Nonlinear path integration explains speed-dependent field shifts in hippocampal place and time cells

Place and time cells encode spatial location and elapsed time in the hippocampal formation. Recent experiments in CA1 have revealed speed-dependent shifts in the receptive fields of these cells, interpreted as evidence for mixed encoding of space and time. Here, we propose that such shifts can instead arise from nonlinear path integration, without explicit temporal coding. We first show that a Continuous Line Attractor model in which velocity is transformed by a saturating function reproduces speed-dependent shifts in estimated position. We then train a Recurrent Neural Network on a 1D path-integration task. After training, the network spontaneously develops place cells with speed-dependent field shifts and a concave relationship between simulated and internally represented speed, despite neither feature being imposed during training. Analysis of the trained network reveals two direction-selective populations and a non-selective population that is progressively silenced by increasing speed, effectively acting as a brake on the integrator. This emergent mechanism produces the saturation of internally represented speed and the resulting shifts in place fields. Together, our models show that speed-dependent place-field shifts can emerge from nonlinear path integration, without requiring explicit temporal coding.