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Deep brain stimulation (DBS) of the subthalamic nucleus reduces the severity of parkinsonian motor symptoms, but the therapeutic mechanisms are not understood. We hypothesize that clinically effective high frequency DBS suppresses disordered neuronal activity in the globus pallidus internus (GPi), a primary output structure of the basal ganglia. In a computational model of the basal ganglia thalamic circuit, periodic high frequency (>100 Hz) stimulation of the subthalamic nucleus reduced the incidence of thalamic cell errors, from the high error rates seen in the parkinsonian case back to the low error rates seen in the normal-healthy case. In contrast, both low frequency (<70 Hz) DBS and high frequency aperiodic DBS failed to alleviate thalamic errors. In high error rate conditions, disordered patterns of GPi activity lead to irregular synaptic inhibition of thalamus. In low error rate conditions, ordered patterns of GPi activity lead to regular synaptic inhibition of thalamus. Linear regression revealed that the variance of the GPi synaptic output accounted for 87-97% of the changes in thalamic error rate. In contrast, the average GPi synaptic output - a measure of total GPi activity - accounted for only 25-50% of the changes in thalamic error rate. Thus, while the firing rate of GPi cells may play some minor role, regularizing the pathological patterns of GPi activity is the mechanism by which DBS treats Parkinsonian motor symptoms.