A single-cell spiking model for the origin of grid-cell patterns

Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity.Author summary: When an animal explores an environment, grid cells activate at multiple spatial locations that form a strikingly-regular triangular pattern. Grid cells are believed to support high-level cognitive functions such as navigation and spatial memory, yet the origin of their activity remains unclear. Here we focus on the hypothesis that grid patterns emerge from a competition between persistent excitation by spatially-selective inputs and the reluctance of a neuron to fire for long stretches of time. Using a computational model, we generate grid-like activity by only spatially-irregular inputs, Hebbian synaptic plasticity, and neuronal adaptation. We study how the geometry of the output patterns depends on the spatial tuning of the inputs and the adaptation properties of single cells. The present work sheds light on the origin of grid-cell firing and makes specific predictions that could be tested experimentally.