Inferring Gene Regulatory Networks by Singular Value Decomposition and Gravitation Field Algorithm

Reconstruction of gene regulatory networks (GRNs) is of utmost interest and has become a challenge computational problem in system biology. However, every existing inference algorithm from gene expression profiles has its own advantages and disadvantages. In particular, the effectiveness and efficiency of every previous algorithm is not high enough. In this work, we proposed a novel inference algorithm from gene expression data based on differential equation model. In this algorithm, two methods were included for inferring GRNs. Before reconstructing GRNs, singular value decomposition method was used to decompose gene expression data, determine the algorithm solution space, and get all candidate solutions of GRNs. In these generated family of candidate solutions, gravitation field algorithm was modified to infer GRNs, used to optimize the criteria of differential equation model, and search the best network structure result. The proposed algorithm is validated on both the simulated scale-free network and real benchmark gene regulatory network in networks database. Both the Bayesian method and the traditional differential equation model were also used to infer GRNs, and the results were used to compare with the proposed algorithm in our work. And genetic algorithm and simulated annealing were also used to evaluate gravitation field algorithm. The cross-validation results confirmed the effectiveness of our algorithm, which outperforms significantly other previous algorithms.     

Analysis of Metabolic Capabilities Using Singular Value Decomposition of Extreme Pathway Matrices

It is now possible to construct genome-scale metabolic networks for particular microorganisms. Extreme pathway analysis is a useful method for analyzing the phenotypic capabilities of these networks. Many extreme pathways are needed to fully describe the functional capabilities of genome-scale metabolic networks, and therefore, a need exists to develop methods to study these large sets of extreme pathways. Singular value decomposition (SVD) of matrices of extreme pathways was used to develop a conceptual framework for the interpretation of large sets of extreme pathways and the steady-state flux solution space they define. The key results of this study were: 1), convex steady-state solution cones describing the potential functions of biochemical networks can be studied using the modes generated by SVD; 2), Helicobacter pylori has a more rigid metabolic network (i.e., a lower dimensional solution space and a more dominant first singular value) than Haemophilus influenzae for the production of amino acids; and 3), SVD allows for direct comparison of different solution cones resulting from the production of different amino acids. SVD was used to identify key network branch points that may identify key control points for regulation. Therefore, SVD of matrices of extreme pathways has proved to be a useful method for analyzing the steady-state solution space of genome-scale metabolic networks.     

Exploring metabolic pathway disruption in the subchronic phencyclidine model of schizophrenia with the Generalized Singular Value Decomposition

Background

One of the major goals in gene and protein expression profiling of cancer is to identify biomarkers and build classification models for prediction of disease prognosis or treatment response. Many traditional statistical methods, based on microarray gene expression data alone and individual genes' discriminatory power, often fail to identify biologically meaningful biomarkers thus resulting in poor prediction performance across data sets. Nonetheless, the variables in multivariable classifiers should synergistically interact to produce more effective classifiers than individual biomarkers.

Results

We developed an integrated approach, namely network-constrained support vector machine (netSVM), for cancer biomarker identification with an improved prediction performance. The netSVM approach is specifically designed for network biomarker identification by integrating gene expression data and protein-protein interaction data. We first evaluated the effectiveness of netSVM using simulation studies, demonstrating its improved performance over state-of-the-art network-based methods and gene-based methods for network biomarker identification. We then applied the netSVM approach to two breast cancer data sets to identify prognostic signatures for prediction of breast cancer metastasis. The experimental results show that: (1) network biomarkers identified by netSVM are highly enriched in biological pathways associated with cancer progression; (2) prediction performance is much improved when tested across different data sets. Specifically, many genes related to apoptosis, cell cycle, and cell proliferation, which are hallmark signatures of breast cancer metastasis, were identified by the netSVM approach. More importantly, several novel hub genes, biologically important with many interactions in PPI network but often showing little change in expression as compared with their downstream genes, were also identified as network biomarkers; the genes were enriched in signaling pathways such as TGF-beta signaling pathway, MAPK signaling pathway, and JAK-STAT signaling pathway. These signaling pathways may provide new insight to the underlying mechanism of breast cancer metastasis.

Conclusions

We have developed a network-based approach for cancer biomarker identification, netSVM, resulting in an improved prediction performance with network biomarkers. We have applied the netSVM approach to breast cancer gene expression data to predict metastasis in patients. Network biomarkers identified by netSVM reveal potential signaling pathways associated with breast cancer metastasis, and help improve the prediction performance across independent data sets.     

Combining Distance Matrices on Identical Taxon Sets for Multi-Gene Analysis with Singular Value Decomposition

We present a simple and effective method for combining distance matrices from multiple genes on identical taxon sets to obtain a single representative distance matrix from which to derive a combined-gene phylogenetic tree. The method applies singular value decomposition (SVD) to extract the greatest common signal present in the distances obtained from each gene. The first right eigenvector of the SVD, which corresponds to a weighted average of the distance matrices of all genes, can thus be used to derive a representative tree from multiple genes. We apply our method to three well known data sets and estimate the uncertainty using bootstrap methods. Our results show that this method works well for these three data sets and that the uncertainty in these estimates is small. A simulation study is conducted to compare the performance of our method with several other distance based approaches (namely SDM, SDM* and ACS97), and we find the performances of all these approaches are comparable in the consensus setting. The computational complexity of our method is similar to that of SDM. Besides constructing a representative tree from multiple genes, we also demonstrate how the subsequent eigenvalues and eigenvectors may be used to identify if there are conflicting signals in the data and which genes might be influential or outliers for the estimated combined-gene tree.     

奇异值分解在磁共振波谱成像中的应用

目的：磁共振波谱成像有7类快速方法,它们都来自快速MRI成像方法。本文提出的奇异值分解波谱成像不同这7类快速方法,它是把MRI中任意轨迹图像重建方法用于波谱成像,这将有利于设计出速度更快的波谱成像数据采集脉冲序列。     

Revealing the Hidden Relationship by Sparse Modules in Complex Networks with a Large-Scale Analysis

One of the remarkable features of networks is module that can provide useful insights into not only network organizations but also functional behaviors between their components. Comprehensive efforts have been devoted to investigating cohesive modules in the past decade. However, it is still not clear whether there are important structural characteristics of the nodes that do not belong to any cohesive module. In order to answer this question, we performed a large-scale analysis on 25 complex networks with different types and scales using our recently developed BTS (bintree seeking) algorithm, which is able to detect both cohesive and sparse modules in the network. Our results reveal that the sparse modules composed by the cohesively isolated nodes widely co-exist with the cohesive modules. Detailed analysis shows that both types of modules provide better characterization for the division of a network into functional units than merely cohesive modules, because the sparse modules possibly re-organize the nodes in the so-called cohesive modules, which lack obvious modular significance, into meaningful groups. Compared with cohesive modules, the sizes of sparse ones are generally smaller. Sparse modules are also found to have preferences in social and biological networks than others.     

Singular Value Decomposition of the Radial Distribution Function for Hard Sphere and Square Well Potentials

We compute the singular value decomposition of the radial distribution function for hard sphere, and square well solutions. We find that decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are well described by a low-order polynomial. We provide a program to calculate in this compact representation for the investigated parameter range.     

酵母转录调控协作网络的分析

协作网通常被用于描述各种社会关系,相似的概念也可以应用到转录调控网络的研究中.针对被调控基因共享转录因子的相似性,可以建立一个被调控基因协作网,同样,根据转录因子调控基因的相似性可以建立一个相对较小的转录因子协作网.对被调控基因协作网的聚类研究发现,大部分的类都显著地富集一个或者多个GO功能注释.进一步的结果分析发现某些GO注释的基因更倾向于共享相似的调控机制.这表明,在协作网中,相对简单的调控机制相似性能捕捉生物功能相关的信息.并且,将在二部图分析中使用的概念--"异常点"引入到协作网的分析中,发现协作网的异常点和致死基因有相关性.综上所述,协作网的方法是分析转录调控网络的一个有用的补充.     

FunHoP: Enhanced Visualization and Analysis of Functionally Homologous Proteins in Complex Metabolic Networks

Cytoscape is often used for visualization and analysis of metabolic pathways. For example, based on KEGG data, a reader for KEGG Markup Language (KGML) is used to load files into Cytoscape. However, although multiple genes can be responsible for the same reaction, the KGML-reader KEGGScape only presents the first listed gene in a network node for a given reaction. This can lead to incorrect interpretations of the pathways. Our new method, FunHoP, shows all possible genes in each node, making the pathways more complete. FunHoP collapses all genes in a node into one measurement using read counts from RNA-seq. Assuming that activity for an enzymatic reaction mainly depends upon the gene with the highest number of reads, and weighting the reads on gene length and ratio, a new expression value is calculated for the node as a whole. Differential expression at node level is then applied to the networks. Using prostate cancer as model, we integrate RNA-seq data from two patient cohorts with metabolism data from literature. Here we show that FunHoP gives more consistent pathways that are easier to interpret biologically. Code and documentation for running FunHoP can be found at https://github.com/kjerstirise/FunHoP.     

Analysis of Serum Inflammatory Mediators Identifies Unique Dynamic Networks Associated with Death and Spontaneous Survival in Pediatric Acute Liver Failure

Background

Tools to predict death or spontaneous survival are necessary to inform liver transplantation (LTx) decisions in pediatric acute liver failure (PALF), but such tools are not available. Recent data suggest that immune/inflammatory dysregulation occurs in the setting of acute liver failure. We hypothesized that specific, dynamic, and measurable patterns of immune/inflammatory dysregulation will correlate with outcomes in PALF.

Methods

We assayed 26 inflammatory mediators on stored serum samples obtained from a convenience sample of 49 children in the PALF study group (PALFSG) collected within 7 days after enrollment. Outcomes were assessed within 21 days of enrollment consisting of spontaneous survivors, non-survivors, and LTx recipients. Data were subjected to statistical analysis, patient-specific Principal Component Analysis (PCA), and Dynamic Bayesian Network (DBN) inference.

Findings

Raw inflammatory mediator levels assessed over time did not distinguish among PALF outcomes. However, DBN analysis did reveal distinct interferon-gamma-related networks that distinguished spontaneous survivors from those who died. The network identified in LTx patients pre-transplant was more like that seen in spontaneous survivors than in those who died, a finding supported by PCA.

Interpretation

The application of DBN analysis of inflammatory mediators in this small patient sample appears to differentiate survivors from non-survivors in PALF. Patterns associated with LTx pre-transplant were more like those seen in spontaneous survivors than in those who died. DBN-based analyses might lead to a better prediction of outcome in PALF, and could also have more general utility in other complex diseases with an inflammatory etiology.