Gamma synchronization of the hippocampal spatial map---topological model

The mammalian hippocampus plays a principal role in producing a cognitive map of space---an internalized representation of the animal's environment. The neuronal mechanisms producing this map depend primarily on the temporal structure of the hippocampal neurons' spiking activity, which is modulated by the oscillatory extracellular electrical field potential. In this paper, we discuss the integrative effect of the gamma rhythm, one of the principal components of these oscillations, on the ability of the place cell ensembles to encode a spatial map. Using methods of algebraic topology and statistical physics, we demonstrate that gamma-modulation of neuronal activity generates a synchronized spiking of dynamical cell assemblies, which enables learning a spatial map at faster timescales.