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Front Comput Neurosci. 2015 Sep 17;9:112. doi: 10.3389/fncom.2015.00112. eCollection 2015.

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

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Department of Biomedical Engineering, University of Southern California Los Angeles, CA, USA.
Graduate College of Biomedical Sciences, Western University of Health Sciences Pomona, CA, USA.


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.


computational modeling; glutamatergic synapse; multi-scale modeling; synaptic modeling; volterra expansion

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