Bridging Hierarchies in Multi-Scale Models of Neural Systems: Look-Up Tables Enable Computationally Efficient Simulations of Non-linear Synaptic Dynamics.

Synapses are critical actors of neuronal transmission as they form the basis of chemical communication between neurons. Accurate computational models of synaptic dynamics may prove important in elucidating emergent properties across hierarchical scales. Yet, in large-scale neuronal network simulations, synapses are often modeled as highly simplified linear exponential functions due to their small computational footprint. However, these models cannot capture the complex non-linear dynamics that biological synapses exhibit and thus, are insufficient in representing synaptic behavior accurately. Existing detailed mechanistic synapse models can replicate these non-linear dynamics by modeling the underlying kinetics of biological synapses, but their high complexity prevents them from being a suitable option in large-scale models due to long simulation times. This motivates the development of more parsimonious models that can capture the complex non-linear dynamics of synapses accurately while maintaining a minimal computational cost. We propose a look-up table approach that stores precomputed values thereby circumventing most computations at runtime and enabling extremely fast simulations for glutamatergic receptors AMPAr and NMDAr. Our results demonstrate that this methodology is capable of replicating the dynamics of biological synapses as accurately as the mechanistic synapse models while offering up to a 56-fold increase in speed. This powerful approach allows for multi-scale neuronal networks to be simulated at large scales, enabling the investigation of how low-level synaptic activity may lead to changes in high-level phenomena, such as memory and learning.

Topographic Organization of Correlation Along the Longitudinal and Transverse Axes in Rat Hippocampal CA3 Due to Excitatory Afferents.

The topographic organization of afferents to the hippocampal CA3 subfield are well-studied, but their role in influencing the spatiotemporal dynamics of population activity is not understood. Using a large-scale, computational neuronal network model of the entorhinal-dentate-CA3 system, the effects of the perforant path, mossy fibers, and associational system on the propagation and transformation of network spiking patterns were investigated. A correlation map was constructed to characterize the spatial structure and temporal evolution of pairwise correlations which underlie the emergent patterns found in the population activity. The topographic organization of the associational system gave rise to changes in the spatial correlation structure along the longitudinal and transverse axes of the CA3. The resulting gradients may provide a basis for the known functional organization observed in hippocampus.

A Computational Model of the Cholinergic Modulation of CA1 Pyramidal Cell Activity.

Dysfunction in cholinergic modulation has been linked to a variety of cognitive disorders including Alzheimer's disease. The important role of this neurotransmitter has been explored in a variety of experiments, yet many questions remain unanswered about the contribution of cholinergic modulation to healthy hippocampal function. To address this question, we have developed a model of CA1 pyramidal neuron that takes into consideration muscarinic receptor activation in response to changes in extracellular concentration of acetylcholine and its effects on cellular excitability and downstream intracellular calcium dynamics. This model incorporates a variety of molecular agents to accurately simulate several processes heretofore ignored in computational modeling of CA1 pyramidal neurons. These processes include the inhibition of ionic channels by phospholipid depletion along with the release of calcium from intracellular stores (i.e., the endoplasmic reticulum). This paper describes the model and the methods used to calibrate its behavior to match experimental results. The result of this work is a compartmental model with calibrated mechanisms for simulating the intracellular calcium dynamics of CA1 pyramidal cells with a focus on those related to release from calcium stores in the endoplasmic reticulum. From this model we also make various predictions for how the inhibitory and excitatory responses to cholinergic modulation vary with agonist concentration. This model expands the capabilities of CA1 pyramidal cell models through the explicit modeling of molecular interactions involved in healthy cognitive function and disease. Through this expanded model we come closer to simulating these diseases and gaining the knowledge required to develop novel treatments.

Generation of Granule Cell Dendritic Morphologies by Estimating the Spatial Heterogeneity of Dendritic Branching.

Biological realism of dendritic morphologies is important for simulating electrical stimulation of brain tissue. By adding point process modeling and conditional sampling to existing generation strategies, we provide a novel means of reproducing the nuanced branching behavior that occurs in different layers of granule cell dendritic morphologies. In this study, a heterogeneous Poisson point process was used to simulate branching events. Conditional distributions were then used to select branch angles depending on the orthogonal distance to the somatic plane. The proposed method was compared to an existing generation tool and a control version of the proposed method that used a homogeneous Poisson point process. Morphologies were generated with each method and then compared to a set of digitally reconstructed neurons. The introduction of a conditionally dependent branching rate resulted in the generation of morphologies that more accurately reproduced the emergent properties of dendritic material per layer, Sholl intersections, and proximal passive current flow. Conditional dependence was critically important for the generation of realistic granule cell dendritic morphologies.

Axonal Anatomy Optimizes Spatial Encoding in the Rat Entorhinal-Dentate System: A Computational Study.

OBJECTIVE: The network architecture connecting neural regions is defined by the organization and anatomical properties of the projecting axons, but its contributions to neural encoding and system function are difficult to study experimentally. METHODS: Using a large-scale, spiking neuronal network model of rat dentate gyrus, the role of the anatomy of the entorhinal-dentate axonal projection was evaluated in the context of spatial encoding by incorporating grid cell activity to provide physiological, spatially-correlated input. The dorso-ventral extents of the entorhinal axon terminal fields were varied to generate different feedforward architectures, and the resulting spatial representations and spatial information scores of the network were evaluated. Position was decoded from the population activity using a point process filter to investigate the contributions of network architecture on spatial encoding. RESULTS: The model predicted the emergence of anatomical gradients within the dentate gyrus for place field size and spatial information along its dorso-ventral axis, which were dependent on the extents of the entorhinal axon terminal fields. The decoding results revealed an optimal performance at an axon terminal field extent of 2 mm that lies within the biological range. CONCLUSION: The axonal anatomy mediates a tradeoff between encoding multiple place field sizes or achieving a high spatial information score, and the combination of both properties is necessary to maximize spatial encoding by a network. SIGNIFICANCE: In total, this paper establishes a mechanistic neuronal network model that, in concert with information-theoretic and statistical methods, can be used to investigate how lower level properties contribute to higher level function.

Network Activity Due to Topographic Organization of Schaffer Collaterals in a Large-Scale Model of Rat CA1.

Connectivity between neural regions, particularly in the hippocampus, is seldom all-to-all or random, yet it is the predominant method by which connectivity is implemented in most models of neuronal networks. We have been developing a computational platform for simulating the trisynaptic circuit of rat hippocampus with which we have constructed a large-scale, biologically-realistic, spiking neuronal network model of the entorhinal-dentate-CA3 system. Using the model, we had demonstrated a non-trivial effect of topographic connectivity on network dynamics and function. In this work, we detail the introduction of the CA1 subregion to the large-scale model. Using anatomical data, we constrained the distribution of axon collaterals, i.e., Schaffer collaterals, projected from CA3 to CA1 and preserved the topographic organization of the projections. Using a simplified multi-compartmental model of CA1 pyramidal cells and a single compartment model of CA1 parvalbumin basket cells, that were connected with disynaptic feedforward inhibition and feedback inhibition, we demonstrate the network activity of the CA1 network given a topographic organization of Schaffer collaterals. From this introduction of CA1 to the large-scale model, we can then observe the successive transformation of spatio-temporal, spiking neural activity as it propagates through the trisynaptic circuit.

Point Process Filtering Estimates of Branching Rate for Neural Dendritic Morphology Generation.

Current parametric approaches to dendritic morphology generation are limited in their ability to replicate realistic branching. A non-parametric approach applying a point process filter and the expectation-maximization algorithm offers a data-based solution that estimates the dendritic branching rate based on observations of bifurcation events in real neurons. Point processes can then be simulated using this branching rate estimate to indicate when a generated morphology should branch. Morphologies generated using this technique match both basic and emergent property distributions of the real neurons used as input into the algorithm. Further refinement of branching angles will allow for a flexible tool to generate realistic morphologies of a variety of neuronal stereotypes.

Decoding Position to Analyze Spatial Information Encoding in a Large-Scale Neuronal Network Model of Rat Dentate Gyrus.

Spatial information is encoded by the hippocampus, and the factors that contribute to the amount of information that can be encoded and the transformation of spatial information through the trisynaptic circuit remain an important issue. A large-scale neuronal network model of the rat entorhinal-dentate system was developed with multicompartmental representations of the neurons within the dentate gyrus. Spatial information was introduced to the network via grid cell activity, and the spatial information encoding capabilities of the network were assessed using a recursive decoding algorithm to estimate the position of a virtual rat using the dentate activity. To obtain a measure for the information that the network could convey, decoding error was calculated for different decoding population sizes. Decoding error decreased exponentially as a function of population size. Therefore, the time constant and the asymptote of the error curve could be used as metrics to compare the changes in encoding performance. In conjunction with the large-scale model, this paradigm can be used to characterize how neural properties, network composition, and the interactions between different subfields affect spatial information encoding.

Model-Based Analysis of Electrode Placement and Pulse Amplitude for Hippocampal Stimulation.

OBJECTIVE: The ideal form of a neural-interfacing device is highly dependent upon the anatomy of the region with which it is meant to interface. Multiple-electrode arrays provide a system that can be adapted to various neural geometries. Computational models of stimulating systems have proven useful for evaluating electrode placement and stimulation protocols, but have yet to be adequately adapted to the unique features of the hippocampus. METHODS: As an approach to understanding potential memory restorative devices, an admittance method-NEURON model was constructed to predict the direct and synaptic response of a region of the rat dentate gyrus to electrical stimulation of the perforant path. RESULTS: A validation of estimated local field potentials against experimental recordings is performed and results of a bilinear electrode placement and stimulation amplitude parameter search are presented. CONCLUSION: The parametric analysis presented herein suggests that stimulating electrodes placed between the lateral and medial perforant path, near the crest of the dentate gyrus, yield a larger relative population response to given stimuli. SIGNIFICANCE: Beyond deepening understanding of the hippocampal tissue system, establishment of this model provides a method to evaluate candidate stimulating devices and protocols.

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.

Place field detection using grid-based clustering in a large-scale computational model of the rat dentate gyrus.

Place cells are neurons in the hippocampus that are sensitive to location within an environment. Simulations of a large-scale, computational model of the rat dentate gyrus using grid cell input have been performed resulting in granule cells that express multiple place fields. The typical method of detecting place fields using a global threshold on this data is unreliable as the characteristics of the place fields from a single neuron can be highly variable. A grid-based implementation of DENCLUE has been developed to calculate local thresholds to identify each place field. An adaptive binning algorithm used to smooth the rate maps was combined with the DENCLUE implementation to adaptively choose the size of the smoothing kernel and reduce the number of free parameters of the total algorithm. A sensitivity analysis was performed using the threshold parameter to demonstrate the robustness of using local thresholds as opposed to using a single global threshold in detecting the place fields resulting from the large-scale simulation. The analysis supports the use of applying local thresholds for place field detection and will be used to further investigate the role of granule cells in hippocampal 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.

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.