What grid cells convey about rat location

We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rat's location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the ≈1–10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code

Stable boundary conditions for Cartesian grid calculations

The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated

Structure of the species-energy relationship

The relationship between energy availability and species richness (the species-energy relationship) is one of the best documented macroecological phenomena. However, the structure of species distribution along the gradient, the proximate driver of the relationship, is poorly known. Here, using data on the distribution of birds in southern Africa, for which species richness increases linearly with energy availability, we provide an explicit determination of this structure. We show that most species exhibit increasing occupancy towards more productive regions (occurring in more grid cells within a productivity class). However, average reporting rates per species within occupied grid cells, a correlate of local density, do not show a similar increase. The mean range of used energy levels and the mean geographical range size of species in southern Africa decreases along the energy gradient, as most species are present at high productivity levels but only some can extend their ranges towards lower levels. Species turnover among grid cells consequently decreases towards high energy levels. In summary, these patterns support the hypothesis that higher productivity leads to more species by increasing the probability of occurrence of resources that enable the persistence of viable populations, without necessarily affecting local population densities

Does Optic Flow Explain the Firing of Grid Cells?

*Problem.* Various cues such as vestibular, sensorimotor, or visual information can lead to the firing of grid cells recorded in entorhinal cortex of rats. A recent model uses boundary vector cells to provide information about the 2D spatial position (Barry et al., Review Neuroscience, 17, 2006). However, boundary vector cells need to know the angle and distance of the boundary wall. In contrast we study the estimation of 2D velocity and change of heading of the rat from optic flow and if this information can lead to grid cell firing.
*Approach.* A simple circular cage is modeled as a 3D world and trajectories of a rat’s movement are simulated. Optic flow for a spherical camera model is calculated for regularly sampled locations on the ground of the cage. This flow information is used in a template model to estimate the rat’s 2D linear velocity and yaw rotational velocity. 2D linear velocities are integrated into the velocity controlled oscillator (VCO) model (Burgess, Hippocampus, 18, 2008) while spatial locations are taken from the original trajectory.
*Result and Conclusion.* If velocity estimates are temporally integrated over ~20min the error summation by path integration prevents generation of a clear grid cell firing pattern by the VCO model. However, for short durations velocity estimates and path integration are accurate. If we assume a reset mechanism that recalibrates the spatial location of the rat grid cell firing can be achieved. Different reset intervals were simulated and the grid score for the firing pattern was calculated. For a reset interval longer than one minute this grid score decreases rapidly. We conclude that grid cell firing is not generated only by optic flow, but that a recalibration of the spatial position using cues other than optic flow occurs at least every minute.
Supported by CELEST (NSF SMA-0835976)