Figure 3. Effects of perturbation in recurrent and feedforward neural network simulations: predictions for experiment.

(a) Simulations of aperiodic (column 1), partially periodic (column 2), and fully periodic (column 3) networks show changes in the population pattern pre-perturbation (first row; ${\gamma }_{inh}=1$) to post-perturbation (second row; ${\gamma }_{inh}=1.33$). Solid vertical lines: pre-perturbation bump locations. (Simulation details in Materials and methods.) (b) Perturbation-induced DRPS in the various networks for two perturbation strengths (${\gamma }_{inh}=1.33$: solid line and filled gray area; ${\gamma }_{inh}=1.66$: dotted line), both relative to the unperturbed case. (c) DRPS width (${\sigma }_{DRPS}$, defined as the standard deviation of the DRPS) as a function of perturbation strength for the different networks. Dashed green line: feedforward networks (predicted, not from simulation). The step-like shape for the partially periodic network is generic; however, the point at which the step occurs may vary from trial to trial. (d–e) Change in spatial tuning period (d) and amplitude (e) as a function of the perturbation strength (see Materials and methods). Change is defined as $|\frac{X_{post}}{X_{pre}}-1|$, where $X$ is the spatial tuning period or amplitude.

Figure 3—figure supplement 1. Changes in spatial tuning period in neural network simulations of the grid cell circuit are due to changes in both the population period and the velocity response of the network.

Change in spatial tuning period (a), population pattern period (b), and the velocity response (c) for the different network architectures (see Materials and methods for definitions of measures). Change is defined for quantity $X$ as $|X_{post}/X_{pre}-1|$, where $X_{pre}$ refers to that quantity measured in the unperturbed (${\gamma }_{inh}=1$) case, and $X_{post}$ refers to that quantity as measured in the perturbed (${\gamma }_{inh}$=1.33, 1.66, 2) cases. It is clear that the spatial tuning period (a) is more strongly influenced by the velocity response (c) than by the population period (b).