A firing rate model of Parkinsonian deficits in interval timing

To account for deficits in interval timing observed in Parkinson's Disease (PD) patients, we develop a model based on the accumulating firing rate of a neural population with recurrent excitation. This model naturally produces the curvilinear accumulation of neural activity introduced to timing psychophysics by Miall (Models of Neural Timing, Elsevier Science, 1996), and implicated in Parkinsonian timing by Malapani and Rakitin (Functional and Neural Mechanisms of Interval Timing, CRC Press, 2003). The parameters essential for our model are the strength of the net neural feedback and the mean rate of inputs to the population from external brain areas. Systematic variations in these parameters reproduce the PD migration effect, in which estimates of long and short intervals drift towards each other, as well as uniform slowing of time estimates observed under other experimental conditions. For example, our model suggests that dopamine depletion in PD patients increases the neural feedback parameter and decreases the effective input parameter for populations involved in the production of time estimates. The model also explains why the migration effect will be associated with a violation of the scalar property, the linear increase in the standard deviation of time estimates with the duration of the target interval that is ubiquitous in healthy participants. We also show that the effect of systematically decreasing the input rate parameter in our model is equivalent to increasing thresholds, so that either of these changes may be associated with the Parkinsonian state.