We propose how a stable network for path integration by oscillatory interference can be constructed from a matrix of many central pattern generator (CPG) circuits, each composed from theta cells with velocity-modulated burst frequencies. It is shown that a target neuron which sums convergent input from multiple theta cells in such a network can synthesize an envelope function that approximates almost any spatial tuning function, and thereby simulate any type of theta-modulated spatial neuron (including place cells, grid cells, and boundary cells). We propose a mechanism by which recurrent connections from spatial neurons back onto theta cells can confer phase stability upon the path integration network. Data from single-unit recordings of theta cells in anterior thalamus of freely behaving rats are shown to support two key predictions of the model: 1) burst frequencies of individual theta cells are modulated as the cosine of the rat's movement direction when running speed is held constant, and 2) the cosine tuning functions of theta cells follow rotations of visual landmark cues. Based on these theoretical and experimental results, we hypothesize that reciprocally connected theta cells and spatially tuned neurons may form a stable network for path integration by oscillatory interference in the rat brain.
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