Model reconstruction

In this section, we describe how we reconstructed the main components of the model: the cornu Ammonis 1 (CA1), the Schaffer collaterals (SC), and the effect of acetylcholine (ACh) on CA1. Each of these main components is itself a compound model of several circuit “building blocks” (Fig 1 and S4 Fig). For each of these subcomponents, we show how, from the sparse data available in the literature (see S3–S24 Tables) and a list of assumptions (section List of assumptions), we arrived at the dense data necessary to ascribe a value for each model parameter. For each “building block” subcomponent, we validate it against available experiment data.

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Fig 1. Overview of the model.

A visualization of a full-scale, right-hemisphere reconstruction of rat CA1 region and its components. The number of cells is reduced to 1% for clarity, and neurons are randomly colored. The CA1 network model integrates entities of different spatial and temporal scales. The different scales also reflect our bottom-up approach to reconstruct the model. Ion channels (1) were inserted into the different morphological types (3) to reproduce electrophysiological characteristics and obtain neuron models (4). Neurons were then connected by synapses to generate an intrinsic CA1 connectome (5). For each intrinsic pathway, synaptic receptors (2) and transmission dynamics were assigned based on single neuron paired recording data (6) to create a functional intrinsic CA1 network model (7). The intrinsic CA1 circuit received synaptic input from CA3 via Schaffer collateral (SC) axons (8). The neuromodulatory influence of cholinergic release on the response of CA1 neurons and synapses was modeled phenomenologically (9). The dynamic response of the CA1 network was simulated with a variety of manipulations to model in vitro and in vivo, intrinsic and extrinsic stimulus protocols while recording intracellularly and extracellularly (10) to validate the circuit at different spatial scales against specific experimental studies (11) and to make experimentally testable predictions (12).

https://doi.org/10.1371/journal.pbio.3002861.g001

Building CA1

To reconstruct a full-scale model of rat CA1, we created biophysical models of its neurons, defined an atlas volume of the region for one hemisphere, placed these neurons in the volume, and connected them together by following and adapting the method described in [27] (S4 Fig).

CA1 neurons

To achieve a full-scale version of CA1, we needed to populate the model with approximately 456,000 cells. We started by curating 43 morphological reconstructions of neurons belonging to 12 morphological types: pyramidal cell (PC), axo-axonic cell (AA), 2 subtypes of bistratified cell (BS), back-projecting cell (BP), cholecystokinin (CCK) positive basket cell (CCKBC), ivy cell (Ivy), oriens lacunosum-moleculare cell (OLM), perforant pathway associated cell (PPA), parvalbumin positive basket cell (PVBC), Schaffer collateral associated cell (SCA), and trilaminar cell (Tri). To increase the morphological variability, we scaled and cloned them producing an initial morphology library of 2,592 reconstructions.

To validate the resulting morphology library, we compared them morphometrically and topologically to the original morphologies. The similarity scores for the distribution of morphological features were statistically similar (S5 Fig, all values R>0.98, p<10⁻²⁵). Using the topological morphology descriptor (TMD) [32], the persistence diagrams (S6 Fig) show an increase in morphological variability introduced by the cloning process (details per m-type in S7 and S8 Figs).

To produce electrical models (e-models), we began by taking 154 single-cell recordings and classifying traces into 4 electrical types (e-types) using Petilla nomenclature [33]: classical accommodating for pyramidal cells and interneurons (cACpyr, cAC), bursting accommodating (bAC), and classical non-accommodating (cNAC). From each trace, we extracted electrical features (e-features) which we used in combination with the curated morphologies to produce and validate 36 single-cell e-models [34,35]. In the case of pyramidal cells e-models, they qualitatively reproduced experimental findings in terms of back-propagating action potential (BPAP) ([36], R = 0.878, p = 0.121) and postsynaptic potential (PSP) attenuation ([37], R = 0.846, p = 0.001, S9 Fig). However, since we constrained the models with somatic not dendritic features, we expected some degree of difference compared with experimental results (see [38]).

To match the proportions of the morpho-electrical type (me-type) composition of the CA1 (S4 Table), we combined the 36 e-models with 2,592 curated morphologies to obtain an initial library of 26,112 unique me-type models. This is the pool of biophysical cell models available to populate the full-scale version of CA1.

Defining the spatial framework

To represent the CA1 spatial volume, we started with a publicly available atlas reconstruction of the hippocampus [39]. Our aim was to create a continuous coordinate system to represent the 3 axes of the hippocampus (longitudinal, transverse, and radial) and a precise vector field for cell placement and orientation (Fig 2). For our building and analysis algorithms to work effectively, we applied a series of post-processing steps (S10 Fig, see section Atlas). Within this process, we redefined the layers parametrically to be consistent with the layer thicknesses in our data sets (section Layers).

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Fig 2. Coordinate system.

Custom parametric coordinates system used as spatial reference for circuit building, circuit segmentation, and for simulation experiments. (A) Longitudinal (l, red), transverse (t, green) and radial (r, blue) axes of the CA1 volume are defined parametrically in range [0,1]. Left: Slice from volume shows radial depth from SO/alveus (r = 0) to SLM/pial (r = 1) and transverse extent from CA3/proximal CA1 (t = 1) to distal CA1/subiculum (t = 0) boundaries. Right: Full volume shows surface grid of transverse vs. longitudinal axes. Longitudinal axis extends from dorsal (l = 0) to ventral (l = 1) CA1. (B) Circuit segmentation for analysis and simulation. Coordinates system used to select CA1 slices of a given thickness (B1) or a cylinders of a given diameter (B2) at specific locations along longitudinal axis. (C) Extracellular electrode placed at a given surface position (left) and channels at selected laminar depth (right) in CA1 volume. (D) Each neuron in the circuit is defined by a unique general identifier (gid), its morphological type (m-type), electrical type (e-type), spatial xyz-coordinates and parameterized ltr-coordinates.

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Placing neurons in the volume

After defining the volume, we wanted the model to match the neuronal density and proportion of cell types in rat CA1. We compiled available data to derive the cellular composition (section Cell composition, see S3 Table) and used it to populate the atlas with soma locations (S11A and S11B Fig). To check the consistency, we validated the resulting cell composition (R = 0.999, p = 1.31×10⁻²⁸) and cell density (R = 0.999, p = 0.0001) (S12B and S12C Fig and S5 Table). At each soma location, we needed to select from the e-model library the neuron that best fits in the space of the layers. To this purpose, we oriented its morphology according to the vector fields (S11C and S11D Fig) and evaluated it against a set of rules that describe the target distribution of neurites per layer (S6 Table). Visually, cells in our model follow the curvature of the hippocampus and the different parts of the cells target the expected layers (S12A Fig). Subject to the multiple constraints of the cell placement algorithm, we placed 456,380 neurons in the volume, utilizing 2,523 unique morphologies, and 25,355 unique neuron models.

Connecting CA1 neurons

To connect the placed neurons, we used the connectome algorithm previously described in [40]. In brief, the algorithm searches for co-localization of axon and postsynaptic neurons within a certain distance to identify a potential synapse (or apposition). After identifying all potential synapses, a subsequent pathway-specific pruning step discards some to match the known bouton densities (S7 Table) and number of synapses per single axon connection (S9 Table). This algorithm has been demonstrated to accurately recreate local connectivity [27–29] as well as higher-order topological features [41]. The resulting intrinsic connectome consisted of about 821 million synapses.

Given the importance of the connectome, we wanted to validate it as widely as possible to mitigate the uncertainty in our assumptions and literature data (S14–S17 Figs). First, we verified the bouton density and number of synapses per connection used in the pruning step was preserved in the generated connectome (bouton density: R = 0.909, p = 0.0120; number of synapses per connection: R = 0.992, p = 2.41×10⁻⁹, S14 Fig and S7 and S9 Tables). Next, we observed that the shape of the distributions for connection probability (S15A Fig), convergence (S16A Fig) and divergence (S17A Fig) were positively skewed as reported experimentally [42]. In the case of mean connection probability, experimental data did not allow a direct comparison because the distance between the neuron pairs tested was typically missing (S15C Fig and S8 Table). For convergence, we found that the subcellular distribution of synapses on different compartments of pyramidal cells in our model was consistent with [43] (R = 0.988, p = 0.012, S16D Fig). For divergence, the model did not always closely match the experimental data for the total number of synapses per axon formed by certain m-types (R = 0.524, p = 0.286, S17C Fig and S10 Table). We compared divergence also in terms of the percentage of synapses formed with PCs or INTs (S17D Fig and S11 Table) and validated the distribution of efferent synapses in the different layers (SO: R = 0.798, p = 0.057; SP: R = 0.905, p = 0.013; SR: R = 0813, p = 0.049; SLM: R = 0.999, p = 4.11×10⁻⁸, S17E Fig and S12 Table). Overall, this suggests the model connectome provides a reasonable approximation based on available data, while the discrepancies can be due, for example, to the small sample size and high variability in axon length recovered from in vitro slices.

To provide functional dynamics for synaptic connections with stochastic neurotransmitter release and short-term plasticity (STP) (see S18 Fig), we used the optimized parameters we previously derived in [34] for the 22 intrinsic synaptic classes of pathways we have identified (S13 and S14 Tables). The model was able to reproduce the PSP amplitudes (S18D Fig, R = 0.999, p = 1.65×10⁻¹⁹) and postsynaptic current (PSC) coefficient of variation (CV) of the first peak (S18E Fig, R = 0.840, p = 0.018) for the pathways with available electrophysiological recordings. After having constrained and validated the synapses, the reconstruction process of the intrinsic CA1 circuit is complete.

Reconstruction of Schaffer collaterals (SC)

An isolated CA1 does not have substantial background activity [44], while normally the network is driven by external inputs. The Schaffer collaterals from CA3 pyramidal cells are the most prominent afferent input to the CA1 and the most studied pathway in the hippocampus [45,46]. Their inclusion allows us to deliver synaptic activity input patterns to the CA1.

To reconstruct the anatomy of Schaffer collaterals, we constrained the number of CA3 fibers and their average convergence on CA1 neurons with literature data (S15 and S16 Tables). Due to scarce topographical information, we distributed synapses uniformly along the transverse and longitudinal axes, while along the radial axis we followed a layer-wise distribution as reported by [5]. The resulting Schaffer collaterals added more than 9 billion synapses to CA1, representing 92% of total modeled synapses. As expected, the synapse laminar distribution (Fig 3A–3C) and mean convergence on PCs and interneurons (Fig 3D and 3E) match experimental values (one-sample t test, p = 0.957 for PCs and p = 0.990 for INTs). Interestingly, other unconstrained properties also match experimental data. The convergence variability is comparable with the upper and lower limits identified by [5] (model PC: 20,878 ± 5,867 synapses and experimental PC: 13,059–28,697, model INT: 12,714 ± 5,541 and experimental INT 7,952–17,476, Fig 3D and 3E). In addition, the axonal divergence from a single CA3 PC is 34,135 ± 185 synapses (S19A Fig), close to the higher end of the ranges measured by [47–49] (15,295–27,440, S19B Fig). Finally, most of the connections formed a single synapse per neuron (1.0 ± 0.2 synapses/connection, S19A Fig), consistent with what has been previously reported [5].

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Fig 3. Schaffer collaterals anatomy and physiology.

(A) Section of a slice of the dorsal CA1 showing neurons in gray and SC synapses in orange (10% of the existing ones). (B) Example of SC synapse placement (orange dots) on one reconstructed PC (in gray). (C–H) Validation of the anatomy (C–E) and physiology (F–H) of the SC. Experimental values can be found in S15–S18 Tables. Density of SC synapses (lower x axis) and PDF (upper x axis) at different depths (radial axis percentage) (C). Distributions of afferent synapses from SC to PC (D) and INT (E). Distribution of PSP amplitudes for SC → PC synapses (F). Distribution of PSC ratio (see text) for SC → CB1R+ (G) and SC → CB1R- (H). Insets in panels F–H report voltage membrane traces of 10 randomly selected pairs of SC → PC, SC → CB1R+, and SC → CB1R- interneurons, respectively. The presynaptic SC is stimulated to fire 8 times at 30 Hz, plus a recovery pulse after 500 ms from the last spike of the train. Solid black lines represent mean values and shaded gray areas the standard deviation. PC, pyramidal cell; PDF, probability density function; PSP, postsynaptic potential; SC, Schaffer collaterals.

https://doi.org/10.1371/journal.pbio.3002861.g003

The CA3 afferent pathway is sparsely connected to the CA1, so the chance of obtaining paired CA3-CA1 neuronal recordings is small between PCs and much smaller from PC to interneurons [50–53]. So, to constrain SC physiology we did not have enough data to follow the parametrization used for intrinsic synapses [34]. Instead, we used the available data (S17 and S18 Tables) and optimized the missing parameters as shown in S19C Fig. The resulting SC→PC synapses match the distribution of EPSP amplitudes as measured by [50] (Fig 3F, experiment: 0.14 ± 0.11 mV, CV = 0.76, model: 0.15 ± 0.12 mV, CV = 0.80, z-test p = 0.709), giving a peak synaptic conductance of 0.85 ± 0.05 nS and N_RRP of 12. The rise and decay time constants of AMPA receptors (respectively 0.4 ms and 12.0 ± 0.5 ms) were obtained by matching [50] EPSP dynamics (S19C Fig, 10% to 90% rise time model: 5.4 ± 0.9 ms and experiment: 3.9 ± 1.8 ms, half-width model: 20.3 ± 2.9 ms and experiment: 19.5 ± 8.0 ms, decay time constant model: 19.5 ± 2.5 ms and experiment: 22.6 ± 11.0 ms). In the case of SC→INT synapses, we distinguished between cannabinoid receptor type 1 negative (CB1R-) and positive (CB1R+) interneurons [54]. SC→CB1R- synapses match EPSC_CBR1−/EPSC_PC experimental ratio [54] (model 6.95 ± 9.20 and experiment 8.15 ± 6.00, z-test p = 0.18, Fig 3G), resulting in a peak conductance of 15.0 ± 1.0 nS and N_RRP of 2. SC→CB1R+ synapses match the EPSC_CBR+/EPSC_PC experimental ratio (model 1.27 ± 1.78 and experiment 1.09 ± 1.44, z-test p = 0.06, Fig 3H), giving peak conductance of 1.5 ± 0.1 nS and N_RRP of 8. SC→INT synapses (all) match the timing in the EPSP-IPSP sequence of [55] (model: 2.69 ± 1.18 ms, experiment: 1.9 ± 0.6 ms, S19 Fig E), yielding a rise and decay constants for AMPA receptors of 0.1 ms and 1.0 ± 0.1 ms, respectively. This short latency gives effective feedforward inhibition, which is a key aspect for the transmission of oscillations from CA3 to CA1 (see below).

We functionally validated SC projections reproducing [56], where the authors examined the basic input–output (I-O) characteristics of SC projections in vitro. The SC pathway is thought to be dominated by feedforward inhibition, which increases the dynamic range of the CA1 network and linearizes the I-O curve [56,57]. Blocking gamma-aminobutyric acid receptor (GABA_AR) drastically reduces the dynamic range of the network resulting in an I-O curve that saturates very quickly. To match the methodology of [56], we set up the simulations to be as close as possible to the experimental conditions (slice of 300 μm, Ca²⁺ 2.4 mM, Mg²⁺ 1.4 mM, 32°C) (Fig 4A) and we used the same sampling strategy: randomly sampling 101 neurons in the slice to find how many SC axons were required to make all of them fire (representing respectively 100% of the input and 100% of output, Fig 4B). To assess the role of feedforward inhibition, we mimic the effect of gabazine by disabling the connections from interneurons. The model captured the quasi-linearization of the I-O response in control conditions (Pearson test on linearity R = 0.992, p = 2.56×10⁻⁹) and the rapid saturation of the CA1 network with the simulated “no GABA” condition (Fig 4B). In control conditions, at 50% of input intensity (Fig 4C) the spiking activity of CA1 SP neurons is rather weak and rapidly suppressed by the feedforward inhibition, while without inhibition CA1 neurons fire for more than 50 ms at high frequency (up to 200 Hz). Taken together, these results suggest the SC projection represents a valid model given the available empirical data.

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Fig 4. Schaffer collaterals validation.

Effect of the feedforward inhibition on the input–output relationship of the network illustrated in a slice experiment. (A) The illustration (redrawn from Fig 1A of [56]) shows the in silico experimental setup. (B) Response of 101 selected neurons to an increasing number of stimulated SC fibers, with and without GABA. The dashed boxes identify the condition (50% of active SC) that is used to show the model’s results in panel C. (C) Raster plots of SP neurons in response to the SC stimulation (orange vertical line) with the overlaying firing rate (blue). On the right, membrane voltage traces of three randomly selected SP neurons in control (black) and no GABA (gray) conditions. SC, Schaffer collaterals.

https://doi.org/10.1371/journal.pbio.3002861.g004

Cholinergic modulation

The behavior of the hippocampus is shaped by several neuromodulators, with acetylcholine (ACh) among the most studied. Cholinergic fibers originate mainly from the medial septum (MS) and have been correlated with phenomena such as theta rhythm, plasticity, memory retrieval, and encoding, as well as pathological conditions such as Alzheimer’s disease [58]. This section describes the reconstruction of a phenomenological model of ACh, quantifying the effects of ACh on neurons and synapses, and developing a novel method to integrate available experimental data (S19 and S20 Tables and Fig 5A and 5B). The data used to build the model was obtained from in vitro application of various cholinergic agonists such as ACh and carbachol (CCh); here, we assume that their effects are comparable [59]. We modeled the effect of ACh on neurons and synapses. The effect on neurons results in an increase in resting membrane potential or firing frequency. We were able to integrate both types of experimental data by estimating the net current that is required to evoke the corresponding changes for a given concentration of ACh (see Eq 9 in Methods). ACh affects synaptic transmission acting principally at the level of release probability [23,60,61] (see Eq 10 in Methods).

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Fig 5. Effects of Acetylcholine on neurons, synapses, and network.

(A) Dose-response modulation of neuronal excitability caused by ACh. Black dots are experimental data points; blue curve represents the fitted equation. The dashed part of the curve indicates regions outside available experimental data. (B) Dose-response modulation of synaptic release. Same color code as in A. (C) Example traces for PC (C1) and interneurons (C2) in sub-threshold and supra-threshold conditions, with different concentrations of ACh. (D) Example traces showing the STP dynamics for PC (D1) and interneurons (D2) at different concentrations of ACh. (E) The illustration shows the in silico experimental setup to analyze network effects of ACh. Different concentrations of CCh are applied to the circuit and multiple types of recordings made in the CA1 (membrane voltage, spike times, LFPs). (F) Mean STTC as a function of ACh concentration. (G) Maximum of the LFP PSD and peak frequency as a function of ACh concentration. (H) The voltage of 100 randomly selected neurons at different levels of ACh. The upper histograms show the instantaneous firing rate. (I) Spike-spike correlation histograms. (J) Spectrogram of the LFP measured in SP at different ACh levels. (K) PSD of the LFP recorded in SP. ACh, acetylcholine; LFP, local field potential; PC, pyramidal cell; PSD, power spectral density; STTC, spike time tiling coefficient.

https://doi.org/10.1371/journal.pbio.3002861.g005

After modeling the effect of ACh on neuron excitability and synaptic transmission, we validated the effect of ACh at the network level against available data (see S21 Table). To accomplish this, we simulated bath application of ACh for a wide range of concentrations (from 0 μM (i.e., control condition) to 1,000 μM) (Fig 5E and 5F). We observed a subthreshold increase in the membrane potential of all neurons for values of ACh lower than 50 μM, without any significant change in spiking activity. At intermediate doses (i.e., 100 μM and 200 μM), the network shifted to a more sustained activity regime. Here, we observed a generalized increase in firing rate as ACh concentration increased and a progressive build-up of coherent oscillations whose frequencies ranged from 8 to 16 Hz (from high theta to low beta frequency bands). The correlation peak between CA1 neurons occurred at 200 μM ACh (Fig 5G and 5H). At very high concentrations (i.e., 500 μM and 1,000 μM), we observed a decrease in the power of network oscillations, which was further confirmed by analysis of local field potential (LFP) (Fig 5I). Power spectral density (PSD) analysis showed a maximum absolute amplitude for 200 μM ACh with a peak frequency of approximately 15 Hz (Fig 5J and 5K). Higher concentrations decreased the maximum amplitude of the PSD while the peak frequency converged toward 17 Hz (Fig 5K). Thus, we observe the emergence of 3 different activity regimes at low, intermediate, and high levels of cholinergic stimulation. It is unclear whether the network behavior we observe is consistent with all experimental findings because of their different methodologies. Nevertheless, this phenomenological model of ACh allows the reproduction of other experiments in which ACh or its receptor agonists are necessary (see, for example, sections Medial septum input and Other frequencies).

Model simulations

By following a data-driven approach and independently validating each model component, we have arrived at a candidate reference model. It can serve as a basis for investigating several scientific questions where parameters are only adjusted to reflect the different experimental setups, rather than tuned to achieve a specific network behavior. A simulation experiment is essentially a model of the experimental setup that is reproduced with as much accuracy as possible within the limits of the circuit model. As presented in the Model reconstruction section we can, for example, simulate slices of a certain thickness, change the extracellular concentration of ions, change temperature, and enable spontaneous synaptic events.

Because a central interest in hippocampus has been its oscillatory activity, here, we show several simulations with particular emphasis on theta oscillations, a prominent network phenomenon observed in the hippocampus in vivo and related to many behavioral correlates [62]. Then, we examine the frequency response band-pass properties of CA1 circuit for a wider range of SC input frequencies.

Theta oscillations

During locomotion and REM sleep, CA1 generates a characteristic rhythmic theta-band (4 to 12 Hz) extracellular field potential [63–67]. Neurons in many other brain regions such as neocortex are phase-locked to these theta oscillations [68,69] suggesting hippocampal theta plays a crucial coordinating role in the encoding and retrieval of episodic memory during spatial navigation [62,70]. Yet, despite more than 80 years of research, the trigger that generates theta oscillations in CA1 remains unclear because of conflicting evidence. This represents an opportunity to use our reference model to investigate these inconsistencies and gain an improved understanding of theta generation. As a first step, we wanted to reproduce a series of experimental data and investigate potential mechanisms proposed in literature [71], namely, intrinsic CA1 generation and extrinsic pacemaker oscillations from CA3 or from MS.

CA1 generation

To investigate possible intrinsic mechanisms of theta rhythm generation in CA1 [72,73], we examined 3 candidate sources of excitation that might induce oscillations: (1) spontaneous synaptic release or miniature postsynaptic potentials (minis or mPSPs); (2) homogeneous random spiking of SC afferent inputs; and (3) varying bath concentrations of extracellular calcium and potassium to induce tonic circuit depolarization. While in their CA1 circuit model [22] reported random synaptic activity was sufficient to induce robust theta rhythms, in our model we found none of these candidates generated robust theta rhythms. For minis, we found setting release probabilities to match empirically reported mPSP rates (S22 Table) led to irregular, wide-band activity in CA1 (see S20 Fig). For random synaptic barrage, varying presynaptic rate to match the mean postynaptic firing rate of pyramidal cells in [22] resulted in irregular beta-band, not regular theta-band oscillations (see S21 and S22 Figs). For tonic depolarization, within a restricted parameter range it was possible to generate theta oscillations around 10 to 12 Hz, but their intensity was variable and episodic (see S23 and S24 Figs). Therefore, we could not find any intrinsic mechanism capable of generating regular theta activity in our circuit model.

CA3 input

To mimic the transmission of CA3 theta oscillations to CA1, we generated SC spike trains across a range of theta-modulated sinusoidal rate functions (signal frequency) at different mean individual rates (cell frequency) (Fig 6A). We delivered these stimuli at 3 different circuit scales (whole circuit, thick slice, and cylinder circuit; see Fig 2) and measured extracellular LFP and intracellular membrane potential. To mimic recordings performed under in vivo and in vitro conditions, we did this using different calcium levels: 1 mM for “in vivo-like” and 2 mM for “in vitro-like.” For LFP, we found CA1 faithfully followed the theta-modulation input frequency at both in vivo-like and in vitro-like calcium levels and at the different circuit scales tested (e.g., 8 Hz, see Fig 6C–6F). However, for the same stimulus, the LFP at in vivo-like calcium levels was around 3 orders of magnitude less powerful than the one at in vitro-like calcium levels (Fig 6B, 6C and 6F) due to CA1 spiking rates being far lower (e.g., in full circuit, pyramidal cell mean firing rate of 0.00018±0.0067 (1 mM) versus 0.25±0.50 Hz (2 mM)). Therefore, due to this very low firing rate, we decided not to analyze results from in vivo-like conditions further and focused on those from the in vitro-like condition only (Fig 6C–6E).

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Fig 6. CA3 theta (8 Hz) oscillatory input entrains CA1 to matched theta oscillation across different scales of circuit.

(A) Schema showing the in silico experimental setup. (B) Dependency of peak frequency (left) and PSD (right) from calcium level, cell and signal frequencies during simulations of a cylinder circuit. (C) Full circuit model (2 mM calcium). LFP recordings from SP (far left), spectrogram (left middle), PSD (right middle), CSD (far right). (D) Slice circuit model (thickness of 300 μm, 2 mM calcium). (E) Cylinder circuit model (radius of 300 μm, 2 mM calcium). (F) Full circuit model (1 mM calcium). Note that PSD has 1,000 times smaller y-axis scaling than the ones in panels A–C. CSD, current source density; LFP, local field potential; PSD, power spectral density.

https://doi.org/10.1371/journal.pbio.3002861.g006

We analyzed the properties of the model LFP and compared them to experimental data. First, we examined whether the circuit size is critical for theta generation. We found that all the 3 circuit scales generated theta oscillations, but slice and cylinder circuits had reduced magnitude of the modulation and LFP power (Fig 6C–6E). Second, across all the scales, the LFP waveform (Fig 6C–6E, left columns) was more asymmetrical with a fast rise and slower decay (mean asymmetry index = −1.34±0.23; see S25 Fig) with respect to what was reported during rat locomotion (asymmetry index = −0.27, [74]) or REM sleep periods (asymmetry index = −0.13, [75]). Third, we observed a strong narrow-band peak of power at the same frequency as the signal that was maintained throughout the entire period of stimulation (Fig 6A–6C, middle left columns). Fourth, consistent with experimental evidence (e.g., Fig 1B in [72]), first- (16 Hz) and second-order (24 Hz) harmonics of the theta modulation frequency were also present (Fig 6A–6C, middle right columns). Fifth, current source density (CSD) showed a highly regular alternating current dipole between layers with a phase reversal between SP and SR (Fig 6A–6C, far right column). This is similar to in vivo LFP recordings in the absence of perforant pathway input [70], which we did not model. Therefore, since the results did not depend qualitatively on circuit size, for the sake of simplicity, we further analyzed only the cylinder circuit.

Next, we looked at how the spiking of different neuronal classes in the model are modulated by theta oscillations ([76–79]; see S23 Table). When the spike times of neurons close to the extracellular recording electrode in SP were compared with the phases of theta-band LFP rhythm (theta trough = 0°), all neuron types were found to respond at roughly the same phase of the theta cycle (Fig 7). As the mean rate of SC afferent spiking increased, more neurons became phase-locked yielding a denser mono-phase distribution for higher signal modulation frequencies (Fig 7A). For example, under stimuli with a 0.4 Hz SC mean spiking frequency and 8 Hz signal modulation, CA1 PCs fired first during the mid-rising phase of theta and were followed by all types of interneurons, whose spiking mostly ended before peak theta, with BS neurons emitting few or no spikes (Fig 7B, left). Phase-locked neurons had a tighter tuning than in vivo, with pyramidal neurons typically firing before interneurons (Fig 7B, middle). When compared with in vivo recordings of phase-locked neurons (see S23 Table), the mean phase angle of model spiking was closely matched for SP_CCKBC but substantially out of phase for SP_AA (Fig 7B, right). Although the angular deviation of phase-locking was generally tighter than observed in vivo (e.g., model versus in vivo for SP_AA 8.9° (n = 4) versus 55.0° (n = 2), SP_PVBC 12.0° (n = 2) versus 68.0° (n = 5), and SP_Ivy 10.9° (n = 19) versus 63.1° (n = 4)).

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Fig 7. CA1 morphological types are homogeneously tuned to CA3 theta oscillatory input.

(A) Neurons for analysis were selected within 100 μm radius of the stratum pyramidale electrode location (top left), shown as shaded region with the arrow indicating the radius of this region. Phase locking angle and strength for a range of individual (CA3) cell frequencies (columns) and modulation frequencies (rows). (B) Phase modulation. Spike discharge probability of all neurons grouped by morphological type (left). Phase locked neurons tuning over theta cycle for each morphological class over a single theta cycle (middle). Experimental validation of phase-locking against in vivo recordings (right) with an arrow representing the mean phase angle (experimental data = black arrow; simulated = colored arrow) and gray shaded sector indicating, where known, the experimental angular deviation. (C) Spiking raster plots. SP_PC cell spiking (top panel); LFP theta rhythm (trace above plot); intereuron spiking (bottom panel). (D) Intracellular traces from morphological cell types (left) and validation against in vivo recordings. Stimulus panels B–D: 0.4 Hz SC mean spiking frequency and 8 Hz signal modulation. All simulations shown for 2 mM calcium. Experimental values in panels B and D can be found respectively in S23 and S24 Tables. LFP, local field potential; PC, pyramidal cell; SC, Schaffer collaterals.

https://doi.org/10.1371/journal.pbio.3002861.g007

For the same neuronal classes in the model, we compared their somatic membrane potentials and mean firing rates to experimental data. Pyramidal cell spiking was closely aligned to theta LFP rhythm although individual neurons did not spike at every cycle (Fig 7C, top). SP_Ivy showed a similar pattern to SP_PC while other types of interneuron participated more sporadically (Fig 7C, bottom). Intracellular voltage traces for pyramidal and ivy cells were also similar albeit with ivy cell firing slightly later and overlapping with other types of interneurons (Fig 7D, left). Mean firing rates during theta were generally lower than observed in vivo except for ivy cells, which were a close match; SP_AA, BS, and BC (CCK+ and PV+) were well below empirical expectations (Fig 7D, right). Theta modulated the amplitude of pyramidal cell membrane potential by 1.57–7.34 mV (for 0.1–0.4 Hz SC axon frequency), consistent with the in vivo range (2–6 mV, [80]). When we compared model population synchrony during theta oscillations with in vivo data [81], we found that the percentage of SP_PC spiking was a poor match around the theta trough (0°) but was a better match around theta peak (180°), while fast-spiking SP_PVBC and to a lesser degree SP_AA were under-recruited (S26 Fig). Overall, for this stimulus the pyramidal-interneuron theta phase order suggests that intrinsic inhibition was activated more powerfully by recurrent than by afferent excitation. Altogether, for the CA3 input, the model does not generate theta at in vivo-like calcium levels but does reliably at in vitro-like ones. However, the phase analysis suggests that the mechanism is different from what is observed in vivo.

Medial septum input

In vivo evidence points to a fundamental role of the MS in theta generation [71]. To model the possible role of MS-mediated disinhibition to CA1 in theta oscillations, we (i) set an in vivo extracellular calcium concentration (1 mM); (ii) applied a tonic depolarizing current (% of rheobase current) to all neurons to represent in vivo background activity; (iii) introduced an additional current to mimic the depolarizing effect of an arhythmic release of ACh from the cholinergic projection (see ACh section); and (iv) applied a theta frequency sinusoidal hyperpolarizing current stimulus only to PV+ CA1 neurons to represent the rhythmic disinhibitory action of the GABAergic projection ([82–84]; see Fig 8A). Due to uncertainty regarding some of these factors, we examined the response over a wide range of physiological conditions (see Methods). Since this required a high number of simulations, we decided to use the cylinder circuit.

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Fig 8. MS disinhibition of parvalbumin-positive (PV+) interneurons induced theta oscillations in CA1.

(A) Simulation setup. All neurons received a tonic depolarizing current in the presence of ACh (“MS OFF” condition). For a given period, an oscillatory hyperpolarizing current was injected into PV+ interneurons only (“MS ON” condition). (B) Example of simulation before and after the onset of disinhibition. LFP in black and theta-filtered LFP in gray. (C) Spectrogram for a range of ACh concentrations (top labels) and tonic depolarization levels (right labels). (D) PSD across different levels of tonic depolarization (right labels) with and without disinhibition. (E) CSD analysis across different ACh concentrations (top labels), with and without disinhibition. (F) Theta band power as a function of the amplitude of oscillatory hyperpolarizing current, ACh concentration, and level of tonic depolarization. B–E: Stimulus disinhibitory modulation amplitude of 0.2 nA. ACh, acetylcholine; CSD, current source density; LFP, local field potential; MS, medial septum; PSD, power spectral density.

https://doi.org/10.1371/journal.pbio.3002861.g008

Prior to the onset of the disinhibitory stimulus (“MS OFF”), the global tonic depolarization resulted in weak, irregular beta-band LFP activity in CA1 but after its onset (“MS ON”), it induced a strong and sustained, regular theta oscillation matching the frequency of the hyperpolarizing stimulus (Fig 8B). For disinhibitory modulation amplitude of 0.2 nA, the LFP waveforms generated were close to symmetrical (mean asymmetry index = 0.25±0.11; see S27 Fig). Over a range of ACh concentrations and tonic depolarization levels, this theta rhythm was robust, narrow banded (Fig 8B and 8C), and generated by a highly regular current source restricted to SP (Fig 8E). Higher ACh concentrations, while slightly reducing theta-band power, reduced the level of beta-band activity (Fig 8C). Increased levels of tonic depolarization enhanced both theta harmonics and higher frequency components (Fig 8C and 8D). We observed that theta-band power was more dependent on the amplitude of the disinhibitory oscillation than on either ACh concentration or tonic depolarization level (Fig 8B and 8F). Therefore, we found MS-mediated disinhibition could strongly induce CA1 theta oscillations.

During theta oscillations, the phase of spiking of different neuronal classes here divided into 2 main groups that were in anti-phase with each other (see Fig 9). As the level of tonic depolarization increased, more phase-locked cells were detected (Fig 9A) and only above 110% depolarization (where 100% represents the depolarization necessary to reach spike threshold) were there a sufficient number of active interneurons to discern this dual grouping. Increasing ACh concentration tended to weaken pyramidal phase locking (Fig 9A). For example, at 120% depolarization and 1 μM ACh, the firing of SP_PC, SP_Ivy, and SP_CCKBC cells was broadly tuned around the theta trough and rising phase, while the firing of SP_AA, BS and SP_PVBC neuron was more narrowly tuned around the peak of the theta rhythm (Fig 9B, left). Neurons with significant phase locking matched this pattern but were even more narrowly tuned (Fig 9B, middle). The phase locking of SP_AA, SP_Ivy and PC closely matched in vivo recordings (see S23 Table) but SP_BS and BC (CCK+ and PV+) were by comparison more than 90 degrees out of phase (Fig 9B, right).

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Fig 9. MS disinhibition induced anti-phase modulation of CA1 neurons during theta cycles.

(A) Neurons for analysis were selected within 100 μm radius of the stratum pyramidale electrode location (top left). Phase locking angle and strength for range of ACh concentration (columns) and levels of tonic depolarization (rows, where 100% represents the spike threshold) for modulation amplitude of A = 0.2 nA. (B) Phase modulation. Spike discharge probability of all neurons grouped by morphological type (left). Phase-locked neurons tuning over theta cycle for each morphological class over a single theta cycle (middle). Experimental validation of phase locking against in vivo recordings (right) with an arrow representing the mean phase angle (experimental data = black arrow; simulated = colored arrow) and gray shaded sector indicating, where known, the experimental angular deviation. (C) Spiking raster plots. SP_PC cell spiking (top panel); LFP theta rhythm (trace above plot); interneuron spiking (bottom panel). Disinhibition is switched on (“MS ON”) at time 10 s. (D) Intracellular traces from morphological cell types (left) and validation against in in vivo recordings. B–D: Stimulus disinhibitory modulation amplitude of A = 0.2 nA, 1 μM ACh and tonic depolarization 120%. Experimental values in panels B and D can be found respectively in S23 and S24 Tables. ACh, acetylcholine; LFP, local field potential; MS, medial septum.

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The voltage traces and rate of spiking during theta oscillations for different neuronal types was also grouped. While SP_PC did not spike on every theta cycle their firing appeared weakly modulated by theta (Fig 9C, top). Whereas for interneurons, SP_AA, BS, and SP_PVBC spiked tightly for most cycles, ivy cells spiked more rarely and SP_CCKBC more tonically (Fig 9C, bottom). Intracellular voltage traces for SP_AA, BS, and SP_PVBC showed they spiked tightly on the rebound from the release of the hyperpolarizing stimulus, whereas SP_PC and other interneurons lacking this were less reactive to theta (Fig 9D, left). Notably, all neurons spiked at a lower average rate than in vivo recordings [76–79] (Fig 9D, right). The population synchrony of SP_PC with theta trough was consistent with in vivo data [81] for a range of disinhibitory stimulus amplitudes, whereas for fast-spiking interneurons like SP_AA and SP_PVBC, synchronization with theta peak only occurred with lower stimulus amplitudes (S28 Fig). Taken together, the MS-mediated disinhibition entrained theta oscillations under in vivo-like conditions, creating a diversity of firing phases between interneuron classes, close to what has been observed experimentally.

In summary, we used the reference model to investigate several possible mechanisms for theta oscillations. For intrinsic mechanisms, we found that spontaneous synaptic release and random afferent synaptic barrage did not induce detectable theta oscillations in the model, while tonic depolarization could induce a variable and unstable theta oscillation at 10 to 12 Hz. For extrinsic mechanisms, both CA3 and MS input induced a stable and stronger theta oscillation but in different ways, where MS disinhibition was more compatible with in vivo data.

Other frequencies

Next we asked whether the reference circuit was capable of propagating gamma oscillation using the commonly used in vitro experimental paradigm of inducing them using bath carbachol (CCh) [85–88]. Specifically, we replicated the setup of [89], where the authors added CCh to generate oscillations in CA3, which were transmitted to CA1 via SC. The simulation conditions were tailored to these in vitro experiments (i.e., 300 μm-thick slices, 2 mM extracellular Ca²⁺, 2 mM extracellular Mg²⁺, 10 μM ACh). We matched the shape and frequency of the input stimulus reported by [89] and followed the same LFP analysis methodology. We observed that gamma oscillatory SC input could entrain the entire CA1 network of the model slice to oscillate at the driving frequency (31 Hz) (S29A Fig). As well as inducing oscillations in CA3, in vitro CCh could alter the response of CA1 neurons to the SC input. Thus, to quantify the effect of CCh on CA1, we repeated the simulation without the influence of CCh. SC inputs, ranging from 15,000 to 100,000 stimulated fibers, were able to induce strong gamma oscillation in the absence of CCh. However, CCh increased the number of inputs needed for stable gamma oscillation, probably due to its weakening effect on synapses (S29B Fig). Therefore, at least for this experimental setup, the circuit was capable of propagating gamma oscillations.

Finally, we investigated how the reference circuit behaved across a much wider range of SC input frequencies. Because the nature of the input was less clear across this range, we used a sinusoidal modulated stimulus. In this case, we isolated the role of SC input and we excluded the influence of modulators as ACh. In particular, we extended SC input for a wider range of cell (0.1 to 0.8 Hz) and modulation frequencies (0.5 to 200 Hz) and measured the corresponding input–output (I-O) gain and spike-spike correlation (Fig 10A). We found I-O gain was not uniform but depended on both cell and signal input frequencies (Fig 10B). The I-O responses of PC and interneurons were different, with interneuron gain greater at lower cell frequencies compared to PCs (Fig 10B). The strongest overall CA1 gain was obtained with a mean CA3 frequency of 0.4 Hz. The spike-spike correlation also depends on both cell and signal input frequencies (Fig 10C–10E, upper). In the case of input cell frequency of 0.4 Hz, we found CA1 spiking activity was strongly correlated for delta- to lower gamma-band input signal frequencies (i.e., between 1 and 30 Hz) but weaker outside this range. Internal CA1-CA1 spike correlation was similar but spanned higher frequencies of the gamma-band (Fig 10C–10E, lower). Therefore, the model predicts that oscillations propagate better within the delta- to low gamma-band range.

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Fig 10. Intermediate frequencies propagate more efficiently through SC.

(A) In silico experimental setup. (B) Ratio between the number of CA1 and CA3 spikes as a function of input cell and signal frequencies. We considered all CA1 neurons (left), CA1 PCs (center) and CA1 interneurons (right). (C) Heatmaps representing the computed STTC values as a function of input cell and signal frequencies, for CA3-CA1 and CA1-CA1 neurons. (D) Examples of CA3 and CA1 spike train (cell frequency of 0.4 Hz, signal frequency of 10 Hz); 100 random CA3 neurons (i.e., SC fibers) and CA1 neurons are selected for clarity. The same neurons are used to compute the STTC and spike-spike correlations (panels D and E). (E) Spike-spike normalized correlation histograms for 4 signal frequencies (cell frequency of 0.4 Hz) for CA3-CA1 and CA1-CA1 neurons. SC, Schaffer collaterals; STTC, spike time tiling coefficient.

https://doi.org/10.1371/journal.pbio.3002861.g010

Main summary

This study presents the reconstruction and simulation of a full-scale, atlas-based reference model of the rat hippocampal CA1 region based on community data and collaboration. We extended and improved the framework of [27] to curate and integrate a wide variety of anatomical and physiological experimental data from synaptic to network levels. We then systematically applied multiple validations for each level of the model. We augmented the resulting highly detailed intrinsic CA1 circuit with a reconstruction of its main input from CA3 and a phenomenological model of neuromodulation by acetylcholine. Importantly, the reference circuit model is, by definition, general. It is capable of addressing a range of research questions because its parameters are adjusted only to different experimental setups, not tuned each time to specifically reproduce individual experimental results. For example, to help explain network activity observed in both health and disease, with the model one can block different neurotransmitters or specific groups of synapses, change the proportions of different cell types, modify synaptic strength or short-term plasticity, or alter the properties of ion channels in specific cell types to study their consequences on network dynamics. However, the range of the research questions it can address is necessarily limited by the current extent of the model and its inputs (see later). To demonstrate its general utility, we were able to simulate different scales of circuits and investigate the generation and transmission of neuronal oscillations, with particular emphasis on theta rhythm, for a variety of stimulus conditions.

Previous work and limitations

While a full review of the many hippocampal circuit models is beyond the scope of the paper, we focus on the progression in both the size and level of detail of large, multiscale models of the rat hippocampus during the last 3 decades (for a comparison of their key features with the present model, see S2 Table). These biologically realistic models aim to explain the complex dynamics of hippocampal activity, in particular the generation and control of rhythmic responses. However, all these models, including the one reported here, are incomplete descriptions of a hippocampal region or regions because of the paucity or even absence of some types of data necessary to constrain them. Moreover, the results of these models are difficult to compare because (1) there is no commonly agreed-upon set of validations with which to benchmark a circuit model against experimental data; and (2) there are fundamental differences in their composition, organization, and underlying assumptions.

In terms of model validation, circuit models of isolated CA1 have, ever since the reports of [72], been expected to generate theta oscillations intrinsically (see [22]). Later research by the same lab, however, raises some doubts about this interpretation of the results. In an isolated whole mouse hippocampal preparation, as used by [72], [90] found that inactivating the subiculum abolished theta (5 Hz) activity in CA1 and the remaining 2.5 Hz oscillations in CA1 matched that of intact CA3 (see their S6 Fig). So the theta oscillations in isolated CA1 observed in [72] might be explained if the subiculum was not removed when isolating CA1 from CA3 (see S10 Fig of [72]). Therefore, these later results imply that CA1 may not be able to generate robust theta oscillations intrinsically but instead its oscillations are induced by subiculum and CA3 inputs, which is what we observed here for CA1 circuit model for CA3 input simulations. Yet, while it is clear from the current model that different mechanisms can generate CA1 theta oscillations (degeneracy; for a review of this concept, see [91]), the cell-class specific phasing of spiking of circuit neurons during theta LFP oscillations does not offer a good overall match to in vivo experimental results [77–79,92].

In terms of model construction, the current model stands out by realistically constraining neurons and their connectivity by the highly curved shape of CA1 rather than by relying on an artificial space as found in other contemporary models. Additionally, it reflects both STP and spontaneous synaptic release, well-established characteristics of central nervous system synapses. In addition, the morphologies and electrical properties of model neurons here are not just copies of the same class exemplars but their properties have been systematically varied to better capture the diverse nature of neuronal circuits and their responses to stimulation. However, compared with [22], some elements are still missing from the current model such as neurogliaform cells, which did not exist in our available data set, and GABA_B R which are not included in our simulations. Yet, neither the current model nor [22] incorporates other established features of CA1 such as dorsal-ventral differences in neuronal and synaptic properties [93] or burst firing of pyramidal neurons [94].

Nonetheless, the current model includes the perforant path-associated and trilaminar interneurons, which were absent from all previous models. In addition, we modeled the NMDA synaptic currents observed in both hippocampal pyramidal cells and interneurons (with specific NMDAR conductance, rise and decay time constants for each pathway) that are absent in the model of [22]. Furthermore, the connectivity algorithm used for the current model generates an intrinsic connectome with more realistic high-order statistics than the more prescriptive approach used in the [22] model (see [42] for the analysis). Unlike [24], we did not replicate the topography of the afferent projections, which may play a role in patterning the circuit response, but did model the projections and circuit at a full rather than reduced scale. Overall, further improvement to our model requires additional experimental data.

While we incorporated key features distributed among previous models into a single, general model (see S2 Table), it is important to recognize that our aims and approach were different, representing a step change in hippocampal modeling. The intention of the framework was first to curate and integrate community data into the model, preserving provenance for reproducibility, in a way that would allow the addition of new datasets from the large hippocampal community. Re-using these data sets and then making them publicly available through the hippocampushub.eu supports the 3R principles (replace, reduce, refine) for the reduction of animal experiments. Each circuit component and the final model was then systematically validated in an open and transparent way to a degree not previously attempted by other research groups. To increase the realism and utility of simulation experiments, we sought to approximate experimental conditions (e.g., slice thickness and location, bath calcium, magnesium and acetylcholine concentrations, and recording temperature) and to increase the capability to manipulate and record from the model (e.g., enable spontaneous synaptic release, alter connectivity, estimate extracellular LFP signals, and apply a variety of stimuli). In short, the aim was to offer a more realistic yet scalable and sustainable approach to model brain regions at full scale.

Lessons learned

In the context of a community effort, the process of curating and integrating available data to reconstruct a brain region and replicating the experimental conditions in silico proved instructive in a number of ways. First, assembling the components to reconstruct a brain region reveals surprising gaps in the available data and knowledge. Notably, for example, while Schaffer collateral input to CA1 has received many decades of attention, especially in terms of long-term plasticity, we found the basic information needed to model this pathway quantitatively, was limited. To address this gap, we devised a multi-step algorithm constrained by the data that were available to parameterize these connections. Second, when data was available it often required further work before it could be used in the model. While an open-source rat hippocampal atlas [39] was crucial to reconstruct CA1, the original volumetric reconstruction was too noisy for our purposes and required additional processing to give smooth layering. This smoothness was necessary to place and orient morphologies accurately in the atlas in relation to the layers. If the morphology was incorrectly placed or oriented, this had a knock-on effect for how the circuit was connected. Similarly, the completeness of morphological reconstructions also affected connectivity. For these reasons, some cell types in our available data set could not be used in the circuit model, sacrificing a small amount of cell type diversity in favor of completeness. Third, setting up simulations to reproduce the desired experimental conditions required careful attention. We offer 2 examples from our research. When reproducing the I-O gain of SC afferent input reported in [56], we initially sampled all neurons in the model slice to plot to the I-O curve. However, the result was poor. We later resolved this by reproducing how the neurons were sampled in the experiments with which we could closely match the empirical curve. When reproducing MS-induced theta oscillations, we initially simulated under default conditions of extracellular calcium concentration at 2 mM, resulting in theta oscillations that occurred episodically and only for a restricted parameter regime. However, when we lowered the extracellular calcium to in vivo levels (1 mM), sparser activity led to more robust and stable theta oscillations.

A community-based modeling approach

The model was built and simulations run through the cooperation of several laboratories each with different expertise. Since we could not access a standardized core set of data made for the purpose of modeling as done previously [27–29], instead, we curated and integrated data from collaborating labs which followed different protocols. The majority of single neuron morphologies and recordings, for example, came from University College London (UCL) [76,95–102]. From these data, single neuron models were created between the Blue Brain Project (BBP) and Italian National Research Council (CNR) [35] and these were then validated by a computational lab at Institute of Experimental Medicine, Budapest (KOKI) [103]. Similarly, physiological data from paired recordings that characterized individual synaptic pathways were provided by an experimental lab in KOKI and then curated and integrated together with BBP [34]. Subsequently, BBP used these single neuron and synapse models to build and share the circuit model so computational labs at BBP, CNR, and KOKI could simulate various hippocampal use cases, only some of which have been presented here. Combining the framework of [27] with community data and collaboration resulted in the generalization and improvement of data curation and integration methods for more varied data, improvements in tools like BluePyOpt for optimizing neurons, and the development of a new tools such as HippoUnit to systematically validate and compare different single neuron models.

This approach offers important features that make an attractive case for adoption by the wider hippocampus community. First, anchoring a circuit model in the volumetric space of a brain region atlas makes mapping experimental data for data integration, validation, and prediction easier than for more abstract spaces and permits investigations at different scales, e.g., a brain slice cut at an arbitrary angle. The Allen Brain Atlas has demonstrated the advantages of registering community experimental data in a common reference atlas [104]. Extending this principle, a common framework appears advantageous for modeling as well. Second, the model components, validations, and circuit are openly available through a dedicated portal (hippocampushub.eu) to maximize transparency and reproducibility. We allow the community to examine how the reference circuit model was built, validated, simulated, and analyzed. We conceived the model to be adopted by the community, extended and improved. Third, while the traditional approach of constructing circuits for a specific use case has short-term advantages for demonstrating proof-of-concept, in the long-term a community reference model must be valid across a range of use cases.

To illustrate its utility, we suggest how the circuit model could be developed by the community to help address key scientific questions concerning structure and function of hippocampus. An example use case under in vitro-like conditions could be to use slice circuit models to study network responses to different stimuli based on observed difference in neuronal and synaptic properties between dorsal and ventral CA1 [93]. Under in vivo-like conditions, the full-scale circuit model could be employed to investigate the factors necessary for the emergence of traveling and standing wave phenomena reported from CA1 LFPs [105]. To increase the level of biological accuracy at the cellular level, for example, a new class of neurons might be added to the circuit (for practical steps required, see S1 Appendix). To achieve greater accuracy at the circuit level, particularly in investigating place cells, significant additions would be necessary to match the current level of biological accuracy in the model. In particular, the anatomy and function of the perforant pathway (PP) would need to be reconstructed using available empirical data as we did here for the SC pathway. This would involve understanding quantitatively the synaptic connectivity and unitary monosynaptic EPSPs from individual PP axons onto CA1 neurons, ideally from single neuron paired recordings. Additionally, the simulation patterns of these PP and SC projection axons would need to reflect the activity of EC and CA3 neurons during rat locomotion to activate place cells realistically. Finally, to model the formation and remapping of place cells, model synaptic connections would need to be endowed with long-term plasticity (e.g., [106]). While the level of effort required is significant, the potential benefits of creating a model-experiment loop, where experimental data are incorporated in the model (experiments to model) and model results used to generate experimentally testable predictions (model to experiments) should not be underestimated in minimizing the cost in terms of animals and materials.

Experimental procedures

In this study, we used 2 data sets for single neuron morphological reconstructions and electrophysiological recordings from the region CA1: Sprague Dawley rat and Wistar rat. Both data sets also include the reconstruction of the layers that were used to estimate the layer thicknesses (see section Layers) and guide the cell placement (see section Soma placement). Note that, while the Wistar rat data set also includes electrophysiological recordings, we did not use them for this model. The experimental procedures have been previously described in [35], but are summarized below.

Sprague Dawley rat data set

Procedures involving animal care and use were approved by the University of London or University College London ethical committees and by the British Home Office with regard to the Animal Scientific Procedures Act 1986 (PPL 80/2131, 80/2598). Hippocampal slices were obtained from young adult rats (Sprague Dawley, 90 to 180 g) as previously described [76,95–102]. Briefly, following deep anesthesia with euthatal solution, young adult rats (Sprague Dawley, 90 to 180 g) were perfused transcardially with ice-cold modified artificial cerebrospinal fluid containing in mM: 248 sucrose, 25.5 NaHcO₃, 3.3 KCl, 1.2 KH₂PO₄, 1 MgSO₄, 2.5 CaCl₂, 15 D-glucose, equilibrated with 95% O₂/5% CO₂; 450 to 500 μm coronal sections were cut, transferred to an interface recording chamber and maintained at 34−36°C in modified ACSF solution for 1 h and then in standard ASCF (in mM: 124 NaCl, 25.5 NaHCO₃, 3.3 KCl, 1.2 KH₂PO₄, 1 MgSO₄, 2.5 CaCl₂, and 15 D-glucose, equilibrated with 95% O₂/5% CO₂) for another hour prior to starting electrophysiological recordings. Single intracellular recordings were made using sharp microelectrodes (tip resistance, 90 to 190 MΩ) filled with 2% biocytin in 2M KMeSO₄ under current-clamp (Axoprobe; Molecular Devices, Palo Alto, California, United States of America). Electrophysiological characteristics of the recorded neurons were obtained from voltage responses to 400 ms current pulses between −1 and +0.8 nA and recorded with pClamp software (Axon Instruments, USA).

Following recording and biocytin filling, slices of 450 to 500 μm were fixed overnight [4% paraformaldehyde (PFA), 0.2% saturated picric acid solution, 0.025% glutaraldehyde solution in 0.1 M phosphate buffer] as previously described [97,107]. Slices were then cut in 50 to 60 μm sections, cryoprotected with sucrose, freeze-thawed, incubated in 1% H₂O₂ and then in 1% sodium borohydride (NaBH4). Slices were incubated overnight in ABC (Vector Laboratories) and then in DAB (3, 3′ diaminobenzidine, Sigma) to reveal the morphology of the recorded neurons. Following washes, sections were postfixed in osmium tetroxide (O_sO₄), dehydrated, cleared with propylene oxide, mounted on slides (Durcupan epoxy resin, Sigma), and cured for 48 h at 56°C. For immunofluorescence staining, slices were incubated in 10% normal goat serum after incubation with NaBH₄. Sections were then incubated overnight in a primary antibody solution containing mouse anti-PV (Sigma), rabbit anti-PV [108] or mouse anti-gastrin/CCK (CURE, UCLA) made up in ABC and then in a solution of secondary antibodies (Avidin-AMCA, FITC and anti-rabbit Texas Red) for 3 h. Following fluorescence visualization, slices were incubated in ABC, DAB, and OsO₄ prior to dehydration and mounting as described above. All neurons were then reconstructed in 3D using a Neurolucida software (MBF Bioscience) and a 100× objective as previously described [107].

Wistar rat data set

The project was approved by the Swiss Cantonal Veterinary Office following its ethical review by the State Committee for Animal Experimentation. All procedures were conducted in conformity with the Swiss Welfare Act and the Swiss National Institutional Guidelines on Animal Experimentation for the ethical use of animals (license VD3389). Hippocampal slices were obtained from young adult rats (Wistar, postnatal 14 to 23 days) as previously described [27,35]. In brief, ex vivo coronal preparations (300 μm thick) were cut in ice-cold aCSF (artificial cerebrospinal fluid) with low Ca²⁺ and high Mg²⁺. The intracellular pipette solution contained (in mM) 110 potassium gluconate, 10 KCl, 4 ATP-Mg, 10 phosphocreatine, 0.3 GTP, 10 HEPES and 13 biocytin, adjusted to 290±300 mOsm/Lt with D-mannitol (2±35 mM) at pH 7.3. Chemicals were from Sigma Aldrich (Stenheim, Germany) or Merck (Darmstadt, Germany). A few somatic whole cell recordings (not used for this model) were performed with Axopatch 200B amplifiers in current clamp mode at 34±1°C bath temperature.

The 3D reconstructions of biocytin-stained cell morphologies were obtained from whole-cell patch-clamp experiments on 300 μm thick brain slices, following experimental and post-processing procedures as previously described [109]. The neurons that were chosen for 3D reconstruction were high contrast, completely stained, and had few cut arbors. Reconstruction used the Neurolucida system (MicroBrightField, USA) and a bright-field light microscope (DM-6B, Olympus, Germany) at a magnification of 100× (oil immersion objective, 1.4 to 0.7 NA). The finest line traced at the 100× magnification with the Neurolucida program was 0.15 μm. The slice shrinkage due to the staining procedure was approximately 25% in thickness (Z-axis). Only the shrinkage of thickness was corrected at the time of reconstruction.

Morphological classification

We classified the morphologies into one of 12 different morphological types (m-types) based on the layer containing their somata and their morphological features. For the classification, we adopted 3 main assumptions. (1) Several subtypes of PCs have been described [108,110–116], but for simplicity we consider the pyramidal cells as a uniform class (SP_PC or simply PC). (2) SP_PVBC and SP_CCKBC were classified as 2 separate m-types. The 2 types of basket cells can be distinguished by biochemical markers and electrical properties, and they show different densities and connectivity [5]. On the contrary, there is no strong evidence for differences in their morphologies and the small number of examples in our possession (3 SP_PVBCs, 1 SP_CCKBCs) prevented us from conducting any systematic classification. While we could have pulled the 2 cell types into one m-type, we kept them separated for the sake of simplicity. (3) We created supersets of m-types based on their principal biochemical marker. In particular, we defined PV+ cells as SP_PVBC, SP_BS, SP_AA, CCK+ cells as SP_CCKBC, SR_SCA, SLM_PPA and SOM+ (somatostatin) cells as SO_OLM, SO_BS, SO_BP, SO_Tri. When the layer is not specified (e.g., BS), we meant all the neurons of this type regardless their soma location.

Morphology curation

We curated the morphological reconstructions extensively prior to insertion in the network model. First, we translated the reconstructions to have their somas centered at coordinates (0,0,0). We reoriented the reconstructions so that their x, y, and z axes coincided respectively with the transverse, radial, and longitudinal axes they followed in the tissue. We considered the cells to be substantially complete, with only a few cuts, so we have not applied any corrections for cuts [27]. The only exception is the PC axon. One particular reconstruction has a relatively long axon (3,646 μm) that spans 1,325 μm along the transverse axis. We assumed this axon to be relatively complete within the CA1 and we used it as a prototype for all the PCs. Validation of the number of synapses per connection, bouton density, and connection probability showed that this assumption is reasonable (see section Building CA1). A subsequent cloning procedure (see section Morphology library) guaranteed that all the PC axons are unique. We removed 2 pyramidal cells due to the complete absence of an axon since at least the axon initial segment (AIS) needs to be present to create electrical models.

We applied a series of corrections as described in [27]. In brief, to comply with the NEURON and CoreNEURON standards, we repaired the reconstructed morphologies using NeuroR [117] (Table 1). In particular, we used this tool to remove unifurcations of dendrites, fix neurites whose type changes along its main branch, fix invalid formats of soma, and remove segments with close to zero length. We used this tool also to correct tissue shrinkage. The correction increased the neurite reach approximately 25% along the z-axis and approximately 10% along the x- and y-axes.

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Table 1. List of software used.

https://doi.org/10.1371/journal.pbio.3002861.t001

Morphology library

To produce morphology variants that fit well in different locations of the space, we applied scaling ±15% of the original reconstructions. This range was a good compromise between the need to change the size but yet to not introduce too much distortion [27]. To increase morphological diversity, we applied a cloning procedure as described in [27]. Some clones showed a wrong distribution of axons and dendrites, and we removed them. In particular, we annotated how different parts of the morphology were positioned within the layers (see section Layers). We used these annotations to guide the cell placement, but it was also useful to discard cells that were too distorted by cloning and had an incorrect distribution of neurons within the layers. Clones were further validated by visual inspections. For OLM cells, a scaling of ±15% was not sufficient to make sure that the axon correctly targeted SLM in all dorso-ventral positions. In this case, we introduced a synthetic axon. In the reconstruction of OLM cell, a chunk of 60 μm axon, which is placed at 85 to 145 μm from the soma, falls in SR and it is relatively simple. To produce morphologies with about 90% to 150% (step of 5%) of the height of the original morphology, we removed the aforementioned chunk of 60 μm axon (93%), only 45 μm of it (95%), or added a multiple of 45 μm (corresponding to a step of 5%) synthetic axon within SR until we reached a 150% scaling.

After we corrected the orientation of the initial set of reconstructions, the cloning procedure changed the branch lengths and rotations, which may have resulted in a change in the main orientation of the cells. Based on visual inspection, the effect on short neurites was negligible. In the case of PCs, the axon is relatively longer and has a clear orientation [118]. In this case, the cloning may significantly alter the orientation of the axon, and this may result in a wrong placement in the circuit (see section Soma placement). To avoid this problem, we renormalized the orientation of the cloned PCs. In particular, we used principal component analysis (PCA) to first determine the principal axis of all axonal points in each cloned morphology. Next, we used the direction of the principal axis to rotate the caudal portion of the arbor onto the x-axis so all pyramidal axon arbors were aligned in the same direction. Finally, to remove an unrealistic degree of variability, we filtered out cloned morphology outliers whose width (z-axis range) was 3.3 times greater than that of the original pyramidal axon arbor from which they were derived. This filtering step rejected about 14% of all pyramidal cell cloned morphologies.

Morphology library validation

Neuronal morphologies were validated at the end of the processing stage (cloning) by comparison of their morphological properties, as well as their topological profiles. Around 100 morphological features from dendritic and axonal neurites were extracted using the NeuroM package [119]. The median over visible spread (MVS) statistical score, defined as the ratio of the absolute value of the difference between the medians of the feature () divided by the overall visible spread (OVS), was computed according to the following formula: (1) to identify the difference between populations of reconstructed P_r and cloned P_c neurons for each feature F. This score is close to zero for similar populations and increases as the difference between the populations increases. Scores below 0.3 indicate good agreement between the 2 populations as their differences are contained within 3 standard deviations (STD). Note that this measurement depends on the sample size, due to the computation of the OVS, which remains small if the sample size is small and therefore the MVS score increases accordingly.

In addition to the traditional morphometrics, the topological profiles of the original reconstructions were compared to those of the processed morphologies (repaired and cloned). The TMD encodes the start and the end radial distances of each branch from the soma surface [120]. The pairs of distances (start, end) are represented in a 2D plane, a representation known as the persistence diagram of the neurons (S6 Fig). The Gaussian kernels of these points are averaged to generate the persistence images (S7 and S8 Figs). The persistence images of 2 populations can be subtracted to study the precise differences between data sets. Note that the robustness of average persistence images depends on the sample size of the population, when only few (less than 3) cells are available these images represent a small subset of the biological population and are therefore not quantitatively reliable.

Electrical type classification

We classified the cells into different electrical types (e-types) based on their firing patterns as defined by the Petilla nomenclature [33]. Some of the firing patterns (i.e., irregular patterns) were too rare and we excluded them. For SP_CCKBC we do not have traces, and we considered them to be classical accommodating (cAC) [96].

Morpho-electrical compositions

The 154 recordings were recorded from different m-types, and we observed that each m-type can show one or more firing patterns with different probabilities. We used this information to derive the morpho-electrical type (me-type) composition (S4 Table).

Ion channels

We considered a set of active membrane properties which included a voltage-gated transient sodium current, 4 types of potassium current (DR-, A-, M-, and D-type), 3 calcium channels (CaN, CaL, and CaT), a nonspecific hyperpolarization-activated cation current (Ih), 2 Ca-dependent potassium channels (KCa and Cagk), and a simple Ca²⁺-extrusion mechanism with a 100 ms time constant. We based channels’ kinetics on previously implemented cell models of hippocampal neurons [121–124].

Single-neuron modeling

Single-cell models are described in previous publications [34,35,125]. In brief, we optimized cell parameters to match electrophysiological features rather than the traces directly. We extracted features using the open-source Electrophys Feature Extraction Library (eFEL, Table 1) or the Blue Brain Python E-feature extraction (BluePyEfe, Table 1). Initial optimizations considered only features from somatic recordings [35], while a subsequent refinement included also the amplitude of the back-propagating action potential (in the apical trunk, 150 and 250 μm from the soma) for PCs [34].

We assumed channels were uniformly distributed in all dendritic compartments except K_A and I_h, which in pyramidal cells are known to increase with distance from the soma [126,127]. Pyramidal cells include K_M in the soma and axon [128], K_A with different kinetics in dendrites, soma and axon [121,129], K_M with a different kinetics in the soma and the axon, Na and K_DR, whereas they do not include K_D since the delayed spiking is not a feature observed in PCs. Given the limited knowledge of the currents in interneurons, we applied the same currents of pyramidal cells with the following exceptions. Dendritic sodium channel densities decay exponentially with distance from the soma (with a length constant of 50 μm) based on [130]. We included K_D since some interneurons show delayed firing. K_A has the same kinetics in somas and dendrites because there is no experimental evidence of a different K_A kinetics in the dendrites of interneurons. We distinguished 2 types of K_A for proximal and distal dendrites [121]. For both pyramidal cells and interneurons, we optimized channel peak conductance independently in the different regions of a neuron (soma, axon, and dendrites).

We performed a multi-objective evolutionary optimization using the open source Blue Brain python optimization library (BluePyOpt, Table 1) [131] to obtain 39 single-cell models. From this set, we excluded 3 models because their me-types are not used in the network model (cAC_SP_Ivy, cAC_SP_PVBC, cNAC_SR_SCA).

Single neuron model validations

We used HippoUnit [103] (Table 1) to validate the electrical models of pyramidal neurons, specifically considering the attenuation of PSP and BPAP.

PSP attenuation

The PSP attenuation test evaluates how much PSP amplitude attenuates as it propagates from different dendritic locations to the soma. To get the behavior from the model, EPSC-like currents (i.e., double exponentials with rise time constant of 0.1 ms, decay time constant of 3 ms, and peak amplitude of 30 pA) were injected into the apical trunk of PCs at varying distances from the soma (100, 200, 300 ± 50 μm), and PSP amplitudes were simultaneously measured at the local site of the injection and in the soma. Finally, the experimental and model data points were fitted using a simple exponential function. The space constants resulting from the fitting were then reported and compared with experimentally observed data in [37].

BPAP attenuation

The BPAP test evaluates the strength of AP back-propagation in the apical trunk at locations of different distances from the soma. The AP is triggered by a step-current of 1 s with an amplitude for which the soma fires at approximately 15 Hz. The values were then averaged over distances of 50, 150, 250, 350 ± 20 μm from the soma. We measured the amplitudes of the first AP at the 4 different dendritic locations and compared them with experimentally observed data in [36].

Library of neuron models

Optimizing all the neurons in the morphology library is computationally expensive. Following [27], we minimized the problem by using Blue Brain Python Cell Model Management (BluePyMM, Table 1) which combines the morphology library with initial single-cell models to produce a library of cell models. The procedure accepts a new combination if the model and experimental features are within 5 STD of the experimental feature. If at least 1 feature is greater than this range, then the new combination is excluded. This strategy also has the advantage of increasing the model variability within the experimental data. In the case of bAC-SLM_PPA, the threshold for accepting new combinations had to be relaxed to 12 STD to obtain some valid models.

Rheobase estimation

For all the single-cell model combinations, we estimated their rheobase with a bisection search until an accuracy of e-3 was reached. The spikes were recorded at the AIS, and the upper bound from the last step of the search was used, to ensure cells spiked in the axon at rheobase.

Atlas

Cell composition

We started by fixing the PC density in SP to 264 ± 32.6 × 10³ mm³ [134]. By combining the PC density and SP volume as extracted from the atlas (1.5789 mm³), we estimated the total number of PCs as 416,842. To estimate the number of cells or cell densities for interneurons, we used the ratio between PCs and the different interneurons as predicted by [5] with several assumptions. In some cases, a cell type has been described as present in several layers. If we only have reconstructions of cells from one layer, we consider all the expected cells to be placed in this layer. In the case of bistratified (BS) cells, we have reconstructions from SO and SP, but [5] also described a small percentage of cells in SR. In this case, we considered the cells from SR to be placed in SP; [5] gave a rough estimation of 1,400 cells for trilaminar cells and radiatum-retrohippocampal cells together in SO. Without any other information, we considered these 2 cell types to have the same proportion, so we estimated the number of trilaminar cells as 700. We ignored the m-types for which we do not have at least 1 reconstruction. The lack of some cell types led to a smaller number of interneurons. To maintain the same E/I ratio of 89:11 [5], we increased the number of interneurons accordingly. The resulting cell composition counts and densities are shown in S3 Table.

Cell placement

Circuit sections

We defined a series of sections of the circuit to be used in analyses and simulations. In particular, we defined nine cylinders equally spanned from position 0.1 to 0.9 along the longitudinal axis, in the middle of the transverse axis (0.5) and with a radius of 300 μm. In addition, we defined 47 consecutive nonoverlapping transverse slices of thickness of 300 μm.

Synapses

Schaffer collaterals (SC)

Cholinergic modulation

To build a model of the effects of cholinergic release, we began by collecting and curating literature findings from bath application experiments in which ACh, carbachol (CCh), or muscarine were used. We extracted data on their effects on neuron excitability (membrane potential, firing rate, S19 Table), synaptic transmission (PSP, PSC, S20 Table), and network activity (extracellular recordings, S21 Table). We subsequently verified that the other experimental conditions (such as cell type, connection type and mouse versus rat provenance) did not produce further data stratification.

Since for each experiment, data was available for both control and drug-applied conditions, we estimated the relative amount of depolarizing current at different concentrations of ACh. For sub-threshold data, we computed the cell type-specific amount of current causing a change in the resting membrane potential equal to the mean value reported in the experiments. For supra-threshold data, we computed the amount of current needed to increase the firing rate from the baseline frequency to the frequency in ACh conditions.

The data points show a dose-dependent increase in depolarizing current. To describe this effect, we fitted a Hill function assuming the ACh-induced current at control condition is zero (R² = 0.691, N = 28). (9) where I_depol is the depolarizing current (in nA) and ACh is the neuromodulator concentration in μm (Fig 5A and 5C). At the synaptic level, the data points show a dose-dependent decrease in the amplitude of the voltage/current response to pre-synaptic stimulation for all pathways analyzed (S20 Table). Since ACh affects synaptic transmission principally at the level of release probability [23,60,61], we used the Tsodyks–Markram model [23,140,141] and introduced scaling factor to make the parameter U_SE (neurotransmitter release probability) dependent on ACh concentration with a Hill function fitted to experimental data (R² = 0.667, N = 27). (10) Where U_SE is the release probability (without ACh), and is the release probability with the dependency on ACh concentration (Fig 5B and 5D).

As a control, we verified that the values of PSP or PSC are proportional to U_SE.

For each network simulation, we applied these equations to compute the effect of ACh concentration on cells and synapses. In particular, we inject the same amount of depolarizing current (Eq 9) to all the cells and apply the same U_SE scaling factor (Eq 10) to all pathways including Schaffer collaterals. All the simulations shown in Fig 5E–5K were run on the cylinder microcircuit with the extracellular calcium concentration set to 2 mM and a duration of 10 s. To disregard the initial ramping activity, we used the last 9 s of the simulation to compute correlation metrics.

MOOC circuit

We built a CA1 microcircuit as part of an MOOC on edx platform (https://www.edx.org/learn/neuroscience/ecole-polytechnique-federale-de-lausanne-simulating-a-hippocampus-microcircuit). This microcircuit shared many features with the current full-scale model of CA1, but there are a series of differences which need be considered. (1) The model uses a simplified volume as described in [27]. In particular, we defined an hexagonal prism of side 243 μm, surrounded by 6 other equivalent prisms to minimize boundary effects. (2) The network consists of 18K neurons, 20M internal synapses, and 34M afferent synapses. (3) Minor differences could also be observed at the level of the connectome and synaptome due to differences in volume, size, and cell orientations.

Simulation

Analysis

Simulations showed an initial transient due to variable initiation and it appeared as an initial high activity of the network. This transient lasted for few ms, but we normally discarded the first 1,000 ms in all the simulation analyses to be sure that the parameters converged into a stable regime.

Statistical analysis

To calculate the slopes in linear fits to the appositions data, we used least-squares solution from the python toolbox (numpy.linalg.lstsq function).

For the fitting of experimental data points of cholinergic modulation, we used the nonlinear least squares solution (scipy.optimize.curve_fit function). Values are expressed as R² coefficients.

For LFP analysis, the augmented Dickey–Fuller (ADF) unit root test was used to determine whether a single channel continuous signal was stationary before analyzing its spectral properties (statsmodels.tsa. stattools.adfuller function). To determine whether single neurons were phase-locked, the Rayleigh Test of randomness of circular data was used to reject the null hypothesis that phase angles of a spike train were uniformly distributed [156]. To compare with empirical results (e.g., [77]), phase analysis results were described by mean ± angular deviation in degrees.

Statistical comparison methodology

Our statistical comparisons between the model and experimental data were guided by the experimental data availability. To streamline the process, we performed statistical comparisons at an aggregate level rather than conducting comparisons for each individual cell type or pathway.

There are 2 main reasons to perform statistical comparisons at an aggregate level. Firstly, there may be a lack of data available at a granular level, such as for cell composition validation. Secondly, for certain parameters, such as bouton density, because we used a multi-objective optimization approach to match experimental data at an aggregate level, it is more appropriate to validate at an aggregate level as well. For these comparisons, we typically use Pearson’s correlation coefficient (scipy.stats.pearsonr). Values are expressed as (Pearson correlation coefficient, p-value).

In cases where we needed to compare a large number of features for a metric, such as in morphology cloning validation, we used similarity scores in addition to correlation analysis. However, in other cases, when only a mean and standard deviation value were available for comparison, as in Schaffer collateral comparison, we used a z-test or t test. Values are expressed as p-value.

Finally, if the experimental data had a very small sample size, such as in the case of population synchrony, we did not perform any statistical and we relied only on qualitative assessments.

Visualization

Model and code availability

The entire model, its components, and the source data can be explored and downloaded from hippocampushub.eu. The entire circuit can be also downloaded from Harvard Dataverse (doi:10.7910/DVN/TN3DUI). Code and input data to reproduce both main and supplementary figures are also available from Harvard Dataverse (doi:10.7910/DVN/UGOQWE).

List of assumptions

Software used

Table 1 lists the software used in the paper.