Gap Junctions between Striatal Fast-Spiking Interneurons Regulate Spiking Activity and Synchronization as a Function of Cortical Activity

Gap junctions affect synchrony and reduce firing frequency

To illustrate the effect of gap junctions on spiking activity and synchrony, a pair of FS interneurons was investigated first. Each of the multicompartmental FS interneurons received independent synaptic input (Kotaleski et al., 2006), resulting in spiking activity as during up-state or awake periods. Spiking patterns in the two reference neurons were compared with simulations in which the two FS interneurons were coupled with a gap junction.

Figure 2A shows an example voltage trace for both the reference (top) and gap junction coupled (bottom) case, when the two FS interneurons receive up-state or awake-state input. The addition of a gap junction changes the spike timing, but also changes the number of spikes. In some cases a new spike is triggered in the neighboring neuron (Fig. 2B, left); in other cases the presence of a gap junction causes the removal of an FS spike (Fig. 2B, right).

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Figure 2.

Role of gap junctions for synchronization in networks of two FS interneurons. A, Example voltage traces for two neurons without (Reference) or with proximal gap junctions (conductance 0.5 nS). The same synaptic input is repeated in both simulations. Note the change in spike number and spike timing. B, Zoomed in version of the traces in A. In the left subgraph a spike appears later in the trace with gap junctions and in addition triggers a spike in the neighboring cell. The right subgraph shows the disappearance of a spike instead. C, Proportion of synchronized spikes as a function of the conductance of the gap junctions. A spike is considered synchronous with another spike in an electrically coupled neuron if it appears within time Δt. D, JPSTH for two reference FS interneurons (D1) and for the FS interneurons coupled with a gap junction conductance 0.5 nS (D2). The diagonal represents synchronized spiking.

The proportion of synchronous spikes increases with gap junction conductances as illustrated in Figure 2C for several time windows, from 5 to 20 ms. Synchrony within these time windows would allow for inhibitory FS inputs to interact or sum in a postsynaptic MS neuron, since their IPSPs then overlap [Koos et al. (2004), their Fig. 2]. Though spike synchrony is observed in the pair of FS interneurons, the effect is quite weak at physiological gap junction conductances [mainly <0.5 nS (Galarreta and Hestrin, 2002)].

In Figure 2D the relative increase in spike synchronization is illustrated further using an JPSTH during 250 ms up-state periods. Figure 2D1 shows that spikes do not synchronize in the reference FS pair devoid of gap junctions, whereas Figure 2D2 shows an increase in spikes occurring within 5 ms of each other when gap junctions are simulated. This is represented by the increase in density of points on the diagonal.

Though the effect of gap junctions is easy to analyze and understand in a two neuron network, a larger network allows for coupling probabilities and interactions more similar to in vivo. Therefore, simulations were performed by providing independent synaptic input to each of the 10 FS interneurons in the network. Cross correlograms were constructed by averaging the cross-correlations calculated between each pair of neurons in the network. For reference, simulations were repeated and the cross-correlation was calculated for a network devoid of gap junctions but receiving identical input as before.

Figure 3A shows that gap junctions produce some synchronization in the network (visible as a peak at 0 ms with width approximately ±5 ms), but the dominant feature is a reduction in overall firing frequency. All interspike intervals, binned at 1 ms, show a decrease. The synchronized peak of the black (with gap junctions) cross-correlogram also lies below the base line of the cross-correlogram for the reference network (gray) devoid of gap junctions. As the gap junction strength is increased, two effects are observed: the proportion of synchronous spikes increases (as seen in Fig. 2C) and the overall activity in the FS network is reduced (Fig. 3B). As demonstrated below, this spike reduction is seen when the network is activated by synaptic inputs, and is not necessarily seen in FS populations activated by current injections (further explained below).

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Figure 3.

Influence of gap junctions on network spiking activity in a 10 FS network. A, Cross correlogram shows increase in synchrony due to gap junctions for the FS network. The black bars show results for the electrically coupled network (proximal gap junctions, 0.5 nS), with a relatively higher rate of synchronous spikes at ±5 ms; the gray bars show the uncoupled reference case, which has a higher rate of spike pairs at all interspike time intervals (bin size 1 ms) (compare with supplemental Fig. S1D, available at www.jneurosci.org as supplemental material). B, Spike frequency as a function of gap junction conductance, showing the decrease in firing as the conductance increases for neurons receiving synaptic input. The reduction is due to loss of charge (shunting) through the gap junctions. C, The occurrences of spike pairs in directly coupled (solid line) or indirectly coupled (dashed line) neurons spiking within Δt equals 5 ms of each other. Increased absolute numbers of synchronized spikes are limited to the directly electrically coupled neurons. The curve for the nondirectly coupled neurons follows what would be expected by chance, as illustrated by the close resemblance with the shuffled version of the coupled neuron case (where direct interactions mediated by gap junctions have been destroyed, but changes in correlation due to a change in firing frequency remain).

The moderate spike synchronization appearing in the network is not widespread; instead only directly coupled FS interneurons synchronize. Spike pairs between directly coupled FS interneurons appear more frequently than those between neurons only indirectly coupled (Fig. 3C). The latter appears only at levels comparable to what would be expected by chance, as illustrated by shuffling the traces of the directly coupled neurons and recalculating the spike pairs. This indicates that there is no global synchronization due to gap junctions in a small network of 10 FS interneurons, receiving simulated synaptic awake-state input, and connected with 30–40% probability with a gap junction to each of the other cells in the network.

Both the shunting behavior and the minimal spike synchronization were verified in a larger 125 FS network (see supplemental Fig. S1, available at www.jneurosci.org as supplemental material). Simulations were performed with uncorrelated input in a large network either with or without gap junctions. A cross-correlogram generated from all pairs of neurons revealed no synchronization, independent of the presence or absence of gap junctions, but firing frequency was reduced in the connected case. If only the interactions between directly coupled neighbors are measured, or a subnetwork is characterized, a small synchronization peak is apparent, as observed in the 10 FS network (results not shown). Nonetheless, there is no global synchronization in the larger network. Thus, the results using a 10 FS neuron network are not due to network size.

Mechanisms underlying the changes in spiking patterns

Depending on the synaptic input, the addition of gap junctions can remove, delay, or even add spikes (Fig. 2A). Despite the fact that the current always flows away from the more depolarized neuron, a range of different spike changes can occur as illustrated in Figure 4. The left column shows a reference FS interneuron pair that is devoid of gap junctions, and the right column displays the same neuron pair with gap junctions on proximal dendrites (0.5 nS). If an FS interneuron that originally spiked as a result of synaptic inputs is electrically coupled to a neuron that does not receive any input, the charge lost to the neighbor can bring the first neuron below threshold and thus prevent spiking (Fig. 4A). The picture changes if the simulations are repeated, but this time the neighbor also receives some subthreshold depolarizing synaptic input. The addition of a gap junction now leads to the transfer of some charge as before from the first to the second neuron, but slightly less than before since the second neuron is also depolarized. Thus the first neuron may still spike, but since the neighboring neuron also received synaptic input, the additional current through the gap junction brings the second neuron above threshold (Fig. 4B). Thus, depending on the degree of activation of nearby neurons, the addition of gap junctions can both add or remove spikes. Figure 4C shows that there does not have to be a spike in either neuron for gap junctions to add a new spike. Here the two neurons are activated one after the other, neither reaching threshold. The addition of gap junctions to this scenario transfers charge from the first neuron activated to the second neuron, which is then able to spike. In rare cases this spike may in turn evoke a spike in the first neuron also.

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Figure 4.

Mechanisms of spike appearance and disappearance in the electrically coupled networks. A, Removal of a spike. In the electrically coupled case the neuron receiving synaptic input loses charge to its nondepolarized neighbor, resulting in a subthreshold response in both neurons. B, Spike-induced triggering of a synchronized spike. The addition of gap junctions can sometimes lead to a sharing of the depolarization with the neighboring neuron, converting its subthreshold depolarization into a spike. C, Addition of a spike due to preceding depolarization of coupled neighboring neurons. First one neuron is depolarized by synaptic input, but not enough to cause a spike. In the presence of gap junctions some of this depolarization is transferred to the neighboring neuron, which brings it closer to threshold, sometimes allowing it to spike when it simultaneously receives additional synaptic input. D, Change in spikes caused by the addition of gap junctions. Solid trace shows the spikes shunted away (case A), dashed line those appearing spontaneously (case C), dash-dotted lines the spikes that are triggered by a spike in a neighboring neuron (case B), and gray dotted trace shows the net reduction in spikes. Note that the addition of spikes (cases B and C) is less common than the removal of spikes, producing a reduction in overall spiking activity with gap junctions.

A quantification using a similar classification as illustrated in Figure 4A–C can be applied to the modeled 10 FS network when activated by up-state synaptic inputs. Figure 4D shows that overall the reduction in spikes (solid line; case A) is larger than the addition of spikes, and spikes appearing spontaneously (dashed line; case C) due to shifting of charge between electrically connected nonspiking neurons are more common than those triggered by spikes in neighboring neurons (dash-dotted line; case B). As gap junction conductance is increased, more spikes are shunted away than added, resulting in a successively larger net reduction of activity (dotted line).

Highly correlated input maintains spiking activity

The reduction in spike frequency is a novel finding and has not been reported in cortical FS interneuron networks. To investigate the source of this difference, simulations are performed using current injection instead of synaptic activation. Since the current shunted through the gap junctions is dependent on the voltage difference between the electrically coupled neurons, shunting should be minimal if neighboring neurons receive identical input. Conversely, shunting should be evident if neurons receive different amounts of current injection.

Figure 5A shows how the I–F curve, produced using somatic current injections, for one FS model neuron depends on the activation level in a neighboring identical neuron when they are connected with a gap junction. If both neurons are injected with the same current, there is no change in firing frequency due to the presence of the gap junctions, because with identical cells and identical inputs there is no shunting in either direction due to symmetry. However if the neighboring neuron receives less current (50%, dashed line; no current, gray line; or hyperpolarizing currents, gray dashed line), then the first neuron will experience a reduction in firing. As the driving current of the first neuron increases, the dependence on the neighboring neuron's degree of activation decreases. This is due to the shape of the I–F curve for the single FS interneuron: as the current increment needed to increase the firing frequency (e.g., 1 Hz) increases higher up on the curve, shunting has a diminished effect on reducing firing frequency. Sodium inactivation and activation of Kv3.1/3.2 affect the shape of the I–F curve in the model. When the sodium and potassium have smaller (faster) time constants, the spike initiation and repolarization are faster; thus, the slope of the I–F curve is steeper and shunting decreases less with higher current injection compared with the control case.

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Figure 5.

Spike frequency reduction depends on input coherence between connected neurons. A, I–F curve for one FS interneuron connected to an identical neighboring FS interneuron with a gap junction. The neighboring neuron receives identical current injection (solid line), half amplitude (dashed line), no current (gray), or hyperpolarizing current (gray dashed). The firing frequency decreases as the difference in current between the two neurons increases. B, Reduction in firing frequency in the 10 FS neurons synaptically activated depends on the correlation of the voltage deflections in neighboring neurons. An increase in correlation between the synaptic input to the FS interneurons leads to a smaller reduction in firing frequency (see also supplemental Fig. S3A, available at www.jneurosci.org as supplemental material). C, Current through the gap junctions during a spike. Increased correlation between the synaptic input to the interneurons produces a smaller difference in the potential across the gap junction. This leads in particular to smaller outward currents through the gap junctions before a spike (arrow), as seen in the spike centered plot of the current. D, Ten identical FS interneurons driven by constant current injections in the range of 55 pA to 65 pA. Proximal gap junctions (0.5 nS) are added at 250 ms and removed again at 500 ms. The population synchronizes easily in the presence of gap junctions, and desynchronizes when they are removed. Note that the same result is achieved with varied FS excitability and identical current injections to all neurons (data not shown).

To test the prediction that nonsynchronous synaptic input leads to spike reduction in the FS network while synchronous (or more coincident) synaptic input does not, a 10 FS interneuron network was simulated with various correlations (for definition of correlation, see Materials and Methods) among the synaptic inputs to different neurons. Figure 5B shows that the reduction in firing frequency is higher when the input has low or no correlation between the electrically coupled FS interneurons. For a successive increase in the coincidence of activated synapses between the neighboring cells in the network, the shunting decreases and finally disappears. Consistent with these results, Figure 5C illustrates that the outward current through the gap junction just before a spike is increased for lower input correlations, making it harder for the FS interneurons to spike. This result does not depend on the method used to change input correlation. Similar qualitative and quantitative effects are seen if all cells in the network are activated at the same times and at the same locations in the dendritic tree. Nonsynchronous inputs are then produced by jittering the activation times at each synapse (see supplemental Fig. S3, available at www.jneurosci.org as supplemental material). Thus, the novel finding of a decrease in spike frequency due to gap junctions is due to lack of correlation among synaptic inputs compared with typical current injection protocols.

To further demonstrate the role of input correlation, and to document that the difference between our results and prior results is due to the use of uncorrelated synaptic activation, simulations of spike synchronization are repeated in response to current injection. For constant current injections above threshold the FS neurons spike regularly and the neighbors are also continuously depolarized, which means that the current losses through gap junctions are minimal, as in Figure 5A (uppermost curve). This suggests that the synchronizing effect of gap junctions would dominate during current injections. Simulations show that, similar to results in Figure 2D for the two neuron network, gap junctions synchronize networks of FS neurons driven by current injection (Fig. 5D). In networks activated with current injections spike frequency can even increase with an increased gap junction conductance (supplemental Fig. S4A, available at www.jneurosci.org as supplemental material), opposite to that seen with synaptic activation. Therefore, the observation that gap junctions reduce spike frequency more so than enhancing synchrony is due to the uncorrelated nature of synaptic input, not due to unusual properties of striatal FS interneurons.

Spike frequency reduction due to gap junctions depends on synaptic input intensity

Just as spike frequency reduction depends on current injection amplitude, it also depends on synaptic input frequency. As a neuron approaches spike threshold the voltage difference across the gap junction increases, leading to an increased outward current through the gap junction. Similarly, increased synaptic input frequency implies more membrane potential fluctuations, producing a larger average voltage difference across the gap junction (Fig. 6B) and thus more shunting on average. Thus, an increase in synaptic inputs is predicted to increase spike frequency reduction by these mechanisms. However, this increase in voltage across the gap junction is sublinear (Fig. 6B, inset), because when inputs arrive more frequently the degree of simultaneous depolarization also increases, reducing the shunting. To evaluate these competing mechanism, simulations were performed to see whether spike frequency reduction decreased with an increase in input frequency, similar to current injection, or increased due to larger voltage differences.

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Figure 6.

Spike frequency reduction decreases as synaptic activation increases in the network with gap junctions. A, At successively higher synaptic activation frequency, a smaller fraction of the spikes is removed in the presence of gap junctions in the 10 FS interneuron network. The fraction removed is the reduction in firing frequency in the network with gap junctions, divided by the firing frequency in the network devoid of gap junctions. B, As the activation frequency per synapse increases (resulting in more spikes in the network), so does the average voltage difference across the gap junction (inset) and the distribution widens, giving rise to larger average currents across the gap junction. C, Despite the average increase in the current through the gap junction during the whole simulation, just before a spike the current through the gap junctions is slightly smaller for high input frequencies. This is because with increased synaptic activation frequency it is more likely that the electrically coupled neighbor is depolarized at the same time. This, together with the flattening shape of the I–F curve (see Fig. 5A), explains the decreased reduction in spike frequencies for higher synaptic input frequencies. D, Change in spike frequency caused by addition of gap junctions as a function of synaptic input activation frequency. Solid trace shows the shunted spikes (see also Fig. 4A), dashed line shows those appearing spontaneously (see also Fig. 4C), and dash-dotted line represents the spikes that are triggered by a neighboring neuron spike (see also Fig. 4B). The gray dotted trace shows that the net reduction in spikes levels off with higher input intensities. E, Increased synaptic activation leads to higher relative spike synchronization. At the higher input, a spike in one neuron more easily triggers a synchronized spike in a neighboring neuron. Also the rate by which spikes are shunted away levels off. The synchrony in the network with gap junctions is higher than the shuffled control traces (where direct interactions mediated by gap junctions are removed). Spikes are considered synchronous if they occurred within 5 ms of each other. Note that even though the reference network devoid of gap junctions spikes more and thus by chance has higher occurrences of spike pairs, spike synchronization is even higher in the subpopulation of directly coupled neighbors despite a lower average firing frequency.

Figure 6A shows that, similar to the result with current injection, the fraction of spikes removed by the presence of gap junctions decreases with increased synaptic input frequency. Before a spike, the neuron is close to threshold and the connected neighbor is also more depolarized due to the increased synaptic input frequency. This results instead in a smaller voltage difference across the gap junctions just before the action potential and thus a decreased outward current for higher input frequencies, as shown in the spike centered plot in Figure 6C. Consequently, the increase in removed spikes is slower than the increase in total spike frequency. In addition, at higher input frequencies a spike is triggered more easily in a neighboring neuron (Fig. 6D, dash-dotted line). The number of added spikes increases proportionally more than the number of spikes removed; thus the net reduction in firing frequency levels out for high synaptic input frequencies. A constant spike frequency reduction translates into a decrease in the proportion of removed spikes because total spike frequency increases with synaptic input frequency.

The relative decrease in spike reduction with increased input synaptic activity may be accompanied by an increase in synchrony in networks with higher synaptic input. Figure 6E shows that the increase in number of synchronized spike pairs (within 5 ms) per neuron pair in the 10 neuron network with gap junctions is greater (solid line) for higher input frequencies, than what is predicted by chance for the same spike frequencies (see shuffled traces, dashed line). If the analysis is reduced to only the directly coupled neighbors, spike synchronization even overcomes the shunting and the average number of spike pairs is higher (dotted line) than that in the network devoid of gap junctions (dash-dotted line).

Correlation detection

What is the possible function for a population of electrically coupled FS interneurons, given that gap junctions reduce firing frequency with uncorrelated inputs, and synchronize firing in response to correlated inputs? The final set of simulations evaluates the response of an FS network to a transient increase in correlation, as may occur during a behavioral task. Figure 7A shows that a striatal FS network of 10 neurons with gap junctions is able to detect rapid changes in correlations between the synaptic inputs to the different neurons. The FS network nearly doubled its firing during a short period (20 ms) of correlated synaptic inputs to neighboring neurons. Note that an FS network devoid of gap junctions would have the same spike frequency throughout because synaptic input frequency is not altered. This indicates that gap junctions allow the FS network to detect correlated activation patterns across the population, even brief periods of correlation, and may relay information on correlation state of the cortex.

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Figure 7.

Coincidence detection in FS networks. A, An FS network with gap junctions can act as a population detector of coincident synaptic inputs. A sudden increase in correlation between the synaptic activation times in the FS interneurons (during 20 ms) is detected by increased spiking in cells of the 10 FS interneuron network. For the unconnected reference case, there is no change in the firing frequency during the time of increased network input correlation between the neurons, because the average frequency of synaptic activation is kept constant. B, Illustration of a 125 FS neuron network with proximal gap junctions. The center neurons receiving 20 ms of correlated input are marked. C, Coincidence detection in the larger 125 FS network. Here, a group of 27 neurons share correlated input for 20 ms, the remaining 98 neurons have no change in the correlation between themselves. The 27 neurons show an increase in firing during the 20 ms if they are gap junction coupled, as was also seen in A. D, A cross-correlogram showing weak local but no global synchronization. Directly coupled neurons show weak synchronization; however, as the subset is increased to include neighboring neurons not directly coupled, the synchronization disappears, indicating that there is no global synchronization.

The results of the 10 FS neuron network results were verified in a larger network of 125 FS neurons, corresponding to a cube of striatum with sides 0.5 mm. To demonstrate correlation detection, only a group of 27 neurons [3 × 3 × 3 cube (Fig. 7B)] were given correlated input during the 20 ms window; all other neurons continued to receive uncorrelated inputs. Similar to the results with the small network, a transient increase in synaptic input correlation produces a brief increase in firing for the gap junction coupled case (Fig. 7C). A cross-correlogram generated for various sized subnetworks within the larger 125 FS network shows that the synchronization is local. As pairs within an increasingly larger subset of the 125 FS network are included in the analysis the weak synchronization peak seen for directly connected neighbors decreases (Fig. 7D). This indicates that there is no global synchronization in the network. Another role proposed for gap junctions is to generate propagating waves of spikes in a network. Such wave activity is not seen in the FS network, because a spike in a reference neuron is rarely followed by a spike in a gap junction coupled neighboring neuron. A spike in a striatal FS neuron is followed by <0.2 spikes within 10 ms in their gap junction connected neighbors for proximal gap junctions and 0.3 spikes within 10 ms for distal gap junctions (supplemental Fig. S1E, available at www.jneurosci.org as supplemental material). This lack of global synchronization or propagated activity is in accordance with the relatively sparse striatal gap junction connectivity (Galarreta and Hestrin, 2001b).