Grid cells in the medial entorhinal cortex (MEC) of mammalian brains show hexagonal firing fields and are thought to encode the animal’s current location in the environment. As the animal moves, grid cells integrate self-motion cues to track the current position relative to a starting reference location. Recent experiments have identified a class of predictive grid cells that encode the animal’s upcoming location 1,2. Continuous attractor networks (CAN) explain how grid cells develop their characteristic hexagonal firing pattern and enable path integration. But how does predictive coding arise within these networks? We developed a biophysically detailed model of a grid cell attractor network constrained by extant data. Through this model, we identified two mechanisms that likely function independently and to varying extents in layers II and III of the MEC 1. These mechanisms help explain the unique characteristics of predictive coding in each of these layers. Our model consists of stellate cells and fast-spiking inhibitory interneurons, equipped with realistic conductances that provide a rich dynamical repertoire. We show that the presence of an HCN conductance can introduce a predictive bias in the positional representation by modulating the excitability of stellate cells. A second mechanism that leads to predictive coding involves direction-specific asymmetries in the connections between interneurons and stellate cells. The extent of predictive coding differs between these two mechanisms. Based on this difference, we hypothesize that the first mechanism is more prominent in layer II, while the second is more dominant in layer III of the MEC. 1. Ouchi, A. \& Fujisawa, S. Predictive grid coding in the medial entorhinal cortex. Science 385, 776–784 (2024). 2. Chaudhuri-Vayalambrone, P. et al. Simultaneous representation of multiple time horizons by entorhinal grid cells and CA1 place cells. Cell Rep. 42, 112716 (2023).