ORIGINAL RESEARCH ARTICLE published: 09 July 2009 NEUROENERGETICS doi: 10.3389/neuro.14.004.2009 Deciphering neuron- compartmentalization in cortical energy metabolism

Renaud Jolivet1*, Pierre J. Magistretti 2,3 and Bruno Weber1

1 Institute of Pharmacology and Toxicology, University of Zurich, Zurich, 2 Mind Institute, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland 3 Center for Psychiatric Neuroscience, University of Lausanne and CHUV, Lausanne, Switzerland

Edited by: Energy demand is an important constraint on neural signaling. Several methods have been Rolf Gruetter, Ecole Polytechnique proposed to assess the energy budget of the brain based on a bottom-up approach in which Fédérale de Lausanne, Switzerland the energy demand of individual biophysical processes are fi rst estimated independently Reviewed by: Kevin L. Behar, , School and then summed up to compute the brain’s total energy budget. Here, we address this of Medicine, Department of Diagnostic question using a novel approach that makes use of published datasets that reported average Radiology, Yale Magnetic Resonance cerebral glucose and oxygen utilization in humans and rodents during different activation Center, USA states. Our approach allows us (1) to decipher neuron-glia compartmentalization in energy Helle S. Waagepetersen, University of Copenhagen, Denmark metabolism and (2) to compute a precise state-dependent energy budget for the brain. Albert Gjedde, Aarhus University Under the assumption that the fraction of energy used for signaling is proportional to the Hospital, Denmark cycling of neurotransmitters, we fi nd that in the activated state, most of the energy (∼80%) *Correspondence: is oxidatively produced and consumed by neurons to support neuron-to-neuron signaling. Renaud Jolivet, University Hospital Glial cells, while only contributing for a small fraction to energy production (∼6%), actually Zurich, Nuclear Medicine, Rämistrasse 100, CH-8091, Zürich, Switzerland. take up a signifi cant fraction of glucose (50% or more) from the blood and provide neurons e-mail: [email protected]fl .ch with glucose-derived energy substrates. Our results suggest that glycolysis occurs for a signifi cant part in whereas most of the oxygen is utilized in neurons. As a consequence, a transfer of glucose-derived metabolites from glial cells to neurons has to take place. Furthermore, we fi nd that the amplitude of this transfer is correlated to (1) the activity level of the brain; the larger the activity, the more metabolites are shuttled from glia to neurons and (2) the oxidative activity in astrocytes; with higher glial pyruvate metabolism, less metabolites are shuttled from glia to neurons. While some of the details of a bottom- up biophysical approach have to be simplifi ed, our method allows for a straightforward assessment of the brain’s energy budget from macroscopic measurements with minimal underlying assumptions.

Keywords: -neuron interactions, brain energy metabolism, brain energy budget, glucose, oxygen

INTRODUCTION Neuron-glia metabolic interactions have been the subject of The energy requirements of the brain are amazingly high; indeed, several recent modeling studies (Aubert et al., 2005, 2007; Hyder while representing only about 2% of the body weight, its oxygen et al., 2006). Most of these studies tend to support the presence of and glucose utilization account for approximately 20% of those an activity-regulated lactate shuttle from astrocytes to neurons as of the whole organism, almost 10 times more than what would be originally proposed by Pellerin and Magistretti (1994). The pres- predicted on a weight basis (Kety, 1957; Magistretti, 2008; Rolfe and ence of this shuttle has recently been reported in slices (Rouach Brown, 1997; Sokoloff, 1960). A similar mismatch is also observed et al., 2008). Similarly, several mathematical methods have been for blood fl ow destined to the brain, which represents over 10% derived to assess the energy budget of the brain. These methods are of cardiac output. A central feature of brain energy metabolism traditionally based on a bottom-up approach in which the energy is that it is tightly coupled to neuronal activity. This tight cou- demand of individual biophysical processes are fi rst estimated pling is at the basis of functional brain-imaging techniques, such independently and then summed up to compute the brain’s total as positron emission tomography and functional magnetic reso- energy budget (Attwell and Laughlin, 2001; Lennie, 2003; Nawroth nance imaging (Magistretti and Pellerin, 1999). However, the exact et al., 2007). Most of these methods focus on energy requirements principles underlying this coupling and in particular the nature rather than on energy supply. and role of neuron-glia metabolic interactions are still a subject Here, we introduce a novel top-down approach that addresses of active research (Gordon et al., 2008; Rouach et al., 2008) and the question of the brain’s energy budget from the opposite perspec- of controversy at times (Hertz et al., 2007). Similarly, the precise tive. We re-analyzed datasets reporting average glucose and oxygen energy budget of the brain and in particular the cost associated utilization in the human and rodent in different activation with neuronal signaling is still not well understood (Attwell and states (Gjedde, 2007). Using these fi gures, it is possible to evaluate Laughlin, 2001; Lennie, 2003). the average tissue ATP production corresponding to the different

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activation states. We then proceed to show that neuronal versus glial all glial cells are pooled together and are hereafter referred to as (i.e. astrocytic) oxygen and glucose metabolism can be evaluated by astrocytes), (ii) that the system is at steady-state which was also combining this fi rst dataset with data reporting the rate of neuronal assumed during the collection of the two datasets to be used and glucose-equivalent oxidation as a function of the rate of cycling (iii) that energy measured as adenosine triphosphate production of neurotransmitters (Hyder et al., 2006; Sibson et al., 1998). This (ATP) is used in the compartment where it is produced. can be achieved with minimal underlying hypotheses. It is then Average CMRglc and CMRO2 lead to the average tissue (T) ATP possible to compute the brain’s energy budget as well as the cycling yield for each state S = 1,…,4 through the following stoichiometric rate of neurotransmitters corresponding to the different activation relation (Gjedde, 2007; Gjedde et al., 2002) states. Finally, using our prediction of the compartmentalization VST ()=+2CMR () Sλ CMR () S (1) of neuronal versus astrocytic glucose and oxygen utilization, it is ATP glc O2 possible to evaluate whether these two cell populations completely Theoretically, λ = 6 yielding a total of 38 ATP molecules per oxidize the glucose they take up or rather import or export glucose- glucose molecule in the case of complete oxidation. Here, we use derived metabolites. λ = 28/6 for a total of 30 ATP molecules, a yield closer to experi- Our results suggest that a signifi cant part of glucose is taken up mental measurements (Berg et al., 2006; Hinkle et al., 1991). It is by astrocytes while oxygen is mostly consumed within the neuronal worth noting however, that we fi nd no signifi cant difference in the population. We fi nd that this bias tends to increase with the level of results reported when using λ = 6. activation. The higher the activation state, the higher the proportion As reviewed in Hyder et al. (2006), the total cycling of neuro- of oxygen being used by neurons and the higher the proportion transmitters V and the neuronal oxidative glucose utilization of glucose entering glia. Moreover, our approach yields an energy cyc(tot) CMRn are linked by budget for different brain states. At high levels of activation, we fi nd glc,ox that about 80% of energy is produced to support neuronal signaling n =+ CMRglc,ox AB Vcyc(tot) (2) while glia only use up a small fraction of energy to recycle neuro- transmitters (5–6%). Finally, we fi nd that the glial population takes with A and B parameters to be determined. As shown in Jolivet up more glucose than it can oxidize while the neurons oxidize more et al. (2009), assuming most of glucose entering the tricarboxylic glucose-derived metabolites than the amount of glucose they take acid (TCA) cycle in neurons is ultimately oxidized (Gjedde, 2007), up. This is suggestive of a transfer of glucose-derived metabolites Eq. 2 can be rewritten from the astrocytes to the neurons. Furthermore, the amplitude of − ⎡1 ⎤ this transfer is shown to be proportional to the level of activity as VA=−1 ()1 rCMR − B (3) cyc(tot)⎣⎢ O2 O2 ⎦⎥ measured by the cycling of neurotransmitters, a fi nding consistent 6 with the astrocyte-neuron lactate shuttle hypothesis (Pellerin and with rO2 the astrocytic contribution to oxygen utilization. All CMRs Magistretti, 1994). While lacking the details of a more biophysical − − in our analysis describe rates measured in µmol g 1 min 1. approach (Attwell and Laughlin, 2001; Nawroth et al., 2007), our From these premises, state S = 1 (no function) can be readily approach yields an energy budget that matches observed tissue identifi ed to V = 0. It follows that the total fraction of energy glucose and oxygen utilization as well as the compartmentalization cyc(tot) used for housekeeping metabolism (tot = n + a) is given by of glucose transport and oxygen utilization between neurons and astrocytes across different levels of brain activation. The resulting V T ()1 fS()= ATP (4) budget is in agreement with the one detailed in the work of Attwell hk,tot T VSATP() and Laughlin (2001) and at the same time supports the view of an activity-regulated transfer of glucose-derived metabolites from and as a consequence, the fraction of energy used for signaling is f ()SfS=−1 (). astrocytes to neurons. s,tot hk,tot To go one step further, we now make the hypothesis that the

MATERIALS AND METHODS fraction of energy used for signaling is proportional to Vcyc(tot) Our goal is to segment energy production in the cerebral gray matter VS() in signaling (s) versus housekeeping or non-signaling components = cyc(tot) fSks,tot() T (5) (hk) and further in astrocytic (a) versus neuronal (n) components. VSATP() The detail of processes contained in these categories is discussed with k a constant to be determined. Combining Eqs 3 and 5 in the “Results” section. By construction, ffff+++ =1. hk,n hk,a s,n s,a leads to To this end, we combine two preexisting datasets. The fi rst dataset is the average tissue glucose (CMR ) and oxygen (CMR ) utiliza- 6 ⎛ Af() S VT () S ⎞ glc O2 rS()=−1 ⎜ s,tot ATP +B⎟ (6) tion computed for the different brain states as defi ned in Gjedde O2 CMR ()S ⎝ k ⎠ (2007). These four states S are: (1) no function, (2) low function/ O2 unconscious, (3) high function/awake and (4) maximum cortical Choosing rO2 for a specifi c state S allows the determination of k. activation. The second dataset is the measured empirical linear rela- Inserting k back in Eq. 6 then determines rO2 for the other states. tion linking the total cycling of neurotransmitters Vcyc(tot) to the neu- In other words, the hypothesis that the fraction of energy used for n ronal oxidative glucose utilization CMRglc,ox as recently reviewed in signaling is proportional to Vcyc(tot) (Eq. 5) makes the astrocytic

Hyder et al. (2006). The following analysis further assumes (i) that contributions to oxygen utilization (rO2) interdependent over dif- cells other than glia or neurons can be neglected (for simplicity, ferent activation states. rO2(S) can then be inserted into Eq. 3 to

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compute Vcyc(tot)(S). The fraction of energy expended by astrocytes and introduce a method to segment energy production of different for signaling is then given by compartments and categories of interest. More specifi cally, we aim at segmenting energy production in the gray matter in signaling NV() S = acyc(tot) versus non-signaling components (housekeeping) and further in fSs,a () T (7) VSATP() glial versus neuronal components. To this end, we combine two preexisting datasets. The fi rst dataset is the empirical linear rela- with N the cost of recycling one neurotransmitter molecule and a tion linking the total cycling of neurotransmitters V to the fS()=− f () S fS (). cyc(tot) s,n s,tot s,a neuronal oxidative glucose utilization CMRn (Hyder et al., 2006) We then estimate the housekeeping metabolism of neurons from glc,ox (see Figures 1A,B). The second dataset is the average tissue glucose the value of B. Assuming that neurons are only fed on glucose in (CMR ) and oxygen (CMR ) utilization computed for the dif- state 1, we write glc O2 ferent brain states S = 1,…,4 (see Figures 1C,D). These four states ( λ + ) S are defi ned as: (1) no function, (2) low function/unconscious, = 62B fShk,n () T (8) (3) high function/awake and (4) maximum cortical activation (see VS() ATP Gjedde, 2007 for further details). It is shown in the “Materials and =− Methods” section that these two datasets are suffi cient to compute and thus fSfhk,a() hk,tot () SfS hk,n (). It is then possible to compute a steady-state budget for gray matter under the hypothesis that the rglc, the astrocytic contribution to glucose utilization by compar- + T energy used for signaling is proportional to V , neglecting cells ing [()fSs,a f hk,a ()]() SVS ATP with the amount of energy produced cyc(tot) by astrocytes computed from the fractions of glucose and oxygen other than glia or neurons and assuming that energy measured as that they use. Some algebra leads to adenosine triphosphate production is used in the compartment where it is produced. For the sake of simplicity, all glial cells are ⎣⎡ fS()+ f () SV⎦⎤ T () S−λ rS ()CMR () S pooled together and are hereafter indiscriminately referred to as rS()= s,a hk,a ATP O2 O2 (9) glc astrocytes or glia. These two datasets are taken from the literature. 2CMRglcc()S All the other results presented in this section have been calculated Finally, we compute the amount of non-oxidized carbons on the basis of these data. released or captured by neurons and astrocytes by comparing the In order to segment energy production between the neuronal utilization of glucose and oxygen in both cell types. To that end, and the glial compartments, it is necessary to know their cor- we use Gjedde (2007) responding glucose and oxygen utilization. Direct and indirect measurements of the compartmentalization of glucose utiliza- =−⎡ ⎤ −−λ[] JScarbons,n()21⎣ rSS glc ()⎦CMR glc () 1 rSS O2 () CMR O2 ()(10) tion are available for various conditions and systems but have

yielded relatively different fi gures with estimates of the glial con- λ for neurons and Jcarbons,a(S)=2rglc(S)CMRglc(S)– rO2(S)CMRO2(S) tribution to glucose utilization (rglc) ranging from about 50% to for astrocytes with Jcarbons being positive if carbons are released or 100% (Nehlig et al., 2004; Tsacopoulos et al., 1988; Véga et al., negative if carbons are required to satisfy for the observed oxygen 2003; Zielke et al., 2007). So far, there is no direct measurement utilization in that compartment. of the glial contribution to oxygen utilization (rO2), however Parameters in this study were chosen as follows. A and B were the relative activities of the TCA cycle could be used as a proxy obtained by fi tting Eq. 2 to the data in Figures 1A,B (least-square fi t; (see Jolivet et al., 2009). It is however very diffi cult to relate these data equally weighted). In the case of humans, because of the lack measurements to the abovementioned brain states S = 1,…,4. As ≈ of data in the range Vcyc(tot) 0, we imposed the value of B to be demonstrated in the “Materials and Methods” section, the values three times smaller than the value of B obtained for rodents to of r (S) become interdependent under the hypothesis that the account for the fact that human glucose utilization in state 1 is O2 fraction of energy used for signaling is proportional to Vcyc(tot). one-third of the one in rodents (see Figures 1C,D) (Gjedde, 2007). In other words, choosing the value of r for any given state −1 −1 O2 This procedure yields A = 0.86, B = 0.1 (µmol g min ) for rodents determines the value of r for all the other states. In the follow- = −1 −1 O2 and A = 1.14, B 003. (µmol g min ) for humans. Finally, we ing analysis, we consider two scenarios. In the fi rst scenario, we ∼ used Na = 2.2 assuming fi rst that GABA constitutes 20% of the assume that glial oxygen utilization is approximately constant total neurotransmitter cycling (Patel et al., 2005) and second that Δ34→ = across all states ( ox,a 0%), consistent with the observation recycling one glutamate molecule requires 2.33 ATPs (Attwell and made in hippocampal slices by Kasischke et al. (2004) that NADH Laughlin, 2001) while recycling one GABA molecule only uses 1.66 autofl uorescence is constant in astrocytic mitochondria upon ATPs (Chatton et al., 2003). activation. In the second scenario, we assume that glial oxygen Δ34→ =+ utilization increases by 15% from state 3 to state 4 ( ox,a 15%) RESULTS (Cruz et al., 2005).

We aim at computing an energy budget of cerebral gray matter for Figure 2 shows rO2 and rglc computed following the procedure different states of activity (Gjedde, 2007). Rather than computing detailed in the “Materials and Methods” section for rats (A) and this budget in a bottom-up fashion by evaluating and then summing humans (B) in the fi rst (solid lines) and the second scenario up the contribution of individual biophysical processes (Attwell (dashed lines). Our method yields results very similar for both and Laughlin, 2001; Nawroth et al., 2007), a useful approch, which species and consistent with experimental fi ndings. We fi nd that rglc however relies on a considerable number of estimates and approxi- is increasing with the level of activation and typically rests between mations, we start from the total steady-state energy production 49% and 78% in humans and between 49% and 98% in rats in

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FIGURE 1 | Cerebral glucose and oxygen utilization derived from the Hyder et al. (2006). Values have been calculated based on measurements n 13 13 literature. (A) Neuronal oxidation of glucose equivalents CMRglc,ox as a of C labeling of glutamate from [1- C]glucose. (C) Average tissue glucose −1 −1 function of the total neurotransmitter cycling Vcyc(tot) in the rodent brain (black) and oxygen (white) utilization in the rodent brain (µmol g min ) (µmol g−1 min−1). (B) Same as in (A) but in the human brain. In both in the four brain states defi ned in the text. (D) Same as in (C) in the (A) and (B), the solid lines indicate the least-square fi t of the data points human brain. Data in (C) and (D) and brain states are adapted from (see Materials and Methods). Data in (A) and (B) are adapted from Gjedde (2007). agreement with in vivo measurements (Nehlig et al., 2004) and parameters convert into about ±5% fl uctuations in the predicted ± other modeling efforts (Hyder et al., 2006). The increase of rglc with value of rO2 and about 19% fl uctuations in the predicted value the level of activation is less prominent in the second scenario than of rglc. However, the compartmentalization is not strongly affected in the fi rst scenario and this effect is more pronounced in humans with most of oxygen being used by neurons in both scenarios, with rglc being almost constant in the latter case. In both species, we most of glucose being used by astrocytes in the fi rst scenario and

fi nd the glial oxygen utilization fraction rO2 to be decreasing with a more balanced situation with about the same amount of glucose the level of activation from about 49% in state 1 to approximately being used by both compartments in the second scenario. Finally,

10% in state 4. Again, these predictions are consistent with experi- we observe that the values computed for rO2 in the activated state mental fi ndings showing that the relative contribution of glia to the are remarkably close to the distribution of mitochondria between total TCA cycle might be higher in anaesthetized animals (∼41%) neurons and glia (Wong-Riley, 1989). (Choi et al., 2002) than in awake animals (∼21%) (Öz et al., 2004). We formulated the two scenarios considered here as an increase

Likewise, we fi nd rO2 values in the range 6–17% in states 3 and 4 of astrocytic oxygen utilization from state 3 to state 4 because it is consistent with measurements in awake humans reporting ∼8% numerically convenient. It is interesting to note however that in the ∼ ∼ (Shen et al., 1999), 10% (Gruetter et al., 2001) and 11% (Lebon second scenario, the astrocytic oxygen utilization (rO2·CMRO2) con- et al., 2002) (calculated from the ratio of TCA cycles as summa- tinuously increases from state 1 to state 4 (Choi et al., 2002; Öz et al., rized in Hyder et al., 2006). Fluctuations in the order of ±5% in the 2004; Serres et al., 2008). We consider that GABA constitutes 20%

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FIGURE 2 | Calculated astrocytic contribution to glucose and oxygen oxygen utilization increases by 15% from state 3 to state 4; dotted).

utilization. (A) Astrocytic contribution to glucose (rglc; red) and oxygen (B) Same as in (A) in the human brain. Shaded areas delimit the ± utilization (rO2; black) in the rodent brain for the fi rst scenario (constant maximal deviations observed with 5% parameter fl uctuations astrocytic oxygen utilization; solid) and the second scenario (astrocytic (see text). of the total neurotransmitter cycling (see Materials and Methods). for rats (A) and humans (B) and details the exact percentages for

If GABA is recycled by astrocytes, it seems surprising that rO2 can be state 4 (C–D). By construction, these four fractions sum up to 1 signifi cantly lower than this value. However, each GABA recycled in all four states. As expected, the fraction of energy dedicated to by astrocytes might lead to the production of NADH and FADH2 housekeeping metabolism decreases with the level of activation requiring a maximum of 1.5 O2 per GABA molecule. Hence, rO2 can while the fraction of energy dedicated to signaling increases with ××< × be smaller than 20% as long as 1. 5 20 100 Vrcyc(tot) O2CMR O2 the level of activation to reach 84% and 86% in rodents and in which is always the case in our results (data not shown). Similarly, it humans respectively. Of these, the astrocytes only contribute for a has been reported by several groups that the rate of glial anaplerotic small fraction of 7% in rodents and 5% in humans. The rest, about synthesis might be as high as one-third of the rate of 80%, is used for neuronal signaling. Our approach yields fi gures for the glutamate-glutamine cycle (Lieth et al., 2001; Merle et al., 2002; the energy budget remarkably similar to the results of Attwell and Sibson et al., 2001; Xu et al., 2004). Glutamine generated in that Laughlin (2001). Interestingly, the computed energy budget is not way might lead to the production of NADH requiring a maximum signifi cantly dependent on the scenario considered, and therefore of 1.5 O2 per glutamine molecule. Hence, rO2 can be smaller than only the fi rst scenario is shown. ×× <× 33% as long as 15./ 1 3 Vrcyc(tot) O2CMR O2 which is always the Using the values of rO2(S) we have derived together with Eq. 3, case in our results (data not shown). it is now possible to compute Vcyc(tot)(S), i.e. the amplitude of

With rO2(S) and rglc(S) available, it is possible to compute the the cycling of neurotransmitters corresponding to brain states … energy budget for four categories of interest. They are the astro- S = 1, ,4. Figure 4 shows Vcyc(tot)(S) calculated in this way for cytic housekeeping metabolism category, the neuronal housekeep- both humans and rodents in both scenarios. This procedure yields ing metabolism category, the astrocytic signaling category and the values in range of experimental measurements. We fi nd values of neuronal signaling category (see Materials and Methods). By con- Vcyc(tot) between 0 and 0.35 for humans and between 0 and 1.17 struction, these categories cover the following biophysical proc- for rodents. Interestingly, these results closely match the ones esses. The housekeeping categories contain all energy demanding reported by Gjedde, obtained with a different approach (Gjedde, ≈ ≈ ≈ processes which are not related to signaling tasks, that is essentially 2007). He fi nds Vcyc(tot)(1) 0, Vcyc(tot)(2) 0.2 and Vcyc(tot)(3) 0.5 for ≈ ≈ maintaining the electrochemical gradient across the cell membrane the rodent, whereas we can deduce Vcyc(tot)(1) 0, Vcyc(tot)(2) 0.2 and + + ≈ by activating the Na /K pump as well as biochemical processes Vcyc(tot)(3) 0.6. Note that the choice of a specifi c scenario does not required to maintain structural integrity. The neuronal signal- affect the results signifi cantly, nor do ±5% fl uctuations in the free ing category contains the energy expended after the activation of parameters (i.e. A, B and Na the average cost of recycling one neu- postsynaptic receptors and after the generation and propagation rotransmitter molecule). of action potentials, mostly due to the activation of the Na+/K+ Finally, it is possible to evaluate the level of neuron-glia meta- pump needed to restore the electrochemical gradients across the bolic exchanges by comparing the balance of oxygen and glucose cell membrane. It also includes the energy required to package utilization in these two compartments. Indeed, complete oxi- neurotransmitters into vesicles at presynaptic terminals. Finally, dation of glucose requires six times more oxygen than glucose the astrocytic signaling category contains the energy used to capture (Gjedde, 2007). Thus, combining the experimental values for and metabolically process neurotransmitters. Figure 3 shows the CMRO2(S), CMRglc(S) (Figures 1C,D) and the values we derived energy budget computed (fi rst scenario) for these four categories for rO2(S), rglc(S) (Figure 2) into Eq. 10, it is possible to compute

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FIGURE 3 | Calculated energy budget for the fi rst scenario. (A) Fractions of (B) Same as in (A) in the human brain. (C) Pie chart of these fractions in state 4 energy spent for astrocytic housekeeping (green), astrocytic signaling (pink), in the rodent brain. (D) Same as in (C) in the human brain. Abbreviations ast and neuronal housekeeping (red) and neuronal signaling (white) in the rodent brain. nrn refer to astrocytes and neurons respectively.

Jcarbons(S). Jcarbons is positive if the compartment exports carbons well as for both scenarios considered in this paper. In all cases, we (net transfer), that is, if the observed oxygen utilization in that observe a strong linear relationship (R2 ≥ 0.99) indicating that the compartment is smaller than six times the observed glucose uti- amplitude of the glia-to-neuron carbon exchange is proportional lization. On the contrary, Jcarbons is negative if the compartment to the activity in the tissue measured as the total cycling of neuro- imports carbons, that is, if the observed oxygen utilization in that transmitters. The overall amplitude of this coupling signifi cantly compartment is larger than six times the observed glucose utili- depends on the scenario considered. It is signifi cantly stronger zation. Doing so, we fi nd that Jcarbons is systematically positive for in the fi rst scenario (constant astrocytic oxygen utilization) than astrocytes, systematically negative for neurons and very close to in the second scenario (astrocytic oxygen utilization increases 0 in the case of state 1 for both the neuronal and the astrocytic by 15% from state 3 to state 4). Finally, the fact that astrocytes compartments. This indicates that carbons are released from the always export more carbons than neurons capture suggests that glial compartment and are at least partially taken up by the neu- a small fraction of carbons is simply released by the system to the ronal compartment. In the case of state 1, glia and neurons are bloodstream consistent with fi ndings that lactate is being released metabolically separated (no fl ux of carbons). The latter result is by the brain in various states (Dalsgaard, 2006). to be expected since the measured ratio CMRO2(1)/CMRglc(1) is Our analysis relies on the choice of three parameters, A and B n very close to 6 indicating a well balanced system. Moreover, we characterizing the linear relation between CMRglc,ox and Vcyc(tot) and imposed that neurons use exclusively glucose in this state when Na representing the average cost of recycling one neurotransmitter computing rglc, thus preventing glia-to-neuron carbon exchanges. molecule. In addition, we have arbitrarily selected two scenarios.

Figure 5 shows the absolute value of Jcarbons versus the level of In the fi rst scenario, we assume constant astrocytic oxygen utiliza- Δ34→ = activation as embodied by the total cycling of neurotransmitters tion ( ox,a 0%), while in the second scenario we assume that

Vcyc(tot)(S). Jcarbons is computed individually for neurons and glia as the astrocytic oxygen utilization increases by 15% from state 3 to

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Δ34→ =+ state 4 ( ox,a 15%). None of the results presented in this paper the balance of glucose utilization from being mostly glial to being was dramatically affected by ±5% fl uctuations of the value of A, B mostly neuronal. As a consequence, the amplitude of the carbon and/or Na. On the contrary, the choice of a scenario for the rela- shuttle from glia to neurons progressively decreases with increasing Δ34→ Δ34→ + tive increase of the astrocytic oxygen utilization has a signifi cant values of ox,a (Figure 5). Increasing ox,a beyond 15%, we fi nd Δ34→ =+ impact on the results as already illustrated in Figures 2 and 5. In that the glia to neuron shuttle stops at ox,a 22% for humans Δ34→ =+ + particular, rglc is signifi cantly smaller with ox,a 15% than with and 23% for rodents yielding a situation where both cell types are Δ34→ = Δ34→ ox,a 0% (Figure 2). Thus, increasing ox,a progressively shifts metabolically independent and releasing excess carbons. Increasing Δ34→ ox,a further, we fi nd that a shuttle from neurons to glia takes place Δ34→ =+ for values ox,a 27% and higher.

DISCUSSION The exact principles underlying the coupling of metabolic processes in register with neuronal activity and in particular the nature and role of neuron-glia metabolic interactions are still a subject of active debate. Here, we have introduced a novel computational approach to decipher neuron-glia compartmentalization in the context of brain energy metabolism. Based on measurements of tissue glu- cose and oxygen utilization in different brain states (Figure 1), our approach allows computing the fractions of oxygen and glucose

taken up by glial cells (rO2 and rglc) and neurons (1-rO2 and 1-rglc respectively; Figure 2). Our approach suggests that a signifi cant portion of glucose is taken up by astrocytes while oxygen is mostly used within the neuronal population and that this bias increases with the level of activation. The exact proportion of astrocytic glu- cose uptake is dependent on the scenario considered with most glucose being taken up by astrocytes in the fi rst scenario and a more balanced situation in the second scenario. We then computed an activity-dependent energy budget for the brain (Figure 3) and assessed the balance of oxygen and glucose in both the neuronal and glial compartments (Figure 5). Finally, we found that there is a probable transfer of glucose-derived metabolites from astrocytes FIGURE 4 | Calculated Vcyc(tot) in the rodent brain (green) and in the human brain (blue) for the fi rst (solid) and the second scenario (dotted). to neurons, the amplitude of which is proportional to the level Shaded areas delimit the maximal deviations observed with ±5% parameter of activity as measured by the cycling of neurotransmitters. Our fl uctuations (see text). Note that V here was calculated by us and differs cyc(tot) approach is systematically applied to both human and rodent data from V as plotted in Figures 1C,D which was taken from the literature. cyc(tot) yielding similar results for both species.

FIGURE 5 | Calculated transfer of carbons. (A) Flux of carbons leaving µmol g−1 min−1). (B) Same as in (A) in the human brain. Shaded areas the astrocytes (black), alternatively entering the neurons (absolute values; delimit the maximal deviations observed with ±5% parameter fl uctuations red), in the rodent brain for the fi rst (solid) and the second scenario (dotted; (see text).

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Our fi ndings are in general agreement with results by Attwell and same procedure can be applied to the glial and neuronal fractions Laughlin (2001) on the cost of cortical computation. With our top- of glucose and oxygen utilization and to the energy budget (not down approach it is not possible to distinguish between the cost of shown). action potentials and the cost of postsynaptic potentials which are Our method is in part based on several assumptions that are pooled together with other mechanisms in the neuronal signaling rather common in the fi eld. It is assumed that cells other than glia component fs,n. It is nevertheless possible to make a rough estimate or neurons can be neglected since these two cell types constitute the of the cost of postsynaptic potentials using the same strategy as used vast majority of cells in the brain and occupy most of the cortical in Eq. 7, that is allocating a fi xed cost to postsynaptic potentials per tissue volume (not counting extracellular space) (Verkhratsky and recycled glutamate molecule while neglecting inhibition. After a Butt, 2007). Even though ATP can be released as a neurotransmitter, quick calculation based on the study by Attwell and Laughlin using notably by astrocytes, this release is unlikely to contribute signifi - only the smallest reported value (that is 25.5 ATP/glutamate as a cantly in comparison to the amount of ATP produced to fuel the result of NMDA, non-NMDA and G-protein coupled receptors), system. Finally, like most modeling work and some experimental we fi nd that postsynaptic potentials would account for 47% of the techniques in the fi eld, our approach is restricted to the steady- total ATP utilization versus 35% for action potentials in humans state condition. It also relies on the hypothesis that the total energy and 58% versus 20% in rodents in the maximally activated state. used for signaling in the tissue is linearly proportional to the total These numbers suggest that postsynaptic potentials might con- cycling of neurotransmitters. While it is obvious that this hypoth- tribute more to the energy budget than originally suggested by esis holds for the cost associated to neurotransmitters recycling, Attwell and Laughlin (2001). This is consistent with the fi nding it is less clear that it holds for action potentials and postsynaptic that metabolic response is more correlated with local fi eld poten- potentials. However, the frequency versus current (f-I) curve of tials, refl ecting principally post-synaptic potentials, that to spiking cortical neurons is close to linear in the presence of noise (Rauch activity (Logothetis et al., 2001). et al., 2003). One can therefore assume that this hypothesis also The fi ndings presented here are also consistent with an activity- holds within a physiologically relevant regime although it may not regulated transfer of glucose-derived metabolites from astro- be valid in pathological cases or at either very low or very high levels cytes to neurons as it was originally proposed by Pellerin and of activation. Also note that our approach is not strictly restricted by Magistretti (1994). Existence of this mechanism has been recently this hypothesis and could easily be extended to non-linear relation- demonstrated in slices (Rouach et al., 2008). Our calculations ships. The analysis would be essentially the same but would then show that such a shuttle from astrocytes to neurons is perfectly require extra data in order to estimate the additional parameters compatible with a relatively low cost associated to the recycling entering into Eq. 5 and characterizing the relation between fSs,tot() of neurotransmitters and with an upregulation of the astrocytic and VScyc(tot)(). oxidative metabolism upon activation. Our approach does not The results derived here rely on a steady-state or quasi steady- allow us to determine the metabolic species involved in this shuttle state condition. In the fi rst few seconds that follow the increase or but there is no doubt that lactate must be an important com- decrease in brain activation, the tissue undergoes fast metabolic ponent of it, given the experimental evidence indicating lactate transitions and the system is undoubtedly out of steady-state. usage by neurons (Schurr and Payne, 2007). Of course the pos- However, upon activation, cerebral blood fl ow reaches a new sta- sibility that several metabolic species contribute to this shuttle tionary level after a few seconds only. Moreover, it was recently cannot be excluded (see, e.g., Pfrieger, 2003). The potential roles shown that sustained neuronal activation raises metabolism to a of this shuttle beyond feeding neurons remains to be determined. new steady-state level (Mangia et al., 2007). In particular, lactate Interestingly, lactate was recently demonstrated to play a direct quickly reaches a new steady-state and so does pyruvate because role in the regulation of the local blood fl ow (Gordon et al., 2008; of the dynamic equilibrium between these metabolites. Similarly, Yamanishi et al., 2006), of neuronal activity in the retrotrapezoid recovery from activation is very slow, taking place over minutes nucleus (Erlichman et al., 2008) as well as in the regulation of to tens of minutes as illustrated by the slow decay of accumulated the local inhibitory activity in the subfornical organ (Shimizu lactate after stimulation (Prichard et al., 1991). Likewise, it seems et al., 2007). reasonable to assume that different anesthetic levels correspond to Our approach relies on the division of brain activity in states different steady-states. Even though our formalism was developed as defi ned by Gjedde (2007). Average tissue glucose and oxygen under the assumption of steady-state conditions, we expect it to be utilization are provided for all these states (Figures 1C,D). While valid except during the short transitions between different steady- this division might be perceived as slightly arbitrary, it allows us states or quasi steady-states. Simulations of such non-steady-state to compute the astrocytic and neuronal fractions of glucose and transitions require alternative modeling methods. oxygen utilization (Figure 2), the energy budget (Figure 3) and As already discussed previously, our approach yields qualita- the net transport of glucose-derived metabolites (Figure 5) for a tively robust results when we apply ±5% fl uctuations in the param- Δ34→ meaningful range of activation levels. These states should not be eters. This is true except for ox,a which characterizes how much considered as fi xed and well-defi ned categories but rather as indi- the astrocytic oxygen utilization increases with activation (from Δ34→ vidual samples along a continuum of brain activation states. For a states 3 to 4). In particular, increasing ox,a progressively shifts better comparison with experimental results, it is then possible to the balance of glucose utilization from being mostly glial to being convert these states into the corresponding amplitude of the cycling mostly neuronal. As a consequence, the amplitude of the carbon of neurotransmitters Vcyc(tot) (Figure 4) as illustrated for the case of shuttle from glia to neurons progressively decreases with increas- Δ34→ Δ34→ the net transport of glucose-derived metabolites (Figure 5). The ing values of ox,a (Figure 5). While the value we chose for ox,a is

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Δ34→ ≈+ in line with the study by Cruz et al. (2005) ( ox,a 16%), some not contribute to an extent that would affect the calculated energy of us have reported larger values in the range of +90% in rodents budget. Similarly, neglecting does not change our fi ndings and +60% in humans (Wyss et al., 2009). However, it should be on the astrocyte-neuron transfer of glucose-derived metabolites. noted that the increase in CMRglc between rest and activation Glycogen utilization can be interpreted as an increase in the effective observed by Wyss and colleagues is about +130%, much larger astrocytic fraction of the total glucose used to feed ATP synthesis. than the values used in this study (+79% in humans and +75% in Furthermore, the end product of glycogenolysis in astrocytes has rats). When increasing CMRglc(4) so as to match such an increase, been reported to be lactate (Dringen et al., 1993). This process is Δ34→ Δ34→ =+ we could increase ox,a as high as ox,a 60% in rodents with consistent with the concept of the astrocyte-neuron lactate shut- no signifi cant qualitative change in the results presented above tle hypothesis rather than with the exchange of substrates in the Δ34→ (not shown). Nevertheless, the importance of ox,a as a control opposite direction (Pellerin et al., 2007). parameter in our approach suggests that the oxidative metabo- It should be further emphasized that our results do not depend lism of astrocytes might play a very important role in the control on any assumption about the distribution of glucose and lactate of metabolic neuron-astrocyte interactions possibly inducing a transporters or on a specifi c scheme of stimulation during activa- change of regime from highly interdependent cell populations at tion. Likewise, they do not depend on the exact route followed the onset of activation when the astrocytic oxidative metabolism by metabolites, the extracellular space very likely being the place is not or only weakly upregulated (Cruz et al., 2005; Kasischke of exchanges between astrocytes and neurons. Furthermore, our et al., 2004) to metabolically disconnected or weakly connected results are independent from the exact pathways involved in glucose cell populations at later stages of stimulation (Wyss et al., 2009). oxidation. More specifi cally, they hold equally well whether lactate The lactate produced in these late stages could diffuse away from or pyruvate is the end product of aerobic glycolysis in neurons the production site, possibly to other brain areas (Dienel and Cruz, (Schurr and Payne, 2007). Finally, our approach bypasses consid- 2004; Dienel and Hertz, 2001). erations on what drives the lactate shuttle, glutamate capture by In our analysis, we have not considered glycogen, a potentially astrocytes (Pellerin and Magistretti, 1994) or activation of astrocytic important energy substrate reservoir localized in astrocytes only. AMPA receptors (Caesar et al., 2008), while producing estimates During strong activation, there is evidence that the stock of glyco- of the cost of recycling glutamate consistent with other studies gen decreases (Swanson et al., 1992). Glycogen has been reported (Attwell and Laughlin, 2001). Future work is needed to experimen- to be continuously degraded and resynthesized (Shulman et al., tally test the predictions and conclusions drawn from the present 2001; Walls et al., 2009). Glucose metabolism via this glycogen shunt modelling work. only produces one ATP versus two generated via the glycolysis. Notwithstanding, our main results should not be signifi cantly ACKNOWLEDGMENTS affected by this simplifi cation even though it implies that our This work was supported by the Swiss National Science Foundation estimate of the astrocytic contribution to the total energy budget (grant PP00B-110751/1), the Novartis Research Foundation and might be slightly overestimated. It is important however to keep the OPO Foundation (to BW). RJ is supported by a fellowship from in mind that most of the ATP is produced oxidatively. Moreover, the Roche Research Foundation and by a research grant from the the size of the glycogen reservoir is relatively small and thus may Forschungskredit der Universität Zürich.

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