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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

Simulation Time varies as a function of the number of synapse instances. Here, simulation time is represented in logarithmic scale. Computation time required for the kinetic synapse model is within the range of 10–20 min, while the computation time required for the IO synapse model ranges between 3 and 30 s. Dashed line represents the speedup of the IO synapse model against the kinetic synapse model based on number of synapses. At low number of synapses, the speedup of the IO synapse model is highest at around 150x faster than the computation time required for the kinetic synapse model. The speedup is shown to be decreasing, but stabilizes at around 50x speedup in later values.
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Figure 6: Simulation Time varies as a function of the number of synapse instances. Here, simulation time is represented in logarithmic scale. Computation time required for the kinetic synapse model is within the range of 10–20 min, while the computation time required for the IO synapse model ranges between 3 and 30 s. Dashed line represents the speedup of the IO synapse model against the kinetic synapse model based on number of synapses. At low number of synapses, the speedup of the IO synapse model is highest at around 150x faster than the computation time required for the kinetic synapse model. The speedup is shown to be decreasing, but stabilizes at around 50x speedup in later values.

Mentions: Of importance, the number of synapses modeled also impacts computational speed. Neurons have a large number of synapses: a typical pyramidal CA1 neuron has been reported to have up to 30,000 synapses (Megìas et al., 2001). The results reported in the previous sections were obtained with 16 synapses. To address this point we varied the number of synapses distributed on the neuron and recorded the simulation times (Figure 6; also see Supplementary Figure 1 for more details). For these simulations the computational contributions of the neuron model were minimized by reducing synaptic weight to 0. The results indicated that the neuron comprised of IO synapse model retains a total calculation time of less than 1 min even in simulations with up to 1000 synapses. Meanwhile, the calculation time required for the kinetic models ranges from 10 min with 10 synapses, to 18 min with 1000 synapses. The number of steps remained almost constant for both models: 400 steps for the IO model, and 40,000 steps for the kinetic model. Measuring the approximate speedup of the IO model in comparison to the kinetic model as a function of the number of synapses gives approximately a 150x speedup at 10 synapses, number which decreases as the number of synapses increases, to finally stabilize at about 50x speedup for 1000 synapses. Additional tests performed at up to 5000 synapses confirm that beyond 1000 synapses, the speedup of the IO synapse model remains around the same at around 50x.


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)

Simulation Time varies as a function of the number of synapse instances. Here, simulation time is represented in logarithmic scale. Computation time required for the kinetic synapse model is within the range of 10–20 min, while the computation time required for the IO synapse model ranges between 3 and 30 s. Dashed line represents the speedup of the IO synapse model against the kinetic synapse model based on number of synapses. At low number of synapses, the speedup of the IO synapse model is highest at around 150x faster than the computation time required for the kinetic synapse model. The speedup is shown to be decreasing, but stabilizes at around 50x speedup in later values.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4585022&req=5

Figure 6: Simulation Time varies as a function of the number of synapse instances. Here, simulation time is represented in logarithmic scale. Computation time required for the kinetic synapse model is within the range of 10–20 min, while the computation time required for the IO synapse model ranges between 3 and 30 s. Dashed line represents the speedup of the IO synapse model against the kinetic synapse model based on number of synapses. At low number of synapses, the speedup of the IO synapse model is highest at around 150x faster than the computation time required for the kinetic synapse model. The speedup is shown to be decreasing, but stabilizes at around 50x speedup in later values.
Mentions: Of importance, the number of synapses modeled also impacts computational speed. Neurons have a large number of synapses: a typical pyramidal CA1 neuron has been reported to have up to 30,000 synapses (Megìas et al., 2001). The results reported in the previous sections were obtained with 16 synapses. To address this point we varied the number of synapses distributed on the neuron and recorded the simulation times (Figure 6; also see Supplementary Figure 1 for more details). For these simulations the computational contributions of the neuron model were minimized by reducing synaptic weight to 0. The results indicated that the neuron comprised of IO synapse model retains a total calculation time of less than 1 min even in simulations with up to 1000 synapses. Meanwhile, the calculation time required for the kinetic models ranges from 10 min with 10 synapses, to 18 min with 1000 synapses. The number of steps remained almost constant for both models: 400 steps for the IO model, and 40,000 steps for the kinetic model. Measuring the approximate speedup of the IO model in comparison to the kinetic model as a function of the number of synapses gives approximately a 150x speedup at 10 synapses, number which decreases as the number of synapses increases, to finally stabilize at about 50x speedup for 1000 synapses. Additional tests performed at up to 5000 synapses confirm that beyond 1000 synapses, the speedup of the IO synapse model remains around the same at around 50x.

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