Potential mechanisms for imperfect synchronization in parkinsonian basal ganglia

Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinson's disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinson's disease.Comment: 27 pages, 9 figure

Mathematical model of subthalamic nucleus neuron - characteristic activity patterns and bifurcation analysis

The subthalamic nucleus (STN) has an important role in the pathophysiology of the basal ganglia in Parkinson's disease. The ability of STN cells to generate bursting rhythms under either transient or sustained hyperpolarization may underlie the excessively synchronous beta rhythms observed in Parkinson's disease. In this study, we developed a conductance-based single compartment model of an STN neuron, which is able to generate characteristic activity patterns observed in experiments including hyperpolarization-induced bursts and post-inhibitory rebound bursts. This study focused on the role of three currents in rhythm generation: T-type calcium (CaT) current, L-type calcium (CaL) current, and hyperpolarization-activated cyclic nucleotide-gated (HCN) current. To investigate the effects of these currents in rhythm generation, we performed a bifurcation analysis using slow variables in these currents. Bifurcation analysis showed that the HCN current promotes single-spike activity patterns rather than bursting in agreement with experimental results. It also showed that the CaT current is necessary for characteristic bursting activity patterns. In particular, the CaT current enables STN neurons to generate these activity patterns under hyperpolarizing stimuli. The CaL current enriches and reinforces these characteristic activity patterns. In hyperpolarization-induced bursts or post-inhibitory rebound bursts, the CaL current allows STN neurons to generate long bursting patterns. Thus, bifurcation analysis explained the synergistic interaction of the CaT and CaL currents, which enables STN neurons to respond to hyperpolarizing stimuli in a salient way. The results of this study implicate the importance of CaT and CaL currents in the pathophysiology of the basal ganglia in Parkinson's disease

Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson's Disease

Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson's disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson's disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson's disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.Comment: 19 pages, 8 figure

Dynamics of desynchronized episodes in intermittent synchronization

Intermittent synchronization is observed in a variety of different experimental settings in physics and beyond and is an established research topic in nonlinear dynamics. When coupled oscillators exhibit relatively weak, intermittent synchrony, the trajectory in the phase space spends a substantial fraction of time away from a vicinity of a synchronized state. Thus to describe and understand the observed dynamics one may consider both synchronized episodes and desynchronized episodes (the episodes when oscillators are not synchronous). This mini-review discusses recent developments in this area. We explain how one can consider variation in synchrony on the very short time-scales, provided that there is some degree of overall synchrony. We show how to implement this approach in the case of intermittent phase locking, review several recent examples of the application of these ideas to experimental data and modeling systems, and discuss when and why these methods may be useful.Comment: 12 pages, 2 figures. Accepted to Frontiers in Physic

Mathematical model of subthalamic nucleus neuron: Characteristic activity patterns and bifurcation analysis

The subthalamic nucleus (STN) has an important role in the pathophysiology of the basal ganglia in Parkinson's disease. The ability of STN cells to generate bursting rhythms under either transient or sustained hyperpolarization may underlie the excessively synchronous beta rhythms observed in Parkinson's disease. In this study, we developed a conductance-based single compartment model of an STN neuron, which is able to generate characteristic activity patterns observed in experiments including hyperpolarization-induced bursts and post-inhibitory rebound bursts. This study focused on the role of three currents in rhythm generation: T-type calcium (CaT) current, L-type calcium (CaL) current, and hyperpolarization-activated cyclic nucleotide-gated (HCN) current. To investigate the effects of these currents in rhythm generation, we performed a bifurcation analysis using slow variables in these currents. Bifurcation analysis showed that the HCN current promotes single-spike activity patterns rather than bursting in agreement with experimental results. It also showed that the CaT current is necessary for characteristic bursting activity patterns. In particular, the CaT current enables STN neurons to generate these activity patterns under hyperpolarizing stimuli. The CaL current enriches and reinforces these characteristic activity patterns. In hyperpolarization-induced bursts or post-inhibitory rebound bursts, the CaL current allows STN neurons to generate long bursting patterns. Thus, the bifurcation analysis explained the synergistic interaction of the CaT and CaL currents, which enables STN neurons to respond to hyperpolarizing stimuli in a salient way. The results of this study implicate the importance of CaT and CaL currents in the pathophysiology of the basal ganglia in Parkinson's disease