Dichotomous impact of afferent sensory noise on grid-patterned firing and path integration in a continuous attractor network model

The continuous attractor network (CAN) model has been effective in explaining grid-patterned firing in the rodent medial entorhinal cortex, with strong lines of experimental evidence and widespread utilities in understanding path integration. A surprising lacuna in CAN analyses is the lack of quantitative studies assessing the impact of sensory noise in the velocity inputs on the emergence of grid-patterned activity and path integration. In addressing this, we employed an established 2D CAN model which received velocity inputs from a virtual animal traversing a 2D arena to generate grid fields. We introduced different levels of Gaussian noise to the afferent velocity inputs to the model and assessed its impact on the network functions in generating grid fields and performing path-integration. We computed a position estimate at each time step using the network activity and quantified position accuracy using the difference between the real and estimated positions. We performed all simulations using several trajectories for the virtual animal, as computed grid scores and position accuracy showed pronounced trajectory-to-trajectory variability even in noise-free cases. We found that the presence of low levels of sensory noise was beneficial to the generation of grid fields, specifically with trajectories where there was no grid-patterned activity in a no-noise scenario. With trajectories where there was grid-patterned activity in the absence of noise, low levels of noise improved position estimation accuracy. In contrast, high levels of sensory noise impaired position estimates as well as grid-patterned activity, although position estimates were more sensitive to sensory noise compared to grid-patterned activity. Together, these analyses demonstrate the manifestation of stochastic resonance in a 2D CAN model, where low levels of sensory noise were beneficial towards the emergence of grid-patterned firing and in tracking position. Next, motivated by the proposed role of border-cells as an error-correction mechanism, we introduced north and east border cells and connected them to grid cells based on co-activity patterns. For different levels of noise, we computed grid scores and position accuracy in the presence vs. absence of border cells. Interestingly, while border inputs led to grid field formation in cases where grid fields were not generated, their presence only had a marginal impact on position accuracy. Together, our analyses suggest that biological CANs could evolve to yield optimal performance in the presence of noise in biological sensory systems, serving as a stabilizing factor yielding functional robustness through the manifestation of stochastic resonance.