Quantification of motor network dynamics in Parkinson’s disease by means of landscape and flux theory

Abstract

The basal ganglia neural circuit plays an important role in motor control. Despite the significant efforts, the understanding of the principles and underlying mechanisms of this modulatory circuit and the emergence of abnormal synchronized oscillations in movement disorders is still challenging. Dopamine loss has been proved to be responsible for Parkinson’s disease. We quantitatively described the dynamics of the basal ganglia-thalamo-cortical circuit in Parkinson’s disease in terms of the emergence of both abnormal firing rates and firing patterns in the circuit. We developed a potential landscape and flux framework for exploring the modulatory circuit. The driving force of the circuit can be decomposed into a gradient of the potential, which is associated with the steady-state probability distributions, and the curl probability flux term. We uncovered the underlying potential landscape as a Mexican hat-shape closed ring valley where abnormal oscillations emerge due to dopamine depletion. We quantified the global stability of the network through the topography of the landscape in terms of the barrier height, which is defined as the potential difference between the maximum potential inside the ring and the minimum potential along the ring. Both a higher barrier and a larger flux originated from detailed balance breaking result in more stable oscillations. Meanwhile, more energy is consumed to support the increasing flux. Global sensitivity analysis on the landscape topography and flux indicates how changes in underlying neural network regulatory wirings and external inputs influence the dynamics of the system. We validated two of the main hypotheses(direct inhibition hypothesis and output activation hypothesis) on the therapeutic mechanism of deep brain stimulation (DBS). We found GPe appears to be another effective stimulated target for DBS besides GPi and STN. Our approach provides a general way to quantitatively explore neural networks and may help for uncovering more efficacious therapies for movement disorders.

Non-equilibrium landscape and flux reveal the stability-flexibility-energy tradeoff in working memory

“…A distinguishing feature of non-equilibrium systems is the presence of nonvanishing steady-state flux. Different from the equilibrium system whose driving force can be expressed to a gradient of an energy function, the neural network as a non-equilibrium system is driven by both the nonvanishing steady-state irreversible probability flux that signifies the violation of detailed balance and the gradient of the potential landscape in the state space:F = J ss / P ss −D�rU [28][29][30][31][32][33]. Moreover, the non-equilibrium steady states can be maintained by the constantly exchanging matter, energy or information with the environment, where the nonvanishing steady-state flux plays a crucial role.…”

“…To address these questions, we developed a general non-equilibrium landscape and flux approach [28,29,[32][33][34] to study a biophysically based working memory model [13,[35][36][37]. We uncovered that the network architecture(both self-excitation within one selective population and mutual inhibition between two populations) plays a crucial role in determining the robustness against noises through quantifying the underlying non-equilibrium potential landscapes.…”

Age-related Spike Timing Dependent Plasticity of Brain-inspired Model of Visual Information Processing with Reinforcement Learning

“…The overall model connectivity is also enhanced by excitatory feedback connections from SC to their corresponding D1 and D2 areas of the Stratum as well as to LIP areas following recently reported findings [27], [28], [29]. Moreover we introduced mutually inhibiting connections between the two SC groups.…”

Simulation Design and Implementation of Voice Landscape Quantification in Virtual Reality Based on Cloud Computing

“…Emotional response is measured by happiness. e results show that in urban green space, natural space, and cultural landscape, due to the significant information content of sound quality or the dramatic impact of the loss of sound quality on the audience's appreciation, it is necessary to determine the place or environment where it is necessary to protect the sound environment [2].…”