Here we sketch the hierarchical message passing thought to underlie predictive coding and expand on the details of between- and within-layer computations. Sensory input is conveyed via ascending prediction errors in superficial pyramidal cells (red arrows, posited to be mediated by fast AMPA glutamate receptor signaling). Posterior expectations are encoded by the activity of deep pyramidal cells. These cells then provide descending priors (black arrows, mediated by slower and more diffuse NMDA and GABA signaling) that inform prediction errors at the lower level – instantiating the computations that remove the expected input, leaving prediction errors to be assimilated or accommodated, depending on their precision (depicted by the balance, hypothesized to be implemented via slower neuromodulators like dopamine, acetylcholine and serotonin, depending on the particular inferential hierarchy). Lateral interactions (horizontal arrows) mediated within-layer predictions about the precision of priors (black) and prediction errors (red).