Fig 1.
In vitro current injection recordings of cell types and of the corresponding model cells.
For each cell type we used the experimental recording (upper trace) to constrain the cell model (middle trace) in response to the same current injection (lower trace). Sources for the experimental data: CA3 pyramidal cell [40], DG granule cell [41], OLM cell [42], and basket cell [43]. The parameter values for the model cells are listed in Table 1.
Fig 2.
Network synaptic connections, titration of external input synapses, and the dynamics of short-term plasticity.
A) Schematic showing the full model. Abbreviations: Pyr, pyramidal cells; OLM, oriens-lacunosum moleculare cells; BC, basket cells; EC, Entorhinal cortex; DG, dentate gyrus. B) In vivo distribution of CA3 place cells firing rates as the rat crossed their place field. Reproduced from [44]. C1) The distribution of CA3 pyramidal cells firing rates in the model case where random trains of synaptic inputs arrived at EC cells at a base rate of 15 Hz. C2) The distribution of CA3 pyramidal cells firing rates in the model case where random trains of synaptic inputs arrived at CA3 pyramidal cells at base rates drawn from a lognormal distribution with an average of 50 Hz and a standard deviation of 40 Hz. D-I: Synaptic model responses match those in experimental recordings. D) Mossy fiber synaptic facilitation [45]. (Scale bars: 50 ms, 100 pA). Parameter values used to reproduce data are listed in Hummos et al. [38]. E) CA3 Pyramidal cell to OLM interneuron [42]. (Scale bars: 20 ms, 1 mV). F) CA3 Pyramidal cell to BC interneuron [46]. (Scale bars: 30 ms, 0.5 mV). G) BC interneuron to CA3 pyramidal cell [47]. (Scale bars: 50 ms, 100 pA). H, I) Recurrent CA3 connections stimulated at 50 Hz, and 20 Hz, respectively [48]. Note that these connections displayed paired pulse facilitation, a phenomenon not included in our synapse model. Therefore, responses to the first stimulus in the train appear larger than in the recordings. (Scale bars: 20 ms, 0.5 mV in E; 50 ms, 0.5 mV in F).
Fig 3.
Model network displayed theta rhythmicity.
External inputs arrived at EC cells in the form of Poisson spikes with a base rate of 15 Hz, chosen to reproduce place cells firing rates (see Methods). A) Network schematic showing the entire model. External input represented by box with random spike trains. B1) Spike raster plot from an example instantiation of the network. B2) P opulation firing rate calculated using a 20 ms sliding window and B3, 4) two membrane potential traces of neurons from the same network instantiation. C) The population power spectrum of CA3 pyramidal cells averaged from 10 network instantiations showing a peak at around 6 Hz. We sampled spike counts from the cell types considered, in 0.1 ms bins, and calculated the Fourier transform of the resulting vector, using a window length of 1024 ms. Shaded areas represent SD. D) Power spectra from four populations of cells in the model showed a peak around 6 Hz: (D1) OLM cells, (D2) BCs, (D3) EC, and (D4) DG.
Fig 4.
Disconnected pyramidal cells show theta spiking oscillations.
A) Schematic of this experiment with isolated pyramidal cells each receiving a unique train of Poisson spikes with base rates derived from a lognormal distribution (mean 50 Hz SD 40 Hz, chosen to reproduce place cells firing rates). B1) Spike raster plot of pyramidal cells showing grossly random firing. B2) Population firing rate calculated using a 20 ms sliding window. B3, 4) Example membrane voltage traces from two neurons. C1) The power spectrum of the spiking activity of pyramidal cells as a population showing a peak at 8 Hz. C2) the spike-triggered average of the ‘u’ current of the Izhikevich model that captures the spike-frequency adaptation of the cells. C3) The inter-spike interval distribution of pyramidal cells. D) Same as in C, but with the time-constant of adaptation lowered from 100 ms to 25 ms, resulting in a power spectrum peak at 17 Hz, to demonstrate the relationship between the spiking oscillations, adaptation current, and the spiking dynamics of pyramidal cells.
Fig 5.
Divergent projections from EC to CA3 produced theta oscillations.
A) Schematic of this experiment where the only active connections were the projections from EC to CA3 pyramidal cells. Model EC neurons lacked any rhythmicity and on average, each EC neuron projected to about 20% of CA3 pyramidal cells (see Methods). B1) Spike raster plot and (B2) population firing rate from one example network. C) The population power spectrum of CA3 pyramidal cells averaged over 10 network instantiations showed a wide based peak in the theta band centered around 9 Hz. D) Pairwise coherence between pyramidal cells is inversely related to the distance separating them (dashed black line), but this relationship is lost when EC neurons were connected to pyramidal cells randomly irrespective of the longitudinal distance (solid red line).
Fig 6.
Recurrent connections produced theta oscillations.
A) Schematic of the minimal network used for this experiment with only pyramidal cells and the synapses connecting them. B1) Spike raster plot and (B2) population firing rate from one example network. Note that in this sub-circuit, the oscillations are easier to identify visually in the firing rate plot. C) The population power spectrum of CA3 pyramidal cells averaged over 10 network instantiations shows a peak at 8 Hz.
Fig 7.
Pyramidal-OLM cells network generates theta through two mechanisms.
A) Schematic showing the pyramidal-OLM cells network with weak pyramidal to OLM synapses (weight set to 2), used in panels B-D. B) Spike raster plot of OLM spikes (B1). The OLM inhibitory currents received by one example pyramidal cell (B2). Note that inhibitory currents occur at a frequency much lower than theta. Spike raster plot of pyramidal cells spikes (B3). C) The population power spectrum of OLM cells (C1), and pyramidal cells (C2). Spectrum averaged from 10 instantiations of the network, shaded areas represent SD. D1) The pyramidal cell spike-triggered average of the adaptation current (dashed red line) and received OLM inhibition (solid blue line). Note that OLM inhibition showed a poor association with pyramidal cells spikes. D2) the inter-spike interval distribution of pyramidal cells remains largely unchanged from freely spiking pyramidal cells (compare with Fig 4C3). E) Schematic showing the network with strong pyramidal to OLM synapses (weight set to 6), used in panels F-H. F1) Spike raster plot of OLM spikes. F2) The OLM inhibitory currents received by one example pyramidal cell. F3) Spike raster plot of pyramidal cells spikes. G) The population power spectrum of OLM cells (G1), and pyramidal cells (G2). H) The pyramidal cell spike-triggered average (H1) of the adaptation current (dashed red line) and received OLM inhibition (solid blue line). Note the close association between OLM inhibition and pyramidal cells spikes. Note that OLM inhibition changes the distribution of the pyramidal cells inter-spike intervals (H2), creating a peak around 110 ms. Power spectrum peaks: C1,2: 6 Hz. G1,2: 8 Hz.
Fig 8.
The role of BCs in theta rhythm generation.
A) Schematic of this network with only pyramidal and basket cells active. B) In the original state, the sub-network failed to generate a significant spectral peak (B1, beyond the small theta peak expected from isolated pyramidal cells activity, see Fig 4). Oscillations remained absent after either removing short-term depression (B2) or doubling connection probability in both directions (B3). Both interventions were necessary to produce robust oscillatory activity (B4). C) Schematic of the network with strong pyramidal to basket cells synapses (weight set to 6), used in panels D-F. Note that short-term depression remained inactivated, and connectivity doubled for this experiment as well. D) Spike raster plot of BC spikes (D1). The BC inhibitory currents received by one example pyramidal cell (D2). The spike raster plot of pyramidal cells spikes (D3). E) The population power spectrum of BCs (E1), and pyramidal cells (E2), arrow pointing to a small emerging 18 Hz peak. F) The pyramidal cell spike-triggered average (F1) of the adaptation current (dashed red line) and received BC inhibition (solid blue line). Note the BC inhibitory current peaking sharply and then decaying back to average around 40 ms. F2) The inter-spike interval distribution of pyramidal cells. Power spectrum peaks: B1-3: 8 Hz. B4: 8 Hz, 18 Hz. E1: 6 Hz, 23 Hz. E2: 6 Hz, 18 Hz.
Fig 9.
Relative contributions of individual theta generators across cholinergic states.
A) Starting with the full EC and CA3 circuits we inactivated each individual generator and observed the changes in relative theta power (power in the 4 to 12 Hz range divided by the entire spectrum 0 to 250 Hz). To normalize, all values were divided by the relative theta power in the full model. Error bars indicate SD. B) The effects of inactivating individual generators in the low cholinergic state, and C) high cholinergic state. D) In the recurrent connections sub-network (D1), relative theta power decreased with higher cholinergic states (D2). A breakdown of cholinergic effects (D3) revealed that this was mainly mediated by the cholinergic suppression of the recurrent connection transmission (RC suppression) in addition to the cholinergic depolarization of pyramidal cells (Pyr depolarize). ACh in increments of 0.1. E) Schematic of the OLM-pyramidal cells network (E1). Relative theta increased with cholinergic state (E2) and a breakdown of cholinergic effects (E3) shows that cholinergic suppression of spike-frequency adaptation in OLM cells (OLM adaptation), and OLM cells depolarization (OLM depolarize) enhanced theta power in the network. In addition, the cholinergic pyramidal cells depolarization (Pyr depolarize) and enhanced burstiness (Pyr burstiness, lower c and d parameters of Izhikevitch model) enhanced theta in this network with a steeper slope. These effects were associated with enhanced OLM cells firing rates (E4).
Table 1.
Model cells parameter values.
Table 2.
Summary of synaptic properties used in the CA3 network model.