Interactions between Inhibitory Interneurons and Excitatory Associational Circuitry in Determining Spatio-Temporal Dynamics of Hippocampal Dentate Granule Cells: A Large-Scale Computational Study

Abstract

This paper reports on findings from a million-cell granule cell model of the rat dentate gyrus that was used to explore the contributions of local interneuronal and associational circuits to network-level activity. The model contains experimentally derived morphological parameters for granule cells, which each contain approximately 200 compartments, and biophysical parameters for granule cells, basket cells, and mossy cells that were based both on electrophysiological data and previously published models. Synaptic input to cells in the model consisted of glutamatergic AMPA-like EPSPs and GABAergic-like IPSPs from excitatory and inhibitory neurons, respectively. The main source of input to the model was from layer II entorhinal cortical neurons. Network connectivity was constrained by the topography of the system, and was derived from axonal transport studies, which provided details about the spatial spread of axonal terminal fields, as well as how subregions of the medial and lateral entorhinal cortices project to subregions of the dentate gyrus. Results of this study show that strong feedback inhibition from the basket cell population can cause high-frequency rhythmicity in granule cells, while the strength of feedforward inhibition serves to scale the total amount of granule cell activity. Results furthermore show that the topography of local interneuronal circuits can have just as strong an impact on the development of spatio-temporal clusters in the granule cell population as the perforant path topography does, both sharpening existing clusters and introducing new ones with a greater spatial extent. Finally, results show that the interactions between the inhibitory and associational loops can cause high frequency oscillations that are modulated by a low-frequency oscillatory signal. These results serve to further illustrate the importance of topographical constraints on a global signal processing feature of a neural network, while also illustrating how rich spatio-temporal and oscillatory dynamics can evolve from a relatively small number of interacting local circuits.

Keywords: associational-commissural fibers; compartmental model; dentate gyrus; inhibition; interneurons; oscillations; spatio-temporal patterns; topography.

FIGURE 1

(Top) Schematic showing local feedback circuits in the dentate gyrus, with the perforant path providing input to both granule cells and basket cells. The hierarchical nature of local projections in the dentate gyrus can be seen in the mossy cell population, which both excites granule cells monosynaptically and inhibits them disynaptically. (Bottom) The number of cells included in the full-scale model matches numbers reported in anatomical studies.

FIGURE 2

(Top) Summary of mossy cell axonal projection, as a function of septo-temporal position in the hippocampus. (Bottom) Summary of axon terminal field extents along both the septo-temporal and transverse axes of the dentate gyrus.

FIGURE 3

Simulation results, at two different scales, for topographically constrained EC-DG networks with feedforward and feedback inhibition. (A1) Simulation results from 1 million granule cells. Despite the random nature of the perforant path input, dentate activity in both granule and basket cells consists of spatio-temporal clusters of spikes. In the million-cell case, only a subset of the full dataset is plotted to keep it from appearing solid black. (B1) The spatio-termporal correlation (STC) confirms the existence of clusters. (A2,B2) Clusters persist when the network is scaled down to 100 k granule cells.

FIGURE 4

Effect of progressively increasing strength of feedback inhibition. As the amount of inhibition increases (A1–A4), pronounced rhythmicity develops in both granule cell and basket cell activity. The presence of this rhythmicity is verified with frequency analysis (B1–B4), which shows a peak developing at approximately 18 Hz.

FIGURE 5

Large amounts of PP excitation (A1), feedback inhibition (A2), and feedforward inhibition (A3) in isolation, with corresponding frequency plots (column B). Of note is the fact that only feedback inhibition can cause oscillatory activity in the network.

FIGURE 6

Effect of increasing strength of perforant path drive in the presence of strong feedback inhibition. When rhythmicity is present in the network, increasing the strength of the perforant path excitatory drive (A1–A4) both strengthens the rhythmicity and increases its freqeuency. As DFT analysis shows, a small 18 Hz peak at the base perforant path strength (B1) becomes a much larger peak centered at about 32 Hz when the synaptic weight of the perforant path input is increased by up to 20x (B2–B4).

FIGURE 7

Effect of increasing the strength of feedforward inhibition. The feedforward component of basket cell inhibition helps to both desynchronize and scale down total granule cell activity. As the strength of the feedforward inhibition increases (A1–A4), total granule cell activity decreases until there’s almost no activity in the network. The 18 Hz peak in the DFTs (B1–B4) also disappears.

FIGURE 8

Initial simulation results after connecting the mossy cell associational pathway. When EPSP magnitudes are set at values reported in the literature, strong synchrony develops in all three dentate cell populations (A1). When synaptic weights are rebalanced to fit the results of the paired-pulse stimulation experiments of Douglas et al. (1983) (A2), rhythmicity in the network disappears, replaced by a large variety of spatio-temporal clusters (A3).

FIGURE 9

Simulation results for two dentate networks that only differ in the topography of the mossy cell projection to granule cells. (Top) Results when mossy cell axonal tree extents vary by their location along the septo-temporal axis of the dentate gyrus, as reported by Zimmer (1971). (Bottom) Results when mossy cells are allowed to project randomly to the granule cell population. Note that the size of the spatio-temporal clusters in granule cells increases substantially in the randomly connected network, as evidenced by the spatio-temporal correlations (B1,B2).

FIGURE 10

Histogram showing inter-spike intervals for each of the cell populations in the model. Inter-spike intervals are very small for basket cells and mossy cells (A1), which makes sense, given that basket cells are fast-spiking interneurons. Granule cells do not exhibit many small inter-spike intervals (A2), but rather, show a peak in the 200–300 ms range. The distribution of inter-spike intervals for entorhinal cortical cells looks exponential (A3), which is expected for a group of cells whose action potentials follow a Poisson process.

FIGURE 11

Simulation results when strengthening and weakening three individual synaptic connections in the granule-mossy-basket cell network. All raster plots show 1,000 ms of activity. (A1,B1) Shows balanced synaptic weights. (A2,B2) Show alterations to the MC-GC synaptic weights. (A3,B3) Show alterations to the MC-BC synaptic weights. (A4,B4) Show alterations to the BC-GC synaptic weights. When the excitatory mossy cell loop is strengthened relative to the inhibitory basket cell loop, a pattern of theta-modulated gamma oscillations develops (A3,A4,B2).

FIGURE 12

Same simulation results as in Figure 11, but showing 4,000 ms of activity to give a better view of the theta-modulated gamma oscillations. (A1,B1) Shows balanced synaptic weights. (A2,B2) Show alterations to the MC-GC synaptic weights. (A3,B3) Show alterations to the MC-BC synaptic weights. (A4,B4) Show alterations to the BC-GC synaptic weights.

FIGURE 13

Discrete Fourier transforms (DFTs) for the data shown in Figures 11 and 12. (A1,B1) Shows balanced synaptic weights. (A2,B2) Show alterations to the MC-GC synaptic weights. (A3,B3) Show alterations to the MC-BC synaptic weights. (A4,B4) Show alterations to the BC-GC synaptic weights.