Stationary envelope synthesis (SES): A universal method for phase coding by neural oscillators
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1
UCLA, Psychology, United States
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2
UCLA, Brain Research Institute, United States
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3
UCLA, Dept of Psychology, United States
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4
Johns Hopkins University, Biomedical Engineering, United States
The rat hippocampus and limbic cortex contain spatially tuned neurons-including place cells, grid cells, and boundary cells-which exhibit firing rate maps with different geometries, but their spike trains are all similarly modulated by 4-12 Hz theta rhythm. These neurons are widely believed to be components of a neural system for path integration, which tracks the rat’s position by integrating the velocity of its movements over time. Burgess et al. (2005) introduced an oscillatory interference model of path integration based on the principle that if an oscillator’s frequency is linearly modulated by movement velocity, then its phase will encode a position signal. This principle has been exploited to show how phase interference between velocity-controlled oscillators (VCOs) can synthesize envelope waveforms that mimic the periodic spatial firing rate maps of grid cells (Burgess et al., 2007; Giocomo et al., 2007; Hasselmo et al., 2007; Burgess 2008). Here we show that these oscillatory interference models of grid cells represent a special case of a more general principle-referred to as stationary envelope synthesis (SES)-whereby phase interference among VCOs can synthesize stationary envelope waveforms that approximate any desired function in a vector space of arbitrary dimensions. A neural architecture for implementing the SES principle is proposed, consisting of a ring oscillator matrix (ROM) which contains a bank of VCOs from which stationary envelope functions can be synthesized (Blair et al., 2008). Simulations are presented to show how a target neuron that sums transiently synchronous inputs from the ROM can synthesize spatial envelopes that mimic the firing rate maps not only of grid cells (as in prior models), but also of place cells and boundary cells. An essential prediction this model architecture is that burst frequencies of some theta cells in the rat brain must be modulated by the cosine of the rat’s movement direction, and we present experimental data showing that this indeed appears to be true for theta cells recorded from the anterior thalamus of freely behaving rats. Based on this theory and evidence, it is conjectured that spatially tuned neurons in hippocampus and cortex sum feedforward inputs from ROM circuits in the thalamus, and then return feedback connections to the thalamus to complete a stable attractor loop which facilitates accurate path integration that is robust to noise. Spatial path integration can be generalized from 2D environments into higher dimensions for tracking the momentary value of any sensory, motor, or memory state that traces a continuous trajectory through an M-dimensional Euclidian vector space. According to the SES principle, a bank of oscillators with frequencies that are modulated by the time derivative of such a trajectory (regardless of its path) should be able generate any desired envelope function in a vector space with any number of dimensions. It is speculated that this capability might be broadly useful for solving problems of invariant pattern recognition, by making it possible to synthesize envelope functions that pick out bounded subsets of a state space that contain all possible transformations of a given recognition target.
Conference:
Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010.
Presentation Type:
Poster Presentation
Topic:
Poster session III
Citation:
Blair
HT,
Welday
A,
Shlifer
G,
Bloom
M and
Zhang
K
(2010). Stationary envelope synthesis (SES): A universal method for phase coding by neural oscillators.
Front. Neurosci.
Conference Abstract:
Computational and Systems Neuroscience 2010.
doi: 10.3389/conf.fnins.2010.03.00239
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Received:
04 Mar 2010;
Published Online:
04 Mar 2010.
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Correspondence:
Hugh T Blair, UCLA, Psychology, Los Angeles, United States, blair@psych.ucla.edu