Temporal delays among place cells determine the frequency of population theta oscillations in the hippocampus

Driven either by external landmarks or by internal dynamics, hippocampal neurons form sequences of cell assemblies. The coordinated firing of these active cells is organized by the prominent "theta" oscillations in the local field potential (LFP): place cells discharge at progressively earlier theta phases as the rat crosses the respective place field ("phase precession"). The faster oscillation frequency of active neurons and the slower theta LFP, underlying phase precession, creates a paradox. How can faster oscillating neurons comprise a slower population oscillation, as reflected by the LFP? We built a mathematical model that allowed us to calculate the population activity analytically from experimentally derived parameters of the single neuron oscillation frequency, firing field size (duration), and the relationship between within-theta delays of place cell pairs and their distance representations ("compression"). The appropriate combination of these parameters generated a constant frequency population rhythm along the septo-temporal axis of the hippocampus, while allowing individual neurons to vary their oscillation frequency and field size. Our results suggest that the faster-than-theta oscillations of pyramidal cells are inherent and that phase precession is a result of the coordinated activity of temporally shifted cell assemblies, relative to the population activity, reflected by the LFP.