Stephan A. van Gils

Synchrony in Parkinson's disease: importance of intrinsic properties of the external globus pallidus

The mechanisms for the emergence and transmission of synchronized oscillations in Parkinsons disease, which are potentially causal to motor deficits, remain debated. Aside from the motor cortex and the subthalamic nucleus, the external globus pallidus (GPe) has been shown to be essential for the maintenance of these oscillations and plays a major role in sculpting neural network activity in the basal ganglia (BG). While neural activity of the healthy GPe shows almost no correlations between pairs of neurons, prominent synchronization in the β frequency band arises after dopamine depletion. Several studies have proposed that this shift is due to network interactions between the different BG nuclei, including the GPe. However, recent studies demonstrate an important role for the properties of neurons within the GPe. In this review, we will discuss these intrinsic GPe properties and review proposed mechanisms for activity decorrelation within the dopamine-intact GPe. Failure of the GPe to desynchronize correlated inputs can be a possible explanation for synchronization in the whole BG. Potential triggers of synchronization involve the enhancement of GPe-GPe inhibition and changes in ion channel function in GPe neurons.

Difference equations with delay

In this note we employ combinatorial arguments to count and classify certain periodic solutions of the delayed difference equationx(n) = f(x(n − k)), withk ≥ 2 given andn ∈ ℤ, The periodic solutions that we consider are formed by combiningk copies of anm- periodic solution of the “ordinary” difference equationx(n) =f(x(n- 1)). We also briefly discuss the possibility of braiding different periodic solutions of the ordinary difference equation into a periodic solution of the delayed version.

Cross-scale effects of neural interactions during human neocortical seizure activity

Significance We show how small-scale (less than millimeters2) neuronal dynamics relates to network activity observed across wide areas (greater than centimeters2) during certain network states, such as seizures. Simulations show how macroscopic network properties can affect frequency and amplitude of ictal oscillations. Additionally, the seizure dynamic suggests that one neuronal function, feedforward inhibition, plays different roles across scales: (i) inhibition at the small-scale wavefront fails, allowing seizure activity to propagate, but (ii) at macroscopic scales, inhibition of the surrounding territory is activated via long-range intracortical connections and creates a distinct pathway to a postictal state. Ultimately, our modeling framework can be used to examine meso- and macroscopic perturbations and evaluate strategies to promote transitions between ictal and nonictal network states. Small-scale neuronal networks may impose widespread effects on large network dynamics. To unravel this relationship, we analyzed eight multiscale recordings of spontaneous seizures from four patients with epilepsy. During seizures, multiunit spike activity organizes into a submillimeter-sized wavefront, and this activity correlates significantly with low-frequency rhythms from electrocorticographic recordings across a 10-cm-sized neocortical network. Notably, this correlation effect is specific to the ictal wavefront and is absent interictally or from action potential activity outside the wavefront territory. To examine the multiscale interactions, we created a model using a multiscale, nonlinear system and found evidence for a dual role for feedforward inhibition in seizures: while inhibition at the wavefront fails, allowing seizure propagation, feedforward inhibition of the surrounding centimeter-scale networks is activated via long-range excitatory connections. Bifurcation analysis revealed that distinct dynamical pathways for seizure termination depend on the surrounding inhibition strength. Using our model, we found that the mesoscopic, local wavefront acts as the forcing term of the ictal process, while the macroscopic, centimeter-sized network modulates the oscillatory seizure activity.

Quantifying HER-2 expression on Circulating Tumor Cells by ACCEPT

Circulating tumor cells (CTCs) isolated from blood can be probed for the expression of treatment targets. Immunofluorescence is often used for both the enumeration of CTC and the determination of protein expression levels related to treatment targets. Accurate and reproducible assessment of such treatment target expression levels is essential for their use in the clinic. To enable this, an open source image analysis program named ACCEPT was developed in the EU-FP7 CTCTrap and CANCER-ID programs. Here its application is shown on a retrospective cohort of 132 metastatic breast cancer patients from which blood samples were processed by CellSearch® and stained for HER-2 expression as additional marker. Images were digitally stored and reviewers identified a total of 4084 CTCs. CTC’s HER-2 expression was determined in the thumbnail images by ACCEPT. 150 of these images were selected and sent to six independent investigators to score the HER-2 expression with and without ACCEPT. Concordance rate of the operators’ scoring results for HER-2 on CTCs was 30% and could be increased using the ACCEPT tool to 51%. Automated assessment of HER-2 expression by ACCEPT on 4084 CTCs of 132 patients showed 8 (6.1%) patients with all CTCs expressing HER-2, 14 (10.6%) patients with no CTC expressing HER-2 and 110 (83.3%) patients with CTCs showing a varying HER-2 expression level. In total 1576 CTCs were determined HER-2 positive. We conclude that the use of image analysis enables a more reproducible quantification of treatment targets on CTCs and leads the way to fully automated and reproducible approaches.

Homoclinic twist bifurcation in a system of two coupled oscillators

We analyse the dynamics of two identical Josephson junctions coupled through a purely capacitive load in the neighborhood of a degenerate symmetric homoclinic orbit. A bifurcation function is obtained applying Lins version of the Lyapunov–Schmidt reduction. We locate in parameter space the region of existence of n-periodic orbits, and we prove the existence of n-homoclinic orbits and bounded nonperiodic orbits. A singular limit of the bifurcation function yields a one-dimensional mapping which is analyzed. Numerical computations of nonsymmetric homoclinic orbits have been performed, and we show the relevance of these computations by comparing the results with the analysis.

Modulated waves in a perturbed Korteweg-de Vries equation

We show the existence of a global branch of modulated waves in a two-mode approximation of a perturbed Korteweg-de Vries equation.

A Rate-Reduced Neuron Model for Complex Spiking Behavior

We present a simple rate-reduced neuron model that captures a wide range of complex, biologically plausible, and physiologically relevant spiking behavior. This includes spike-frequency adaptation, postinhibitory rebound, phasic spiking and accommodation, first-spike latency, and inhibition-induced spiking. Furthermore, the model can mimic different neuronal filter properties. It can be used to extend existing neural field models, adding more biological realism and yielding a richer dynamical structure. The model is based on a slight variation of the Rulkov map.

Simulating Idiopathic Parkinson’s Disease by In Vitro and Computational Models

In general there is a wide gap between experimental animal results, especially with respect to neuroanatomical data, and computational modeling. In order to be able to investigate the anatomical and functional properties of afferent and efferent connections between the different nuclei of the basal ganglia, similar studies need to be performed as described in this review for the Substantia Nigra. These studies, though very time-consuming, are essential to decide which pathways play important roles in normal functioning and therefore need to be included in modeling studies. In addition, it should be known what neuroanatomical changes take place resulting from the neurodegeneration associated with Parkinson’s disease and how they affect network behavior. For instance, the direct effects of DBS on motor control are of interest, but since DBS has a low threshold to side effects, additional non-motor pathways are expected to be involved. Including these pathways in network models may shed light on the extent and effect of stimulation. Similarly, as PPN stimulation may have a beneficial influence on gait and balance, different pathways are important regarding the different motor symptoms of Parkinson’s disease.

The prototype equation for delayed negative feedback: periodic solutions

In this chapter we study the nonlinear equation