A network of spiking neurons that can represent interval timing: mean field analysis.

Department of Neurobiology and Anatomy, The University of Texas Medical School at Houston, 6431 Fannin St., Houston, TX 77030, USA.
Journal of Computational Neuroscience (Impact Factor: 2.09). 04/2011; 30(2):501-13. DOI: 10.1007/s10827-010-0275-y
Source: PubMed

ABSTRACT Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.

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    Frontiers in Psychology 11/2014; 5:1263. · 2.80 Impact Factor
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    ABSTRACT: Recent work in computational neuroscience and cognitive psychology suggests that a set of cells that decay exponentially could be used to support memory for the time at which events took place. Analytically and through simulations on a biophysical model of an individual neuron we demonstrate that exponentially decaying firing with a range of time constants up to minutes could be implemented using a simple combination of wellknown neural mechanisms. In particular we consider firing supported by calcium controlled cation current. When the amount of calcium leaving the cell during an interspike interval is larger than the calcium influx during a spike, an overall decay in calcium concentration can be exponential, resulting in exponential decay of the firing rate. The time constant of the decay can be several orders of magnitude larger than the time constant of calcium clearance and it could be controlled externally via a variety of biologically plausible ways. The ability to flexibly and rapidly control time constants could enable working memory of temporal history to be generalized to other variables in computing spatial and ordinal representations. © 2014 Wiley Periodicals, Inc.
    Hippocampus 08/2014; · 4.30 Impact Factor
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    ABSTRACT: The processing of time intervals in the sub- to supra-second range by the brain is critical for the interaction of primates with their surroundings in activities, such as foraging and hunting. For an accurate processing of time intervals by the brain, representation of physical time within neuronal circuits is necessary. I propose that time dimension of the physical surrounding is represented in the brain by different types of neuronal oscillators, generating spikes or spike bursts at regular intervals. The proposed oscillators include the pacemaker neurons, tonic inputs, and synchronized excitation and inhibition of inter-connected neurons. Oscillators, which are built inside various circuits of brain, help to form modular clocks, processing time intervals or other temporal characteristics specific to functions of a circuit. Relative or absolute duration is represented within neuronal oscillators by "neural temporal unit," defined as the interval between regularly occurring spikes or spike bursts. Oscillator output is processed to produce changes in activities of neurons, named frequency modulator neuron, wired within a separate module, represented by the rate of change in frequency, and frequency of activities, proposed to encode time intervals. Inbuilt oscillators are calibrated by (a) feedback processes, (b) input of time intervals resulting from rhythmic external sensory stimulation, and (c) synchronous effects of feedback processes and evoked sensory activity. A single active clock is proposed per circuit, which is calibrated by one or more mechanisms. Multiple calibration mechanisms, inbuilt oscillators, and the presence of modular connections prevent a complete loss of interval timing functions of the brain.
    Frontiers in Psychology 08/2014; · 2.80 Impact Factor

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