Repetitive thoughts and motor programs including perseveration are bridge symptoms characteristic of obsessive compulsive disorder (OCD), schizophrenia and in the co-morbid overlap of these conditions. The above pathologies are sensitive to altered activation and kinetics of dopamine  and  receptors that differently influence sequence learning and recall. Recognizing start and stop elements of motor and cognitive behaviors has crucial importance. During chunking, frequent components of temporal strings are concatenated into single units. We extended a published computational model (Asabuki et al. 2018), where two populations of neurons are connected and simulated in a reservoir computing framework. These neural pools were adopted to represent D1 and D2 striatal neuronal populations. We investigated how specific neural and striatal circuit parameters can influence start/stop signaling and found that asymmetric intra-network connection probabilities, synaptic weights and differential time constants may contribute to signaling of start/stop elements within learned sequences. Asymmetric coupling between the striatal  and  neural populations was also demonstrated to be beneficial. Our modeling results predict that dynamical differences between the two dopaminergic striatal populations and the interaction between them may play complementary roles in chunk boundary signaling. Start and stop dichotomies can arise from the larger circuit dynamics as well, since neural and intra-striatal connections only partially support a clear division of labor.