Local oxygen homeostasis during various neuronal network activity states in the mouse hippocampus

Abstract

Cortical information processing comprises various activity states emerging from timed synaptic excitation and inhibition. However, the underlying energy metabolism is widely unknown. We determined the cerebral metabolic rate of oxygen (CMRO₂) along a tissue depth of <0.3 mm in the hippocampal CA3 region during various network activities, including gamma oscillations and sharp wave-ripples that occur during wakefulness and sleep. These physiological states associate with sensory perception and memory formation, and critically depend on perisomatic GABA inhibition. Moreover, we modelled vascular oxygen delivery based on quantitative microvasculature analysis. (1) Local CMRO₂ was highest during gamma oscillations (3.4 mM/min), medium during sharp wave-ripples, asynchronous activity and isoflurane application (2.0–1.6 mM/min), and lowest during tetrodotoxin application (1.4 mM/min). (2) Energy expenditure of axonal and synaptic signaling accounted for >50% during gamma oscillations. (3) CMRO₂ positively correlated with number and synchronisation of activated synapses, and neural multi-unit activity. (4) The median capillary distance was 44 µm. (5) The vascular oxygen partial pressure of 33 mmHg was needed to sustain oxidative phosphorylation during gamma oscillations. We conclude that gamma oscillations featuring high energetics require a hemodynamic response to match oxygen consumption of respiring mitochondria, and that perisomatic inhibition significantly contributes to the brain energy budget.

Introduction

The mammalian brain is an organ with a high metabolic rate. In the human body, it utilises about 20% of the oxygen and about 25% of the glucose at rest.^1,2 Therefore, the vital function of the brain critically depends on sufficient vascular supply and proper performance of mitochondria, i.e. oxidative phosphorylation.^2–4 Molecular oxygen is the final electron acceptor of the mitochondrial respiratory chain. Therefore, oxygen consumption provides a reliable indirect measure of the cerebral metabolic rate.^1,5 Higher brain functions are exceptionally vulnerable to acute metabolic stress, which has long been known from experimental neurology and clinical medicine. In particular, symptoms such as visual field narrowing and unconsciousness being accompanied with slow-wave activity in the EEG occur very rapidly during ischemia in both animals and humans, whereas evoked neuronal responses and ion distributions are more resistant.^4,6 Similarly, different stages of anaesthesia are associated with (i) the progressive loss of higher brain functions, such as reaction time, memory and consciousness, (ii) the switch to low-frequency high-voltage activity in the EEG and (iii) a substantial reduction of cerebral metabolic rate.^7,8 Positron emission tomography measurements, for example, revealed a decrease in cerebral energy expenditure of about 45% during anaesthesia-induced loss of consciousness.⁹ These observations suggest a strong relationship between the complexity of brain functions and cerebral metabolic rate.^3,4,6,9 However, the energy expenditure(s) of specific activity states in local neuronal networks that underlie the emergence of higher brain functions are widely unknown.^4,10

The present study was designed to determine both cerebral metabolic rate and vascular oxygen supply during diverse network activity states in situ. These states were (i) gamma oscillations (30–100 Hz) and (ii) sharp wave-ripples, both of which naturally occur in vivo. Gamma oscillations emerge in many cortical areas, usually in awake mammals, including humans. They have been associated with sensory perception, attentional selection, voluntary movement and memory formation.^11,12 Sharp wave-ripples occur during “off-line” states of the brain, associated with consummatory behaviors, such as immobility, eating and grooming, and non-REM sleep. They assist in transferring compressed hippocampal information to distributed neocortical circuits to support memory consolidation.^12,13 The two specific activities significantly rely on rhythmic perisomatic inhibition of pyramidal cells by GABAergic interneurons.^4,14–16 The further states were (iii) spontaneous asynchronous neuronal activity and activities in the presence of (iv) volatile anaesthetic, isoflurane and (v) voltage-gated sodium channel blocker, tetrodotoxin (TTX).

We used local field potential recordings and measurements of the tissue oxygen concentration in acute slices of the mouse hippocampus. This in situ approach permits the induction of specific activity states under well-defined experimental conditions, such as constant glucose and oxygen supply, as well as recordings with high spatiotemporal resolution.^15,17,18 In addition, we applied immunohistochemistry and mathematical modeling to provide quantitative estimations of local cerebral metabolic rate of oxygen (CMRO₂), intercapillary distance (ICD) and vascular oxygen supply.

Materials and methods

Ethical statement

Mice were purchased from Charles-River (Sulzfeld, Germany) and handled in accordance with the European directive 2010/63/EU and with consent of the animal welfare officers at University of Heidelberg (licenses, T56/11 and T45/14). Experiments were performed and reported in accordance with the ARRIVE guidelines.

Preparation of entorhinal-hippocampal slices

Male C57BL/6 mice (p26–30) were anaesthetised with CO₂ and decapitated. The brain was quickly removed and maintained in cooled (4℃) artificial cerebrospinal fluid (ACSF), saturated with 95% O₂ and 5% CO₂. After removal of frontal brain structures and the cerebellum, horizontal entorhinal-hippocampal slices (400 µm) were prepared using a vibratome (VT 1000s, Leica, Bensheim, Germany). These acute slices were stored in a Haas-type interface chamber at 34 ± 1℃ for recovery of at least 2 h as well as for experimental recordings.¹⁷ Slices with incomplete entorhinal-hippocampal structures were rejected. Slices were randomly assigned to experimental groups. The gas supply to the interface chamber was 1.5 l/min (95% O₂ and 5% CO₂).

Recording solutions and drugs

Acute slices were constantly supplied with heated (34 ± 1℃) recording solution, i.e. ACSF containing: 129 mM NaCl, 3 mM KCl, 1.25 mM NaH₂PO₄, 1.8 mM MgSO₄, 1.6 mM CaCl₂, 26 mM NaHCO₃, and 10 mM glucose. The pH was 7.3 when the recording solution was saturated with 95% O₂ and 5% CO₂.

Gamma oscillations were induced by bath application of muscarinic receptor agonist, carbachol.^17,19,20 Action potentials and membrane depolarisation were suppressed by bath application of TTX and muscarinic receptor antagonist, atropine. To induce an anaesthesia-like state in situ, 1.5% (vol/vol) isoflurane (Baxter, Unterschleißheim, Germany)^21,22 was applied using an Isoflurane Vapor 19.3 (Dräger, Lübeck, Germany). Carbachol was purchased from Tocris (Bristol, United Kingdom) and TTX from Biotrend (Köln, Germany). All other salts and atropine were from Sigma-Aldrich (Taufkirchen, Germany).

Recordings of local field potentials and oxygen concentration

The local field potential was recorded with glass electrodes (tip diameter 3–5 µm) that were pulled from GB150F-8P borosilicate filaments (Science Products GmbH, Hofheim, Germany) with a PC-10 vertical micropipette puller (Narishige International Ltd, London, UK) and backfilled with ACSF. The glass electrode was positioned in stratum pyramidale of the CA3 region with a mechanical micromanipulator (MX-4, Narishige). Extracellular field potentials were low-pass filtered at 3 kHz, and digitised at 10 kHz using CED 1401 interface and processed with Spike2 software (Cambridge Electronic Design, Cambridge, UK) for offline analysis.

Offline signal analysis of 150 s long data segments from local field potential recordings was performed using custom-made scripts in MATLAB 2015a (The MathWorks, Inc., Natick, MA, USA). Recordings of gamma oscillations were low-pass filtered with a digital Butterworth algorithm at 200 Hz cutoff frequency and processed with Welch’s algorithm and fast Fourier transform with a Hamming window size of 32,768 points for calculation of the power spectral density (power) (bin size of 0.3052 Hz). Gamma oscillations were analysed for two parameters, i.e. peak power and full width at half-maximum (FWHM).¹⁸ Recordings of sharp wave-ripples were band-pass filtered with a Butterworth algorithm between 5 and 60 Hz corner frequencies to detect the transient sharp wave component. Amplitude and frequency of sharp waves were measured and averaged.^16,23 Ripples superimposed on the sharp wave were analysed using continuous wavelet transformation.^16,23 Multi-unit activity was assessed by high-pass filtering of the local field potential with a Butterworth algorithm at 700 Hz corner frequency. The threshold for unit detection was set to 4.5 standard deviations of the local field potential during spontaneous asynchronous activity and the correctness of unit detection was checked visually.

The oxygen recordings were carried out with Clark-type oxygen microsensor, OX-10 (Unisense, Aarhus, Denmark) that was connected to a 4-channel Microsensor Multimeter (Unisense). The small tip size (10 µm) of the O₂-sensor ensures reliable recordings; the built-in guard cathode removes all oxygen from the electrolyte reservoir. The O₂-sensor has a spatial resolution of about the tip diameter (8–12 µm). This small dimension minimises the damage to tissue when forwarding the O₂-sensor into brain tissue.^5,17 The O₂-sensor was polarised with −800 mV overnight prior to recording and calibrated before and between experiments using a two point calibration, where ACSF (salinity 11‰) was saturated with 0% O₂ and 100% N₂ as well as 95% O₂ and 5% CO₂ at 34℃. Oxygen depth profiles were measured in stratum pyramidale of CA3 by stepwise forwarding the O₂-sensor into the tissue (Figure 1(a)). The step size of 23 µm along the axis of the O₂-sensor at an angle of 60° towards the slice surface resulted in vertical steps of ∼20 µm. The O₂-sensor was forwarded into the slice until the oxygen concentration increased again because of oxygen supply from the recording solution flowing underneath. Oxygen depth profiles reflect the oxygen concentration as a function of slice depth and were finally used in a mathematical reaction-diffusion model to estimate the local CMRO₂ in a tissue volume of 1 × 10⁻⁵ to 2.25 × 10⁻⁵mm³ [V = (d/2)²× π × L, with d corresponding to the tip diameter of the O₂-sensor, and L corresponding to the mean tissue depth of 199.2 µm]. Oxygen depth profiles were recorded during various network states, i.e. gamma oscillations, sharp wave-ripples, asynchronous activity or activity in the presence of isoflurane, and, subsequently, in the presence of TTX and atropine, which served as reference condition in each slice. The oxygen concentration in ACSF saturated with 95% O₂ at 34℃ was 941 µM. The corresponding oxygen partial pressure (pO₂) was 684.3 mmHg (pO₂ = (p_atm − p_vapor) × 95%, with atmospheric pressure, p_atm = 760 mmHg and water vapor pressure, p_vapor = 39.7 mmHg at 34℃). Thus, the factor to convert µM to mmHg was 0.73 mmHg/µM.

Figure 1.

Local recordings during various network activity states in acute slices. (a) Schematic overview of the experimental setup with combined recordings of the local field potential and the oxygen concentration in stratum pyramidale of the CA3 region. For each activity state, sample traces of the local field potential and the corresponding wavelet transform (heat scale) are shown (b–f). (b) Gamma oscillations were induced by bath application of muscarinic agonist, carbachol (5 µM), (c) recurrent sharp wave-ripples (SPW-R) or (d) asynchronous neuronal network activity (ASYN) occurred spontaneously. The low activity states were induced by (e) 1.5% (vol/vol) isoflurane (ISO) or (f) TTX (0.5 µM) and atropine (1 µM) to block action potentials. The wavelet transform is shown only for the first sharp wave labelled with the red asterisk. The O₂-sensor was forwarded into the acute slice (thickness of 400 µm) with a vertical step size of ∼20 µm to measure the oxygen concentration at defined depths (Figure 2).

Laminin staining and imaging

For immunostaining of blood vessels, acute slices were fixed in paraformaldehyde (4%, 0.1 M phosphate buffer; Applichem, Darmstadt, Germany) and rinsed in 0.1 M phosphate-buffered salt solution (PBS). After incubation in 30% sucrose overnight, slices were cut into thin sections (25 µm) with a CM1850 cryostat (Leica Microsystems GmbH, Nussloch, Germany). Nonspecific immunoglobulin reactions were blocked with 10% normal goat serum (Life Technologies GmbH, Darmstadt, Germany) for 60 min. The primary antibody was a polyclonal rabbit anti-laminin antibody (Thermo Fisher Scientific, Waltham, USA; Cat# PA5-16287, RRID:AB_10985513), and the secondary antibody was biotinylated goat anti-rabbit (Vector Laboratories, Burlingame, USA; Cat# BA-1000, RRID:AB_2313606).²⁴ Sections were incubated with the primary antibody for ∼36 h and with secondary antibody for 24 h at 4℃. Afterwards, sections were incubated overnight with avidin and biotinylated horseradish peroxidase (Vectastain Elite ABC Kit, Vector Laboratories, Peterborough, UK). Laminin was visualised by adding peroxidase substrate (0.05% DAB reagent in 0.03% H₂O₂ in PBS) for <5 min then the reaction was stopped by adding PBS. Stained sections were placed on object plates and dried overnight. Sections were then exposed to xylol (Sigma-Aldrich) for 10 min and embedded with Entellan® (Merck Millipore, Schwalbach, Germany).

Virtual z-stacks (1 µm) of sections with stained capillaries were acquired with a BX-53 microscope (Olympus Deutschland GmbH, Hamburg, Germany) equipped with a 40× Plan N UIS2 Olympus objective and a Retiga 2000R-F-CLR-12 camera (QImaging, Surrey, Canada). The Neurolucida® software (MBF Bioscience) was used to take z-stacks and to subsequently quantify ICDs in stratum pyramidale of the CA3 region. The distance between an arbitrary point (x₁, y₁, z₁) on the wall of a capillary to the most proximal point (x₂, y₂, z₂) on the wall of a neighbouring capillary was measured. Capillaries were defined as vessels with a diameter less than 7 µm.^25,26 Based on our own histological control experiments and published data,^27,28 ICDs were multiplied by a factor of 1.25 to correct for tissue shrinkage due to the staining procedure.

Mathematical reaction-diffusion model

Local CMRO₂ was estimated by reproducing the measured interstitial pO₂ depth profiles with the reaction-diffusion model.²⁹ For mathematical modeling, MATLAB 2012a (MathWorks) with the optimisation tool box was used. The model describes the oxygen dynamics consisting of diffusive oxygen transport and metabolic oxygen consumption within a slice. It is given by the following differential equation

$$\frac{d({\mathit{pO}}_2^i)}{\mathit{dt}}=I_{\mathit{influx}}^{i-\mathit{diff}}-v_{\mathit{consumption}}^i-I_{\mathit{efflux}}^{i-\mathit{diff}}$$ (1)

The slice was discretised by n layers with 1 µm thickness ($\Delta x$), where i denotes the index of the layer. The change in pO₂ within layer i on the left-hand side of equation (1) is determined by the sum of the diffusive oxygen influx, the diffusive oxygen efflux and the local oxygen consumption rate on the right-hand side of the equation.

Diffusive influx of oxygen in the i-th layer is given by Fick’s law

$$I_{\mathit{influx}}^{i-\mathit{diff}}=D_i·\frac{({\mathit{pO}}_2^{i-1}-{\mathit{pO}}_2^i)/\Delta x}{\Delta x}$$ (2)

Diffusive efflux of oxygen is given by

$$I_{\mathit{efflux}}^{i-\mathit{diff}}=D_i·\frac{({\mathit{pO}}_2^i-{\mathit{pO}}_2^{i+1})/\Delta x}{\Delta x}$$ (3)

This gives the mass balance equation

$$I_{\mathit{influx}}^{i+1-\mathit{diff}}=I_{\mathit{efflux}}^{i-\mathit{diff}}$$ (4)

This states that the oxygen that leaves the i-th layer as diffusive efflux is the diffusive influx into the i + 1-th layer. For D, we used the constant value of 1.6 × 10³µm²/s.²⁹

For the local oxygen consumption rate, we assume Michaelis–Menten type kinetics in each layer i³⁰

$$v_{\mathit{consumption}}^i=A\frac{{\mathit{pO}}_2^i}{{\mathit{pO}}_2^i+K_m^{{\mathit{pO}}_2}}$$ (5)

where A is a constant depicting the maximal oxygen consumption rate. As long as the local pO₂ is well above the Km of 3 mmHg,²¹ the oxygen consumption rate is homogenous and constant throughout the whole slice.

At the top of the slice, Neumann boundary conditions were used because the pO₂ at the surface was constant through rapid gas exchange in the recording chamber

$${\mathit{pO}}_2^1=\mathit{const}.$$ (6)

The second boundary condition was given by the local oxygen minimum measured in each slice, where the oxygen diffusion is zero (Dirichlet boundary conditions)

$$I_{\mathit{efflux}}^{\text{min}-\mathit{diff}}=0$$ (7)

For each experimental depth profile, the parameter A, representing the maximal CMRO₂, was determined by minimizing the square distance (R²-value) between measured values and model simulation. Pearson correlation coefficient was used as measure of fit quality. Subsequently, we used the values of A to calculate the decrease of pO₂ in neuronal tissue between capillaries by solving equation (1) at physiological capillary pO₂ values as input. From the resulting pO₂ traces, we calculated the local CMRO₂ given by equation (5) within neuronal tissue under physiological in vivo conditions. The local saturation of the respiratory chain, i.e. the fractional CMRO₂, is given by the quotient on the right-hand side of equation (5). We validated the model with oxygen depth profiles from dead hippocampal slices (Supplementary material in reference Kann et al.¹⁷) resulting in CMRO₂ of <0.1 mM/min.

In other reports, CMRO₂ is given in µmol/g/min of brain tissue.^2,31,32 To convert these values in mM/min for our discussion, we assume that the density of gray matter is roughly about 1.05 g/ml.²¹ Thus, the CMRO₂ of about 1.8 µmol/g/min measured in anaesthetised rats at 37℃ corresponds to approximately 1.9 mM/min.^32,33

Statistics

Data are presented as mean ± SEM or median with 25th and 75th percentile derived from n slices from N mice. Statistical significance, p < 0.05 or confidence interval (CI) was determined using SigmaPlot 12.5 (Systat Software, San Jose, CA) and GraphPad Prism (GraphPad Software Inc., La Jolla, USA). Data distribution was checked for normality with Shapiro–Wilk test. Comparisons among paired data were made with Wilcoxon signed-rank test. Comparisons among unpaired data were made with Kruskal–Wallis ANOVA on ranks followed by Dunn's post hoc test. To test for correlations, the correlation coefficient r and CI were computed using the Spearman correlation. Figures were generated with MATLAB 2015a (MathWorks), and CorelDRAW (Corel Corporation, Ottawa, Ontario, Canada).

Results

Network activity states and local CMRO₂

We determined the characteristics of various network activity states and measured the concomitant tissue oxygen concentrations in stratum pyramidale of the hippocampal CA3 region in acute slices (Figure 1(a)). Notably, densely packed pyramidal cells receive strong perisomatic GABAergic inhibition in stratum pyramidale.^4,18,20 Cholinergic gamma oscillations (Figure 1(b)) were persistent and had a mean frequency of 37.4 ± 0.5 Hz (n = 40 slices, N = 18 mice).^17,19,20 Persistent gamma oscillations in the range of minutes have been also observed during certain tasks in vivo.^4,34 Recurrent sharp wave-ripples appeared spontaneously in the absence of drugs and were recorded in ventral slices (Figure 1(c)). Sharp waves had a frequency of 2.7 ± 0.2 Hz (n = 18, N = 13) and were superimposed with the typical ‘ripple' oscillation frequency of 243.0 ± 3.9 Hz.^15,16,35 The other network states featured lower levels of activity and synchrony. These were asynchronous activity, which was spontaneously present without transient gamma oscillations or sharp-wave ripples (Figure 1(d)),^17,29 an anaesthesia-like state in the presence of isoflurane (Figure 1(e))³⁶ and a reference state, i.e. the suppression of action potentials and membrane depolarisation by TTX and muscarinic antagonist, atropine (Figure 1(f)). These data show that acute entorhinal-hippocampal slices can reliably express various network activity states, without occurrence of activity switches or pathological activity.

We next explored the oxygen metabolism during each activity state. In the interface recording chamber, the pO₂ above the slice is clamped, i.e. 684.3 mmHg in our experimental settings, because of rapid gas exchange (95% O₂ and 5% CO₂ at 1.5 l/min). Oxygen diffuses into the tissue and is consumed by active neurons and glial cells. We firstly recorded oxygen depth profiles with a vertical step size of ∼20 µm (Figure 2(a)).^29,37 To obtain a precise quantification, we secondly calculated the local CMRO₂ of each activity state (Table 1) by fitting the oxygen depth profiles to the mathematical reaction-diffusion model (Figure 2(a)).²⁹ Notably, gamma oscillations were associated with the highest local CMRO₂ (3.4 mM/min) among all activities (Figure 2(b) and (c)). Albeit showing a trend, the differences between sharp-wave ripples (2.0 mM/min), asynchronous activity (1.7 mM/min) and the anaesthesia-like state (1.6 mM/min) were not significant (Figure 2(b) and (c)). By contrast, CMRO₂ was always significantly lower in the presence of TTX and atropine (Figure 2(b)). These data show that gamma oscillations are associated with the highest local CMRO₂ and that >50% of cerebral metabolic rate underlying neural information processing during gamma oscillations accounts for axonal and synaptic signaling.^38,39

Figure 2.

Local CMRO₂ during network activity states. (a) Oxygen depth profiles recorded in the same slice during gamma oscillations (blue boxes) and, subsequently, in the presence of TTX (orange boxes). The boxes represent experimentally determined oxygen concentrations at defined depths. Solid black curves represent the fits applied to the depth profiles using a mathematical model to compute the local CMRO₂. (b) Local CMRO₂ was assessed during various network activity states. Asterisks denote significance between gamma oscillations (n = 40, N = 18), sharp-wave ripples (n = 18, N = 13), asynchronous activity (n = 19, N = 9) or isoflurane (n = 14, N = 8) and the reference state, TTX (n = 91, N = 42) (GAM vs. TTX, p < 0.01, Wilcoxon signed rank test; SPW-R vs. TTX, t(17) = 5.83, p < 0.01, paired t-test; ASYN vs. TTX, t(18) = 3.76, p < 0.01, paired t-test; ISO vs. TTX, t(17) = 3.62, p < 0.01, paired t-test; H(3) = 65.98, p < 0.01, Kruskal–Wallis ANOVA on ranks; Dunn’s post hoc test). (c) The CMRO₂ during each activity state was normalised to CMRO₂ obtained in TTX in the same slice, and averages of the normalised CMRO₂ were calculated (H(3) = 48.1, p < 0.01, Kruskal–Wallis ANOVA on ranks; Dunn’s post hoc test). The asterisk denotes significance between normalised CMRO₂ during gamma oscillations to all other groups. Statistical significance is marked by asterisks (p < 0.05).

Table 1.

CMRO₂ and goodness of fit (R²-value) of various network activity states.

Activity state	CMRO2 (mM/min)		R2-values
	Median	Range	Median	Range
GAM	3.4	2.9–3.8	0.984	0.971–0.991
SPW-R	2.0	1.8–2.4	0.993	0.987–0.996
ASYN	1.7	1.3–2.1	0.994	0.994–0.996
ISO	1.6	1.4–1.8	0.994	0.992–0.996
TTX	1.4	1.2–1.8	0.994	0.988–0.997

GAM: gamma oscillations (30–100 Hz); SPW-R: recurrent sharp wave-ripples; ASYN: spontaneous asynchronous network activity; ISO: low activity state in the presence of 1.5% (vol/vol) isoflurane; TTX: low activity state in the presence of tetrodotoxin (0.5 μM) and atropine (1 μM).

Correlations between local field potential characteristics and local CMRO₂

We next explored the correlations between the characteristics of the local field potential and CMRO₂ during each network activity state. We note that the local field potential characteristics primarily arise from synaptic activity, i.e. postsynaptic currents.^20,40,41 For gamma oscillations, we computed both peak power and FWHM of the power spectrum (Figure 3(a)). Peak power increases with number and synchrony of postsynaptic currents at gamma-frequency. FWHM increases with jitter in the timing of postsynaptic currents. Peak power and FWHM exhibited a negative correlation (Figure 3(b)). Correlation analysis revealed an increase of CMRO₂ with peak power (Figure 3(c)) and a decrease of CMRO₂ with FWHM (Figure 3(d)).

Figure 3.

Local field potential characteristics and CMRO₂ during network activity states. The characteristics of local field potentials during gamma oscillations (a–d) and sharp-wave ripples (e, f) were analysed. (a) The power of gamma oscillations was calculated and peak power and FWHM were estimated in each slice (n = 40, N = 18). (b) Peak power and FWHM showed a negative correlation (r = −0.682, CI = −0.822 to −0.463, p < 0.01, Spearman correlation). (c) CMRO₂ and peak power showed a positive correlation (r = 0.393, CI = 0.083 to 0.633, p = 0.01, Spearman correlation). (d) CMRO₂ and FWHM showed a negative correlation (r = −0.404, CI = −0.641 to −0.096, p < 0.01, Spearman correlation). (e) The mean amplitude of sharp waves (gray trace) was estimated from band-pass filtered sharp wave-ripples (black trace) in each slice (n = 18, N = 13). (f) CMRO₂ and sharp wave amplitude showed a positive correlation (r = 0.517, CI = 0.051 to 0.798, p = 0.03, Spearman correlation).

For sharp wave-ripples, we analysed two components, i.e. the transient sharp wave and the superimposed high-frequency oscillation (ripples) (Figure 3(e)).^14,16,35 The correlation analysis revealed that CMRO₂ increased with the amplitude of the sharp wave (Figure 3(f)). There was neither a correlation between sharp wave amplitude and ripple frequency (r = 0.003, CI = −0.476 to 0.481; n = 18, N = 13) nor CMRO₂ and ripple frequency (r = 0.025, CI = −0.459 to 0.497; n = 18, N = 13). These data indicate that the local CMRO₂ during gamma oscillations and sharp wave-ripples increase with the level of synaptic activity and synchronisation.

Local field potentials primarily reflect synaptic activity. In order to analyse the correlation between action potential frequency and CMRO₂, we applied high-pass filtering to extract multi-unit activity for each activity state (Figure 4(a) to (d)). Gamma oscillations showed the highest frequency of multi-unit activity (spikes) followed by sharp wave-ripples, asynchronous activity and the anaesthesia-like state (Figure 4(e)). Plotting the calculated spike frequencies of these activity states to cover a broader spectrum, we found a clear positive correlation between multi-unit activity and CMRO₂ (Figure 4(f)).

Figure 4.

Multi-unit activity and CMRO₂ during network activity states. (a–d) Local field potential recordings (upper traces) were 700 Hz high-pass filtered (middle traces) to apply threshold detection of extracellularly recorded action potentials (lower traces). Spiking frequencies were determined during (a) gamma oscillations (n = 40, N = 18), (b) sharp-wave ripples (n = 18, N = 13), (c) asynchronous activity (n = 19, N = 9) and (d) isoflurane (n = 14, N = 8). (e) Statistical comparison between multi-unit frequencies of network activities (H(3) = 69.44, p < 0.01, Kruskal–Wallis ANOVA on ranks; Dunn’s post hoc test). (f) Plotting the data from the four activity states (a–d) reveals a clear positive correlation between spiking frequency and CMRO₂ (r = 0.852, CI = 0.781 to 0.901, p < 0.01, Spearman correlation).

Vascular oxygen supply during specific network activity states

Sufficient nutrient and oxygen delivery in vivo are achieved by the complex geometry of the cerebral vascular system as well as the tight neurovascular coupling.^10,42,43 The pO₂ is highest within and adjacent to capillaries.^21,43–45 However, it decays along the diffusion distance into the cortical parenchyma because of oxygen consumption of active neurons and glial cells.^21,29 To get insight into the relationships between vascularisation, oxygen supply and putative oxygen shortage – and thus impairment of oxidative phosphorylation in mitochondria – during network activity states, we visualised capillaries in the hippocampus with a laminin staining and estimated the ICD (Figure 5(a) and (b)). The ICD was about 44 µm in stratum pyramidale (Figure 5(b)) when corrected for tissue shrinkage because of the staining procedure (Materials and Methods). Note that local field potentials and oxygen depth profiles were recorded in stratum pyramidale.

Figure 5.

Vascular oxygen supply and CMRO₂ during network activity states. (a) Anti-laminin immunohistochemistry (upper panel, scale bar 200 µm) was used to measure distances (n = 299) between capillaries (intercapillary distance, ICD) in stratum pyramidale of the CA3 region in fixed hippocampal slices (n = 12, N = 7). ICDs were measured between an arbitrary point on a randomly selected vessel wall to the closest neighbouring vessel wall (lower panel, scale bar 50 µm). (b) The ICD distribution has a median of about 44 µm. All values were corrected by 25% for tissue shrinking because of the staining procedure. (c) The decay in oxygen concentration (pO₂, right y-axis) along the diffusion distance from the capillary was modelled based on median CMRO₂ (Figure 3(b)) of gamma oscillations (blue), sharp wave-ripples (pink) and asynchronous activity (green) for physiological pO₂-levels of cortical capillaries, i.e. 15 mmHg (solid line), 23 mmHg (dotted line) and 35 mmHg (dashed line). The grey bands were computed with 25- and 75-percentiles of each CMRO₂. Decays were modelled up to ½ICD, i.e. ∼22 µm. The horizontal red line marks the hypoxic threshold (11 µM, 8 mmHg) for disturbances of neuronal function. (d) The decay of CMRO₂ during network activity states was modelled as a function of distance from the capillary for a physiological pO₂ of 23 mmHg reported for cortical capillaries. The grey bands were computed with 25- and 75-percentiles of CMRO₂. (e) The fraction of CMRO₂ at ½ICD (22 µm) is given as a function of the maximal CMRO₂ for capillary pO₂ levels of 15 mmHg (crosses), 23 mmHg (squares) and 35 mmHg (circles). The red line indicates the fractional CMRO₂ of 72.7% calculated for the hypoxic threshold of 8 mmHg in the tissue. Fractional CMRO₂ was modelled using individual estimates (small symbols) and median averages (large symbols) for the maximal CMRO₂ calculated for gamma oscillations (blue), sharp wave-ripples (magenta) and asynchronous activity (green). Note that CMRO₂ decreases because of incomplete saturation of the mitochondrial respiratory chain in consequence of oxygen consumption.

Based on these data, we mathematically modelled the decay of the tissue oxygen concentration up to ½ICD (22 µm in stratum pyramidale), i.e. the location at which respiring mitochondria might experience the lowest availability of oxygen (Figure 5(c)). The decay of the oxygen concentration was modelled with the average values of CMRO₂ for gamma oscillations, sharp wave-ripples and asynchronous activity and with reasonable pO₂ values that were experimentally determined in cortical capillaries, i.e. 15 mmHg, 23 mmHg and 35 mmHg.^21,43,44,46 At a capillary pO₂ of 15 mmHg, sharp wave-ripples and gamma oscillations were associated with decays of the tissue oxygen concentration close to the hypoxic threshold (8.2–13.7 µM; 6–10 mmHg).^37,47,48 During gamma oscillations, even a capillary pO₂ of 23 mmHg resulted in a critically low tissue oxygen concentration at ½ICD (∼22 µm). By contrast, a capillary pO₂ of 35 mmHg provided sufficiently high tissue oxygen concentrations (availability) during these three activity states.

Low availability of oxygen might significantly constrain the rate of oxidative phosphorylation in mitochondria located remote from capillaries.^21,47 Therefore, we modelled the decay of CMRO₂ with increasing distance from capillaries for a capillary pO₂ of 23 mmHg, the mean value reported for the olfactory bulb glomerular layer and the somatosensory cortex of unstressed, awake, resting mice.⁴³ Indeed, CMRO₂ decayed along the diffusion distance during gamma oscillations, sharp wave-ripples and asynchronous activity; this decay was strongest for gamma oscillations (Figure 5(d)). Note that saturation of complex IV in the respiratory chain is only about 88% at a capillary pO₂ of 23 mmHg, and it further decreases to about 81% at 13 mmHg (½ICD) (Materials and Methods, equation (5)).

Next, we estimated the fractional CMRO₂, i.e. the saturation of the respiratory chain at a given local tissue oxygen level, at ½ICD for all individual oxygen depth profiles recorded for gamma oscillations, sharp wave-ripples and asynchronous activity (Figure 5(e)). At capillary pO₂ of 23 mmHg and 15 mmHg, most of the profiles during gamma oscillations resulted in fractional CMRO₂ below 85% and 75%, respectively. The latter value is close to the fractional CMRO₂ (72.7%) calculated for the hypoxic threshold of 8 mmHg. Given that neuronal mitochondria operate near-limit during gamma oscillations (Figure 2(c)),¹⁷ a hemodynamic response would be required to raise blood flow and oxygen availability in the capillary (pO₂ between 23 and 55 mmHg), at least for this specific network activity state.^4,49,50

Finally, we performed robust estimations about tissue oxygen availability and hemodynamic responses (Figure 6). For this purpose, we used our experimental data to generate distribution functions for CMRO₂ (normal distributions) and ICD (lognormal distribution). For capillary oxygen concentration, lognormal distributions were generated based on reported ranges (equal to 5% and 95% quantiles).⁴³ We resampled model parameter values from these distributions and set the hypoxic threshold to 11 µM (8 mmHg), at which disturbances of neuronal function were shown in situ and in vivo.^21,37,47,48 In vivo, the hemodynamic response has been reported to result in an increase of the capillary pO₂ of 10–15 mmHg.^50–52 For gamma oscillations, our model predicts that 34.1% of the tissue is hypoxic at ½ICD given the absence of a hemodynamic response; this value is reduced to 14.4% if a hemodynamic response increases the capillary pO₂ by 10 mmHg (from 23 mmHg to 33 mmHg). During asynchronous activity, about 11.9% of the tissue is hypoxic in the absence of a hemodynamic response. Similar small fractions of tissue hypoxia have been described during normoxia in vivo.^21,50

Figure 6.

Tissue pO₂ and hemodynamic response during asynchronous activity and gamma oscillations. (a, b) CMRO₂ during asynchronous activity (a, grey histogram) and gamma oscillations (b, black histogram) was resampled (n = 5000 values, each) on basis of experimental data. Cumulative distributions (CDs) are given as blue graphs. (c) ICD was resampled (n = 5000 values) on basis of experimental data (black histogram). The cumulative distribution is given as a blue graph. The distribution of the capillary pO₂ was modelled for (d) a baseline condition (black histogram) with a median of 23 mmHg (31.5 µM);⁴³ and (e) a hemodynamic response (magenta histogram) with a median of 33 mmHg (45.2 µM). Cumulative distributions are given as blue graphs. Using the sampled distributions (a–e), the oxygen concentration at a distance of ½ICD from the capillary was estimated. The distribution of oxygen concentration was estimated for (f) asynchronous activity in the absence of a hemodynamic response (grey histogram) and gamma oscillations in the absence (g) (black histogram) and presence of a hemodynamic response (h) (magenta histogram). (i) Cumulative distributions are shown for asynchronous activity without a hemodynamic response (grey graph), gamma oscillations without a hemodynamic response (black graph), and gamma oscillations in the presence of a hemodynamic response (magenta graph). The vertical line (red) marks the hypoxic threshold (11 µM, 8 mmHg) for disturbances of neuronal function.

These data show that significant decays in tissue oxygen concentration and CMRO₂ occur during specific network activity states. Moreover, gamma oscillations are by far the most energy-demanding network activity state and likely require a hemodynamic response.

Discussion

Network activity states in hippocampal slices

We assessed CMRO₂ during various network activity states in acute slices of the mouse hippocampus. Gamma oscillations and sharp wave-ripples are rhythmic network activities that rely on the precise synaptic interplay between excitatory pyramidal cells and GABAergic interneurons, particularly parvalbumin-positive, fast-spiking basket cells.^4,19,53 The two oscillations are functionally associated with neural information processing in vivo. Gamma oscillations have a role in sensory perception, motor activity, memory formation, and attention.^11,12 Sharp wave-ripples arise in the hippocampus during waking immobility, consummatory behaviour and slow-wave sleep. Sharp wave-ripples have been implicated in memory consolidation, erasure of hippocampal memory traces and certain aspects of active spatial navigation.^12,13 Spontaneous asynchronous activity in (unstimulated) brain slices varies with recording condition (submerged versus interface) and type of preparation.^17,29,33 Neuronal activity during this state is often lower than in awake or moderately anaesthetized animals and humans.^31,33,54 Overall, this activity might reflect transient periods of desynchronized activity in the non-exploring awake brain or during non-REM sleep. Application of isoflurane represents an anaesthesia-like activity state; neural activity is largely reduced but action potentials still occur sparsely.³⁶ Application of TTX and atropine generally blocks both action potentials and muscarinic receptor-mediated membrane depolarisation.²⁹ However, miniature synaptic events are still present because of spontaneous quantal transmitter release.

CMRO₂ during network activity states

We show that the CMRO₂ during spontaneous asynchronous activity and the anaesthesia-like state was similar; the reference state (TTX and atropine) was associated with the lowest CMRO₂. These values were higher compared with most other in vitro studies, in which oxygen consumption rates ranged from 0.47 mM/min to 1.9 mM/min during spontaneous activity or electrical stimulation in cortical slices from rats and mice.^33,55,56 Whether this reflects our use of the interface recording chamber and/or mice at postnatal day 28 is currently unclear. By contrast, we found overall lower values of CMRO₂ compared with rat organotypic hippocampal slice cultures.²⁹ This might be caused by substantial structural, functional and metabolic recovery during the culture period, the species and the use of Biopore membranes in the interface recording chamber.^2,29,33 Interestingly, CMRO₂ during spontaneous asynchronous activity was similar to the anaesthesia-like state and recurrent sharp wave-ripples. This likely reflects the low baseline activity in acute brain slices,^31,33,54 which partially differs from slice cultures.²⁹ In addition, it might indicate that sharp wave-ripples represent an energy-saving mode of neural information processing (consolidation). Indeed, sharp wave-ripples also occur during slow-wave sleep, which is associated with lower CMRO₂ and glucose utilisation.⁵⁷ By contrast, gamma oscillations were associated with a CMRO₂ of 3.4 mM/min thus reflecting the highest energy expenditure. This value differs from in vivo studies. In anaesthetized rats and mice, CMRO₂ ranges between 1.9 mM/min and 2.7 mM/min, depending on the brain structure and level of anaesthesia.^32,58,59 The much higher CMRO₂ obtained during gamma oscillations in acute slices and slice cultures²⁹ might be explained by the significant reduction of network activities and energy metabolism during anaesthesia of about half,^9,31,43,60 the persistent nature of the gamma oscillations in hippocampal slices, and the high spatial resolution of oxygen recordings in our study, thus reflecting CMRO₂ in a small local neuronal network.

The high energy expenditure of neurons during gamma oscillations is most likely caused by the persistent increase in the rates of action potentials and postsynaptic potentials in pyramidal cells and inhibitory interneurons.^4,61 The underlying ion fluxes tend to dissipate the ion gradients across the neural membranes. In order to maintain neural excitability, various ion transport processes are activated. These processes are finally powered by ATP mainly generated by oxidative phosphorylation in mitochondria.^2,4 We show that >50% of the cerebral metabolic rate underlying neural information processing during gamma oscillations accounts for axonal and synaptic signaling. Similar energetic costs of action potentials (8.7%) and synaptic transmission (48.5%) were calculated for the gray matter of awake resting humans using a comprehensive bottom-up glucose oxidation-derived energy budget.⁶²

We found specific correlations between CMRO₂ and local field potential characteristics in acute hippocampal slices (ex vivo). CMRO₂ positively correlated with gamma oscillation power, sharp wave amplitude and multi-unit activity; it negatively correlated with FWHM of gamma oscillations. This suggests that energy expenditure during the two oscillations increases with the level of neuronal spiking, synaptic activity and synchronisation. Similarly, CMRO₂ has been shown to track multi-unit activity across different brain regions and stimulus conditions in vivo.^63,64 Overall, the energy expenditure of synaptic activity is higher than that of neuronal spiking.^4,5,38 Sharp wave-ripples associated with much lower CMRO₂ compared with persistent gamma oscillations. This might reflect the transient nature of sharp waves and, perhaps, a lower level of synaptic excitation and inhibition underlying their generation.¹⁶

Synaptic inhibition during fast network oscillations

In addition to excitation, GABA inhibition is essential for the generation of gamma oscillations and sharp wave-ripples.^14,20,65,66 In fact, previous studies have shown that inhibitory GABAergic currents in the perisomatic region of pyramidal cells, i.e. stratum pyramidale in hippocampal slices, largely contribute to the local field potential during gamma oscillations^20,40,53 and sharp wave-ripples.^15,16,66 This reflects the strongly dominating inhibitory input to the perisomatic region of pyramidal cells by GABAergic interneurons.^18,67–69

We show that the power of gamma oscillations and the amplitude of sharp waves positively correlate with CMRO₂ and that FWHM negatively correlates with CMRO₂. Therefore, rhythmic perisomatic GABA inhibition and synchronisation are likely associated with significant energy expenditure that contributes to the neuronal energy budget of specific network activity states.^38,61 The underlying mechanism might include the postsynaptic ion homeostasis in pyramidal cells but also the high firing rates (>20 Hz) of basket cells during gamma oscillations. Indeed, these interneurons are enriched with mitochondria and cytochrome c oxidase and have an extensive axon arborisation.^4,65,70,71 Moreover, the local cerebral glucose utilization in stratum pyramidale is close to that in stratum radiatum, i.e. the apical dendritic region receiving mainly excitatory synaptic input.^68,72 Overall, GABAergic interneurons have been reported to demand about 20% of the neuronal oxidative metabolism.⁶² Further experimental studies are required to dissect the energy usage of synaptic inhibition during specific network activity states.^4,61

In terms of clinical medicine, the exquisite sensitivity of gamma oscillations and, in particular, fast-spiking inhibitory basket cells to metabolic stress might contribute to the initiation of ictal epileptiform events and/or spreading depolarization in patients suffering from traumatic brain injury, stroke or migraine.^73,74 Spreading depolarizations are waves of abrupt, near-complete breakdown of neural transmembrane ion gradients in the cerebral gray matter, with a high risk of lesion development;⁷⁴ they differ from a simple loss of evoked neuronal responses.

Neurovascular architecture and hemodynamic response

In the cortex, nutrients and oxygen are supplied via the vascular system and tight neurovascular coupling.^42,43,58 Oxygen diffuses from the capillaries over a distance of ∼½ICD into the cortical parenchyma; along this way, it is consumed by neurons and glial cells. We determined a mean ICD of about 44 µm in stratum pyramidale of CA3. This value is in agreement with other studies on hippocampal and neocortical regions of mice.^21,22,25,75 We calculated that during gamma oscillations, a capillary pO₂ of less than 23 mmHg was associated with the significant decrease in the fractional CMRO₂ and tissue oxygen concentration, i.e. close to the hypoxic threshold at ½ICD (∼22 µm). It is unknown at which fractional CMRO₂ alterations in gamma oscillations occur. However, gamma oscillations rely on intact neuronal network functions, and even modest alterations in the axon and presynaptic endings of basket cells might be harmful.⁴ By contrast, a capillary pO₂ of greater than 33 mmHg provided sufficient tissue oxygen concentrations (availability). This indicates that gamma oscillations require a hemodynamic response and provide an explanation for observations made in vivo.^4,49,76 Indeed, activity-dependent hemodynamic responses were reported to increase the capillary pO₂ by up to 15 mmHg in vivo.^50–52 Conversely, even moderate changes in capillary density and neurovascular coupling, for example, in age-associated cerebrovascular disease and Alzheimer’s disease in human patients, might significantly alter gamma oscillations and, thus, higher brain functions, such as voluntary movement, attentional selection and memory formation.^4,77–82 The tight neurovascular coupling is mainly regulated by neuronal glutamatergic signaling and vascular responses in arteriole smooth muscle cells and capillary pericytes.^26,42 Glutamate activates ionotropic and metabotropic receptors and thus controls the hemodynamic response, mainly through release of nitric oxide from neurons as well as epoxyeicosatrienoic acids, prostaglandins and potassium from astrocytes.⁴² In addition, cortical endothelial cells can release nitric oxide upon astrocytic and blood flow stimuli.^42,83 However, there is growing evidence that cortical interneurons, including GABAergic basket cells, might contribute to neurovascular coupling.^58,77,84

In summary, our data show that energy expenditure is strongly dependent on the neuronal network activity state and may reach critical levels during higher brain functions.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Deutsche Forschungsgemeinschaft within the Collaborative Research Center 1134 (projects B02, A01 and A03).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Authors’ contributions

JS, AD, HGH and OK designed the research; JS, NB, JM and SB performed research; JS, NB, IEP, JM, SB and MB analysed data; JS, NB and OK wrote the manuscript. All authors have approved the final version of the manuscript and agree to be accountable for all aspects of the work.