulated conditions ( $\Delta {\text{CMR}}_{\text{glc}-\text{N}}^{\text{ANLS}}=0$ ), as oxidative energy from glucose or glycogen is provided by lactate produced in the astrocyte and shuttled to the neuron. The slope of ATP production from glycogenolysis as a function of ${\text{V}}_{\text{NTcycle}}$ takes into account glutamate reuptake and conversion to glutamine, which gives:

$$\Delta {\text{V}}_{\text{ATP}-\text{A}}^{\text{ANLS}}=2\times \Delta {\text{V}}_{\text{NTcycle}}$$ (28)

On the other hand, because the neuronal ATP production that supports signaling is derived from oxidation in neurons of the lactate produced by astrocytes, the neuronal ATP production rate is given by $\Delta {\text{V}}_{\text{ATP}-\text{N}}^{\text{ANLS}}=30\times \Delta {\text{V}}_{\text{NTcycle}}$ . The predicted relative rates of astrocytic and neuronal ATP production as a function of the measured value of $\Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ for brain signaling above the resting awake state is then given by the ratio of the latter two equations, that is:

$$\Delta {\text{V}}_{\text{ATP}-\text{A}}^{\text{ANLS}}/\Delta {\text{V}}_{\text{ATP}-\text{ox}-\text{N}}^{\text{ANLS}}=2/30=0.067$$ (29)

The values used for the calculation were obtained from the best linear fits of the meta-analysis of rat ¹³C MRS studies (Figure 5(a) and Table SI-5; see also ‘Results’) with ${\text{V}}_{\text{NTcycle}-\text{RA}}=0.57$ , ${\text{CMR}}_{\text{glc}-\text{A}-\text{RA}}=0.32$ , ${\text{CMR}}_{\text{glc}-\text{N}-\text{RA}}=0.56$ , and ${\text{CMR}}_{\text{glc}-\text{RA}}=0.88$ , all in units of ${\text{μmol g}}^{-\text{1}}{\text{\hspace{0.17em}min}}^{-\text{1}}$ . It should be noted that, although the ¹³C MRS studies measured oxidative glucose metabolism, in the resting awake state the rates of oxidative and total glucose metabolism are similar.

Materials and methods

To test the GSG model, data sets were analyzed in which the rate of glycogenolysis, total glucose consumption, and total oxidative glucose consumption were measured over a wide range of cerebral metabolic rates above the resting awake state, ranging from sensory stimulation in awake rats to seizure (for experimental details and rate calculations see SI Section 7). As described in detail in SI Section 7, three conditions were examined, physiological activation, sustained seizure, and ischemia, where a brief description of each of the studies is provided along with details of the calculations performed to obtain $\Delta {\text{V}}_{\text{Gnet}}$ , $\Delta {\text{V}}_{\text{NTcycle}}$ and either $\Delta {\text{CMR}}_{\text{glc}}$ or $\Delta {\text{CMR}}_{\text{glc-ox}}$ if not reported in the original published studies. The rates from each study used to test the model are given in Table SI-2. More detailed derivations of all equations are provided in SI Sections 2–7, and statistical analyses of data are provided in the figures and their legends in the main text and SI. All fitted data passed tests for normality of residuals by the Shapiro-Wilk (W) test and homoscedasticity. Relationships between fluxes were assessed by linear least-squares (LS) regression (sensory stimulation data) without weighting or with 1/x sum-of-squares weighting (sensory stimulation plus seizure data). LS fits of rate increment data ( $\Delta {\text{V}}_{\text{i}}$ versus $\Delta {\text{V}}_{\text{NTcycle}}$ ) were constrained through the origin, whereas LS fits of absolute rate data ( ${\text{V}}_{\text{i}}$ versus ${\text{V}}_{\text{NTcycle}}$ ) were not constrained, yielding slope and y-intercept. LS regression, hypothesis testing and plotting were performed using GraphPad Prism 8.0.2 (GraphPad Software, San Diego, CA). The uncertainty of regressed slopes is given as ± SD as well as 95% CI in the figures.

Results

Relationship between $\Delta {\text{V}}_{\text{Gnet}}$ and $\Delta {\text{CMR}}_{\text{glc}}$

A test of the prediction of the GSG model that $\Delta {\text{V}}_{\text{Gnet}}=\Delta {\text{CMR}}_{\text{glc}-\text{N}}=\Delta {\text{CMR}}_{\text{glc}}$ (equation (9)) was obtained by plotting ${\text{V}}_{\text{Gnet}}$ versus $\Delta {\text{CMR}}_{\text{glc}}$ . In the case of sensory stimulation (Figure 2(a)), the predicted slope of 1.0 (blue line) was slightly below the 95% CI of the measured slope (black line) of 1.15 ± 0.04 (95% CI 1.03 – 1.26), and within the 95% CI of the measured slope (Figure 2(b), black line, 0.96 ± 0.05) when all conditions (seizure, ischemia) were included. These conditions resulted in the highest reported rates of glucose metabolism. In the ANLS model, no predicted relationship exists between $\Delta {\text{V}}_{\text{Gnet}}$ and $\Delta {\text{CMR}}_{\text{glc}}$ because all incremental glucose consumption during increased activity is localized in the astrocyte, which contradicts the experimental findings.

Figure 2.

Predicted relationships between neuronal and astrocyte glucose and glycogen metabolism and energetics. The predicted slopes from the GSG model (blue lines) and ANLS model (brown lines) are plotted together with the experimental data and their least squares best fit (dotted lines represent 95% confidence intervals, CI_95%; see Results and SI Section 7 and Table SI-2 for values and references). The units of $\Delta {\text{V}}_{\text{Gnet}}$ are μmol g⁻¹min⁻¹ (expressed in glucose units).

(a,b) $\Delta {\text{V}}_{\text{Gnet}}$ versus $\Delta {\text{CMR}}_{\text{glc}}$ tests the degree of glucose sparing during activation, without (a) or with (b) data acquired during seizure and ischemia.

(c,d) $\Delta {\text{V}}_{\text{Gnet}}$ versus $\Delta {\text{V}}_{\text{NTcycle}}$ tests whether there is a linear relationship during activation, without (c) or with (d) data acquired during seizure, consistent with direct coupling between glycogenolytic ATP production and neuronal activity.

(e,f) $\Delta {\text{V}}_{\text{ATP-Gnet}}$ versus $\Delta {\text{V}}_{\text{ATP-ox-N}}$ tests the predicted relationship between incremental ATP synthesis from nonoxidative glycogenolysis versus neuronal glucose oxidation. The best linear solutions to the experimental data without (e) and with (f) seizure data give slopes in agreement with the GSG model (blue line) (prediction 0.20; e, slope = 0.205 ± 0.008, 95% CI 0.184-0.227; f, slope = 0.178, 95% CI 0.14–0.22). In contrast, if glycogenolysis is coupled to neuronal oxidation of astrocytic lactate by the ANLS mechanism (which would experimentally also have been measured as glucose oxidation), then a slope of 0.067 is predicted, which is 3-fold lower than the experimental data (bottom curve). Also shown (top curve) is the value of $\Delta {\text{V}}_{\text{ATP-A}}$ calculated from the GSG model, which includes glycogen oxidation ( $\Delta {\text{V}}_{\text{ATP}-\text{tot}-\text{Gnet}}$ ) equation (19) (e, slope = 0.409; f, slope = 0.381).

Relationship between $\Delta {\text{V}}_{\text{Gnet}}$ and $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ (i.e., ${\text{C}}_{\text{VNTcycle}}\times \Delta {\text{V}}_{\text{NTcycle}}$ )

A test of the prediction of the GSG model expressed in equation (10) was obtained by plotting $\Delta {\text{V}}_{\text{Gnet}}$ versus $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ . Because of the reduced oxidative metabolism of blood glucose by astrocytes due to glycogenolysis early during activation, we assigned $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ to the neuron. During sensory stimulation in normal awake rats, $\Delta {\text{V}}_{\text{Gnet}}$ increased linearly with $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ (Figure 2(c), black line, slope = 2.05 ± 0.09), in agreement with the GSG model (blue line, slope = 2.0, P = 0.59 for difference between slopes). A similar slope was found by including data obtained from seizing animals (Figure 2(d), slope = 1.78 ± 0.15). In contrast, according to equation (27) the predicted slope from the ANLS model (brown line, slope = 2/3 = 0.667) falls well outside the 95% confidence interval (CI_95%) of the experimental best linear fit to the data.

Relationship between $\Delta {\text{V}}_{\text{ATP}-\text{Gnet}}$ and $\Delta {\text{V}}_{\text{ATP}-\text{ox}-\text{N}}$

The relationship between astrocytic and neuronal signaling-related energetics was determined by plotting $\Delta {\text{V}}_{\text{ATP}-\text{Gnet}}$ (calculated from the measured $\Delta {\text{V}}_{\text{Gnet}}$ values (first term of equation (19)) versus $\Delta {\text{V}}_{\text{ATP}-\text{ox}-\text{N}}$ (equation (20)). As seen in Figure 2(e) (only physiological stimulation, filled symbols) and Figure 2(f) (with seizure data, open symbols), the GSG model predicted slope of 6/30 = 0.20 is within the 95% CI of the slopes determined from experimental measurements (Figure 2(e), slope = 0.205; Figure 2(f), slope =0.178). In contrast, the predicted slope of the ANLS model of 2/30 = 0.067 (equation (29)) is 3-fold lower than the experimentally determined values, indicating the majority of astrocytic functional energy consumption is not coupled to glutamate transport and conversion to glutamine (see Figure 1 and SI Section 5). If $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ took place in the astrocyte, the ANLS-predicted slope would be further reduced due to $\Delta {\text{V}}_{\text{NTcycle}}$ being lower than calculated from ${\text{CMR}}_{\text{glc}-\text{ox}}$ . Also shown is the GSG model prediction of the calculated value of $\Delta {\text{V}}_{\text{ATP}-\text{A}}$ for inclusion of oxidative glycogenolysis equation (22). The rate of ATP production from glycogen oxidation is predicted to be approximately the same as from nonoxidative glycogenolysis.

Evidence for glucose sparing from studies in which $\Delta {\text{V}}_{\text{Gnet}}=0$

To further test the GSG model we compared (Figure 3) the slope of $\Delta {\text{CMR}}_{\text{glc}}$ versus $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ for studies in which $\Delta {\text{V}}_{\text{Gnet}}$ was active (green dashed line) with studies in which glycogenolysis was blocked pharmacologically or by the experimental conditions ( $\Delta {\text{V}}_{\text{Gnet}}=0$ , blue lines). Due to the additional nonoxidative glucose metabolism in the astrocyte, the GSG model predicts that the slope of $\Delta {\text{CMR}}_{\text{glc}}$ versus $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ should be 5/2-fold higher than when complete sparing takes place (equation (15)). When glycogenolysis was active, the measured best-fit slope was 1.89 (dashed blue line) with a 95% CI between 1.77 and 2.02. For comparison, data are plotted from Dienel et al. ²² for awake rats in which glycogenolysis was pharmacologically inhibited, and from Patel et al. ³¹ for anesthetized rats undergoing seizure under hyperglycemic conditions in which the rate of glycogenolysis (calculated from ¹³C-labeled lactate dilution) was negligible (SI Section 7). The solid blue line gives the predicted slope from the GSG model when astrocytic nonoxidative glycolysis of blood borne glucose completely replaces glycogenolysis at a rate of (5/2) × 1.89 = 4.73, which is within the 95% CI of the measured value of 4.50 (95% CI 3.34–5.65). This result further supports a key role of glycogenolysis in sparing glucose to support neuronal signaling.

Figure 3.

Predicted effect of blocking glycogenolysis on the rates of oxidative and nonoxidative glucose consumption in awake and anesthetized rats. Plots of $\Delta {\text{CMR}}_{\text{glc}}$ versus $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ (both expressed in glucose units) for studies in which the rate of brain signaling was enhanced by sensory stimulation and seizure (black symbols) and studies in which glycogenolysis $\Delta {\text{V}}_{\text{Gnet}}$ is blocked either pharmacologically (blue triangles) or by the experimental conditions (blue circle). See Table SI-2 for values and references.

Comparison of ${\text{V}}_{\text{ATP}-\text{A}}$ versus $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ below the resting awake state with prediction of the GSG model

To test the hypothesis that in non-activated states functional neuronal and astrocytic ATP expenditures are determined by the GSG mechanism we performed a meta-analysis on studies performed in the rat in which ¹³C MRS was used to measure neuronal and astrocytic fluxes of oxidative glucose metabolism. From these fluxes, ( ${\text{V}}_{\text{TCA}-\text{N}}$ , ${\text{V}}_{\text{g}}$ , and ${\text{V}}_{\text{PC}}$ , given in Table SI-4) we used equation (23) to calculate the rate of astrocytic ATP production ( ${\text{V}}_{\text{ATP}-\text{A}}$ ) and plotted the results versus $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ calculated using equation (24). The best fit linear slope of 0.355 ± 0.044 was similar to the predicted slope from the GSG model of 0.357 (P = 0.97 for difference of slopes; Figure 4). The agreement with the GSG model supports the assumption that the relationship between astrocytic and neuronal functional ATP requirements is determined by the glucose sparing mechanism in the activated state. The slope of the relationship between ${\text{V}}_{\text{ATP}-\text{A}}$ versus ${\text{V}}_{\text{NTcycle}}$ is given by multiplying the experimental slope by 26.65 (equation (21)) yielding 9.46 ± 1.17, in good agreement with the predicted value of 9.48 (equation (19)).

Figure 4.

Calculated ${\text{V}}_{\text{ATP}-\text{A}}$ versus $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ from experimental rat data and predicted slope from the GSG model. ${\text{V}}_{\text{ATP}-\text{A}}$ versus $\Delta {\text{V}}_{\text{ATP}-\text{N}}$ calculated from ¹³C MRS studies of rat cerebral cortex metabolism at different levels of electrical activity ranging from near isoelectricity (deep pentobarbital anesthesia) to the resting awake state (see equation (23), SI Section 3, and Tables SI-3, SI-4, and SI-5). The best fit line (black) to the slope of the experimental data is in good agreement with the prediction of the GSG model (blue).

Determination of ${\text{C}}_{\text{VNTcycle}}$ from meta-analysis of ¹³C MRS studies

The value of ${\text{C}}_{\text{VNTcycle}}$ was determined by performing a meta-analysis of published ¹³C MRS studies of rat cerebral cortex. As shown in Figure 5(a) over a range of activity from isoelectricity to the awake state, the best linear fit has a slope of 0.784 ± 0.063. Because the measurements of ${\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ and ${\text{V}}_{\text{NTcycle}}$ contain contributions from glutamatergic and GABAergic neurons we also performed a meta-analysis of studies reporting the fluxes through the separate glutamate and GABA pools. As shown in Figure 5(b) and (c), similar best linear fit slopes of 0.812 ± 0.11 and 0.763 ± 0.089 were found. In addition, when the separate glutamate and GABA fluxes were added together (Figure 5(d)) the best linear fit slope was similar (0.812 ± 0.091), to the complete set of measurements in Figure 5(a). In Figure 5(a), we also plot in different colors results from mouse (blue), tree shrew (green), and human (red) cerebral cortex (see Table SI-9 for references). The data from these species are all within the experimental scatter of the rat data, which supports and extends previous findings of a similar relationship between rats and humans. ²⁴

Nonoxidative glycolysis versus oxidative glucose consumption in human and rat cerebral cortex

To test the prediction of the GSG model in human cerebral cortex, as expressed in equations (25) and (26), we calculated $\text{d}[\text{Lac}]/\text{dt}$ by analyzing the time course of lactate concentration measured by functional Magnetic Resonance Spectroscopy (fMRS) from four studies of human visual or motor cortex during photic or motor stimulation from the laboratories of Mangia and Gruetter.^32–37 The studies were chosen because they^33,35–37 obtained time resolution on the order of 20 seconds by the use of a high field 7 T magnet and by averaging across subjects undergoing the same stimulation paradigm. Figure 6(a) plots the values of $\text{d}[\text{Lac}]/\text{dt}$ calculated from a lactate measurement centered at 40 or 45 seconds after the start of stimulation versus the average value of $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ ( $0.05{\text{μmol g}}^{-\text{1}}{\text{min}}^{-\text{1}}$ , Table SI-8) from [¹⁸F]fluorodeoxyglucose-positron emission tomography (FDG-PET) studies of stimulated human visual cortex. The best linear fit slope of the relationship between $\Delta {\text{V}}_{\text{Lac}}$ and $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ was measured to be 2.65 ± 0.26 (Figure 6(a)), which agrees with the predicted slope of 2.76 (equation (25)). For each individual study the standard deviation of ${\text{V}}_{\text{Lac}}$ , based on Cramer Rao lower bounds of the lactate measurements, was approximately $\pm 0.4{\text{μmol g}}^{-1}{\min }^{-1}$ , which is consistent with the SD of the slope. In contrast, if there were no glycogenolysis the predicted slope from equation (26) is 1.0 (green line in Figure 6(a)), which is well outside of the uncertainty of the experimental measurements, supporting a highly active net glycogenolysis at a rate predicted by the GSG model. In Figure 6(b), we included the summed measurements of $\Delta {\text{CMR}}_{\text{glc-nonox}}+\Delta {\text{V}}_{\text{Gnet-nonox}}$ in rats undergoing physiological stimulation. A best linear fit slope of 3.12 ± 0.21 was determined, again in agreement with the GSG prediction.

Figure 6.

$\Delta {\text{V}}_{\text{Lac}}$ and $\Delta {\text{CMR}}_{\text{glc}-\text{nonox}}+\Delta {\text{V}}_{\text{Gnet}}$ versus $\Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ during sensory stimulation in human and rat cerebral cortex. (a) The measured slope of the initial rate of lactate production in human brain from four studies versus the average increase in $\Delta {\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ (expressed in glucose units) (Table SI-8) was 2.65 ± 0.26, which is not significantly different (P=0.69) from the prediction of the glucose sparing model of 2.76 (blue line). For comparison, the slope predicted should there be no glycogen metabolism (inactive glycogenolysis) is Y = 1.0 (green line), supporting the presence of highly active glycogenolysis.

(b) Plot of $\Delta {\text{CMR}}_{\text{glc}-\text{nonox}}+\Delta {\text{V}}_{\text{Gnet}}$ (non oxidative) versus $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ (expressed in glucose units) including measurements from studies of activated rat cortex (Table SI-2) and human data (orange filled circles). The best fit slope determined from the rat data was 3.14 ± 0.32 (R²=0.628), which is in agreement with the GSG model and the human lactate results, and well above the prediction if there were no astrocytic nonoxidative glycogenolysis (green line, Y = 1.0).

Glucose transport limitation and maximum rate of $\Delta {\text{V}}_{\text{NTcycle}}$

To test whether glucose transport can be limiting for cerebral glucose metabolism, we compared the measured ratios of regional ${\text{CMR}}_{\text{glc}}$ during sensory stimulation with ${\text{CMR}}_{\text{glc}-\text{RA}}$ from studies of human (Figure 7(a))^38–43 and rat (Figure 7(b))^22,44–47 cerebral cortex. Plotted as horizontal lines are the predicted ${\text{V}}_{\text{GT}-\text{max}}$ calculated using the reversible two state Michaelis-Menten (MM) model ⁴⁸ and published transport constants ^48,49 under physiological fed (plasma glucose of 7 mM rat, 5 mM human) and fasting (plasma glucose of 5 mM rat, 3.5 mM human) conditions. The two state reversible MM model has been shown to be valid in this range of glucose concentrations. ⁴⁸ It is seen that under euglycemic conditions the measured values of ${\text{CMR}}_{\text{glc}}$ are below the glucose transport limit, consistent with human studies reporting altered electrical activity in response to stimuli at blood glucose levels below 3.0 mM range. ⁵⁰ In contrast, in the absence of glucose sparing by glycogenolysis, the calculated values of ${\text{CMR}}_{\text{glc}}$ are all above the glucose transport limit even under plasma normoglycemia. The higher values are due to the need for nonoxidative astrocytic glycolysis from glucose in the absence of glucose sparing by glycogenolysis. The calculated ${\text{V}}_{\text{GT}-\text{max}}$ values under normoglycemia are supported by Dienel and colleagues (Figure 3(e) in Dienel ⁵¹ ) who found in rat cerebral cortex that regional unidirectional glucose entry (which is equal to ${\text{V}}_{\text{GT}-\text{max}}$ ) as a function of glucose phosphorylation is linear with a slope of 1.59, similar to the calculated value of ${\text{V}}_{\text{GT}-\text{max}}/{\text{CMR}}_{\text{glc}-\text{RA}}$ of 1.57.

Figure 7.

Measured increase in ${\text{CMR}}_{\text{glc}}$ in rat and human cerebral cortex during sensory stimulation and predicted increase in CMR_glc in the absence of glucose sparing. (a) Comparison of ${\text{CMR}}_{\text{glc}}$ measured using FDG-PET in human visual cortex during photic stimulation (blue) versus the value of CMR_glc predicted should there be no glucose sparing by glycogenolysis (orange). All values are normalized to the resting awake state ( ${\text{CMR}}_{\text{glc}-\text{RA}}$ ). The dashed horizontal lines are the calculated maximum glucose transport rates ( ${\text{V}}_{\text{GT}-\text{max}}$ ) under normoglycemic (5.0 mM, ${\text{V}}_{\text{GT}-\text{max}-\text{norm}}$ ) and physiological hypoglycemic (3.5 mM, ${\text{V}}_{\text{GT}-\text{max}-\text{hypo}}$ ) plasma glucose concentrations. The values used and references are tabulated in Table SI-6.

(b) The same plot using data from regional measurements of rat cerebral cortex during sensory stimulation (Table SI-2 for values and references). For the rat physiological fed and fasting plasma glucose levels are 7.0 mM and 5.0 mM, respectively. ⁶⁵ The two bars for the reference Dienel et al. 2007 indicate separate measurementsin the somatosensory and parietal cortex. The two bars for the reference Collins et al. 1987 indicate rates obtained under two visual stimulation frequencies.

We further tested the GSG model by comparing the calculated $\Delta {\text{V}}_{\text{NTcycle}}$ from measured values of $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ and equation (1) with the predicted $\Delta {\text{V}}_{\text{NTcycle}-\text{max}}=0.6\times {\text{CMR}}_{\text{glc}-\text{RA}}$ from the GSG model equation (13)). For studies under physiological stimulation the highest estimate of ${\text{CMR}}_{\text{glc}\text{-RA}}$ in cerebral cortex was approximately $1.0{\text{μmol g}}^{-\text{1}}{\text{min}}^{-\text{1}}$ . This value is expressed in glucose units, and should not be confused with the pyruvate dehydrogenase complex rate that is expressed in triose units. Using this value, the predicted $\Delta {\text{V}}_{\text{NTcycle}-\text{max}}=0.6{\text{μmol\hspace{0.17em}g}}^{-\text{1}}{\text{min}}^{-\text{1}}$ . For rats undergoing physiological stimulation (Figure 3, Figure 7(b), and Table SI-2), the highest measured increment was $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}=0.34{\text{μmol\hspace{0.17em}g}}^{-\text{1}}{\text{min}}^{-\text{1}}$ (Table SI-2), and when used in equation (1) gives $\Delta {\text{V}}_{\text{NTcycle}-\text{max}}=0.43{\text{μmol\hspace{0.17em}g}}^{-\text{1}}{\text{min}}^{-\text{1}}$ . The calculated increments in $\Delta {\text{V}}_{\text{NTcycle}}$ in studies performed during chemically induced seizures were also below the predicted maximum value with the exception of the report by Chapman et al. ⁵² that was approximately 2-fold higher. However, as described in the Discussion, this study was performed under hyperglycemic conditions that would have circumvented the glucose transport limitation.

Validity of the linearity predictions of the GSG model

The GSG model predicts that the relationships between neuronal and astrocytic carbohydrate metabolism (equations (2) and (10)), as well as associated glycolytic and oxidative ATP production (equations (19) and (21)), are linear with ${\text{V}}_{\text{NTcycle}}$ over the full range of neuronal signaling. Although the experimental results are limited, for all of the available cases analyzed (see Figures 2 to 6) the values of R² were higher than 0.85, thus supporting the linearity assumption in the GSG model.

Summary of calculations and comparisons with experimental results

In Table SI-1, we summarize the predictions of the model, experimental results and the relevant equations. Table SI-1 also includes the values for ${\text{V}}_{\text{ATP}-\text{A}}$ versus ${\text{V}}_{\text{NTcycle}}$ predicted by the GSG model should the pyruvate represented by the ${\text{V}}_{\text{PC}}$ flux not be fully oxidized via pyruvate recycling. As shown in Fig. SI-1, the calculated experimental relationship for this alternate possibility is in agreement with the GSG model.

Discussion

The GSG model predicts that glucose sparing is necessary due to glucose transport limitations across the blood brain barrier (BBB). Evidence that glucose transport can be limiting for metabolism include ¹³C-MRS measurements that showed under moderate hypoglycemic conditions glycogenolysis can replace a significant fraction of ATP produced by glucose oxidation, thus temporarily extending the duration of neuronal signaling before failure of brain function. ⁵³ Similarly, normal electrical activity during hypoglycemia in awake rats was significantly extended by preemptively increasing brain glycogen concentration using a displaceable phosphorylase inhibitor. ⁵⁴ Moreover, bicuculline-induced seizure electroencephalographic activity in fasted animals was maintained up to the point of glycogen depletion.^21,55 Notably, seizures could be restored by injections of glucose but not by oxidation of accumulated lactate, consistent with our conclusion that astrocytes support neuronal energetic needs through glucose sparing for glycolytic and oxidative metabolism, as opposed to a lactate shuttle mechanism and only oxidation.^3,4,56

The experimental data we analyzed were obtained within approximately the first 5 minutes after the onset of stimulation (see Table SI-2). Given ${\text{V}}_{\text{Gnet}}=2\times {\text{C}}_{\text{VNTcycle}}\times \Delta {\text{V}}_{\text{NTcycle}}=0.4-0.68$ µmol g⁻¹min⁻¹ and a glycogen level of 10 − 12 μmol g⁻¹ (both expressed in glucose equivalent units), ²⁰ we find that the GSG mechanism can be sustained for 15-30 minutes during physiological stimulation. However, it is likely that sustained glycogenolysis lasts at most 5 to 10 minutes due to increases over time in glucose transporter activity. Intense stimulations can, in fact, be sustained longer and extend beyond the point when net glycogenolysis eventually ceases if, for example, glucose transport increases through the recruitment of glucose transporter (GLUT) proteins to the endothelial membrane, as occurs in muscle. ⁵⁷ Evidence that a similar response to extended stimulated activity occurs in the brain are findings that cerebral GLUT1 proteins on the BBB begin to upregulate their activity by 3 minutes after the start of seizure and reach sufficiently high activity to sustain seizure activity for at least an hour.^58,59 In parallel, GLUT4 proteins are quickly mobilized to the presynaptic plasma membrane from internal stores ⁶⁰ to support increased glycolysis, ⁶¹ followed by slower mitochondrial recruitment to presynaptic terminals for increasing oxidative capacity. ⁶² Therefore, GSG is proposed to support the transition before the upregulation of glucose transport across the BBB and across presynaptic plasma membranes to meet the increased neuronal demand for glucose upon activation.

In the GSG model, a direct neuronal coupling is assumed between neuronal glucose oxidation and glutamate and GABA synthesis. Thus, astrocytic energetics are largely driven by neuronal K⁺ release, as opposed to neurotransmitter release. Based on the results of the meta-analysis the experimental value of ${\text{C}}_{\text{VNTcycle}}$ can be potentially explained by the PMAS model of Hertz and colleagues.^16,25 In this model, which is described in more detail in the SI Section 6 (Fig. SI-3), the synthesis of glutamate (and subsequent synthesis of GABA) from glutamine in the neuron via phosphate-activated glutaminase (PAG) is coupled to neuronal glucose oxidation by the PMAS with a constant given by ${\text{C}}_{\text{PMAS}}=0.5$ . However, only a fraction ( ${\text{F}}_{\text{PMAS}}$ ) of the neuronal oxidative metabolism is coupled to neurotransmitter glutamate synthesis from glutamine. The relationship between ${\text{C}}_{\text{PMAS}}$ , ${\text{F}}_{\text{PMAS}}$ , and ${\text{C}}_{\text{VNTcycle}}$ is given by ${\text{C}}_{\text{VNTcycle}}={\text{C}}_{\text{PMAS}}\times (1/{\text{F}}_{\text{PMAS}})$ . Studies in which brain glucose metabolism was displaced by ketones are consistent with values of F_PMAS as low as 0.5, ⁶³ consistent with the calculated ${\text{C}}_{\text{VNTcycle}}$ (0.784). Further studies are needed to conclusively demonstrate that the PMAS mechanism is highly active in vivo when the displacement fraction is taken into account.

In addition to the ¹³C MRS data from the rat, there have been studies on several other species including the mouse, tree shrew and human cerebral cortex. As shown in Figure 5(a), the results in these species all fall within the range of the rat data for ${\text{CMR}}_{\text{glc}-\text{ox}-\text{N}}$ versus ${\text{V}}_{\text{NTcycle}}$ . Unfortunately, the data available on astrocytic metabolic fluxes in other species are more limited. As shown in Fig. SI-2, values of ${\text{CMR}}_{\text{glc}-\text{ox}-\text{A}}$ and ${\text{V}}_{\text{NTcycle}}$ in the tree shrew visual cortex ⁶⁴ are similar to values reported for rat cerebral cortex. Interestingly, the slope of ${\text{CMR}}_{\text{glc}-\text{ox}-\text{A}}$ versus ${\text{V}}_{\text{NTcycle}}$ in that study, with the two points grouped based on a ${\text{V}}_{\text{NTcycle}}$ cutoff, is higher than the meta-analysis slope from the rat. However, given the small range of activity, more studies will be needed to assess potential inter species differences.

There are several limitations to validation of the GSG model. The most significant limitation is the need for direct measurements of the cellular location of the incremental oxidative and nonoxidative glucose metabolism during the first minutes of stimulation in the awake state to validate the assignment to the neuron. However, the agreement between the GSG model predictions and measured incremental glucose (oxidative and total) and glycogen metabolism (Figure 2), as well as the agreement between the energetics above and below the resting awake state (Figures 2 and 4), strongly supports the assignment of the incremental glucose metabolism to the neuron. Should a significant fraction of $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ be associated with the astrocyte, the experimental slope of $\Delta {\text{V}}_{\text{Gnet}}$ versus $\Delta {\text{CMR}}_{\text{glc}-\text{ox}}$ would be less than the measured value due to a reduced need for glucose sparing. Furthermore, as shown in Figure 3, blocking glycogenolysis results in the predicted increase in total glucose consumption, which would not be the case if the initial increase in glucose oxidation occurred in the astrocyte. Additional evidence of a major assignment of glucose metabolism to neurons is supported by the study of Patel et al. ¹³ who found a similar fractional increment in total glucose consumption in isolated synaptosomes and whole tissue of rat cerebrum during bicuculline-seizures.

In summary, comprehensive analysis of the major predictions of the GSG model, and comparison with those of the ANLS model, demonstrates that the GSG model can explain a wide range of experimental findings related to astrocytic and neuronal energetics during brain activation. Glucose sparing has the functional benefit of ensuring propagation of neuronal signaling even when glucose transport may become limiting due to extreme firing rates or non-physiological conditions, ultimately preserving signaling fidelity even at the highest activity level. In contrast, the ANLS model is incomplete and incorrectly assigns the cellular basis, magnitudes, and relationships of major pathway fluxes. These differences have a high impact on interpretation of results of functional metabolic studies in activated brain.