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

Hu EY, Bouteiller JM, Song D, Baudry M, Berger TW - Front Comput Neurosci (2015)

Bottom Line: These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, University of Southern California Los Angeles, CA, USA.

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.

No MeSH data available.


Related in: MedlinePlus

Synapse models can have various representations, which differ in computational efficiency and model detail. (A) The exponential synapse is a commonly used synapse model that produces a postsynaptic response from a simplistic equation. The result is fast but lacks more complex dynamics typically seen in an actual synapse. (B) The EONS synapse model is a detailed, parametric model of a hippocampal glutamate synapse. Markov kinetic state models and other additional mechanisms govern the overall postsynaptic response, resulting in an accurate and nonlinear response more characteristic of the response that would be observed in an actual glutamatergic synapse. (C) The IO synapse model uses the Volterra functional power series to faithfully reproduce the nonlinear details seen in the EONS/RHENOMS model. As this IO synapse model characterizes the dynamic relationships between the input events and the corresponding output, much of the computationally intensive calculations are waived through the use of this methodology. (D) Schematic representation of the computation time required and the detailed accuracy of each model. The IO synapse model can provide a much more accurate representation than the exponential synapse, while computationally lighter than the parametric EONS synapse model.
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Figure 1: Synapse models can have various representations, which differ in computational efficiency and model detail. (A) The exponential synapse is a commonly used synapse model that produces a postsynaptic response from a simplistic equation. The result is fast but lacks more complex dynamics typically seen in an actual synapse. (B) The EONS synapse model is a detailed, parametric model of a hippocampal glutamate synapse. Markov kinetic state models and other additional mechanisms govern the overall postsynaptic response, resulting in an accurate and nonlinear response more characteristic of the response that would be observed in an actual glutamatergic synapse. (C) The IO synapse model uses the Volterra functional power series to faithfully reproduce the nonlinear details seen in the EONS/RHENOMS model. As this IO synapse model characterizes the dynamic relationships between the input events and the corresponding output, much of the computationally intensive calculations are waived through the use of this methodology. (D) Schematic representation of the computation time required and the detailed accuracy of each model. The IO synapse model can provide a much more accurate representation than the exponential synapse, while computationally lighter than the parametric EONS synapse model.

Mentions: Here, we propose to use the Volterra functional power series (Berger et al., 2010) to capture the dynamics of the nonlinear systems in a very compact form and use them to bridge hierarchical scales (Figure 1). Unlike previous nonlinear synapses, modeling with the Volterra series does not impose any predefined structural assumption on the system it models—the model is instead defined by input-output relations extracted from the data itself, thus making it a functional “input-output” model of the system. The Input-Output (IO) model uses kernels to represent the functional properties of the system modeled, effectively replicating the dynamics and behavior of the process without requiring a priori knowledge on its internal structure and its underlying mechanisms. Furthermore, the Volterra-based model requires little computational power. The Input-Output model can therefore reduce complex nonlinear differential systems into input-output transformations, which describe the causal relationship between the input and output properties of the system, while maintaining the nonlinear dynamics of the system model and reducing its computational complexity (Marmarelis and Marmarelis, 1978). The generality of this methodology means that it can be applied to various phenomena, including those from mechanical systems (Bharathy et al., 2008), biomedical systems (Berger et al., 1988a,b; Jo et al., 2007; Song et al., 2009a,b) and economics (Tu et al., 2012).


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

Hu EY, Bouteiller JM, Song D, Baudry M, Berger TW - Front Comput Neurosci (2015)

Synapse models can have various representations, which differ in computational efficiency and model detail. (A) The exponential synapse is a commonly used synapse model that produces a postsynaptic response from a simplistic equation. The result is fast but lacks more complex dynamics typically seen in an actual synapse. (B) The EONS synapse model is a detailed, parametric model of a hippocampal glutamate synapse. Markov kinetic state models and other additional mechanisms govern the overall postsynaptic response, resulting in an accurate and nonlinear response more characteristic of the response that would be observed in an actual glutamatergic synapse. (C) The IO synapse model uses the Volterra functional power series to faithfully reproduce the nonlinear details seen in the EONS/RHENOMS model. As this IO synapse model characterizes the dynamic relationships between the input events and the corresponding output, much of the computationally intensive calculations are waived through the use of this methodology. (D) Schematic representation of the computation time required and the detailed accuracy of each model. The IO synapse model can provide a much more accurate representation than the exponential synapse, while computationally lighter than the parametric EONS synapse model.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4585022&req=5

Figure 1: Synapse models can have various representations, which differ in computational efficiency and model detail. (A) The exponential synapse is a commonly used synapse model that produces a postsynaptic response from a simplistic equation. The result is fast but lacks more complex dynamics typically seen in an actual synapse. (B) The EONS synapse model is a detailed, parametric model of a hippocampal glutamate synapse. Markov kinetic state models and other additional mechanisms govern the overall postsynaptic response, resulting in an accurate and nonlinear response more characteristic of the response that would be observed in an actual glutamatergic synapse. (C) The IO synapse model uses the Volterra functional power series to faithfully reproduce the nonlinear details seen in the EONS/RHENOMS model. As this IO synapse model characterizes the dynamic relationships between the input events and the corresponding output, much of the computationally intensive calculations are waived through the use of this methodology. (D) Schematic representation of the computation time required and the detailed accuracy of each model. The IO synapse model can provide a much more accurate representation than the exponential synapse, while computationally lighter than the parametric EONS synapse model.
Mentions: Here, we propose to use the Volterra functional power series (Berger et al., 2010) to capture the dynamics of the nonlinear systems in a very compact form and use them to bridge hierarchical scales (Figure 1). Unlike previous nonlinear synapses, modeling with the Volterra series does not impose any predefined structural assumption on the system it models—the model is instead defined by input-output relations extracted from the data itself, thus making it a functional “input-output” model of the system. The Input-Output (IO) model uses kernels to represent the functional properties of the system modeled, effectively replicating the dynamics and behavior of the process without requiring a priori knowledge on its internal structure and its underlying mechanisms. Furthermore, the Volterra-based model requires little computational power. The Input-Output model can therefore reduce complex nonlinear differential systems into input-output transformations, which describe the causal relationship between the input and output properties of the system, while maintaining the nonlinear dynamics of the system model and reducing its computational complexity (Marmarelis and Marmarelis, 1978). The generality of this methodology means that it can be applied to various phenomena, including those from mechanical systems (Bharathy et al., 2008), biomedical systems (Berger et al., 1988a,b; Jo et al., 2007; Song et al., 2009a,b) and economics (Tu et al., 2012).

Bottom Line: These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, University of Southern California Los Angeles, CA, USA.

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.

No MeSH data available.


Related in: MedlinePlus