Brain lactate kinetics: Modeling evidence for neuronal lactate uptake upon activation

Abstract

A critical issue in brain energy metabolism is whether lactate produced within the brain by astrocytes is taken up and metabolized by neurons upon activation. Although there is ample evidence that neurons can efficiently use lactate as an energy substrate, at least in vitro, few experimental data exist to indicate that it is indeed the case in vivo. To address this question, we used a modeling approach to determine which mechanisms are necessary to explain typical brain lactate kinetics observed upon activation. On the basis of a previously validated model that takes into account the compartmentalization of energy metabolism, we developed a mathematical model of brain lactate kinetics, which was applied to published data describing the changes in extracellular lactate levels upon activation. Results show that the initial dip in the extracellular lactate concentration observed at the onset of stimulation can only be satisfactorily explained by a rapid uptake within an intraparenchymal cellular compartment. In contrast, neither blood flow increase, nor extracellular pH variation can be major causes of the lactate initial dip, whereas tissue lactate diffusion only tends to reduce its amplitude. The kinetic properties of monocarboxylate transporter isoforms strongly suggest that neurons represent the most likely compartment for activation-induced lactate uptake and that neuronal lactate utilization occurring early after activation onset is responsible for the initial dip in brain lactate levels observed in both animals and humans.

• astrocyte-neuron lactate shuttle
• brain energy metabolism
• mathematical model
• monocarboxylate transporter

Full text

Brain lactate kinetics: Modeling evidence for neuronal
lactate uptake upon activation
Agne` s Aubert*, Robert Costalat
†
, Pierre J. Magistretti
‡
, and Luc Pellerin*
§
*De´ partement de Physiologie, Universite´ de Lausanne, 1005 Lausanne, Switzerland; †Institut National de la Sante´ et de la Recherche Me´ dicale U678,
Universite´ Pierre et Marie Curie, 75013 Paris, France; and ‡Brain and Mind Institute, Ecole Polytechnique Fe´de´ rale de Lausanne and Centre de Neurosciences
Psychiatriques, Department of Psychiatry, Centre Hospitalier Universitaire Vaudois, 1011 Lausanne, Switzerland
Edited by Marcus E. Raichle, Washington University School of Medicine, St. Louis, MO, and approved September 22, 2005 (received for review June 28, 2005)
A critical issue in brain energy metabolism is whether lactate
produced within the brain by astrocytes is taken up and metabo-
lized by neurons upon activation. Although there is ample evi-
dence that neurons can efficiently use lactate as an energy sub-
strate, at least in vitro, few experimental data exist to indicate that
it is indeed the case in vivo. To address this question, we used a
modeling approach to determine which mechanisms are necessary
to explain typical brain lactate kinetics observed upon activation.
On the basis of a previously validated model that takes into
account the compartmentalization of energy metabolism, we de-
veloped a mathematical model of brain lactate kinetics, which was
applied to published data describing the changes in extracellular
lactate levels upon activation. Results show that the initial dip in
the extracellular lactate concentration observed at the onset of
stimulation can only be satisfactorily explained by a rapid uptake
within an intraparenchymal cellular compartment. In contrast,
neither blood flow increase, nor extracellular pH variation can be
major causes of the lactate initial dip, whereas tissue lactate
diffusion only tends to reduce its amplitude. The kinetic properties
of monocarboxylate transporter isoforms strongly suggest that
neurons represent the most likely compartment for activation-
induced lactate uptake and that neuronal lactate utilization occur-
ring early after activation onset is responsible for the initial dip in
brain lactate levels observed in both animals and humans.
astrocyte-neuron lactate shuttle 兩brain energy metabolism 兩mathematical
model 兩monocarboxylate transporter
Brain energy metabolism is considered nearly fully aerobic
(1), with glucose as the major energy substrate of neurons,
at rest and during activation. Some observations, however,
made with functional brain imaging methods challenged this
classical view. Fox and Raichle (2) observed a mismatch
between the increases in cerebral metabolic rate of glucose and
the relatively smaller increase in cerebral metabolic rate of O
2
during somatosensory and visual activations. As a conse-
quence, it was postulated that brain activation can lead to a
disproportionate stimulation of glycolysis despite the presence
of sufficient oxygen levels. This hypothesis was substantiated
by the finding that an increase in lactate levels within the
activated area is obtained under different stimulation para-
digms and modalities (3–6). As a consequence, one of the
critical issues in brain energy metabolism concerns our un-
derstanding of brain lactate metabolism and especially its
compartmentalization between neurons and astrocytes (7–9).
Interpretation of lactate kinetics in terms of cellular produc-
tion, utilization, or disposal remains complex. For instance, Hu
and Wilson (10) found an initial dip of extracellular lactate
concentration in the rat hippocampus, and an early decrease
in tissue lactate was recently reported by Mangia et al. (11)
using
1
H magnetic resonance spectroscopy. This initial lactate
dip was interpreted by Hu and Wilson as a consequence of
lactate consumption by neurons, a view that was challenged by
Mangia et al. The difficulty in interpreting such kinetics lies in
its dependence on various physiological factors. Therefore, it
seems important to make a synthesis from the various lactate
kinetics data and identify the different possible physiological
determinants for lactate kinetics. The aim of this work was to
quantify the contribution of various physiological mechanisms
to brain lactate kinetics. This quantification relies on a review
of experimental data and a mathematical model of lactate
exchanges, based on a previously validated model of compart-
mentalized energy metabolism (12). Our modeling approach
takes into account all mechanisms that are known to deter-
mine extracellular lactate concentration and includes a sys-
tematic study of the effect of changing these parameters.
Specifically, we studied the effect of cellular production or
consumption, regional cerebral blood flow (CBF), exchanges
through the blood–brain barrier (BBB) and extracellular pH
variation, which in turn can affect BBB exchanges. Focusing on
the question of the initial dip of the extracellular or tissue
lactate concentration, we show that it cannot be satisfactorily
explained either by an early increase in CBF or pH variations;
furthermore, tissue lactate diffusion could only reduce the
amplitude of this dip. Thus, we conclude that the lactate initial
dip is a consequence of an increased lactate consumption by
some cells or a decrease of lactate production during the first
10–20 s of stimulation. An analysis of magnetic resonance
spectroscopy data shows that the latter hypothesis is quite
unlikely, so that cell lactate consumption must occur at the
beginning of the stimulation. Moreover, based on the kinetic
properties of the various isoforms of monocarboxylate trans-
porters (MCTs), we show that neurons are better candidates
than astrocytes to be these early lactate-consuming cells. Thus,
the presence of an initial lactate dip strongly suggests that
lactate consumption by neurons occurs from the very start of
stimulation.
Description of the Model
Model of Lactate Kinetics. The present model is designed to allow
a rigorous and systematic reasoning on extracellular lactate
kinetics, so it is intentionally reduced to those elements that
are central to this reasoning: (i) production or uptake by cells,
(ii) exchange through the BBB, (iii) diffusion of lactate
through the tissue, and (iv) pH variations. Extracellular and
capillary lactate concentrations are expressed in mM and
denoted as LAC
e
and LAC
c
, respectively. Volumes and blood
flow values are expressed per unit tissue volume. Thus, V
c
and
V
e
are the dimensionless capillary and extracellular space
volume fraction, respectively, and the capillary blood f low
CBF(t) is expressed in s
⫺1
. The subscript 0 refers to baseline
steady-state values. The equation set is based on elements of
our previously developed models (12, 13).
Conflict of interest statement: No conflicts declared.
This paper was submitted directly (Track II) to the PNAS office.
Abbreviations: CBF, cerebral blood flow; BBB, blood–brain barrier; MCT, monocarboxylate
transporter.
§To whom correspondence should be addressed. E-mail: luc.pellerin@unil.ch.
© 2005 by The National Academy of Sciences of the USA
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November 8, 2005
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Mass balance of extracellular and capillary lactate leads to the
following system of differential equations:
V
e
dLAC
e
dt ⫽J
mb
⫺J
Diff
⫺J
BBB
,[1]
V
c
dLAC
c
dt ⫽J
Cap
⫹J
BBB
,[2]
where J
mb
is the difference between lactate release by some cells
(astrocytes or neurons) and lactate uptake by other cells (neu-
rons or astrocytes), J
Diff
is the flux of diffusion of lactate through
the extracellular space, J
BBB
is the rate of lactate transport
through the BBB, and J
Cap
is the blood flow contribution to
capillary lactate variation. All of these rates are expressed in
mmol per s per unit tissue volume (in liters). Contribution of
sensor to lactate fluxes and the influence of lactate diffusion
coefficient can be neglected (see Supporting Text, which is
published as supporting information on the PNAS web site, for
details).
Neural tissue contribution.
In a simple approach, diffusion of lactate
through the extracellular space could be described as an ex-
change between the stimulated region, with lactate concentra-
tion LAC
e
, and remote brain regions, with concentration LAC
e,0
.
The flux of diffusion from the stimulated region toward the
remote regions, as a first approximation, will be proportional to
D
e
(LAC
e
⫺LAC
e,0
), D
e
being the extracellular diffusion coef-
ficient of lactate. We can thus write J
Diff
as
␤
1
(LAC
e
⫺LAC
e,0
),
␤
1
being a positive constant. The J
mb
term obviously depends on
LAC
e
, so we write J
mb
as
␤
2
(LAC
e,0
⫺LAC
e
)⫹J(t), where J(t)
is an input function that includes all phenomena that are not
explicitly taken into account in Eq. 1, namely the variation of
intracellular lactate and pH gradient across cell membranes.
Especially, cellular lactate production, as well as intracellular
diffusion of lactate, can contribute to lactate kinetics only by
intracellular lactate concentration, so that their possible effect is
included in the input function J(t). Setting
␤
⫽
␤
1
⫹
␤
2
,wecan
write the total tissue contribution to extracellular lactate varia-
tion as:
J
tissue
⫽J
mb
⫺J
Diff
⫽J共t兲⫹
␤
共LAC
e,0
⫺LAC
e
兲.[3]
We have investigated alternative hypotheses for the input term
J(t), especially:
(J1) Based on the results of our previous model (12), we
assumed that J(t) first decreases below the baseline value J
0
, then
increases above the baseline, so that we set:
J共t兲⫽
再
共1⫹
␣
Ji
兲J
0
for 0 ⱕtⱕt
i
␣
Ji
⬍0
共1⫹
␣
J
兲J
0
for t
i
⫹t
J
ⱕtⱕt
end
␣
J
⬎0
J
0
for t⫽0or t ⱖt
end
⫹t
J
[4]
and J(t) linearly increases for t
i
ⱕtⱕt
i
⫹t
J
and linearly decreases
for t
end
ⱕtⱕt
end
⫹t
J
. The constants
␣
Ji
and
␣
J
represent the J(t)
decrease (at the stimulation onset) and increase fractions,
respectively.
(J2) J(t) is constant from 0 ⱕtⱕt
i
, namely
␣
Ji
⫽0. Thus the
increase in J(t) is only delayed with regard to the CBF increase.
Brain-blood transport of lactate.
We have considered various
hypotheses:
(H1) Lactate is supposed to leave the extracellular space
through the BBB by means of a facilitated passive transport of
Michaelis-Menten type (14):
J
BBB
⫽T
max
冉
LAC
e
K
t
⫹LAC
e
⫺LAC
c
K
t
⫹LAC
c
冊
,[5]
where T
max
and K
t
are, respectively, the maximum transport rate
and Michaelis constant (12, 13).
(H2) We took into account the effect of extracellular and
capillary H
⫹
ion concentrations on lactate transport through the
BBB by setting:
J
BBB
⫽T
max
冉
LAC
e
H
e
⫹
K
H
⫹LAC
e
H
e
⫹
⫺LAC
c
H
c
⫹
K
H
⫹LAC
c
H
c
⫹
冊
,[6]
where K
H
is a constant expressed in mM
2
. This formula is a
simplified version of a more general equation for carrier-
mediated symport (15). H
e
⫹
and H
c
⫹
, the extracellular and
capillary proton concentrations respectively, are taken as input
terms.
Based on data from the literature about extracellular pH
variations, we considered the following hypotheses:
Alk-acid: To describe the experimental data of many authors,
for instance (16, 17), consisting of an extracellular alkalinization
followed by an acidification, we set:
pH
e
⫽pH
e,0
⫹A
1
te
⫺t兾
␶
1⫺A
2
te
⫺t兾
␶
2with
␶
1
⬍
␶
2
.[7]
Acid: Because other data (17) only show an acidification,
preceded by a small delay t
d
, we also tested the following
equation:
pH
e
⫽pH
e,0
⫺A
3
共t⫺t
d
兲e
⫺
共
t⫺t
d兲
兾
␶
3for tⱖt
d
[8]
with pH
e
remaining at its baseline value pH
e,0
for 0 ⱕt⬍t
d
.
Because of the lack of reliable data about capillary pH
variation, we tested in each case two extreme hypotheses: either
capillary pH remains constant or its kinetics follows that of
extracellular pH.
Blood flow through capillaries.
The CBF through capillaries, CBF(t),
is an input function, based on the model of Buxton et al. (18) and
magnetic resonance data, namely
CBF共t兲⫽
再
共1⫹
␣
F
兲CBF
0
for t
F
ⱕtⱕt
end
CBF
0
for t⫽0or t ⱖt
end
⫹t
F
,
[9]
while CBF(t) linearly increases for 0 ⬍t⬍t
F
and decreases for
t
end
ⱕtⱕt
end
⫹t
F
.
Blood flow contribution to LAC
c
variation.
The CBF contribution to
capillary concentration changes is given by J
Cap
⫽CBF(t)(LAC
a
⫺LAC
v
), where LAC
a
and LAC
v
are the arterial and venous
lactate concentrations, respectively. Based on our preceding
models (12, 13), we write:
J
Cap
⫽CBF共t兲LAC
a
⫺CBF共t兲LAC
v
⫽2CBF共t兲共LAC
a
⫺LAC
c
兲.[10]
A similar equation was already put forward by Gjedde (19) for
oxygen. In a preceding study, we showed that this simple
formulation is nearly equivalent to more complex ones, based on
partial differential equations (20).
Model of Neuronal and Astrocytic Membrane Lactate-H
ⴙ
Cotransport.
To investigate which cells, neurons or astrocytes, are more likely
to consume or produce lactate under various circumstances, the
transmembrane flux of lactate via MCTs was described by using
the following equation:
J
mb
⫽T
max,ie
冉
LAC
i
H
i
⫹
K
Hie
⫹LAC
i
H
i
⫹
⫺LAC
e
H
e
⫹
K
Hie
⫹LAC
e
H
e
⫹
冊
,
[11]
Aubert et al. PNAS
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November 8, 2005
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vol. 102
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no. 45
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16449
NEUROSCIENCE

where LAC
i
and H
i
⫹
are the intracellular lactate and hydrogen
ion concentrations, respectively; T
max,ie
is the maximal transport
rate through the cell membrane; and K
Hie
is the product of the
Michaelis constant by a mean H
⫹
concentration, namely K
Hie
⫽
Kt䡠10
⫺4.3
. We computed J
mb
兾T
max,ie
as a function of the intra-
cellular lactate concentration LAC
i
, in two cases: low K
t
(neu-
rons) or higher K
t
(astrocytes).
Results
Typical Simulations and Comparison to Experimental Data. In this
section, we compare typical results obtained by using our model
to the experimental data of Hu and Wilson (10), which are
displayed in Figs. 1Aand 2A. Using an enzyme-based lactate
microsensor, Hu and Wilson measured in vivo, with high tem-
poral resolution, extracellular lactate levels in the dentate gyrus
of the rat hippocampus, after a 5-s electrical stimulation of the
perforant pathway.
Unique activation.
Fig. 1Bshows a typical simulation of extracel-
lular lactate changes as a function of time with a 70-s CBF
increase, which was chosen to match the duration of the in-
creased oxygen supply, as ref lected by measured pO
2
[figure 5 in
Hu and Wilson’s paper (21)]. Extracellular lactate concentration
(LAC
e
) increases, with a peak at 177% of its baseline value 73 s
after stimulation onset, and a time constant for LAC
e
relaxation
of ⬇247 s, which is in good agreement with the values published
by Hu and Wilson, i.e., ⬇230 s (10). Most importantly, we could
reproduce the LAC
e
initial dip at stimulation onset (for 0 ⱕtⱕ
23 s) as reported by Hu and Wilson. It must be emphasized that
in this stimulation, cellular contribution J(t) first decreases (for
0ⱕtⱕ18 s), then increases (for 18 s ⱕtⱕ70 s), which causes
a similar variation of J
Tissue
. This initial decrease of J(t)is
essential to obtain a significant initial dip, as discussed below.
Repetitive activation.
Fig. 2Bshows a typical simulation of extra-
cellular lactate changes as a function of time obtained with a
repetitive activation consisting of 10 cycles, Eqs. 1-5being
applied to each cycle. The duration of the CBF increase in the
simulation was chosen on the basis of the duration of the
increased oxygen supply, as ref lected by pO
2
measured by Hu
and Wilson (figure 2 in ref. 10). Sustained elevation of lactate
levels up to a maximum level of 206% was obtained, close to the
reported experimental 204% value (Fig. 2 A). Moreover, at each
new stimulation, a dip in lactate concentration was observed, the
amplitude of which increased with repeated stimulations from
10.5% up to 24.5% of the baseline value.
Robustness of the Model. To test the robustness of these results, we
studied the effect of independent modifications of each of the
main parameters, over a wide range, on the LAC
e
time course
(some of the results being displayed in Table 1). Note that
Fig. 1. Changes of extracellular lactate concentration on a single stimula-
tion. (A) Experimental data. Extracellular lactate concentration, measured by
Hu and Wilson (10) in rat brain hippocampus, after a 5-s electrical stimulation
of the perforant pathway. [Reproduced with permission from ref. 10 (Copy-
right 1997, Blackwell, Oxford).] (B) Typical simulation of extracellular lactate
(LACe) changes as a function of time in the case of a sustained activation with
a 70-s blood flow (CBF) increase. According to hypothesis J1, because of the
cellular contribution J(t), JTissue first decreases for 0 ⬍t⬍18 s, then increases
for 18 s ⬍t⬍70 s. (C) Simulated rates. Temporal evolution of JTissue,JBBB, and
JCap.LACeis expressed as percent of LACe,0, the basal extracellular lactate
concentration. Parameter values (14, 18, 19, 22) are Ve⫽0.2, Vc⫽0.0055,
␤
⫽
0.001 s⫺1,J0⫽0.001 mM䡠s⫺1,Tmax ⫽0.0061 mM䡠s⫺1,Kt⫽3.5 mM (hypothesis
H1), CBF0⫽0.01 s⫺1, and LACa⫽0.3 mM, so that at steady-state values for
lactate are LACe⫽1.19 mM, LACc⫽0.35 mM. Stimulation parameter values
are
␣
F⫽0.8, tF⫽5s,
␣
Ji ⫽⫺0.8, ti⫽18 s,
␣
J⫽4.73, tJ⫽5s,andtend ⫽70 s.
Fig. 2. Changes of extracellular lactate concentration on repetitive stimu-
lation. (A) Experimental data. Measured variation in extracellular lactate
concentration, obtained by Hu and Wilson (10) in rat brain hippocampus,
during a sequence of 5-s electrical stimulations of the perforant pathway with
2-min rest intervals. [Reproduced with permission from ref. 10 (Copyright
1997, Blackwell, Oxford).] (B) Typical simulation of extracellular lactate (LACe)
changes as a function of time in the case of a repetitive activation. All
parameters are the same as in Fig. 1, except that
␣
Ji ⫽⫺1.5 and
␣
J⫽3.85, to
match the amplitude of the first initial dip reported by Hu and Wilson (10). (C)
Simulated rates. Note the time evolution of the initial dip of JTissue.
16450
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parameters J
0
,T
max
,K
t
,CBF
0
,LAC
a
, and
␤
result in various
values of LAC
e,0
and dip amplitude. It must be emphasized that
the CBF increase fraction
␣
F
has nearly no effect on the initial
dip, but the initial decrease of lactate production by cells and兾or
increase in lactate uptake,
␣
Ji
, has a dramatic effect.
Conditions Necessary to Observe an Initial Dip of Extracellular Lactate
Concentration.
Unique activation.
If we consider Eq. 1, we see that
the initial dip can only be caused by a decrease in J
Tissue
⫽J
mb
⫺J
Diff
⫽J(t)⫹
␤
(LAC
e,0
⫺LAC
e
), or an increase in J
BBB
, or both.
Because LAC
e
is lower than its resting value, we can note that a
possible increase in J
BBB
can only be caused by a decrease in
LAC
c
, which in turn must be caused by the CBF increase. To
obtain an initial dip comparable to the data of Hu and Wilson
(10), i.e., a maximal decrease in LAC
e
of ⬇0.07 mM at 18 s, J
BBB
must be increased by a factor of 4. If CBF was dramatically
increased, LAC
c
would be nearly equal to arterial lactate con-
centration, a low value of which is LAC
a
⫽0.3 mM. Then a
simple calculation shows that J
BBB
is multiplied by no more than
1.08. Even if we consider LAC
c
⫽0 mM, J
BBB
is only multiplied
by a factor 1.56. Thus, the lactate wash-out through the BBB,
caused by CBF increase, cannot be the main contributing factor
to the LAC
e
initial dip. Conversely, the findings of the current
study support the claim that the initial LAC
e
dip originates in a
decrease in J
Tissue
below its baseline value at stimulation onset.
Furthermore, the existence of the initial dip can only be caused
by a decrease in the cell contribution term J(t), because the
decrease in LAC
e
below its baseline value makes the term
␤
(LAC
e,0
⫺LAC
e
) positive. The importance of this initial
decrease of cellular contribution can be seen in Table 1 by
comparing the columns
␣
Ji
⫽⫺0.8 and
␣
Ji
⫽0, which emphasizes
the role of an increase in cell lactate consumption or a reduction
of cell lactate production.
Repetitive activation.
In Hu and Wilson’s paper (10) repetitive
activation induces a progressive increase of the initial dip
compared with the preceding cycle. We investigated the origin,
tissular or hemodynamic, of this increase in lactate dip ampli-
tude. In the case of a repetitive activation, the first initial dip is
caused by the initial undershoot of J
mb
, as previously discussed.
When the extracellular lactate concentration increases, the
situation becomes more complex, because J
BBB
and the
⫺
␤
(LAC
e,0
⫺LAC
e
) term, which reflects the effect of extracel-
lular lactate concentration both on extracellular diffusion and
cell membrane transport of lactate, are enhanced because of the
high level of LAC
e
. For instance, in the case of the last initial dip
in Fig. 2B, the amplitude of which is 24.5% of the lactate baseline
value, about half of this amplitude is caused by the initial dip in
J
Tissue
, the remaining part being caused by J
BBB
. Therefore, the
increase in amplitude of the initial dip under repetitive stimu-
lations can be caused by increased consumption by cell, diffu-
sion, and lactate washout by CBF.
Influence of pH Variation. Because pH changes can modify lactate
exchanges by modifying the rate of the lactate-proton symport
through the BBB, we replaced hypothesis H1 with hypothesis H2,
i.e., we took into account the effect of H
⫹
concentrations.
Parameter values were carefully chosen to match experimental
data, especially those published by Xiong and Stringer (17).
Obviously, any extracellular acidification will increase the J
BBB
term, and thus will tend to favor the extracellular lactate dip,
whereas capillary acidification will not favor the dip. The main
findings are summarized in Fig. 3, taking into account various
hypotheses for extracellular pH variation as described in Eqs. 7
or 8. First, if extracellular acidification only occurs (Fig. 3B Left),
the extracellular lactate dip is slightly increased (at most 6% of
the baseline value instead of 5.7%). Second, an initial extracel-
lular alkalinization reduces the initial dip from 5.7% to 5.2%.
Neuronal and Astrocytic Lactate-H
ⴙ
Cotransport. The characteristics
of the intraparenchymal cells make them more or less likely to
take up or produce lactate during activation. To determine which
cell type, namely neurons or astrocytes, is more likely to consume
lactate, we assumed that lactate transport via MCTs through the
cell membrane can be defined by Eq. 11. In these conditions (Fig.
4), the astrocytic capacity to consume lactate when intracellular
lactate is decreased appears to be low compared with neurons,
for instance, even if intracellular lactate equals 0, J
mb
only
reaches ⫺0.25䡠T
max,ie
, while it reaches ⫺0.63䡠T
max,ie
for neurons.
Conversely, astrocytes are more likely to secrete lactate in the
interstitial space than neurons with increasing intracellular
concentration.
Discussion
The possibility that intraparenchymally formed lactate could act
as a significant energy substrate for neurons has been substan-
tiated by a number of in vitro,ex vivo, and in vivo observations
(for review, see ref. 23). Nevertheless, a clear description of brain
lactate kinetics has become essential for defining its key role in
neuroenergetics. Some attempts have been made in the past to
provide a better description of brain lactate kinetics. Kuhr and
colleagues (24) developed a model to interpret their measure-
ments of extracellular, arterial, and venous lactate in rats in vivo,
under various conditions. Although their model does not include
the BBB, their data suggest that lactate clearance from brain
tissue by the bloodstream plays only a minor role, whereas most
tissue lactate would be recycled to pyruvate. More recently,
Leegsma-Vogt and colleagues (25) developed a model of arte-
riovenous lactate differences that is in favor of brain lactate
utilization as an energy substrate. Finally, on the basis of a
Table 1. Effect of parameter values on the extracellular lactate (LAC
e
) kinetics
Parameter
LAC
e,0
,
mM
Initial dip, % of baseline
Peak, % of
baseline
␶
decrease
,s
␣
Ji
⫽⫺0.8
␣
Ji
⫽0
␣
Ji
⫽⫺0.8
␣
F
⫽0.8
␣
F
⫽0.8
␣
F
⫽0
Values of Fig. 1A1.19 5.7 0.2 5.5 177 247
0.0005 ⬍J
0
⬍0.0015 mM䡠s
⫺1
0.7–1.81 4.6–5.4 0.2–0.2 4.6–5.3 164–178 191–334
0.004 ⬍T
max
⬍0.01 mM䡠s
⫺1
1.81–0.83 3.6–8 0.1–0.4 3.4–7.6 153–202 476–135
2⬍K
t
⬍5 mM 0.91–1.48 7.4–4.5 0.4–0.1 6.8–4.3 197–164 184–318
0.008 ⬍CBF
0
⬍0.012 s
⫺1
1.21–1.18 5.6–5.6 0.2–0.1 5.2–5.3 175–178 253–245
0.3 ⬍LAC
a
⬍0.96 mM 1.19–2.21 5.7–3.0 0.2–0.1 5.5–2.9 177–142 247–358
0.0005 ⬍
␤
⬍0.0015 s
⫺1
1.19–1.19 5.7–5.4 0.2–0.2 5.4–5.2 181–173 248–245
Parameter values were varied around mean values drawn from literature (14, 18, 19, 22). When values are displayed as two numbers,
the first corresponds to the minimum value of the parameter, the second to the maximum value of the parameter.
␶
decrease is the time
constant for LACerelaxation.
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previous model describing the relationships between brain elec-
trical activity, energy metabolism, and hemodynamics (13), some
of us developed a model of compartmentalized energy metab-
olism between neurons and astrocytes (12). This theoretical
study suggested that the following mechanisms could occur, at
least during the initial 10–20 s of a sustained stimulation: (i)at
the beginning of the stimulation, neurons would undergo an
increased mitochondrial activity that would consume lactate,
part of which would be supplied by the extracellular pool, and (ii)
intracellular astrocytic lactate levels may slightly decrease be-
cause of lactate consumption by neurons, but this phenomenon
would be progressively overwhelmed by the stimulation of
astrocytic glycolysis. Glycolysis would result in a delayed increase
in astrocytic NADH, a suggestion that is fully consistent with the
NADH fluorescence data of Kasischke et al. (26). The next step,
presented in this article, was to determine whether the purported
neuronal lactate consumption is necessary to explain experi-
mental lactate kinetics.
A Comprehensive Description of Brain Lactate Kinetics Requires
Enhanced Lactate Consumption upon Activation. By taking param-
eter values consistent with brain data for humans or animals, we
were able to simulate extracellular lactate time courses that
compared rather remarkably with the experimental data of Hu
and Wilson (10) obtained in the rat hippocampus, by using
rapid-response lactate sensor during both sustained and repet-
itive stimulations of the perforant pathway. Our analysis shows
that CBF increase cannot explain the lactate initial dip in the
case of a unique stimulation. Furthermore, CBF increase cannot
entirely account for the increased amplitude of lactate dips
occurring upon repetitive stimulations, which could also be
caused by cell uptake and tissue diffusion. Second, we investi-
gated the effect of pH variations on lactate kinetics. Indeed,
because of the lactate兾proton cotransport, an acidification of
extracellular space would favor proton outflow through the BBB
whereas an alkalinization would have the opposite effect. Ac-
cording to the recent review by Chesler (27), stimulated activity,
seizure, or spreading depression are generally associated with an
initial interstitial alkaline shift followed by an acidosis that can
persist for minutes. These facts would indicate that pH transients
are a poor candidate for the lactate initial dip. However, in some
instances, the initial alkalinization is absent. To complete our
interpretation of the data of Hu and Wilson (10) in the hip-
pocampus, we incorporated in our model the extracellular pH
data of Xiong and Stringer (17). Those authors found either an
alkalinization followed by an acidification, in the CA1 area after
Schaffer collaterals’ stimulation, or a delayed acidification in the
dentate gyrus after stimulation of the perforant path. Further-
more, we assumed that capillary pH is not decreased, which is an
extreme case that favors proton outflow through the BBB. In any
case, our results show that only a small contribution of pH
variation may occur (Fig. 3), but cannot be sufficient to explain
the initial dip. Thus, using a reductio ad absurdum-like approach,
our results strongly indicate that the lactate initial dip has mainly
a metabolic origin, at least when the lactate level is below its
baseline value, being caused by either an increase in lactate
consumption by some cells, a decrease in lactate production by
other cells, or both. If we assume that the main phenomenon is
a decrease in lactate production relative to its baseline value, we
can estimate an order of magnitude of this decrease, based on the
magnetic resonance spectroscopy data of Mangia et al. (11), in
which tissue lactate is decreased by ⬇40% within 5 s. Assuming
a tissue lactate concentration of ⬇1 mM, it would correspond to
a decrease in lactate production of ⬇0.08 mM䡠s
⫺1
. Such calcu-
lations lead to the implausible conclusion that resting metabo-
lism would be fairly high and entirely anaerobic. Therefore, we
can conclude that an increase in cellular lactate consumption by
certain cells remains the only possible mechanism to explain
most of the lactate initial dip. We can note that extracellular
Fig. 4. The ratio between the transmembrane flux of lactate via MCTs (Jmb)
and the maximal transport rate through the cell membrane (Tmax,ie)asa
function of the intracellular lactate concentration (LACi), in two cases: (i)Kt⫽
0.7 mM for neurons (thin solid line), and (ii)Kt⫽3.5 mM for astrocytes (thick
solid line). Lactate transport via MCTs through cellular membrane is defined
by Eq. 11. Other parameter values are LACe⫽1.19 mM, Hi
⫹⫽10⫺4.1 mM, He
⫹⫽
10⫺4.3 mM (which corresponds to an equilibrium value of 0.75 mM for intra-
cellular lactate).
Fig. 3. Effect of pH variations on lactate levels. (A) Effect of pH variation on
LACetime course in the case of a unique activation (hypothesis H2). The effect
of extracellular and capillary H⫹ion concentrations on blood– brain transport
of lactate are taken into account by using Eq. 6instead of Eq. 5. Parameter
values are KH⫽3.5 ⫻10⫺4.3 mM2,pHe,0 ⫽7.3, and pHc,0 ⫽7.38. Stimulation
parameters are A1⫽0.164, A2⫽0.114, A3⫽0.025,
␶
1⫽10.7 s,
␶
2⫽15.4 s,
␶
3
⫽21 s, and td⫽12.75 s. All other parameter values are the same as in Fig. 1.
(B) Extracellular and capillary pH time courses (pHeand pHc). (Left) Acid case:
pHeundergoes an acidification (17), whereas pHceither decreases (dashed
line) or remains constant (dotted line). (Right) Alk-acid case: pHeundergoes an
alkalinization followed by an acidification (16, 17), whereas pHceither follows
pHeevolution (dashed line) or remains constant (dotted line). (C) Correspond-
ing time evolution of extracellular lactate, in the acid case (Left) and the
alk-acid case (Right). Solid line indicates no pH variation (hypothesis H1);
dashed line indicates that both pHeand pHcvary, according to B Left or B
Right, respectively; dotted line indicates only pHevaries, according to B Left or
B Right, respectively.
16452
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www.pnas.org兾cgi兾doi兾10.1073兾pnas.0505427102 Aubert et al.

lactate diffusion is not a mechanism that can underlie the first
initial dip of lactate, because it can only induce the opposite
effect, namely a limitation of the decrease in extracellular lactate
concentration.
As pointed out above, the most likely explanation for the
observed lactate kinetics upon stimulation is enhanced lactate
uptake by some cells followed by enhanced production by others
(although it does not exclude that these two processes can
overlap over a certain period). Previous studies performed on
cultured cells had indicated that among brain cells neurons can
take up and use lactate as an oxidative substrate (28) whereas
astrocytes constitutively produce large amounts of lactate (29).
More recently, it was shown that lactate represents a preferential
oxidative substrate over glucose for neurons (30, 31). In contrast,
it was not the case for astrocytes that rather displayed a
substantial glycolytic metabolism with lactate production (31).
The distribution of MCTs that are involved in lactate transport
is also consistent with the metabolic preference of each cell type.
It was found that astrocytes express MCT1 and MCT4 whereas
neurons contain MCT2 (32). Our analysis clearly indicates that
the subtype of MCT expressed by each cell type would favor
either export or import of lactate as a function of its metabolic
preference. Thus, in the case of increased glycolytic activity,
astrocytes are better equipped to release lactate as their intra-
cellular concentration increases. In contrast, neurons would
more efficiently take up lactate than astrocytes with increased
oxidation and a drop in their intracellular lactate concentration.
Altogether, these observations strongly suggest that early lac-
tate-consuming cells are neurons whereas late producers would
be astrocytes. Finally, to estimate the contribution of lactate (vs.
glucose) to neuronal extra pyruvate supply, we carried out a
determination of glucose f luxes based on a similar model (see
Supporting Text and Figs. 5 and 6, which are published as
supporting information on the PNAS web site, for details).
Results show that lactate uptake contribution would be com-
prised between 29% and 60% of the additional pyruvate supply
to neurons. It is thus clear that lactate uptake by neurons
represents a significant contribution to neuroenergetics upon
activation.
Concordance Between the Proposed Description of Brain Lactate
Kinetics and Other Related Aspects of Brain Energy Metabolism. The
description of brain lactate kinetics obtained with our modeling
approach is consistent with several obser vations and previous
models describing different aspects of brain energy metabolism.
First, it was previously shown that NADH levels in neural tissue
vary in a biphasic manner upon stimulation (33). In addition,
Kasischke and coworkers (26) have demonstrated that the initial
dip in NADH occurs in dendrites of neurons, whereas the late
peak takes place in astrocytes. Because it is well known that the
lactate兾pyruvate ratio critically depends on the NADH兾NAD
⫹
ratio (34), the present description of a biphasic change in
extracellular lactate concentration upon activation that ref lects
both an increased consumption by neurons and production by
astrocytes would be entirely consistent with this view. Moreover,
a recent modeling of brain energy metabolism that takes into
account a metabolic compartmentalization between neurons
and astrocytes provides a coherent framework to explain the
biphasic behavior of both the NADH兾NAD
⫹
ratio and extra-
cellular lactate concentration (12). A physiological mechanism
to explain the differential activation of glycolysis in astrocytes
and oxidative metabolism in neurons has been proposed previ-
ously and is known as the astrocyte-neuron lactate shuttle (7, 9).
Our analysis of lactate kinetics supports this model as it further
emphasizes the necessity of cellular lactate consumption early
upon activation followed by distinct cellular lactate production
later on. The fact that neurons are predicted to be the lactate-
consuming cells whereas astrocytes would be the lactate pro-
ducers is in agreement with the main tenets of this model.
Furthermore, recent observations made in vivo suggest that
indeed lactate production by non-neuronal cells (presumably
astrocytes) increases with enhanced glutamatergic activation,
whereas consumption of lactate by neurons (at the expense of
glucose) also increases (35). Thus, our description of brain
lactate kinetics provides a unifying framework to explain a
number of in vitro,ex vivo, and in vivo data.
We thank Dr. Karl A. Kasischke for stimulating discussions and supply-
ing us with raw data; t wo referees for useful comments; and Julia Parafita
and Marie Evo for their help. This work was supported by the Fondation
pour la Recherche Me´dicale (A.A.), the Action Concerte´e Incitative
‘‘Neurosciences Inte´gratives et Computationnelles’’ (French Ministr y of
Research) (R.C.), and Swiss Fonds National de la Recherche Scienti-
fique Grants 31-00A0-100679 (to L.P.) and 31-56930-99 (to P.J.M.).
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