Time-evolving controllability of effective connectivity networks during seizure progression.

Over one third of the estimated 3 million people with epilepsy in the United States are medication resistant. Responsive neurostimulation from chronically implanted electrodes provides a promising treatment alternative to resective surgery. However, determining optimal personalized stimulation parameters, including when and where to intervene to guarantee a positive patient outcome, is a major open challenge. Network neuroscience and control theory offer useful tools that may guide improvements in parameter selection for control of anomalous neural activity. Here we use a method to characterize dynamic controllability across consecutive effective connectivity (EC) networks based on regularized partial correlations between implanted electrodes during the onset, propagation, and termination regimes of 34 seizures. We estimate regularized partial correlation adjacency matrices from 1-s time windows of intracranial electrocorticography recordings using the Graphical Least Absolute Shrinkage and Selection Operator (GLASSO). Average and modal controllability metrics calculated from each resulting EC network track the time-varying controllability of the brain on an evolving landscape of conditionally dependent network interactions. We show that average controllability increases throughout a seizure and is negatively correlated with modal controllability throughout. Our results support the hypothesis that the energy required to drive the brain to a seizure-free state from an ictal state is smallest during seizure onset, yet we find that applying control energy at electrodes in the seizure onset zone may not always be energetically favorable. Our work suggests that a low-complexity model of time-evolving controllability may offer insights for developing and improving control strategies targeting seizure suppression.

Spectral guided sparse inverse covariance estimation of metabolic networks in Parkinson's disease.

In neurodegenerative disorders, a clearer understanding of the underlying aberrant networks facilitates the search for effective therapeutic targets and potential cures. [18F]-fluorodeoxyglucose (FDG) positron emission tomography (PET) imaging data of brain metabolism reflects the distribution of glucose consumption known to be directly related to neural activity. In FDG PET resting-state metabolic data, characteristic disease-related patterns have been identified in group analysis of various neurodegenerative conditions using principal component analysis of multivariate spatial covariance. Notably, among several parkinsonian syndromes, the identified Parkinson's disease-related pattern (PDRP) has been repeatedly validated as an imaging biomarker of PD in independent groups worldwide. Although the primary nodal associations of this network are known, its connectivity is not fully understood. Here, we describe a novel approach to elucidate functional principal component (PC) network connections by performing graph theoretical sparse network derivation directly within the disease relevant PC partition layer of the whole brain data rather than by searching for associations retrospectively in whole brain sparse representations. Using sparse inverse covariance estimation of each overlapping PC partition layer separately, a single coherent network is detected for each layer in contrast to more spatially modular segmentation in whole brain data analysis. Using this approach, the major nodal hubs of the PD disease network are identified and their characteristic functional pathways are clearly distinguished within the basal ganglia, midbrain and parietal areas. Network associations are further clarified using Laplacian spectral analysis of the adjacency matrices. In addition, the innate discriminative capacity of the eigenvector centrality of the graph derived networks in differentiating PD versus healthy external data provides evidence of their validity.

COUSCOus: improved protein contact prediction using an empirical Bayes covariance estimator.

BACKGROUND: The post-genomic era with its wealth of sequences gave rise to a broad range of protein residue-residue contact detecting methods. Although various coevolution methods such as PSICOV, DCA and plmDCA provide correct contact predictions, they do not completely overlap. Hence, new approaches and improvements of existing methods are needed to motivate further development and progress in the field. We present a new contact detecting method, COUSCOus, by combining the best shrinkage approach, the empirical Bayes covariance estimator and GLasso. RESULTS: Using the original PSICOV benchmark dataset, COUSCOus achieves mean accuracies of 0.74, 0.62 and 0.55 for the top L/10 predicted long, medium and short range contacts, respectively. In addition, COUSCOus attains mean areas under the precision-recall curves of 0.25, 0.29 and 0.30 for long, medium and short contacts and outperforms PSICOV. We also observed that COUSCOus outperforms PSICOV w.r.t. Matthew's correlation coefficient criterion on full list of residue contacts. Furthermore, COUSCOus achieves on average 10% more gain in prediction accuracy compared to PSICOV on an independent test set composed of CASP11 protein targets. Finally, we showed that when using a simple random forest meta-classifier, by combining contact detecting techniques and sequence derived features, PSICOV predictions should be replaced by the more accurate COUSCOus predictions. CONCLUSION: We conclude that the consideration of superior covariance shrinkage approaches will boost several research fields that apply the GLasso procedure, amongst the presented one of residue-residue contact prediction as well as fields such as gene network reconstruction.

Sparse networks of directly coupled, polymorphic, and functional side chains in allosteric proteins.

Recent studies have highlighted the role of coupled side-chain fluctuations alone in the allosteric behavior of proteins. Moreover, examination of X-ray crystallography data has recently revealed new information about the prevalence of alternate side-chain conformations (conformational polymorphism), and attempts have been made to uncover the hidden alternate conformations from X-ray data. Hence, new computational approaches are required that consider the polymorphic nature of the side chains, and incorporate the effects of this phenomenon in the study of information transmission and functional interactions of residues in a molecule. These studies can provide a more accurate understanding of the allosteric behavior. In this article, we first present a novel approach to generate an ensemble of conformations and an efficient computational method to extract direct couplings of side chains in allosteric proteins, and provide sparse network representations of the couplings. We take the side-chain conformational polymorphism into account, and show that by studying the intrinsic dynamics of an inactive structure, we are able to construct a network of functionally crucial residues. Second, we show that the proposed method is capable of providing a magnified view of the coupled and conformationally polymorphic residues. This model reveals couplings between the alternate conformations of a coupled residue pair. To the best of our knowledge, this is the first computational method for extracting networks of side chains' alternate conformations. Such networks help in providing a detailed image of side-chain dynamics in functionally important and conformationally polymorphic sites, such as binding and/or allosteric sites.

Parkinson's disease progression: Increasing expression of an invariant common core subnetwork.

Notable success has been achieved in the study of neurodegenerative conditions using reduction techniques such as principal component analysis (PCA) and sparse inverse covariance estimation (SICE) in positron emission tomography (PET) data despite their widely differing approach. In a recent study of SICE applied to metabolic scans from Parkinson's disease (PD) patients, we showed that by using PCA to prespecify disease-related partition layers, we were able to optimize maps of functional metabolic connectivity within the relevant networks. Here, we show the potential of SICE, enhanced by disease-specific subnetwork partitions, to identify key regional hubs and their connections, and track their associations in PD patients with increasing disease duration. This approach enabled the identification of a core zone that included elements of the striatum, pons, cerebellar vermis, and parietal cortex and provided a deeper understanding of progressive changes in their connectivity. This subnetwork constituted a robust invariant disease feature that was unrelated to phenotype. Mean expression levels for this subnetwork increased steadily in a group of 70 PD patients spanning a range of symptom durations between 1 and 21 years. The findings were confirmed in a validation sample of 69 patients with up to 32 years of symptoms. The common core elements represent possible targets for disease modification, while their connections to external regions may be better suited for symptomatic treatment.

Learning gene regulatory networks using gaussian process emulator and graphical LASSO.

Large amounts of research efforts have been focused on learning gene regulatory networks (GRNs) based on gene expression data to understand the functional basis of a living organism. Under the assumption that the joint distribution of the gene expressions of interest is a multivariate normal distribution, such networks can be constructed by assessing the nonzero elements of the inverse covariance matrix, the so-called precision matrix or concentration matrix. This may not reflect the true connectivity between genes by considering just pairwise linear correlations. To relax this limitative constraint, we employ Gaussian process (GP) model which is well known as computationally efficient non-parametric Bayesian machine learning technique. GPs are among a class of methods known as kernel machines which can be used to approximate complex problems by tuning their hyperparameters. In fact, GP creates the ability to use the capacity and potential of different kernels in constructing precision matrix and GRNs. In this paper, in the first step, we choose the GP with appropriate kernel to learn the considered GRNs from the observed genetic data, and then we estimate kernel hyperparameters using rule-of-thumb technique. Using these hyperparameters, we can also control the degree of sparseness in the precision matrix. Then we obtain kernel-based precision matrix similar to GLASSO to construct kernel-based GRN. The findings of our research are used to construct GRNs with high performance, for different species of Drosophila fly rather than simply using the assumption of multivariate normal distribution, and the GPs, despite the use of the kernels capacity, have a much better performance than the multivariate Gaussian distribution assumption.

Unsupervised Network Analysis of the Plastic Supraoptic Nucleus Transcriptome Predicts Caprin2 Regulatory Interactions.

The supraoptic nucleus (SON) is a group of neurons in the hypothalamus responsible for the synthesis and secretion of the peptide hormones vasopressin and oxytocin. Following physiological cues, such as dehydration, salt-loading and lactation, the SON undergoes a function related plasticity that we have previously described in the rat at the transcriptome level. Using the unsupervised graphical lasso (Glasso) algorithm, we reconstructed a putative network from 500 plastic SON genes in which genes are the nodes and the edges are the inferred interactions. The most active nodal gene identified within the network was Caprin2. Caprin2 encodes an RNA-binding protein that we have previously shown to be vital for the functioning of osmoregulatory neuroendocrine neurons in the SON of the rat hypothalamus. To test the validity of the Glasso network, we either overexpressed or knocked down Caprin2 transcripts in differentiated rat pheochromocytoma PC12 cells and showed that these manipulations had significant opposite effects on the levels of putative target mRNAs. These studies suggest that the predicative power of the Glasso algorithm within an in vivo system is accurate, and identifies biological targets that may be important to the functional plasticity of the SON.

Multiple Response Regression for Gaussian Mixture Models with Known Labels.

Multiple response regression is a useful regression technique to model multiple response variables using the same set of predictor variables. Most existing methods for multiple response regression are designed for modeling homogeneous data. In many applications, however, one may have heterogeneous data where the samples are divided into multiple groups. Our motivating example is a cancer dataset where the samples belong to multiple cancer subtypes. In this paper, we consider modeling the data coming from a mixture of several Gaussian distributions with known group labels. A naive approach is to split the data into several groups according to the labels and model each group separately. Although it is simple, this approach ignores potential common structures across different groups. We propose new penalized methods to model all groups jointly in which the common and unique structures can be identified. The proposed methods estimate the regression coefficient matrix, as well as the conditional inverse covariance matrix of response variables. Asymptotic properties of the proposed methods are explored. Through numerical examples, we demonstrate that both estimation and prediction can be improved by modeling all groups jointly using the proposed methods. An application to a glioblastoma cancer dataset reveals some interesting common and unique gene relationships across different cancer subtypes.

The huge Package for High-dimensional Undirected Graph Estimation in R.

We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data. This package implements recent results in the literature, including Friedman et al. (2007), Liu et al. (2009, 2012) and Liu et al. (2010). Compared with the existing graph estimation package glasso, the huge package provides extra features: (1) instead of using Fortan, it is written in C, which makes the code more portable and easier to modify; (2) besides fitting Gaussian graphical models, it also provides functions for fitting high dimensional semiparametric Gaussian copula models; (3) more functions like data-dependent model selection, data generation and graph visualization; (4) a minor convergence problem of the graphical lasso algorithm is corrected; (5) the package allows the user to apply both lossless and lossy screening rules to scale up large-scale problems, making a tradeoff between computational and statistical efficiency.