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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.

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Variance of the measurement and spike timing errors. (A) Error measurement variances computed from the PRCs of the Hodgkin-Huxley neuron [Equation (32)]. Each individual variance is parametrized by the bias current Ii. (B) Error variance between spike times generated by the noiseless Hodgkin-Huxley neuron and its reduced PIF counterpart. (C) The spike timing error variance due to each source of noise, obtained from simulations of the Hodgkin-Huxley neuron follow the pattern of the theoretically derived measurement error shown in (A). The spike timing error variances are obtained by setting, at each time, one of the σn's to a nonzero value and the rest to zero. The spikes generated by the Hodgkin-Huxley neuron are compared with the spikes generated by its reduced PIF counterpart. The variance of the differences between two spike times are normalized by the nonzero σn mentioned before. (D) The spike timing variance due to the simultaneous presence of multiple noise sources approximates the sum of spike timing variances due to individual noise sources. Blue curve shows the spike timing variance obtained by simulating Hodgkin-Huxley equations using nonzero values for all σn, n = 1, 2, 3, 4. Red curve shows the sum of spike timing variances obtained in (C) with proper scaling.
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Figure 3: Variance of the measurement and spike timing errors. (A) Error measurement variances computed from the PRCs of the Hodgkin-Huxley neuron [Equation (32)]. Each individual variance is parametrized by the bias current Ii. (B) Error variance between spike times generated by the noiseless Hodgkin-Huxley neuron and its reduced PIF counterpart. (C) The spike timing error variance due to each source of noise, obtained from simulations of the Hodgkin-Huxley neuron follow the pattern of the theoretically derived measurement error shown in (A). The spike timing error variances are obtained by setting, at each time, one of the σn's to a nonzero value and the rest to zero. The spikes generated by the Hodgkin-Huxley neuron are compared with the spikes generated by its reduced PIF counterpart. The variance of the differences between two spike times are normalized by the nonzero σn mentioned before. (D) The spike timing variance due to the simultaneous presence of multiple noise sources approximates the sum of spike timing variances due to individual noise sources. Blue curve shows the spike timing variance obtained by simulating Hodgkin-Huxley equations using nonzero values for all σn, n = 1, 2, 3, 4. Red curve shows the sum of spike timing variances obtained in (C) with proper scaling.

Mentions: We show in Figure 3A the variance of the measurement error in (32) associated with each source of noise of the reduced PIF neuron for the unitary noise levels σin = 1, n = 1, 2, 3, 4. The variances given by (32) are plotted as a function of the bias current Ii. Clearly, the noise arising in dendritic stimulus processing (Wi1) induces the largest error, and together with noise in the potassium channels (Wi2), these errors are about two magnitudes larger in variance than those induced by the noise sources in the sodium channels (Wi3, Wi4).


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

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

Variance of the measurement and spike timing errors. (A) Error measurement variances computed from the PRCs of the Hodgkin-Huxley neuron [Equation (32)]. Each individual variance is parametrized by the bias current Ii. (B) Error variance between spike times generated by the noiseless Hodgkin-Huxley neuron and its reduced PIF counterpart. (C) The spike timing error variance due to each source of noise, obtained from simulations of the Hodgkin-Huxley neuron follow the pattern of the theoretically derived measurement error shown in (A). The spike timing error variances are obtained by setting, at each time, one of the σn's to a nonzero value and the rest to zero. The spikes generated by the Hodgkin-Huxley neuron are compared with the spikes generated by its reduced PIF counterpart. The variance of the differences between two spike times are normalized by the nonzero σn mentioned before. (D) The spike timing variance due to the simultaneous presence of multiple noise sources approximates the sum of spike timing variances due to individual noise sources. Blue curve shows the spike timing variance obtained by simulating Hodgkin-Huxley equations using nonzero values for all σn, n = 1, 2, 3, 4. Red curve shows the sum of spike timing variances obtained in (C) with proper scaling.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Variance of the measurement and spike timing errors. (A) Error measurement variances computed from the PRCs of the Hodgkin-Huxley neuron [Equation (32)]. Each individual variance is parametrized by the bias current Ii. (B) Error variance between spike times generated by the noiseless Hodgkin-Huxley neuron and its reduced PIF counterpart. (C) The spike timing error variance due to each source of noise, obtained from simulations of the Hodgkin-Huxley neuron follow the pattern of the theoretically derived measurement error shown in (A). The spike timing error variances are obtained by setting, at each time, one of the σn's to a nonzero value and the rest to zero. The spikes generated by the Hodgkin-Huxley neuron are compared with the spikes generated by its reduced PIF counterpart. The variance of the differences between two spike times are normalized by the nonzero σn mentioned before. (D) The spike timing variance due to the simultaneous presence of multiple noise sources approximates the sum of spike timing variances due to individual noise sources. Blue curve shows the spike timing variance obtained by simulating Hodgkin-Huxley equations using nonzero values for all σn, n = 1, 2, 3, 4. Red curve shows the sum of spike timing variances obtained in (C) with proper scaling.
Mentions: We show in Figure 3A the variance of the measurement error in (32) associated with each source of noise of the reduced PIF neuron for the unitary noise levels σin = 1, n = 1, 2, 3, 4. The variances given by (32) are plotted as a function of the bias current Ii. Clearly, the noise arising in dendritic stimulus processing (Wi1) induces the largest error, and together with noise in the potassium channels (Wi2), these errors are about two magnitudes larger in variance than those induced by the noise sources in the sodium channels (Wi3, Wi4).

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