On the origin of ultraslow spontaneous Na⁺ fluctuations in neurons of the neonatal forebrain

Abstract

Spontaneous neuronal and astrocytic activity in the neonate forebrain is believed to drive the maturation of individual cells and their integration into complex brain-region-specific networks. The previously reported forms include bursts of electrical activity and oscillations in intracellular Ca²⁺ concentration. Here, we use ratiometric Na⁺ imaging to demonstrate spontaneous fluctuations in the intracellular Na⁺ concentration of CA1 pyramidal neurons and astrocytes in tissue slices obtained from the hippocampus of mice at postnatal days 2–4 (P2–4). These occur at very low frequency (∼2/h), can last minutes with amplitudes up to several millimolar, and mostly disappear after the first postnatal week. To further investigate their mechanisms, we model a network consisting of pyramidal neurons and interneurons. Experimentally observed Na⁺ fluctuations are mimicked when GABAergic inhibition in the simulated network is made depolarizing. Both our experiments and computational model show that blocking voltage-gated Na⁺ channels or GABAergic signaling significantly diminish the neuronal Na⁺ fluctuations. On the other hand, blocking a variety of other ion channels, receptors, or transporters including glutamatergic pathways does not have significant effects. Our model also shows that the amplitude and duration of Na⁺ fluctuations decrease as we increase the strength of glial K⁺ uptake. Furthermore, neurons with smaller somatic volumes exhibit fluctuations with higher frequency and amplitude. As opposed to this, larger extracellular to intracellular volume ratio observed in neonatal brain exerts a dampening effect. Finally, our model predicts that these periods of spontaneous Na⁺ influx leave neonatal neuronal networks more vulnerable to seizure-like states when compared with mature brain.

NEW & NOTEWORTHY Spontaneous activity in the neonate forebrain plays a key role in cell maturation and brain development. We report spontaneous, ultraslow, asynchronous fluctuations in the intracellular Na⁺ concentration of neurons and astrocytes. We show that this activity is not correlated with the previously reported synchronous neuronal population bursting or Ca²⁺ oscillations, both of which occur at much faster timescales. Furthermore, extracellular K⁺ concentration remains nearly constant. The spontaneous Na⁺ fluctuations disappear after the first postnatal week.

INTRODUCTION

Spontaneous neuronal activity is a hallmark of the developing central nervous system (1) and has been described in terms of intracellular Ca²⁺ oscillations both in neurons and astrocytes (2–5) and bursts of neuronal action potentials (6–8). This activity is believed to promote the maturation of individual cells and their integration into complex brain-region-specific networks (1, 9–11). In the rodent hippocampus, early network activity and Ca²⁺ oscillations are mainly attributed to the excitatory role of GABAergic transmission originating from inhibitory neurons (6, 12–14).

The excitatory action of GABAergic neurotransmission is one of the most notable characteristics that distinguish neonate brain from the mature brain, where GABA typically inhibits neuronal networks (1, 6, 8–10, 12, 15–17). Although recent work has also called the inhibitory action of GABA on cortical networks into question (18), there are many other pathways that could play a significant role in the observed spontaneous activity in neonate brain (discussed in this section below). Additional key features of the early network oscillations in the hippocampus include their synchronous behavior across most of the neuronal network, modulation by glutamate, recurrence with regular frequency, and a limitation to early postnatal development (3, 6, 12).

More recently, Felix and co-workers (2) reported a new form of seemingly spontaneous activity in acutely isolated tissue slices of hippocampus and cortex of neonatal mice. It consists of spontaneous fluctuations in intracellular Na⁺, which occur to similar degrees at room temperature and physiological temperature both in astrocytes and neurons and were observed in ∼21% of pyramidal neurons and ∼32% of astrocytes tested. Na⁺ fluctuations are ultraslow in nature, averaging ∼2 fluctuations/h, are not synchronized between cells, and are not significantly affected by an array of pharmacological blockers for various channels, receptors, and transporters. Only using the voltage-gated Na⁺ channel (VGSC) blocker tetrodotoxin (TTX) diminished the Na⁺ fluctuations in neurons and astrocytes, indicating that they are driven by the generation of neuronal action potentials. In addition, neuronal fluctuations were significantly reduced by the application of the GABA_A receptor antagonist bicuculline, suggesting the involvement of GABAergic neurotransmission (2).

This paper follows up on the latter study (2) and uses dual experiment-theory approach to systematically confirm, and further investigate, the properties of neuronal Na⁺ fluctuations in the neonate hippocampal CA1 area and to identify the pathways that generate and shape them. Notably, a range of factors that play a key role in controlling the dynamics of extra- and intracellular ion concentrations are not fully developed in the neonate forebrain (14, 19–22). These factors, such as the cellular uptake capacity of K⁺ from the extracellular space (ECS), the expression levels of the three isoforms (α1, α2, and α3) of the Na⁺/K⁺ pump that restore resting Na⁺ and K⁺ concentrations, the ratio of intra- to extracellular volumes, and the magnitude of relative shrinkage of the ECS in response to neuronal stimulus, all increase with age and cannot be easily manipulated experimentally (20). The gap-junctional network between astrocytes is also less developed in neonates and therefore has a lower capacity for the spatial buffering of ions, neurotransmitters released by neurons, and metabolites (19, 20). At the same time, the synaptic density and expression levels of most isoforms of AMPA and N-methyl-d-aspartate (NMDA) receptors are very low in neonates and only begin to increase rapidly during the second week (14). Additionally, although GABAergic synapses develop earlier than their glutamatergic counterparts, synaptogenesis is incomplete and ongoing. Therefore, synapses of varying strengths exist across the network. Each of these aspects impacts the others and their individual specific roles in the early spontaneous activity is consequently difficult to test experimentally. Their involvement in neonatal Na⁺ fluctuations will therefore be addressed for the first time by the data-driven modeling approach here.

We use ratiometric Na⁺ imaging in tissue slices of the hippocampal CA1 region obtained from neonate animals at postnatal days 2–4 (P2–4) and juveniles at P14–21 to record intracellular Na⁺ fluctuations in both age groups. We begin by reporting the key statistics about spontaneous Na⁺ fluctuations observed in neonates and juveniles. Next, we develop a detailed network model, consisting of pyramidal cells and inhibitory neurons, which also incorporates the exchange of K⁺ in the ECS with astrocytes and perfusion solution in vitro (or vasculature in intact brain). Individual neurons are modeled by Hodgkin-Huxley type formalism for membrane potential and rate equations for intra- and extracellular ion concentrations. In addition to closely reproducing our experimental results, the model provides new key insights into the origin of spontaneous slow Na⁺ oscillations in neonates. Furthermore, our model also predicts that the network representing a developing brain is more prone to seizure-like excitability when compared with mature brain.

MATERIALS AND METHODS

Experimental Methods

Relevant abbreviations and source of chemicals.

Relevant abbreviations and source of chemicals are as follows: MPEP, 2-methyl-6-(phenylethynyl)pyridine, from Tocris; APV, (2 R)-amino-5-phosphonovaleric acid; (2 R)-amino-5-phosphonopentanoate, from Cayman Chemical; NBQX, 2,3-dioxo-6-nitro-1,2,3,4-tetrahydrobenzo[f]quinoxaline-7-sulfonamide, from Tocris; CGP-55845, (2S)-3-[[(1S)-1-(3,4-dichlorophenyl)ethyl]amino-2-hydro xypropyl](phenylmethyl)phosphinic acid hydrochloride, from Sigma-Aldrich; NNC-711, 1,2,5,6-tetrahydro-1-[2-[[(diphenylmethylene)amino]oxy]ethyl]-3-pyridinecarboxylic acid hydrochloride, from Tocris; SNAP-5114, 1-[2-[tris(4-methoxyphenyl)methoxy]ethyl]-(S)-3-piperidinecarboxylic acid, from Sigma-Aldrich.

Preparation of tissue slices.

This study was carried out in accordance with the institutional guidelines of the Heinrich Heine University Düsseldorf, as well as the European Community Council Directive (2010/63/EU). All experiments were communicated to and approved by the animal welfare office of the animal care and use facility of the Heinrich Heine University Düsseldorf (Institutional Act No.: O52/05). In accordance with the German Animal Welfare Act (Articles 4 and 7), no formal additional approval for the postmortem removal of brain tissue was necessary. In accordance with the recommendations of the European Commission (23), juvenile mice were first anaesthetized with CO₂ before the animals were quickly decapitated, whereas animals younger than P10 received no anesthetics.

Acute brain slices with a thickness of 250 µm were generated from mice (Mus musculus, Balb/C; both sexes) using methods previously published (24). An artificial cerebrospinal fluid (ACSF) containing (in mM): 2 CaCl₂, 1 MgCl₂ 125 NaCl, 2.5 KCl, 1.25 NaH₂PO₄, 26 NaHCO₃, and 20 glucose was used throughout all experiments and preparation of animals younger than P10. For animals at P10 or older, a modified ACSF (mACSF) was used during preparation, containing a lower CaCl₂ concentration (0.5 mM), and a higher MgCl₂ concentration (6 mM) but being otherwise identical to the normal ACSF. Both solutions were bubbled with 95% O₂-5% CO₂ to produce a pH of ∼7.4 throughout experiments, and each had an osmolarity of 308–312 mOsm/L. Immediately after slicing, the slices were transferred to a water bath and incubated at 34°C with 0.5–1 µM sulforhodamine 101 (SR101) for 20 min, followed by 10 min in 34°C ACSF without SR101. During experiments, slices were continuously perfused with ACSF at room temperature. For experiments utilizing antagonists, these were dissolved in ASCF and bath applied for 15 min before the beginning, and subsequently throughout the measurements.

Sodium imaging.

Slices were dye-loaded using the bolus injection technique (via use of a picospritzer 3, Parker, Cologne, Germany), and cells were imaged at a depth of 30–60 µm under the slice surface. The sodium-sensitive ratiometric dye SBFI-AM (sodium-binding benzofuran isophthalate-acetoxymethyl ester; Invitrogen, Schwerte, Germany) was used for detection of Na⁺. SBFI was excited alternatingly at 340 nm (Na⁺-insensitive wavelength) and 380 nm (Na⁺-sensitive wavelength) by a PolychromeV monochromator (Thermo Fisher Scientific, Eindhoven, Netherlands). Emission was collected above 420 nm from defined regions of interest (ROIs) drawn around cell somata using an upright microscope (Nikon Eclipse FN-1, Nikon, Düsseldorf, Germany) equipped with a Fluor ×40/0.8W immersion objective (Nikon), and attached to an ORCA FLASH 4.0 LT camera (Hamamatsu Photonics Deutschland GmbH, Herrsching, Germany). The imaging software used was NIS-elements AR v4.5 (Nikon, Düsseldorf, Germany). For the identification of astrocytes (25), SR101 was excited at 575 nm and its emission collected above 590 nm.

Dual imaging of Na⁺ and Ca²⁺.

Slices were simultaneously bolus-loaded with the Na⁺-sensitive dye, SBFI-AM, and with the Ca²⁺-indicator OGB1-AM (Oregon Green BAPTA 1-acetoxymethyl ester; Invitrogen, Schwerte, Germany). SBFI was imaged as stated in the Sodium imaging section, and OGB1 was excited at 488 nm with emission collected above 505 nm. Ca²⁺-imaging experiments with OGB1 were performed at 32 ± 1°C, for which an ACSF containing (in mM): 2 CaCl₂, 1 MgCl₂, 136.5 NaCl, 4 KCl, 1.3 NaH₂PO₄, 18 NaHCO₃, and 10 glucose, titrated to pH 7.4, was used.

K⁺-sensitive microelectrodes.

Changes in [K⁺]_e were detected using ion-selective microelectrodes, with tops placed 50 µm below the surface of the slice. These were built as described previously (26, 27) using borosilicate glass capillaries with filament. Tips were silanized via exposure to vaporized hexamethyldisilazane (Fluka, Buchs, Switzerland), before being filled with valinomycin (Ionophore I, Cocktail B, Fluka). Capillaries were then backfilled with 100 mM KCl, and reference electrodes were filled with 150 mM NaCl/1 mM HEPES (titrated to pH 7.0 with NaOH). The electrodes were calibrated immediately before and directly after experiments using solutions with defined K⁺ concentrations.

Data analysis and statistics.

For each ROI, a ratio of the sensitive and insensitive emissions was calculated and analyzed using OriginPro 9.0 software (OriginLab Corporation, Northampton, MA). Changes in fluorescence ratio were converted to mM Na⁺ on the basis of an in-situ calibration performed as reported previously (28, 29). A signal was defined as being any change from the baseline, if Na⁺ levels exceeded 3 SDs of the baseline noise. Each series of experiments was performed on at least four different animals, with “n” reflecting the total number of individual cells analyzed. Values from experiments mentioned in the text are presented as means ± SE, and values taken from models are presented as means ± SD.

Computational Methods

The basic equations for the membrane potential of individual neurons, various ion channels, and synaptic currents used in our model are adopted from (30). The network topology follows the scheme for hippocampus from the same work. As shown in Fig. 1, the network consists of pyramidal cells and fast-spiking interneurons with five to one ratio. The results reported in this paper are from a network with 100 excitatory and 20 inhibitory neurons. Astrocytes are not explicitly illustrated as cellular entities in Fig. 1 but included in the model through their ability to take up K⁺. Of note, increasing or decreasing the network size does not change the conclusions from the model. We tested a network with 25 excitatory and five inhibitory neurons and found similar results. Each inhibitory neuron makes synaptic connections with five adjacent postsynaptic pyramidal neurons (I-to-E synapses). Thus, five excitatory neurons and one inhibitory neuron constitute one “domain.” As shown in the results, we observed significant variability in the neuronal behavior. Approximately 21% of neurons tested exhibited Na⁺ fluctuations. Furthermore, the amplitude, duration, and frequency of the fluctuations varied over a wide range, pointing toward a heterogeneity in the network topology. To incorporate the observed variability in the neuronal behavior, the synaptic strengths vary randomly from one domain to another. For inhibitory-to-inhibitory (I-to-I), excitatory-to-excitatory (E-to-E), and excitatory-to-inhibitory (E-to-I) synapses, we consider all-to-all connections. However, restricting these synapses spatially does not change the conclusions in the paper. We remark that if one wishes to use a network of a different size with all-to-all connections, the maximum strength of these three types of synaptic inputs will need to be scaled according to the network size.

Figure 1.

Network schematic showing connections between adjacent neurons within the two neuronal layers. The network consists of pyramidal (E) and inhibitory (I) neurons at five to one ratio, where five excitatory neurons and one inhibitory neuron make one domain. In addition to synaptic inputs, we also consider the diffusion of extracellular K⁺ between neighboring cells and incorporate the effect of glial K⁺ uptake. Incorporating Na⁺ and Cl⁻ diffusion in the extracellular space does not change our conclusions (not shown) and is therefore not included in the model.

The equations for individual cells are modified and extended to incorporate the dynamics of various ion species in the intra- and extracellular spaces of the neurons using the formalism previously developed in Refs. 31–37. The change in the membrane potential, V_m, for both excitatory and inhibitory neurons in the network is controlled by various Na⁺ (I_Na), K⁺ (I_K), and Cl⁻ (I_Cl) currents, current due to Na⁺/K⁺-ATPase (I_pump), and random inputs from neurons that are not a part of the network ($I_{stoch}^{Ex}$), and is given as

$$C\frac{d{V}_m^{Ex,In}}{dt}=I_{Na}^{Ex,In}+I_K^{Ex,In}+\mathrm{ }{I}_{Cl}^{Ex,In}+I_{pump}^{Ex,In}+I_{stoch}^{Ex/In}.$$ (1)

The superscripts Ex and In correspond to excitatory and inhibitory neurons, respectively. The Na⁺ and K⁺ currents consist of active currents corresponding to fast sodium and delayed rectifier potassium channels ($I_{Na}^F$ and $I_K^{DR}$), passive leak currents ($I_{Na}^{leak}$ and $I_K^{leak}$), and excitatory synaptic currents ($I_{Na}^{syn}$ and $I_K^{syn}$). The chloride currents consist of contributions from passive leak current ($I_{Cl}^{leak})$ and inhibitory synaptic currents ($I_{Cl}^{syn}$). In this paper, we use positive and negative conventions for all inward (causing positive change in V_m) and outward currents, respectively.

$$I_{Na}^{Ex,In}=I_{Na}^F+I_{Na}^{leak}+I_{Na}^{syn},$$

$$I_K^{Ex,In}=I_K^{DR}+I_K^{leak}+I_K^{syn},$$

$$I_{Cl}^{Ex,In}=I_{Cl}^{leak}+I_{Cl}^{syn}.$$

The equations for active neuronal currents are given as

$$I_{Na}^F=g_{Na}{m}_{\mathrm{\infty }}^{3}h(V_{Na}-V_m),$$

$$I_K^{DR}=g_k{n}^4(V_K-V_m),$$

where g_Na, g_k, m_∞, h, and n represent the maximum conductance of fast Na⁺ channels, maximum conductance of delayed rectifier K⁺, steady state gating variable for fast Na⁺ activation, fast Na⁺ inactivation variable, and delayed rectified K⁺ activation variable. As in Ref. 30, the gating variables and peak conductances for $I_{Na}^F$, $I_K^{DR}$, and leak currents for the pyramidal neurons in this study are based on the model of Ermentrout and Kopell (38), which is a reduction of a model due to Traub and Miles (39). The equations for fast-spiking inhibitory neurons are taken from the model in Refs. 40 and 41, which is a reduction of the multicompartmental model described in Ref. 42. These equations were originally chosen such that the model would result in the intrinsic frequency as a function of stimulus strength observed in pyramidal cells and fast-spiking inhibitory neurons, respectively. The gating variables obey the following equations:

$$x_{\mathrm{\infty }}=\mathrm{ }\frac{{\alpha }_x}{{\alpha }_x+{\beta }_x},\mathrm{ }{\tau }_x=\mathrm{ }\frac{1}{{5(\alpha }_x+{\beta }_x)},\mathrm{ }for\mathrm{ }x=m,n,h.$$

Here, x_∞ and τ_x represent the steady state and time constant of the gating variable, respectively. The factor 5 in τ_x results from the fact that the Hodgkin and Huxley original formalism was based on electrophysiological data scaled at 6.3°C (43). They suggested multiplying the forward and reverse rates (α_x and β_x) by a factor of 5 if the model is supposed to represent experiments at room temperature. The rates α_x and β_x for the channel activation and inactivation are calculated using the equations below.

$${\alpha }_n=\frac{-0.01(V_m+34)}{\exp \hspace{0.17em}\left(-0.1\left(V_m+34\right)\right)-1},$$

$${\beta }_n=0.125\hspace{0.17em}\mathrm{e}\mathrm{x}\mathrm{p}\hspace{0.17em}(-\frac{V_m+44}{80}),$$

$${\alpha }_h=0.07\hspace{0.17em}\mathrm{e}\mathrm{x}\mathrm{p}\hspace{0.17em}(-\frac{V_m+58}{20}),$$

$${\beta }_h=\frac{1}{\exp \hspace{0.17em}\left(-0.1\left(V_m+28\right)\right)+1},$$

$${\alpha }_m=\frac{0.1(V_m+35)}{1-\mathrm{e}\mathrm{x}\mathrm{p}\hspace{0.17em}(-\frac{V_m+35}{10})},$$

$${\beta }_m=4\mathrm{e}\mathrm{x}\mathrm{p}(-\frac{V_m+60}{10}).$$

The leak currents are given by

$$I_{Na}^{leak}=g_{Na}^{leak}(V_{Na}-V_m),$$

$$I_K^{leak}=g_K^{leak}(V_K-V_m),$$

$$I_{Cl}^{leak}=g_{Cl}^{leak}(V_{Cl}-V_m),$$

where V_Na, V_K, and V_Cl are the reversal potentials for Na⁺, K⁺, and Cl⁻ currents, respectively, and are updated according to the instantaneous values of respective ion concentrations.

The functional form of stochastic current ($I_{stoch}^{Ex/In}$) received by each neuron is also based on Ref. 30 and is given as follows:

$$I_{stoch}=-g_{stoch}{s}_{stoch}{V}_m,$$

where g_stoch represents the maximal conductance associated with the stochastic synaptic input and is set to 1 for both cell types. The gating variable s_stoch decays exponentially with time constant τ_stoch = 100 ms during each time step Δt, that is,

$$s_{stoch}=s_{stoch}\hspace{0.17em}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{\Delta t}{{2\text{×}\tau }_{stoch}}\right).$$

At the end of each time step, s_stoch jumps to 1 with probability Δt × f_stoch/1,000, where f_stoch is the mean frequency of the stochastic inputs. These equations simulate the arrival of external synaptic input pulses from the neurons that are not included in the network (30).

The excitatory and inhibitory synaptic currents corresponding to AMPA, NMDA, and GABA receptors are given by the equations below,

$$I_{Na}^{syn}=G_{AMPA/NMDA}{S}_{AMPA/NMDA}\left(V_{Na}-V_m\right),$$

$$I_K^{syn}=G_{AMPA/NMDA}{S}_{AMPA/NMDA}\left(V_K-V_m\right),$$

$$I_{Cl}^{syn}=G_{GABA}{S}_{GABA}(V_{Cl}-V_m).$$

G_AMPA/NMDA, G_GABA, S_AMPA/NMDA, and S_GABA represent the synaptic conductance and gating variables for AMPA and NMDA (represented by a single excitatory current) and GABA receptors. To incorporate the observed variability in neuronal behavior, we randomly select the maximal conductance value for I-to-E synapses inside a single domain from a Gaussian distribution between 0.1 and 3.0 mS/cm². To model the excitatory role of GABAergic neurotransmission observed in neonate brain, we change the sign of G_GABA from positive to negative.

The change in synaptic gating variables for both excitatory and inhibitory neurons is modeled as in Ref. 30. That is,

$$\frac{dS}{dt}=\frac{1}{2}\left(1+\tanh \hspace{0.17em}\left(\frac{V_m}{4}\right)\right)\frac{1-S}{{\tau }_R}-\frac{S}{{\tau }_D},$$ (2)

where τ_R and τ_D represent the rise and decay time constants for synaptic signals. The reversal potentials used in the above equations are calculated using the Nernst equilibrium potential equations, that is,

$$V_K=26.64\mathrm{l}\mathrm{n}\hspace{0.17em}\left(\frac{[{\text{K}}^{+}{]}_{\text{o}}}{[{\text{K}}^{+}{]}_{\text{i}}}\right),$$

$$V_{\mathrm{Na}}=26.64\mathrm{l}\mathrm{n}\hspace{0.17em}\left(\frac{[{\text{Na}}^{+}{]}_{\text{o}}}{[{\text{Na}}^{+}{]}_{\text{i}}}\right),$$

$$V_{\mathrm{C}l}=26.64\mathrm{l}\mathrm{n}\hspace{0.17em}\left(\frac{[{\text{C}\text{l}}^{+}{]}_{\text{i}}}{[{\text{C}\text{l}}^{+}{]}_{\text{o}}}\right),$$

where [K⁺]_o/i, [Na⁺]_o/i, and [Cl⁻]_o/i represent the concentration of Na⁺, K⁺, and Cl⁻ outside and inside the neuron, respectively. We consider the ECS as a separate compartment surrounding each cell, having a volume of ∼15% of the intracellular space (ICS) in the hippocampus of adult brain (44, 45) and ∼40% of the ICS in neonates (46, 47). Each neuron exchanges ions with its ECS compartment through active and passive currents, and the Na⁺/K⁺-ATPase. The ECS compartment can also exchange K⁺ with the glial compartment, perfusion solution (or vasculature in intact brain), and the ECS compartments of the nearby neurons (48–50).

The change in [K⁺]_o is a function of I_K, I_pump, uptake by glia surrounding the neuron (I_glia), diffusion between the neuron and bath perfusate (I_diff1), and lateral diffusion between adjacent neurons (I_diff2).

$$\frac{d[{\text{K}}^{+}{]}_{\text{o}}}{dt}=-\gamma \beta I_K+2\gamma {\beta I}_{pump}+I_{glia}-I_{diff1}+I_{diff2},$$ (3)

where β is the ratio of ICS to ECS. We set β = 7 in adult and 2.5 in neonates to incorporate the larger ECS (∼15% and ∼40% of the ICS in adults and neonates, respectively) observed in neonates (46, 47). To see how the relative volume of ECS affects the behavior of spontaneous Na⁺ fluctuations, we vary β over a wide range in some simulations of neonate network. We remark that using β = 2.5 in the network representing the adult brain (mature inhibition) didn’t cause spontaneous Na⁺ fluctuations (not shown). γ = 3 × 10⁴/(F × r_in) is the conversion factor from current units to flux units, where F and r_in are the Faraday’s constant and radius of the neuron, respectively. The factor 2 in front of I_pump is due to the fact that the Na⁺/K⁺ pump extrudes two K⁺ in exchange for three Na⁺.

The rate of change of [Na⁺]_i is controlled by I_Na and I_pump (31), that is,

$$\frac{d[{\mathrm{N}\mathrm{a}}^{+}{]}_{\mathrm{i}}}{dt}=\gamma I_{Na}+3\gamma I_{pump}.$$ (4)

The equations modeling I_pump, I_glia, and I_diff1 are given as

$$I_{pump}=-\frac{\rho }{1+\mathrm{e}\mathrm{x}\mathrm{p}\hspace{0.17em}\left(\right(25-\left[{\mathrm{N}\mathrm{a}}^{+}{]}_{\mathrm{i}}\right)/3)}\frac{1}{1.0+exp(5.5-[{\mathrm{K}}^{+}{]}_{\mathrm{o}})}.$$

$$I_{diff1}={ϵ}_K\left(\right[{\mathrm{K}}^{+}{]}_{\mathrm{o}}-\left[{\mathrm{K}}^{+}{]}_{bath}\right),$$

$$I_{glia}=\frac{G_{glia}}{1+\mathrm{ }\mathrm{e}\mathrm{x}\mathrm{p}\hspace{0.17em}\left(10\right(3-\left[{\mathrm{K}}^{+}{]}_{\mathrm{o}}\right))},$$

where ρ is the pump strength and is a function of available oxygen concentration in the tissue ([O₂]) or perfusion solution (51), that is

$$\rho =\frac{{\rho }_{max}}{1+\mathrm{e}\mathrm{x}\mathrm{p}\hspace{0.17em}\left(\frac{20-\left[{\mathrm{O}}_2\right]}{3}\right)}.$$

and ρ_max, G_glia, ϵ_k, and [K⁺]_bath represent the maximum Na⁺/K⁺ pump strength, maximum glial K⁺ uptake, constant for K⁺ diffusion to vasculature or bath solution, and K⁺ concentration in the perfusion solution, respectively. The change in oxygen concentration is given by the following rate equation (51).

$$\frac{d[{\mathrm{O}}_2{]}_{\mathrm{o}}}{dt}=\mathrm{\alpha }{I}_{pump}+{ϵ}_0\left(\right[{\mathrm{O}}_2{]}_{bath}-\left[{\mathrm{O}}_2{]}_{\mathrm{o}}\right),$$ (5)

where [O₂]_bath is the bath oxygen concentration in the perfusion solution, α converts flux through Na⁺/K⁺ pumps (mM/s) to the rate of oxygen concentration change [mg/(L × s)], and ε₀ is the diffusion rate constant for oxygen from bath solution to the neuron. We also incorporate lateral diffusion of K⁺ (I_diff2) between adjacent neurons where the extracellular K⁺ of each neuron in the excitatory layer diffuses to/from the nearest neighbors in the same layer and one nearest neuron in the inhibitory layer. That is,

$$I_{diff2}=\frac{D_k}{{dx}^2}\left(\right[{\mathrm{K}}^{+}{]}_{\mathrm{o},\mathrm{i}+1}^{\mathrm{E}\mathrm{x}}+[{\mathrm{K}}^{+}{]}_{\mathrm{o},\mathrm{i}-1}^{\mathrm{E}\mathrm{x}}+[{\mathrm{K}}^{+}{]}_{\mathrm{o},\mathrm{i}}^{\mathrm{I}\mathrm{n}}-3\left[{\mathrm{K}}^{+}{]}_{\mathrm{o},\mathrm{i}}^{\mathrm{E}\mathrm{x}}\right),$$

where the subscript i indicates the index of the neuron with which the exchange occurs, D_k is the diffusion coefficient of K⁺, and dx represents the separation between neighboring cells. The diffusion of K⁺ in the inhibitory layer is modified so that each inhibitory neuron exchanges K⁺ with the two nearest neighbors in the same layer and five nearest neighbors in the excitatory layer. The separation between neighboring neurons in the inhibitory layer is five times that of neighboring neurons in the excitatory layer.

To simplify the formalism, [K⁺]_i and [Na⁺]_o are linked to [Na⁺]_i as previously described (31, 36, 37, 52, 53).

$$[{\mathrm{K}}^{+}{]}_{\mathrm{i}}=140+(18-\left[{\mathrm{N}\mathrm{a}}^{+}{]}_{\mathrm{i}}\right),$$

$$[{\mathrm{N}\mathrm{a}}^{+}{]}_{\mathrm{o}}=144+\beta ([{\mathrm{N}\mathrm{a}}^{+}{]}_{\mathrm{i}}-18).$$

[Cl⁻]_i and [Cl⁻]_o are given by the conservation of charge inside and outside the cell, respectively.

$$[{\mathrm{C}\mathrm{l}}^{-}{]}_{\mathrm{i}}=[{\mathrm{N}\mathrm{a}}^{+}{]}_{\mathrm{i}}+{[\mathrm{K}}^{+}{]}_{\mathrm{i}}-150,$$

$$[{\mathrm{C}\mathrm{l}}^{-}{]}_{\mathrm{o}}=[{\mathrm{N}\mathrm{a}}^{+}{]}_{\mathrm{o}}+{[\mathrm{K}}^{+}{]}_{\mathrm{o}}.$$

The number 150 in the above equation represents the concentration of impermeable anions. The values of various parameters used in the model are given in Table 1.

Table 1.

Values and meanings of various parameters used in the model

Parameter	Value and Unit, Excitatory (left) and Inhibitory Neuron (right)	Description
C	1.0 µF/cm2	Membrane capacitance
γ	3 × 104/(F × rin) mM cm2/(s μA)	Current to concentration conversion factor
rin	6 µm	Radius of the neuron
β	2.5	Ratio of ICS to ECS
$G_{Cl}^L$	0.001 mS/cm2	Conductance of Cl− leak channels
$G_{Na}^F$	165 mS/cm2, 35 mS/cm2	Maximal conductance of fast Na+ channels
$G_K^{DR}$	80 mS/cm2, 9 mS/cm2	Maximal conductance of delayed rectified K+ channels
$G_K^L$	0.02 mS/cm2	Conductance of K+ leak channels
$G_{Na}^L$	7.6 µS/cm2, 8.55 µS/cm2	Conductance of Na+ channels
$G_{\text{AMPA}/\text{NMDA}}$	1 µS/cm2	Maximal conductance of E-to-E and E-to-I synapses
$G_{GABA}^{ii}$	10 µS/cm2	Maximal conductance of I-to-I synapses
$G_{GABA}^{ie}$	0.1–3.0 mS/cm2	Maximal conductance of I-to-E synapses
${\tau }_R$	0.1 ms	Rise constant for synaptic gating
${\tau }_D$	4.0 ms, 30.0 ms	Decay constant for synaptic gating
fstoch	1 Hz, 0.1 Hz	Mean arrival frequency of stochastic input
ρmax	29 mM/s	Maximum Na+/K+ pump strength
[O2]bath	32 mg/L	Oxygen concentration in the bath solution
α	5.3 g/mol	Conversion factor from Na+/K+-ATPase current to oxygen consumption rate
${\epsilon }_0$	0.17 s−1	Oxygen diffusion constant
Gglia	60 mM/s	Maximum glia K+ uptake
${ϵ}_K$	3 s−1	Constant for K+ diffusion between ECS and bath solution (blood vassals in vivo)
$[K^{+}{]}_{\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{h}}$	3.0 mM	K+ concentration in the bath solution in vitro or in vasculature in vivo
DK	2.5 × 10−5 cm2/s	Diffusion coefficient of K+ in the ECS
dx	200 µm	Distance between adjacent neurons

Numerical Methods

The rate equations were solved in Fortran 90 using the midpoint method, with a time step of 0.02 ms. The statistical analysis of the data obtained from simulations is performed in MATLAB. Codes reproducing key results are available upon request from authors. Significance was determined using Student’s t tests (***P < 0.001).

RESULTS

Pyramidal Neurons in Neonate Hippocampus Exhibit Spontaneous Ultraslow Na^± Fluctuations

Acutely isolated parasagittal slices from hippocampi of neonatal mice (P2–4) were bolus-stained with the sodium-sensitive ratiometric dye SBFI-AM along the CA1 region (Fig. 2A1). Experimental measurements lasted for 60 min, with an imaging frequency of 0.2 Hz. Astrocytes were identified via SR101 staining (Fig. 2A1), and were analyzed separately to the neurons in the pyramidal layer. Out of the measured cells, 21% of neurons (n = 73/350) and 32% of astrocytes (n = 57/179) showed detectable fluctuations in their intracellular Na⁺ concentrations (Fig. 2, A2 and B). Detection threshold was calculated individually for each cell, and was defined as being 3 times the standard deviation of the baseline noise of each ROI analyzed (this ranged from 0.57 to 2.2 mM). Astrocyte Na⁺ fluctuations were 11.3 ± 1.95 min long, at a frequency of 2.0 ± 0.2 signals/h and with average amplitudes of 2.7 ± 0.1 mM. Neuronal Na⁺ fluctuations had an average duration of 11.5 ± 0.6 min. They occurred at a frequency of 1.52 ± 0.1 fluctuations/hour with average amplitudes of 1.9 ± 0.05 mM. The high variability in the shapes of fluctuations is demonstrated in Fig. 2A2. Apparent synchronicity between cells of the same or different classes was only observed rarely, confirming the observations reported in our earlier study (2).

Figure 2.

In situ experiments. A1: images showing representative stainings in the CA1 region of the neonatal (P4; top) and juvenile (P18; bottom) hippocampus. In the merge, SBFI is shown in green and SR101 in magenta. ROIs representing cell bodies of neurons and astrocytes are labeled with numbers and letters, respectively. Scale bars: 50 µm. A2: Na⁺ fluctuations in the ROIs as depicted in (A1). B: the percentage of pyramidal neurons and astrocytes showing activity for each age group and the total number of cells measured. C: scatter plot showing the peak amplitude and duration of neuronal fluctuations within the two indicated age groups. P, postnatal day; ROI, regions of interest; SBFI, sodium-binding benzofuran isophthalate; SR101, sulforhodamine 101.

In addition, SBFI-loaded cells in the stratum radiatum, but not stained by SR101, were analyzed as a separate group. Of these SR101-negative cells, 28% showed Na⁺ fluctuations (n = 33/118; not shown). The properties of these fluctuations were comparable with those seen in the two other cell types (pyramidal neurons and SR101-positive astrocytes), with an average amplitude of 2.17 ± 0.17 mM, duration of 9.3 ± 0.47 min and frequency of 1.81 ± 0.15 fluctuations per hour. It should be noted that although the SR101-negative group is likely to contain some interneurons, the identity of these cannot be conclusively determined. The group may also encompass immature astrocytes that do not yet take up the SR101 marker (see Ref. 25).

To investigate the developmental profile of the fluctuations, the same protocol was repeated in hippocampal tissue from juvenile (P14–20) mice. Here, only 5.3% of all measured neurons (n = 7/132) and 4.3% of all measured astrocytes (n = 1/23) showed fluctuations in their intracellular Na⁺ concentrations (Fig. 2B). This strong reduction confirmed the significant down-regulation of spontaneous Na⁺ oscillations from neonatal to juvenile animals reported recently (2). However, the properties of the neuronal fluctuations themselves remained unchanged during postnatal development, with the average amplitude, frequency, and duration being 1.9 ± 0.13 mM, 2 ± 0.3 fluctuations/h, and 6.5 ± 0.9 min in juvenile tissue (Fig. 2C).

Spontaneous Na^± Fluctuations Are Reproduced by a Computational Model with Excitatory GABAergic Neurotransmission

To explore the properties and mechanisms of neonate neuronal Na⁺ fluctuations, we developed a computational model consisting of CA1 pyramidal cells and inhibitory neurons as detailed in the methods section. Resulting typical time traces of intracellular Na⁺ from four randomly selected excitatory neurons in a network representative of the juvenile hippocampus (where GABAergic neurotransmission is inhibitory) are shown in the right panel of Fig. 3A. Na⁺ in individual neurons shows minor irregular fluctuations of less than 0.05 mM around the resting values mostly because of the random synaptic inputs from the network. However, no clear large-amplitude fluctuations can be seen in the network. To mimic neonates, we invert the sign of I-to-E and I-to-I synaptic inputs, making the GABAergic neurotransmission excitatory. The depolarizing inhibition results in the occurrence of spontaneous Na⁺ fluctuations in the low mM range in individual neurons that persist for several minutes (Fig. 3A, left column). In some cases, the peak amplitude of oscillations reached values of more than 5 mM.

Figure 3.

Simulated spontaneous activity in four example neurons with excitatory GABAergic neurotransmission representing neonatal hippocampus (A, left) and mature inhibition representing juvenile hippocampus (A, right). Gray bar indicates three times the average standard deviation in experimental traces upwards of the mean. B: experimental data, showing excerpts from example measurements shown in Fig. 2 both from neonatal neurons (P2–4, left; cell 3, top; cell 5, bottom) and juvenile neurons (P14–21, right; cell 1, top; cell 2, bottom). Traces show changes in intracellular Na⁺ concentration over 17 min, a time course directly comparable with (A). P, postnatal day.

The simulated data show a comparable pattern of irregular fluctuations to the experimental results (Fig. 3B). The properties of these events are very similar—with peak amplitudes mostly in the 1–3 mM range and durations spanning over several minutes. However, the simulated data also appears to show a high rate of low amplitude spiking, apparently absent from the experimental traces. As mentioned in the section Pyramidal Neurons in Neonate Hippocampus Exhibit Spontaneous Ultraslow Na⁺ Fluctuations above, the detection threshold for experimental data ranged from 0.57 to 2.2 mM (see also Fig. 3B), and the imaging frequency was kept at 0.2 Hz to prevent phototoxic effects during the long-lasting continuous recordings. Fast, low amplitude transients as revealed in simulated experiments are thus below the experimental detection threshold, as indicated in Fig. 3.

Neonate Network Does Not Exhibit Spontaneous Fluctuations in [K⁺]_o

Since the dynamics of Na⁺ and K⁺ are generally coupled in mature brain, we next look at K⁺ concentration in the ECS of individual neurons ([K⁺]_o) in the network to see if it exhibits similar spontaneous fluctuations. A sample trace for a randomly selected neuron is shown in Fig. 4A (gray). As clear from the figure, there are only minimal fluctuations in [K⁺]_o (peak amplitudes of residual changes are < 0.05 mM) with respect to the resting state when compared with the much larger [Na⁺]_i fluctuations in the same cell (gray line in Fig. 4A). Next, we recorded [K⁺]_o traces for all pyramidal neurons in the network and calculated the mean [K⁺]_o (averaged over all excitatory neurons). The mean [K⁺]_o as a function of time shows that all excitatory neurons in the network exhibit very small changes in the [K⁺]_o, which are essentially canceled out at the network level (Fig. 4A, black line). These small fluctuations diminish further when I-to-I and I-to-E synaptic inputs are blocked, mimicking the effect of bicuculline (not shown).

Figure 4.

Simulated spontaneous fluctuations in intracellular Na⁺ ([Na⁺]_i) are not coupled with significant fluctuations in extracellular K⁺ ([K⁺]_o). [K⁺]_o (A) and [Na⁺]_i (C) time traces from a randomly selected excitatory neuron (gray) and averaged over the entire excitatory network (black). B: ion-sensitive electrode experiments showed no detectable spontaneous changes in extracellular K⁺ in neonatal tissue. Note the artifact occurring when the electrode touches the slice surface.

These results obtained in our simulations are in agreement with experiments in neonatal brain slices utilizing ion-sensitive microelectrodes, which were used to measure changes in [K⁺]_e. During these measurements, the average [K⁺]_e in the slices was found to be 2.66 ± 0.005 mM (n = 9 slices; Fig. 4B). Comparing the average noise level before impalement of the slices with that after impalement revealed that the threshold for detection of changes in [K⁺]_e was 0.09 ± 0.03 mM. This would make the small peaks predicted by the model (∼0.05 mM, Fig. 4A) unlikely to be resolvable by this method. In line with this, no spontaneous changes in [K⁺]_e were detected in neonatal slices (Fig. 4B).

The mean intracellular Na⁺ fluctuates slightly more than the mean [K⁺]_o (Fig. 4C, black line). However, a comparison between the traces showing the average Na⁺ over all excitatory neurons in the network and that from the single neuron indicates that the amplitude of Na⁺ fluctuations varies from cell to cell and that they are not necessarily phase-locked.

The Model Replicates the Observed Effects of TTX and Other Blockers

We next performed imaging experiments in which various blockers were applied. Addition of 0.5 µM TTX reduced the number of neurons showing fluctuations to 4% (n = 7/167), suggesting a dependence on action potential generation via the opening of voltage-gated Na⁺ channels (Fig. 5A). However, blocking of glutamatergic receptors with a cocktail containing APV (100 µM), NBQX (25 µM), and MPEP (25 µM) (targeting NMDA, AMPA/kainate, and mGluR5 receptors, respectively) had no effect on the number of neurons showing fluctuations (21% active, n = 33/155) (Fig. 5A). Additionally, the role of GABAergic signaling was tested via combined application of bicuculline (10 µM), CGP-55845 (5 µM), NNC-711 (100 µM), and SNAP-5114 (100 µM) (antagonists for GABA_A receptors, GABA_B receptors, GABA transporters GAT1, and GAT2/3, respectively). This combination of antagonists reduced the number of active neurons to a similar degree as TTX (3% active, n = 5/158; Fig. 5A). These data are concordant with the results previously published (2) and suggest that the slow fluctuations in intracellular Na⁺ are produced by the accumulation of Na⁺ during trains of action potentials, triggered by GABAergic transmission.

Figure 5.

Inhibiting GABA_A receptors or voltage-gated Na⁺ channels eliminates intracellular Na⁺ ([Na⁺]_i) fluctuations, whereas blocking glutamatergic synaptic inputs has little effect. A: bar plot showing the percentage of neurons exhibiting Na⁺ fluctuations as determined in experiments under the four conditions simulated in B. That is, the percentage of neurons exhibiting Na⁺ fluctuations in slices from juveniles under control conditions (black) and in the presence of 0.5 µM TTX to block voltage-gated Na⁺ channels (gray), a cocktail containing APV (100 µM), NBQX (25 µM), and MPEP (25 µM) to block glutamatergic receptors (purple), and a combined application of bicuculline (10 µM), CGP-55845 (5 µM), NNC-711 (100 µM), and SNAP-5114 (100 µM) to block GABAergic signaling (cyan). B: time trace of [Na⁺]_i from a randomly selected excitatory neuron in the network in control conditions (depolarizing inhibition, representing neonatal brain; black, top), with voltage-gated Na⁺ channels blocked (gray, top), glutamatergic synapses blocked (purple, bottom), and GABAergic synapses blocked (cyan, bottom). APV, (2 R)-amino-5-phosphonovaleric acid; (2 R)-amino-5-phosphonopentanoate; CGP-55845, (2S)-3-[[(1S)-1-(3,4-dichlorophenyl)ethyl]amino-2-hydro xypropyl](phenylmethyl)phosphinic acid hydrochloride; MPEP, 2-methyl-6-(phenylethynyl)pyridine; NBQX, 2,3-dioxo-6-nitro-1,2,3,4-tetrahydrobenzo[f]quinoxaline-7-sulfonamide; NNC-711, 1,2,5,6-tetrahydro-1-[2-[[(diphenylmethylene)amino]oxy]ethyl]-3-pyridinecarboxylic acid hydrochloride; SNAP-5114, 1-[2-[tris(4-methoxyphenyl)methoxy]ethyl]-(S)-3-piperidinecarboxylic acid.

The pharmacological profile of the experimentally observed Na⁺ fluctuations in the neonatal brain summarized above strongly suggests that the excitatory effect of GABAergic neurotransmission plays a key role in their generation, whereas glutamatergic activity contributes very little. Before making model-based predictions, we first confirm that our model reproduces these key observations in our experiments. We first incorporate the effect of TTX in the model by setting the peak conductance of voltage-gated Na⁺ channels to zero. We also mimic the effect of blocking ionotropic glutamate receptors with CNQX and APV by setting E-to-E and E-to-I synaptic conductances to zero. Finally, we mimic the effect of blocking GABAergic transmission on the activity of the network and set the I-to-I and I-to-E synaptic currents to zero, thereby removing all GABA_A-receptor-related effects. The model results are largely in line with observations, where we see that inhibiting GABA-related currents and voltage-gated Na⁺ channels mostly eliminate Na⁺ fluctuations and blocking NMDA and AMPA synaptic inputs has little effect on the observed spontaneous activity (Fig. 5B).

Spontaneous Na⁺ Fluctuations Are Shaped by Neuronal Morphology and Glial K⁺ Uptake Capacity

As pointed out in the introduction, significant changes occur in the physical and functional properties of the neurons during postnatal maturation at the synaptic, single cell, and network levels (14, 20). Therefore, we use the model to examine if changes in some key physical and functional characteristics of the network such as the neuronal radius (r_in), the ratio of ICS to ECS (β), and glial K⁺ uptake rate play any role in the observed Na⁺ fluctuations. In the following, we show Na⁺ time traces for four randomly selected excitatory neurons. We observe that smaller neurons in general exhibit larger Na⁺ fluctuations (P > 0.001, Fig. 6A, left). Both the amplitude and frequency of fluctuations decrease as we increase r_in (Fig. 6A, center). The panel on the right in Fig. 6A (and Fig. 6, B and C) shows the average amplitude of Na⁺ fluctuations as we change the parameter of interest.

Figure 6.

The neuronal radius, ratio of ECS to ICS (β), and K⁺ uptake capacity of glia affect spontaneous Na⁺ fluctuations in the model. A: time traces of intracellular Na⁺ ([Na⁺]_i) for five excitatory neurons from a network representing neonatal brain with a neuronal radius of 3 µm (left panels) and 9 µm (middle panels). The panel on the right shows the mean amplitude of Na⁺ fluctuations (averaged over all pyramidal neurons in the network) under the two conditions. The error bars indicate the standard deviation of the mean. β was fixed at 2.5. B: same as A at β = 1 (left) and 10 (middle). C: same as A with maximum glial K⁺ buffering strength G_glia=12 mM/s (left) and G_glia = 96 mM/s (right). The radius of individual neurons is set at 6 µm in both B and C. ***P < 0.001. ECS, extracellular space; ICS, intracellular space.

The observed fraction of ECS with respect to ICS in neonates is ∼40% (β = 2.5) (46, 47), compared with adult animals where ECS is ∼15% of the ICS (β ∼ 7) (44, 45). We vary β from 1 to 10 to see how it affects Na⁺ fluctuations. An opposite trend as compared with neuronal radius can be seen when we change β, where larger β results in Na⁺ fluctuations that are larger in amplitude and have longer duration (Fig. 6B, middle) compared with those in neurons with smaller β values (P > 0.001, Fig. 6B, left). Thus the relative larger ECS in neonates does not favor the generation of large Na⁺ fluctuations, but on the contrary dampens ion changes. We remark that with the exception of Fig. 6B, all simulations in this paper are performed at β = 2.5. In Fig. 6B, we report results at the smallest and largest values tested to show how drastic changes in this parameter can affect the behavior of slow Na⁺ fluctuations.

The expression levels of astrocytic channels and transporters involved in K⁺ uptake [Na⁺/K⁺ ATPase, Kir4.1 channels, and Na⁺/K⁺/Cl⁻ co-transporter 1 (NKCC1)] and connexins forming gap junctions are low in neonates (19, 21, 54). Astrocytes in the neonate brain, therefore, have a lower capacity for uptake of extracellular K⁺ released by neurons (20, 55). To analyze the influence of glial K⁺ uptake, we varied the maximum glial K⁺ uptake strength in the model from 12 mM/s [significantly lower than 66 mM/s—the value used for mature neurons in Ref. 31] to 96 mM/s to see how it affects Na⁺ fluctuations. We observed a strong effect of varying peak glial K⁺ uptake on the amplitude and frequency of Na⁺ fluctuations (P > 0.001). Overall, the amplitude and frequency of Na⁺ fluctuations decrease as we increase peak glial K⁺ uptake (Fig. 6C). This occurs because a stronger glial K⁺ uptake leads to decreased excitability of neurons, and consequently weaker [Na⁺]_i fluctuations.

As pointed out in the introduction, Na⁺/K⁺ ATPase changes significantly with age. For example, the expression levels of all three isoforms (α1, α2, and α3) of the Na⁺/K⁺ pump that restore resting Na⁺ and K⁺ concentrations in rats increase stepwise by more than fourfold from P3–4 to P21–22 (20). To mimic the changes in the expression level of Na⁺/K⁺ ATPase and how it affects slow Na⁺ fluctuations, we change the maximum strength of the Na⁺/K⁺ pump (ρ_max) in the model. Although increasing the pump strength beyond the value given in Table 1 (we increased ρ_max by up to a factor of 3) did not significantly affect Na⁺ fluctuations, decreasing ρ_max by 40% increases their mean amplitude (Fig. 7). Furthermore, the frequency of Na⁺ fluctuations decreases from 3.17/h to 2.54/h as we decrease ρ_max by 40%, whereas the average duration does not change significantly.

Figure 7.

A significant decrease in the strength of Na⁺/K⁺ pump increases the amplitude of Na⁺ fluctuations in the simulations. Average amplitude of spontaneous Na⁺ fluctuations (averaged over all pyramidal neurons in the network) as a function of maximum pump strength (normalized with respect to the control value given in Table 1). ***P < 0.001.

Link to Synchronous Neonatal Network Activity

The pharmacological properties of the Na⁺ fluctuations share similarities with other spontaneous developmental activity patterns, including the well-described giant depolarizing potentials (GDPs) (8). These GDPs are associated with transient elevations in [Ca²⁺]_i, termed early network oscillations (ENOs) (6), which require near-physiological temperatures. In our earlier study (2), increasing the ACSF temperature from room temperature to 33–35°C, had no effect on either the duration, amplitude, or frequency of the Na⁺ fluctuations in neurons, suggesting that these signals are not strictly linked to each other.

To further experimentally investigate possible links between the two phenomena, we used a dual staining approach to be able to monitor Na⁺ and Ca²⁺ signaling sequentially in the same set of cells. To this end, neonatal slices (number of slices n = 4; number of neurons analyzed n = 202) were loaded with both SBFI and OGB (Fig. 8A). To reduce damage and phototoxic effects during the long-lasting Na⁺ recordings, slices were first measured using the excitation wavelength specific for the Na⁺-sensitive SBFI for an hour, at room temperature, with a frequency of 0.2 Hz. Thereafter, the temperature of the perfusion saline was gradually raised to 32 ± 1°C, at which point Ca²⁺ imaging was performed for a further 20 min at 4 Hz (Fig. 8B).

Figure 8.

Dual imaging experiments. A: images show a section of the CA1 region of a P4 hippocampal slice stain with both OGB-1 and SBFI (individual stainings shown below). Scale bars indicate 20 µm. B: traces from individual cells as shown in A. Room temperature Na⁺ measurements (left) were followed by an increase to 32°C at which point Ca²⁺ measurements were conducted (right). C: lack of correlation between levels of Ca²⁺ activity as measured by area under the trace and number of Ca²⁺ at least 2% over the baseline value, and the presence or lack of Na⁺ fluctuations in the same cell. OGB-1, Oregon Green BAPTA 1-acetoxymethyl ester; SBFI, sodium-binding benzofuran isophthalate.

The level of Ca²⁺ activity was analyzed both by counting the number of events that exhibited peaks reflecting a change in fluorescence emission by at least of 2% relative to the baseline as well as by integrating the area over the curve for the entire recording of an individual cell. As expected, we found synchronized, repetitive Ca²⁺ signaling in the neuronal cell population (Fig. 8B) at near physiological temperature, confirming the occurrence of synchronous neonatal network activity under these conditions. Comparing those cells which had displayed Na⁺ fluctuations against those that had not revealed no distinction in their level of Ca²⁺ activity (Fig. 8C). These results demonstrate that there is no clear correlation between cells undergoing slow spontaneous Na⁺ fluctuations and their ability to contribute to synchronized Ca²⁺ oscillations.

The Model Shows Synchronized Bursting in Populations of Neurons

The network representing the neonatal brain shows clear synchronous bursting activity in subpopulations of neurons without making any changes to the parameters (Fig. 9A). In line with previous observations, the time scale of these events is shorter (∼150 ms) as compared with Na⁺ fluctuations (6–8, 56; Fig. 9A1). Although our model does not incorporate intracellular Ca²⁺ dynamics, which precludes computational investigation of the synchronous Ca²⁺ fluctuations observed in our experiments and elsewhere (2–5), we believe that the synchronous bursting activity shown here would lead to the observed synchronous intracellular Ca²⁺ fluctuations. In its current form, the model is also not equipped to properly investigate the correlation between slow Na⁺ fluctuations and GDPs. Incorporating such details is beyond the scope of this study and is the subject of our future research (see discussion). The number of cells exhibiting synchronous bursting increases as we increase the connectivity among cells or consider a common input from a source outside the network, for example, one representing the input from CA3 to CA1 region.

Figure 9.

Subpopulations of neurons in the model network representing neonatal brain exhibit synchronized bursting behavior. A: raster plot showing the spiking activity of all excitatory neurons as a function of time. Each dot represents a spike by the neuron number indicated along vertical axis at a given time (horizontal axis). An example of synchronized burst is shown in A1. A2: the spiking activity of three neurons (dots on the top) in the network with the intracellular Na⁺ ([Na⁺]_i) (lines). Black, red, and blue color each correspond to one neuron. The inset shows an expanded view of a sample burst by each neuron. The synchronous bursting disappears by fully blocking GABA synaptic currents (B) and gets more prevalent after raising temperature to a physiological value of 35°C (C).

To see if any correlation between the bursting behavior and Na⁺ fluctuations exists in the model, we identified two neurons in the network that show similar pattern of intermittent bursting activity and plot [Na⁺]_i for both neurons (black and red traces in Fig. 9A2) with their firing patterns (black and red dots in Fig. 9A2). Despite having similar bursting behavior, both cells exhibit [Na⁺]_i with different amplitudes. The duration of both events is also different as [Na⁺]_i of the cell indicated by the red line will go above the threshold for the event detection later and drop below sooner. Another example neuron exhibit longer bursts (Fig. 9A2, inset) but [Na⁺]_i peaks with even smaller amplitude and shorter duration (blue line and dots in Fig. 9A2). We also identified neurons with sporadic and synchronized bursting activity but no detectable [Na⁺]_i fluctuations (that is, the change in [Na⁺]_i failed to go above the event detection threshold) and vice versa (not shown). This result shows that although short-lived synchronous bursts can occur on top of long-lived [Na⁺]_i events, they do not control the characteristics of the slow [Na⁺]_i fluctuations. Both can also occur independent of each other.

Blocking GABA synaptic currents, mimicking the effect of bicuculline prevents the synchronous bursting events from occurring (Fig. 9B). Upon closer inspection, we noticed that blocking I-to-E synaptic inputs are more effective in disrupting these events whereas I-to-I connections only play a minor role (not shown). Similarly, blocking E-to-E and E-to-I connections affect these events moderately (not shown). The synchronous activity is also disrupted by partially blocking VGSCs, mimicking the effect of TTX ($G_{Na}^F$ was decreased by 50%, not shown). Decreasing the K⁺ buffering capacity of glia and strength of Na⁺/K⁺-ATPase or increasing the radius of individual cells and ratio of intracellular to extracellular volume (β) do not affect such events significantly (not shown). This points to another difference between the short-lived synchronous bursting activity and long-lived Na⁺ fluctuations where these microenvironmental variables play a significant role.

Next, we test the effect of temperature on the synchronous bursting activity in the model. Note that the model presented in the Computational Methods section is valid at room temperature only. Thus, we incorporate the effect of raising temperature to physiological values by following the approach proposed by Hodgkin and Huxley (43), where the forward and reverse rates for the channels activation and inactivation (α_x, β_x in Computational Methods) and peak conductance of the channels are multiplied by a factor Q₁₀ = a^(T−T0)/10. Here a = 3, T is the temperature that the model is supposed to represent in °C (here T = 35°C), and T0 = 6.3°C. In our formalism, temperature also appears in the Nernst equilibrium potentials (V_K, V_Na, and V_Cl in Computational Methods). Simulating the model after this change shows that the frequency of synchronous bursts increases at physiological temperature (Fig. 9C) and mostly disappear as the temperature drops below the room temperature. Moreover, the Na⁺ fluctuations persist at physiological temperature (not shown).

The Model Predicts That Neonatal Brain Is More Excitable in Response to External Stimuli

Significant evidence shows that the neonatal brain is more excitable in response to external stimuli or insults as compared with adult brain (57–60). For example, the frequency of seizure incidences is highest in the immature human brain (15, 61, 62). Critical periods where the animal brain is prone to seizures have also been well-documented (15). Various epileptogenic agents and conditions, including an increase in [K⁺]_o, result in sigmoid-shaped age dependence of seizure susceptibility in postnatal hippocampus (15, 63–65). The developmental changes in GABAergic function are suspected to play a key role in the change in seizure threshold and the higher incidences of seizures in neonates (16, 66).

To test this hypothesis, we next investigate how excitatory GABAergic neurotransmission affects the excitability of the network in response to different levels of [K⁺]_o. In the model, we take the average frequency of action potential (AP) generation (average number of spikes per minute per neuron) of all excitatory neurons as a measure of the susceptibility of the network to excited states such as seizures. As illustrated in Fig. 10, the overall AP frequency is significantly larger in the network with depolarizing inhibition (representing the neonatal brain) than the network with mature inhibition (representing a mature network). For all [K⁺]_o values tested, the average AP frequency in the neonatal network is doubled that of mature network. Thus, our simulation predicts that depolarizing inhibition strongly increases the excitability of the network, indicating a significantly lower threshold for highly excited states such as seizure in neonates (Fig. 10). Our simulations also show that decreasing the radius of neurons or the K⁺ uptake capacity of astrocytes further increases the vulnerability of neonate brain to highly excited states (not shown).

Figure 10.

Depolarizing inhibition leaves the model network more prone to excited states such as seizures. Bar plot showing the number of spikes per minute averaged over all excitatory neurons as we systematically increase K⁺ concentration in the bath. The black and gray bars correspond to neural network with normal and depolarizing inhibition, respectively. The error bars indicate the standard deviation of the mean. ***P < 0.001.

DISCUSSION

Spontaneous neuronal and astrocytic activity is the hallmark of the developing brain and drives cell differentiation, maturation, and network formation (1–11). In the neonate hippocampus, this activity is mostly attributed to the excitatory effect of GABAergic neurotransmission (13). Although spontaneous activity has also been shown in cortical neuronal networks, these appear to originate primarily from pacemaker cells in the piriform cortex and are driven by a separate mechanism involving both glutamate and GABA (67). In contrast, hippocampal early network oscillations stem solely from GABA released by interneurons. Hippocampal interneurons constitute a diverse group of cells, including the fast-spiking inhibitory neurons simulated in this study. These cells have previously been implicated in the generation of early network activity in the hippocampus and cortex as the timing of their synapse formation around pyramidal cells closely match that of the appearance of giant depolarizing potentials in the neonatal brain. Additionally, the optogenetic blocking of their activity was shown to halt spontaneous giant depolarizing potentials almost entirely (68).

The excitatory effect of GABA on neurons is related to the higher expression of the Na⁺/K⁺/Cl⁻ cotransporter (NKCC) as compared with the K⁺/Cl⁻ cotransporter (KCC) in the first week after birth. This results in elevated intracellular Cl⁻, leading to an outwardly directed Cl⁻ gradient (69–71), and in an efflux of Cl⁻ when GABA_A receptor channels open, causing the postsynaptic neuron to depolarize (18). Notably, and as opposed to neurons, astrocytes do not show a developmental switch to KCC2, but maintain high expression levels of NKCC1 expression into adulthood (72). [Cl⁻]_i thus continues to be relatively high, and the resulting depolarization upon activation of GABA_A receptors can induce opening of voltage-gated Ca²⁺ channels (73, 74). In the hippocampus of mice, GABA_A receptor-mediated astrocytic Ca²⁺ signaling is thus present throughout development (19, 75).

In this study, we report spontaneous, ultraslow fluctuations in the intracellular Na⁺ concentration of CA1 pyramidal neurons and astrocytes in tissue slices from mouse hippocampus, recorded using ratiometric Na⁺ imaging, thereby confirming our recent observations (2). As reported in the latter study, these spontaneous fluctuations are primarily present during the first postnatal week and rapidly diminish afterwards. Unlike the giant depolarizing potentials (GDPs) and early network Ca²⁺ oscillations observed in the hippocampus previously (3, 6, 12), the Na⁺ fluctuations reported here are not synchronous, involve only about a quarter of all pyramidal cells recorded, are not significantly modulated by glutamatergic neurotransmission, and do not occur with regular frequency. Furthermore, these fluctuations are extremely rare (∼2/h), long-lasting (each fluctuation lasting up to several minutes), and strongly attenuated by the application of TTX to block VGSCs and application of inhibitors of GABAergic neurotransmission. A range of other pharmacological blockers targeting various channels, receptors, co-transporters, or transporters did not significantly affect these fluctuations (Fig. 5 and Ref. 18).

To investigate the origin of the spontaneous neuronal Na⁺ fluctuations further, we developed a detailed computational model that represents a hippocampal network, incorporating the three main cell types (pyramidal cells, inhibitory neurons, and astrocytes) and ion concentration dynamics in principal neurons and the extracellular space. In agreement with observations from our experimental data presented here and the earlier experimental study (2), the computational results suggest that voltage-gated Na⁺ channels and the excitatory effect of GABAergic neurotransmission play key roles in the generation of the ultraslow Na⁺ fluctuations. Our simulation results also show that these fluctuations occur at the individual neuronal level, are not phase-locked, and are not strictly a network phenomenon, thereby confirming experimental results. Moreover, the fluctuations are confined to intracellular Na⁺ and are not observed in extracellular K⁺, further supporting the conclusion that these fluctuations are a local phenomenon.

Because synaptogenesis is ongoing during the first postnatal week, synapses across the neuronal network display varying strengths. This means that although activity such as GDPs can happen synchronously across populations, individual synapses will experience different levels of Na⁺ influx in response to action potentials. A neuron with a large number of strong synapses from an interneuron would therefore have a larger influx of Na⁺ (considering the depolarizing inhibition in the neonate brain) than neurons with fewer, weaker connections. The pattern of connectivity and variations in GABA release between several interneurons could therefore explain the unusually long, irregular, asynchronous fluctuations seen in individual neurons here, as they might arise from the summation of inputs. This mechanism is also compatible with the results gained from the dual staining experiments (Fig. 8), which showed no correlation between levels of synchronized Ca²⁺ activity, and the presence or lack of Na⁺ fluctuations in individual cells. These results suggest that the two activity patterns are not present sequentially during development but are rather two different patterns generated in the same population of cells.

In addition to the outwardly directed Cl⁻ gradient and the excitatory action of GABA, the neonate forebrain in the first week after birth is in a constant state of flux where many functional and morphological changes occur along with the differentiation and maturation of cells and the cellular network (6, 12, 14, 20, 76). Two of the most significant changes include the still ongoing gliogenesis and astrocyte maturation (77–79). Immature astrocytes have a reduced glial uptake capacity for K⁺ as well as for glutamate compared with the mature brain (19, 20, 80). Furthermore, the neonate brain exhibits an increased volume fraction of the ECS (46, 47, 81). These factors along with the morphological properties of cells, play key roles in ion concentration dynamics. Indeed, we found the behavior of intracellular Na⁺ fluctuations to be strongly reliant on neuronal radius. However, the larger extra- to intracellular volume ratio appears to suppress Na⁺ fluctuations, suggesting that the larger relative ECS observed in neonates does not play a significant mechanistic role in the generation of spontaneous activity. Our model also suggests that increasing glial K⁺ uptake capacity results in decreasing the amplitude and frequency of Na⁺ fluctuations in the individual neurons and thus may play a role in their suppression at later stages of postnatal development.

Convincing evidence shows that the developing brain is more excitable as compared with adult brain. This is supported by the significantly higher frequency of seizures in the neonatal brain (15, 61, 62). The higher occurrence of seizures is primarily attributed to the excitatory effect of GABA (82). Based on the above analysis, we believe that the inability of astrocytes to effectively take up extracellular K⁺ and morphological changes together with the inverted Cl⁻ gradients leave the developing brain more susceptible to highly excited states such as seizures. As a proof of concept, we exposed our model network to increasing concentrations of K⁺ in the bath solution, similar to experimental protocols used to generate epileptiform activity in brain slices. Indeed, we found that the network representing the neonate brain is unable to cope with the elevated extracellular K⁺ concentration efficiently and exhibits higher excitability as we increase bath K + . Decreasing the radius of neurons or the K⁺ uptake capacity of astrocytes further increases the vulnerability of neonate brain to higher excitability (not shown).

To summarize, our dual experiment-theory approach asserts that the ultraslow, long-lasting, spontaneous intracellular Na⁺ fluctuations observed in neonate brain are nonsynchronous, not coupled with fluctuations in extracellular K⁺, and only occur in a fraction of neurons [and astrocytes, see Fig. 2 (18)]. These fluctuations are most likely due to a combination of factors with the excitatory GABAergic neurotransmission and action potential generation playing dominant roles. In addition, other conditions in the neonate brain such as decreased K⁺ uptake capacity of astrocytes and morphological properties of neurons also play key roles. Furthermore, glutamatergic and other pathways do not seem to make notable contributions to the Na⁺ fluctuations. The combination of factors described above also provides an environment in the neonate brain that is conducive to seizure-like states. Thus, the experimental and computational work presented here provides deep insights into this newly observed phenomenon and its possible link with seizure-like states in the developing brain.

Finally, we remark that our model is a simpler representation of a very complex reality and involves several simplifying assumptions. Specifically, Ca²⁺ signaling in both neurons and astrocytes and neurotransmitter uptake through transporters is not taken into account. Furthermore, gap junctional coupling between astrocytes develops during the first postnatal week (54) and is not explicitly incorporated in the model. Instead, the effect of change in astrocytic coupling is approximated by changing their K⁺ buffering capacity. Neonatal astrocytes differ from mature astrocytes in other significant ways as well. They exhibit a more negative membrane potential as compared with mature astrocytes and express a variety of rectifying K⁺ conductances. In addition to deficient K⁺ homeostatic capacity, the nonlinear interaction between these channels (with expression levels different than mature astrocytes) may result in the function of neonatal astrocytes that is significantly different than their mature counterparts (55, 83). Moreover, strong evidence supports the existence of GABA_A currents in astrocytes that would affect the function of neonatal astrocytes differently than the mature astrocytes (74, 84–86). Additionally, the model only approximates CA1 region, ignoring the CA3-CA1 connectivity and the properties of CA3 neurons, which are crucial for the origination of GDPs and their propagation to CA1 region (8, 56, 87, 88). Thus, in its current form, the model is not equipped to properly investigate the correlation between slow Na⁺ fluctuations and GDPs. Incorporating these key factors in the model and addressing several remaining questions about this exciting topic is the subject of our future research.

GRANTS

This work was supported by NIH through Grant R01AG053988 (G. Ullah), the Deutsche Forschungsgemeinschaft through Grant SPP1757:Ro2327/8-2 (C. R. Rose), and a start-up fund of the SPP1757 (L. Felix).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

C.R.R. and G.U. conceived and designed research; C.P., L.F., and S.D. performed experiments; C.P., L.F., and S.D. analyzed data; C.P., L.F., C.R.R., and G.U. interpreted results of experiments; C.P., L.F., and S.D. prepared figures; C.P. and L.F. drafted manuscript; C.P., L.F., C.R.R., and G.U. edited and revised manuscript; C.P., L.F., C.R.R., and G.U. approved final version of manuscript.