Modeling neuron-glia interactions: from parametric model to neuromorphic hardware

Modeling Nonlinear Synaptic Dynamics: A Laguerre-Volterra Network Framework for Improved Computational Efficiency in Large Scale Simulations

Synapses are key components in signal transmission in the brain, often exhibiting complex non-linear dynamics. Yet, they are often crudely modelled as linear exponential equations in large-scale neuron network simulations. Mechanistic models that use detailed channel receptor kinetics more closely replicate the nonlinear dynamics observed at synapses, but use of such models are generally restricted to small scale simulations due to their computational complexity. Previously, we have developed an ``input-output'' (IO) synapse model using the Volterra functional series to estimate nonlinear synaptic dynamics. Here, we present an improvement on the IO synapse model using the extbf{Laguerre-Volterra network (LVN) framework. We demonstrate that utilization of the LVN framework helps reduce memory requirements and improves the simulation speed in comparison to the previous iteration of the IO synapse model. We present results that demonstrate the accuracy, memory efficiency, and speed of the LVN model that can be extended to simulations with large numbers of synapses. Our efforts enable complex nonlinear synaptic dynamics to be modelled in large-scale network models, allowing us to explore how synaptic activity may influence network behavior and affects memory, learning, and neurodegenerative diseases.

A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics

In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Complete Neuron-Astrocyte Interaction Model: Digital Multiplierless Design and Networking Mechanism

Glial cells, also known as neuroglia or glia, are non-neuronal cells providing support and protection for neurons in the central nervous system (CNS). They also act as supportive cells in the brain. Among a variety of glial cells, the star-shaped glial cells, i.e., astrocytes, are the largest cell population in the brain. The important role of astrocyte such as neuronal synchronization, synaptic information regulation, feedback to neural activity and extracellular regulation make the astrocytes play a vital role in brain disease. This paper presents a modified complete neuron-astrocyte interaction model that is more suitable for efficient and large scale biological neural network realization on digital platforms. Simulation results show that the modified complete interaction model can reproduce biological-like behavior of the original neuron-astrocyte mechanism. The modified interaction model is investigated in terms of digital realization feasibility and cost targeting a low cost hardware implementation. Networking behavior of this interaction is investigated and compared between two cases: i) the neuron spiking mechanism without astrocyte effects, and ii) the effect of astrocyte in regulating the neurons behavior and synaptic transmission via controlling the LTP and LTD processes. Hardware implementation on FPGA shows that the modified model mimics the main mechanism of neuron-astrocyte communication with higher performance and considerably lower hardware overhead cost compared with the original interaction model.

The volterra functional series is a viable alternative to kinetic models for synaptic modeling--calibration and benchmarking

Synaptic transmission is governed by a series of complex and highly nonlinear mechanisms and pathways in which the dynamics have a profound influence on the overall signal sent to the postsynaptic cell. In simulation, these mechanisms are often represented through kinetic models governed by state variables and rate law equations. Calculations of such ordinary differential equations (ODEs) in kinetic models can be computationally intensive, and although algorithms have been optimally developed to handle ODEs efficiently, simulation of numerous, large and complex kinetic models requires a prohibitively large amount of computational power. Here we present an alternative representation of ionotropic glutamatergic receptors AMPAr and NMDAr kinetic models consisting of input-output surrogates of the receptor models which can capture the nonlinear dynamics seen in the kinetic models. We benchmark this Input-Output (IO) synapse model and compare it with kinetic receptor models to evaluate the simulation time required when using either synapse model, as well as the number of time steps each model needs for simulation. While remaining faithful to the original dynamics of the model, our results indicate that the IO synapse model requires less simulation time than the kinetic models under conditions which elicit normal physiological responses, thereby improving computational efficiency while preserving the complex non-linear dynamics of the receptors. These IO surrogates therefore constitute an appealing alternative to kinetic models in large scale networks simulations.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.