Mathematical regularities of irregular neural codes for space
Much of the thinking about neural population codes was motivated in the past decades by reports on neurons with highly stereotyped tuning functions. Indeed, neurons are often observed to exhibit smooth, unimodal tuning to an encoded variable, centered around preferred stimuli that vary across the neural population. Recent experiments, however, have uncovered neural response functions that are much less stereotyped and regular than observed previously. Some of the most striking examples have been observed in the hippocampus and its associated brain areas. The classical view has been that hippocampal place cells are active only in a compact region of space and exhibit a stereotyped tuning to position. In contrast to this expectation, however, place cells in large environments typically fire in multiple locations, and the multiple firing fields of individual cells, as well as those of the whole population, vary in size and shape. We recently discovered that a remarkably simple mathematical model, in which firing fields are generated by thresholding a realization of a random Gaussian process, accounts for the statistical properties of place fields in precise quantitative detail. The model captures the statistics of field sizes and positions, and generates new quantitative predictions on the statistics of field shapes and topologies. These predictions are quantitatively verified in multiple recent data sets from bats and rodents, in one, two, and three dimensions, in both small and large environments. Together, these results imply that common mechanisms underlie the diverse statistics observed in the different experiments. I will discuss a mechanistic model, which suggests that the random Gaussian process statistics arise due to random connectivity within the CA3-CA1 hippocampal circuit. If time permits I will present another recent work, in which we uncover simple principles underlying the spatial selectivity in a new class of neurons in the medial entorhinal cortex, with tuning curves that are significantly less regular than those of classical grid cells.