Parkinsonian tremor and simplification in network dynamics

We explore the behavior of richly connected inhibitory neural networks unde r parameter changes that correspond to weakening of synaptic efficacies bet ween network units, and show that transitions from irregular to periodic dy namics are common in such systems. The weakening of these connections leads to a reduction in the number of units that effectively drive the dynamics and thus to simpler behavior. We hypothesize that the multiple interconnect ing loops of the brain's motor circuitry, which involve many inhibitory con nections, exhibit such transitions. Normal physiological tremor is irregula r while other forms of tremor show more regular oscillations. Tremor in Par kinson's disease, for example, stems from weakened synaptic efficacies of d opaminergic neurons in the nigro-striatal pathway, as in our general model. The multiplicity of structures involved in the production of symptoms in P arkinson's disease and the reversibility of symptoms by pharmacological and surgical manipulation of connection parameters suggest that such a neural network model is appropriate. Furthermore, fixed points that can occur in t he network models are suggestive of akinesia in Parkinson's disease. This m odel is consistent with the view that normal physiological systems can be r egulated by robust and richly connected feedback networks with complex dyna mics, and that loss of complexity in the feedback structure due to disease leads to more orderly behavior. (C) 1999 Society for Mathematical Biology.