Intraglomerular gap junctions enhance interglomerular synchrony in a sparsely connected olfactory bulb network

Abstract

Key points

• Despite sparse connectivity, population‐level interactions between mitral cells (MCs) and granule cells (GCs) can generate synchronized oscillations in the rodent olfactory bulb.

• Intraglomerular gap junctions between MCs at the same glomerulus can greatly enhance synchronized activity of MCs at different glomeruli.

• The facilitating effect of intraglomerular gap junctions on interglomerular synchrony is through triggering of mutually synchronizing interactions between MCs and GCs.

• Divergent connections between MCs and GCs make minimal direct contribution to synchronous activity.

Abstract

A dominant feature of the olfactory bulb response to odour is fast synchronized oscillations at beta (15–40 Hz) or gamma (40–90 Hz) frequencies, thought to be involved in integration of olfactory signals. Mechanistically, the bulb presents an interesting case study for understanding how beta/gamma oscillations arise. Fast oscillatory synchrony in the activity of output mitral cells (MCs) appears to result from interactions with GABAergic granule cells (GCs), yet the incidence of MC–GC connections is very low, around 4%. Here, we combined computational and experimental approaches to examine how oscillatory synchrony can nevertheless arise, focusing mainly on activity between ‘non‐sister’ MCs affiliated with different glomeruli (interglomerular synchrony). In a sparsely connected model of MCs and GCs, we found first that interglomerular synchrony was generally quite low, but could be increased by a factor of 4 by physiological levels of gap junctional coupling between sister MCs at the same glomerulus. This effect was due to enhanced mutually synchronizing interactions between MC and GC populations. The potent role of gap junctions was confirmed in patch‐clamp recordings in bulb slices from wild‐type and connexin 36‐knockout (KO) mice. KO reduced both beta and gamma local field potential oscillations as well as synchrony of inhibitory signals in pairs of non‐sister MCs. These effects were independent of potential KO actions on network excitation. Divergent synaptic connections did not contribute directly to the vast majority of synchronized signals. Thus, in a sparsely connected network, gap junctions between a small subset of cells can, through population effects, greatly amplify oscillatory synchrony amongst unconnected cells.

Key points

• Despite sparse connectivity, population‐level interactions between mitral cells (MCs) and granule cells (GCs) can generate synchronized oscillations in the rodent olfactory bulb.

• Intraglomerular gap junctions between MCs at the same glomerulus can greatly enhance synchronized activity of MCs at different glomeruli.

• The facilitating effect of intraglomerular gap junctions on interglomerular synchrony is through triggering of mutually synchronizing interactions between MCs and GCs.

• Divergent connections between MCs and GCs make minimal direct contribution to synchronous activity.

Abbreviations

Cx36

connexin‐36

EPL

external plexiform layer

EPSC

excitatory postsynaptic current

GC

granule cell

IPSC

inhibitory postsynaptic current

KO

knock‐out

LFP

local field potential

MC

mitral cell

OSN

olfactory sensory neuron

OR

odorant receptor

TC

tufted cell

WT

wild‐type

Introduction

Fast neural oscillations in the gamma frequency (40–90 Hz; ‘gamma oscillations’) band are a common feature of many brain circuits and thought to be involved in such functions as sensory integration (Gray et al. 1989; Wang, 2010). A major mechanism driving gamma oscillations involves reciprocal synaptic interactions between pools of glutamatergic and GABAergic cells (Wang, 2010; Buzsáki & Wang, 2012). Synchronized oscillations can result from feedback loops wherein activated glutamatergic cells provide correlated inputs onto GABAergic cells, which in turn inhibit the glutamatergic cells; this is followed by synchronized reactivation of glutamatergic cells as they recover from inhibition. The high frequency of the oscillations in part reflects the fast kinetics of the underlying AMPA receptors on GABAergic cells and GABA_A receptors on glutamatergic cells. Excitatory connections amongst the pool of glutamatergic cells may also facilitate the oscillations generated by such feedback loops in some circuits (Fisahn et al. 1998; Traub et al. 2004). Besides gamma oscillations, many brain circuits engage in somewhat slower beta (15–40 Hz) oscillations that may rely on similar interactions between excitatory and inhibitory cells (Kopell et al. 2000; Whittington et al. 2000; David et al. 2015; Kay, 2015).

The mammalian olfactory bulb presents an interesting case study for understanding how specific neural connectivity patterns influence synchronized oscillations. The bulb displays robust odour‐evoked oscillations at both beta and gamma frequencies (Adrian, 1950; Freeman, 1972; Gray & Skinner, 1988) that appear to be at least in part due to excitatory–inhibitory feedback loops involving the output mitral and tufted cells (MC/TCs), and GABAergic granule cells (GCs; Rall & Shepherd, 1968; Friedman & Strowbridge, 2003; Lagier et al. 2004; Schoppa, 2006a,b; Fourcaud‐Trocmé et al. 2014; Fukunaga et al. 2014; Osinski & Kay, 2016). The bulb is also highly ordered, with small groups of 20–25 MCs and ∼50 TCs associated with single odorant receptor (OR)‐specific glomeruli. However, working against the synchronized oscillations is the fact that connections between GCs and at least MCs appear to be quite sparse (Kim et al. 2011). The estimated incidence of connections for nearby MCs and GCs based on pair‐cell recordings is ∼4% (Kato et al. 2013), and this probably drops off steeply with increasing spatial separation (Egger & Urban, 2006). This low incidence of connections probably reflects in part the limited number and branching of MC lateral dendrites (Orona et al. 1984). In addition, connections within MC/TC and GC cell pools are limited. GCs appear to make few if any electrical or inhibitory connections with each other (Schoppa, 2006a,b), while the only connected MC/TCs are sister cells affiliated with the same glomeruli that form connexin 36 (Cx36)‐mediated gap junctions (Schoppa & Westbrook, 2002; Christie et al. 2005; Pimentel & Margrie, 2008; Maher et al. 2009). Because a circuit's engagement in rapid oscillations depends on connection rate (Wang, 2010), these connectivity features raise questions about how fast synchronized oscillations develop in the bulb, especially for unconnected, non‐sister MCs affiliated with different glomeruli (Kashiwadani et al. 1999; Schoppa, 2006a). Functionally, such ‘interglomerular’ synchrony may be critical for odour perception, as it could facilitate downstream integration of information about different odour‐activated ORs (Mori et al. 1999; Brody & Hopfield, 2003).

Here, we assessed the role that neural connectivity has in shaping fast synchronized activity amongst non‐sister MCs affiliated with different glomeruli in the bulb. We propose and will test the hypothesis that the potent intraglomerular gap junctions between sister MCs at one glomerulus dramatically enhance interglomerular synchrony through population effects. Computational studies of a sparsely connected MC–GC network were first used to explore the plausibility of this hypothesis. We then tested in rodent bulb slices whether eliminating intraglomerular gap junctions in Cx36 knock‐out (KO) mice decreased synchronized activity, using local field potential (LFP) measurements and whole‐cell patch‐clamp recordings in pairs of MCs. In addition, we explored the extent to which interglomerular synchrony reflected direct divergent connections between MCs and GCs, as an alternative to a population‐level mechanism.

Methods

Ethical approval

All experiments were approved by the Institutional Animal Care and Use Committee at the University of Colorado Anschutz Medical Campus. The authors understand the ethical principles under which The Journal of Physiology operates and our work complies with The Journal’s animal ethics checklist.

General computational methods and cellular parameters

For all simulations, we used NEURON, version 7.1 (Hines & Carnevale, 1997). The computational model is available from the SenseLab ModelDB database at http://senselab.med.yale.edu (Hines et al. 2004). Simulations were run on a multiprocessing cluster of the Department of Pharmacology at the University of Colorado Anschutz Medical Campus.

Our network model comprised two glomeruli, each with 10 associated MCs, along with a population of GCs contacting the lateral dendrites of the MCs, 30 GCs per dendritic section (Fig. 1 A). All cells were placed along a single horizontal axis, which represented the physical separation of the two glomeruli and the location of the dendrodendritic synapses along the MC lateral dendrite. The 10 MCs associated with each glomerulus shared the same horizontal location. In the modelling of connections between MCs and GCs, a maximal incidence of connections was set to be such that any one GC connected with at most 4 of the 20 MCs (4 MCs per GC) with a single synapse. Similar results were obtained if the peak GC‐to‐MC connection rate was varied between 3 and 5 MCs per GC. To account for the geometry of MC lateral dendrites in the external plexiform layer (EPL), we also subjected the incidence of GC–MC connections to a decaying exponential probability with distance between the MC and GC cell bodies (Fig. 1 B), given by:

$$P_{\mathrm{c}}(d)=P_{\mathrm{c}}(0){\mathrm{e}}^{-d/{\delta }_{\mathrm{f}}}$$ (1)

where P _c(d) reflected the connection probability between a MC and GC with cell bodies separated by a distance d, P _c(0) was the connection probability for no separation, and δ_f was the distance at which the connection probability fell by ∼63%. The value for δ_f = 288 μm that we used approximated the analysis of Egger & Urban (2006). That study described the fall‐off of the rate at which one GC contacted two MCs, which we translated here for the rate at which one GC contacted one MC. All GC‐to‐MC connections were reciprocal, meaning that MCs also excited GCs, and GCs did not form any direct connections with each other.

Figure 1. Non‐sister MCs are weakly synchronized in a sparsely connected GC–MC network that lacks intraglomerular gap junctions.

A, basic model and simulation design. All network models consisted of two glomeruli (Glom A, red; Glom B, blue), each with 10 associated MCs. GCs, 30 per dendritic section, were distributed along the lengths of the MC lateral dendrites. Simulations were performed with the two glomeruli separated by a distance D _GlomA‐B between 0 μm (line 0 at top) and 720 μm. The lateral dendrites of MCs are illustrated much simplified in terms of the number of sections used in the computations. B, GC‐to‐MC connection probability was subjected to an exponentially decaying fall‐off as a function of distance between GC and MC cell bodies (see Methods). Illustrated is the situation for two glomeruli separated by 360 μm. Each trace (red or blue) represents the relative connection probability of a GC to MCs affiliated with one glomerulus as it changes its position with respect to the MC somata. C, example simulated membrane voltage traces (spikes truncated) from a model with no intraglomerular gap junctions. Traces reflect two example MCs and a GC. Horizontal lines at left indicate –65 mV. D and E, time course of synchronized activity amongst MCs affiliated with the same glomerulus (D) or between the two glomeruli (E) for D _GlomA‐B = 72 μm. As calculated (see Methods), the traces indicate synchronized activity within a 5 ms window. F and G, relationship between average synchrony in MCs between the two glomeruli, S _GlomA‐B, versus D _GlomA‐B for the MC–GC model lacking intraglomerular gap junctions (F). Simulations with no GC‐to‐MC connections (G). The white curves in F reflect exactly chance‐level (S _GlomA‐B = 1.0) of observing spikes in the MCs that occur with the specified lag time, assuming random spiking.

For modelling the morphology, passive membrane properties, and active conductances of each MC in the model, we used Davison's NEURON‐translated, non‐reduced version of Bhalla and Bower's 286‐compartment MC (Bhalla & Bower, 1993; Davison et al. 2000). For each GC, we used Davison's four‐compartment version of Bhalla and Bower's GC (Davison et al. 2003). Most compartments of the MC lateral dendrite were 80 μm in length, with a few sections being 40 μm, with a mean length of 72 μm. The total length of each lateral dendrite, divided into 23 sections, was 1650 μm. Neurotransmitter‐mediated currents at MC–GC synapses were modelled as double‐exponentials with rise and decay time constants (τ) and conductance values that were mainly based on published experimental measurements (Schoppa, 2006a,b): AMPA receptors at MC‐to‐GC synapses (τ_rise = 0.6 ms; τ_decay = 3 ms; maximal conductance = 0.5 nS); NMDA receptors at MC‐to‐GC synapses (τ_rise = 2 ms; τ_decay = 20 ms; maximal conductance = 0.05 nS); GC‐to‐MC inhibition (τ_rise = 0.8 ms; τ_decay = 4 ms; maximal conductance = 1.6 nS). Activation of a synapse (MC‐to‐GC or GC‐to‐MC) occurred when the presynaptic cell fired an action potential plus a synaptic delay of 0.6–1.8 ms. To drive all models, we applied a noisy stimulating current (2 s duration) at the distal end of the MCs’ apical dendrites. Noise in the input was added by toggling the injected current on or off randomly every 0.1–5 ms. The amplitude of the current when ‘on’ was 1 nA, making the cells fire around the in vivo spiking rate of 20 Hz (Doucette & Restrepo, 2008). This noise decorrelated signals in an unconnected network. For each condition, simulations were repeated 10 times with different random seeds.

In those simulations that included gap junctions, we applied the method of Migliore and co‐workers (2005) to couple the primary dendrites of sister MCs. All MCs at one glomerulus were coupled to each other (Pimentel & Margrie, 2008) with a gap junction conductance (0.85 nS) that was sufficient to reproduce mean observed coupling ratios between same‐glomerulus MCs (∼4%; Schoppa & Westbrook, 2002). It is notable that, in our model, intraglomerular gap junctions synchronized same‐glomerulus MCs through direct electrical coupling of spikes (often termed a ‘spikelet’). This contrasts with a mechanism proposed previously that involves electrical coupling of an AMPA receptor‐mediated depolarization (Schoppa & Westbrook, 2002; Christie et al. 2005). The issue of how exactly intraglomerular spike coupling originates, however, has remained controversial (Migliore et al. 2005; Pimentel & Margrie, 2008), and so we reasoned that a simplified intraglomerular synchronizing mechanism was sufficient.

Quantification of synchrony in the model output

To examine the time course of synchronized activity in the MC output from the model, we developed a metric for each of the two glomeruli (Glom A and Glom B) that reflected the number of synchronized spikes occurring within 5 ms across the 10 associated sister MCs (Figs 1 D and 3 B). This intraglomerular synchrony function was computed by convolving the spike response of each MC of a glomerulus with a 5 ms rectangular function, quantized to 0.1 ms, then summing across all MCs for that glomerulus. A second measure that reflected the time course of synchronized activity between the two glomeruli was derived from the product of the two within‐glomerulus functions, scaled by the mean values of the metric for each glomerulus (Figs 1 E and 3 D). A similar procedure was used to quantify the time course of synchronous activity between GCs that were most proximal to the two glomeruli (Figs 2 B and C, and 3 C and D). Correlations in the degree to which MCs and GCs across glomeruli were synchronized (Figs 2 E and 3 H) were determined by analysing the product functions that reflected synchrony between glomeruli on an oscillation cycle‐by‐cycle basis. For constructing the correlation plots, we compared the peak‐to‐trough amplitudes of each oscillation in the product function for MCs with the corresponding oscillation in GCs. To account for the fact that the oscillations in MCs and GCs were offset in time, each MC oscillation peak was paired to the closest corresponding peak in GCs occurring within 40 ms.

Figure 3. Gap junctions between sister MCs augment interglomerular synchrony in a two‐glomerulus network.

Aa, schematic diagram illustrating mutual synchronization in a sparsely connected network of MCs and GCs. Left, synchronized populations of MCs at different glomeruli (A and B) provide coordinated inputs into a population of GCs. Right, GCs synchronized by these inputs in turn provide coordinated inputs into MCs, thereby causing their synchrony. The illustrated networks are much simplified, with only 4 MCs per glomerulus. Cross‐talk between glomeruli is introduced by the GC in the second row that is excited by M_A2 and inhibits M_B1. Ab, all‐to‐all gap junctions (GJs) between MCs at each glomerulus (Pimentel & Margrie, 2008) provide an independent mechanism to synchronize sister MCs. This could help trigger the mutually synchronizing MC–GC interactions shown in Aa. B–D, time course of synchronized activity for a model with a glomerular separation of 72 μm that included intraglomerular gap junctions. Illustrated traces reflect synchrony time courses for MCs affiliated with the same glomerulus (B), GCs proximal to the same glomerulus (C), and MCs and GCs affiliated with different glomeruli (D). Note the large increase in synchronization both within and between glomeruli, as compared to the situation without gap junctions (see Figs 1 D and E, and 2 B and C). E, relationship between the average synchrony in MCs between the two glomeruli, S _GlomA‐B, and distance between glomeruli for the model with gap junctions. White curves reflect chance‐level of synchrony (S _GlomA‐B = 1.0). F, comparison of S _GlomA‐B values for lag = 0 ms in a model with (grey trace) and without (blue trace) intraglomerular gap junctions. Except for gap junctions, all other parameters in the two models were identical. G, relationship between the average degree of synchrony in GCs across the two glomeruli and the distance between glomeruli for the model with gap junctions. H, synchronized activity across glomeruli was correlated between MCs and GCs in the model with gap junctions. Line reflects fit to linear regression with correlation coefficient = 0.65.

Figure 2. Synchronized activity in GCs in a sparsely connected MC–GC network with no intraglomerular gap junctions.

A, schematic diagram of analysis. Synchrony between GCs was assessed for the subset of 30 GCs that made connections most proximal to the cell bodies of the MCs at each of the two glomeruli. B and C, time course of synchronized activity, both amongst GCs proximal to the same glomerulus (B) or between the two glomeruli (C; green trace). In C, the between‐glomeruli synchrony function for GCs is shown overlaid with the same function for MCs (purple trace; same as in Fig. 1 E) to allow comparison of the two cell types. The presence of rapid synchronized oscillations that alternate in time between MCs and GCs indicates that synchrony was due to fast reciprocal synaptic interactions between the two cell types. D, relationship between the average synchrony in GCs across the two glomeruli, S _GlomA‐B, and distance between glomeruli. White curves reflect chance‐level of GC synchrony (S _GlomA‐B = 1.0). E, scatter‐plot relating the amplitude of the individual MC and GC oscillations (as in C) indicates that synchronized activity was highly correlated between MCs and GCs. Line reflects fit to linear regression with correlation coefficient = 0.58. Pairing of the GC and MC peaks in the analysis was based on co‐occurrences within 40 ms.

To quantify the degree of synchrony between the two glomerular populations of MCs (S _GlomA‐B) across the entire time course of the simulation (Figs 1 F and 3 E), we first measured synchrony between every pair‐wise combination of MCs (one at each glomerulus) by comparing the number of coincident spikes of two trains within a 5 ms interval to the number of coincident spikes expected by chance if a homogeneous Poisson process generated the spikes. This score S _MC‐MC was:

$$S_{\mathrm{MC}-\mathrm{MC}}=N_{\mathrm{coinc}}/2\nu \mathrm{\Delta }{N}_{\mathrm{spikes},\mathrm{ref}}$$ (2)

where N _coinc was the actual number of coincident spikes between the two trains that occurred within a time window of Δ = 5 ms, ν was the spike frequency of the comparing train, and N _spikes,ref was the total number of spikes in the reference train. S _GlomA‐B reflected the mean value of S _MC‐MC for all pair‐wise comparisons. A similar procedure was used to quantify mean synchronous activity between GCs that were proximal to each glomerulus (Figs 2 D and 3 G).

Electrophysiological recordings

Electrophysiological recordings were made in horizontal olfactory bulb slices (300–350 μm in thickness) obtained from wild‐type (WT) or Cx36 KO mice (Cx36^–/–; C57/B6‐129SvEv mixed background; Deans et al. 2001) at postnatal age 14–31 days or Sprague–Dawley rats at postnatal age 9–14 days, of both sexes. Wild‐type controls for the KO experiments included Cx36^+/+ littermates as well as unrelated C57/B6‐129SvEv mice. Cx36 KO mice were generously provided by Dr David Paul (Harvard University). Unrelated C57/B6‐129SvEv wild‐type mice as well as wild‐type Sprague–Dawley rats were obtained from Charles River Laboratories (Wilmington, MA, USA). While housed in the University of Colorado Anschutz Medical Campus animal facility, animals had full and continuous access to food and water. The preparation of bulb slices and genotyping of Cx36 KO mice were as previously described (Schoppa et al. 1998; Gire et al. 2012). In slice preparation, animals were anaesthetized by inhalation of isoflurane prior to decapitation. Slices were viewed under differential interference contrast optics at ×40 magnification (Axioskop; Carl Zeiss, Thornwood, NY, USA). Brain slices were prepared from 60 rodents across all experiments. Slice recordings were performed at 28–33°C. In a subset of recordings (in Fig. 10), slices underwent further sectioning to remove olfactory cortical areas.

Figure 10. LFP oscillations in slices with and without olfactory cortex.

A, traces of LFPs recorded in the EPL during theta frequency OSN stimulation in rat bulb slices with (top) and without (bottom) olfactory cortex. For each recording, 3 consecutive sweeps are displayed reflecting 175 ms periods following the first burst in the theta stimulus. Displayed data were band‐pass filtered at 10–1000 Hz or 10–100 Hz (overlaid, smoother traces). B, unfiltered LFPs in the glomerular layer (single sweeps) recorded in the same experiments as in A, from slices with (left) and without (right) olfactory cortex. Responses to the entire theta stimulus (four stimulus bursts) are shown. C, power spectra derived from the EPL LFP recordings in A from slices with (left) and without (right) olfactory cortex. Traces reflect spectra from LFPs recorded during 175 ms periods after each of the four stimulus bursts. D, integrated power (30–55 Hz) in the EPL LFP plotted against the magnitude of the glomerular layer LFP recorded in the same experiment. Data from slices with (black symbols) and without (grey symbols) olfactory cortex are superimposed (4 recordings each).

The base extracellular solution for all recordings contained (in mm) 125 NaCl, 25 NaHCO₃, 1.25 NaH₂PO₄, 25 glucose, 3 KCl, 2–3 CaCl₂, and 0.5–1 MgCl₂ (pH 7.3), and was oxygenated (95% O₂, 5% CO₂). For recordings of local field potentials (LFPs), a glass patch‐pipette recording electrode filled with extracellular solution (resistance 5–7 MΩ) was placed in the EPL, within 50 μm of the mitral cell layer. For whole‐cell patch measurements of IPSCs in MCs, identified cells in the MC layer were patched with pipettes (4–8 MΩ) that contained a solution composed of 125 potassium gluconate, 2 MgCl₂, 0.025 CaCl₂, 1 EGTA, 2 NaATP, 0.5 NaGTP, 10 Hepes, along with Alexa‐488 (50–100 μm) to allow the visualization of MC dendritic processes. An identical pipette solution was used in whole‐cell recordings from GCs. All LFP and whole‐cell recordings were made with a Multi‐Clamp 700B dual patch‐clamp amplifier (Molecular Devices, Sunnyvale, CA, USA) and were low‐pass filtered at 1–2 kHz using an eight‐ pole Bessel filter and digitized at 10–15 kHz. Data were acquired using Axograph X software on a Macintosh G5. Recordings with a series resistance larger than 20 MΩ were discarded. Epifluorescence was captured by an Axiocam HSm (Zeiss) camera; images were acquired using AxioVision software. Reported holding potential (V _hold) values for voltage‐clamp experiments were corrected for liquid junction potentials.

For electrical stimulation of olfactory sensory neuron (OSN) axons, a patch pipette (0.5 MΩ) containing the extracellular solution was placed in the olfactory nerve (ON) layer. The OSN stimulus, triggered by a biphasic stimulus isolation unit (BSI‐950; Dagan, Minneapolis, MN, USA), was applied as a pattern (25–500 μA intensity) consisting of four short bursts (three 0.1 ms pulses separated by 10 ms) each in turn separated by 250 ms (4 Hz). Each 4 Hz (‘theta’) stimulus pattern was applied once every 20 s. In experiments testing for the role of divergent connections between MCs and GCs (Figs 7 and 8), cell activity was induced by application of potassium (K⁺), either via the bath in recordings in MC pairs or via puff‐application near the MC layer with a picospritzer (Parker Hannifin Corp., Cleveland, OH, USA; 200–500 ms pulses) for most GC pair recordings. Puff‐application of K⁺ for the GC recordings was typically required as we found that bath‐applied K⁺ was generally ineffective in inducing high frequency barrages of excitatory postsynaptic currents (EPSCs). In experiments involving K⁺ puffs, a high concentration (1 m) was used; however, the puffer pipettes were placed 200–450 μm away from the test cells and facing the perfusion flow such that the local K⁺ concentration was likely to be much lower. For the analysis of EPSCs in response to puffs, 5–19 puffs were applied. The responses to OSN stimulation in rat bulb slices to which the K⁺‐evoked responses were compared were presented in previous articles (Schoppa, 2006a,b), but the results were analysed differently here.

Figure 7. Synchronized IPSCs in non‐sister MCs do not reflect divergent connections from single GCs.

A–C, divergent GC‐to‐MC connections (diagram in A) were tested by recording from two MCs in the presence of glutamate receptor antagonists (NBQX and dl‐AP5) in rat olfactory bulb slices. A high‐K⁺ (23 mm) solution drove an increase in IPSC frequency in a MC (B) and spikes in a GC (current‐clamp recording in C), indicating effective stimulation. Delays in B and C were due to the fact that K⁺ was bath applied. D, analysis of K⁺‐evoked IPSCs (at V _hold = –52 mV) in a pair of MCs (same as in B). Illustrated are sample traces (left), an image of the dye‐filled MCs (middle; Alexa‐488, 100 μm), and histogram of IPSC time lags (right). Scale bar = 50 μm. E, summary plot of synchronization indices for K⁺‐evoked IPSCs as a function of IPSC frequency (n = 18 MCs from 9 pairs). The low level of IPSC coupling in these experiments is consistent with a lack of divergent GC‐to‐MC connections. Circles and squares reflect IPSC recordings conducted, respectively, at depolarized (≥–62 mV; outward currents) or hyperpolarized (V _hold = –107 mV; inward currents) holding potentials. F, left, summary plot of synchronization indices as a function of IPSC frequency for IPSCs evoked by theta frequency stimulation of OSNs in rat bulb slices (n = 28 MCs from 14 pairs; same raw data as in Schoppa, 2006a). All recordings were conducted at hyperpolarized holding potentials (V _hold ≤ –107 mV). F, right, example IPSC time‐lag distribution that contributed to the summary plot. Overlaid is a fitted Gaussian with SD = 0.70 ms.

Figure 8. Synchronized EPSCs in GCs do not reflect divergent connections from single MCs.

A–C, divergent MC‐to‐GC connections (diagram in A) were tested by recording from two GCs in the presence of a GABA_A receptor blocker (gabazine). Puff application of K⁺ (1 m, 200–450 μm away from the test cells) resulted in a transient increase in the frequency of EPSCs in a GC (B) and action potentials (APs) in a MC (C). EPSC/AP plots reflect mean (±SEM) frequency values over multiple puffs (41 for MC, 6 for GC) that were normalized to the peak values observed with each puff. D, analysis of K⁺‐evoked EPSCs (at V _hold = –82 mV) in a pair of GCs. Illustrated are sample traces (left) and a histogram of EPSC time lags (right). E, summary plot of synchronizations indices (S _EPSC,GC) for K⁺‐evoked EPSCs in GCs as a function of EPSC frequency. Data reflect 5 GC pairs in which K⁺ was puff applied (squares) and 2 pairs in which K⁺ (18–23 mm) was bath applied (diamonds). F, left, summary plot of EPSC synchronization indices as a function of EPSC frequency for EPSCs evoked by theta frequency stimulation of OSNs in rat bulb slices (n = 22 GCs from 11 pairs; same raw data as in Schoppa, 2006b). F, right, example EPSC time‐lag distribution that contributed to the summary plot.

Analysis of electrophysiological recordings

For all LFP responses to theta stimulus patterns (Figs 4 and 10), 175 ms segments were analysed following the stimulus bursts. EPL LFP data were band‐pass filtered between 10 and 100 Hz, 10 and 1000 Hz, or 0.3 and 1 kHz with a 4th‐order Butterworth filter prior to construction of power spectra. Traces and power spectra were notch‐filtered between 59.9 and 60.1 Hz to remove 60 Hz line noise. Power spectra reflected 10–20 response trials.

Figure 4. Synchronized LFP oscillations are reduced in connexin 36 knockout (Cx36 KO) mice.

A, experimental protocol: two electrodes were placed in mouse olfactory bulb slices to record beta/gamma LFP oscillations in the external plexiform layer (EPL) and an LFP in an adjacent glomerulus (Glom). Responses were to theta frequency stimulation of OSN axons (four stimulus bursts; not shown). MCL = mitral cell layer; GCL = granule cell layer. B, unfiltered LFPs (single sweeps) recorded in glomeruli adjacent to the EPL recording sites in C. Responses to the entire theta stimulus are shown. C, LFPs (top/black: WT mice; bottom/blue: Cx36 KO mice) recorded in the EPL in the same experiment as B. For each recording, 3 consecutive sweeps are displayed reflecting 175 ms periods following the first burst in the theta stimulus. Displayed data were band‐pass filtered at 10–1000 Hz or 10–100 Hz (overlaid, smoother traces). D, same raw data as in C but filtered at 0.3–1 kHz. E, main panel: power spectra derived from the EPL LFP recordings in C for WT (black) and Cx36 KO (blue) mice. Thicker traces reflect the average spectra from LFPs recorded during 175 ms epochs after each of four stimulus bursts; thinner traces reflect analysis of a 175 ms control period just preceding the first stimulus burst. Inset: mean integrated beta/gamma (23–57 Hz) power measured following each of four stimulus bursts in the theta stimulus for all experiments (WT, n = 36; Cx36 KO, n = 42). F, average power spectra (±SEM) derived from EPL LFP recordings in which the simultaneously recorded glomerular LFP was ≥0.3 mV (WT, n = 16; Cx36 KO, n = 15). The grey trace reflects subtraction of the KO trace (blue) from the WT trace (black). G, integrated power (23–57 Hz) in the EPL LFP plotted against the glomerular LFP recorded in the same experiment. Lines reflect fits to linear regression of the WT (slope = 0.095) and Cx36KO (slope = 0.037) data. Data values (WT, n = 36; Cx36 KO, n = 42) reflect means of 175 ms epochs following each of the 4 stimulus bursts.

We tested whether IPSCs were synchronized in each MC pair (Figs 5 and 7) by running an event detection algorithm (in Axograph X) that detected IPSCs and then constructing histograms (1 ms bins) reflecting the distribution of time lags between the IPSCs in the two MCs. The event detection was run twice for each pair, using each of the MCs as the reference cell, yielding two histograms per pair. The two histograms were near mirror‐images of each other; some minor differences resulted from the fact that the IPSC event detection was performed in finite 175 time windows, as well as differences in IPSC frequency. From the histograms, a number of values were extracted. First, an IPSC synchronization index associated with each reference MC (S _IPSC,MC) was computed using:

$$\begin{array}{c}\hfill S_{\mathrm{IPSC},\mathrm{MC}}=(\mathrm{Coun}{\mathrm{t}}_{\le 1.5\mathrm{ms}}-\mathrm{Coun}{\mathrm{t}}_{\mathrm{mean},>1.5\mathrm{ms}})/N_{\mathrm{IPSC}}\end{array}$$ (3)

where Count_≤1.5 was the number of time lags that were in a 3 ms window centred at zero lag, Count_{mean,>1.5 ms} was the mean number of time lags in other 3 ms windows in the histogram, and N _IPSC was the number of IPSCs in the reference MC. A specific S _IPSC,MC value (expressed as a percentage in the text and figures) thus reflected the fraction of IPSCs in a reference MC above chance that had an IPSC in the other MC within 1.5 ms. A synchronization index for each pair of MCs, S _IPSC,pair, was also computed from the mean of the two S _IPSC,MC values for the pair. S _IPSC,pair values were used for statistical comparisons. Similar methods were used to determine EPSC synchronization indices (S _EPSC,GC and S _EPSC,pair) from recordings of EPSCs in GC pairs (Fig. 8). It is notable that values for S _IPSC,MC tended to be small, even for histograms with obvious peaks. This in part reflected the narrowness of the peaks in the histograms together with the fact that the peaks were often slightly offset from zero lag; thus the 3 ms window centred at zero typically included histogram bins that were not part of the peak.

Figure 5. Cx36 KO reduces synchrony of IPSCs in pairs of MCs affiliated with different glomeruli.

A, analysis of IPSCs evoked by theta frequency stimulation of OSNs in a pair of MCs from WT mice. Illustrated are 175 ms periods of sample current traces (left; V _hold = –57 mV; grey and black reflect the two MCs), examples of IPSCs that appeared to be synchronized (arrows at left; enlarged in middle), and a histogram reflecting the time lags between IPSCs in the same two MCs (right). Overlaying the histogram is a fit with a four‐parameter Gaussian function that yielded a standard deviation (SD) value of 1.0 ms. B, histogram as in A but for a different MC pair recording. For this histogram, the baseline used for the fitted Gaussian (SD = 1.0 ms) was determined from troughs adjacent to the peak. C, analysis of IPSCs in a pair of MCs from Cx36 KO mice. Illustrated are sample traces (left), an image of the dye‐filled MCs (middle; Alexa‐488, 100 μm), and a histogram of IPSC time lags (right). In the image, the glomeruli to which the MCs sent their apical dendrites are demarcated. Scale bar = 50 μm. Horizontal line in histogram reflects mean of all count values. D, standard deviation (SD) values derived from Gaussian fits of IPSC time‐lag distributions plotted as a function of the lag value at which the peak was observed. Data reflect 6 MC pairs from WT mice with the largest peaks (s/n _IPSC >2.5); each pair produced two data points (same symbols) reflecting the fact that distributions were determined using each MC in the pair as the reference MC. The SD values and the absolute values of the peak position for each pair were similar but not identical. E, IPSC synchronization index (S _IPSC,MC) plotted as a function of IPSC frequency for WT (left; 12 MC pair recordings) and Cx36 KO (right; 9 MC pair recordings) mice. Each MC pair recording had two associated S _IPSC,MC values. This reflected the fact that the analysis was run twice, using each MC as the reference cell. The two largest S _IPSC,MC values are from the same MC pair; one of the values corresponds to the histogram in B. E, box‐plots summarizing IPSC synchronization indices (S _IPSC,pair) for MC pairs from WT and Cx36 KO mice. S _IPSC,pair was the mean of the two S _IPSC,MC values for each pair. ^* P = 0.013, Mann–Whitney test. G, values for the signal‐to‐noise ratio, s/n _IPSC,MC, calculated by dividing the peak in each IPSC time‐lag distribution to the standard deviation of the integrated counts in off‐peak bins. Data reflect same experiments as E. H, box plots summarizing signal‐to‐noise ratios, s/n _IPSC,pair, for each pair (mean of the two s/n _IPSC,MC values). ^* P < 0.01, Mann–Whitney test.

In some of the comparisons of IPSCs in MC pairs, additional indices reflecting the signal‐to‐noise (s/n _IPSC,MC and s/n _IPSC,pair) were computed from the IPSC time‐lag distributions, where:

$$\begin{array}{ccc}\hfill s/n_{\mathrm{IPSC},\mathrm{MC}}& =& (\mathrm{Coun}{\mathrm{t}}_{\le 1.5\mathrm{ms}}-\mathrm{Coun}{\mathrm{t}}_{\mathrm{mean},>1.5\mathrm{ms}})/\hfill \\ & & {\sigma }_{>10\mathrm{ms}}.\hfill \end{array}$$ (4)

In this expression σ_>10 ms was the standard deviation of the number of events in all 3 ms windows in a histogram that were centred at time lags ≥11 ms (a value chosen to avoid inclusion of troughs that sometimes appeared adjacent to peaks in the histograms; see Fig. 5 B). A threshold of s/n _IPSC,pair >2.5 was used to determine whether a MC pair had significant IPSC synchronization. Assuming that the noise was normally distributed, this threshold value corresponded to a ∼99% probability that a peak near zero in the IPSC time‐lag distribution did not simply reflect noise.

From WT histograms with clear peaks near zero (those with s/n _IPSC,pair >2.5), we also calculated the probability above chance of observing synchronized IPSCs at the level represented by the bin with the largest time‐lag counts.

Statistics

Data are reported as mean ± standard error of the mean (SEM) or, for non‐normally distributed data, as median with interquartile range (IQR; values at 25% and 75% of the distribution of ranked values). Statistical tests, as indicated for each experiment in the Results section, included: Student's t test for normally distributed data (two‐tailed with equal or unequal variance, as appropriate); one‐way ANCOVA; Mann–Whitney or Kolmogorov–Smirnov tests (two‐tailed) for non‐normally distributed data. Statistical analyses were performed in Microsoft Office Excel.

Results

Computational modelling of the impact of intraglomerular gap junctions on interglomerular synchrony

We first assessed computationally (in NEURON; Hines & Carnevale, 1997) whether intraglomerular gap junctions between MCs at the same glomerulus can augment synchronous activity amongst non‐sister MCs at different glomeruli. Our model (Fig. 1 A and B; see Methods for details) consisted of two glomeruli (Glom A and Glom B) of varying separation (up to 720 μm), each with 10 associated MCs (20 MCs total), and a large population of granule cells (GCs; minimum number = 1380) distributed along the MCs’ lateral dendrites. Sparseness in the connections (Kim et al. 2011; Kato et al. 2013) in our standard model was introduced by having each GC make a single reciprocal synapse with, at most, four of the 20 MCs (connection incidence ≤ 0.2). Also, the incidence of GC–MC connection decayed sharply with distance between the MC and GC cell bodies (Egger & Urban, 2006). The morphology and intrinsic properties of individual MCs and GCs were modelled as before (Bhalla & Bower, 1993; Davison et al. 2000), while kinetic and conductance parameters for the MC‐to‐GC glutamatergic and GC‐to‐MC GABAergic synapses were based mainly on published experimental measurements made while stimulating olfactory sensory neurons (OSNs) with a theta frequency pattern that mimicked the breathing cycle (Schoppa, 2006a,b). A noisy excitatory current (2 s duration) was applied at the distal end of the MCs’ apical dendrites as an input. Our model of the bulb included only MCs and GCs and not other cells in the bulb, as available data suggest that interactions between MCs and GCs mainly control fast oscillatory activity (Rall & Shepherd, 1968; Lagier et al. 2004; Schoppa, 2006a,b; Fukunaga et al. 2014).

We initially considered the ability of the model to produce oscillatory synchrony in MC spiking in simulated voltage traces (Fig. 1 C) in the absence of intraglomerular gap junctions. To evaluate the general form of synchrony across time, synchronized spike activity across all MCs at one glomerulus was first determined from the number out of the 10 sister MCs that were spiking within 5 ms of each other; interglomerular synchrony was reflected in the scaled product of these functions for the two glomeruli. Five milliseconds was chosen as the window to evaluate synchrony based on the synaptic integration times of downstream pyramidal cells in the piriform cortex (Luna & Schoppa, 2008). When glomeruli were separated by the minimal distance (72 μm), the measures for both intra‐ and interglomerular synchrony (Fig. 1 D and E) displayed clear, repeated peaks and troughs, indicative of oscillatory synchrony in spiking. The ∼50 ms separation between peaks indicated oscillations at ∼20 Hz, within the beta frequency range (see Discussion). To quantify synchrony between two glomeruli across the entire 2 s simulation, we computed a parameter S _GlomA‐B that reflected the mean probability above chance (where for chance S _GlomA‐B = 1) that any two MCs affiliated with separate glomeruli (Glom A and B) spiked within a 5 ms window. The oscillatory behaviour in interglomerular synchrony was moreover quantified by calculating the S _GlomA‐B parameter in simulated trace‐pairs that were time‐shifted by varying lags. As can be seen in the heat‐map (Fig. 1 F) and summary plot (see Fig. 3 F), S _GlomA‐B had a value of ∼1.2 in unshifted simulated traces (corresponding to lag = 0 ms), meaning that there were ∼20% more synchronized spikes than would be expected by chance. This parameter did not vary substantially with distance between the glomeruli (D _GlomA‐B) up to ∼300 μm. The synchronous activity was also clearly oscillatory, based on the fact that S _GlomA‐B achieved values less than one when the simulated traces were time‐shifted by 20–30 ms (Fig. 1 F). The synchronized activity was abolished when GC–MC connections were removed (Fig. 1 G), indicating that the activity was not due to properties of the input into the model.

To examine whether the synchronized oscillatory activity generated by our model reflected rapid reciprocal interactions between MCs and GCs, we expanded our analysis to GCs in our model, specifically focusing on the 30 GCs that provided inputs most proximal to the MC cell bodies at the two glomeruli (Fig. 2 A). Because of passive dendritic filtering, the GABAergic inputs from these GCs were the most likely to impact MC spiking. Using an analysis of spiking for these ‘proximal’ GCs similar to that performed for the two glomerular networks of MCs (Fig. 1 D–F), we found that GCs, like MCs, displayed significant synchronized oscillations (Fig. 2 B–D). Also, the synchronized activity in MCs and GCs associated with different glomeruli (Fig. 2 C) alternated in time, as expected if each oscillation cycle reflected rapid reciprocal interactions between the two cell types. Notably, we also found that synchrony levels between MCs and GCs were well correlated on an oscillation cycle‐by‐cycle basis (Fig. 2 E; correlation coefficient = 0.58, P < 10⁻³⁴). Such a correlation would be consistent with the MC and GC pools in our model engaging in mutually synchronizing interactions with each other, i.e. a situation in which MCs were being synchronized by a pool of synchronized GCs, while GCs were being synchronized by the pool of synchronized MCs (diagram in Fig. 3 Aa).

These results suggest that a sparsely connected network of MCs and GCs in the absence of intraglomerular gap junctions can produce synchrony for nearby glomeruli through mutually synchronizing interactions, although the level of synchronized activity was modest. We next added intraglomerular gap junctions to the model (Fig. 3 Ab) by interconnecting all MCs at each glomerulus (Pimentel & Margrie, 2008) with a gap junction conductance (0.85 nS) that was sufficient to reproduce mean observed electrical coupling ratios between same‐glomerulus MCs (∼4%; Schoppa & Westbrook, 2002). We reasoned that intraglomerular gap junctions could enhance interglomerular synchrony by helping the circuit overcome a problem inherent in a mechanism involving mutually synchronizing interactions: if MCs are synchronized by a pool of synchronized GCs, and vice versa, what initiates the synchronized activity? Importantly, intraglomerular gap junctions provide an independent mechanism to synchronize a subset of the MCs, those connected with the same glomerulus. As long as the GCs with which these MCs form connections are part of a larger pool of GCs that interconnect glomeruli, the intraglomerular gap junctions could trigger interglomerular synchrony.

We found in our simulations that intraglomerular gap junctions indeed increased both intra‐ and interglomerular synchrony, as reflected in the parameters used to quantify synchronous activity in MCs across time (compare peak magnitudes of red and purple traces in Fig. 3 B and D with those traces in Fig. 1 D and E) as well as in the mean measure of synchrony (S _GlomA‐B; Fig. 3 E and F). The peak S _GlomA‐B value was ∼1.9 versus ∼1.2 for a model without gap junctions but otherwise identical parameters, indicating that gap junctions enhanced synchrony levels above chance for non‐sister MCs by more than a factor of 4. We also observed large increases in the degree to which GCs were synchronized with respect to each other (compare Fig. 3 C and G with Fig. 2 B and D), while synchronous activity between MCs versus GCs remained highly correlated (Fig. 3 H; correlation coefficient = 0.65, P < 10⁻²⁶). Such results were expected if the enhanced interglomerular MC synchrony was due to an enhancement in the mutually synchronizing interactions between MCs and GCs.

Intraglomerular gap junctions facilitate synchrony in non‐sister MCs: experiments

Having demonstrated the plausibility that intraglomerular gap junctions can enhance interglomerular synchrony with modelling, we next sought to address the functional role of the gap junctions in brain slice experiments using connexin (Cx) 36 knock‐out (Cx36 KO) mice. Because KO of Cx36 eliminates intraglomerular electrical coupling (Christie et al. 2005), our modelling predicted that synchronized oscillations should be much reduced in these mice.

As a first test, we examined KO effects on extracellular local field potential (LFP) oscillations in the external plexiform layer (EPL) of the bulb that reflect synchronized synaptic interactions between MC lateral dendrites and GC apical dendrites (Rall & Shepherd, 1968; Fig. 4 A). Fast LFP oscillations at beta/gamma frequencies similar to those observed in vivo can be easily evoked in bulb slices by electrical stimulation of olfactory sensory neurons (OSNs; Friedman & Strowbridge, 2003; Lagier et al. 2004; Gire & Schoppa, 2008). To account for possible effects of Cx36 KO on local network excitation (Christie & Westbrook, 2006; Vaaga & Westbrook, 2016), which could indirectly impact the magnitude of beta/gamma oscillations, all LFP recordings in the EPL were conducted while simultaneously recording LFPs in adjacent glomeruli. These signals, which can be quite large and long‐lasting, reflect local network excitation (Gire & Schoppa, 2009). During these dual LFP recordings, OSN stimulation (50–500 μA) resulted in robust beta/gamma oscillations in the EPL (Fig. 4 C, E and F), along with significant glomerular LFP signals in wild‐type (WT) mice (Fig. 4 B), as expected. However, the beta/gamma oscillations in Cx36 KO mice were much smaller. This was quantified first by comparing the beta/gamma power (integrated between 23 and 57 Hz) measured under similar, high levels of network excitation (glomerular LFP ≥ 0.3 mV). The beta/gamma power under these conditions was reduced by ∼60% in KO (Cx36 KO: median = 23 μV², IQR = 12–34 μV², n = 15; WT: median = 55 μV², IQR = 33–83 μV², n = 16; P < 0.005, Mann–Whitney test). Furthermore, across differing levels of network excitation, Cx36 KO reduced the steepness of the dependence of fast oscillation amplitude on the glomerular LFP (Fig. 4 G; 61% reduction in the slope of a fitted line; P = 0.041 in one‐way ANCOVA). The effects of Cx36 KO also appeared to be strongest in the beta/gamma range. The oscillatory power at frequencies below 20 Hz was indistinguishable between WT and KO (Fig. 4 F) and differences lessened at frequencies ≥ 80 Hz. At very high frequencies (≥0.3 kHz) the oscillatory power in Cx36 KO versus WT was indistinguishable (Fig. 4 D; Cx36 KO: median integrated power between 0.3 and 1 kHz = 60 μV², IQR = 30–79 μV², n = 15; WT: median = 54 μV², IQR = 42–80 μV², n = 16; P > 0.2, Mann–Whitney test; all experiments with glomerular LFP ≥ 0.3 mV). In terms of the glomerular LFP, amplitudes for Cx36 KO and WT across all experiments were similar (Cx36 KO: mean ± SEM = 0.26 ± 0.03 mV, n = 42; WT: 0.32 ± 0.03 mV, n = 36; P = 0.15, Student's t test).

We additionally assessed the effect of Cx36 KO on inhibitory postsynaptic currents (IPSCs) recorded in pairs of MCs affiliated with different glomeruli (Fig. 5; maximal glomerular separation = 110 μm; V _hold = –57 mV). Synchronization of these inhibitory signals has been directly linked to synchronized spike activity in non‐sister MCs in rat bulb slices (Schoppa, 2006a). As expected, in WT mice, we often observed a high incidence of synchronized IPSCs in the MC pairs following OSN stimulation, as evidenced by peaks near zero in distributions of time lags between IPSCs in the two MCs (Fig. 5 A and B). In six MC pair recordings with the clearest such peaks (with s/n _IPSC,pair > 2.5; see below), the time scale of the synchronous activity was typically quite fast, in the order of 1–2 ms (mean standard deviation of Gaussian functions fitted to histograms = 1.4 ± 0.2, n = 12 histograms from 6 pairs; Fig. 5 D), and the peaks of the histograms were generally centred within 0.5 ms of zero. The level of synchronous activity was also quite high: the peak values of these histograms corresponded to 61 ± 13% more synchronized events than would be expected by chance. In sharp contrast, only 1 of 9 pair‐cell recordings from Cx36 KO mice displayed evidence for stimulus‐evoked synchronized activity based on IPSC time‐lag distributions (example with no synchrony in Fig. 5 C).

To further quantify the differences in stimulus‐evoked IPSCs between WT and Cx36 KO across all pair‐cell recordings, an IPSC synchronization index (S _IPSC,MC) was computed from the fraction of IPSCs in one MC that had an IPSC in the other MC that was within 1.5 ms, above that expected by chance (Fig. 5 E; see Methods). The values for the two MCs for each pair were then averaged to produce a pair‐specific IPSC synchronization index (S _IPSC,pair; Fig. 5 F). Across all recordings, Cx36 KO significantly reduced synchrony by this measure (Cx36 KO: median S _IPSC,pair = –0.3%, IQR = –1.0 to 1.5%, n = 9 pair recordings; WT: median S _IPSC,pair = 2.4%, IQR = 1.1–4.0%, n = 12 pair recordings; P = 0.013, Mann–Whitney test). The synchrony differences between WT and Cx36 KO were also striking when we accounted for noise in the IPSC time‐lag distributions (Fig. 5 G and H), as estimated from the standard deviation of the off‐peak histogram values. The signal‐to‐noise ratio (s/n _IPSC,pair) was markedly reduced by Cx36 KO (Cx36 KO: median = –0.4, IQR = –0.9 to 1.3, n = 9 pair recordings; WT: median = 2.3, IQR = 1.1–3.9, n = 12 pair recordings; P < 0.01, Mann–Whitney test). Thus, by a number of measures, eliminating intraglomerular gap junctions reduced synchronized IPSCs in non‐sister MCs. It is notable that Cx36 KO reduced the synchrony of IPSCs in these datasets without impacting the frequency of the IPSCs (mean ± SEM = 35 ± 3 Hz for Cx36 KO, n = 18; 38 ± 3 Hz for WT, n = 24; P = 0.45, Student's t test; see x‐axis values in Fig. 5 E). This argued that KO effects on the synchronized IPSCs were independent of potential effects of eliminating gap junctions on local network excitation (Christie & Westbrook, 2006; Vaaga & Westbrook, 2016). In dual recordings in which we measured both MC IPSCs as well as the level of local network excitation with the glomerular LFP (Fig. 4 B), IPSC frequency was well correlated to the glomerular LFP (see Fig. 6 C; WT: Pearson's r = 0.44, P = 0.0029; Cx36 KO: Pearson's r = 0.70, P = 0.000030).

Figure 6. MC IPSCs in WT and Cx36 KO generally have similar frequency and amplitude properties.

A, example recordings of spontaneous IPSCs (sIPSCs) in MCs. Illustrated are sample traces consecutively recorded from WT (top, left) and Cx36 KO (bottom, left) mice, along with cumulative amplitude (top, right; ≥227 IPSC events) and instantaneous frequency plots (bottom, right). In the plots, WT and KO curves are overlaid. B, summary histograms of sIPSC amplitude and frequency. Data reflect means ± SEM from 20 MCs in WT, 16 MCs in KO. C, summary of frequency measurements for IPSCs evoked by OSN stimulation, plotted as a function of the glomerular LFP that was simultaneously recorded. The plot has more data points than number of MC recordings (16 MCs for WT, 16 MCs for Cx36 KO), reflecting the fact that, for each recording, multiple OSN stimulation intensities were often used in order to sample different levels of network activity. Data were fitted with lines to estimate Pearson's correlation coefficients (0.44 for WT, 0.70 for KO). D, summary of evoked IPSC amplitude measurements for the same recordings as C. Note that the IPSC amplitudes were larger in WT when the glomerular LFP was larger (>0.2 mV, vertical dashed line). We attribute WT's larger IPSCs under these conditions to summating, synchronous events (see text).

An additional potential caveat with the effects of Cx36 KO on synchrony was that it was due to other, unexpected developmental alterations in the bulb circuitry in the constitutive KO mouse. Changes in the incidence of dendrodendritic synaptic connections between MCs and GCs, for example, could have reduced the beta/gamma oscillations instead of, or in addition to, reduced intraglomerular electrical coupling. Arguing against this possibility, however, were the properties of the spontaneous IPSCs (sIPSCs) in MCs that were recorded in the period prior to OSN stimulation (Fig. 6 A). Because these sIPSCs probably reflected a mixture of GABA release events from single synapses (miniature IPSCs) as well as unitary IPSCs reflecting action potential firing in single GCs, a change in the GC–MC connection rate should have altered the frequency and/or amplitude of these events. In contrast to this prediction, no differences were observed (mean amplitude ± SEM = 12.2 ± 1.0 pA for Cx36 KO, n = 16; 13.4 ± 1.3 pA for WT, n = 20; P = 0.50, Student's t test; mean frequency ± SEM = 11.1 ± 1.6 Hz for Cx36 KO; 10.1 ± 2.0 Hz for WT; P = 0.73, Student's t test; Fig. 6 B). A lack of an effect of KO on connectivity was also supported by the similar frequencies of MC IPSCs evoked by OSN stimulation noted above (Fig. 6 C). Interestingly, we found that the amplitudes of the evoked IPSCs were often smaller in KO versus WT but in a manner that depended on the level of local network excitation (as monitored by the glomerular LFP; Fig. 6 D). Under weak excitatory conditions (glomerular LFP ≤ 0.2), the evoked IPSC amplitudes in WT versus KO were similar (mean ± SEM = 16 ± 2 pA for Cx36 KO, n = 14; 19 ± 2 pA for WT, n = 6; P = 0.46, Student's t test). We attribute WT's larger‐amplitude IPSCs at higher levels of network excitation to be the result of the greater synchronized activity under these conditions (Fig. 4 G); this could result in detected IPSCs that reflect multiple, summating unitary events.

Function of divergent connections between MCs and GCs

Thus far, we have provided both theoretical and experimental evidence for a model of generating beta/gamma synchronized oscillations in the bulb that involves population‐level interactions between GCs and MCs, combined with gap junctions between sister MCs (model summarized in Fig. 3 A). We next wondered how synchrony was influenced by direct divergent connections amongst the neurons, either from single GCs onto multiple MCs (Fig. 7 A) or single MCs onto multiple GCs (Fig. 8 A). Such mechanisms are distinct from a population‐level mechanism of synchronization in that transmitter release from a single cell rather than a group of synchronized cells coordinates spiking in the other cell type. The low ∼4% incidence of connections measured in MC–GC pair recordings (Kato et al. 2013) would correspond, assuming random connections, to a very small ∼0.2% probability that any single MC makes divergent contacts onto any two nearby GCs, yet viral tracing studies have suggested that MC–GC connections are non‐random (Willhite et al. 2006; Kim et al. 2011). Within subpopulations of MCs and GCs with high connection rates, the rate of divergent connections could be higher. Thus, we next sought to test the contribution of direct divergent connections to synchronized activity. Rats rather than mice were used for these studies (Figs 7, 8, 9), since we would be taking advantage of a large data bank of pair‐cell recordings of synaptic activity evoked by OSN stimulation in rat bulb slices for comparisons (reported in Schoppa, 2006a,b but analysed differently here).

Figure 9. Population‐level mechanism can produce precise synchrony in MC–GC network.

A, dual patch‐clamp recordings from unconnected MC–GC pairs were made to test whether a population‐level mechanism could produce precise synchrony. B, sample traces of MC IPSCs (inward currents at V _hold = –107 mV) and GC voltage recorded simultaneously. The IPSC late in the MC trace synchronized to the GC spike reflected GABA release from a GC synchronized to the test GC rather than the test GC itself. C, histogram of time lags between GC spikes and MC IPSCs for the experiment in B. Overlaid is a fitted Gaussian with SD = 1.2 ms. Note that the peak of the histogram is at ∼–0.5 ms rather than at 1–2 ms, as would be expected if the MC IPSCs reflected GABA release from the test GC.

The contribution of divergent GC‐to‐MC connections to synchronized activity was assessed by recording IPSCs in pairs of non‐sister MCs (V _hold ≥ −62 mV or −107 mV) in the presence of glutamate receptor antagonists (NBQX, 20 μm, and dl‐AP5, 50 μm). A high concentration of K⁺ (bath applied at 13–28 mm) was used as a stimulus. The glutamate receptor antagonists should have blocked the synchronizing drive from MC/TCs onto different GCs such that any synchronized K⁺‐evoked IPSCs in a pair of MCs above that expected by chance should reflect divergent inputs from a single GC. In fact, though, the K⁺‐evoked IPSCs (Fig. 7 B) were generally not synchronized in the MCs (Fig. 7 D and E; median S _IPSC,pair = –0.8%, IQR = –2.0 to 0.2%, n = 9 MC pairs), appearing at a low level in only one pair (S _IPSC,pair = 3.2; s/n _IPSC,pair = 2.6). This compares to a high level of synchrony of MC IPSCs evoked by OSN stimulation in rat (median S _IPSC,pair = 7.6%, IQR = 2.6–11.4%, n = 14 pairs; P < 0.005, Mann–Whitney test; Fig. 7 F). The low level of synchrony in the K⁺‐evoked IPSCs was not because K⁺ was an ineffective stimulus, since the frequency of K⁺‐evoked IPSCs was comparable to that due to OSN stimulation (Fig. 7 E and F); K⁺ also consistently drove high levels of spike activity in GCs (n = 4; Fig. 7 C). Thus, the large majority of the synchronized IPSCs in MCs did not reflect divergent GC‐to‐MC connections.

Analogous methods were used and similar results obtained when we examined the contribution of divergent MC‐to‐GC connections (Fig. 8 A) to synchronous activity in GC pairs. Here, K⁺‐evoked excitatory postsynaptic currents (EPSCs; V _hold = –77 mV) were recorded in GCs in the presence of the GABA_A receptor antagonist gabazine (6 μm) to block most synchronized activity in MCs. K⁺ (puff applied at 1 m, 200–500 ms puffs; see Methods) elicited both transient barrages of EPSCs in GCs (n = 7 pairs; Fig. 8 B) and spikes in MCs (n = 4 cells; Fig. 8 C), yet the EPSCs were consistently not synchronized (mean EPSC synchronization index, S _EPSC,pair = −0.3 ± 0.4%, n = 7 GC pairs; Fig. 8 D and E). This contrasts with the synchronous activity that was observed in GC pairs following OSN stimulation (S _EPSC,pair = 5.6 ± 2.2%, n = 11 GC pairs; Fig. 8 F; P = 0.032 in Student's t test comparing OSN and K⁺‐evoked EPSCs). In the gabazine experiments, the GCs displayed two kinetically distinct populations of K⁺‐evoked EPSCs (Schoppa, 2006b; Balu et al. 2007). Results reported above and shown in Fig. 8 were based only on the slower class of EPSCs (τ_decay = ∼5 ms) reflecting dendrodendritic excitatory inputs from MC/TC lateral dendrites. Notably, an absence of synchrony due to divergent connections was also observed when we specifically analysed K⁺‐evoked rapid EPSCs (τ_decay = ∼1.5 ms; S _EPSC,pair = 0.3 ± 0.7%, n = 5 GC pairs).

While these results indicated that the synchronous synaptic events in the MC–MC and GC–GC pair‐cell recordings generally did not reflect divergent inputs, a feature of the synchronized IPSCs following OSN stimulation that was somewhat puzzling in this light was its high temporal precision (Fig. 5 A and B; mean SD of fitted Gaussian = ∼1.4 ms). A divergent connection mechanism should naturally produce more precise synchrony than a population‐level mechanism, given that, with the latter, the timing of IPSCs in two MCs would be impacted by variations in spike times in different GCs. A convenient measure of the precision of population‐level synchrony in the MC–GC circuit was provided by recordings from cell‐pairs that included a MC and a GC but that lacked synaptic connections with each other (n = 9; Fig. 9 A). In such pairs, any MC IPSCs that were synchronized to spikes in the test GC had to reflect GABA release events from GCs synchronized to the test GC rather than the test GC itself; hence the time lags between GC spikes/MC IPSCs included population‐level differences in GC spike times. In five GC–MC pairs in which the MC had IPSCs time‐locked to GC spikes (example in Fig. 9 B and C; mean increase above chance = 245 ± 102%; mean offset of histogram peak = −0.1 ± 0.3 ms), the precision of synchrony of the MC IPSCs/GC spikes was in fact quite high (mean SD value of fitted Gaussian functions to GC spike–MC IPSC time lags = 1.1 ± 0.2 ms). Hence, the high precision of IPSC synchrony in MC pairs is not inconsistent with a population‐level mechanism of synchronization.

Cortical feedback does not contribute to synchronized activity in bulb slices

Finally, we wondered whether excitatory feedback from the olfactory cortex, which can impact the frequency of bulbar oscillations (Martin et al. 2004; Lowry & Kay, 2007; Fourcaud‐Trocmé et al. 2011; Boyd et al. 2012; David et al. 2015), contributed to fast oscillatory synchrony in our bulb slices. Our mouse and rat bulb slices generally also included portions of the anterior olfactory nucleus and piriform cortex, leaving open the possibility that OSN stimulation in our experiments could have excited cortical cells that provide feedback. Furthermore, OSN stimulation drives fast EPSCs in GCs (see above) that have been attributed to cortical feedback (Balu et al. 2007). Feedback axons could provide an alternative/additional mechanism to synchronize GCs distinct from our proposed population‐level mechanism (Fig. 3 A). However, deliberately sectioning cortical regions from our rat slice preparation did not significantly impact LFP oscillations recorded in the EPL (Fig. 10 A–D; integrated power between 23 and 57 Hz, No‐cortex slices: mean ± SEM = 30 ± 3 μV², n = 4; With‐cortex slices: 21 ± 2 μV², n = 4; P = 0.09 in Student's t test). Sectioning also did not impact the level of local network excitation assayed with the glomerular LFP (No‐cortex slices: mean ± SEM = 0.14 ± 0.02 mV; With‐cortex slices: mean ± SEM = 0.17 ± 0.01 mV; P = 0.27, Student's t test). While these results are by no means evidence against cortical feedback having a role in synchronizing GCs, they do argue that the oscillatory synchrony in our in vitro brain slices was completely due to intrinsic bulbar circuitry.

Discussion

In this study, we combined computational and experimental methods to examine mechanisms that shape beta/gamma frequency synchronized oscillations in the olfactory bulb, focusing mainly on activity amongst non‐sister MCs affiliated with different glomeruli (interglomerular synchrony). Our main findings included: (1) intraglomerular gap junctions between sister MCs affiliated with the same glomerulus greatly enhanced the ability of a computational model of sparsely connected MCs and GCs to generate interglomerular synchrony; (2) knock‐out of Cx36 reduced gamma LFP oscillations and synchronized IPSCs in pairs of non‐sister MCs, providing experimental support for a model in which intraglomerular gap junctions enhance interglomerular synchrony; and (3) divergent connections between MCs and GCs did not contribute directly to the vast majority of the observed synchronous synaptic activity. These points are discussed below.

Mechanisms that shape oscillatory synchrony in the olfactory bulb

The question of what drives synchronized beta/gamma oscillations in the olfactory bulb (Adrian, 1950) has received considerable attention over the past several decades. Starting with the early work of Rall & Shepherd (1968), computational and experimental studies have provided evidence that such oscillations in the bulb result from a fast excitatory–inhibitory feedback loop involving populations of MCs and GCs (Rall & Shepherd, 1968; Davison et al. 2003; Lagier et al. 2004; Schoppa, 2006a,b; Fukunaga et al. 2014). Our studies here extend substantially on those results by supporting a role for intraglomerular gap junctions in enhancing the efficacy of the feedback loop in generating beta/gamma oscillations. The effects of the gap junctions were quite large. In the sparsely connected network of MCs and GCs that we modelled, synchronized activity above chance was increased by a factor of 4 by the addition of intraglomerular gap junctions. In addition, in experiments, extracellular LFP oscillations were reduced by ∼60% when intraglomerular gap junctional coupling was abolished in Cx36 KO animals. Synchronous IPSCs in pairs of non‐sister MCs were nearly eliminated. We suggest, and our data support, that the critical role for intraglomerular gap junctions lies in the fact that beta/gamma oscillations result from rapid mutually synchronizing interactions between MCs and GCs, i.e. where synchronized activity in one cell population depends on synchronized activity in the other (Fig. 3 A). Within this system, intraglomerular gap junctions act as a trigger for the mutually synchronizing interactions by providing an independent mechanism to synchronize subsets of MCs affiliated with the same glomerulus.

An important technical issue in interpreting the results of Cx36 KO in our experimental studies was that KO could have impacted the oscillations by reducing the level of network excitation (Christie & Westbrook, 2006; Vaaga & Westbrook, 2016). To delineate KO effects that were independent of network excitation, the recordings of LFP oscillations in the EPL were normalized to an LFP that was simultaneously recorded within nearby glomeruli. This LFP can report local network excitation (Gire & Schoppa, 2009). In addition, in recordings of IPSCs in MC pairs, results were normalized to the IPSC frequency. Our electrophysiological recordings of sIPSCs and evoked IPSCs also suggested that the effects of Cx36 KO on synchrony were not due to developmental alterations in GC–MC connections in the constitutive KO mouse. Certainly, our results do not exclude the possibility that some circuit alterations occur in this mouse, and additional inducible Cx36 KO or pharmacological studies are needed. Questions about the specificity of various gap junction blockers available now (e.g. see Kirson et al. 1998; Gribble et al. 2000; Schoppa & Westbrook, 2002; Thompson & Lummis, 2008; Tovar et al. 2009) limit their utility at this time.

Amongst the underlying assumptions of our proposed mechanism of generating beta/gamma oscillations is that the incidence of connections between MCs and GCs is very low. If MCs and GCs were densely connected, single MCs could synchronize a significant fraction of the local population of GCs through direct divergent connections and vice versa. In this case, the need for intraglomerular gap junctions to trigger fast oscillations could be much reduced. However, arguing that connectivity is quite low is the 4% MC‐to‐GC connection rate between closely spaced MCs and GCs measured in pair‐cell recordings (Kato et al. 2013). Also, evidence was obtained from K⁺‐application experiments that divergent MC‐to‐GC or GC‐to‐MC connections did not contribute directly at a high level to the synchronized synaptic activity observed in the MC–MC and GC–GC pairs. It should be emphasized that our results by no means exclude a functional role for divergent connections. Such divergent connections, which could occur at a higher level amongst subpopulations of more highly connected MC–GCs (Willhite et al. 2006; Kim et al. 2011) or exist at a low level throughout the circuit, could have a triggering function not unlike intraglomerular gap junctions in facilitating network synchrony (McTavish et al. 2012). Indeed, in preliminary modelling studies, we found that adjusting the maximal MC–GC connection rate from 20% to 25% increased synchrony by ∼20% (T. McTavish, personal communication). This change in connection rate corresponded to increasing the incidence of divergent connections from 4% to 6.25%.

Another assumption of the proposed mechanism is our general mechanistic framework for synchronized activity, i.e. that it is due to a fast excitatory/inhibitory feedback loop involving MCs and GCs. Several computational studies have suggested that gamma oscillations in the bulb instead involve a fundamentally different mechanism wherein shared, noisy GC‐to‐MC synaptic inputs occurring over a slow envelope of inhibition interact with the fast oscillatory intrinsic properties of MCs (Bathellier et al. 2006; Galán et al. 2006; Brea et al. 2009; Marella & Ermentrout, 2010; Burton et al. 2012). It is important, however, to point out that the argument for using slow inhibition in those models was the slow time course of lateral inhibition in MCs that has been observed experimentally upon application of a single stimulus pulse (Urban & Sakmann, 2002; Bathellier et al. 2006). GC‐to‐MC inhibition appears to be much more rapid (<10 ms duration) during theta frequency stimulation conditions that produce gamma oscillations, apparently reflecting the properties of A‐type K⁺ channels in GCs (Schoppa & Westbrook, 1999; Schoppa, 2006b). In addition, pair‐cell recordings in MCs and GCs in vitro (Schoppa, 2006a,b) display synchronized rapid IPSCs and EPSCs, respectively, providing direct experimental support for a mechanism involving rapid reciprocal interactions.

A final point about mechanisms of bulbar oscillations pertains to the MC–GC model used in the computational component of our study. The model was certainly much reduced in scope, including only MCs and GCs. The oscillations could involve other neurons, for example GABAergic short‐axon cells in the granule cell layer or parvalbumin‐positive GABAergic cells in the EPL (Kato et al. 2013). However, the lack of evidence at this time that these cells are involved in beta/gamma oscillations, as well as the evidence implicating GCs (e.g. Fukunaga et al. 2014), motivated us to focus on MC–GC interactions. The intrinsic and synaptic conductances of the cells within the model were also simplified. For example, GCs in the model lacked two conductance features that may be important for controlling the frequency of bulbar oscillations (Osinski & Kay, 2016): voltage‐gated calcium channels and voltage‐dependent block of NMDA receptors by magnesium. Our model produced oscillations at ∼20 Hz (within the beta range; Gray & Skinner, 1988), but inclusion of these aspects could in principle cause a shift to gamma (40–90 Hz). In addition, MCs in our model lacked the persistent sodium current that underlies the intrinsic oscillatory properties of these cells (Desmaisons et al. 1999). While our model was incomplete, we believe that it was sufficient to establish the plausibility of the hypothesis that intraglomerular gap junctions can enhance interglomerular synchrony, forming the basis for the Cx36 KO experiments. Further modelling and experiments are needed to understand better synchronization in MC–GC dynamical systems that involve interplay between MC intrinsic oscillations and network‐level mechanisms.

Broader significance

Fast synchronized oscillations in the beta/gamma range are of course common throughout the brain, occurring in such well‐studied circuits as the hippocampus and neocortex. As in the bulb, these oscillations are commonly due to rapid feedback loops involving pools of excitatory and inhibitory cells (Wang, 2010; Buzsáki & Wang, 2012). However, beyond that there appear to be some important differences. Whereas bulbar oscillations reflect a mechanism involving a sparsely connected MC–GC network, combined with facilitatory gap junctions between subsets of MCs, many other circuits appear to be able to generate fast oscillations due to interactions between excitatory and inhibitory cells alone (Wang, 2010; Buzsáki & Wang, 2012). This difference may reflect the higher connection rates between excitatory and inhibitory cells in other circuits (e.g. 50–75% in neocortex, Holmgren et al. 2003; ∼60% in barrel cortex layer 2, Avermann et al. 2012; 20% in piriform cortex, Stokes & Isaacson, 2010). Another unique feature of the bulb is in the properties of ascending inputs. Because of the strong convergence in OR‐specific OSNs to glomeruli, MCs at different glomeruli cannot be synchronized by divergent OSN axons. Our results here nevertheless do demonstrate some general principles that may be more broadly applicable. For example, a high connection rate between excitatory and inhibitory cells is by no means a requirement for large‐scale fast oscillations. Also, the fact that synchrony between glomeruli in the bulb is enhanced by intraglomerular connections demonstrates that a network, through population effects, can transfer high‐level synchrony amongst a subnetwork of connected cells to cells that are not at all connected.

What might be the functional significance for olfaction of having a system in which high‐amplitude synchronized oscillations arise through a mechanism that combines sparse MC–GC connections and intraglomerular gap junctions? One way to address this question is to consider the advantages of having sparse MC–GC connections. Such a system would, for example, enable single GCs to contact many more MCs, and thereby participate in synchronizing many more glomerular modules of MCs. If, as has been suggested (Mori et al. 1999; Brody & Hopfield, 2003), synchronization between glomeruli helps the olfactory cortex ‘bind’ information about different ORs leading to odour perception, each GC could, in effect, be involved in facilitating the perception of many different odours. Sparse connectivity could, in addition, function to reduce the ability of inhibitory inputs to stop back‐propagating action potentials in MC lateral dendrites (Lowe, 2002; Xiong & Chen, 2002). This effect could facilitate the spread of synchronized oscillations across space. A system in which intraglomerular gap junctions greatly enhance interglomerular synchrony enables the network to preserve such advantages of sparse connectivity. Future studies, including behavioural experiments, will be required to delineate the actual higher‐level functions of intraglomerular gap junctions for olfaction.

Additional information

Competing interests

None declared.

Author contributions

Experiments were performed in the labs of N.E.S. and D.R. Conception and design of the experiments: F.P., T.S.M., L.E.H., D.R., N.E.S. Collection, analysis and interpretation of data: F.P., T.S.M., N.E.S. Drafting the article or revising it critically for important intellectual content: F.P., T.S.M., L.E.H., D.R., N.E.S. All authors approved the final version of the manuscript. All authors agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.

Funding

This work was supported by NIH grants R01DC000566 (D.R. and N.E.S.), F31DC009369 (T.S.M.) and R01LM009254 (L.E.H.).