Theta oscillations optimize a speed-precision trade-off in phase coding neurons

Theta-band oscillations (3-8 Hz) in the mammalian hippocampus organize the temporal structure of cortical inputs, resulting in a phase code that enables rhythmic input sampling for episodic memory formation and spatial navigation. However, it remains unclear what evolutionary pressures might have driven the selection of theta over higher-frequency bands that could potentially provide increased input sampling resolution. Here, we address this question by introducing a theoretical framework that combines the efficient coding and neural oscillatory sampling hypotheses, focusing on the information rate (bits/s) of phase coding neurons. We demonstrate that physiologically realistic noise levels create a trade-off between the speed of input sampling, determined by oscillation frequency, and encoding precision in rodent hippocampal neurons. This speed-precision trade-off results in a maximum information rate of ∼1-2 bits/s within the theta frequency band, thus confining the optimal oscillation frequency to the low end of the spectrum. We also show that this framework accounts for key hippocampal features, such as the preservation of the theta band along the dorsoventral axis despite physiological gradients, and the modulation of theta frequency and amplitude by running speed. Extending the analysis beyond the hippocampus, we propose that theta oscillations could also support efficient stimulus encoding in the visual cortex and olfactory bulb. More broadly, our framework lays the foundation for studying how system features, such as noise, constrain the optimal sampling frequencies in both biological and artificial brains.