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Gao T, Deng B, Wang J, Wang J, Yi G. The passive properties of dendrites modulate the propagation of slowly-varying firing rate in feedforward networks. Neural Netw 2022; 150:377-391. [DOI: 10.1016/j.neunet.2022.03.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Revised: 01/12/2022] [Accepted: 03/02/2022] [Indexed: 10/18/2022]
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2
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Population rate coding in recurrent neuronal networks with unreliable synapses. Cogn Neurodyn 2011; 6:75-87. [PMID: 23372621 DOI: 10.1007/s11571-011-9181-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2011] [Revised: 07/09/2011] [Accepted: 11/05/2011] [Indexed: 10/15/2022] Open
Abstract
Neuron transmits spikes to postsynaptic neurons through synapses. Experimental observations indicated that the communication between neurons is unreliable. However most modelling and computational studies considered deterministic synaptic interaction model. In this paper, we investigate the population rate coding in an all-to-all coupled recurrent neuronal network consisting of both excitatory and inhibitory neurons connected with unreliable synapses. We use a stochastic on-off process to model the unreliable synaptic transmission. We find that synapses with suitable successful transmission probability can enhance the encoding performance in the case of weak noise; while in the case of strong noise, the synaptic interactions reduce the encoding performance. We also show that several important synaptic parameters, such as the excitatory synaptic strength, the relative strength of inhibitory and excitatory synapses, as well as the synaptic time constant, have significant effects on the performance of the population rate coding. Further simulations indicate that the encoding dynamics of our considered network cannot be simply determined by the average amount of received neurotransmitter for each neuron in a time instant. Moreover, we compare our results with those obtained in the corresponding random neuronal networks. Our numerical results demonstrate that the network randomness has the similar qualitative effect as the synaptic unreliability but not completely equivalent in quantity.
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Lefebvre J, Longtin A, Leblanc VG. Responses of recurrent nets of asymmetric ON and OFF cells. J Biol Phys 2010; 37:189-212. [PMID: 22379229 DOI: 10.1007/s10867-010-9207-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2010] [Accepted: 10/17/2010] [Indexed: 11/24/2022] Open
Abstract
A neural field model of ON and OFF cells with all-to-all inhibitory feedback is investigated. External spatiotemporal stimuli drive the ON and OFF cells with, respectively, direct and inverted polarity. The dynamic differences between networks built of ON and OFF cells ("ON/OFF") and those having only ON cells ("ON/ON") are described for the general case where ON and OFF cells can have different spontaneous firing rates; this asymmetric case is generic. Neural responses to nonhomogeneous static and time-periodic inputs are analyzed in regimes close to and away from self-oscillation. Static stimuli can cause oscillatory behavior for certain asymmetry levels. Time-periodic stimuli expose dynamical differences between ON/OFF and ON/ON nets. Outside the stimulated region, we show that ON/OFF nets exhibit frequency doubling, while ON/ON nets cannot. On the other hand, ON/ON networks show antiphase responses between stimulated and unstimulated regions, an effect that does not rely on specific receptive field circuitry. An analysis of the resonance properties of both net types reveals that ON/OFF nets exhibit larger response amplitude. Numerical simulations of the neural field models agree with theoretical predictions for localized static and time-periodic forcing. This is also the case for simulations of a network of noisy integrate-and-fire neurons. We finally discuss the application of the model to the electrosensory system and to frequency-doubling effects in retina.
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Hutt A, Longtin A. Effects of the anesthetic agent propofol on neural populations. Cogn Neurodyn 2010; 4:37-59. [PMID: 19768579 PMCID: PMC2837528 DOI: 10.1007/s11571-009-9092-2] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2009] [Revised: 08/29/2009] [Accepted: 08/31/2009] [Indexed: 11/30/2022] Open
Abstract
The neuronal mechanisms of general anesthesia are still poorly understood. Besides several characteristic features of anesthesia observed in experiments, a prominent effect is the bi-phasic change of power in the observed electroencephalogram (EEG), i.e. the initial increase and subsequent decrease of the EEG-power in several frequency bands while increasing the concentration of the anaesthetic agent. The present work aims to derive analytical conditions for this bi-phasic spectral behavior by the study of a neural population model. This model describes mathematically the effective membrane potential and involves excitatory and inhibitory synapses, excitatory and inhibitory cells, nonlocal spatial interactions and a finite axonal conduction speed. The work derives conditions for synaptic time constants based on experimental results and gives conditions on the resting state stability. Further the power spectrum of Local Field Potentials and EEG generated by the neural activity is derived analytically and allow for the detailed study of bi-spectral power changes. We find bi-phasic power changes both in monostable and bistable system regime, affirming the omnipresence of bi-spectral power changes in anesthesia. Further the work gives conditions for the strong increase of power in the δ-frequency band for large propofol concentrations as observed in experiments.
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Affiliation(s)
- Axel Hutt
- INRIA CR Nancy - Grand Est, CS20101, 54603 Villers-ls-Nancy Cedex, France
| | - Andre Longtin
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, ON K1N-6N5 Canada
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Miller VH, Jansen BH. Oscillatory neural network for pattern recognition: trajectory based classification and supervised learning. BIOLOGICAL CYBERNETICS 2008; 99:459-471. [PMID: 18807066 DOI: 10.1007/s00422-008-0253-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2008] [Accepted: 08/28/2008] [Indexed: 05/26/2023]
Abstract
Computer algorithms that match human performance in recognizing written text or spoken conversation remain elusive. The reasons why the human brain far exceeds any existing recognition scheme to date in the ability to generalize and to extract invariant characteristics relevant to category matching are not clear. However, it has been postulated that the dynamic distribution of brain activity (spatiotemporal activation patterns) is the mechanism by which stimuli are encoded and matched to categories. This research focuses on supervised learning using a trajectory based distance metric for category discrimination in an oscillatory neural network model. Classification is accomplished using a trajectory based distance metric. Since the distance metric is differentiable, a supervised learning algorithm based on gradient descent is demonstrated. Classification of spatiotemporal frequency transitions and their relation to a priori assessed categories is shown along with the improved classification results after supervised training. The results indicate that this spatiotemporal representation of stimuli and the associated distance metric is useful for simple pattern recognition tasks and that supervised learning improves classification results.
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Affiliation(s)
- Vonda H Miller
- The Boeing Company, 13100 Space Center Blvd, MC 2-10, Houston, TX, 77059, USA.
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Hutt A, Sutherland C, Longtin A. Driving neural oscillations with correlated spatial input and topographic feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021911. [PMID: 18850869 DOI: 10.1103/physreve.78.021911] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2008] [Revised: 04/25/2008] [Indexed: 05/26/2023]
Abstract
We consider how oscillatory activity in networks of excitable systems depends on spatial correlations of random inputs and the spatial range of feedback coupling. Analysis of a neural field model with topographic delayed recurrent feedback reveals how oscillations in certain frequency bands, including the gamma band, are enhanced by increases in the input correlation length. Further, the enhancement is maximal when this length exceeds the feedback coupling range. Suppression of oscillatory power occurs concomitantly in other bands. These effects depend solely on the ratio of input and feedback length scales. The precise positions of these bands are determined by the synaptic constants and the delays. The results agree with numerical simulations of the model and of a network of stochastic spiking neurons, and are expected for any noise-driven excitable element networks.
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Affiliation(s)
- Axel Hutt
- INRIA CR Nancy-Grand Est, CS20101, 54603 Villers-ls-Nancy Cedex, France.
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Hospedales TM, van Rossum MCW, Graham BP, Dutia MB. Implications of noise and neural heterogeneity for vestibulo-ocular reflex fidelity. Neural Comput 2008; 20:756-78. [PMID: 18045014 DOI: 10.1162/neco.2007.09-06-339] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The vestibulo-ocular reflex (VOR) is characterized by a short-latency, high-fidelity eye movement response to head rotations at frequencies up to 20 Hz. Electrophysiological studies of medial vestibular nucleus (MVN) neurons, however, show that their response to sinusoidal currents above 10 to 12 Hz is highly nonlinear and distorted by aliasing for all but very small current amplitudes. How can this system function in vivo when single cell response cannot explain its operation? Here we show that the necessary wide VOR frequency response may be achieved not by firing rate encoding of head velocity in single neurons, but in the integrated population response of asynchronously firing, intrinsically active neurons. Diffusive synaptic noise and the pacemaker-driven, intrinsic firing of MVN cells synergistically maintain asynchronous, spontaneous spiking in a population of model MVN neurons over a wide range of input signal amplitudes and frequencies. Response fidelity is further improved by a reciprocal inhibitory link between two MVN populations, mimicking the vestibular commissural system in vivo, but only if asynchrony is maintained by noise and pacemaker inputs. These results provide a previously missing explanation for the full range of VOR function and a novel account of the role of the intrinsic pacemaker conductances in MVN cells. The values of diffusive noise and pacemaker currents that give optimal response fidelity yield firing statistics similar to those in vivo, suggesting that the in vivo network is tuned to optimal performance. While theoretical studies have argued that noise and population heterogeneity can improve coding, to our knowledge this is the first evidence indicating that these parameters are indeed tuned to optimize coding fidelity in a neural control system in vivo.
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Affiliation(s)
- Timothy M Hospedales
- Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh, Edinburgh EH1 2QL, U.K.
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Köndgen H, Geisler C, Fusi S, Wang XJ, Lüscher HR, Giugliano M. The dynamical response properties of neocortical neurons to temporally modulated noisy inputs in vitro. ACTA ACUST UNITED AC 2008; 18:2086-97. [PMID: 18263893 DOI: 10.1093/cercor/bhm235] [Citation(s) in RCA: 79] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Cortical neurons are often classified by current-frequency relationship. Such a static description is inadequate to interpret neuronal responses to time-varying stimuli. Theoretical studies suggested that single-cell dynamical response properties are necessary to interpret ensemble responses to fast input transients. Further, it was shown that input-noise linearizes and boosts the response bandwidth, and that the interplay between the barrage of noisy synaptic currents and the spike-initiation mechanisms determine the dynamical properties of the firing rate. To test these model predictions, we estimated the linear response properties of layer 5 pyramidal cells by injecting a superposition of a small-amplitude sinusoidal wave and a background noise. We characterized the evoked firing probability across many stimulation trials and a range of oscillation frequencies (1-1000 Hz), quantifying response amplitude and phase-shift while changing noise statistics. We found that neurons track unexpectedly fast transients, as their response amplitude has no attenuation up to 200 Hz. This cut-off frequency is higher than the limits set by passive membrane properties (approximately 50 Hz) and average firing rate (approximately 20 Hz) and is not affected by the rate of change of the input. Finally, above 200 Hz, the response amplitude decays as a power-law with an exponent that is independent of voltage fluctuations induced by the background noise.
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Affiliation(s)
- Harold Köndgen
- Department of Physiology, University of Bern, Bern CH-3012, Switzerland
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Fujita K, Kashimori Y, Kambara T. Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli. BIOLOGICAL CYBERNETICS 2007; 97:293-305. [PMID: 17805559 DOI: 10.1007/s00422-007-0175-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2006] [Accepted: 07/27/2007] [Indexed: 05/17/2023]
Abstract
Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.
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Affiliation(s)
- Kazuhisa Fujita
- Department of Information Network Science, Graduate School of Information Systems, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan.
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Masuda N, Okada M, Aihara K. Filtering of Spatial Bias and Noise Inputs by Spatially Structured Neural Networks. Neural Comput 2007; 19:1854-70. [PMID: 17521281 DOI: 10.1162/neco.2007.19.7.1854] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
With spatially organized neural networks, we examined how bias and noise inputs with spatial structure result in different network states such as bumps, localized oscillations, global oscillations, and localized synchronous firing that may be relevant to, for example, orientation selectivity. To this end, we used networks of McCulloch-Pitts neurons, which allow theoretical predictions, and verified the obtained results with numerical simulations. Spatial inputs, no matter whether they are bias inputs or shared noise inputs, affect only firing activities with resonant spatial frequency. The component of noise that is independent for different neurons increases the linearity of the neural system and gives rise to less spatial mode mixing and less bistability of population activities.
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Affiliation(s)
- Naoki Masuda
- Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako, Japan.
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Coombes S, Doiron B, Josić K, Shea-Brown E. Towards blueprints for network architecture, biophysical dynamics and signal transduction. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2006; 364:3301-18. [PMID: 17090461 DOI: 10.1098/rsta.2006.1903] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We review mathematical aspects of biophysical dynamics, signal transduction and network architecture that have been used to uncover functionally significant relations between the dynamics of single neurons and the networks they compose. We focus on examples that combine insights from these three areas to expand our understanding of systems neuroscience. These range from single neuron coding to models of decision making and electrosensory discrimination by networks and populations and also coincidence detection in pairs of dendrites and dynamics of large networks of excitable dendritic spines. We conclude by describing some of the challenges that lie ahead as the applied mathematics community seeks to provide the tools which will ultimately underpin systems neuroscience.
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Affiliation(s)
- Stephen Coombes
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.
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