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

Eric Y Hu,Dong Song,Theodore W Berger,Jean-Marie C Bouteiller,Michel Baudry

doi:10.3389/fncom.2015.00112

Abstract

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.

Highlights

Computational multi-scale and large-scale modeling are increasingly used to gain insights on brain functions and dysfunctions (Dyhrfjeld-Johnsen et al, 2007; Bouteiller et al, 2011; Hendrickson et al, 2013; Mattioni and Le Novère, 2013; Dougherty et al, 2014; Yu et al, 2014)
The results clearly indicate that the IO synapse model is capable of replicating the complex functional dynamics of a detailed glutamatergic synapse model, while significantly reducing computational complexity, thereby enabling simulations on larger temporal and spatial scales
The AMPAr current is calculated through the following equation: IAMPA = nbAMPA × g2O2 + g3O3 + g4O4 × (V − Vrev) where IAMPAI is the total current contributed by AMPAr, On represent the open states with associated conductances gn with n being the number of glutamate molecules bound, and Vrev is the reversal potential of AMPAr.nbAMPA, which represents the number of AMPA receptors, was set to 80 in the EONS synapse model, which fits the range of approximately 46–174 AMPAr reported in hippocampal synapse (Matsuzaki et al, 2001); AMPAr dynamics are known to be relatively fast (Robert and Howe, 2003), with currents returning to baseline in less than 30 ms

Summary

Introduction

Computational multi-scale and large-scale modeling are increasingly used to gain insights on brain functions and dysfunctions (Dyhrfjeld-Johnsen et al, 2007; Bouteiller et al, 2011; Hendrickson et al, 2013; Mattioni and Le Novère, 2013; Dougherty et al, 2014; Yu et al, 2014). A large number of receptors, mechanisms, and pathways modulate synaptic strength, function, and plasticity. Nonlinear synapses for large-scale models and pathological cases, multi- and large-scale models are essential for taking into account relevant processes that take place at all levels. Mathematical models that simulate physiological systems are developed to depict the system of interest, or at least provide a reasonable view of some of its inherent mechanisms and functions. Markov kinetic state models (MSM) represent a popular choice of model structure used to represent many dynamical physiological systems (Prinz et al, 2011). Integration of a large number of kinetic models with varying temporal dynamics without simplification can increase the computational loads, leading to prohibitively long simulation times

Methods

Results

Conclusion