Theta oscillations optimize information rate in the hippocampus

Low-frequency oscillations shape how neurons sample their synaptic inputs, hence regulating information exchange among neural circuits. In the hippocampus, theta oscillations (4-8 Hz) enable the temporal organization of cortical inputs, resulting in a phase code. However, the advantages of the specific theta band over other frequency ranges remain unclear. It is possible that this specific frequency range is optimizing a trade-off between information throughput and biophysical constraints of the neuronal substrate. To test this hypothesis, we analyze a physiologically constrained model of the rodent hippocampus comprising stochastic leaky integrate-and-fire neurons driven by oscillations. By estimating the information rate of the phase code for a range of noise and frequency levels, we identify a trade-off between sampling frequency and coding precision. We observe that, under physiological noise levels, theta-band oscillations optimize the speed-precision trade-off, maximizing information rate. Further, we demonstrate that theta optimizes this trade-off throughout the entire dorsoventral axis of the hippocampus with its pronounced gradients of several physiological properties. In addition, we find that maintaining an optimal information rate relies on the concurrent modulation of both frequency and amplitude, hence explaining the locomotion speed-dependent modulations of the hippocampal theta oscillation that are observed in rodents and humans. Overall, our results suggest that low-frequency oscillations are adapted to maximize the information rate of neural sampling given the temporal and biophysical constraints under which neural circuits operate. Author Summary In the hippocampus, a prominent oscillation in the theta band (4-8 Hz) allows single neurons to rhythmically sample and represent the ever-changing input signals coming from the cortex. However, it remains unclear why this hippocampal rhythm lies within the theta band. Here, we show that neurons that use oscillations to sample noisy input signals face a trade-off between their sampling speed (i.e., the frequency) and their coding precision (i.e., the accuracy of the representation). We find that, for simulated hippocampal neurons, this trade-off is optimized precisely within the theta band. Importantly, our framework allows us to explain other fundamental properties of the hippocampus while having implications for other brain areas that might use similar sampling mechanisms. In summary, we provide an explanation as to why oscillations in the hippocampus are confined within the theta band, and lay down the foundations to study how properties of single neurons determine the optimal sampling frequencies in a particular neural circuit.