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Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources.

Lazar AA, Zhou Y - Front Comput Neurosci (2014)

Bottom Line: For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding.Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given.We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, Columbia University New York, NY, USA.

ABSTRACT
We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

No MeSH data available.


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The variance of the measurement and spike timing error associated with the sodium channels (blue) and the potassium channels (red) of the Hodgkin-Huxley equations with alternative noise sources parametrized by the bias current I. (A) The variance of the measurement error computed from PRCs of Hodgkin-Huxley equations, with NNa = 1 and NK = 1. Actual variance with different number of ion channels is inversely proportional to NNa and NK, respectively. (B) Spike timing variance obtained in simulations by comparing the spike times generated by the Hodgkin-Huxley neuron with channel noise and the spike times generated by its reduced PIF counterpart. Blue curve is obtained by using NNa = 5 × 104, NK = ∞, and normalized to 1 sodium channel. Red curve is obtained by using NK = 5 × 104, NNa = ∞, and normalized to 1 potassium channel.
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Figure 5: The variance of the measurement and spike timing error associated with the sodium channels (blue) and the potassium channels (red) of the Hodgkin-Huxley equations with alternative noise sources parametrized by the bias current I. (A) The variance of the measurement error computed from PRCs of Hodgkin-Huxley equations, with NNa = 1 and NK = 1. Actual variance with different number of ion channels is inversely proportional to NNa and NK, respectively. (B) Spike timing variance obtained in simulations by comparing the spike times generated by the Hodgkin-Huxley neuron with channel noise and the spike times generated by its reduced PIF counterpart. Blue curve is obtained by using NNa = 5 × 104, NK = ∞, and normalized to 1 sodium channel. Red curve is obtained by using NK = 5 × 104, NNa = ∞, and normalized to 1 potassium channel.

Mentions: We first evaluate (𝔼[εikNa]2)(Ii) using the PRCs. The PRCs are obtained by letting NNa = NK = ∞ and thereby making the system deterministic. Since the measurement error variance for fixed Ii is proportional to (NNa)−1, it is shown in Figure 5A as a function of the bias current Ii for NNa = 1. Similarly, the variance of the measurement error for NK = 1 is shown in Figure 5A, and it is proportional to (NK)−1 for a fixed Ii. We notice that, when the number of channels is the same, the measurement error due to the sodium channels is of the same order of magnitude with the measurement error due to the potassium channels. However, the number of sodium channels is typically 3–4 times larger than the number of potassium channels. Therefore, in contrast to the previous case, the error induced by sodium channels shall be larger than that induced by potassium channels.


Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources.

Lazar AA, Zhou Y - Front Comput Neurosci (2014)

The variance of the measurement and spike timing error associated with the sodium channels (blue) and the potassium channels (red) of the Hodgkin-Huxley equations with alternative noise sources parametrized by the bias current I. (A) The variance of the measurement error computed from PRCs of Hodgkin-Huxley equations, with NNa = 1 and NK = 1. Actual variance with different number of ion channels is inversely proportional to NNa and NK, respectively. (B) Spike timing variance obtained in simulations by comparing the spike times generated by the Hodgkin-Huxley neuron with channel noise and the spike times generated by its reduced PIF counterpart. Blue curve is obtained by using NNa = 5 × 104, NK = ∞, and normalized to 1 sodium channel. Red curve is obtained by using NK = 5 × 104, NNa = ∞, and normalized to 1 potassium channel.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4150400&req=5

Figure 5: The variance of the measurement and spike timing error associated with the sodium channels (blue) and the potassium channels (red) of the Hodgkin-Huxley equations with alternative noise sources parametrized by the bias current I. (A) The variance of the measurement error computed from PRCs of Hodgkin-Huxley equations, with NNa = 1 and NK = 1. Actual variance with different number of ion channels is inversely proportional to NNa and NK, respectively. (B) Spike timing variance obtained in simulations by comparing the spike times generated by the Hodgkin-Huxley neuron with channel noise and the spike times generated by its reduced PIF counterpart. Blue curve is obtained by using NNa = 5 × 104, NK = ∞, and normalized to 1 sodium channel. Red curve is obtained by using NK = 5 × 104, NNa = ∞, and normalized to 1 potassium channel.
Mentions: We first evaluate (𝔼[εikNa]2)(Ii) using the PRCs. The PRCs are obtained by letting NNa = NK = ∞ and thereby making the system deterministic. Since the measurement error variance for fixed Ii is proportional to (NNa)−1, it is shown in Figure 5A as a function of the bias current Ii for NNa = 1. Similarly, the variance of the measurement error for NK = 1 is shown in Figure 5A, and it is proportional to (NK)−1 for a fixed Ii. We notice that, when the number of channels is the same, the measurement error due to the sodium channels is of the same order of magnitude with the measurement error due to the potassium channels. However, the number of sodium channels is typically 3–4 times larger than the number of potassium channels. Therefore, in contrast to the previous case, the error induced by sodium channels shall be larger than that induced by potassium channels.

Bottom Line: For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding.Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given.We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, Columbia University New York, NY, USA.

ABSTRACT
We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

No MeSH data available.


Related in: MedlinePlus