Hidden Quantum Processes, Quantum Ion Channels, and 1/ fθ-Type Noise.

In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from [Formula: see text] and [Formula: see text] channel kinetics, in order to identify the source of [Formula: see text]-type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately [Formula: see text]-type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous [Formula: see text]-type Lorentzian weights, in which the spectral exponent [Formula: see text] is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to [Formula: see text]-type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond [Formula: see text]-type -noise, including applications to animal models and possible impact on quantum foundations.

Robust adaptive deep brain stimulation control of in-silico non-stationary Parkinsonian neural oscillatory dynamics.

Objective. Closed-loop deep brain stimulation (DBS) is a promising therapy for Parkinson's disease (PD) that works by adjusting DBS patterns in real time from the guidance of feedback neural activity. Current closed-loop DBS mainly uses threshold-crossing on-off controllers or linear time-invariant (LTI) controllers to regulate the basal ganglia (BG) Parkinsonian beta band oscillation power. However, the critical cortex-BG-thalamus network dynamics underlying PD are nonlinear, non-stationary, and noisy, hindering accurate and robust control of Parkinsonian neural oscillatory dynamics.Approach. Here, we develop a new robust adaptive closed-loop DBS method for regulating the Parkinsonian beta oscillatory dynamics of the cortex-BG-thalamus network. We first build an adaptive state-space model to quantify the dynamic, nonlinear, and non-stationary neural activity. We then construct an adaptive estimator to track the nonlinearity and non-stationarity in real time. We next design a robust controller to automatically determine the DBS frequency based on the estimated Parkinsonian neural state while reducing the system's sensitivity to high-frequency noise. We adopt and tune a biophysical cortex-BG-thalamus network model as an in-silico simulation testbed to generate nonlinear and non-stationary Parkinsonian neural dynamics for evaluating DBS methods.Main results. We find that under different nonlinear and non-stationary neural dynamics, our robust adaptive DBS method achieved accurate regulation of the BG Parkinsonian beta band oscillation power with small control error, bias, and deviation. Moreover, the accurate regulation generalizes across different therapeutic targets and consistently outperforms current on-off and LTI DBS methods.Significance. These results have implications for future designs of closed-loop DBS systems to treat PD.

Cell proliferation in the brains of NMDAR NR1 transgenic mice.

We have used genetically engineered NMDA receptor NR1+/- mice in which the gene for the NR1 subunit was modified in such a way that these mice express only 50% of the NR1 subunit. The NR1 subunit is necessary for NMDA receptor channel function. We investigated the effects of reduced NMDA receptor function on cell proliferation in the hippocampus and the amygdala of the adult mouse brain. Transgenic (NR1+/-) and wild-type (NR1+/+) mice were injected with BrdU. We collected brain sections cutting through the rostro-caudal extension of the entire hippocampus of the NR1+/- and NR1+/+ (wild-type) mice. The phenotype of BrdU-positive cells was identified by double labeling with antibodies to neuronal or glial markers. Our results show that the NR1+/- mice, which express the NMDAR NR1 subunit at a low level, have a significant (p<0.01) increase in the number of BrdU-positive cells in the dentate gyrus and the amygdala compared to NR1+/+ mice. Some of these dividing cells express the neuronal marker NeuN. Our results indicate that low expression of the NR1 subunit significantly increases cell proliferation and neurogenesis, suggesting that low NMDARs activity contributes to the increase in cell proliferation in the adult brain.

A New Statistical Model of Electroencephalogram Noise Spectra for Real-Time Brain-Computer Interfaces.

OBJECTIVE: A characteristic of neurological signal processing is high levels of noise from subcellular ion channels up to whole-brain processes. In this paper, we propose a new model of electroencephalogram (EEG) background periodograms, based on a family of functions which we call generalized van der Ziel-McWhorter (GVZM) power spectral densities (PSDs). To the best of our knowledge, the GVZM PSD function is the only EEG noise model that has relatively few parameters, matches recorded EEG PSD's with high accuracy from 0 to over 30 Hz, and has approximately 1/fθ behavior in the midfrequencies without infinities. METHODS: We validate this model using three approaches. First, we show how GVZM PSDs can arise in a population of ion channels at maximum entropy equilibrium. Second, we present a class of mixed autoregressive models, which simulate brain background noise and whose periodograms are asymptotic to the GVZM PSD. Third, we present two real-time estimation algorithms for steady-state visual evoked potential (SSVEP) frequencies, and analyze their performance statistically. RESULTS: In pairwise comparisons, the GVZM-based algorithms showed statistically significant accuracy improvement over two well-known and widely used SSVEP estimators. CONCLUSION: The GVZM noise model can be a useful and reliable technique for EEG signal processing. SIGNIFICANCE: Understanding EEG noise is essential for EEG-based neurology and applications such as real-time brain-computer interfaces, which must make accurate control decisions from very short data epochs. The GVZM approach represents a successful new paradigm for understanding and managing this neurological noise.

Optimal causal filtering for 1 /fα-type noise in single-electrode EEG signals.

Understanding the mode of generation and the statistical structure of neurological noise is one of the central problems of biomedical signal processing. We have developed a broad class of abstract biological noise sources we call hidden simplicial tissues. In the simplest cases, such tissue emits what we have named generalized van der Ziel-McWhorter (GVZM) noise which has a roughly 1/fα spectral roll-off. Our previous work focused on the statistical structure of GVZM frequency spectra. However, causality of processing operations (i.e., dependence only on the past) is an essential requirement for real-time applications to seizure detection and brain-computer interfacing. In this paper we outline the theoretical background for optimal causal time-domain filtering of deterministic signals embedded in GVZM noise. We present some of our early findings concerning the optimal filtering of EEG signals for the detection of steady-state visual evoked potential (SSVEP) responses and indicate the next steps in our ongoing research.

Markers of apoptosis: methods for elucidating the mechanism of apoptotic cell death from the nervous system.

Apoptosis is a highly conserved energy-requiring program for non-inflammatory cell death that is important in both normal physiology and disease. Numerous techniques have been used to study apoptosis. In the nervous system, apoptosis is necessary for normal development, but it also occurs in many acute and chronic pathologic conditions. This review places commonly used markers of apoptosis and their detection in the context of what is now known about the process of apoptosis. We review the potential role of apoptosis in nervous system and neurodegenerative disorders (Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis). We then describe important morphological, immunocytochemical, and molecular genetic markers for apoptosis, including proteases, signal transduction molecules, and mitochondrial proteins. The possibility of manipulating apoptosis therapeutically in conditions of too many or too few cells is under active investigation.

A patient with post-traumatic stress disorder developing stiff person syndrome: is there a correlation?

Stiff person syndrome (SPS) is an uncommon disorder characterized by progressive muscle stiffness, rigidity, and axial muscle spasms. It is presumed to be an autoimmune process, with glutamic acid decarboxylase antibodies present in most cases. Here, we present a case report of a patient diagnosed with post-traumatic stress disorder (PTSD) acquired by sexual trauma and by exposure to the severely wounded soldiers she attended as a nurse. Subsequently, she developed SPS confirmed by serology. The possibility of an association between PTSD and SPS is theorized, given their relationship to the GABAergic system. Further studies examining the relation between PTSD and SPS should be initiated.