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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

Graphical representation of the first five Laguerre basis functions. The basis functions are scaled with coefficients and summed to produce the first order response to the system. Furthermore, these basis functions are multiplied with each other to produce the functions used for reproducing nonlinear responses.
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Figure 3: Graphical representation of the first five Laguerre basis functions. The basis functions are scaled with coefficients and summed to produce the first order response to the system. Furthermore, these basis functions are multiplied with each other to produce the functions used for reproducing nonlinear responses.

Mentions: A visualization of the Laguerre basis functions is shown in Figure 3. The basis functions are then scaled with coefficient values that are fitted to provide the appropriate response when all functions are convolved with the input signal and summed. To capture nonlinear responses, the basis functions are cross multiplied with each other as described previously. These functions together correspond to one set of basis functions with one given decay value, p. Because of the complexities of receptor responses, two sets of basis functions are used with different decay values represented by p. The first set covers the general response of the system within a short time frame to capture the overall waveform. The other covers a much longer time frame and accounts for slower mechanisms, such as desensitization. We found that using two basis function sets yield better approximation of the dynamics seen in the original kinetic models. The p-values were determined via gradient descent to find the optimal decay values with the lowest absolute error while fitting the data. The fitting process is further elaborated later in the description on coefficient estimation.


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)

Graphical representation of the first five Laguerre basis functions. The basis functions are scaled with coefficients and summed to produce the first order response to the system. Furthermore, these basis functions are multiplied with each other to produce the functions used for reproducing nonlinear responses.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4585022&req=5

Figure 3: Graphical representation of the first five Laguerre basis functions. The basis functions are scaled with coefficients and summed to produce the first order response to the system. Furthermore, these basis functions are multiplied with each other to produce the functions used for reproducing nonlinear responses.
Mentions: A visualization of the Laguerre basis functions is shown in Figure 3. The basis functions are then scaled with coefficient values that are fitted to provide the appropriate response when all functions are convolved with the input signal and summed. To capture nonlinear responses, the basis functions are cross multiplied with each other as described previously. These functions together correspond to one set of basis functions with one given decay value, p. Because of the complexities of receptor responses, two sets of basis functions are used with different decay values represented by p. The first set covers the general response of the system within a short time frame to capture the overall waveform. The other covers a much longer time frame and accounts for slower mechanisms, such as desensitization. We found that using two basis function sets yield better approximation of the dynamics seen in the original kinetic models. The p-values were determined via gradient descent to find the optimal decay values with the lowest absolute error while fitting the data. The fitting process is further elaborated later in the description on coefficient estimation.

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