A Million-Plus Neuron Model of the Hippocampal Dentate Gyrus: Critical Role for Topography in Determining Spatiotemporal Network Dynamics.

GOAL: This paper describes a million-plus granule cell compartmental model of the rat hippocampal dentate gyrus, including excitatory, perforant path input from the entorhinal cortex, and feedforward and feedback inhibitory input from dentate interneurons. METHODS: The model includes experimentally determined morphological and biophysical properties of granule cells, together with glutamatergic AMPA-like EPSP and GABAergic GABAA-like IPSP synaptic excitatory and inhibitory inputs, respectively. Each granule cell was composed of approximately 200 compartments having passive and active conductances distributed throughout the somatic and dendritic regions. Modeling excitatory input from the entorhinal cortex was guided by axonal transport studies documenting the topographical organization of projections from subregions of the medial and lateral entorhinal cortex, plus other important details of the distribution of glutamatergic inputs to the dentate gyrus. Information contained within previously published maps of this major hippocampal afferent were systematically converted to scales that allowed the topographical distribution and relative synaptic densities of perforant path inputs to be quantitatively estimated for inclusion in the current model. RESULTS: Results showed that when medial and lateral entorhinal cortical neurons maintained Poisson random firing, dentate granule cells expressed, throughout the million-cell network, a robust nonrandom pattern of spiking best described as a spatiotemporal "clustering." To identify the network property or properties responsible for generating such firing "clusters," we progressively eliminated from the model key mechanisms, such as feedforward and feedback inhibition, intrinsic membrane properties underlying rhythmic burst firing, and/or topographical organization of entorhinal afferents. CONCLUSION: Findings conclusively identified topographical organization of inputs as the key element responsible for generating a spatiotemporal distribution of clustered firing. These results uncover a functional organization of perforant path afferents to the dentate gyrus not previously recognized: topography-dependent clusters of granule cell activity as "functional units" or "channels" that organize the processing of entorhinal signals. This modeling study also reveals for the first time how a global signal processing feature of a neural network can evolve from one of its underlying structural characteristics.

A bi-directional communication paradigm between parallel NEURON and an external non-neuron process.

In order to accurately model the pattern of activation due to electrical stimulation of the hippocampus, a multi-scale computational approach is necessary. At the system level, the Admittance Method (ADM) is used to calculate the extracellular voltages created by a stimulating electrode. At the network and cellular levels, a large-scale multi-compartmental neuron network is used to calculate cellular activation. This paper presents a bi-directional communication paradigm between the NEURON model and an external surrogate for the ADM solver, where at each time step, neurons share their membrane currents with the external process, and the external process shares calculated extracellular voltages with the neuronal network. This work constitutes an important first step towards a full multi-scale NEURON-ADM model with bi-directional communication.

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

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.

Topography-dependent spatio-temporal correlations in the entorhinal-dentate-CA3 circuit in a large-scale computational model of the Rat Hippocampus.

The correlation due to different topographies was characterized in a large-scale, biologically-realistic, computational model of the rat hippocampus using a spatio-temporal correlation analysis. The effect of the topographical projection between the following subregions of the hippocampus was investigated: the entorhinal to dentate projection, the entorhinal to CA3 projection, and the mossy fiber to CA3 projection. Through this work, analysis was performed on the individual and combined effects of these projections on the activity of the principal neurons of the dentate gyrus and CA3. The simulations show that uncorrelated input transmitted through the entorhinal-to-dentate or entorhinal-to-CA3 projection causes spatio-temporally correlated activity in the principal neurons that manifest as spike clusters. However, if the mossy fiber system provides uncorrelated input to the CA3, then the CA3 activity remains uncorrelated. When considering the transfer of correlation through the dentate, this analysis suggests that the mossy fiber system do not imbue any correlation to the activity as it propagates from the granule cells of the dentate to the CA3. With the spatio-temporal correlation analysis, the influence of each topographical projection on the transfer of correlation can be investigated as additional subregions and neuron types are added to the large-scale model.

A million-plus neuron model of the hippocampal dentate gyrus: Dependency of spatio-temporal network dynamics on topography.

This paper describes a million-plus granule cell compartmental model of the rat hippocampal dentate gyrus, including excitatory, perforant path input from the entorhinal cortex, and feedforward and feedback inhibitory input from dentate interneurons. The model includes experimentally determined morphological and biophysical properties of granule cells, together with glutamatergic AMPA-like EPSP and GABAergic GABAA-like IPSP synaptic excitatory and inhibitory inputs, respectively. Each granule cell was composed of approximately 200 compartments having passive and active conductances distributed throughout the somatic and dendritic regions. Modeling excitatory input from the entorhinal cortex was guided by axonal transport studies documenting the topographical organization of projections from subregions of the medial and lateral entorhinal cortex, plus other important details of the distribution of glutamatergic inputs to the dentate gyrus. Results showed that when medial and lateral entorhinal cortical neurons maintained Poisson random firing, dentate granule cells expressed, throughout the million-cell network, a robust, non-random pattern of spiking best described as spatiotemporal "clustering". To identify the network property or properties responsible for generating such firing "clusters", we progressively eliminated from the model key mechanisms such as feedforward and feedback inhibition, intrinsic membrane properties underlying rhythmic burst firing, and/or topographical organization of entorhinal afferents. Findings conclusively identified topographical organization of inputs as the key element responsible for generating a spatio-temporal distribution of clustered firing. These results uncover a functional organization of perforant path afferents to the dentate gyrus not previously recognized: topography-dependent clusters of granule cell activity as "functional units" that organize the processing of entorhinal signals.

The role of topography in the transformation of spatiotemporal patterns by a large-scale, biologically realistic model of the rat dentate gyrus.

A large-scale, biologically realistic, computational model of the rat hippocampus is being constructed to study the input-output transformation that the hippocampus performs. In the initial implementation, the layer II entorhinal cortex neurons, which provide the major input to the hippocampus, and the granule cells of the dentate gyrus, which receive the majority of the input, are modeled. In a previous work, the topography, or the wiring diagram, connecting these two populations had been derived and implemented. This paper explores the consequences of two features of the topography, the distribution of the axons and the size of the neurons' axon terminal fields. The topography converts streams of independently generated random Poisson trains into structured spatiotemporal patterns through spatiotemporal convergence achievable by overlapping axon terminal fields. Increasing the axon terminal field lengths allowed input to converge over larger regions of space resulting in granule activation across a greater area but did not increase the total activity as a function of time as the number of targets per input remained constant. Additional simulations demonstrated that the total distribution of spikes in space depends not on the distribution of the presynaptic axons but the distribution of the postsynaptic population. Analyzing spike counts emphasizes the importance of the postsynaptic distribution, but it ignores the fact that each individual input may be carrying unique information. Therefore, a metric should be created that relates and tracks individual inputs as they are propagated and integrated through hippocampus.

The contribution of relative activation levels between populations of cells to network activity in a large-scale biologically realistic model of the hippocampus.

In previously published work, we showed the progress we've made towards creating a large-scale, biologically realistic model of the rat hippocampus, starting with the projection from entorhinal cortex (EC) to the dentate gyrus (DG). We created the model to help us study how the common components of neurobiological systems in mammals - large numbers of neurons with intricate, branching morphologies; active, non-linear membrane properties; nonuniform distributions throughout membrane surface of these non-linear conductances; non-uniform and topographic connectivity between pre- and post-synaptic neurons; and activity-dependent changes in synaptic function - combine and contribute to give a particular brain region its "neural processing" properties. In this work, we report on the results of a series of simulations we ran to test the role of feed-forward and feedback inhibition in the dentate gyrus. We find that a) the system shows rhythmic bands of activity only in the presence of feedback inhibition, b) that the frequency of rhythmicity increases with increasing amounts of feed-forward inhibition, c) that it decreases with increasing amounts of feedback inhibition, and d) that strong excitatory inputs appear to enhance and prolong the amount of rhythmicity in the system.

Implementation of topographically constrained connectivity for a large-scale biologically realistic model of the hippocampus.

In order to understand how memory works in the brain, the hippocampus is highly studied because of its role in the encoding of long-term memories. We have identified four characteristics that would contribute to the encoding process: the morphology of the neurons, their biophysics, synaptic plasticity, and the topography connecting the input to and the neurons within the hippocampus. To investigate how long-term memory is encoded, we are constructing a large-scale biologically realistic model of the rat hippocampus. This work focuses on how topography contributes to the output of the hippocampus. Generally, the brain is structured with topography such that the synaptic connections formed by an input neuron population are organized spatially across the receiving population. The first step in our model was to construct how entorhinal cortex inputs connect to the dentate gyrus of the hippocampus. We have derived realistic constraints from topographical data to connect the two cell populations. The details on how these constraints were applied are presented. We demonstrate that the spatial connectivity has a major impact on the output of the simulation, and the results emphasize the importance of carefully defining spatial connectivity in neural network models of the brain in order to generate relevant spatiotemporal patterns.

Implementation of activity-dependent synaptic plasticity rules for a large-scale biologically realistic model of the hippocampus.

A large-scale computational model of the hippocampus should consider plasticity at different time scales in order to capture the non-stationary information processing behavior of the hippocampus more accurately. This paper presents a computational model that describes hippocampal long-term potentiation/depression (LTP/LTD) and short-term plasticity implemented in the NEURON simulation environment. The LTP/LTD component is based on spike-timing-dependent plasticity (STDP). The short-term plasticity component modifies a previously defined deterministic model at a population synapse level to a probabilistic model that can be implemented at a single synapse level. The plasticity mechanisms are validated and incorporated into a large-scale model of the entorhinal cortex projection to the dentate gyrus. Computational expense of the added plasticity was also evaluated and shown to increase simulation time by less than a factor of two. This model can be easily included in future large-scale hippocampal simulations to investigate the effects of LTP/LTD and short-term plasticity in conjunction with other biological considerations on system function.

Towards a large-scale biologically realistic model of the hippocampus.

Real neurobiological systems in the mammalian brain have a complicated and detailed structure, being composed of 1) large numbers of neurons with intricate, branching morphologies--complex morphology brings with it complex passive membrane properties; 2) active membrane properties--nonlinear sodium, potassium, calcium, etc. conductances; 3) non-uniform distributions throughout the dendritic and somal membrane surface of these non-linear conductances; 4) non-uniform and topographic connectivity between pre- and post-synaptic neurons; and 5) activity-dependent changes in synaptic function. One of the essential, and as yet unanswered questions in neuroscience is the role of these fundamental structural and functional features in determining "neural processing" properties of a given brain system. To help answer that question, we're creating a large-scale biologically realistic model of the intrinsic pathway of the hippocampus, which consists of the projection from layer II entorhinal cortex (EC) to dentate gyrus (DG), EC to CA3, DG to CA3, and CA3 to CA1. We describe the computational hardware and software tools the model runs on, and demonstrate its viability as a modeling platform with an EC-to-DG model.