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: 1.74). 04/2011; 30(2):501-13. DOI: 10.1007/s10827-010-0275-y
Source: PubMed


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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Available from: Harel Z Shouval, May 16, 2014
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    • "The role of sensory areas—especially primary sensory areas—has long been regarded as providing a faithful representation of the external world (Felleman and Van Essen, 1991; Goldman-Rakic , 1988; Kandel et al., 2000; Miller and Cohen, 2001); several studies have shown that these areas convey sensory information (Ghazanfar and Schroeder, 2006; Hubel and Wiesel, 1962, 1968; Lemus et al., 2010; Liang et al., 2013), while others have shown causal roles in sensory perception (Glickfeld et al., 2013; Jaramillo and Zador, 2011; Sachidhanandam et al., 2013; Znamenskiy and Zador, 2013). However, this view has recently been challenged by observations that sensory cortices represent not only stimulus features, but also non-sensory information (Abolafia et al., 2011; Ayaz et al., 2013; Brosch et al., 2011; Fontanini and Katz, 2008; Gavornik and Bear, 2014; Jaramillo and Zador, 2011; Keller et al., 2012; Niell and Stryker, 2010; Niwa et al., 2012; Pantoja et al., 2007; Samuelsen et al., 2012; Serences, 2008; Shuler and Bear, 2006; St anis xor et al., 2013; Zelano et al., 2011). In the visual modality, it has been shown that V1 can predict the learned typical interval between a stimulus and a reward (Chubykin et al., 2013; Shuler and Bear, 2006), and that the ability to learn such intervals depends on cholinergic input from the basal forebrain (Chubykin et al., 2013). "
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    ABSTRACT: Most behaviors are generated in three steps: sensing the external world, processing that information to instruct decision-making, and producing a motor action. Sensory areas, especially primary sensory cortices, have long been held to be involved only in the first step of this sequence. Here, we develop a visually cued interval timing task that requires rats to decide when to perform an action following a brief visual stimulus. Using single-unit recordings and optogenetics in this task, we show that activity generated by the primary visual cortex (V1) embodies the target interval and may instruct the decision to time the action on a trial-by-trial basis. A spiking neuronal model of local recurrent connections in V1 produces neural responses that predict and drive the timing of future actions, rationalizing our observations. Our data demonstrate that the primary visual cortex may contribute to the instruction of visually cued timed actions. Copyright © 2015 Elsevier Inc. All rights reserved.
    Neuron 03/2015; 86(1). DOI:10.1016/j.neuron.2015.02.043 · 15.05 Impact Factor
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    • "Furthermore, as an increase in the activity of motor neurons is commonly accompanied by a general increase in the rate of the firing of neurons in various upstream circuits , a proportional increase will be seen in neuronal oscillators in the cortical and cerebellar circuits. An increased activity of oscillator circuit, according to various models, such as recurrent feedback excitation (Gavornik and Shouval, 2011), and facilitation type of short-term plasticity (Regehr, 2012) is likely to enhance the rate of the change of the activity of the proposed FM neurons. The preceding claim is supported by a study, which reported an increased rate of the change in the activity of neurons , undergoing positive modulation, when animals reported shorter anticipatory time intervals in motor tasks (Lebedev et al., 2008). "
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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; 5. DOI:10.3389/fpsyg.2014.00816 · 2.80 Impact Factor
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    • "A question not answered here is how single neurons or a population of neurons can develop firing rate functions with a desired form. Possible answers are provided by previous work showing how single neurons with active conductances (Durstewitz, 2004; Shouval and Gavornik, 2011) or networks of interacting neurons (Gavornik et al., 2009; Gavornik and Shouval, 2011) can be tuned to, or even learn de-novo, specific temporal dynamics. "
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    ABSTRACT: The "Scalar Timing Law," which is a temporal domain generalization of the well known Weber Law, states that the errors estimating temporal intervals scale linearly with the durations of the intervals. Linear scaling has been studied extensively in human and animal models and holds over several orders of magnitude, though to date there is no agreed upon explanation for its physiological basis. Starting from the assumption that behavioral variability stems from neural variability, this work shows how to derive firing rate functions that are consistent with scalar timing. We show that firing rate functions with a log-power form, and a set of parameters that depend on spike count statistics, can account for scalar timing. Our derivation depends on a linear approximation, but we use simulations to validate the theory and show that log-power firing rate functions result in scalar timing over a large range of times and parameters. Simulation results match the predictions of our model, though our initial formulation results in a slight bias toward overestimation that can be corrected using a simple iterative approach to learn a decision threshold.
    Frontiers in Human Neuroscience 06/2014; 8:438. DOI:10.3389/fnhum.2014.00438 · 2.99 Impact Factor
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