We therefore asked how ACC activity was affected by the changing transition probabilities mapping the first-step actions to second-step states and reward probabilities in the second-step states. Because of the limited number of blocks that subjects performed in imaging sessions, we performed separate regression analyses for sessions for which we have sufficient coverage of the different states of the transition probabilities (Figure 5A; n = 3 mice, 5 sessions, 589 neurons, 1,252 trials) and reward probabilities (Figure 5B; n = 3 mice, 10 sessions, 1,152 neurons, 2,426 trials). These analyses predicted neuronal activity as a function of events in the current trial, the state of the transition or reward probabilities respectively, and their interactions. Though each analysis used only a subset of imaging sessions, the representation of current trial events (Figures 5A and 5B, top panels) was in both cases very similar to that for the full dataset (Figure 3E). As both the transition and reward probabilities determine which first-step action is correct, effects common to these two analyses could in principle be mediated by changes in first-step action values rather than the reward or transition probabilities themselves, but effects that are specific to one or other analysis cannot.
