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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

Structure of the EONS synapse model. (A) For every presynaptic event, the EONS synapse calculates the probability of vesicle release based on past release events. (B) For the original EONS synapse model, in the event of a vesicle release, glutamate diffusion is calculated and depending on postsynaptic receptor location, the result is used for deriving the open states in the kinetic models of the receptors. (C) The IO synapse model accounts for both the diffusion and kinetic receptor dynamics to calculate the predicted open states of the receptors. The open states are used to calculate conductances and resulting currents based on the postsynaptic potential. The calculated response is then passed on to the NEURON model.
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Figure 2: Structure of the EONS synapse model. (A) For every presynaptic event, the EONS synapse calculates the probability of vesicle release based on past release events. (B) For the original EONS synapse model, in the event of a vesicle release, glutamate diffusion is calculated and depending on postsynaptic receptor location, the result is used for deriving the open states in the kinetic models of the receptors. (C) The IO synapse model accounts for both the diffusion and kinetic receptor dynamics to calculate the predicted open states of the receptors. The open states are used to calculate conductances and resulting currents based on the postsynaptic potential. The calculated response is then passed on to the NEURON model.

Mentions: The framework of the IO synapse model follows a modular structure similar to the original EONS model—see Figure 2 for an overview. The IO synapse model contains three components: the presynaptic release component, the AMPAr component, and the NMDAr component. Using such a modular structure allows for additional components to be easily implemented and integrated in the future. The presynaptic release component uses the Dittman model of facilitation/depression (Dittman et al., 2000), with the parameters described in Song et al. (2009b) to approximate the short term plasticity seen in experimental studies. This model calculates the probability of vesicle release. A random number generator compared with the calculated release probability determines whether a release event occurs or not. If a release event takes place, it is passed on to the AMPAr and NMDAr Input-Output models. The AMPAr IO receptor model calculates the conductance values of AMPAr. For NMDAr, due to the additional complexity of the magnesium block of the channel, the open state probability is calculated first; the receptor conductance is then calculated with the following two equations, as stated in Ambert et al. (2010):g0=g1+g2-g11+eαψmgmax=g01+(Mg02+K0)e-δzFψm∕RTgNMDA=gmax×O(t)where g0 represents the total conductance in the absence of any magnesium, g1, g2 represent the open state conductances with one glutamate bound and 2 glutamate molecules bound, respectively. g1is set at 40 pS while g2 is set at 247 pS. represents the external magnesium concentration and is set The value α = 0.01 represents the steepness of the transition between g1 and g2. represents the external magnesium concentration and is set at 1 mM. K0 is the equilibrium constant for magnesium set at 3.57,F is Faraday's Constant (9.64867.104 C mol−1), R is the molecular gas constant (8.31434 J mol−1 K−1), and T is the temperature at 273.15 K. The variable ψm represents the affinity between NMDAr and magnesium, which is dependent on the postsynaptic potential of the synapse; the value is set to 0.8. Here we utilize the open state O(t) as the output data during training of the IO receptor model of the NMDA receptor; the estimated conductance is then calculated from the predicted open state value by the IO receptor 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)

Structure of the EONS synapse model. (A) For every presynaptic event, the EONS synapse calculates the probability of vesicle release based on past release events. (B) For the original EONS synapse model, in the event of a vesicle release, glutamate diffusion is calculated and depending on postsynaptic receptor location, the result is used for deriving the open states in the kinetic models of the receptors. (C) The IO synapse model accounts for both the diffusion and kinetic receptor dynamics to calculate the predicted open states of the receptors. The open states are used to calculate conductances and resulting currents based on the postsynaptic potential. The calculated response is then passed on to the NEURON model.
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Related In: Results  -  Collection

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Figure 2: Structure of the EONS synapse model. (A) For every presynaptic event, the EONS synapse calculates the probability of vesicle release based on past release events. (B) For the original EONS synapse model, in the event of a vesicle release, glutamate diffusion is calculated and depending on postsynaptic receptor location, the result is used for deriving the open states in the kinetic models of the receptors. (C) The IO synapse model accounts for both the diffusion and kinetic receptor dynamics to calculate the predicted open states of the receptors. The open states are used to calculate conductances and resulting currents based on the postsynaptic potential. The calculated response is then passed on to the NEURON model.
Mentions: The framework of the IO synapse model follows a modular structure similar to the original EONS model—see Figure 2 for an overview. The IO synapse model contains three components: the presynaptic release component, the AMPAr component, and the NMDAr component. Using such a modular structure allows for additional components to be easily implemented and integrated in the future. The presynaptic release component uses the Dittman model of facilitation/depression (Dittman et al., 2000), with the parameters described in Song et al. (2009b) to approximate the short term plasticity seen in experimental studies. This model calculates the probability of vesicle release. A random number generator compared with the calculated release probability determines whether a release event occurs or not. If a release event takes place, it is passed on to the AMPAr and NMDAr Input-Output models. The AMPAr IO receptor model calculates the conductance values of AMPAr. For NMDAr, due to the additional complexity of the magnesium block of the channel, the open state probability is calculated first; the receptor conductance is then calculated with the following two equations, as stated in Ambert et al. (2010):g0=g1+g2-g11+eαψmgmax=g01+(Mg02+K0)e-δzFψm∕RTgNMDA=gmax×O(t)where g0 represents the total conductance in the absence of any magnesium, g1, g2 represent the open state conductances with one glutamate bound and 2 glutamate molecules bound, respectively. g1is set at 40 pS while g2 is set at 247 pS. represents the external magnesium concentration and is set The value α = 0.01 represents the steepness of the transition between g1 and g2. represents the external magnesium concentration and is set at 1 mM. K0 is the equilibrium constant for magnesium set at 3.57,F is Faraday's Constant (9.64867.104 C mol−1), R is the molecular gas constant (8.31434 J mol−1 K−1), and T is the temperature at 273.15 K. The variable ψm represents the affinity between NMDAr and magnesium, which is dependent on the postsynaptic potential of the synapse; the value is set to 0.8. Here we utilize the open state O(t) as the output data during training of the IO receptor model of the NMDA receptor; the estimated conductance is then calculated from the predicted open state value by the IO receptor 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