Weak and equally balanced synaptic inputs to interneurons in the CA1 hippocampus characterize in vivo rhythmic states

Brain coding strategies are enabled by the balance of synaptic inputs that individual neurons receive as determined by the networks in which they reside. Inhibitory cell types contribute to brain function in distinct ways but recording from specific, inhibitory cell types during behaviour to determine their contributions is difficult. In particular, the in vivo activities of vasoactive intestinal peptide-expressing interneuron specific 3 (IS3) cells in the hippocampus that only target other inhibitory cells are unknown at present. We perform a massive, computational exploration of possible synaptic inputs to IS3 cells using multi-compartment models and optimized synaptic parameters. We find that asynchronous in vivo-like states that are sensitive to additional theta-timed inputs exist when excitatory and inhibitory synaptic conductances are equally balanced and there are low amounts of correlated inputs. Thus, using a generally applicable computational approach we predict the existence of balanced states in hippocampal circuits during rhythmic activities.


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A dizzying array of morphological, molecular, and electrophysiological details for di erent cell 25 types exist and appropriate classi cations are being determined (Zeng and Sanes, 2017). How 26 these di erent cell types contribute to brain function is challenging to determine, but it is clear 27 that a homeostatic balance of cell excitability, together with excitatory and inhibitory synaptic 28 inputs is essential for normal brain function ( to confer computational bene ts, with inhibition being recognized as a crucial shaper of these 31 asynchronous activities (Isaacson and Scanziani, 2011;Treviño, 2016). Recently, in directly tting a 32 deterministic ring network model to several sets of in vivo multi-neuron data, it was found that 33 the intrinsically generated variability obtained in experiment was mainly due to feedback inhibition 34 (Stringer et al., 2016). In essence, it is critical to understand these inhibitory components. However, 35 we are cognisant of the much more diverse nature of inhibitory cells relative to excitatory cells in 36 our brains, despite their smaller overall numbers ( relative to in vitro studies. Further, the smaller numbers and sizes of inhibitory cells as well as being 40 in hard to access locations create additional challenges for identi cation and patching. Indeed, the 41 activity of several inhibitory cell types in vivo remains unknown. 42 One such cell type that su ers from these di culties are hippocampal CA1 interneuron spe-43 ci c type 3 (IS3) interneurons. IS3 cells are a vasoactive intestinal polypeptide-positive (VIP+) and 44 calretinin-positive (CR+) cell type with cell bodies found in the stratum radiatum and stratum pyra- 45 midale of the CA1 (Acsády et al., 1996a,b; Gulyás et al., 1996;Chamberland and Topolnik, 2012), 46 an area in CA1 more predominantly populated by pyramidal cells as well as some parvalbumin-  (Destexhe and Paré, 1999). To move toward an understanding of IS3 cell contributions to brain 71 function, we use a computational approach by necessity, as recording from these cell types in vivo is 72 not possible at the present time. We explore what excitatory and inhibitory inputs could bring about 73 asynchronous states in IS3 cells and also be sensitive to theta frequency inputs as has been shown 74 in vitro (Tyan et al., 2014). We nd that excitatory and inhibitory synaptic currents need to be equally 75 balanced with correlated inputs (common inputs) and small numbers of excitatory and inhibitory 76 synapses and low presynaptic input ring rates. This work contributes to an understanding of 77 excitatory and inhibitory balances in hippocampal circuits. 78

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Due to the diversity and details of inhibitory cells it is challenging to understand their roles and 80 contributions in brain circuits and behaviours. We use a computational approach to simulate in 81 vivo activities so as to determine how much and what balance of excitatory and inhibitory synaptic 82 inputs inhibitory cell subtypes might receive in the behaving animal. We illustrate this in the Figure 1 83 schematic for IS3 cells that we examine here. 84 We use our previously developed multi-compartment models of IS3 cells in which the electro-   Color scheme is the same as in B. Since this plot shows a common input scenario, note that the 'lines' in the raster plot are actually a series of dots (9 dots for excitatory and 4 dots for inhibitory) representing groups of synapses receiving the same (i.e., common) presynaptic spike trains.

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Methods section. To perform parameter explorations of input regimes that yield in vivo-like states, 90 we rst considered the types of layer-speci c excitatory and inhibitory inputs to IS3 cells. Within 91 the hippocampus, IS3 cells have dendrites that extend into the stratum radiatum and stratum 92 pyramidale, which allows them to receive excitatory inputs from both CA3 and entorhinal cortex.  HC metric = 3) is also shown in Figure 2. 115 In Figure 3 we show results from our full set of parameter explorations using SDprox1 and SD-116 prox2 models and with common or independent inputs. From our CBDR plots we can immediately 117 observe that common excitatory inputs promote in vivo-like or HC states since there are more white 118 pixels (HC metric=3) in the two right columns of A clutter-based dimensional reordering (CBDR) plot of a parameter exploration for the SDprox1 model with common excitatory and inhibitory inputs. Excitatory input parameters are indicated by the scale bars on the y-axis and inhibitory input parameters are indicated by the scale bars on the x-axis, with parameter ranges shown in parentheses. Each pixel represents a 10 second simulation where the color of the pixel indicates the high-conductance (HC) metric score for the particular set of parameters. Using the scale bars, one can extrapolate the precise parameters of each individual pixel. Note that the height and width of the pixels are of equal size to the lengths of the smaller scale bars on the y-and x-axes. For example, going from bottom to top at an interval of the length of the larger scale bar, the excitatory spike rate increases in increments of 5 Hz. Likewise, going from bottom to top at an interval of the length of the smaller scale bar, the number of excitatory synapses increases in increments of 18 synapses, until it reaches the length of the larger scale bar, at which point it restarts the count. Similarly, the inhibitory spike rate increases in increments of 10 Hz going from left to right, and the number of inhibitory synapses increases in increments of 4 synapses. (Right): Output from one of the parameter sets (HC metric=3, white pixel) as indicated by the arrow. The top subplot shows the 10 second simulated voltage trace from the pixel indicated in the Left CBDR plot. Bottom subplot shows the raster plot of the presynaptic inputs where inhibitory inputs are shown in red, proximal excitatory inputs are shown in blue and distal excitatory inputs are shown in green. Note that these plots do not contain any information regarding the synaptic locations of the inputs, which are chosen randomly.        are approximately equal. We note that since synaptic inputs are not present at the same location 148 and our metrics do not take spatial aspects into consideration, an EI metric value of zero does not 149 necessarily mean that inputs are perfectly balanced in terms of amount and spatial spread. In To determine subspaces of parameter sets as well as uncover relationships between HC states 170 and balances between excitation and inhibition, we divided the parameter space into 16 pools by 171 splitting each parameter into high and low ranges as speci ed in Table 1. The acronym naming 172 scheme we use is given in Table 2 and we use these acronyms in subsequent gures. 173 In Figure     It is interesting to note that having a larger amount of inputs did not necessarily result in 185 higher mean spike rates. 186 We plot our EI metrics for the 16 pools in  202 To determine what sort of inputs IS3 cells might receive in vivo, we perform a deeper exploration of 203 our parameter sets. That is, despite already doing millions of simulations (see Methods), we perform 204 additional simulations to probe and understand the robustness of our HC or in vivo-like states. We 205 do this by obtaining a representative scenario from each pool that is robust, as determined by 206 using a procedure that cycles through several random seeds. The procedure is described in the 207 Methods, and in Figure 6 we show the voltage output from a representative scenario from each 208 pool that is robustly HC for a given set of random seeds. Also shown in Figure 6 are raster plots 209 of the excitatory and inhibitory synaptic inputs. The synaptic input parameters for each of the 210 representative scenarios is given in Figure 6 Table 2, labels L or H represent "low" or "high" parameter ranges, NI or NE represents "number" of "inhibitory" or "excitatory" synapses, and IS or ES represents "inhibitory" or "excitatory" "spike" rates. The smaller axes refer to each quarter of the entire large square. Axis labels are the same for SDprox1 and SDprox2.  Table 1).       given pool (see Figure 6). Note that excitatory common inputs are plotted on the x-axis and inhibitory common inputs are plotted on the y-axis.

Moving closer to predicting synaptic inputs to IS3 cells in vivo
(x-axis and y-axis ranges: 1 to 10 common inputs).

Conductance (nS)
Current (pA) Figure 8. Inhibitory or excitatory currents (y-axes: -1100 pA to +1100 pA) and conductances (y-axes: 0 nS to 16 nS) recorded when excitatory or inhibitory currents are respectively removed completely (x-axes: 1000 ms to 10,000 ms). Top panels: excitatory (blue) and inhibitory (red) currents recorded in representative HC scenarios of the SDprox1 and SDprox2 models. Bottom panels: excitatory (blue) and inhibitory (red) conductances recorded in representative HC scenarios of the SDprox1 and SDprox2 models. The legend denotes inputs that would connect to IS3 cell proximal dendrites (P), inputs that would connect to IS3 cell distal dendrites (D), connections that are hypothetical (i.e. non-con rmed; C), as well as inputs with relative timing during the theta-cycle phase that are hypothetical (T). For the input populations with hypothetical relative theta-cycle timing, we estimated that they would spike 1_4 of a phase after either CA3 or EC3 input populations spike, depending on where the dendrites of those cell types are likely to be positioned. In this work we explored synaptic input parameter spaces that generate in vivo-like scenarios for IS3 314 cell models. We found that when there is a low amount of common inputs with equally balanced 315 excitatory and inhibitory conductances, in vivo-like states are present as well as a sensitivity to 316 additional theta-timed inputs. It was possible to have in vivo-like states with a larger amount of 317 input, but then there is an inhibitory dominance and the sensitivity to additional inputs is lost. 318 We found this to be due to lower input resistances with the larger synaptic input currents. It is 319 interesting to note that IS3 cells have been found to have high input resistances relative to other 320 cell types (Tyan et al., 2014). If IS3 cells are to preferentially control other inhibitory cell types at 321 theta frequencies in vivo as they do in vitro (Tyan et al., 2014), then it is reasonable to expect that IS3 322 cells need to be able to be recruited with preferred ring at theta to be able to exert this in uence. 323 Therefore, we predict that IS3 cells in vivo have weak inputs with equally balanced conductances. 324 We note that the vast majority of studies regarding in vivo excitatory-inhibitory balances have been    components of the HC metric. 434 We used a simple rst-order synaptic kinetic model to simulate our postsynaptic e ects. Al-435 though there is evidence that short-term synaptic depression exists for inputs onto VIP+ cells in 436 neocortex (Karnani et al., 2016b), it is unknown whether this is also the case for VIP+ IS3 cells 437 in hippocampus. Given the high levels of random activity in our simulations, it is unclear how 438 implementing synaptic depression would change our results, but it is likely that the overall synaptic 439 currents and conductances generated during higher spike rate input regimes will be smaller. As well, 440 in our synaptic model, we assume that there is a 0% failure rate (i.e. all common synapses succeed 441 at transmitting an EPSC/IPSC at the same time), which is unlikely to be the case. interneuron speci c characteristics as channel data speci c to IS3 cells is not available at present. 470 They include transient and persistent sodium channels and A-type and delayed recti er potassium 471 channels. Also, to re ect subthreshold activities observed in IS3 cells, intrinsic noise was included 472 as done in our previous models (Morin et al., 2010). Although it is expected that there are more ion 473 channel types in IS3 cells, we did not include any additional ones in building these models, but rather 474 focused on a minimal set since this was su cient to capture IS3 cell features. Direct immunological 475 evidence was obtained for delayed recti er potassium channels in dendritic portions of IS3 cells but 476 it is at present unknown about other channel types (Guet-McCreight et al., 2016). Here, we use two 477 of our models that captured IS3 cell electrophysiological features, one that has A-type potassium 478 channels in the dendrites (SDprox1) and one that does not (SDprox2). The speci cs of these models 479 with their somato-dendritic ion channel distributions are given in Table 3. 480 20 of 33 Synaptic model and parameters 481 We use excitatory and inhibitory synaptic parameters that were obtained from optimal ts to the 482 experimental data (Guet-McCreight et al., 2017). We use NEURON's Exp2Syn synapse model, which 483 describes synapses as two-state kinetic schemes: Where i is the synaptic current, G is the synaptic conductance, E is the reversal potential, V is the 486 membrane potential, weight is the synaptic weight, factor is a NEURON process that is used to to be Schae er collateral inputs from CA3 to IS3 cell proximal dendrites. Evoked EPSC responses 494 generated from stimulation in stratum lacunsom-moleculare were assumed to be inputs from 495 entorhinal cortex layer III (ECIII) to IS3 cell distal dendrites (Witter, 2010). 496 For excitatory synapse models, we applied a reversal potential of 0 mV, and applied a linear 497 distance-dependent weight rule, according to the weight of the best t for proximal dendrites (i.e. synapses spread across the dendritic arbor of the model. 539 We also investigate whether synaptic inputs are common or independent (Figure 1, Figure   540 Supplement 2A). Inputs that are common means that a presynaptic input forms multiple synaptic 541 inputs onto the IS3 cell model, and thus these common inputs are assigned identical spike trains.

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Independent inputs, simply means that each synapse has a unique spike train (i.e., a di erent 543 random seed is used). For common input parameter searches, we use numbers of 9 common  Table 4. 554 We perform our parameter search in the following manner. The locations of inhibitory and   In this example set of parameters, the common input scenario (Figure 1, Figure Supplement  To obtain a representative scenario from each pool, we use the following procedure: For each 594 pool, we go through the list of HC scenarios obtained for that pool (see Figure 4). The  and Paré (1999), we would expect a depolarization of at least 10 mV (i.e. an average membrane 645 potential greater than -60 mV in our model). We also know that neurons in vivo tend to show more 646 irregular spiking activity (Destexhe et al., 2003). We specify that the interspike interval coe cient of 647 variation (ISICV) must be greater than 0.8. This is based on a lower limit for the ISICV of neurons in 648 middle temporal cortex of alert macaque monkeys during constant-motion stimulation (Stevens 649 and Zador, 1998). Alternatively, for neurons in visual cortex and middle temporal cortex of cats and 650 macaque monkeys, it had also been found that ISICVs greater than 0.5 could be expected in vivo for 651 neurons that are spiking above 30 Hz (Softky and Koch, 1993). 652 Excitatory and inhibitory balance metrics 653 To get a sense of the balance between excitation and inhibition in our explorations, we de ne two 654 EI metrics. In the rst metric (Equation 6) Where N is number of synapses and f is spike rate for excitatory (E) and inhibitory (I) inputs. The  inhibitory inputs, the number of inputs is increased until the spike train PSD at 8 Hz is larger than 696 80 spikes 2 _Hz and there are less than 240 spikes. The results from doing this is given in Table 5. 697 Given these estimates, we apply 27 excitatory theta-timed synapses per layer-speci c excitatory 698 population (i.e. CA3 and ECIII, in Figure 9). Likewise, for inhibitory cell populations we chose to 699 apply 8 synapses per layer-speci c population (i.e. bistrati ed, neurogliaform, OLM, IS1, and IS2, in To ensure that this intrinsic noise in our models was not having a major e ect on our 709 our HC state scenarios, we re-did our simulations without the intrinsic noise while keeping the 710 random seeds for synaptic locations and presynaptic spike times xed. As shown in Figure 6, Figure   711 Supplement 3, this did not a ect the consistency of our HC scenario results. 712 Changing the number of common inputs 713 As described above, we estimate the number of common inputs to use for excitatory and inhibitory 714 synapses at 9 and 4 respectively, and our examinations focused on scenarios with common inputs 715 as they promoted in vivo-like states (see Results). However, these particular numbers are estimates 716 and it is unclear whether they might strongly a ect in vivo-like states. Thus, as described below, 717 we did further investigations using our robust, representative scenarios. We varied the number of 718 excitatory and inhibitory common inputs from 1 (i.e. independent) to 10, and in these additional  731 From this analysis, we further con rmed that the number of common excitatory inputs does in 732 fact have a strong in uence on our HC metric (Figure 6, Figure Supplement 4), whereas the impact 733 of the number of common inhibitory inputs is comparatively milder. Interestingly, the number 734 of common inputs shows an impact not only on the subthreshold membrane potential standard 735 deviation (Figure 6, Figure Supplement 6), but also on the mean subthreshold membrane potential 736 (Figure 6, Figure Supplement 5), and the mean spike rate (Figure 6, Figure Supplement 8).  intuitively,the subthreshold membrane potential appears to mildly decrease as the number of 738 common excitatory inputs is increased. This may be because when excitatory presynaptic spikes are 739 more distributed (i.e. more independent) the membrane potential will be more consistently larger. 740 On the other hand, when excitatory presynaptic spike times are correlated (i.e. more common), the 741 increase in membrane potential caused by synaptic events will be more occasional and transient 742 (and possibly even be partially removed from the analysis when spikes are cut from the traces), 743 leaving the mean subthreshold membrane potential more hyperpolarized. 744 As was observed previously (i.e. Example raster plot of the spike times of synapses using parameter values as shown. Color scheme is the same as in B. Since this plot shows a common input scenario, note that the 'lines' in the raster plot are actually a series of dots (9 dots for excitatory and 4 dots for inhibitory) representing groups of synapses receiving the same (i.e., common) presynaptic spike trains.   Table 1).  and conductances (y-axes: 0 nS to 16 nS) recorded when excitatory or inhibitory currents are not removed completely (i.e. the only measure taken is by changing the holding potential to their respective reversal potentials; x-axes: 1000 ms to 10,000 ms). Top panels: excitatory (blue) and inhibitory (red) currents recorded in representative HC scenarios of the SDprox1 and SDprox2 models. Bottom panels: excitatory (blue) and inhibitory (red) conductances recorded in representative HC scenarios of the SDprox1 and SDprox2 models. Inhibitory or excitatory currents (y-axes: -1000 pA to +1000 pA) and conductances (y-axes: 0 nS to 14 nS) recorded during HC input scenarios + theta-timed inputs (same protocol as in Figure 8; x-axes: 9000 ms to 10,000 ms). Top panels: excitatory (blue) and inhibitory (red) currents recorded in representative HC scenarios of the SDprox1 and SDprox2 models. Bottom panels: excitatory (blue) and inhibitory (red) conductances recorded in representative HC scenarios of the SDprox1 and SDprox2 models. Note that we zoomed in to the last second of the simulation in order to better visualize the time-scale of theta 1060 SDprox1 SDprox2