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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.


Related in: MedlinePlus

SNR of identified DSP kernels. Noise added using SDE (31), with 10σi1 = 10σi2 = σi3 = σi4 = σ. (A) Kernel h1111. In-sets provide a comparison between the original and the identified kernel. (B) Kernel h1112. In-sets are identified kernels. Original kernel is on the lower left. (C) Kernel h2211. In-sets provide a comparison between the original and the identified kernel. (D) Kernel h2212. In-sets are identified kernels. Original kernel is on the lower left.
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Figure 9: SNR of identified DSP kernels. Noise added using SDE (31), with 10σi1 = 10σi2 = σi3 = σi4 = σ. (A) Kernel h1111. In-sets provide a comparison between the original and the identified kernel. (B) Kernel h1112. In-sets are identified kernels. Original kernel is on the lower left. (C) Kernel h2211. In-sets provide a comparison between the original and the identified kernel. (D) Kernel h2212. In-sets are identified kernels. Original kernel is on the lower left.

Mentions: First, we evaluated the effect of noise on the quality of identification of DSP kernels of Neuron 1 in Figure 7 with a BSG modeled by the SDE (31) with 10σi1 = 10σi2 = σi3 = σi4 = σ. Figure 9 shows the SNR of the identified DSP kernels in Figure 7 across several noise levels σ. As expected, the general trend for all four kernels is decreasing SNR with increasing noise levels. We notice that the identified feedforward DSP kernels have similar shape as the original kernel, even at high noise levels. However, the feedback DSP kernels undergo a change in shape at high noise levels. We can see that the time instance of the peak amplitude in the first order feedback kernel is shifted to an earlier time instance.


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

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

SNR of identified DSP kernels. Noise added using SDE (31), with 10σi1 = 10σi2 = σi3 = σi4 = σ. (A) Kernel h1111. In-sets provide a comparison between the original and the identified kernel. (B) Kernel h1112. In-sets are identified kernels. Original kernel is on the lower left. (C) Kernel h2211. In-sets provide a comparison between the original and the identified kernel. (D) Kernel h2212. In-sets are identified kernels. Original kernel is on the lower left.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 9: SNR of identified DSP kernels. Noise added using SDE (31), with 10σi1 = 10σi2 = σi3 = σi4 = σ. (A) Kernel h1111. In-sets provide a comparison between the original and the identified kernel. (B) Kernel h1112. In-sets are identified kernels. Original kernel is on the lower left. (C) Kernel h2211. In-sets provide a comparison between the original and the identified kernel. (D) Kernel h2212. In-sets are identified kernels. Original kernel is on the lower left.
Mentions: First, we evaluated the effect of noise on the quality of identification of DSP kernels of Neuron 1 in Figure 7 with a BSG modeled by the SDE (31) with 10σi1 = 10σi2 = σi3 = σi4 = σ. Figure 9 shows the SNR of the identified DSP kernels in Figure 7 across several noise levels σ. As expected, the general trend for all four kernels is decreasing SNR with increasing noise levels. We notice that the identified feedforward DSP kernels have similar shape as the original kernel, even at high noise levels. However, the feedback DSP kernels undergo a change in shape at high noise levels. We can see that the time instance of the peak amplitude in the first order feedback kernel is shifted to an earlier time instance.

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