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

A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation

Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

Adaptive octree meshes for simulation of extracellular electrophysiology

Objective.The interaction between neural tissues and artificial electrodes is crucial for understanding and advancing neuroscientific research and therapeutic applications. However, accurately modeling this space around the neurons rapidly increases the computational complexity of neural simulations.Approach.This study demonstrates a dynamically adaptive simulation method that greatly accelerates computation by adjusting spatial resolution of the simulation as needed. Use of an octree structure for the mesh, in combination with the admittance method for discretizing conductivity, provides both accurate approximation and ease of modification on-the-fly.Main results.In tests of both local field potential estimation and multi-electrode stimulation, dynamically adapted meshes achieve accuracy comparable to high-resolution static meshes in an order of magnitude less time.Significance.The proposed simulation pipeline improves model scalability, allowing greater detail with fewer computational resources. The implementation is available as an open-source Python module, providing flexibility and ease of reuse for the broader research community.

Neuroprosthetics: from sensorimotor to cognitive disorders

Neuroprosthetics is a multidisciplinary field at the interface between neurosciences and biomedical engineering, which aims at replacing or modulating parts of the nervous system that get disrupted in neurological disorders or after injury. Although neuroprostheses have steadily evolved over the past 60 years in the field of sensory and motor disorders, their application to higher-order cognitive functions is still at a relatively preliminary stage. Nevertheless, a recent series of proof-of-concept studies suggest that electrical neuromodulation strategies might also be useful in alleviating some cognitive and memory deficits, in particular in the context of dementia. Here, we review the evolution of neuroprosthetics from sensorimotor to cognitive disorders, highlighting important common principles such as the need for neuroprosthetic systems that enable multisite bidirectional interactions with the nervous system.

The Flow of Axonal Information Among Hippocampal Subregions: 1. Feed-Forward and Feedback Network Spatial Dynamics Underpinning Emergent Information Processing

The tri-synaptic pathway in the mammalian hippocampus enables cognitive learning and memory. Despite decades of reports on anatomy and physiology, the functional architecture of the hippocampal network remains poorly understood in terms of the dynamics of axonal information transfer between subregions. Information inputs largely flow from the entorhinal cortex (EC) to the dentate gyrus (DG), and then are processed further in the CA3 and CA1 before returning to the EC. Here, we reconstructed elements of the rat hippocampus in a novel device over an electrode array that allowed for monitoring the directionality of individual axons between the subregions. The direction of spike propagation was determined by the transmission delay of the axons recorded between two electrodes in microfluidic tunnels. The majority of axons from the EC to the DG operated in the feed-forward direction, with other regions developing unexpectedly large proportions of feedback axons to balance excitation. Spike timing in axons between each region followed single exponential log-log distributions over two orders of magnitude from 0.01 to 1 s, indicating that conventional descriptors of mean firing rates are misleading assumptions. Most of the spiking occurred in bursts that required two exponentials to fit the distribution of inter-burst intervals. This suggested the presence of up-states and down-states in every region, with the least up-states in the DG to CA3 feed-forward axons and the CA3 subregion. The peaks of the log-normal distributions of intra-burst spike rates were similar in axons between regions with modes around 95 Hz distributed over an order of magnitude. Burst durations were also log-normally distributed around a peak of 88 ms over two orders of magnitude. Despite the diversity of these spike distributions, spike rates from individual axons were often linearly correlated to subregions. These linear relationships enabled the generation of structural connectivity graphs, not possible previously without the directional flow of axonal information. The rich axonal spike dynamics between subregions of the hippocampus reveal both constraints and broad emergent dynamics of hippocampal architecture. Knowledge of this network architecture may enable more efficient computational artificial intelligence (AI) networks, neuromorphic hardware, and stimulation and decoding from cognitive implants.

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.

Admittance Method for Estimating Local Field Potentials Generated in a Multi-Scale Neuron Model of the Hippocampus

Significant progress has been made toward model-based prediction of neral tissue activation in response to extracellular electrical stimulation, but challenges remain in the accurate and efficient estimation of distributed local field potentials (LFP). Analytical methods of estimating electric fields are a first-order approximation that may be suitable for model validation, but they are computationally expensive and cannot accurately capture boundary conditions in heterogeneous tissue. While there are many appropriate numerical methods of solving electric fields in neural tissue models, there isn't an established standard for mesh geometry nor a well-known rule for handling any mismatch in spatial resolution. Moreover, the challenge of misalignment between current sources and mesh nodes in a finite-element or resistor-network method volume conduction model needs to be further investigated. Therefore, using a previously published and validated multi-scale model of the hippocampus, the authors have formulated an algorithm for LFP estimation, and by extension, bidirectional communication between discretized and numerically solved volume conduction models and biologically detailed neural circuit models constructed in NEURON. Development of this algorithm required that we assess meshes of (i) unstructured tetrahedral and grid-based hexahedral geometries as well as (ii) differing approaches for managing the spatial misalignment of current sources and mesh nodes. The resulting algorithm is validated through the comparison of Admittance Method predicted evoked potentials with analytically estimated LFPs. Establishing this method is a critical step toward closed-loop integration of volume conductor and NEURON models that could lead to substantial improvement of the predictive power of multi-scale stimulation models of cortical tissue. These models may be used to deepen our understanding of hippocampal pathologies and the identification of efficacious electroceutical 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.

ROOTS: An Algorithm to Generate Biologically Realistic Cortical Axons and an Application to Electroceutical Modeling

Advances in computation and neuronal modeling have enabled the study of entire neural tissue systems with an impressive degree of biological realism. These efforts have focused largely on modeling dendrites and somas while largely neglecting axons. The need for biologically realistic explicit axonal models is particularly clear for applications involving clinical and therapeutic electrical stimulation because axons are generally more excitable than other neuroanatomical subunits. While many modeling efforts can rely on existing repositories of reconstructed dendritic/somatic morphologies to study real cells or to estimate parameters for a generative model, such datasets for axons are scarce and incomplete. Those that do exist may still be insufficient to build accurate models because the increased geometric variability of axons demands a proportional increase in data. To address this need, a Ruled-Optimum Ordered Tree System (ROOTS) was developed that extends the capability of neuronal morphology generative methods to include highly branched cortical axon terminal arbors. Further, this study presents and explores a clear use-case for such models in the prediction of cortical tissue response to externally applied electric fields. The results presented herein comprise (i) a quantitative and qualitative analysis of the generative algorithm proposed, (ii) a comparison of generated fibers with those observed in histological studies, (iii) a study of the requisite spatial and morphological complexity of axonal arbors for accurate prediction of neuronal response to extracellular electrical stimulation, and (iv) an extracellular electrical stimulation strength-duration analysis to explore probable thresholds of excitation of the dentate perforant path under controlled conditions. ROOTS demonstrates a superior ability to capture biological realism in model fibers, allowing improved accuracy in predicting the impact that microscale structures and branching patterns have on spatiotemporal patterns of activity in the presence of extracellular electric fields.

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.

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.

Simple models of quantitative firing phenotypes in hippocampal neurons: Comprehensive coverage of intrinsic diversity

Patterns of periodic voltage spikes elicited by a neuron help define its dynamical identity. Experimentally recorded spike trains from various neurons show qualitatively distinguishable features such as delayed spiking, spiking with or without frequency adaptation, and intrinsic bursting. Moreover, the input-dependent responses of a neuron not only show different quantitative features, such as higher spike frequency for a stronger input current injection, but can also exhibit qualitatively different responses, such as spiking and bursting under different input conditions, thus forming a complex phenotype of responses. In previous work, the comprehensive knowledge base of hippocampal neuron types Hippocampome.org systematically characterized various spike pattern phenotypes experimentally identified from 120 neuron types/subtypes. In this paper, we present a complete set of simple phenomenological models that quantitatively reproduce the diverse and complex phenotypes of hippocampal neurons. In addition to point-neuron models, we created compact multi-compartment models with up to four compartments, which will allow spatial segregation of synaptic integration in network simulations. Electrotonic compartmentalization observed in our compact multi-compartment models is qualitatively consistent with experimental observations. The models were created using an automated pipeline based on evolutionary algorithms. This work maps 120 neuron types/subtypes in the rodent hippocampus to a low-dimensional model space and adds another dimension to the knowledge accumulated in Hippocampome.org. Computationally efficient representations of intrinsic dynamics, along with other pieces of knowledge available in Hippocampome.org, provide a biologically realistic platform to explore the large-scale interactions of various neuron types at the mesoscopic level.

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.

Evolving Simple Models of Diverse Intrinsic Dynamics in Hippocampal Neuron Types

The diversity of intrinsic dynamics observed in neurons may enhance the computations implemented in the circuit by enriching network-level emergent properties such as synchronization and phase locking. Large-scale spiking network models of entire brain regions offer a platform to test theories of neural computation and cognitive function, providing useful insights on information processing in the nervous system. However, a systematic in-depth investigation requires network simulations to capture the biological intrinsic diversity of individual neurons at a sufficient level of accuracy. The computationally efficient Izhikevich model can reproduce a wide range of neuronal behaviors qualitatively. Previous studies using optimization techniques, however, were less successful in quantitatively matching experimentally recorded voltage traces. In this article, we present an automated pipeline based on evolutionary algorithms to quantitatively reproduce features of various classes of neuronal spike patterns using the Izhikevich model. Employing experimental data from Hippocampome.org, a comprehensive knowledgebase of neuron types in the rodent hippocampus, we demonstrate that our approach reliably fit Izhikevich models to nine distinct classes of experimentally recorded spike patterns, including delayed spiking, spiking with adaptation, stuttering, and bursting. Importantly, by leveraging the parameter-exploration capabilities of evolutionary algorithms, and by representing qualitative spike pattern class definitions in the error landscape, our approach creates several suitable models for each neuron type, exhibiting appropriate feature variabilities among neurons. Moreover, we demonstrate the flexibility of our methodology by creating multi-compartment Izhikevich models for each neuron type in addition to single-point versions. Although the results presented here focus on hippocampal neuron types, the same strategy is broadly applicable to any neural systems.

GABAa excitation and synaptogenesis after Status Epilepticus - A computational study

The role of GABAergic neurotransmission on epileptogenesis has been the subject of speculation according to different approaches. However, it is a very complex task to specifically consider the action of the GABAa neurotransmitter, which, in its dependence on the intracellular level of Cl-, can change its effect from inhibitory to excitatory. We have developed a computational model that represents the dentate gyrus and is composed of three different populations of neurons (granule cells, interneurons and mossy cells) that are mutually interconnected. The interconnections of the neurons were based on compensation theory with Hebbian and anti-Hebbian rules. The model also incorporates non-synaptic mechanisms to control the ionic homeostasis and was able to reproduce ictal discharges. The goal of the work was to investigate the hypothesis that the observed aberrant sprouting is promoted by GABAa excitatory action. Conjointly with the abnormal sprouting of the mossy fibres, the simulations show a reduction of the mossy cells connections in the network and an increased inhibition of the interneurons as a response of the neuronal network to control the activity. This finding contributes to increasing the changes in the connectivity of the neuronal circuitry and to increasing the epileptiform activity occurrences.

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 which 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 bi-linear 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.

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.