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Diffusion approximation-based simulation of stochastic ion channels: which method to use?

Pezo D, Soudry D, Orio P - Front Comput Neurosci (2014)

Bottom Line: We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC-which is the fastest and most accurate method.For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy.Consequently, MC modeling may be the best method for detailed multicompartment neuron models-in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.

View Article: PubMed Central - PubMed

Affiliation: Centro Interdisciplinario de Neurociencia de Valparaíso, Universidad de Valparaíso Valparaíso, Chile.

ABSTRACT
To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie's method for Markov Chains (MC) simulation is highly accurate, yet it becomes computationally intensive in the regime of a high number of channels. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA). Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties-such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Goldwyn et al., 2011; Linaro et al., 2011; Dangerfield et al., 2012; Orio and Soudry, 2012; Schmandt and Galán, 2012; Güler, 2013; Huang et al., 2013a), comparing all of them in a set of numerical simulations that assess numerical accuracy and computational efficiency on three different models: (1) the original Hodgkin and Huxley model, (2) a model with faster sodium channels, and (3) a multi-compartmental model inspired in granular cells. We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC-which is the fastest and most accurate method. For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy. Consequently, MC modeling may be the best method for detailed multicompartment neuron models-in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.

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Simulations of the stochastic HH model under voltage clamp. (A) Voltage trace applied to simulated channels in a 100-ms simulation, repeated 2000 times. Blue and green rectangles represent the 5-ms intervals that are expanded in the left and right columns of the figure, respectively. (B) Detail of the voltage traces corresponding to the time windows analyzed in (C–F). Note the different vertical scales. (C) Mean of open sodium channels during the subthreshold (left) and action potential (right) regimes, for the simulation algorithms tested. (D) Mean of open potassium channels. (E) Variance of open sodium channels. (F) Variance of open potassium channels. NNa = 500, NK = 160. Very similar results were obtained with NNa = 5000, NK = 1600 (see text).
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Figure 2: Simulations of the stochastic HH model under voltage clamp. (A) Voltage trace applied to simulated channels in a 100-ms simulation, repeated 2000 times. Blue and green rectangles represent the 5-ms intervals that are expanded in the left and right columns of the figure, respectively. (B) Detail of the voltage traces corresponding to the time windows analyzed in (C–F). Note the different vertical scales. (C) Mean of open sodium channels during the subthreshold (left) and action potential (right) regimes, for the simulation algorithms tested. (D) Mean of open potassium channels. (E) Variance of open sodium channels. (F) Variance of open potassium channels. NNa = 500, NK = 160. Very similar results were obtained with NNa = 5000, NK = 1600 (see text).

Mentions: A third test, to check how the different DA methods can reproduce the variability of channel openings obtained with MC modeling, consists on recording the response of the model channels to a fixed voltage trajectory obtained from a stochastic simulation. The voltage trace is shown in Figure 2A and it contains an action potential as well as a noisy background (zoomed in Figure 2B). With each model and condition, 2000 independent simulations were run and the time evolution of open channels was recorded. At each point in time, the mean and variance of the open channels was calculated. In addition to the comparison with the behavior of MC simulation, we compared to the expected mean of open channels which is calculated by applying the same voltage clamp simulation to deterministic HH channels. Moreover, we can compute the expected variance as explained in Methods.


Diffusion approximation-based simulation of stochastic ion channels: which method to use?

Pezo D, Soudry D, Orio P - Front Comput Neurosci (2014)

Simulations of the stochastic HH model under voltage clamp. (A) Voltage trace applied to simulated channels in a 100-ms simulation, repeated 2000 times. Blue and green rectangles represent the 5-ms intervals that are expanded in the left and right columns of the figure, respectively. (B) Detail of the voltage traces corresponding to the time windows analyzed in (C–F). Note the different vertical scales. (C) Mean of open sodium channels during the subthreshold (left) and action potential (right) regimes, for the simulation algorithms tested. (D) Mean of open potassium channels. (E) Variance of open sodium channels. (F) Variance of open potassium channels. NNa = 500, NK = 160. Very similar results were obtained with NNa = 5000, NK = 1600 (see text).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4217484&req=5

Figure 2: Simulations of the stochastic HH model under voltage clamp. (A) Voltage trace applied to simulated channels in a 100-ms simulation, repeated 2000 times. Blue and green rectangles represent the 5-ms intervals that are expanded in the left and right columns of the figure, respectively. (B) Detail of the voltage traces corresponding to the time windows analyzed in (C–F). Note the different vertical scales. (C) Mean of open sodium channels during the subthreshold (left) and action potential (right) regimes, for the simulation algorithms tested. (D) Mean of open potassium channels. (E) Variance of open sodium channels. (F) Variance of open potassium channels. NNa = 500, NK = 160. Very similar results were obtained with NNa = 5000, NK = 1600 (see text).
Mentions: A third test, to check how the different DA methods can reproduce the variability of channel openings obtained with MC modeling, consists on recording the response of the model channels to a fixed voltage trajectory obtained from a stochastic simulation. The voltage trace is shown in Figure 2A and it contains an action potential as well as a noisy background (zoomed in Figure 2B). With each model and condition, 2000 independent simulations were run and the time evolution of open channels was recorded. At each point in time, the mean and variance of the open channels was calculated. In addition to the comparison with the behavior of MC simulation, we compared to the expected mean of open channels which is calculated by applying the same voltage clamp simulation to deterministic HH channels. Moreover, we can compute the expected variance as explained in Methods.

Bottom Line: We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC-which is the fastest and most accurate method.For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy.Consequently, MC modeling may be the best method for detailed multicompartment neuron models-in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.

View Article: PubMed Central - PubMed

Affiliation: Centro Interdisciplinario de Neurociencia de Valparaíso, Universidad de Valparaíso Valparaíso, Chile.

ABSTRACT
To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie's method for Markov Chains (MC) simulation is highly accurate, yet it becomes computationally intensive in the regime of a high number of channels. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA). Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties-such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Goldwyn et al., 2011; Linaro et al., 2011; Dangerfield et al., 2012; Orio and Soudry, 2012; Schmandt and Galán, 2012; Güler, 2013; Huang et al., 2013a), comparing all of them in a set of numerical simulations that assess numerical accuracy and computational efficiency on three different models: (1) the original Hodgkin and Huxley model, (2) a model with faster sodium channels, and (3) a multi-compartmental model inspired in granular cells. We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC-which is the fastest and most accurate method. For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy. Consequently, MC modeling may be the best method for detailed multicompartment neuron models-in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.

No MeSH data available.


Related in: MedlinePlus