Nonlinear effects of intrinsic dynamics on temporal encoding in a model of avian auditory cortex

Neurons exhibit diverse intrinsic dynamics, which govern how they integrate synaptic inputs to produce spikes. Intrinsic dynamics are often plastic during development and learning, but the effects of these changes on stimulus encoding properties are not well known. To examine this relationship, we simulated auditory responses to zebra finch song using a linear-dynamical cascade model, which combines a linear spectrotemporal receptive field with a dynamical, conductance-based neuron model, then used generalized linear models to estimate encoding properties from the resulting spike trains. We focused on the effects of a low-threshold potassium current (K_LT) that is present in a subset of cells in the zebra finch caudal mesopallium and is affected by early auditory experience. We found that K_LT affects both spike adaptation and the temporal filtering properties of the receptive field. The direction of the effects depended on the temporal modulation tuning of the linear (input) stage of the cascade model, indicating a strongly nonlinear relationship. These results suggest that small changes in intrinsic dynamics in tandem with differences in synaptic connectivity can have dramatic effects on the tuning of auditory neurons.     

A pedagogical walkthrough of computational modeling and simulation of Wnt signaling pathway using static causal models in MATLAB

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.     

Generalized optimal spatial filtering using a kernel approach with application to EEG classification

Common spatial patterns (CSP) has been widely used for finding the linear spatial filters which are able to extract the discriminative brain activities between two different mental tasks. However, the CSP is difficult to capture the nonlinearly clustered structure from the non-stationary EEG signals. To relax the presumption of strictly linear patterns in the CSP, in this paper, a generalized CSP (GCSP) based on generalized singular value decomposition (GSVD) and kernel method is proposed. Our method is able to find the nonlinear spatial filters which are formulated in the feature space defined by a nonlinear mapping through kernel functions. Furthermore, in order to overcome the overfitting problem, the regularized GCSP is developed by adding the regularized parameters. The experimental results demonstrate that our method is an effective nonlinear spatial filtering method.     

Hallucinogen persisting perception disorder in neuronal networks with adaptation

We study the spatiotemporal dynamics of neuronal networks with spike frequency adaptation. In particular, we compare the effects of adaptation being either a linear or nonlinear function of neural activity. We find that altering parameters controlling the strength of synaptic connections in the network can lead to spatially structured activity suggestive of symptoms of hallucinogen persisting perception disorder (HPPD). First, we study how both networks track spatially homogeneous flickering stimuli, and find input is encoded as continuous at lower flicker frequencies when the network??s synapses exhibit more net excitation. Mainly, we study instabilities of stimulus-driven traveling pulse solutions, representative of visual trailing phenomena common to HPPD patients. Visual trails are reported as discrete afterimages in the wake of a moving input. Thus, we analyze several solutions arising in response to moving inputs in both networks: an ON state, stimulus-locked pulses, and traveling breathers. We find traveling breathers can arise in both networks when an input moves beyond a critical speed. These possible neural substrates of visual trails occur at slower speeds when the modulation of synaptic connectivity is increased.     

Quantitative measures of cortical functional connectivity: A state-of-the-art brief survey

The modern concepts of quantitative measurement of the strength of functional and effective cortical connectivity in neurocognitive networks (large-scale distributed brain systems of interacting neuronal populations that are believed to underlie cognitive processing) are reviewed. The two main classes of the methods of connectivity assessment (linear and nonlinear) are discussed. In the class of linear methods, in addition to coherence routinely used to measure the strength of functional links, the vector autoregressive modeling of multichannel EEG is discussed in detail. The latter technique allows the estimation of both functional and effective connectivity, i.e., the measures such as directed transfer function (DTF) and direct partial coherence (PDC) extensively used in cognitive neuroscience. The impact of volume conduction on different estimates of connectivity is considered and the imaginary part of complex-valued coherence as a way to reduce the artificial influence of volume conduction is discussed. Independent component analysis (ICA) and transfer entropy as a method of estimating direct influence are reviewed in the class of nonlinear methods.     

A Class of Ratio-Cum-Product-Type Estimator

The problem of estimating the population mean using an auxiliary information has been dealt with in literature quite extensively. Ratio, product, linear regression and ratio-type estimators are well known. A class of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimator and a product-type estimator) which are, in fact, the particular cases of it. At optimum value of α, the proposed estimator is as efficient as linear regression estimator.     

Preprocessing of two-dimensional gel electrophoresis images

Proteomics produces a huge amount of two-dimensional gel electrophoresis images. Their analysis can yield a lot of information concerning proteins responsible for different diseases or new unidentified proteins. However, an automatic analysis of such images requires an efficient tool for reducing noise in images. This allows proper detection of the spots' borders, which is important in protein quantification (as the spots' areas are used to determine the amounts of protein present in an analyzed mixture). Also in the feature-based matching methods the detected features (spots) can be described by additional attributes, such as area or shape. In our study, a comparison of different methods of noise reduction is performed in order to find out a method best suited for reducing noise in gel images. Among the compared methods there are the classical methods of linear filtering, e.g., the mean and Gaussian filtering, the nonlinear method, i.e., median filtering, and also the methods better suited for processing of nonstationary signals, such as spatially adaptive linear filtering and filtering in the wavelet domain. The best results are obtained by filtering of gel images in the wavelet domain, using the BayesThresh method of threshold value determination.     

Estimation and comparison of changes in the presence of informative right censoring: conditional linear model

A general linear regression model for the usual least squares estimated rate of change (slope) on censoring time is described as an approximation to account for informative right censoring in estimating and comparing changes of a continuous variable in two groups. Two noniterative estimators for the group slope means, the linear minimum variance unbiased (LMVUB) estimator and the linear minimum mean squared error (LMMSE) estimator, are proposed under this conditional model. In realistic situations, we illustrate that the LMVUB and LMMSE estimators, derived under a simple linear regression model, are quite competitive compared to the pseudo maximum likelihood estimator (PMLE) derived by modeling the censoring probabilities. Generalizations to polynomial response curves and general linear models are also described.     

On an Efficient Regression Type Estimator

The regression type estimator proposed by KAUR (1985) is considered. Another expression for the approximated mean square error (AMSE), to a first degree of approximation, is obtained. This AMSE is also minimized with respect to a parameter α. Three numerical examples are included. These numerical examples show that this estimator is not significantly more efficient than regression estimator and with respect to ratio and sample mean estimators, it does not always exhibit a high efficiency, as was contended by KAUR (1985). Moreover, an upper bound for the relative precision of the proposed estimator with respect to linear regression estimator is derived.     

The blu Blur: mutation of a vesicular glutamate transporter reduces the resolution of zebrafish vision

Vesicular transporters mediate the packaging of neurotransmitters into synaptic vesicles and can therefore control the amount of neurotransmitter released into the synaptic cleft. In this issue of Neuron, Smear et al. demonstrate that mutation of a vesicular glutamate transporter (Vglut) found in the retinal ganglion cells (RGCs) of zebrafish alters both the synaptic transmission and connectivity between RGCs and their targets, limiting the transfer of visually evoked activity from RGCs and degrading behaviors that depend on high-acuity vision.     

Direction selectivity of excitation and inhibition in simple cells of the cat primary visual cortex

Direction selectivity in simple cells of primary visual cortex, defined from their spike responses, cannot be predicted using linear models. It has been suggested that the shunting inhibition evoked by visual stimulation is responsible for the nonlinear component of direction selectivity. Cortical inhibition would suppress a neuron's firing when stimuli move in the nonpreferred direction, but would allow responses to stimuli in the preferred direction. Models of direction selectivity based solely on input from the lateral geniculate nucleus, however, propose that the nonlinear response is caused by spike threshold. By extracting excitatory and inhibitory components of synaptic inputs from intracellular records obtained in vivo, we demonstrate that excitation and inhibition are tuned for the same direction, but differ in relative timing. Further, membrane potential responses combine in a linear fashion. Spike threshold, however, quantitatively accounts for the nonlinear component of direction selectivity, amplifying the direction selectivity of spike output relative to that of synaptic inputs.     

SNARE proteins and schizophrenia: linking synaptic and neurodevelopmental hypotheses

Much of the focus of neurobiological research into schizophrenia is based on the concept that disrupted synaptic connectivity underlies the pathology of the disorder. Disruption of synaptic connectivity is proposed to be a consequence of both disrupted synaptic transmission in adulthood and abnormalities in the processes controlling synaptic connectivity during development of the central nervous system. This synaptic hypothesis fits with neurodevelopmental models of schizophrenia and our understanding of the mechanisms of antipsychotic medication. This conceptual model has fostered efforts to define the exact synaptic pathology further. Synaptic proteins are obvious candidates for such studies, and the integral role of the SNARE complex, and SNARE-associated proteins, in synaptic transmission will ensure that it is the focus of much of this research. Significant new insights into the role of this complex are arising from new mouse models of human disease. Here the evidence from both animal and human clinical studies showing that the SNARE complex has a key role to play in the aetiology and pathogenesis of schizophrenia is discussed.     

Regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements

We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.     

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.     

An Efficient Regression Type Estimator in Survey Sampling

For the estimation of population mean in simple random sampling, an efficient regression-type estimator is proposed which is more efficient than the conventional regression estimator and hence than mean per unit estimator, ratio and product estimators and many other estimators proposed by various authors. Some numerical examples are included for illustration.     

Nitric oxide: an unconventional messenger in the nervous system of an orthopteroid insect

Nitric oxide (NO) is a membrane-permeant messenger molecule generated from the amino acid L-arginine. NO can activate soluble guanylyl cyclase leading to the formation of cyclic GMP (cGMP) in target cells. In the nervous system, NO/cGMP signalling is thought to play essential roles in synaptic plasticity during development and also in the mature animal. This paper examines biochemical, cell biological, and physiological investigations of NO/cGMP signalling in the nervous system of the locust, a commonly used neurobiological preparation. Biochemical investigations suggest that an identical enzyme is responsible for both NO synthase (NOS) and NADPH-diaphorase activity after tissue fixation. Immunocytochemical staining of an olfactory center in the locust brain shows that NOS-immunoreactivity colocalizes with NADPH-diaphorase at the cellular level. The cytochemical staining of NO donor and target cells in adult animals suggests functions in olfaction, vision, and sensorimotor integration. During development, NO is implicated in axonal outgrowth and synaptogenesis. The cellular distribution of NO-responsive cells in neural circuits reflects potential functions of NO as a retrograde synaptic messenger, as an intracellular messenger, and as a lateral diffusible messenger independent of conventional synaptic connectivity.     

Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-Term Plastic Synapses

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.     

Novel use of matched filtering for synaptic event detection and extraction

Efficient and dependable methods for detection and measurement of synaptic events are important for studies of synaptic physiology and neuronal circuit connectivity. As the published methods with detection algorithms based upon amplitude thresholding and fixed or scaled template comparisons are of limited utility for detection of signals with variable amplitudes and superimposed events that have complex waveforms, previous techniques are not applicable for detection of evoked synaptic events in photostimulation and other similar experimental situations. Here we report on a novel technique that combines the design of a bank of approximate matched filters with the detection and estimation theory to automatically detect and extract photostimluation-evoked excitatory postsynaptic currents (EPSCs) from individually recorded neurons in cortical circuit mapping experiments. The sensitivity and specificity of the method were evaluated on both simulated and experimental data, with its performance comparable to that of visual event detection performed by human operators. This new technique was applied to quantify and compare the EPSCs obtained from excitatory pyramidal cells and fast-spiking interneurons. In addition, our technique has been further applied to the detection and analysis of inhibitory postsynaptic current (IPSC) responses. Given the general purpose of our matched filtering and signal recognition algorithms, we expect that our technique can be appropriately modified and applied to detect and extract other types of electrophysiological and optical imaging signals.     

Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.     

A Bayesian compressed-sensing approach for reconstructing neural connectivity from subsampled anatomical data

In recent years, the problem of reconstructing the connectivity in large neural circuits ("connectomics") has re-emerged as one of the main objectives of neuroscience. Classically, reconstructions of neural connectivity have been approached anatomically, using electron or light microscopy and histological tracing methods. This paper describes a statistical approach for connectivity reconstruction that relies on relatively easy-to-obtain measurements using fluorescent probes such as synaptic markers, cytoplasmic dyes, transsynaptic tracers, or activity-dependent dyes. We describe the possible design of these experiments and develop a Bayesian framework for extracting synaptic neural connectivity from such data. We show that the statistical reconstruction problem can be formulated naturally as a tractable L (1)-regularized quadratic optimization. As a concrete example, we consider a realistic hypothetical connectivity reconstruction experiment in C. elegans, a popular neuroscience model where a complete wiring diagram has been previously obtained based on long-term electron microscopy work. We show that the new statistical approach could lead to an orders of magnitude reduction in experimental effort in reconstructing the connectivity in this circuit. We further demonstrate that the spatial heterogeneity and biological variability in the connectivity matrix-not just the "average" connectivity-can also be estimated using the same method.