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

Low-frequency oscillations shape how neurons sample their synaptic inputs, regulating information exchange across networks. In the hippocampus, theta-band oscillations (3-8 Hz) reorganize cortical input signals temporally, resulting in a phase code. However, the reason hippocampal oscillations are limited to low frequencies like the theta band remains unclear. Here, we derive a theoretical framework for neuronal phase coding to show that realistic noise levels create a trade-off between sampling speed (controlled by oscillation frequency) and encoding precision in hippocampal neurons. This speed-precision trade-off produces a maximum in information rate within the theta band of ~1-2 bits/s. Additionally, we demonstrate that our framework explains other key hippocampal properties, such as the preservation of theta along the dorsoventral axis despite various physiological gradients, and the modulation of theta frequency and amplitude by the animals running speed. Extending our analysis to extra-hippocampal areas, we propose that theta oscillations may also support efficient encoding of stimuli in visual cortex and olfactory bulb. More broadly, we lay the groundwork for rigorously studying how system constraints determine optimal sampling frequency regimes for phase coding neurons in biological and artificial brains. Author SummaryThe rodent hippocampus exhibits prominent oscillations in the theta band (3-8 Hz) during exploration, enabling individual neurons to rhythmically sample and represent sensory signals from the cortex. However, the reason behind the specific frequency of this hippocampal rhythm has remained unclear. In this study, we developed a biologically-based theoretical framework to demonstrate that neurons using oscillations to efficiently sample noisy signals encounter a trade-off between their sampling speed (i.e., oscillation frequency) and their coding precision (i.e., reliability of encoding). Notably, our findings reveal that this trade-off is optimized precisely within the theta band, while also providing insights into other fundamental features. In conclusion, we offer an explanation grounded in efficient coding for why hippocampal oscillations are confined to the theta band and establish a foundation for exploring how the properties of individual neurons determine optimal sampling frequencies in specific neural circuits.