¹Institute of Theoretical and Experimental Biophysics of the Russian Academy of Sciences, Pushchino, Russia
²Sirius University of Science and Technology, Sochi, Russia
³National Research University "Higher School of Economics", Moscow, Russia

Abstract. The theta rhythm synchronizes neural activity in the processes of attention and memory. However, the mechanisms of synchronization of neural activity during theta rhythm generation are not known. We propose a mathematical model explaining the distribution of the CA1 field neurons over the theta rhythm phase. We examined a network consisting of 10 types of inhibitory cells: (PV) parvalbumin and (CCK) cholecystokinin basket cells, axo-axonal, bistratified, neurogliaform,  perforant path-associated, interneuronal-specific (subtypes R-O and RO-O), Ivy and OLM neurons. The network received four excitatory inputs from the CA3 field, the medial entorhinal cortex, and two types of local pyramidal neurons of the CA1 field. We have shown that it is possible to fit the parameters of connections in the model that neurons form experimentally observed phase relationships relative to the theta rhythm. For most types of neurons, excitatory inputs add up and give a maximum near the peak of discharges in the theta cycle. The peak of inhibitory inputs falls on the opposite phase of the theta rhythm, due to this, activity slows down from the opposite phase of the theta rhythm. The model steadily reproduces the phase relations over the entire frequency range of the theta rhythm for most types of interneurons.

Key words: pyramidal neurons, interneurons, theta rhythm, CA1 field, gradient descent, meanfield models of neurons, Izhikevich neuron