  Our brain is a complex information processing network in which the nervous
system receives information from the environment to quickly react to incoming
events or learns from experience to sharp our memory. In the nervous system,
the brain states translate collective activities of neurons interconnected via
synaptic connections. In this paper, we study coupled effects of channels and
synaptic dynamics under the stochastic influence of healthy brain cells with
applications to Parkinson's disease (PD). In particular, we investigate the
effects of random inputs in a subthalamic nucleus (STN) cell membrane potential
model. The STN bursting phenomena and parkinsonian hypokinetic motor symptoms
are closely connected, as electrical and chemical maneuvers modulating STN
bursts are sufficient to ameliorate or mimic parkinsonian motor deficits. Deep
brain stimulation (DBS) of the STN is an important surgical technique used in
the treatment to improve PD symptoms. Our numerical results show that the
random inputs strongly affect the spiking activities of the STN neuron not only
in the case of healthy cells but also in the case of PD cells in the presence
of DBS treatment. Specifically, the existence of a random refractory period
together with random input current in the system may substantially influence an
increased irregularity of spike trains of the output neurons.
