Controlling Phase Noise in Oscillatory Interference Models of Grid Cell Firing

Abstract

Oscillatory interference models account for the spatial firing properties of grid cells in terms of neuronal oscillators with frequencies modulated by the animal's movement velocity. The phase of such a "velocity-controlled oscillator" (VCO) relative to a baseline (theta-band) oscillation tracks displacement along a preferred direction. Input from multiple VCOs with appropriate preferred directions causes a grid cell's grid-like firing pattern. However, accumulating phase noise causes the firing pattern to drift and become corrupted. Here we show how multiple redundant VCOs can automatically compensate for phase noise. By entraining the baseline frequency to the mean VCO frequency, VCO phases remain consistent, ensuring a coherent grid pattern and reducing its spatial drift. We show how the spatial stability of grid firing depends on the variabilityinVCOphases,e.g.,aphaseSDof3msper125mscycleresultsinstablegridsfor1min.Finally,couplingNVCOswithsimilarpreferred directions as a ring attractor, so that their relative phases remain constant, produces grid cells with consistently offset grids, and reduces VCO phase variability of the order square root of N. The results suggest a viable functional organization of the grid cell network, and highlight the benefit of integrating displacement along multiple redundant directions for the purpose of path integration.

Entorhinal neurons exhibit cue locking in rodent VR

“…However, with prolonged experience, grid-patterns 38 disambiguated the two sides, forming a single global representation of the space, consistent with increasing 39 emphasis being placed on self-motion cues (Carpenter et al, 2015). Similarly, computational work has also 40 highlighted the necessity of landmark information as a means to reset accumulated errors in path integration 41 networks (Banino et al, 2018;Burgess and Burgess, 2014). However, the mechanisms by which this reset 42 occurs and by which the relative importance of different information sources can be modulated remains 43…”

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“…They have been proposed to additionally encode the position of the animal via their relative theta firing phasea 'phase code' (Blair et al, 2008;Monaco et al, 2011;Welday et al, 2011)building on previous theoretical work on 'velocitymodulated oscillatory interference models' (Burgess et al, 2007;Hasselmo et al, 2007). The proposed neural architecture comprises subcortical banks of velocity-modulated 'ring attractors' (Blair et al, 2014(Blair et al, , 2008Burgess and Burgess, 2014), in which a bump of activity is hypothesized to periodically traverse a network that is topologically arranged as a ring. Each ring works as a path integrator that tracks the distance traveled in a particular direction by the velocity-modulated precession of its phase relative to a reference theta oscillation.…”

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“…Осцилляторно-интерференционная модель. Эта модель продвигается командой Нила Бёрджесса с соавторами [65][66][67][68]. Модель основана на предположении о существовании контролируемых скоростью осцилляторов (КСО) (velocity-controlled oscillators -VCO в терминологии авторов).…”

“…12. Интерференция сигналов на клетке решетки при различных направлениях скорости [66]. VCO -контролируемые скоростью осцилляторы, Grid cell -клетка решетки.…”