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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.

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SNR reconstruction error of encoded signals with a total of M = 2 circuits (4 neurons). Color legend: (Blue) σi1 = σ, σi2 = σi3 = σi4 = 0. (Green) σi2 = σ, σi1 = σi3 = σi4 = 0. (Red) σi3 = σ, σi1 = σi2 = σi4 = 0. (Black) σi4 = σ, σi1 = σi2 = σi3 = 0. (Magenta) 10σi1 = 10σi2 = σi3 = σi4 = σ. In-sets (on the left) are typical reconstructions that yield corresponding SNR indicated by arrows. The top left in (A) shows an example of reconstruction (green) whose SNR is 25 dB when compared to the original signal (blue). (A) SNR of reconstruction of u1(t). (B) SNR of reconstruction of u21(t) = u2(t, t).
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Figure 4: SNR reconstruction error of encoded signals with a total of M = 2 circuits (4 neurons). Color legend: (Blue) σi1 = σ, σi2 = σi3 = σi4 = 0. (Green) σi2 = σ, σi1 = σi3 = σi4 = 0. (Red) σi3 = σ, σi1 = σi2 = σi4 = 0. (Black) σi4 = σ, σi1 = σi2 = σi3 = 0. (Magenta) 10σi1 = 10σi2 = σi3 = σi4 = σ. In-sets (on the left) are typical reconstructions that yield corresponding SNR indicated by arrows. The top left in (A) shows an example of reconstruction (green) whose SNR is 25 dB when compared to the original signal (blue). (A) SNR of reconstruction of u1(t). (B) SNR of reconstruction of u21(t) = u2(t, t).

Mentions: Figure 4A shows the SNR of the reconstruction of signal u1(t) against different noise strength. Figure 4B shows the SNR of the reconstruction of signal u21(t) = u2(t, t). The reconstruction SNR in Figure 4A largely matches the inverse ordering of noise strength of each of the individual noise sources shown in Figure 3A. DSP noise sources degrade the reconstruction performance most strongly while noise sources associated with gating variables m and h have a much smaller effect for the same variance level. Since the variance of measurement error is the sum of error variance in each variable, the case when 10σ1 = 10σ2 = σ3 = σ4 = σ exhibits the lowest performance.


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

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

SNR reconstruction error of encoded signals with a total of M = 2 circuits (4 neurons). Color legend: (Blue) σi1 = σ, σi2 = σi3 = σi4 = 0. (Green) σi2 = σ, σi1 = σi3 = σi4 = 0. (Red) σi3 = σ, σi1 = σi2 = σi4 = 0. (Black) σi4 = σ, σi1 = σi2 = σi3 = 0. (Magenta) 10σi1 = 10σi2 = σi3 = σi4 = σ. In-sets (on the left) are typical reconstructions that yield corresponding SNR indicated by arrows. The top left in (A) shows an example of reconstruction (green) whose SNR is 25 dB when compared to the original signal (blue). (A) SNR of reconstruction of u1(t). (B) SNR of reconstruction of u21(t) = u2(t, t).
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4150400&req=5

Figure 4: SNR reconstruction error of encoded signals with a total of M = 2 circuits (4 neurons). Color legend: (Blue) σi1 = σ, σi2 = σi3 = σi4 = 0. (Green) σi2 = σ, σi1 = σi3 = σi4 = 0. (Red) σi3 = σ, σi1 = σi2 = σi4 = 0. (Black) σi4 = σ, σi1 = σi2 = σi3 = 0. (Magenta) 10σi1 = 10σi2 = σi3 = σi4 = σ. In-sets (on the left) are typical reconstructions that yield corresponding SNR indicated by arrows. The top left in (A) shows an example of reconstruction (green) whose SNR is 25 dB when compared to the original signal (blue). (A) SNR of reconstruction of u1(t). (B) SNR of reconstruction of u21(t) = u2(t, t).
Mentions: Figure 4A shows the SNR of the reconstruction of signal u1(t) against different noise strength. Figure 4B shows the SNR of the reconstruction of signal u21(t) = u2(t, t). The reconstruction SNR in Figure 4A largely matches the inverse ordering of noise strength of each of the individual noise sources shown in Figure 3A. DSP noise sources degrade the reconstruction performance most strongly while noise sources associated with gating variables m and h have a much smaller effect for the same variance level. Since the variance of measurement error is the sum of error variance in each variable, the case when 10σ1 = 10σ2 = σ3 = σ4 = σ exhibits the lowest performance.

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