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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

Examples of functional identification when the generated spikes do not fully explore the space of feedback kernels. (A) Original first order feedforward kernel (black) and identified projection of the kernel (red). (B) Original first order feedback kernel (black) and identified projection of the kernel (red). (C) Original second order feedforward kernel. (D) Identified projection of second order feedforward kernel. (E) Error of identified second order feedforward kernel. (F) Original second order feedback kernel. (G) Identified projection of second order feedback kernel. (H) Error of identified second order feedback kernel.
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Figure 11: Examples of functional identification when the generated spikes do not fully explore the space of feedback kernels. (A) Original first order feedforward kernel (black) and identified projection of the kernel (red). (B) Original first order feedback kernel (black) and identified projection of the kernel (red). (C) Original second order feedforward kernel. (D) Identified projection of second order feedforward kernel. (E) Error of identified second order feedforward kernel. (F) Original second order feedback kernel. (G) Identified projection of second order feedback kernel. (H) Error of identified second order feedback kernel.

Mentions: Additionally, as discussed in Remark 4.2, BSG noise sources may degrade severely the identification of feedback kernels when the spike trains generated in trials are not sufficient for exploring the two spike input spaces. We show an example of the later in Figure 11. The two BSGs have higher bias currents and lower input current magnitude. The later was achieved by scaling down the magnitude of the DSP kernels. The combined effect results in regular spiking intervals in both neurons. The identification result under noiseless conditions is shown in Figure 11. Note that since the t-transform of the Hodgkin-Huxley neuron is not exact, a small error is introduced even if intrinsic noise is not present. We see that the feedforward DSP kernels can be identified quite well, yielding SNRs of around 17 dB. However, the feedback DSP kernels are not well identified. In particular, the identified second-order feedback kernel has a wide spread, similar to the high noise case in Figure 9D. This suggest that the spike pattern is not sufficiently exploring the space of feedback kernels. A large number of frequency components are only weakly sampled and they can be very easily contaminated by noise. The presence of both intrinsic noise sources can exacerbate the condition further. This effect is confirmed with a simulation of the circuit using Integrate-and-Fire (IAF) neurons. Since the t-transform for the IAF neuron is exact (Lazar and Tóth, 2004), both feedback kernels can be identified even if the generated spikes only weakly explore certain frequency components. However, by artificially adding a small measurement error to the t-transform of the circuit with IAF neurons, similar results to those in Figure 11 can be obtained (data not shown).


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

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

Examples of functional identification when the generated spikes do not fully explore the space of feedback kernels. (A) Original first order feedforward kernel (black) and identified projection of the kernel (red). (B) Original first order feedback kernel (black) and identified projection of the kernel (red). (C) Original second order feedforward kernel. (D) Identified projection of second order feedforward kernel. (E) Error of identified second order feedforward kernel. (F) Original second order feedback kernel. (G) Identified projection of second order feedback kernel. (H) Error of identified second order feedback kernel.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 11: Examples of functional identification when the generated spikes do not fully explore the space of feedback kernels. (A) Original first order feedforward kernel (black) and identified projection of the kernel (red). (B) Original first order feedback kernel (black) and identified projection of the kernel (red). (C) Original second order feedforward kernel. (D) Identified projection of second order feedforward kernel. (E) Error of identified second order feedforward kernel. (F) Original second order feedback kernel. (G) Identified projection of second order feedback kernel. (H) Error of identified second order feedback kernel.
Mentions: Additionally, as discussed in Remark 4.2, BSG noise sources may degrade severely the identification of feedback kernels when the spike trains generated in trials are not sufficient for exploring the two spike input spaces. We show an example of the later in Figure 11. The two BSGs have higher bias currents and lower input current magnitude. The later was achieved by scaling down the magnitude of the DSP kernels. The combined effect results in regular spiking intervals in both neurons. The identification result under noiseless conditions is shown in Figure 11. Note that since the t-transform of the Hodgkin-Huxley neuron is not exact, a small error is introduced even if intrinsic noise is not present. We see that the feedforward DSP kernels can be identified quite well, yielding SNRs of around 17 dB. However, the feedback DSP kernels are not well identified. In particular, the identified second-order feedback kernel has a wide spread, similar to the high noise case in Figure 9D. This suggest that the spike pattern is not sufficiently exploring the space of feedback kernels. A large number of frequency components are only weakly sampled and they can be very easily contaminated by noise. The presence of both intrinsic noise sources can exacerbate the condition further. This effect is confirmed with a simulation of the circuit using Integrate-and-Fire (IAF) neurons. Since the t-transform for the IAF neuron is exact (Lazar and Tóth, 2004), both feedback kernels can be identified even if the generated spikes only weakly explore certain frequency components. However, by artificially adding a small measurement error to the t-transform of the circuit with IAF neurons, similar results to those in Figure 11 can be obtained (data not shown).

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