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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 reconstruction of the signals. (A) SNR of u1(t). (B) SNR of u21(t) = u2(t, t). (Blue) NNa = N, NK = 0.3NNa. (Green) NNa = N, NK = ∞. (Red) NNa = ∞, NK = N.
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Figure 6: SNR of reconstruction of the signals. (A) SNR of u1(t). (B) SNR of u21(t) = u2(t, t). (Blue) NNa = N, NK = 0.3NNa. (Green) NNa = N, NK = ∞. (Red) NNa = ∞, NK = N.

Mentions: We now show how ion channel noise sources affect the decoding of the input signal. We varied the number of sodium channels NNa and fixed the number of potassium channels to be NK = 0.3NNa, a ratio typically used for Hodgkin-Huxley neurons with the alternative noise source model. By decoding the input stimulus we show how increasing the number of ion channels improves the faithfulness of signal representation. The SNR of the reconstruction of u1(t) and u21(t) are depicted in Figure 6. SNR goes down to about 4 dB when 600 sodium channels and 180 potassium channels are used. This corresponds to a membrane area of about 10 μm2 with a density of 60 μm2 in sodium channels and 18 μm2 in potassium channels (Goldwyn et al., 2011). We also tested the reconstruction for the case when one type of ion channels is infinitely large, i.e., deterministic, while varying the number of ion channels of the other type. The result is also shown in Figure 6. The noise from the dendritic tree shall have similar effect on the representation since the voltage equation is the same as in Section 3.3.2.


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

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

SNR of reconstruction of the signals. (A) SNR of u1(t). (B) SNR of u21(t) = u2(t, t). (Blue) NNa = N, NK = 0.3NNa. (Green) NNa = N, NK = ∞. (Red) NNa = ∞, NK = N.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: SNR of reconstruction of the signals. (A) SNR of u1(t). (B) SNR of u21(t) = u2(t, t). (Blue) NNa = N, NK = 0.3NNa. (Green) NNa = N, NK = ∞. (Red) NNa = ∞, NK = N.
Mentions: We now show how ion channel noise sources affect the decoding of the input signal. We varied the number of sodium channels NNa and fixed the number of potassium channels to be NK = 0.3NNa, a ratio typically used for Hodgkin-Huxley neurons with the alternative noise source model. By decoding the input stimulus we show how increasing the number of ion channels improves the faithfulness of signal representation. The SNR of the reconstruction of u1(t) and u21(t) are depicted in Figure 6. SNR goes down to about 4 dB when 600 sodium channels and 180 potassium channels are used. This corresponds to a membrane area of about 10 μm2 with a density of 60 μm2 in sodium channels and 18 μm2 in potassium channels (Goldwyn et al., 2011). We also tested the reconstruction for the case when one type of ion channels is infinitely large, i.e., deterministic, while varying the number of ion channels of the other type. The result is also shown in Figure 6. The noise from the dendritic tree shall have similar effect on the representation since the voltage equation is the same as in Section 3.3.2.

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