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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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Diagram of the neural circuit that is spike timing equivalent with the one in Figure 1 highlighting the duality between neural decoding and functional identification. Note that the input stimuli and the DSP projections are reordered to reflect that the unknowns are the DSP projections. The input stimuli u11(t), u12(t1, t2), and the kernel representation of spikes (see also Section 2.2.2) are intrinsic to the neural circuit. The DSP projections are interpreted as inputs.
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Figure 7: Diagram of the neural circuit that is spike timing equivalent with the one in Figure 1 highlighting the duality between neural decoding and functional identification. Note that the input stimuli and the DSP projections are reordered to reflect that the unknowns are the DSP projections. The input stimuli u11(t), u12(t1, t2), and the kernel representation of spikes (see also Section 2.2.2) are intrinsic to the neural circuit. The DSP projections are interpreted as inputs.

Mentions: Although decoding and functional identification are seemingly two different problems, they are closely related. By exploiting the commutative property of linear operators, we can rearrange the diagram of the neural circuit model of Figure 1 into the form shown in Figure 7. We notice that the outputs of Figure 7 and those of Figure 1 are spike time equivalent, as long as the RKs K21 and K22 have large enough bandwidth. In what follows we will evaluate the four Volterra terms, i.e., the four dendritic currents feeding the BSG of Neuron 1 in Figure 7.


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

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

Diagram of the neural circuit that is spike timing equivalent with the one in Figure 1 highlighting the duality between neural decoding and functional identification. Note that the input stimuli and the DSP projections are reordered to reflect that the unknowns are the DSP projections. The input stimuli u11(t), u12(t1, t2), and the kernel representation of spikes (see also Section 2.2.2) are intrinsic to the neural circuit. The DSP projections are interpreted as inputs.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Diagram of the neural circuit that is spike timing equivalent with the one in Figure 1 highlighting the duality between neural decoding and functional identification. Note that the input stimuli and the DSP projections are reordered to reflect that the unknowns are the DSP projections. The input stimuli u11(t), u12(t1, t2), and the kernel representation of spikes (see also Section 2.2.2) are intrinsic to the neural circuit. The DSP projections are interpreted as inputs.
Mentions: Although decoding and functional identification are seemingly two different problems, they are closely related. By exploiting the commutative property of linear operators, we can rearrange the diagram of the neural circuit model of Figure 1 into the form shown in Figure 7. We notice that the outputs of Figure 7 and those of Figure 1 are spike time equivalent, as long as the RKs K21 and K22 have large enough bandwidth. In what follows we will evaluate the four Volterra terms, i.e., the four dendritic currents feeding the BSG of Neuron 1 in Figure 7.

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