Unraveling the dynamics and structure of grid cells as a spatial map in the brain

Grid cells, defined by their strikingly periodic spatial responses in open fields, have spurred widespread theoretical interest, and numerous models have been proposed to explain how grids are formed, how they are differentiated from the others, and how they might use idiothetic (self motion) information to path integrate. This dissertation leverages unique grid cell data together with computational and mathematical approaches to unravel grid cell dynamics and structure during navigation in general. First, we analyze several extensive datasets of grid cells recorded in 2-dimensional (2D) environments under a number of experimental manipulations, and show that the multi-dimensional network activity of grid cells is embedded into a two-dimensional continuous attractor manifold. Second, we analyze grid cell responses on linear 1-dimensional (1D) tracks to extract an underlying 2D grid structure. Combining Fourier analytical methods and numerical refinements, we show that the system remains in the same dynamical regime during navigation in 2D and 1D environments. Finally, we introduce a state-space point process filter to track the temporal evolution of spatial tuning curves and examine the error accumulation of grid cell system. We show that we can accurately infer the drift of the internal estimate of positions subsumed in the grid cell system as a path integrator.