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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

Accuracy of the IO synapse model with various input frequencies. The normalized RMS error is plotted for the 3rd order IO synapse model simulated at fixed (blue) and variable (red) time step simulations and for the 4th order IO synapse model simulated at fixed (green) and variable (purple) time step simulations. With the 3rd order model, the error noticeably increases at higher frequencies. The 4th order model yields constant error at all tested frequencies.
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Figure 5: Accuracy of the IO synapse model with various input frequencies. The normalized RMS error is plotted for the 3rd order IO synapse model simulated at fixed (blue) and variable (red) time step simulations and for the 4th order IO synapse model simulated at fixed (green) and variable (purple) time step simulations. With the 3rd order model, the error noticeably increases at higher frequencies. The 4th order model yields constant error at all tested frequencies.

Mentions: The 3rd order IO receptor models were trained with a random interval train input having a mean frequency of 2 Hz. This frequency value was chosen to reflect the typical firing rate of hippocampal CA1 and CA3 neurons (Berger et al., 1988a). However, the mean firing rate (MFR) can often vary widely within hippocampal pyramidal cells, even during the resting state (Ranck, 1973). We therefore opted to evaluate how the accuracy of the IO synapse model varied with different input frequencies. Thus, 3rd and 4th order IO synapse models were trained with randomized input events. The input events used for training consisted of a concatenation of random Poisson trains with a mean frequency of 2 and 10 Hz. The responses of the IO synapse models were then validated against the original EONS synapse model results for accuracy measurement. The input events for the validation tests consisted of Poisson randomized input events with a range of mean frequency values, as shown in Figure 5. IO synapse model simulations were conducted in both fixed time step and variable time step. Fixed time step was simulated with an interval of 0.1 ms; this corresponds to the bin size used for training the receptor models. Variable time step was used to further reduce calculation time for the IO synapse model. The method used was CVODE, an algorithm readily available in NEURON (Hines and Carnevale, 1997). The error for both simulations were compared with each other to assess whether there were discrepancies between fixed and variable time steps.


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)

Accuracy of the IO synapse model with various input frequencies. The normalized RMS error is plotted for the 3rd order IO synapse model simulated at fixed (blue) and variable (red) time step simulations and for the 4th order IO synapse model simulated at fixed (green) and variable (purple) time step simulations. With the 3rd order model, the error noticeably increases at higher frequencies. The 4th order model yields constant error at all tested frequencies.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 5: Accuracy of the IO synapse model with various input frequencies. The normalized RMS error is plotted for the 3rd order IO synapse model simulated at fixed (blue) and variable (red) time step simulations and for the 4th order IO synapse model simulated at fixed (green) and variable (purple) time step simulations. With the 3rd order model, the error noticeably increases at higher frequencies. The 4th order model yields constant error at all tested frequencies.
Mentions: The 3rd order IO receptor models were trained with a random interval train input having a mean frequency of 2 Hz. This frequency value was chosen to reflect the typical firing rate of hippocampal CA1 and CA3 neurons (Berger et al., 1988a). However, the mean firing rate (MFR) can often vary widely within hippocampal pyramidal cells, even during the resting state (Ranck, 1973). We therefore opted to evaluate how the accuracy of the IO synapse model varied with different input frequencies. Thus, 3rd and 4th order IO synapse models were trained with randomized input events. The input events used for training consisted of a concatenation of random Poisson trains with a mean frequency of 2 and 10 Hz. The responses of the IO synapse models were then validated against the original EONS synapse model results for accuracy measurement. The input events for the validation tests consisted of Poisson randomized input events with a range of mean frequency values, as shown in Figure 5. IO synapse model simulations were conducted in both fixed time step and variable time step. Fixed time step was simulated with an interval of 0.1 ms; this corresponds to the bin size used for training the receptor models. Variable time step was used to further reduce calculation time for the IO synapse model. The method used was CVODE, an algorithm readily available in NEURON (Hines and Carnevale, 1997). The error for both simulations were compared with each other to assess whether there were discrepancies between fixed and variable time steps.

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