Research

Tremor is one of the cardinal symptoms of Parkinson's disease. The neurophysiology of tremor is not completely understood, and so far it has not been possible to distinguish tremor from voluntary hand movements based on local brain signals. Here, we re-analyzed magnetoencephalography and local field potential recordings from the subthalamic nucleus of six patients with Parkinson's disease. Data were obtained after withdrawal from dopaminergic medication (Med Off) and after administration of levodopa (Med On). Using gradient-boosted tree learning, we classified epochs as tremor, self-paced fist-clenching, static forearm extension or tremor-free rest. While decoding performance was low when using subthalamic activity as the only feature (balanced accuracy mean: 38%, std: 7%), we could distinguish the four different motor states when considering cortical and subthalamic features (balanced accuracy mean: 75%, std: 17%). Adding a single cortical area improved classification by 17% on average, as compared to classification based on subthalamic activity alone. In most patients, the most informative cortical areas were sensorimotor cortical regions. Decoding performance was similar in Med On and Med Off. Our results demonstrate the advantage of monitoring cortical signals in addition to subthalamic activity for movement classification. By combining cortical recordings, subcortical recordings and machine learning, future adaptive systems might be able to detect tremor specifically and distinguish between several motor states.

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We examine the stability and qualitative dynamics of stochastic neuronal networks specified as multivariate non-linear Hawkes processes and related point-process generalized linear models that incorporate both auto- and cross-history effects. In particular, we adapt previous theoretical approximations based on mean field and mean field plus 1-loop correction to incorporate absolute refractory periods and other auto-history effects. Furthermore, we extend previous quasi-renewal approximations to the multivariate case, i.e. neuronal networks. The best sensitivity and specificity performance, in terms of predicting stability and divergence to nonphysiologically high firing rates in the examined simulations, was obtained by a variant of the quasi-renewal approximation. 

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Effective representations of recordings of epileptic activity for seizure prediction are high-dimensional, which prevents their visualization. Here we introduce and evaluate methods to find low-dimensional (2D or 3D) descriptors of these high-dimensional representations, which are amenable for visualization. Once low-dimensional descriptors are found, it is useful to identify structure in them. We evaluate clustering algorithms to automatically identify this structure. In addition, typical recordings of epileptic activity are long, extending for several days or weeks. We present and assess extensions of the previous methods to handle large datasets. 

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Motor adaptation to perturbations is provided by learning mechanisms operating in the cerebellum and basal ganglia. The cerebellum normally performs motor adaptation through supervised learning using information about movement error provided by visual feedback. However, if visual feedback is critically distorted, the system may disengage cerebellar error-based learning and switch to reinforcement learning mechanisms mediated by basal ganglia. Yet, the exact conditions and mechanisms of cerebellum and basal ganglia involvement in motor adaptation remain unknown. We use mathematical modeling to simulate control of planar reaching movements that relies on both error-based and non-error-based learning mechanisms. We show that for learning to be efficient only one of these mechanisms should be active at a time. We suggest that switching between the mechanisms is provided by a special circuit that effectively suppresses the learning process in one structure and enables it in the other. To do so, this circuit modulates learning rate in the cerebellum and dopamine release in basal ganglia depending on error-based learning efficiency. We use the model to explain and interpret experimental data on error- and non-error-based motor adaptation under different conditions.

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In this study, we explore the functional role of striatal cholinergic interneurons, hereinafter referred to as tonically active neurons (TANs), via computational modeling; specifically, we investigate the mechanistic relationship between TAN activity and dopamine variations and how changes in this relationship affect reinforcement learning in the striatum. TANs pause their tonic firing activity after excitatory stimuli from thalamic and cortical neurons in response to a sensory event or reward information. During the pause striatal dopamine concentration excursions are observed. However, functional interactions between the TAN pause and striatal dopamine release are poorly understood. Here we propose a TAN activity-dopamine relationship model and demonstrate that the TAN pause is likely a time window to gate phasic dopamine release and dopamine variations reciprocally modulate the TAN pause duration. Furthermore, this model is integrated into our previously published model of reward-based motor adaptation to demonstrate how phasic dopamine release is gated by the TAN pause to deliver reward information for reinforcement learning in a timely manner. We also show how TAN-dopamine interactions are affected by striatal dopamine deficiency to produce poor performance of motor adaptation.

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It is widely accepted that the basal ganglia (BG) play a key role in action selection and reinforcement learning. However, despite considerable number of studies, the BG architecture and function are not completely understood. Action selection and reinforcement learning are facilitated by the activity of dopaminergic neurons, which encode reward prediction errors when reward outcomes are higher or lower than expected. The BG are thought to select proper motor responses by gating appropriate actions, and suppressing inappropriate ones. The direct striato-nigral (GO) and the indirect striato-pallidal (NOGO) pathways have been suggested to provide the functions of BG in the two-pathway concept. Previous models confirmed the idea that these two pathways can mediate the behavioral choice, but only for a relatively small number of potential behaviors. Recent studies have provided new evidence of BG involvement in motor adaptation tasks, in which adaptation occurs in a non-error-based manner. In such tasks, there is a continuum of possible actions, each represented by a complex neuronal activity pattern. We extended the classical concept of the two-pathway BG by creating a model of BG interacting with a movement execution system, which allows for an arbitrary number of possible actions. The model includes sensory and premotor cortices, BG, a spinal cord network, and a virtual mechanical arm performing 2D reaching movements. The arm is composed of 2 joints (shoulder and elbow) controlled by 6 muscles (4 mono-articular and 2 bi-articular). The spinal cord network contains motoneurons, controlling the muscles, and sensory interneurons that receive afferent feedback and mediate basic reflexes. Given a specific goal-oriented motor task, the BG network through reinforcement learning constructs a behavior from an arbitrary number of basic actions represented by cortical activity patterns. Our study confirms that, with slight modifications, the classical two-pathway BG concept is consistent with results of previous studies, including non-error based motor adaptation experiments, pharmacological manipulations with BG nuclei, and functional deficits observed in BG-related motor disorders. 

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It is proved that bounded solutions of modified (θ-twisted) cohomological equations for expanding circle maps are θ-Hölder continuous but are not (θ+γ)-Hölder continuous for every γ>0 at almost every point. This gives new examples of "nonlinear" Weierstrass-like functions for which the optimal \holder exponent at most points is known.

The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.

We generalize two classical results of Maizel and Pliss that describe relations between hyperbolicity properties of linear system of difference equations and its ability to have a bounded solution for every bounded inhomogeneity. We also apply one of this generalizations in shadowing theory of diffeomorphisms to prove that some sort of limit shadowing is equivalent to structural stability.

We prove that Lipschitz inverse shadowing for nonsingular flows is equivalent to structural stability.

In this paper, the notion of the Lipschitz inverse shadowing property with respect to two classes of d-methods that generate pseudotrajectories of dynamical systems is introduced. It is shown that if a diffeomorphism of a Euclidean space has the Lipschitz inverse shadowing property on the trajectory of an individual point, then the Mañé analytic strong transversality condition must be satisfied at this point. This result is used in the proof of the main theorem: a diffeomorphism of a smooth closed manifold that has the Lipschitz inverse shadowing property is structurally stable.

The hepatitis C virus (HCV) belongs to Flaviviridae family and causes hazardous liver diseases leading frequently to cirrhosis and hepatocellular carcinoma. HCV is able to rapidly acquire drug resistance and for this reason there is currently no effective anti-HCV therapy in spite of appearance of new potential drugs. Mathematical models are relevant to predict the efficacy of potential drugs against virus or host targets. One of the promising targets for development of new drugs is the viral NS3 protease. Here we developed a stochastic model of the subgenomic HCV replicon replication in Huh-7 cells and in the presence of the NS3 protease inhibitors. Along with consideration of the stochastic nature of the subgenomic HCV replicon replication, the model takes into account the existence and generation of main NS3 protease drug resistant mutants, namely BILN-2061 (A156T, D168V, R155Q), VX-950 (A156S, A156T, T54A) and SCH-503034 (A156T, A156S, T54A). The model reproduces well the viral RNA kinetics in the cell from the moment of the subgenomic HCV replicon transfection to steady state, as well as the viral RNA suppression kinetics in the presence of NS3 protease inhibitors BILN-2061, VX-950 and SCH-503034. We showed that the resistant mutants should be taken into account for the correct description of biphasic kinetics of the viral RNA suppression. The mutants selected in the presence of different inhibitor concentrations have maximal replication capacity in the given inhibitor concentration range. Our model can be used to interpret the results of the new anti-HCV drug testing in replicon systems, as well as to predict the efficacy of new potential drugs and optimize the mode of their use.

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As an RNA virus, hepatitis C virus (HCV) is able to rapidly acquire drug resistance, and for this reason the design of effective anti-HCV drugs is a real challenge. The HCV subgenomic replicon-containing cells are widely used for experimental studies of the HCV genome replication mechanisms, for drug testing in vitro and in studies of HCV drug resistance. The NS3/4A protease is essential for virus replication and, therefore, it is one of the most attractive targets for developing specific antiviral agents against HCV. We have developed a stochastic model of subgenomic HCV replicon replication, in which the emergence and selection of drug resistant mutant viral RNAs in replicon cells is taken into account. Incorporation into the model of key NS3 protease mutations leading to resistance to BILN-2061 (A156T, D168V, R155Q), VX-950 (A156S, A156T, T54A) and SCH 503034 (A156T, A156S, T54A) inhibitors allows us to describe the long term dynamics of the viral RNA suppression for various inhibitor concentrations. We theoretically showed that the observable difference between the viral RNA kinetics for different inhibitor concentrations can be explained by differences in the replication rate and inhibitor sensitivity of the mutant RNAs. The pre-existing mutants of the NS3 protease contribute more significantly to appearance of new resistant mutants during treatment with inhibitors than wild-type replicon. The model can be used to interpret the results of anti-HCV drug testing on replicon systems, as well as to estimate the efficacy of potential drugs and predict optimal schemes of their usage.

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We prove that spaces of Keplerian curvilinear orbits, all orbits and elliptic orbits with marked pericenter cannot carry a norm, compatible with their standard topology. We also prove that the space of Keplerian elliptic orbits without marked pericenter cannot carry a norm, compatible with the natural metrics on it.