Limits...
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

Examples of Volterra kernels. (A) First order kernels of quadrature pair of Gabor functions modeling the receptive fields of simple cells. (B) Second order kernel modeling receptive fields of complex cells. (C) The mechanics of the two dimensional convolution operation between the u2 (S1 = 0.8, 𝔻2 = [0, 0.8] × [0, 0.8]) and h11i2. u2(t1, t2) = u1(t1)u1(t2) is shown in the background. The inset shows the second order Volterra kernel h11i2 rotated 180° around origin [see also (B)]. (h11i2 is only shown in a restricted domain and is zero elsewhere). For t = 0.3, the output of the convolution is the integral of the product of the rotated Volterra kernel and the signal underneath. Since the convolution is evaluated on the diagonal t = t1 = t2, the second order kernel shifts, as t increases, along the arrow on the diagonal. See also Supplementary Figure 5E.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4150400&req=5

Figure 2: Examples of Volterra kernels. (A) First order kernels of quadrature pair of Gabor functions modeling the receptive fields of simple cells. (B) Second order kernel modeling receptive fields of complex cells. (C) The mechanics of the two dimensional convolution operation between the u2 (S1 = 0.8, 𝔻2 = [0, 0.8] × [0, 0.8]) and h11i2. u2(t1, t2) = u1(t1)u1(t2) is shown in the background. The inset shows the second order Volterra kernel h11i2 rotated 180° around origin [see also (B)]. (h11i2 is only shown in a restricted domain and is zero elsewhere). For t = 0.3, the output of the convolution is the integral of the product of the rotated Volterra kernel and the signal underneath. Since the convolution is evaluated on the diagonal t = t1 = t2, the second order kernel shifts, as t increases, along the arrow on the diagonal. See also Supplementary Figure 5E.

Mentions: The two filters are Gaussian modulated sinusoids, that are typically used to model receptive fields of simple cells in the primary visual cortex (V1) where the variables denote space instead of time (Lee, 1996; Dayan and Abbott, 2001). In addition, the two filters are quadrature pair in phase. Both filters are illustrated in Figure 2A. The response of applying the input stimulus u1on the temporal filters with impulse response gcand gsis given by ∫𝔻1gc(t − s)u1(s)ds and ∫𝔻1gs(t − s)u1(s)ds, respectively.


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

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

Examples of Volterra kernels. (A) First order kernels of quadrature pair of Gabor functions modeling the receptive fields of simple cells. (B) Second order kernel modeling receptive fields of complex cells. (C) The mechanics of the two dimensional convolution operation between the u2 (S1 = 0.8, 𝔻2 = [0, 0.8] × [0, 0.8]) and h11i2. u2(t1, t2) = u1(t1)u1(t2) is shown in the background. The inset shows the second order Volterra kernel h11i2 rotated 180° around origin [see also (B)]. (h11i2 is only shown in a restricted domain and is zero elsewhere). For t = 0.3, the output of the convolution is the integral of the product of the rotated Volterra kernel and the signal underneath. Since the convolution is evaluated on the diagonal t = t1 = t2, the second order kernel shifts, as t increases, along the arrow on the diagonal. See also Supplementary Figure 5E.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Examples of Volterra kernels. (A) First order kernels of quadrature pair of Gabor functions modeling the receptive fields of simple cells. (B) Second order kernel modeling receptive fields of complex cells. (C) The mechanics of the two dimensional convolution operation between the u2 (S1 = 0.8, 𝔻2 = [0, 0.8] × [0, 0.8]) and h11i2. u2(t1, t2) = u1(t1)u1(t2) is shown in the background. The inset shows the second order Volterra kernel h11i2 rotated 180° around origin [see also (B)]. (h11i2 is only shown in a restricted domain and is zero elsewhere). For t = 0.3, the output of the convolution is the integral of the product of the rotated Volterra kernel and the signal underneath. Since the convolution is evaluated on the diagonal t = t1 = t2, the second order kernel shifts, as t increases, along the arrow on the diagonal. See also Supplementary Figure 5E.
Mentions: The two filters are Gaussian modulated sinusoids, that are typically used to model receptive fields of simple cells in the primary visual cortex (V1) where the variables denote space instead of time (Lee, 1996; Dayan and Abbott, 2001). In addition, the two filters are quadrature pair in phase. Both filters are illustrated in Figure 2A. The response of applying the input stimulus u1on the temporal filters with impulse response gcand gsis given by ∫𝔻1gc(t − s)u1(s)ds and ∫𝔻1gs(t − s)u1(s)ds, respectively.

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