8213028
Are scale-free networks robust to measurement errors?
BackgroundMany complex random networks have been found to be scale-free. Existing literature on scale-free networks has rarely considered potential false positive and false negative links in the observed networks, especially in biological networks inferred from high-throughput experiments. Therefore, it is important to study the impact of these measurement errors on the topology of the observed networks.ResultsThis article addresses the impact of erroneous links on network topological inference and explores possible error mechanisms for scale-free networks with an emphasis on Saccharomyces cerevisiae protein interaction networks. We study this issue by both theoretical derivations and simulations. We show that the ignorance of erroneous links in network analysis may lead to biased estimates of the scale parameter and recommend robust estimators in such scenarios. Possible error mechanisms of yeast protein interaction networks are explored by comparisons between real data and simulated data.ConclusionOur studies show that, in the presence of erroneous links, the connectivity distribution of scale-free networks is still scale-free for the middle range connectivities, but can be greatly distorted for low and high connecitivities. It is more appropriate to use robust estimators such as the least trimmed mean squares estimator to estimate the scale parameter γ under such circumstances. Moreover, we show by simulation studies that the scale-free property is robust to some error mechanisms but untenable to others. The simulation results also suggest that different error mechanisms may be operating in the yeast protein interaction networks produced from different data sources. In the MIPS gold standard protein interaction data, there appears to be a high rate of false negative links, and the false negative and false positive rates are more or less constant across proteins with different connectivities. However, the error mechanism of yeast two-hybrid data may be very different, where the overall false negative rate is low and the false negative rates tend to be higher for links involving proteins with more interacting partners.
10817560
Information assessment on predicting protein-protein interactions
BackgroundIdentifying protein-protein interactions is fundamental for understanding the molecular machinery of the cell. Proteome-wide studies of protein-protein interactions are of significant value, but the high-throughput experimental technologies suffer from high rates of both false positive and false negative predictions. In addition to high-throughput experimental data, many diverse types of genomic data can help predict protein-protein interactions, such as mRNA expression, localization, essentiality, and functional annotation. Evaluations of the information contributions from different evidences help to establish more parsimonious models with comparable or better prediction accuracy, and to obtain biological insights of the relationships between protein-protein interactions and other genomic information.ResultsOur assessment is based on the genomic features used in a Bayesian network approach to predict protein-protein interactions genome-wide in yeast. In the special case, when one does not have any missing information about any of the features, our analysis shows that there is a larger information contribution from the functional-classification than from expression correlations or essentiality. We also show that in this case alternative models, such as logistic regression and random forest, may be more effective than Bayesian networks for predicting interactions.ConclusionsIn the restricted problem posed by the complete-information subset, we identified that the MIPS and Gene Ontology (GO) functional similarity datasets as the dominating information contributors for predicting the protein-protein interactions under the framework proposed by Jansen et al. Random forests based on the MIPS and GO information alone can give highly accurate classifications. In this particular subset of complete information, adding other genomic data does little for improving predictions. We also found that the data discretizations used in the Bayesian methods decreased classification performance.
2217384
A semiparametric approach for marker gene selection based on gene expression data
MOTIVATION
Identification of differentially expressed genes is a major issue in gene expression data analysis and selection of marker genes is critical in tumor classification using gene expression data. In this paper, we propose a semiparametric two-sample test to identify both differentially expressed genes and select marker genes for sample classification.


RESULTS
A simulation study shows that the proposed method is more robust and powerful than the methods, generally used such as t-tests and non-parametric rank-sum tests, when the sample size is small. Cross-validation shows that the sample classification based on genes selected using this semiparametric method has lower misclassification rates.


CONTACT
hongyu.zhao@yale.edu.
11712321
HAPLORE: a program for haplotype reconstruction in general pedigrees without recombination
MOTIVATION
Haplotype reconstruction is an essential step in genetic linkage and association studies. Although many methods have been developed to estimate haplotype frequencies and reconstruct haplotypes for a sample of unrelated individuals, haplotype reconstruction in large pedigrees with a large number of genetic markers remains a challenging problem.


METHODS
We have developed an efficient computer program, HAPLORE (HAPLOtype REconstruction), to identify all haplotype sets that are compatible with the observed genotypes in a pedigree for tightly linked genetic markers. HAPLORE consists of three steps that can serve different needs in applications. In the first step, a set of logic rules is used to reduce the number of compatible haplotypes of each individual in the pedigree as much as possible. After this step, the haplotypes of all individuals in the pedigree can be completely or partially determined. These logic rules are applicable to completely linked markers and they can be used to impute missing data and check genotyping errors. In the second step, a haplotype-elimination algorithm similar to the genotype-elimination algorithms used in linkage analysis is applied to delete incompatible haplotypes derived from the first step. All superfluous haplotypes of the pedigree members will be excluded after this step. In the third step, the expectation-maximization (EM) algorithm combined with the partition and ligation technique is used to estimate haplotype frequencies based on the inferred haplotype configurations through the first two steps. Only compatible haplotype configurations with haplotypes having frequencies greater than a threshold are retained.


RESULTS
We test the effectiveness and the efficiency of HAPLORE using both simulated and real datasets. Our results show that, the rule-based algorithm is very efficient for completely genotyped pedigree. In this case, almost all of the families have one unique haplotype configuration. In the presence of missing data, the number of compatible haplotypes can be substantially reduced by HAPLORE, and the program will provide all possible haplotype configurations of a pedigree under different circumstances, if such multiple configurations exist. These inferred haplotype configurations, as well as the haplotype frequencies estimated by the EM algorithm, can be used in genetic linkage and association studies.


AVAILABILITY
The program can be downloaded from http://bioinformatics.med.yale.edu.
7867544
A statistical method for identifying differential gene-gene co-expression patterns
MOTIVATION
To understand cancer etiology, it is important to explore molecular changes in cellular processes from normal state to cancerous state. Because genes interact with each other during cellular processes, carcinogenesis related genes may form differential co-expression patterns with other genes in different cell states. In this study, we develop a statistical method for identifying differential gene-gene co-expression patterns in different cell states.


RESULTS
For efficient pattern recognition, we extend the traditional F-statistic and obtain an Expected Conditional F-statistic (ECF-statistic), which incorporates statistical information of location and correlation. We also propose a statistical method for data transformation. Our approach is applied to a microarray gene expression dataset for prostate cancer study. For a gene of interest, our method can select other genes that have differential gene-gene co-expression patterns with this gene in different cell states. The 10 most frequently selected genes, include hepsin, GSTP1 and AMACR, which have recently been proposed to be associated with prostate carcinogenesis. However, genes GSTP1 and AMACR cannot be identified by studying differential gene expression alone. By using tumor suppressor genes TP53, PTEN and RB1, we identify seven genes that also include hepsin, GSTP1 and AMACR. We show that genes associated with cancer may have differential gene-gene expression patterns with many other genes in different cell states. By discovering such patterns, we may be able to identify carcinogenesis related genes.
11367648
Inferring protein-protein interactions through high-throughput interaction data from diverse organisms
MOTIVATION
Identifying protein-protein interactions is critical for understanding cellular processes. Because protein domains represent binding modules and are responsible for the interactions between proteins, computational approaches have been proposed to predict protein interactions at the domain level. The fact that protein domains are likely evolutionarily conserved allows us to pool information from data across multiple organisms for the inference of domain-domain and protein-protein interaction probabilities.


RESULTS
We use a likelihood approach to estimating domain-domain interaction probabilities by integrating large-scale protein interaction data from three organisms, Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster. The estimated domain-domain interaction probabilities are then used to predict protein-protein interactions in S.cerevisiae. Based on a thorough comparison of sensitivity and specificity, Gene Ontology term enrichment and gene expression profiles, we have demonstrated that it may be far more informative to predict protein-protein interactions from diverse organisms than from a single organism.


AVAILABILITY
The program for computing the protein-protein interaction probabilities and supplementary material are available at http://bioinformatics.med.yale.edu/interaction.
17735073
On problems and conjectures on adjointly equivalent graphs
For a graph G, let h(G,x) denote its adjoint polynomial and @b(G) denote the minimum real root of h(G,x). Two graphs H and G are said to be adjointly equivalent if h(H,x)=h(G,x). Let F"1={G|@b(G)>-4} and F"2={G|@b(G)>=-4}. In this paper, we give a necessary and sufficient condition for two graphs H and G in F"i to be adjointly equivalent, where i=1,2. We also solve some problems and conjectures proposed by Dong et al. (Discrete Math. 258 (2002) 303-321).
1139392
Pathway analysis using random forests classification and regression
MOTIVATION
Although numerous methods have been developed to better capture biological information from microarray data, commonly used single gene-based methods neglect interactions among genes and leave room for other novel approaches. For example, most classification and regression methods for microarray data are based on the whole set of genes and have not made use of pathway information. Pathway-based analysis in microarray studies may lead to more informative and relevant knowledge for biological researchers.


RESULTS
In this paper, we describe a pathway-based classification and regression method using Random Forests to analyze gene expression data. The proposed methods allow researchers to rank important pathways from externally available databases, discover important genes, find pathway-based outlying cases and make full use of a continuous outcome variable in the regression setting. We also compared Random Forests with other machine learning methods using several datasets and found that Random Forests classification error rates were either the lowest or the second-lowest. By combining pathway information and novel statistical methods, this procedure represents a promising computational strategy in dissecting pathways and can provide biological insight into the study of microarray data.


AVAILABILITY
Source code written in R is available from http://bioinformatics.med.yale.edu/pathway-analysis/rf.htm.
37263695
A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs
Let P(G,@l) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P(H,@l)=P(G,@l) implies [email protected]?G. Koh, Teo and Chia conjectured that for any integers n and k with n>=k+2>=4, the complete tripartite graph K(n-k,n,n) is chromatically unique. Let K(n,m,r)-S denote the graph obtained by deleting all edges in S from the complete tripartite K(n,m,r). In this paper, we establish that for any positive integer n>=m>=r>=2, the chromatic equivalence class of K(n,m,r) is contained in the family {K(x,y,z)-S|1==2k and k>=2.
12416682
Handling multiple testing while interpreting microarrays with the Gene Ontology Database
BackgroundThe development of software tools that analyze microarray data in the context of genetic knowledgebases is being pursued by multiple research groups using different methods. A common problem for many of these tools is how to correct for multiple statistical testing since simple corrections are overly conservative and more sophisticated corrections are currently impractical. A careful study of the nature of the distribution one would expect by chance, such as by a simulation study, may be able to guide the development of an appropriate correction that is not overly time consuming computationally.ResultsWe present the results from a preliminary study of the distribution one would expect for analyzing sets of genes extracted from Drosophila, S. cerevisiae, Wormbase, and Gramene databases using the Gene Ontology Database.ConclusionsWe found that the estimated distribution is not regular and is not predictable outside of a particular set of genes. Permutation-based simulations may be necessary to determine the confidence in results of such analyses.
1436574
Scheduling multiple DAGs onto heterogeneous systems
The problem of scheduling a single DAG onto heterogeneous systems has been studied extensively. In this paper, we focus on the problem of scheduling more than one DAG at the same time onto a set of heterogeneous resources. The aim is not only to optimize the overall makespan, but also to achieve fairness, defined on the basis of the slowdown that each DAG would experience as a result of competing for resources with other DAGs. Two policies particularly focussing to deliver fairness are presented and evaluated along with another four policies that can be used to schedule multiple DAGs.