Rapid Desynchronization of an Electrically Coupled Interneuron Network with Sparse Excitatory Synaptic Input

Summary Electrical synapses between interneurons contribute to synchronized firing and network oscillations in the brain. However, little is known about how such networks respond to excitatory synaptic input. To investigate this, we studied electrically coupled Golgi cells (GoC) in the cerebellar input layer. We show with immunohistochemistry, electron microscopy, and electrophysiology that Connexin-36 is necessary for functional gap junctions (GJs) between GoC dendrites. In the absence of coincident synaptic input, GoCs synchronize their firing. In contrast, sparse, coincident mossy fiber input triggered a mixture of excitation and inhibition of GoC firing and spike desynchronization. Inhibition is caused by propagation of the spike afterhyperpolarization through GJs. This triggers network desynchronization because heterogeneous coupling to surrounding cells causes spike-phase dispersion. Detailed network models predict that desynchronization is robust, local, and dependent on synaptic input properties. Our results show that GJ coupling can be inhibitory and either promote network synchronization or trigger rapid network desynchronization depending on the synaptic input.

Time course of the coupling coefficient (Mean ± SE) when no drugs are applied (n = 4 pairs). Bottom: Time course of the effect of bath application of 25 µM mefloquine on the coupling coefficient (Mean ± SE, n = 5 pairs). Note that the coupling coefficient was stable with time under control conditions while mefloquine application strongly reduced the coupling coefficient. (C) Voltage traces of an electrically coupled GoC pair while stimulating mossy fiber (MF) input into one of the cells (4 stimuli at 100 Hz). Black traces: MF stimulation is just subthreshold in GoC1 and causes no hyperpolarization in GoC2. Blue traces: MF stimulation triggers a spike in GoC1 which causes a hyperpolarization in GoC2. Steady current in GoC1 was used to adjust the spike probability. (D) Voltage traces of an electrically coupled GoC pair while stimulating MF input into one of the cells (4 stimuli at 100 Hz) before and after mefloquine application. After application of 25 µM mefloquine, the hyperpolarization in the postsynaptic cell disappeared indicating that Cx36 containing gap junctions are responsible for the inhibitory gap junction potential. These data indicate that the spike AHP causes the inhibition in GoC2. Relation between the pause duration and CC. Lower CC resulted in shorter pause durations (same data set as in (A)). (C) Phase response curves (PRC) for two different levels of electrical coupling (low coupling: red, CC: 2-15% mean 9% n = 11; high coupling: blue, CC: 15-31% mean 23% n = 11). Low electrical coupling (red) resulted in a smaller spike delay than high coupling (blue). All experiments are included regardless tonic firing frequency or whether depressions were evoked with parallel fiber or mossy fiber stimulation. Circles present mean ± SE. Data was binned in phase bins of 0.1 (* 2π radians). Both groups were significantly different       Current-clamp and voltage-clamp recordings were performed with a Multiclamp 700B amplifier (Molecular Devices). Data was low-pass filtered at 10 kHz and digitized at 20-50 kHz.

Supplemental
Recordings were acquired with Neuromatic (http://www.neuromatic.thinkrandom.com/) running within the IgorPro environment (Wavemetrics). Golgi cells (GoCs) were selected as described in (Kanichay and Silver, 2008). In addition their morphology was assessed by biocytin labeling except in a few cases where Alexa 594 (100 µM; Invitrogen) was added to the internal solution and the cells were visualized with a CCD camera as described previously (Kanichay and Silver, 2008) or with 2-photon imaging. After acquiring I/V and f/I relationships at the beginning of experiments, 10 µM gabazine and 500 nM strychnine were routinely added to the bath to block synaptic inhibition (except where stated otherwise). The GoC membrane time constant was 9.8 ± 2.4 ms (mean ± SD, n = 44). After blocking synaptic inhibition, some GoCs that were silent or had a very low firing frequency were injected with a steady positive current so their firing frequency reflected that typically observed in mice in vivo (2-10 Hz) (Barmack and Yakhnitsa, 2008;Ros et al., 2009). Mossy fibre (MF) and Parallel fibre (PF) stimulation was performed as previously described (Kanichay and Silver, 2008). To test that GoCs were not directly stimulated, EPSCs were visually inspected for latency (> 1.5 ms), shape, and short-term plasticity during a 100 Hz pulse train. Moreover, at the end of the experiment, responses were blocked by 10 µM NBQX and 50 µM APV (Rs < 20 MΩ). For measurements of MF evoked disynaptic IPSCs Golgi cells were held at the reversal potential for excitatory synaptic input. The IPSC conductance was calculated based on the calculated Clreversal potential (-58 mV) and the maximal NBQX-sensitive IPSC response during 10 pulses at 100 Hz.
The following protocols were used to determine whether Golgi cells were coupled by chemical inhibitory synapses. During paired GoC recordings, before adding gabazine and strychnine, we

Data acquisition and analysis
Recordings were analyzed with Neuromatic and Origin 8 (OriginLab). All figure traces were digitally filtered at 7 kHz using a binomial smoothing function. The membrane potential was not corrected for the junction potential. To determine input resistance and coupling coefficient (CC) negative current (typically 5 -100 pA) was applied to silence spontaneous spiking. Input resistance was calculated from a 200 ms, -200 pA pulse. Cells were regarded coupled when the CC was > 1 %. Pooled data are expressed as mean ± SE unless stated otherwise. Sample means were compared with a two sided Wilcoxon signed rank test and considered significant at P < 0.05. Phase-response curves and cross-correlograms were calculated as previously described (Dugue et al., 2009). The cross-correlations in Fig.3C,D were calculated as following; first stimulation was regarded in-phase if the stimulation occurred within ± 0.1 of the cycle around the expected spike time. Only sweeps (~100 -200) were selected where cells showed 2 consecutive synchronized spikes before stimulation. Second, the peristimulus time histogram (PSTH) of the spike times in a 300 ms time window before stimulation or in a 400 ms time window after stimulation were constructed for both cells (10 ms bins). Finally, both PSTH were filtered with a 3-point adjacent average filter and cross-correlated. The pause duration was defined as the interval between the stimulus and the second PSTH bin after the stimulus that was larger than the mean bin height before the stimulus.

Neurolucida reconstructions and Electron microscopy
After recordings, slices were placed in a fixative containing 4% paraformaldehyde and 1.25% glutaraldehyde in 0.1 M phosphate buffer (PB; pH 7.4) and left for several days. Slices were cryoprotected in 10% and 20% sucrose solutions (in 0.1 M PB) for 45 min followed by freezing and thawing. After several washes in PB, slices were embedded in 1% agarose and resectioned at 60 µm thickness. Biocytin was visualized using avidin-biotin-horseradish peroxidase complex. Sections were then dehydrated and embedded in epoxy resin (Durcupan) as described earlier (Biro et al., 2005). The GoC reconstruction used for the network simulations was processed according to (Golding et al., 2005). Three-dimensional light microscopic reconstructions of the cells were performed with the Neurolucida system (MicroBrightField) using a 100x oil-immersion objective. Light micrographs of each close apposition were used for the EM identification of the GJs. 70 nm serial sections were cut with an ultramicrotome. All close appositions between the filled processes of the two cells were checked on the ultrathin sections in the EM (Tamas et al., 2000).

Immunohistochemistry
Adult (P45) male Wistar rats and P16 male mice were deeply anesthetized with ketamine and xylazine. They were perfused through the aorta, first with 0.9 % saline for 1 minute, then with were taken with a confocal laser scanning microscope (FV1000, Olympus Europe) using a 20X (NA= 0.75) or a 60X (NA=1.35) objective. Automated sequential acquisition of multiple channels was used. Z-stack images were collected (at 0.5 -2 µm Z directional steps). Either single confocal images or maximum intensity Z-projection images (6-15 images) are presented. For preembedding immunohistochemistry twenty three day-old C57BL6 mice were anesthetized and perfusion fixed first with a fixative containing 2% paraformaldehyde and 0.5% glutaraldehyde in 0.1M Na-acetate buffer (pH 6) for 2 minutes, followed by a fixative containing 2% paraformaldehyde and 0.5% glutaraldehyde in 0.1M Borate buffer (pH 8.5) for 30 minutes. The immunogold reactions were carried out as described in (Lorincz et al., 2002) using an anti-mGluR2/3 antibody (1:250; Chemicon, Temecula, CA).

Golgi cell model and network simulations
The model of the GoC pair and the GoC network were build using neuroConstruct (Neuroconstuct.org; (Gleeson et al., 2007)) and simulations were performed with NEURON (Carnevale and Hines, 2006) running on a standard desktop computer (pair), on a multicore Dell 9600, the SilverLab 240 core Lenovo cluster (network) or LEGION, the UCL supercomputer (network). For the network model a different GoC reconstruction than the ones for the 2-cell model in Fig.6 was used because it had a more complete axon, which contributed ~30% to the input conductance. Active conductances were implemented as previously described (Solinas et al., 2007). In short, the GoC model contains 2 types of Ca 2+ currents with high and low activation threshold (I Ca-HVA , I Ca-LVA ); 2 Ca 2+ buffer mechanisms; two types of h-current (I HCN1 , I HCN2 ); 3 voltage dependent K + currents (I KA , I Kslow (M-type), I Kv ), a mixed voltage and Ca 2+ dependent K + current (I KC ) and a purely Ca 2+ dependent K + current (I KAHP , SK-type), and 3 types of Na + current (a transient I NaT , a persistent I NaP and a resurgent I NaR ). The specific membrane resistance was 47.6 kΩ.cm 2 , the specific axial resistance 100 Ω.cm and the specific membrane capacitance 1 µF.cm -2 . As in the original publication, all active conductances were placed in the soma without modification. The conductance waveform of the AMPA receptor type MF synapses (Kanichay and Silver, 2008) was based on measured EPSCs and had a single exponential rise ( 0 = 0.1 ms) and a dual exponential decay ( 1 = 0.7 ms, A 1 = 0.7 nS,  2 = 2.5 ms, A 2 = 0.2 nS, E reversal = 0 mV). The PF input conductance waveform had a single exponential rise ( 0 = 0.1 ms) and a single exponential decay ( 1 = 1.06 ms, A 1 = 0.67 nS, E reversal = 0 mV) (Dieudonne, 1998). Gaussian noise was added to the GoC pair model to reproduce the interspike interval variability observed in vitro (Solinas et al., 2007). In the network model, background synaptic noise was implemented with random trains of 20 MF synapses at 2 Hz each and 100 PF synapses at 0.5 Hz each. The somatic leak conductance for each cell was drawn from a uniform distribution (0 to 26 x 10 -5 S.cm -2 ; E reversal , -55 mV) to increase the heterogeneity in input resistance and intrinsic firing frequencies across the GoC population.
Spontaneous firing rate of individual cells in the network varied between 2 and 9 Hz with the majority firing between 6 and 9 Hz.
The thickness of the GCL modeled was determined experimentally by averaging measurements from the furrows to the apex of lobule 4 & 5Cb (80.6 µm, n=3). The footprint of the cuboid modeled (350 µm x 350 µm) was based on 2 considerations. 1) The number of electrical connections per GoC was not significantly different from a 600x600 µm network (Fig.S6B), and 2) Simulations with the larger network produced qualitatively similar results. GoCs were randomly distributed within the 350x35x80 µm rectangular box at a measured density of 4607 ± 166 cells/mm 3 . Whether any 2 Golgi cells in the network model were electrically coupled was determined based on the radial distance between their somata. Thus first the radial distance between the somata of a pair of cells within the model was determined. Second, whether a connection was made was determined according to the experimentally obtained coupling probability function (P c , see the Boltzmann function in Fig.7A, blue trace). This was implemented in Neuroconstruct with a Heaviside function (equation (1)). The Heaviside function takes as argument the subtraction of the probability function (P c ) with a random number between 0 and 1.
If the Heaviside function returned 1 the two cells made a connection. Finally, when a GoC pair had an electrical connection the conductance of the electrical synapse was determined based on the radial distance between their somata. We did this as follows; In Fig.7B we experimentally determined the relation between coupling coefficient (CC) and radial distance between GoC somata (exponential function, blue). However, this does not give us directly the relation between CC and the conductance of the electrical synapse. To determine this empirically, we used the 2cell model (using the reconstructed cell for the network modeling). An electrical synapse was randomly positioned between the 2 cells on the dendrites, the electrical synapse conductance varied from 0 to 5 nS and the CC determined. This was repeated for 20 randomly positioned electrical synapses and averaged (Fig.S6A). This relation between coupling conductance (nS) and coupling coefficient (%) was fit with a dual exponential function; Coupling Conductance = 0.576 * exp(CC / 12.4) + 0.000590 * exp(CC / 2.79) -0.564. This equation in conjunction with the equation for the spatial dependence of CC (exponential fit, Fig.7B, blue) gives the relation between the coupling conductance of the electrical synapse and the radial distance between GoC somata. We checked that randomly chosen coupled cells in the network gave coupling coefficients that matched well to the data in Fig.7B. For the network model only 1 GJ contact was made between each connected pair.
To model synchronous MF input in the GoC pair model, 20 randomly selected MF synapses were simultaneously activated (Fig.6I,J,K). However, for the network simulations ( Fig.7, 8,9) eight randomly selected MF synapses were activated per directly innervated cell. Each of these synapses became active after a random delay (uniform distribution) between 0 and 5 ms and remained activated at a mean rate of 200 Hz (Poisson distribution) for 10 ms. In addition, 50 randomly selected PF synapses per innervated cell were activated, 2 ms after the MF input started, each with a random delay between 0 and 5 ms. These PF synapses remained active for 15 ms at a mean rate of 350 Hz. In accordance with in vivo data, this pattern of input triggered predominantly spike doublets at ~100 to 250 Hz, and occasionally single or triplet spike responses. For every simulation in Fig.7E, F, Fig.8B, C, E, F and Fig.9A-D a different network