The place cell activity is information-efficient constrained by energy.

Spatial representation is a crucial function of animal's brain. However, there is still no uniform explanation of how the spatial code is formed in different dimensional spaces to date. The main reason why place cell exhibits unique activity pattern is that the animal needs to retrieve and process spatial information. In this paper, we constructed a constrained optimization model based on information theory to explain the place field formation across species in different dimensional spaces. We proposed the following question that, using only limited amount of neural energy, how to organize the spiking locations (place field) in the available environment to obtain the most efficient spatial information representation? We solved this conditional functional extremum problem by variational techniques. The results showed that on the condition of limited neural energy, the place field will comply with a Gaussian-form distribution automatically to convey the largest amount information per spike. We also found that the animal's natural habitat property and locomotion experience statistics affected the symmetry of spatial representation in different dimensions. These findings not only reconcile the argument of whether the spatial codes of place cell are isotropic, but also provide an explanation of place field formation by an information-theoretic approach. Furtherly, this research revealed the energy economical and information efficient properties underlie the spatial representation system of the brain.