True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher dimensional space. We show that the linearized version of the steady state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.
doi:10.1109/TCBB.2013.41
PMCID: PMC4090023
PMID: 24334389
Chemical reaction networks; cell signaling; VEGF; EGF; linear conservation laws; analytical solution; bilinear systems; minimally parameterized solutions
Given a single index, the receiver operational characteristic (ROC) curve analysis is routinely utilized for characterizing performances in distinguishing two conditions/groups in terms of sensitivity and specificity. Given the availability of multiple data sources (referred to as multi-indices), such as multimodal neuroimaging data sets, cognitive tests, and clinical ratings and genomic data in Alzheimer’s disease (AD) studies, the single-index-based ROC underutilizes all available information. For a long time, a number of algorithmic/analytic approaches combining multiple indices have been widely used to simultaneously incorporate multiple sources. In this study, we propose an alternative for combining multiple indices using logical operations, such as “AND,” “OR,” and “at least n” (where n is an integer), to construct multivariate ROC (multiV-ROC) and characterize the sensitivity and specificity statistically associated with the use of multiple indices. With and without the “leave-one-out” cross-validation, we used two data sets from AD studies to showcase the potentially increased sensitivity/specificity of the multiV-ROC in comparison to the single-index ROC and linear discriminant analysis (an analytic way of combining multi-indices). We conclude that, for the data sets we investigated, the proposed multiV-ROC approach is capable of providing a natural and practical alternative with improved classification accuracy as compared to univariate ROC and linear discriminant analysis.
doi:10.1109/TCBB.2012.141
PMCID: PMC4085147
PMID: 23702553
Alzheimer’s dementia (AD); multiple indices; multiV-ROC; receiver operational characteristic (ROC)
High-throughput expression technologies, including gene expression array and liquid chromatography – mass spectrometry (LC-MS) etc., measure thousands of features, i.e. genes or metabolites, on a continuous scale. In such data, both linear and nonlinear relations exist between features. Nonlinear relations can reflect critical regulation patterns in the biological system. However they are not identified and utilized by traditional clustering methods based on linear associations. Clustering based on general dependencies, i.e. both linear and nonlinear relations, is hampered by the high dimensionality and high noise level of the data. We developed a sensitive nonparametric measure of general dependency between (groups of) random variables in high-dimensions. Based on this dependency measure, we developed a hierarchical clustering method. In simulation studies, the method outperformed correlation- and mutual information (MI) – based hierarchical clustering methods in clustering features with nonlinear dependencies. We applied the method to a microarray dataset measuring the gene expression in cell-cycle time series to show it generates biologically relevant results. The R code is available at http://userwww.service.emory.edu/~tyu8/GDHC.
doi:10.1109/TCBB.2013.99
PMCID: PMC3905248
PMID: 24334400
clustering; association rule; non-linear association; high-throughput data
Analysis of molecular interaction networks is pervasive in systems biology. This research relies almost entirely on graphs for modeling interactions. However, edges in graphs cannot represent multiway interactions among molecules, which occur very often within cells. Hypergraphs may be better representations for networks having such interactions, since hyperedges can naturally represent relationships among multiple molecules. Here, we propose using hypergraphs to capture the uncertainty inherent in reverse engineering gene-gene networks. Some subsets of nodes may induce highly varying subgraphs across an ensemble of networks inferred by a reverse engineering algorithm. We provide a novel formulation of hyperedges to capture this uncertainty in network topology. We propose a clustering-based approach to discover hyperedges. We show that our approach can recover hyperedges planted in synthetic data sets with high precision and recall, even for moderate amount of noise. We apply our techniques to a data set of pathways inferred from genetic interaction data in S. cerevisiae related to the unfolded protein response. Our approach discovers several hyperedges that capture the uncertain connectivity of genes in relevant protein complexes, suggesting that further experiments may be required to precisely discern their interaction patterns. We also show that these complexes are not discovered by an algorithm that computes frequent and dense subgraphs.
doi:10.1109/TCBB.2013.71
PMCID: PMC4051496
PMID: 24384702
Biology and genetics; hypergraphs; graphs and networks
Binary (0,1) matrices, commonly known as transactional databases, can
represent many application data, including gene-phenotype data where
“1” represents a confirmed gene-phenotype relation and
“0” represents an unknown relation. It is natural to ask what
information is hidden behind these “0”s and “1”s.
Unfortunately, recent matrix completion methods, though very effective in many
cases, are less likely to infer something interesting from these (0,1)-matrices.
To answer this challenge, we propose IndEvi, a very succinct and
effective algorithm to perform independent-evidence-based transactional database
transformation. Each entry of a (0,1)-matrix is evaluated by “independent
evidence” (maximal supporting patterns) extracted from the whole matrix
for this entry. The value of an entry, regardless of its value as 0 or 1, has
completely no effect for its independent evidence. The experiment on a
gene-phenotype database shows that our method is highly promising in ranking
candidate genes and predicting unknown disease genes.
doi:10.1109/TCBB.2011.58
PMCID: PMC4047992
PMID: 21422495
Transactional database; binary matrix; frequent item set mining; maximal biclique; phenotype; disease gene; prioritization; matrix completion
A Bayesian alignment model (BAM) is proposed for alignment of liquid chromatography-mass spectrometry (LC-MS) data. BAM belongs to the category of profile-based approaches, which are composed of two major components: a prototype function and a set of mapping functions. Appropriate estimation of these functions is crucial for good alignment results. BAM uses Markov chain Monte Carlo (MCMC) methods to draw inference on the model parameters and improves on existing MCMC-based alignment methods through 1) the implementation of an efficient MCMC sampler and 2) an adaptive selection of knots. A block Metropolis-Hastings algorithm that mitigates the problem of the MCMC sampler getting stuck at local modes of the posterior distribution is used for the update of the mapping function coefficients. In addition, a stochastic search variable selection (SSVS) methodology is used to determine the number and positions of knots. We applied BAM to a simulated data set, an LC-MS proteomic data set, and two LC-MS metabolomic data sets, and compared its performance with the Bayesian hierarchical curve registration (BHCR) model, the dynamic time-warping (DTW) model, and the continuous profile model (CPM). The advantage of applying appropriate profile-based retention time correction prior to performing a feature-based approach is also demonstrated through the metabolomic data sets.
doi:10.1109/TCBB.2013.25
PMCID: PMC3993096
PMID: 23929872
Alignment; Bayesian inference; block Metropolis-Hastings algorithm; liquid chromatography-mass spectrometry (LC-MS); Markov chain Monte Carlo (MCMC); stochastic search variable selection (SSVS)
With well over one thousand specialized biological databases in use today, the task of automatically identifying novel, relevant data for such databases is increasingly important. In this paper, we describe practical machine learning approaches for identifying MEDLINE documents and Swiss-Prot/TrEMBL protein records, for incorporation into a specialized biological database of transport proteins named TCDB. We show that both learning approaches outperform rules created by hand by a human expert. As one of the first case studies involving two different approaches to updating a deployed database, both the methods compared and the results will be of interest to curators of many specialized databases.
doi:10.1109/TCBB.2009.83
PMCID: PMC3980937
PMID: 21393656
Bioinformatics (genome or protein) databases; Clustering, classification, and association rules; text mining; biomedical text classification; data mining
Modeling of biological networks is a difficult endeavour, but exploration of this problem is essential for understanding the systems behaviour of biological processes. In this contribution, developed for sparse data, we present a new continuous Bayesian graphical learning algorithm to cotemporally model proteins in signaling networks and genes in transcriptional regulatory networks. In this continuous Bayesian algorithm the correlation matrix is singular because the number of time points is less than the number of biological entities (genes or proteins). A suitable restriction on the degree of the graph’s vertices is applied and a Metropolis-Hastings algorithm is guided by a BIC-based posterior probability score. Ten independent and diverse runs of the algorithm are conducted, so that the probability space is properly well-explored. Diagnostics to test the applicability of the algorithm to the specific data sets are developed; this is a major benefit of the methodology. This novel algorithm is applied to two time course experimental data sets: 1) protein modification data identifying a potential signaling network in chondrocytes; and 2) gene expression data identifying the transcriptional regulatory network underlying dendritic cell maturation. This method gives high estimated posterior probabilities to many of the proteins’ directed edges that are predicted by the literature; for the gene study, the method gives high posterior probabilities to many of the literature-predicted sibling edges. In simulations, the method gives substantially higher estimated posterior probabilities for true edges and true subnetworks than for their false counterparts.
doi:10.1109/TCBB.2010.95
PMCID: PMC3954570
PMID: 20855920
Biological system modeling; statistical computing; multivariate statistics; correlation and regression analysis; signal transduction networks; transcriptional regulatory networks; biological network modeling
Nature possesses a secret formula for the energy as a function of the structure of a protein. In protein design, approximations are made to both the structural representation of the molecule and to the form of the energy equation, such that the existence of a general energy function for proteins is by no means guaranteed. Here we present new insights towards the application of machine learning to the problem of finding a general energy function for protein design. Machine learning requires the definition of an objective function, which carries with it the implied definition of success in protein design. We explored four functions, consisting of two functional forms, each with two criteria for success. Optimization was carried out by a Monte Carlo search through the space of all variable parameters. Cross-validation of the optimized energy function against a test set gave significantly different results depending on the choice of objective function, pointing to relative correctness of the built-in assumptions. Novel energy cross-terms correct for the observed non-additivity of energy terms and an imbalance in the distribution of predicted amino acids. This paper expands on the work presented at ACM-BCB, Orlando FL , October 2012.
doi:10.1109/TCBB.2013.113
PMCID: PMC3919130
PMID: 24384706
Biology and Genetics; Physics; Chemistry; Protein design; energy function; machine learning; correlation; rotamers; dead-end elimination
Reliable inference of transcription regulatory networks is still a challenging task in the field of computational biology. Network component analysis (NCA) has become a powerful scheme to uncover the networks behind complex biological processes, especially when gene expression data is integrated with binding motif information. However, the performance of NCA is impaired by the high rate of false connections in binding motif information and the high level of noise in gene expression data. Moreover, in real applications such as cancer research, the performance of NCA in simultaneously analyzing multiple candidate transcription factors (TFs) is further limited by the small sample number of gene expression data. In this paper, we propose a novel scheme, stability-based NCA, to overcome the above-mentioned problems by addressing the inconsistency between gene expression data and motif binding information (i.e., prior network knowledge). This method introduces small perturbations on prior network knowledge and utilizes the variation of estimated TF activities to reflect the stability of TF activities. Such a scheme is less limited by the sample size and especially capable to identify condition-specific TFs and their target genes. Experiment results on both simulation data and real breast cancer data demonstrate the efficiency and robustness of the proposed method.
PMCID: PMC3652899
PMID: 24407294
transcription regulatory network; network component analysis; stability analysis; transcription factor activity; target genes identification
Models of regulatory networks become more difficult to construct and understand as they grow in size and complexity. Large models are usually built up from smaller models, representing subsets of reactions within the larger network. To assist modelers in this composition process, we present a formal approach for model composition, a wizard-style program for implementing the approach, and suggested language extensions to the Systems Biology Markup Language to support model composition. To illustrate the features of our approach and how to use the JigCell Composition Wizard, we build up a model of the eukaryotic cell cycle “engine” from smaller pieces.
doi:10.1109/TCBB.2008.64
PMCID: PMC3773227
PMID: 20431147
Modeling; composition; fusion; flattening; SBML
DNA copy number variation (CNV) accounts for a large proportion of genetic variation. One commonly used approach to detecting CNVs is array-based comparative genomic hybridization (aCGH). Although many methods have been proposed to analyze aCGH data, it is not clear how to combine information from multiple samples to improve CNV detection. In this paper, we propose to use a matrix to approximate the multisample aCGH data and minimize the total variation of each sample as well as the nuclear norm of the whole matrix. In this way, we can make use of the smoothness property of each sample and the correlation among multiple samples simultaneously in a convex optimization framework. We also developed an efficient and scalable algorithm to handle large-scale data. Experiments demonstrate that the proposed method outperforms the state-of-the-art techniques under a wide range of scenarios and it is capable of processing large data sets with millions of probes.
doi:10.1109/TCBB.2012.166
PMCID: PMC3715577
PMID: 23702561
CNV; aCGH; total variation; spectral regularization; convex optimization
High throughput technologies enable researchers to measure expression levels on a genomic scale. However, the correct and efficient biological interpretation of such voluminous data remains a challenging problem. Many tools have been developed for the analysis of GO terms that are over- or under-represented in a list of differentially expressed genes. However, a previously unexplored aspect is the identification of changes in the way various biological processes interact in a given condition with respect to a reference. Here, we present a novel approach that aims at identifying such interactions between biological processes that are significantly different in a given phenotype with respect to normal. The proposed technique uses vector-space representation, SVD-based dimensionality reduction, differential weighting, and bootstrapping to asses the significance of the interactions under the multiple and complex dependencies expected between the biological processes. We illustrate our approach on two real data sets involving breast and lung cancer. More than 88 percent of the interactions found by our approach were deemed to be correct by an extensive manual review of literature. An interesting subset of such interactions is discussed in detail and shown to have the potential to open new avenues for research in lung and breast cancer.
doi:10.1109/TCBB.2012.65
PMCID: PMC3748606
PMID: 22547431
Phenotype-specific interactions; biological processes; microarrays; gene ontology; single value decomposition
Enormous data collection efforts and improvements in technology have made large genome-wide association studies a promising approach for better understanding the genetics of common diseases. Still, the knowledge gained from these studies may be extended even further by testing the hypothesis that genetic susceptibility is due to the combined effect of multiple variants or interactions between variants. Here we explore and evaluate the use of a genetic algorithm to discover groups of SNPs (of size 2, 3, or 4) that are jointly associated with bipolar disorder. The algorithm is guided by the structure of a gene interaction network, and is able to find groups of SNPs that are strongly associated with the disease, while performing far fewer statistical tests than other methods.
doi:10.1109/TCBB.2011.145
PMCID: PMC3748153
PMID: 22025762
Biology and Genetics; Evolutionary Computing and Genetic Algorithms; Graphs and Networks
The correct interpretation of many molecular biology experiments depends in an essential way on the accuracy and consistency of the existing annotation databases. Such databases are meant to act as repositories for our biological knowledge as we acquire and refine it. Hence, by definition, they are incomplete at any given time. In this paper, we describe a technique that improves our previous method for predicting novel GO annotations by extracting implicit semantic relationships between genes and functions. In this work, we use a vector space model and a number of weighting schemes in addition to our previous latent semantic indexing approach. The technique described here is able to take into consideration the hierarchical structure of the Gene Ontology (GO) and can weight differently GO terms situated at different depths. The prediction abilities of 15 different weighting schemes are compared and evaluated. Nine such schemes were previously used in other problem domains, while six of them are introduced in this paper. The best weighting scheme was a novel scheme, n2tn. Out of the top 50 functional annotations predicted using this weighting scheme, we found support in the literature for 84 percent of them, while 6 percent of the predictions were contradicted by the existing literature. For the remaining 10 percent, we did not find any relevant publications to confirm or contradict the predictions. The n2tn weighting scheme also outperformed the simple binary scheme used in our previous approach.
doi:10.1109/TCBB.2008.29
PMCID: PMC3712327
PMID: 20150671
Gene function prediction; gene annotation; Gene Ontology; vector space model; latent semantic indexing; weighting schemes
The local conformation of RNA molecules is an important factor in determining their catalytic and binding properties. The analysis of such conformations is particularly difficult due to the large number of degrees of freedom, such as the measured torsion angles per residue and the interatomic distances among interacting residues. In this work, we use a nearest-neighbor search method based on the statistical mechanical Potts model to find clusters in the RNA conformational space. The proposed technique is mostly automatic and may be applied to problems, where there is no prior knowledge on the structure of the data space in contrast to many other clustering techniques. Results are reported for both single residue conformations, where the parameter set of the data space includes four to seven torsional angles, and base pair geometries, where the data space is reduced to two dimensions. Moreover, new results are reported for base stacking geometries. For the first two cases, i.e., single residue conformations and base pair geometries, we get a very good match between the results of the proposed clustering method and the known classifications with only few exceptions. For the case of base stacking geometries, we validate our classification with respect to geometrical constraints and describe the content, and the geometry of the new clusters.
doi:10.1109/TCBB.2010.128
PMCID: PMC3679554
PMID: 21173460
RNA conformation; clustering; potts model; statistical mechanics
PMCID: PMC3646588
PMID: 19644178
The problem of identifying the proteins in a complex mixture using tandem mass spectrometry can be framed as an inference problem on a graph that connects peptides to proteins. Several existing protein identification methods make use of statistical inference methods for graphical models, including expectation maximization, Markov chain Monte Carlo, and full marginalization coupled with approximation heuristics. We show that, for this problem, the majority of the cost of inference usually comes from a few highly connected subgraphs. Furthermore, we evaluate three different statistical inference methods using a common graphical model, and we demonstrate that junction tree inference substantially improves rates of convergence compared to existing methods. The python code used for this paper is available at http://noble.gs.washington.edu/proj/fido.
doi:10.1109/TCBB.2012.26
PMCID: PMC3389307
PMID: 22331862
Mass spectrometry; protein identification; graphical models; Bayesian inference
Molecular dynamics trajectories are very data-intensive thereby limiting sharing and archival of such data. One possible solution is compression of trajectory data. Here, trajectory compression based on conversion to the coarse-grained model PRIMO is proposed. The compressed data is about one third of the original data and fast decompression is possible with an analytical reconstruction procedure from PRIMO to all-atom representations. This protocol largely preserves structural features and to a more limited extent also energetic features of the original trajectory.
doi:10.1109/TCBB.2011.141
PMCID: PMC3505254
PMID: 22025759
proteins; all-atom reconstruction; PRIMO; molecular dynamics simulation; compression; coarse-grained model
Microarray gene expression data often contain missing values. Accurate estimation of the missing values is important for down-stream data analyses that require complete data. Nonlinear relationships between gene expression levels have not been well-utilized in missing value imputation. We propose an imputation scheme based on nonlinear dependencies between genes. By simulations based on real microarray data, we show that incorporating non-linear relationships could improve the accuracy of missing value imputation, both in terms of normalized root mean squared error and in terms of the preservation of the list of significant genes in statistical testing. In addition, we studied the impact of artificial dependencies introduced by data normalization on the simulation results. Our results suggest that methods relying on global correlation structures may yield overly optimistic simulation results when the data has been subjected to row (gene) – wise mean removal.
doi:10.1109/TCBB.2010.73
PMCID: PMC3624752
PMID: 20733236
gene expression; statistical analysis; missing value
Epithelia are sheets of connected cells that are essential across the animal kingdom. Experimental observations suggest that the dynamical behavior of many single-layered epithelial tissues has strong analogies with that of specific mechanical systems, namely large networks consisting of point masses connected through spring-damper elements and undergoing the influence of active and dissipating forces. Based on this analogy, this work develops a modeling framework to enable the study of the mechanical properties and of the dynamic behavior of large epithelial cellular networks. The model is built first by creating a network topology that is extracted from the actual cellular geometry as obtained from experiments, then by associating a mechanical structure and dynamics to the network via spring-damper elements. This scalable approach enables running simulations of large network dynamics: the derived modeling framework in particular is predisposed to be tailored to study general dynamics (for example, morphogenesis) of various classes of single-layered epithelial cellular networks. In this contribution we test the model on a case study of the dorsal epithelium of the Drosophila melanogaster embryo during early dorsal closure (and, less conspicuously, germband retraction).
doi:10.1109/TCBB.2012.126
PMCID: PMC3558995
PMID: 23221083
Epithelium; Cellular network; Nonlinear dynamical model; Spring-damper system; Discrete element method; Early dorsal closure; Morphogenesis
The HIV-1 genome is highly heterogeneous. This variation affords the virus a wide range of molecular properties, including the ability to infect cell types, such as macrophages and lymphocytes, expressing different chemokine receptors on the cell surface. In particular, R5 HIV-1 viruses use CCR5 as a coreceptor for viral entry, X4 viruses use CXCR4, whereas some viral strains, known as R5X4 or D-tropic, have the ability to utilize both coreceptors. X4 and R5X4 viruses are associated with rapid disease progression to AIDS. R5X4 viruses differ in that they have yet to be characterized by the examination of the genetic sequence of HIV-1 alone. In this study, a series of experiments was performed to evaluate different strategies of feature selection and neural network optimization. We demonstrate the use of artificial neural networks trained via evolutionary computation to predict viral coreceptor usage. The results indicate the identification of R5X4 viruses with a predictive accuracy of 75.5 percent.
doi:10.1109/TCBB.2007.1074
PMCID: PMC3523352
PMID: 18451438
Computational intelligence; evolutionary computation; artificial neural networks; HIV; AIDS; phenotype prediction; tropism; dual-tropic viruses
Although many feature selection methods for classification have been developed, there is a need to identify genes in high-dimensional data with censored survival outcomes. Traditional methods for gene selection in classification problems have several drawbacks. First, the majority of the gene selection approaches for classification are single-gene based. Second, many of the gene selection procedures are not embedded within the algorithm itself. The technique of random forests has been found to perform well in high dimensional data settings with survival outcomes. It also has an embedded feature to identify variables of importance. Therefore, it is an ideal candidate for gene selection in high dimensional data with survival outcomes. In this paper, we develop a novel method based on the random forests to identify a set of prognostic genes. We compare our method with several machine learning methods and various node split criteria using several real data sets. Our method performed well in both simulations and real data analysis. Additionally, we have shown the advantages of our approach over single-gene based approaches. Our method incorporates multivariate correlations in microarray data for survival outcomes. The described method allows us to best utilize the information available from microarray data with survival outcomes.
doi:10.1109/TCBB.2012.63
PMCID: PMC3495190
PMID: 22547432
Cancer; Gene selection; Iterative feature elimination; Microarrays; Random Forest; Survival
RNA-Seq is widely used in transcriptome studies, and the detection of differentially expressed genes (DEGs) between two classes of individuals, e.g. cases vs controls, using RNA-Seq is of fundamental importance. Many statistical methods for DEG detection based on RNA-Seq data have been developed and most of them are based on the read counts mapped to individual genes. On the other hand, genes are composed of exons and the distribution of reads for the different exons can be heterogeneous. We hypothesize that the detection accuracy of differentially expressed genes can be increased by analyzing individual exons within a gene and then combining the results of the exons. We therefore developed a novel program, termed CEDER, to accurately detect DGEs by combining the significance of the exons. CEDER first tests for differentially expressed exons yielding a p-value for each, and then gives a score indicating the potential for a gene to be differentially expressed by integrating the p-values of the exons in the gene. We showed that CEDER can significantly increase the accuracy of existing methods for detecting DEGs on two benchmark RNA-Seq datasets and simulated datasets.
doi:10.1109/TCBB.2012.83
PMCID: PMC3488134
PMID: 22641709
RNA-Seq; gene expression; differentially expressed gene; high-throughput sequencing; combined p-value statistic
Using the Matt structure alignment program, we take a tour of protein space, producing a hierarchical clustering scheme that divides protein structural domains into clusters based on geometric dissimilarity. While it was known that purely structural, geometric, distance-based measures of structural similarity, such as Dali/FSSP, could largely replicate hand-curated schemes such as SCOP at the family level, it was an open question as to whether any such scheme could approximate SCOP at the more distant superfamily and fold levels. We partially answer this question in the affirmative, by designing a clustering scheme based on Matt that approximately matches SCOP at the superfamily level, and demonstrates qualitative differences in performance between Matt and DaliLite. Implications for the debate over the organization of protein fold space are discussed. Based on our clustering of protein space, we introduce the Mattbench benchmark set, a new collection of structural alignments useful for testing sequence aligners on more distantly homologous proteins.
doi:10.1109/TCBB.2011.70
PMCID: PMC3355523
PMID: 21464511
SCOP; hierarchical classification; structure alignment; fold space; automated classification