Electrical synapses and transient signals in feedforward canonical circuits

As information about the world traverses the brain, the signals exchanged between neurons are passed and modulated by synapses, or specialized contacts between neurons. While neurotransmitter-based synapses tend to be either relay excitatory or inhibitory pulses of influence on the postsynaptic neuron, electrical synapses, composed of plaques of gap junction channels, are always-on transmitters that can either excite or inhibit a coupled neighbor. A growing body of evidence indicates that electrical synapses, similar to their chemical counterparts, are modified in strength during physiological neuronal activity. The synchronizing role of electrical synapses in neuronal oscillations has been well established, but their impact on transient signal processing in the brain is much less understood. Here we constructed computational models based on the canonical feedforward neuronal circuit, and included electrical synapses between inhibitory interneurons. We provided discrete closely-timed inputs to the circuits, and characterize the influence of electrical synapses on both the subthreshold summation and spike trains in the output neuron. Our simulations highlight the diverse and powerful roles that electrical synapses play even in simple circuits. Because these canonical circuits are represented widely throughout the brain, we expect that these are general principles for the influence of electrical synapses on transient signal processing across the brain. Author Summary The role that electrical synapses play in neural oscillations, network synchronization and rhythmicity is well established, but their role neuronal processing of transient inputs is much less understood. Here we used computational models of canonical feedforward circuits and networks to investigate how the strength of electrical synapses regulates the flow of transient signals passing through those circuits. We show that because the influence of electrical synapses on coupled neighbors can be either inhibitory or excitatory, their role in network information processing is heterogeneous.. Because of the widespread existence of electrical synapses between interneurons as well as a growing body of evidence for their plasticity, we expect such effects play a significant role in how the brain processes transient inputs.


Introduction
3B, black lines). As electrical synapse strength increases, for ∆tinp < 4 ms we noted increased delays in 119 Int1 spiking due to increased leak from the electrical synapse, but decreased delays in Int2 spiking due to 120 the spikelet it received from Int1; together these effects result in a synchronizing effects of electrical 121 coupling in this regime of input timing. Together, these changes in the timing of inhibition allowed for 122 increased PSP peaks in Tgt (Fig. 3C), but dramatically decreased of the integration window in Tgt for 123 ∆tinp between 2 and 4 ms (Fig. 3D), and increased the excited AUC (Fig. 3E). Hence, within Model 2a, 124 electrical coupling enhanced Tgt input integration for specifically timed inputs, with increased PSP peaks 125 within a narrowed integration window of the PSP. In the same circuit, for more than ~4 ms of ∆tinp, small 126 increases in electrical synapse strength only served to increase leak in Int2 well after the spikelet had 127 finished, ultimately delaying its spike. Larger increases in electrical synapse strength, however, allowed 128 for the spikelet from Int1 to directly elicit spiking in Int2, which spiked earlier than it might have 129 otherwise (Fig. 3B, lower right). The net effect allows the PSP in Tgt to increase by small amounts in 130 peak ( Fig. 3C) but the shortened integration window, resulting from the earlier spike in Int2, effectively 131 prevents summation of the two Src inputs in Tgt. Thus, the varied effects of increased leak or excitatory 132 spikelets resulting from an electrical synapse with varied strengths within even a simple circuit (Model 133 2a) increases flexibility for responses to signals passing through that circuit, compared to the same circuit 134 with single interneuron (Model 1b). 135 A direct comparison between Model 1b, with one interneuron, and the most-strongly coupled 136 results of Model 2a, is not apt, however: maintaining the synaptic parameters (see Methods) for Models 137 1b and 2a, meant that the total inhibitory conductance from Int to Tgt was doubled while the excitatory 138 conductance from Src to Int was halved (see mismatch of dashed black lines and yellow lines in Fig. 3B). 139 To explore a more consistent comparison of these two models, we ran the simulation again as Model inhibitory input compared to Model 2a (compare Fig. 3 (Fig. 4C), and the area under the excitatory part of the PSP was also expanded for 156 stronger GGABA→Int (Fig. 4D). Further, in the presence of stronger reciprocal inhibition, increased electrical 157 coupling shifted the integration windows and AUCs to favor larger values of ∆tinp (Fig. 4C, D). Thus, 158 electrical and inhibitory synapses compete for impact on the PSP. 159 Thus, similar to our previous demonstration [23], electrical synapse between inhibitory 160 interneurons and their impact through inhibitory synapses onto a target work together in diverse ways to 161 control the processing of transient signals passing through a circuit. We also note that changes in 162 electrical synapse strength can potentially halve or double the PSP (Fig. 3C1)

167
To study a population of Tgt neurons of separate channels, we embedded 50 units of the 168 canonical circuit into a network (Model Na, Fig. 5A), with electrical coupling between the Int neurons. To 169 each Src neuron in the layer of 50, we provided identically sized inputs drawn from Gaussian 170 distributions of input times with a standard deviation of inp (Fig. 5B). In order to study spiking rather 171 than subthreshold activity in the Tgt population, we increased GAMPA from the Src to the Tgt (GAMPA→Tgt) 172 and decreased GAMPA from Src to Int (GAMPA→Int) in each unit, along with additional increases to Tgt 173 excitability (see Methods) in order to elicit spiking in the Tgt neurons within 5-6 ms of Src spiking 174 We compared our two network models by plotting the gain in spiking properties due to electrical 188 synapses relative to the uncoupled case (Gelec = 0) across input time distributions for the Int (Fig. 7A) 189 and Tgt (Fig. 7B) populations. While the input was Gaussian, the Tgt distributions were often not 190 Gaussian; therefore, we measured mean spike times, standard deviations of spike times, maximal density 191 and total density of spiking, along with the relative latency. We observed that most of the effects that 192 electrical synapses exerted on the output Tgt distribution were strongest for small inp. We quantified the mutual information between the spike time distributions of Src and Tgt, as well 207 as the transmission efficiency from Src to Tgt (Fig. 8). For wider input distributions, we expected that 208 mutual information would be larger due to increased entropy in both the input and output. Without any 209 reciprocal inhibition within the Int layer, electrical coupling contributed to decreases in Src and Tgt 210 mutual information, and more so with smaller input distributions (Fig. 8A, top row), as a result of 211 dispersed Tgt spiking (cf. Fig. 6). Hence the transmission efficiency also decreased with electrical 212 coupling, with more notable decreases with smaller inp (Fig. 8B, top row). The largest decrease was 213 roughly 35%. 214 For the uncoupled case with no reciprocal inhibition, each Src elicited a single spike within its 215 and resulted in maximal mutual information and 100% transmission efficiency (Fig. 8A&B, top row). As 217 interneuron reciprocal inhibition was added and spiking in the Int population decreased, some neurons 218 within the Tgt distribution were able to spike much faster but with less uncertainty, creating a smaller 219 distribution (Fig. 6B) and smaller entropy; as a result, reciprocal inhibition led to decreases in both 220 mutual information and transmission efficiency. Electrical synapses in a local network regulate subthreshold summation of inputs in the target 233 neuron. Stronger electrical coupling allowed the target neuron to integrate its source inputs with higher 234 summed PSP peaks, yet limited time windows for further inputs to summate. Furthermore, changes in 235 electrical coupling in a local network of interneurons, possibly via electrical synapse plasticity, led to 236 more flexibility in regulating subthreshold summation than a global inhibitory neuron with varied 237 excitability. However, our results also showed that reciprocal inhibition between the electrically coupled 238 interneuron pair expanded the integration window and the area under the curve of the target PSP, 239 especially for relatively larger differences in input timings. This suggests that the competition between the 240 electrical coupling and reciprocal inhibition within the local interneuron networks could regulate the 241 ability for the target neuron to either be a coincidence detector or an integrator. 242 At a network level, we find that electrical coupling of the interneuron population modulates the 243 target population activity over different distribution of input timings. Similar to the subthreshold effect, 244 increase in electrical synapse strength led to a more delayed, yet more concentrated activity in the 245 interneuron population, effectively synchronizing their activity. Hence, stronger electrical coupling 246 allowed stronger earlier response of the target layer activity but weaker response afterwards. However, 247 because the activity of the interneurons was limited within a smaller temporal window due to electrical 248 coupling, inhibition towards the target population was limited in time, hence the output activity was more 249 sustained compared to uncoupled cases. As a result, electrical coupling allowed earlier yet more spread 250 out responses and effectively reduced both the mutual information and the transmission efficiency, but 251 mainly for small input distribution sizes. One implication of this is, although corrupting the integrity of 252 input-output temporal coding, electrical coupling between the interneurons could increase temporal 253 heterogeneity as inputs coming from different sources arrive too closely with each other. On the contrary, 254 reciprocal inhibition within this population decreased the interneuron activity, which led to much less 255 decrease of target response in presence of electrical coupling. However, for closely-timed input 256 distributions, the target temporal code distribution was also changed towards less output timing spread, 257 especially for electrically uncoupled or weak coupled cases, resulting in loss of mutual information and 258 transmission efficiency in the presence of reciprocal inhibition.

External input to Src neurons: 299
In all cases, only Src received external input: a brief 20-30 ms of 200-300 pA DC input, 300 sufficiently to evoke a single action potential in in Src (eq. 7). For Models 1b, and 2a, a norm , b, we varied 301 the arrival time differences between input to Src2 and input to Src1 as tinp from 0 to 20 ms. For Models 302 Na and Nb, timings of Src inputs were drawn from a normal distribution with standard deviation as inp in 303 which we varied from 1 to 10 ms. 304

Synaptic connections and different network configurations: 306
For synaptic inputs, neurons can either excite each other via AMPA synapses, inhibit each other 307 via GABA synapses or couple with each other via electrical synapses, as described in eqs 8-11. Src sends 308 AMPA excitatory input to Tgt and Int separately sufficiently to drive Int to spike and for Tgt to receive a 309 noticeable EPSP (Models 1a -2b) or to spike (Models Na, Nb). Int sends GABAergic inhibitory input to 310 Tgt. In our simulations, Ints are either only electrically coupled (Models 2a, 2a norm and Na) or both 311 electrically coupled and reciprocally inhibit each other (Models 2b, Nb). 312 (8) ( ) = + + Electrical synapses were implemented as symmetric linear resistance, as shown in eq. 9. For two 314 coupled Int neurons, we varied the electrical synapse conductance of from 0 -8 nS (unless otherwise 315 noted), corresponding to coupling coefficients (cc.) of roughly 0 -0.33. For larger coupled networks 316 (Models Na,b), Ints are electrically coupled homogeneously in an all-to-all manner (Fig. 5A, 6A), with 317 each coupling conductance scaled to the number of Ints as Gelec = Gelec /NInt. 318 Chemical synapses were implemented with a single exponential decay as described in eqs. 10-11, 320 and implemented following the example of The conductance parameters were either fixed or varied as in Table 2

Subthreshold investigation: 342
For subthreshold investigations (Fig. 1 -4), we obtained the net postsynaptic potential (PSP) of 343 the Tgt neuron and quantified the peak potential, duration (or integration window) and area under the 344 curve (AUC) of the positive portion of the PSP (Fig. 1B). 345

Network activity investigation: 346
For each set of parameter , we obtained the raw distribution of spike times X(C{Xk(ci)} 347 population C aggregated from all Xk(ci), which is the spike time array of neuron ci in simulation k th . To easily compare between different initial input distributions, we generally normalized all 353 quantifications to the Src population (Fig. 5 -7). More specifically, for each XC = X(Cwe defined 354 normalized mean spike time as the difference between the mean of XC and that of XSrc. The normalized 355 standard deviation was the standard deviation of XC normalized over the standard deviation of XSrc. 356 For each XC = X(Cwe calculated the spike density from the smoothed histograms of spikes 357 times. More specifically, each array of spike times XC was histogrammed with a bin width that equals to 358 one-tenth of the inp in order to avoid under-sampling with small inp and over-sampling with large inp; 359 then it was smoothed by convoluting with a Hanning window of size 20 to obtain the un-normalized 360 density dC(t). For visualization, the spike times were translated relative to the mean Src spike time 361 distributions, whereas the densities were scaled over the maximum density of the Src distribution to 362 calculate the normalized density DC(t). Note: neither DC(t) nor dC(t) represented estimated probability 363 density function, because the smoothed histograms were not normalized by their number of samples. 364 For quantification comparison, we defined normalized maximum density as the maximum density 365 of dC(t) normalized over that of dSrc(t). The normalized total response was calculated by normalizing the 366 area under the curve of dC(t) over that of dSrc(t) (note: neither DC(t) nor dC(t) represented estimated 367 probability density function, hence AUC was not necessarily 1). Lastly, the relative latency was defined 368 as the time point which dC(t) reached 10% of maximum Src density, scaled by the standard deviation of 369 Src spike time distribution XSrc.
Additionally, gain of a particular property Q of a spike time distribution due to a parameter set  371 was defined as the difference between itself and the same property when the electrical coupling parameter 372 in set equals to 0, in other words Gain[Q()] = Q() -Q(electrically uncoupled). 373

Mutual information and transmission efficiency: 374
For network investigation, we also quantified the mutual information and transmission efficiency 375 between the Src and Tgt population spike time distribution (Fig 8). Here we considered Src to be an input 376 channel, whereas Tgt to be an output channel. 377 For each XC = X(Cwe estimated the probability function p(C) by histogramming the spike 378 time arrays XC with a fixed bin width of 0.01ms. The joint probability function p(Src, Tgt) of Src and Tgt 379 was also estimated by histogramming all the spike time pairs of (XSrc XTgt) with similar bin widths. We 380 consider any missing spike (for example with cases that Srci did not induce any spike in Tgti due to certain 381 network configurations or parameter set) to take the value of max(XC) + 2XC) to account for more 382 accurate estimation of the marginal distribution of both Src and Tgt. Taking these cases out led to 383 misrepresentation of the marginal distribution and join distribution. nS, from top to bottom). The top row of each set is Model Na (Fig. 5), with ΣGGABA→Int = 0 while the second, 575 third and fourth rows represent Model Nb (Fig. 6), with ΣGGABA→Int ≠ 0. The first column of each heat map 576 always represents the uncoupled case, with 0 gain as indicated in white (see Methods). Within each heat 577 map, electrical coupling ΣGelec is varied on the x axis and input distribution size σinp is varied on the y axis.