BACKGROUND: Single-cell RNA sequencing (sc-RNASeq) data illuminate transcriptomic heterogeneity but also possess a high level of noise, abundant missing entries and sometimes inadequate or no cell type annotations at all. Bulk-level gene expression data lack direct information of cell population composition but are more robust and complete and often better annotated. We propose a modeling framework to integrate bulk-level and single-cell RNASeq data to address the deficiencies and leverage the mutual strengths of each type of data and enable a more comprehensive inference of their transcriptomic heterogeneity. Contrary to the standard approaches of factorizing the bulk-level data with one algorithm and (for some methods) treating single-cell RNASeq data as references to decompose bulk-level data, we employed multiple deconvolution algorithms to factorize the bulk-level data, constructed the probabilistic graphical models of cell-level gene expressions from the decomposition outcomes, and compared the log-likelihood scores of these models in single-cell data. We term this framework backward deconvolution as inference operates from coarse-grained bulk-level data to fine-grained single-cell data. As the abundant missing entries in sc-RNASeq data have a significant effect on log-likelihood scores, we also developed a criterion for inclusion or exclusion of zero entries in log-likelihood score computation. RESULTS: We selected nine deconvolution algorithms and validated backward deconvolution in five datasets. In the in-silico mixtures of mouse sc-RNASeq data, the log-likelihood scores of the deconvolution algorithms were strongly anticorrelated with their errors of mixture coefficients and cell type specific gene expression signatures. In the true bulk-level mouse data, the sample mixture coefficients were unknown but the log-likelihood scores were strongly correlated with accuracy rates of inferred cell types. In the data of autism spectrum disorder (ASD) and normal controls, we found that ASD brains possessed higher fractions of astrocytes and lower fractions of NRGN-expressing neurons than normal controls. In datasets of breast cancer and low-grade gliomas (LGG), we compared the log-likelihood scores of three simple hypotheses about the gene expression patterns of the cell types underlying the tumor subtypes. The model that tumors of each subtype were dominated by one cell type persistently outperformed an alternative model that each cell type had elevated expression in one gene group and tumors were mixtures of those cell types. Superiority of the former model is also supported by comparing the real breast cancer sc-RNASeq clusters with those generated by simulated sc-RNASeq data. CONCLUSIONS: The results indicate that backward deconvolution serves as a sensible model selection tool for deconvolution algorithms and facilitates discerning hypotheses about cell type compositions underlying heterogeneous specimens such as tumors.

Clustering unlabeled image data using deep neural network (DNN) models is under active investigation. Most existing approaches transform the data through embedding operations and cluster the embedded data, and the embedding is learned to fit the data. In some applications, the embedding model is explicitly given due to the concerns of generalizability, transferability, privacy and security. Despite rapid progress in self-supervised learning, clustering data with a fixed embedding is rarely explored. We propose an Merge & Expand (ME) algorithm to cluster image data using a fixed embedding and a DNN classification model. ME achieves a comparable level of accuracy with some state-of-the-art algorithms. It further demarcates the "clean" and "unclean" images where their geometric relations in the embedded space are compatible and incompatible with their cluster structure respectively. Finally, we validate ME with three datasets and discuss its potential extension.

BACKGROUND: Gene Set Enrichment Analysis (GSEA) is a powerful tool to identify enriched functional categories of informative biomarkers. Canonical GSEA takes one-dimensional feature scores derived from the data of one platform as inputs. Numerous extensions of GSEA handling multimodal OMIC data are proposed, yet none of them explicitly captures combinatorial relations of feature scores from multiple platforms. RESULTS: We propose multivariate GSEA (MGSEA) to capture combinatorial relations of gene set enrichment among multiple platform features. MGSEA successfully captures designed feature relations from simulated data. By applying it to the scores of delineating breast cancer and glioblastoma multiforme (GBM) subtypes from The Cancer Genome Atlas (TCGA) datasets of CNV, DNA methylation and mRNA expressions, we find that breast cancer and GBM data yield both similar and distinct outcomes. Among the enriched functional categories, subtype-specific biomarkers are dominated by mRNA expression in many functional categories in both cancer types and also by CNV in many functional categories in breast cancer. The enriched functional categories belonging to distinct combinatorial patterns are involved different oncogenic processes: cell proliferation (such as cell cycle control, estrogen responses, MYC and E2F targets) for mRNA expression in breast cancer, invasion and metastasis (such as cell adhesion and epithelial-mesenchymal transition (EMT)) for CNV in breast cancer, and diverse processes (such as immune and inflammatory responses, cell adhesion, angiogenesis, and EMT) for mRNA expression in GBM. These observations persist in two external datasets (Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) for breast cancer and Repository for Molecular Brain Neoplasia Data (REMBRANDT) for GBM) and are consistent with knowledge of cancer subtypes. We further compare the characteristics of MGSEA with several extensions of GSEA and point out the pros and cons of each method. CONCLUSIONS: We demonstrated the utility of MGSEA by inferring the combinatorial relations of multiple platforms for cancer subtype delineation in three multi-OMIC datasets: TCGA, METABRIC and REMBRANDT. The inferred combinatorial patterns are consistent with the current knowledge and also reveal novel insights about cancer subtypes. MGSEA can be further applied to any genotype-phenotype association problems with multimodal OMIC data.

Ambiguity in genetic codes exists in cases where certain stop codons are alternatively used to encode non-canonical amino acids. In selenoprotein transcripts, the UGA codon may either represent a translation termination signal or a selenocysteine (Sec) codon. Translating UGA to Sec requires selenium and specialized Sec incorporation machinery such as the interaction between the SECIS element and SBP2 protein, but how these factors quantitatively affect alternative assignments of UGA has not been fully investigated. We developed a model simulating the UGA decoding process. Our model is based on the following assumptions: (1) charged Sec-specific tRNAs (Sec-tRNASec) and release factors compete for a UGA site, (2) Sec-tRNASec abundance is limited by the concentrations of selenium and Sec-specific tRNA (tRNASec) precursors, and (3) all synthesis reactions follow first-order kinetics. We demonstrated that this model captured two prominent characteristics observed from experimental data. First, UGA to Sec decoding increases with elevated selenium availability, but saturates under high selenium supply. Second, the efficiency of Sec incorporation is reduced with increasing selenoprotein synthesis. We measured the expressions of four selenoprotein constructs and estimated their model parameters. Their inferred Sec incorporation efficiencies did not correlate well with their SECIS-SBP2 binding affinities, suggesting the existence of additional factors determining the hierarchy of selenoprotein synthesis under selenium deficiency. This model provides a framework to systematically study the interplay of factors affecting the dual definitions of a genetic codon.

In large-scale networks, certain topological patterns may occur more frequently than expected from a null model that preserves global (such as the density of the graph) and local (such as the connectivity of each node) properties of the graph. These network motifs are the building blocks of large-scale networks and may confer functional/mechanistic implications of their underlying processes. Despite active investigations and rich literature in systems biology, network motifs are less explored in social network studies. In this work, we modified and improved the method from Milo et al. 2002 to detect significantly enriched motifs in both directed and undirected networks. We applied this method to identify 3-node and 4-node motifs from the datasets of 18 networks (4 directed and 14 undirected) covering social interactions, co-authorships, web document hyperlinks, neuronal circuitry, protein-protein interactions (PPI), trophic relations in a food web, and others. Presence and absence of enriched motifs provide rich information regarding each type of network relations. In undirected networks, triangles are enriched in almost all datasets, suggesting the prevalence of transitivity in diverse networks. However, 4-node structures lacking transitivity -- diamonds and stars -- are also enriched in the majority of undirected networks. In directed networks, variations of feed-forward loops are over-represented in the networks of web document and political web log hyperlinks as well as neuronal connections. In contrast, the food web is enriched with unidirectional motifs with distinct trophic levels. These results reveal the nature of distinct types of networks and invite further explorations on the relations of network structures and types of relations.

Quantum systems are promising candidates of future computing and information processing devices. In a large system, information about the quantum states and processes may be incomplete and scattered. To integrate the distributed information we propose a quantum version of probabilistic graphical models. Variables in the model (quantum states and measurement outcomes) are linked by several types of operators (unitary, measurement, and merge/split operators). We propose algorithms for three machine learning tasks in quantum probabilistic graphical models: a belief propagation algorithm for inference of unknown states, an iterative algorithm for simultaneous estimation of parameter values and hidden states, and an active learning algorithm to select measurement operators based on observed evidence. We validate these algorithms on simulated data and point out future extensions toward a more comprehensive theory of quantum probabilistic graphical models.

BACKGROUND: Cancer is a complex disease where various types of molecular aberrations drive the development and progression of malignancies. Large-scale screenings of multiple types of molecular aberrations (e.g., mutations, copy number variations, DNA methylations, gene expressions) become increasingly important in the prognosis and study of cancer. Consequently, a computational model integrating multiple types of information is essential for the analysis of the comprehensive data. RESULTS: We propose an integrated modeling framework to identify the statistical and putative causal relations of various molecular aberrations and gene expressions in cancer. To reduce spurious associations among the massive number of probed features, we sequentially applied three layers of logistic regression models with increasing complexity and uncertainty regarding the possible mechanisms connecting molecular aberrations and gene expressions. Layer 1 models associate gene expressions with the molecular aberrations on the same loci. Layer 2 models associate expressions with the aberrations on different loci but have known mechanistic links. Layer 3 models associate expressions with nonlocal aberrations which have unknown mechanistic links. We applied the layered models to the integrated datasets of NCI-60 cancer cell lines and validated the results with large-scale statistical analysis. Furthermore, we discovered/reaffirmed the following prominent links: (1) Protein expressions are generally consistent with mRNA expressions. (2) Several gene expressions are modulated by composite local aberrations. For instance, CDKN2A expressions are repressed by either frame-shift mutations or DNA methylations. (3) Amplification of chromosome 6q in leukemia elevates the expression of MYB, and the downstream targets of MYB on other chromosomes are up-regulated accordingly. (4) Amplification of chromosome 3p and hypo-methylation of PAX3 together elevate MITF expression in melanoma, which up-regulates the downstream targets of MITF. (5)Mutations of TP53 are negatively associated with its direct target genes. CONCLUSIONS: The analysis results on NCI-60 data justify the utility of the layered models for the incoming flow of cancer genomic data. Experimental validations on selected prominent links and application of the layered modeling framework to other integrated datasets will be carried out subsequently.

Complex phenotypes such as the transformation of a normal population of cells into cancerous tissue result from a series of molecular triggers gone awry. We describe a method that searches for a genetic network consistent with expression changes observed under the knock-down of a set of genes that share a common role in the cell, such as a disease phenotype. The method extends the Nested Effects Model of Markowetz et al. (2005) by using a probabilistic factor graph to search for a network representing interactions among these silenced genes. The method also expands the network by attaching new genes at specific downstream points, providing candidates for subsequent perturbations to further characterize the pathway. We investigated an extension provided by the factor graph approach in which the model distinguishes between inhibitory and stimulatory interactions. We found that the extension yielded significant improvements in recovering the structure of simulated and Saccharomyces cerevisae networks. We applied the approach to discover a signaling network among genes involved in a human colon cancer cell invasiveness pathway. The method predicts several genes with new roles in the invasiveness process. We knocked down two genes identified by our approach and found that both knock-downs produce loss of invasive potential in a colon cancer cell line. Nested effects models may be a powerful tool for inferring regulatory connections and genes that operate in normal and disease-related processes.

Correlated changes of nucleic or amino acids have provided strong information about the structures and interactions of molecules. Despite the rich literature in coevolutionary sequence analysis, previous methods often have to trade off between generality, simplicity, phylogenetic information, and specific knowledge about interactions. Furthermore, despite the evidence of coevolution in selected protein families, a comprehensive screening of coevolution among all protein domains is still lacking. We propose an augmented continuous-time Markov process model for sequence coevolution. The model can handle different types of interactions, incorporate phylogenetic information and sequence substitution, has only one extra free parameter, and requires no knowledge about interaction rules. We employ this model to large-scale screenings on the entire protein domain database (Pfam). Strikingly, with 0.1 trillion tests executed, the majority of the inferred coevolving protein domains are functionally related, and the coevolving amino acid residues are spatially coupled. Moreover, many of the coevolving positions are located at functionally important sites of proteins/protein complexes, such as the subunit linkers of superoxide dismutase, the tRNA binding sites of ribosomes, the DNA binding region of RNA polymerase, and the active and ligand binding sites of various enzymes. The results suggest sequence coevolution manifests structural and functional constraints of proteins. The intricate relations between sequence coevolution and various selective constraints are worth pursuing at a deeper level.

We develop and analyze game-theoretic algorithms for predicting coordinate binding of multiple DNA binding regulators. The allocation of proteins to local neighborhoods and to sites is carried out with resource constraints while explicating competing and coordinate binding relations among proteins with affinity to the site or region. The focus of this paper is on mathematical foundations of the approach. We also briefly demonstrate the approach in the context of the -phage switch.

BACKGROUND: Gene regulation and metabolic reactions are two primary activities of life. Although many works have been dedicated to study each system, the coupling between them is less well understood. To bridge this gap, we propose a joint model of gene regulation and metabolic reactions. RESULTS: We integrate regulatory and metabolic networks by adding links specifying the feedback control from the substrates of metabolic reactions to enzyme gene expressions. We adopt two alternative approaches to build those links: inferring the links between metabolites and transcription factors to fit the data or explicitly encoding the general hypotheses of feedback control as links between metabolites and enzyme expressions. A perturbation data is explained by paths in the joint network if the predicted response along the paths is consistent with the observed response. The consistency requirement for explaining the perturbation data imposes constraints on the attributes in the network such as the functions of links and the activities of paths. We build a probabilistic graphical model over the attributes to specify these constraints, and apply an inference algorithm to identify the attribute values which optimally explain the data. The inferred models allow us to 1) identify the feedback links between metabolites and regulators and their functions, 2) identify the active paths responsible for relaying perturbation effects, 3) computationally test the general hypotheses pertaining to the feedback control of enzyme expressions, 4) evaluate the advantage of an integrated model over separate systems. CONCLUSION: The modeling results provide insight about the mechanisms of the coupling between the two systems and possible "design rules" pertaining to enzyme gene regulation. The model can be used to investigate the less well-probed systems and generate consistent hypotheses and predictions for further validation.

We develop a method for integrating time series expression profiles and factor-gene binding data to quantify dynamic aspects of gene regulation. We estimate latencies for transcription activation by explaining time correlations between gene expression profiles through available factor-gene binding information. The resulting aligned expression profiles are subsequently clustered and again combined with binding information to determine groups or subgroups of co-regulated genes. The predictions derived from this approach are consistent with existing results. Our analysis also provides several hypotheses not implicated in previous studies.

We develop a new framework for inferring models of transcriptional regulation. The models in this approach, which we call physical models, are constructed on the basis of verifiable molecular attributes of the underlying biological system. The attributes include, for example, the existence of protein-protein and protein-DNA interactions in gene regulatory processes, the directionality of signal transduction in protein-protein interactions, as well as the signs of the immediate effects of these interactions (e.g., whether an upstream gen activates or represses the downstream genes). Each attribute is included as a variable in the model, and the variables define a collection of annotated random graphs. Possible configurations of these variables (realizations of the underlying biological system) are constrained by the available data sources. Some of the data sources such as factor-binding data (location data) involve measurements that are directly tied to the variables in the model. Other sources such as gene knock-outs are functional in nature and provide only indirect evidence about the (physical) variables. We associate each knock-out effect in the deletion mutant data with a set of causal paths (molecular cascades) that could in principle explain the effect, resulting in aggregate constraints about the physical variables in the model. The most likely setting of all the variables is found by the max-product algorithm. By testing our approach on datasets related to the pheromone response pathway in S. cerevisiae, we demonstrate that the resulting transcriptional models are consistent with previous studies about the pathway. Moreover, we show that the approach is capable of predicting gene knock-out effects with high degree of accuracy in a cross-validation setting. The method also implicates likely molecular cascades responsible for each observed knock-out effect. The inference results are robust against variations in the model parameters. We can extend the approach to include other data sources such as time course expression profiles. We also discuss coordinated regulation and the use of automated experiment design