Neurodegenerative diseases, including Alzheimer, Parkinson, Huntington, and amyotrophic lateral sclerosis, are a prominent class of neurological diseases currently without a cure. They are characterized by an inexorable loss of a specific type of neurons. The selective vulnerability of specific neuronal clusters (typically a subcortical cluster) in the early stages, followed by the spread of the disease to higher cortical areas, is a typical pattern of disease progression. Neurodegenerative diseases share a range of molecular and cellular pathologies, including protein aggregation, mitochondrial dysfunction, glutamate toxicity, calcium load, proteolytic stress, oxidative stress, neuroinflammation, and aging, which contribute to neuronal death. Efforts to treat these diseases are often limited by the fact that they tend to address any one of the above pathological changes while ignoring others. Lack of clarity regarding a possible root cause that underlies all the above pathologies poses a significant challenge. In search of an integrative theory for neurodegenerative pathology, we hypothesize that metabolic deficiency in certain vulnerable neuronal clusters is the common underlying thread that links many dimensions of the disease. The current review aims to present an outline of such an integrative theory. We present a new perspective of neurodegenerative diseases as metabolic disorders at molecular, cellular, and systems levels. This helps to understand a common underlying mechanism of the many facets of the disease and may lead to more promising disease-modifying therapeutic interventions. Here, we briefly discuss the selective metabolic vulnerability of specific neuronal clusters and also the involvement of glia and vascular dysfunctions. Any failure in satisfaction of the metabolic demand by the neurons triggers a chain of events that precipitate various manifestations of neurodegenerative pathology.

To make an optimal decision we need to weigh all the available options, compare them with the current goal, and choose the most rewarding one. Depending on the situation an optimal decision could be to either “explore” or “exploit” or “not to take any action” for which the Basal Ganglia (BG) is considered to be a key neural substrate. In an attempt to expand this classical picture of BG function, we had earlier hypothesized that the Indirect Pathway (IP) of the BG could be the subcortical substrate for exploration. In this study we build a spiking network model to relate exploration to synchrony levels in the BG (which are a neural marker for tremor in Parkinson's disease). Key BG nuclei such as the Sub Thalamic Nucleus (STN), Globus Pallidus externus (GPe) and Globus Pallidus internus (GPi) were modeled as Izhikevich spiking neurons whereas the Striatal output was modeled as Poisson spikes. The model is cast in reinforcement learning framework with the dopamine signal representing reward prediction error. We apply the model to two decision making tasks: a binary action selection task (similar to one used by Humphries et al., 2006) and an n-armed bandit task (Bourdaud et al., 2008). The model shows that exploration levels could be controlled by STN's lateral connection strength which also influenced the synchrony levels in the STN-GPe circuit. An increase in STN's lateral strength led to a decrease in exploration which can be thought as the possible explanation for reduced exploratory levels in Parkinson's patients. Our simulations also show that on complete removal of IP, the model exhibits only Go and No-Go behaviors, thereby demonstrating the crucial role of IP in exploration. Our model provides a unified account for synchronization, action section, and explorative behavior.

Osborne Reynolds’s seminal idea of stretching and folding being the basis of fluid mixing has a direct bearing on the interpretation of mixing processes involving dynamical systems tools, in particular, horseshoe maps. Horseshoes offer the only direct, mathematically rigorous, experimental verification of chaos in a flow. In this work these ideas are formalized and developed, with the goal of exploiting the concepts in experimental mixing studies, particularly in the case of alternating doubly symmetric flows. Methods to represent and to identify horseshoes are developed. Application examples to three different flows—focusing primarily on errors arising from imperfect placement and reconstruction—are presented.

Many computational models of the basal ganglia (BG) have been proposed over the past twenty-five years. While computational neuroscience models have focused on closely matching the neurobiology of the BG, computational cognitive neuroscience (CCN) models have focused on how the BG can be used to implement cognitive and motor functions. This review article focuses on CCN models of the BG and how they use the neuroanatomy of the BG to account for cognitive and motor functions such as categorization, instrumental conditioning, probabilistic learning, working memory, sequence learning, automaticity, reaching, handwriting, and eye saccades. A total of 19 BG models accounting for one or more of these functions are reviewed and compared. The review concludes with a discussion of the limitations of existing CCN models of the BG and prescriptions for future modeling, including the need for computational models of the BG that can simultaneously account for cognitive and motor functions, and the need for a more complete specification of the role of the BG in behavioral functions.

Recurrent neural networks with associative memory properties are typically based on fixed-point dynamics, which is fundamentally distinct from the oscillatory dynamics of the brain. There have been proposals for oscillatory associative memories, but here too, in the majority of cases, only binary patterns are stored as oscillatory states in the network. Oscillatory neural network models typically operate at a single/common frequency. At multiple frequencies, even a pair of oscillators with real coupling exhibits rich dynamics of Arnold tongues, not easily harnessed to achieve reliable memory storage and retrieval. Since real brain dynamics comprises of a wide range of spectral components, there is a need for oscillatory neural network models that operate at multiple frequencies. We propose an oscillatory neural network that can model multiple time series simultaneously by performing a Fourier-like decomposition of the signals. We show that these enhanced properties of a network of Hopf oscillators become possible by operating in the complex-variable domain. In this model, the single neural oscillator is modeled as a Hopf oscillator, with adaptive frequency and dynamics described over the complex domain. We propose a novel form of coupling, dubbed “power coupling,” between complex Hopf oscillators. With power coupling, expressed naturally only in the complex-variable domain, it is possible to achieve stable (normalized) phase relationships in a network of multifrequency oscillators. Network connections are trained either by Hebb-like learning or by delta rule, adapted to the complex domain. The network is capable of modeling N-channel electroencephalogram time series with high accuracy and shows the potential as an effective model of large-scale brain dynamics.