Interneuronal mechanisms of hippocampal theta oscillation in full-scale model of the CA1 circuit

The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct in terneuronal types spontaneously emerged from the isolated CA1 circuit without rhythmic inputs. Perturbation experiments identified parvalbumin-expressing interneurons and neurogliaform cells, as well as interneuronal diversity itself, as important factors in theta generation. These simulations reveal new insights into the spatiotemporal organization of the CA1 circuit during theta oscillations.


Introduction
gamma oscillation was phase-locked to the theta rhythm ( Figure 3A, 3B and 4C), as it is in the bio-1 logical CA1, representing cross-frequency coupling (Soltesz and Deschenes, 1993;Bragin et al., 1995; 2 Buzsáki et al., 2003;Jensen and Colgin, 2007;Belluscio et al., 2012). The highest amplitude of the 3 gamma oscillations in the model was observed at the theta trough (0 o /360 o ) in the pyramidal layer 4 LFP analog ( Figure 4C). Because the current study focused primarily on theta oscillations and exper- 5 imental data from the isolated CA1 are available only for the theta rhythm (Goutagny et al., 2009;6 Amilhon et al., 2015), the gamma oscillations were not examined further in the present study. 7 These results demonstrate that, in spite of gaps in our knowledge, our model was sufficiently well- 8 constrained by experimental data that it generated theta and gamma oscillations on its own, without 9 extrinsic rhythmic inputs or deliberate tuning of intrinsic parameters. 10 Although in this paper we generally refrained from deliberately compensating for missing param- 11 eters, it is of course possible to do so. For example, as mentioned above, no sufficiently detailed 12 information was available for certain interneuron types. Therefore, these lesser-known interneurons 13 were not included in the model, which meant that inhibition received by the pyramidal cells was 14 probably weaker than in the biological situation. Indeed, the pyramidal cells in our model described 15 above (Figures 3 and 4) tended to fire more than they typically do so during theta oscillations in 16 vivo (e.g., Soltesz and Deschenes (1993); Robbe et al. (2006)). Is the higher firing frequency of the 17 pyramidal cells related to the weaker inhibition? To answer to latter question, in a subset of the 18 simulations we artificially scaled up inhibition in the model to match the inhibitory synapse numbers 19 on CA1 pyramidal cells that were expected from electron microscopic reconstructions of pyramidal 20 cell dendrites and somata (Megías et al., 2001;Bezaire and Soltesz, 2013). The rationale for scaling 21 up inhibition in this way was that, as described in detail in Bezaire and Soltesz (2013), the estimates 22 of local inhibitory inputs to pyramidal cells were different when based on experimental observations 23 of presynaptic anatomy (local boutons available for synapsing from distinct types of intracellularly 24 filled and reconstructed interneurons) as opposed to postsynaptic anatomy ( inhibitory post-synaptic 25 densities on pyramidal cell dendrites). In simulations with the model containing this rationally scaled 26 up inhibition, only 1% of the pyramidal cells were active, and they fired at a low rate of 1.8 Hz 27 (data not shown), closely resembling the in vivo condition (Soltesz and Deschenes, 1993;Robbe et al., falling phase of the theta cycle (Colgin and Moser, 2010); note that PV+ cells receive a high number 1 of excitatory inputs on their dendrites compared to other interneuron classes (Gulyas et al., 1999). 2 A comparison of the model and the anesthetized in vivo data is illustrated in Figure 5D, where the 3 arrows indicate the shift required for the model phase preferences ( Figure 5A) to equal the in vivo 4 ( Figure 5B) phase preferences; note that the required shifts (arrows) are small for all interneuron types 5 except PV+ basket and ivy cells. A clear majority of the interneuronal types in the model showed 6 phase preferences similar to the in vivo condition where rhythmically discharging afferent inputs are 7 present, indicating that theta-preferential discharges are to a large extent determined by the wiring 8 properties of the CA1 circuit itself. 9 Perturbation experiments indicate a key role for interneuronal diver- 10 sity in the emergence of spontaneous theta 11 Importantly, the ability to generate theta oscillations, phase-locked gamma oscillations, and theta-12 related phase-preferential firing of distinct interneuronal subtypes was not a universal property of the 13 model. As shown in Figure 6A, our strongly constrained model only exhibited spontaneous theta 14 oscillations at certain levels of afferent excitation. The results described above  were 15 obtained with an afferent excitation level of 0.65 Hz (labeled as "Control" in Figure 6A), meaning 16 that each excitatory afferent cell excited the model network with a Poisson-distributed spike train 17 having a Poisson mean interspike interval (ISI) corresponding to a firing rate of 0.65 Hz. When the 18 excitation level decreased below 0.65 Hz, the theta rhythm fell apart, and when the excitation level 19 increased beyond 0.80 Hz, theta power also started to drop significantly as the oscillation frequency 20 rose out of theta range ( Figure 6 and Figure 6 -figure supplement 1), evolving into a beta oscillation 21 (Engel and Fries, 2010). These data indicate that while synaptic-cellular organization of the CA1 22 circuit enables the intrinsic, within-CA1 generation of theta waves, the circuit is predisposed to exhibit 23 theta oscillations only under particular excitatory input conditions. The observation that, under 24 certain conditions the model network can oscillate at frequencies between 12 and 20 Hz, is in agreement 25 with recent experimental findings that rhythmic driving of septal PV+ cells can reliably entrain the 1 hippocampus in a 1:1 ratio up to frequencies of 20 Hz (Dannenberg et al., 2015). 2 Does the parameter sensitivity of the theta rhythm also apply to recurrent excitation from pyra-3 midal cells and inhibition from CA1 interneurons? In order to answer the latter question, we tested 4 whether the theta rhythm was differentially sensitive to the contribution of each inhibitory cell type 5 ( Figure 6B). We characterized the contribution of each local CA1 cell type to the theta rhythm by 6 muting the output of the cell type so that its activity had no effect on the network. First, we stud- 7 ied the role of the recurrent collaterals of pyramidal cells, which contact mostly interneurons and, 8 less frequently, other pyramidal cells (Bezaire and Soltesz, 2013). When we muted all the outputs 9 from pyramidal cells, theta rhythm disappeared (bar labeled "Pyr" in Figure 6B), indicating that the 10 recurrent collaterals of pyramidal cells play a key role in theta oscillations. 11 Interestingly, muting the relatively rare CA1 pyramidal cell to pyramidal cell excitatory connections 12 alone (each pyramidal cell contacts 197 other pyramidal cells in the CA1; Bezaire and Soltesz (2013)) 13 was sufficient to collapse the theta rhythm (bar labeled "None" in Figure 6C); key roles for inter- 14 pyramidal cell excitatory synapses within CA1 have been suggested for sharp wave ripple oscillations 15 as well (Maier et al., 2011). Furthermore, the parameter-sensitivity of the theta rhythm was also 16 apparent when examining the role of pyramidal cell to pyramidal cell connections, because theta power 17 dramatically decreased when these connections were either increased (doubled) or decreased (halved) 18 from the biologically observed 197 ( Figure 6C). Next, we investigated the effects of muting the output 19 from each interneuron type. Silencing the output from any of the fast-spiking, PV family interneurons 20 (PV+ basket, axo-axonic, or bistratified cells), CCK+ basket cells, or neurogliaform cells also strongly 21 reduced theta power in the network ( Figure 6B). In contrast, muting other interneuronal types (S.C.-A 22 cells, O-LM cells, or ivy cells) had no effect on this form of theta oscillations generated by the intra-23 CA1 network ( Figure 6B). In additional disinhibition studies simulating optogenetic experimental 24 configurations, partial muting of all PV+ outputs (PV+ basket, bistratified, and axo-axonic cells 25 together) had a larger effect than partial muting of all SOM+ outputs (O-LM and bistratified cells); 26 see Figure 6D. Reassuringly, these results were in overall agreement with experimental data from the 27 isolated CA1 preparation indicating that optogenetic silencing of PV+ cells, but not SOM+ cells 1 such as the O-LM cells, caused a marked reduction in theta oscillations (Amilhon et al., 2015). The 2 differential effects of silencing PV+ versus SOM+ cells could also be obtained in a rationally simplified 3 model called the Network Clamp, where a single pyramidal cell was virtually extracted from the full-4 scale CA1 network with all of its afferent synapses intact (for further details, see Bezaire et al. (2016)). 5 Since the diverse sources of inhibition from the various interneuronal types are believed to enable 6 networks to achieve more complex behaviors, including oscillations (Soltesz, 2006;Rotstein et al., 7 2005; Kepecs and Fishell, 2014), we next tested if reducing the diversity of interneurons in the model 8 would affect its ability to produce spontaneous theta oscillations. Surprisingly, giving all interneurons 9 a single electrophysiological profile appeared to create conditions that were not conducive for the ap-10 pearance of spontaneous theta oscillations regardless of which interneuronal profile was used ( Figure   11 6E; note that the cells still differed in the strengths, distribution, and identities of their incoming 12 and outgoing connections after this manipulation). To probe this finding further, we focused on PV+ 13 basket cells, which have been implicated in theta generation in vivo (Soltesz and Deschenes, 1993;  Figure 4B). We gradually altered ("morphed") the properties of all other 16 model interneuron types until they became PV+ basket cells, by first converging their electrophysio-17 logical profiles, then additionally their synaptic kinetics and incoming synapse weights, then also their 18 incoming synapse numbers, and finally their outgoing synaptic weights and numbers ( Figure 6F; Table   19 7). Theta was not apparent in any intermediate steps nor in the final network where all interneurons 20 had become PV+ basket cells ("All PV+B" in Figure 6F). Furthermore, introduction of cell to cell 21 variability in the resting membrane potential of interneurons in the "All PV+B" configuration at the 22 biologically observed values for PV+ basket cells also failed to restore theta ("Var PV+B" in Figure   23 6F shows results with standard deviation of (SD) = 8 mV in the resting membrane potential; SD = 5 24 mV and SD = 2 mV also yielded no theta; biological SD value: approximately 5 mV in Tricoire et al.  To rule out the possibility that the lack of theta could be due to an inappropriate excitation level 3 in these reduced diversity configurations, we subjected the "All PV+ B" network to a wide range of 4 incoming excitation levels ( Figure 6G). Theta rhythm did not appear at any of these excitation levels. 5 While we could not rule out a hypothetical theta regime somewhere in the parameter space of such 6 low-diversity configurations, any theta solution space would likely be smaller and more elusive than 7 we were able to determine in the control configuration ( Figure 6A). 8 Taken together, these results indicated, for the first time, that interneuronal diversity itself is an 9 important factor in the emergence of spontaneous theta oscillations from the CA1 network. In agreement with previous predictions (Capogna, 2011), the perturbation experiments described 13 above suggested that neurogliaform cells were a necessary component for spontaneous theta to arise 14 in the isolated CA1. We wondered why muting the output from neurogliaform cells, but not the closely 15 related ivy cells, affected theta oscillations ( Figure 6B), especially since there were fewer neurogliaform 16 cells than ivy cells, and they were less theta modulated ( Figure 5A). These two model interneuron  Figure 6H). To test whether the contribution of the GABA B receptors was due to their slow kinetics, 23 we artificially sped up the GABA B IPSPs so that they had GABA A kinetics but conserved their 24 characteristic large charge transfer. This alteration was implemented by scaling up the GABA A 25 synaptic conductance at neurogliaform cell output synapses to achieve a similar total charge transfer 1 as the control GABA A,B mixed synapse ( Figure 6 -figure supplement 2). As shown in Figure 6H 2 (green bar), theta activity was restored when the neurogliaform cell output synapses had no slow 3 GABA B component, only a scaled up fast GABA A IPSP with a charge transfer equivalent to the 4 mixed GABA A,B synapses. Therefore, muting the neurogliaform cells strongly disrupted the theta 5 oscillations not because the theta oscillations required the slow kinetics of GABA B IPSPs specifically, 6 but because the slow kinetics enabled a large total charge transfer. Emergence of theta oscillations from a biological data-driven, full-9 scale model of the CA1 network 10 We produced a biologically detailed, full-scale CA1 network model constrained by extensive experi-  emerged from the network model without explicit encoding, rhythmic inputs or purposeful tuning of 16 intra-CA1 parameters (all anatomical connectivity parameters were exactly as previously published 17 in Bezaire and Soltesz (2013)). Cell type-specific perturbations of the network showed that each in- 18 terneuronal type contributed uniquely to the spontaneous theta oscillation, and that the presence 19 of diverse inhibitory dynamics was a necessary condition for sustained theta oscillations. In addi-20 tion to characterizing roles for specific network components, these model results generally suggest 21 that the presence of diverse interneuronal types and the intrinsic circuitry of the CA1 network are 22 sufficient and necessary to enable the isolated CA1 to oscillate at spontaneous theta rhythms while 23 supporting distinct phase preferences of each class of hippocampal neuron. These abilities may serve 24 to maintain the stability and robustness of the theta oscillation mechanism as it operates in vivo 1 in diverse behavioral states. The theta rhythm is thought to be important for organizing disparate  Importantly, theta oscillations appeared only within certain levels of excitatory afferent activ-    Our results obtained using the 0.65 Hz excitation indicated that the CA1 model network exhibited 10 phenomena that corresponded well with experimental results, for example, on the differential roles of results also provided the interesting insight that GABA B receptors may play important roles in slow 16 oscillations such as the theta rhythm not because their slow kinetics pace the oscillations, but because 17 their slow kinetics enable a massive charge transfer. This insight was illuminated by the fact that 18 slow GABA B synapses were not necessary for theta as long as their large charge was carried by the 19 fast GABA A synapses. However, we had to increase the conductance of the GABA A synapse almost 20 300 times to achieve a similar charge transfer as that conveyed by the GABA B synapse. Such a large 21 conductance is not biologically realistic, indicating that the key role for GABA B synapses may be 22 to allow the temporal distribution of the large synaptic charge transfer. Indeed, the importance of 23 GABA B receptors has also been indicated by a number of recent experimental studies, for example,  showed that the relatively rare pyramidal cell to pyramidal cell local excitatory connections were also 8 required. 9 Based on our results, we hypothesize that the inhibitory and excitatory connections within CA1 10 that were identified to be critical in our perturbation ("muting") simulations ( Figure 6B) interact 11 to generate the theta waves in the model as follows. Pyramidal cells preferentially discharge at 12 the trough of the LFP analog, strongly recruiting especially the PV+ basket and bistratified cells 13 (green and brown raster plots in Figure 3C), which, in turn, cause a silencing of the pyramidal cells 14 (blue raster plot in Figure 3C) for about the first third of the rising half (i.e., from 0 o to about 15 60 o ) of the LFP analog theta cycle. As the pyramidal cells begin to emerge from this period of strong 16 inhibition, initially only a few, then progressively more and more pyramidal cells reach firing threshold, 17 culminating in the highest firing probability at the theta trough, completing the cycle. The progressive 18 recruitment of pyramidal cells during the theta cycle appears to be paced according to gamma (see blue 19 raster plot in Figure 3C), and it is likely that the intra-CA1 collaterals of the discharging pyramidal 20 cells play key roles in the step-wise (gamma-paced) recruitment of more and more pyramidal cells 21 as the cycle approaches the following trough. The predicted key roles for physiological pyramidal 22 cell to pyramidal cell connections in theta-gamma generation during running may be tested in future 23 experiments.

Rationale for bases of comparison between modeling results with ex-
Because our model represented the isolated CA1 network, the modeling results were compared 3 with experimental data from the isolated CA1 preparation when possible. Modeling results for which 4 no corresponding experimental data were available from the isolated CA1 preparation, such as the 5 phase preferential firing of individual interneuron types during theta oscillations, were compared with 6 in vivo data from anesthetized animals ( Figure 5B). Experimental results from anesthetized animals 7 offered the most complete data set (e.g., no experimental data were available on CCK basket cells 8 and neurogliaform cells from awake animals, see Figure 5 -figure supplement 2). Out of the four 9 interneuronal types for which in vivo data were available from both the awake and anesthetized connectivity; see Table 3 in Bezaire and Soltesz (2013)), some of the electrophysiology data used for 19 constructing the single cell models (Supplementary Material) came from the mouse. In addition, the 20 experimental data on the isolated CA1 preparation were obtained from both rat (Goutagny et al., is no reported evidence for major, systematic differences in key parameters such as the phase specific 24 firing of rat and mouse interneurons in vivo, we did not compare our modeling results with rat and 25 mouse data separately.

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A final point concerns the nature of the theta rhythm that emerged in our model. In general, the 1 in vivo theta rhythm has been reported to be either atropine resistant or atropine sensitive, where the 2 former is typically associated with walking and may not be dependent on neuromodulatory inputs, 3 while the latter requires intact, rhythmic cholinergic inputs (Kramis et al., 1975). Given that our 4 model did not explicitly represent neuromodulatory inputs, it is likely that the theta that emerged 5 from our model most closely resembled the atropine resistant form. However, it also plausible that 6 both forms of theta benefit from occurring in a network that is predisposed to oscillate at the theta 7 frequency, as the model network results suggested. 8 An accessible approach to modeling that balances detail, scale, flex-9 ibility and performance 10 Our results from the strictly data-driven, full-scale CA1 model are consistent with those of earlier 11 models that elegantly demonstrated the basic ingredients capable of producing emergent network os-  2014)) and others. 14 We developed a flexible and biologically relevant model that uses computational resources effi- 15 ciently, positioning the model to be used by the broader community for many future questions. Im- 16 portantly, the model can be run on the Neuroscience Gateway, an online portal for accessing supercom- 17 puters that does not require technical knowledge of supercomputing (https://www.nsgportal.org/). 18 The model is public, well documented, and also well characterized in experimentally relevant terms  The behavior of each cell type was characterized using a current injection sweep that matched NEURON's double exponential synapse mechanism (Exp2Syn), with each connection comprising an 5 experimentally observed number of synapses (see Table 1). 6 The connections between cells were determined with the following algorithm, for each postsynaptic 7 and presynaptic cell type combination:  we distributed these connections uniformly across the available incoming inhibitory synapses onto 14 interneurons that we had calculated for that layer. We calculated available incoming synapses by 15 using published experimental observations of inhibitory synapse density on interneuron dendrites by 16 cell class and layer in CA1, which we combined with known anatomical data regarding the dendritic 17 lengths of each interneuron type per layer. We therefore made the following assumption: All available  The electrophysiology of each cell was tuned using a combination of manual and optimization 22 techniques. We first fit each cell's resting membrane potential, capacitance, time constant, and input  To determine the synaptic weights and kinetics for those connections that have not yet been 10 experimentally characterized, we used a novel modeling strategy we call Network Clamp, described in 11 Bezaire et al. (2016). As experimental paired recording data were not available to directly constrain 12 the synapse properties, we instead constrained the firing rate of the cell in the context of the in 13 vivo network, for which experimental data have been published. We innervated the cell with the 14 connections it was expected to receive in vivo, and then sent artificial spike trains through those 15 connections, ensuring that the properties of the spike trains matched the behavior expected from each 16 cell in vivo during theta (firing rate, level of theta modulation, preferred theta firing phase). Next, 17 we adjusted the weight of the afferent excitatory synapses onto the cell (starting from experimentally 18 observed values for other connections involving that cell type) until the cell achieved a realistic firing 19 rate similar to had been experimentally observed in vivo. 20

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As none of the model neurons in the CA1 network are spontaneously active, it was necessary to pro- neurotransmitter release (Kavalali, 2015), we modeled the activation of CA3 and entorhinal synapses 2 as independent Poisson stochastic processes. The model neurons were connected to a subset of these 3 afferents, such that they received a constant level of excitatory synaptic input. 4 We constrained the synapse numbers and positions of the stimulating afferents using anatomical 5 data. To constrain the afferent synapse weights, we used an iterative process to determine the com-  Table 6). First, we used the output of an 8 initial full-scale simulation to run network clamp simulations on a single interneuron type, altering 9 the incoming afferent synapse weights (but not the incoming spike trains) until the interneuron type 10 fired at a reasonable rate. Then, we applied the synaptic weight to the afferent connections onto that 11 interneuron type in the full-scale model. The resulting simulation then led to a new network dynamic 12 as the constrained activity of that interneuron type caused changes in other interneuron activity. We

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We analyzed the results of each simulation with standard neural data analysis methods provided pyramidal neuron spikes (Szűcs, 1998), the periodogram of the SDF, and the spectrogram of the LFP 24 analog. We determined the dominant theta and gamma frequencies for the network as the peak in 25 the power spectral density estimate obtained by the spectrogram, and confirmed that those peaks 26 are identical for the SDF and the LFP analog. After finding a dominant theta or gamma frequency, 1 we then analyzed the level of modulation and preferred firing phase for each cell type. Finally, we 2 calculated the firing rate of each cell type.
3 LFP analog 4 We calculated an approximation of the LFP generated by the model neurons based on the method   5 We calculated the preferred firing theta phases of each cell, using all the spikes of that cell type that 6 occurred after the first 50 ms of the simulation, relative to the filtered LFP analog. The spike times 7 were converted to theta phases, relative to the troughs of the LFP analog theta cycle in which they 8 fired. We then subjected the spike phases to a Rayleigh test to determine the level of theta modulation

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For the GABA B -related simulations, we ran three of each condition and then performed an ANOVA 19 to test for significance in the difference of theta power among the conditions.

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Cross correlation of theta and gamma 1 To investigate whether a relationship existed between the simultaneous theta and gamma oscillations 2 found in the LFP analog of our control simulation, we filtered the LFP analog signal within the theta 3 range (5-10 Hz) and the gamma range (25-80 Hz). We applied a Hilbert transform to each filtered 4 signal and then compared the phase of the theta-filtered signal with the envelope of the gamma-filtered 5 signal to determine the extent to which theta could modulate the gamma oscillation. Unified Cluster. 20 We would like to thank the University of Texas' Texas Advanced Computing Center team, the San  Williams for the use of their spectrogram analysis script.     0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.12e+07 0.00e+00 0.00e+00 Bis 2.35e+05 3.54e+05 5.76e+05 2.64e+05 0.00e+00 6.40e+05 3.12e+07 8.85e+05 6.80e+04 CCK+B 1.41e+05 2.12e+05 9.79e+05 5.64e+05 0.00e+00 2.62e+05 3.24e+07 5.31e+05 8.32e+04 Ivy 3.53e+05 5.30e+05 3.42e+06 2.11e+06 1.00e+06 2.23e+06 1.28e+08 1.33e+06 4.08e+05 NGF 0.00e+00 0.00e+00 0.00e+00 0.00e+00 6.09e+05 0.00e+00 4.36e+07 0.00e+00 0.00e+00 O-LM 1.18e+05 1.77e+05 1.44e+06 0.00e+00 4.65e+05 9.84e+04 2.49e+07 4.42e+05 1.60e+05 Pyr 7.19e+05 2.43e+06 0.00e+00 2.38e+05 0.00e+00 1.17e+07 6.14e+07 7.03e+06 1.26e+05 PV+B 5.73e+04 8.62e+04 1.37e+05 7.05e+04 0.00e+00 0.00e+00 5.83e+07 2.16e+05 9.60e+03 SC-A 8.82e+03 1.33e+04 1.30e+05 1.06e+05 0.00e+00 1.97e+04 3.74e+06 3.32e+04 1.44e+04 CA3 1.23e+07 2.56e+07 1.44e+07 3.39e+07 0.00e+00 0.00e+00 3.73e+09 6.69e+07 1.55e+06 ECIII 1.43e+06 1.91e+06 4.02e+06 0.00e+00 3.75e+06 0.00e+00 8.09e+08 0.00e+00 4.58e+05     Table 4: Current injection levels used to characterize interneuron current sweeps in Figure  2D-2G.   Table 7: Peak, theta and gamma frequencies and powers of the pyramidal cell spike density function using Welch's Periodogram. As in Figure 6 -figure supplement 1, networks where no pyramidal cells spiked -resulting in zero power within the spectral analysis of the pyramidal cell spike density function -have their peak frequencies listed as "n/a" for "not available".      Table 6 for sources of experimental data.  Table 6 for further details.    Figure 6H. These traces are from pyramidal cells clamped at -50 mV during a paired recording from a presynaptic neurogliaform cell with a GABA A reversal potential of -60 mV and a GABA B reversal potential of -90 mV. The currents shown are averages from 10 recordings. Scale bar = 100 ms and 5 pA. The ion channel characterized in this figure was an Na v channel, inserted into a single compartment 10 cell of diameter and length 16.8 microns (a soma) with a density such that the maximum, macroscopic 11 conductance was .001 µS/cm 2 . The reversal potential of the channel was +55 mV and the settings 12 during the characterization protocol were: temperature=34 degrees Celsius, axial resistance = 210 13 ohm*cm, [Ca2+] internal = 5.0000e-06 mM, specific membrane capacitance = 1 µF/cm 2 . For activation 14 steps, the cell was held at -120 mV and then stepped to potential levels ranging from -60 mV to +80 15 mV. For inactivation steps, the cell was held at various potential levels ranging from -120 mV to +40 16 mV for 500 ms and then stepped to +20 mV. Each current injection step is recorded in a separate file, 17 with activation step files following the name convention of stepto_[stepped-to potential in mV].dat 18 and inactivation step files following the name convention of hold_[held-at potential in mV].dat. 19 For the synaptic responses, the postsynaptic cell was voltage-clamped at -50 mV and the reversal 20 potential of the synapse was kept at its natural (as defined in the network model code) potential. A 21 spike was triggered in the presynaptic cell and the current response was measured in the postsynaptic 22 cell at the soma. This recording was repeated 10 times, with a randomly chosen connection location 23 each time, and the response was then averaged. In all paired recordings with the pyramidal cell as 24 postsynaptic cell, the sodium channels were blocked to prevent a suprathreshold response.  Figure 3 -Source Data 5 This zip file contains 3 files. First, it includes the LFP.dat file which contains the raw, theta-filtered, 6 and gamma-filtered LFP analog traces (the raw local field potential (LFP) analog was calculated 7 from the network activity as detailed in the Methods section). Second, the zip file contains Mem-8 brane_Potentials.txt, which includes the full duration, intracellular somatic membrane potential 9 recordings from the specific cells shown in Figure 3. Third, it includes the SpikeRasterLocal.dat 10 file which includes the spike times for the length of the entire simulation, from the specific cells dis- 11 played in raster shown in Figure 3. The spike times of every single cell in the network are available 12 in the CRCNS repository. Note that the displayed spike raster in Figure 3 has been downsampled in 13 such a way as to preserve its visual appearance while reducing the image size and load time. Function is detailed in the Methods section. The power spectra of the SDFs shown in Figure 4 were 21 obtained via a one-sided periodogram using Welch's method where segments have a 50% overlap with 22 a Hamming Window. The spectra for each cell type was normalized to itself so that each cell type 23 could use the full range of colors in the colorbar to show the shape of its spectra, despite different 1 absolute peak powers for different cell types. Note that the specrogram was computed from the raw of that type, and calculated theta phases (relative to the theta-filtered LFP analog) of each spike.
From the list of spike phases per cell type, the preferred theta phase, level of theta modulation, and network condition studied in Figure 6. Second, it contains a file called Mapping_Network_Condition.txt that maps the names of the simulations (used in the header of Pyramidal_SDF_All_Conditions.txt) 1 to the bar labels in the graphs of Figure 6. where segments have a 50% overlap and a Hamming Window. The highest power within the theta 7 oscillation frequency range of 5 -10 Hz is reported in Figure 6, and the frequency at which the highest 8 power occurred is reported in Figure 6 -figure supplement 2. Table 6 also lists the power and frequency 9 for each condition.
10 Figure 6F included three statistically independent simulations from each network condition (control 11 + two experimental conditions). We performed a one-way analysis of variance (ANOVA) of the peak 12 power of the pyramidal cell SDF within the theta frequency range, including all three simulations 13 from each of the three conditions, grouped by condition.