Phillip J. Hendrickson

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.

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.

Predicting EMG with generalized Volterra kernel model

Generalized Volterra kernel model (GVM) is developed in spirits of the generalized linear model (GLM) and used to predict EMG signals based on M1 cortical spike trains during a prehension task. The GVM for EMG consists of a cascade of a multiple-input-single-output Volterra kernel model (VM) and an exponential activation function. Without loss of generality, the exponential activation function constrains the unbounded VM output within the positive range, which fully covers the dynamic range of the rectified EMG signals. Results show that GVMs are more accurate than the VMs due to this asymptotic property.

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.

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.

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.

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.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.

Optimizing electrode placement using a multiscale model of the hippocampus

The hippocampus is associated with consolidating short-term memory into long-term memory. Therefore, damage to the hippocampus can result in neurological conditions such as Alzheimers, dementia, and other diseases that affect memory. One way of helping patients affected by these conditions is to create a neural prosthesis that replicates the function of the damaged section of the hippocampus. This prosthetic device is built by a) creating an input-output model of the transformation between the still-intact portions of the hippocampus, and b) “instantiating” that model into custom VLSI hardware thats attached to upstream recording electrodes and downstream stimulating electrodes. However, a phenomenon thats still not well understood is the neural response to the electrical stimulation: thus, a multi-scale computational model has been developed to study the response to biphasic stimulation in a rat hippocampus.

Estimation of initiated local field potential by neurons in heterogeneous tissue environment using admittance method

In order to decode the relationship between the activity of neuronal networks in the brain and the physiological response, multiple recording methods are available to monitor the spatial-temporal response of the neurons. Compared to single neuron recording that is useful for finding neuronal response, local field potential (LFP) recording allows for analysis of a larger neuronal network response. LFP is a combinational effect of the asynchronous action potentials from multiple neurons and can be recorded using implanted microelectrodes. Accurately calculating the LFP of a simulated neuronal network allows for optimal electrode placement for electrical stimulation and recording. The simulated LFP on a proximal recording electrode due to the neuronal firings of a multineuron network can be compared with the recorded LFP from a relevant experiment. In this work we compare two different methods for solving multineuron network field potentials.

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.