Tensor Entropy for Uniform Hypergraphs

Lü³

et al. 2020

Preprint

Self Cite

The combined analysis of genome structure and function over time, and how these changes affect cellular phenotype, is referred to as the 4D Nucleome (4DN). 4DN analysis is necessary to fully understand how a cell operates, but 4DN analysis tools are currently underdeveloped. We present the "4DNvestigator", a user-friendly toolbox for the analysis of time-series genome structure, measured by genome-wide chromosome conformation capture (Hi-C), and genome function, measured by RNA sequencing (RNAseq).

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

4DNvestigator: Time Series Genomic Data Analysis Toolbox

Lindsly

Lü³

et al. 2020

Preprint

Self Cite

“…We can construct -uniform hypergraphs from Hi-C contact matrices by computing the multi-correlations of genomic loci. Tensor entropy, an extension of network entropy, measures the uncertainty or disorganization of uniform hypergraphs [ 24 ]. Tensor entropy can be computed from the same entropy formula (1) with generalized singular values from tensor theory [ 24 , 25 ].…”

Section: Tensor Entropymentioning

confidence: 99%

“…Tensor entropy, an extension of network entropy, measures the uncertainty or disorganization of uniform hypergraphs [ 24 ]. Tensor entropy can be computed from the same entropy formula (1) with generalized singular values from tensor theory [ 24 , 25 ]. We provide the definitions for multi-correlation and generalized singular values, the algorithm to compute tensor entropy, and an application of tensor entropy on Hi-C data in Supplementary Materials ‘Tensor Entropy’.…”

Section: Tensor Entropymentioning

confidence: 99%

4DNvestigator: time series genomic data analysis toolbox

Lindsly

Liu

et al. 2021

Nucleus

Self Cite

Data on genome organization and output over time, or the 4D Nucleome (4DN), require synthesis for meaningful interpretation. Development of tools for the efficient integration of these data is needed, especially for the time dimension. We present the ‘4DNvestigator’, a user-friendly network-based toolbox for the analysis of time series genome-wide genome structure (Hi-C) and gene expression (RNA-seq) data. Additionally, we provide methods to quantify network entropy, tensor entropy, and statistically significant changes in time series Hi-C data at different genomic scales.

“…The von Neumann entropy of a network, introduced by Braunstein et al ( 23 ), is a spectral measure used in structural pattern recognition. The intuition behind this measure is linking the graph Laplacian to density matrices from quantum mechanics and measuring the complexity of the networks in terms of the von Neumman entropy of the corresponding density matrices ( 58 , 59 ). In addition, the measure can be viewed as the information theoretic Shannon entropy: that is,

where

are the normalized eigenvalues of the Laplacian matrix of a network such that

1

.…”

Section: Methodsmentioning

confidence: 99%

Network dynamics of hypothalamic feeding neurons

Sweeney

Proc. Natl. Acad. Sci. U.S.A.

Rajapakse

et al. 2021

Self Cite

Mutations in the melanocortin 4 receptor (MC4R) result in hyperphagia and obesity and are the most common cause of monogenic obesity in humans. Preclinical rodent studies have determined that the critical role of the MC4R in controlling feeding can be mapped in part to its expression in the paraventricular nucleus of the hypothalamus (paraventricular nucleus [PVN]), where it regulates the activity of anorexic neural circuits. Despite the critical role of PVN MC4R neurons in regulating feeding, the in vivo neuronal activity of these cells remains largely unstudied, and the network activity of PVN MC4R neurons has not been determined. Here, we utilize in vivo single-cell endomicroscopic and mathematical approaches to determine the activity and network dynamics of PVN MC4R neurons in response to changes in energy state and pharmacological manipulation of central melanocortin receptors. We determine that PVN MC4R neurons exhibit both quantitative and qualitative changes in response to fasting and refeeding. Pharmacological stimulation of MC4R with the therapeutic MC4R agonist setmelanotide rapidly increases basal PVN MC4R activity, while stimulation of melanocortin 3 receptor (MC3R) inhibits PVN MC4R activity. Finally, we find that distinct PVN MC4R neuronal ensembles encode energy deficit and energy surfeit and that energy surfeit is associated with enhanced network connections within PVN MC4R neurons. These findings provide valuable insight into the neural dynamics underlying hunger and energy surfeit.