In behaving rodents, CA1 pyramidal neurons receive spatially-tuned depolarizing synaptic input while traversing a specific location within an environment called its place. Midbrain dopamine neurons participate in reinforcement learning, and bursts of action potentials riding a depolarizing wave of synaptic input signal rewards and reward expectation. Interestingly, slice electrophysiology in vitro shows that both types of cells exhibit a pronounced reduction in firing rate (adaptation) and even cessation of firing during sustained depolarization. We included a five state Markov model of NaV1.6 (for CA1) and NaV1.2 (for dopamine neurons) respectively, in computational models of these two types of neurons. Our simulations suggest that long-term inactivation of this channel is responsible for the adaptation in CA1 pyramidal neurons, in response to triangular depolarizing current ramps. We also show that the differential contribution of slow inactivation in two subpopulations of midbrain dopamine neurons can account for their different dynamic ranges, as assessed by their responses to similar depolarizing ramps. These results suggest long-term inactivation of the sodium channel is a general mechanism for adaptation.