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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

Comparison between the IO synapse model and the original EONS synapse model. (A) Expected EPSC response from the original EONS synapse model (blue) and the IO synapse model (red, dashed). The error difference between the two traces is plotted in black, to allow for comparison on when the two models diverge. Both simulations were run in the single synapse configuration and in voltage-clamped conditions. (i) through (x) designate individual or double responses to events within the first 2 s of presynaptic activity - the NRMSE of each response is presented in Table 1. Scatterplot on bottom right shows direct comparison of y-values (current) between the two models, where each point represents a different time point in the results. Results are shown to be nearly identical to each other, with only minor differences as shown in the error comparison and scatterplot. (B) Response from the EONS synapse model (blue) and the IO synapse model (red) when connected to a neuron model within the NEURON simulation environment. (C) Somatic response in a neuron model using the EONS synapse model (blue) and the IO synapse model (Red, dotted) within the NEURON simulation environment. In the simulation, stochastic vesicle release was disabled for consistency and all synapses fired in response to a pre-synaptic event. Both responses are nearly identical. The minor differences noted in the synaptic current as shown in the other comparisons do not significantly affect the response of the postsynaptic cell.
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Figure 4: Comparison between the IO synapse model and the original EONS synapse model. (A) Expected EPSC response from the original EONS synapse model (blue) and the IO synapse model (red, dashed). The error difference between the two traces is plotted in black, to allow for comparison on when the two models diverge. Both simulations were run in the single synapse configuration and in voltage-clamped conditions. (i) through (x) designate individual or double responses to events within the first 2 s of presynaptic activity - the NRMSE of each response is presented in Table 1. Scatterplot on bottom right shows direct comparison of y-values (current) between the two models, where each point represents a different time point in the results. Results are shown to be nearly identical to each other, with only minor differences as shown in the error comparison and scatterplot. (B) Response from the EONS synapse model (blue) and the IO synapse model (red) when connected to a neuron model within the NEURON simulation environment. (C) Somatic response in a neuron model using the EONS synapse model (blue) and the IO synapse model (Red, dotted) within the NEURON simulation environment. In the simulation, stochastic vesicle release was disabled for consistency and all synapses fired in response to a pre-synaptic event. Both responses are nearly identical. The minor differences noted in the synaptic current as shown in the other comparisons do not significantly affect the response of the postsynaptic cell.

Mentions: Results and simulation times for both the IO synapse model and the original platform were compared under the same simulation conditions (20 s simulated time, 2 Hz Poisson random interval train input) to evaluate performance of the IO synapse model in terms of accuracy and speed. For the original platform, simulations were run in Java, the native language code of the EONS/RHENOMS synaptic platform. The IO synapse model was prototyped first in MATLAB, then ported to the NEURON simulation environment. Two scenarios were explored in these studies. For the first one, synapse models were simulated alone (independently from their connected neuron) and compared for speed and accuracy (i.e., in a simulated voltage-clamped condition). The NRMS error was 3.3%, making the IO synapse model a reliable alternative to the original platform. Further investigation highlights the differences in error for individual events (or pairs of events if they are close to each other) for the first 2 s with presynaptic activity. This duration was chosen as it equals the memory window of the IO synapse model. Consequently, the response of the IO synapse model takes into account the nonlinear interactions induced by previous events that are within a 2 s timeframe of the current time point. Table 1 shows the NRMS error for the events indicated as shown in Figure 4A. Here, we see that some error is present even in the first few events without any previous activity. This error would indicate that lower order nonlinearities are being partly compensated in the model to better fit higher order linearities. The error overall remains fairly constant at around 3% until reaching the 10th event, where the last three events indicated are shown to deviate more significantly. Furthermore the direction of the error is different in comparison between the first few events and the following, as seen in the error difference chart on the top of Figure 3. In the first few events, the IO synapse model has more under-estimate error, whereas in the last few events observed, the error consisted in over-estimation of the output. Such analysis shows that the IO synapse model is accurate not only according to the overall RMS error, but even high order nonlinearities are well fitted in the model. This results in some compensation from the lower order nonlinear interactions, but in return responses that must consider up to 10 events in the past are still described accurately by the IO synapse model.


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)

Comparison between the IO synapse model and the original EONS synapse model. (A) Expected EPSC response from the original EONS synapse model (blue) and the IO synapse model (red, dashed). The error difference between the two traces is plotted in black, to allow for comparison on when the two models diverge. Both simulations were run in the single synapse configuration and in voltage-clamped conditions. (i) through (x) designate individual or double responses to events within the first 2 s of presynaptic activity - the NRMSE of each response is presented in Table 1. Scatterplot on bottom right shows direct comparison of y-values (current) between the two models, where each point represents a different time point in the results. Results are shown to be nearly identical to each other, with only minor differences as shown in the error comparison and scatterplot. (B) Response from the EONS synapse model (blue) and the IO synapse model (red) when connected to a neuron model within the NEURON simulation environment. (C) Somatic response in a neuron model using the EONS synapse model (blue) and the IO synapse model (Red, dotted) within the NEURON simulation environment. In the simulation, stochastic vesicle release was disabled for consistency and all synapses fired in response to a pre-synaptic event. Both responses are nearly identical. The minor differences noted in the synaptic current as shown in the other comparisons do not significantly affect the response of the postsynaptic cell.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 4: Comparison between the IO synapse model and the original EONS synapse model. (A) Expected EPSC response from the original EONS synapse model (blue) and the IO synapse model (red, dashed). The error difference between the two traces is plotted in black, to allow for comparison on when the two models diverge. Both simulations were run in the single synapse configuration and in voltage-clamped conditions. (i) through (x) designate individual or double responses to events within the first 2 s of presynaptic activity - the NRMSE of each response is presented in Table 1. Scatterplot on bottom right shows direct comparison of y-values (current) between the two models, where each point represents a different time point in the results. Results are shown to be nearly identical to each other, with only minor differences as shown in the error comparison and scatterplot. (B) Response from the EONS synapse model (blue) and the IO synapse model (red) when connected to a neuron model within the NEURON simulation environment. (C) Somatic response in a neuron model using the EONS synapse model (blue) and the IO synapse model (Red, dotted) within the NEURON simulation environment. In the simulation, stochastic vesicle release was disabled for consistency and all synapses fired in response to a pre-synaptic event. Both responses are nearly identical. The minor differences noted in the synaptic current as shown in the other comparisons do not significantly affect the response of the postsynaptic cell.
Mentions: Results and simulation times for both the IO synapse model and the original platform were compared under the same simulation conditions (20 s simulated time, 2 Hz Poisson random interval train input) to evaluate performance of the IO synapse model in terms of accuracy and speed. For the original platform, simulations were run in Java, the native language code of the EONS/RHENOMS synaptic platform. The IO synapse model was prototyped first in MATLAB, then ported to the NEURON simulation environment. Two scenarios were explored in these studies. For the first one, synapse models were simulated alone (independently from their connected neuron) and compared for speed and accuracy (i.e., in a simulated voltage-clamped condition). The NRMS error was 3.3%, making the IO synapse model a reliable alternative to the original platform. Further investigation highlights the differences in error for individual events (or pairs of events if they are close to each other) for the first 2 s with presynaptic activity. This duration was chosen as it equals the memory window of the IO synapse model. Consequently, the response of the IO synapse model takes into account the nonlinear interactions induced by previous events that are within a 2 s timeframe of the current time point. Table 1 shows the NRMS error for the events indicated as shown in Figure 4A. Here, we see that some error is present even in the first few events without any previous activity. This error would indicate that lower order nonlinearities are being partly compensated in the model to better fit higher order linearities. The error overall remains fairly constant at around 3% until reaching the 10th event, where the last three events indicated are shown to deviate more significantly. Furthermore the direction of the error is different in comparison between the first few events and the following, as seen in the error difference chart on the top of Figure 3. In the first few events, the IO synapse model has more under-estimate error, whereas in the last few events observed, the error consisted in over-estimation of the output. Such analysis shows that the IO synapse model is accurate not only according to the overall RMS error, but even high order nonlinearities are well fitted in the model. This results in some compensation from the lower order nonlinear interactions, but in return responses that must consider up to 10 events in the past are still described accurately by the IO synapse model.

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