Boosting Probabilistic Graphical Model Inference by Incorporating Prior Knowledge from Multiple Sources

Inferring regulatory networks from experimental data via probabilistic graphical models is a popular framework to gain insights into biological systems. However, the inherent noise in experimental data coupled with a limited sample size reduces the performance of network reverse engineering. Prior knowledge from existing sources of biological information can address this low signal to noise problem by biasing the network inference towards biologically plausible network structures. Although integrating various sources of information is desirable, their heterogeneous nature makes this task challenging. We propose two computational methods to incorporate various information sources into a probabilistic consensus structure prior to be used in graphical model inference. Our first model, called Latent Factor Model (LFM), assumes a high degree of correlation among external information sources and reconstructs a hidden variable as a common source in a Bayesian manner. The second model, a Noisy-OR, picks up the strongest support for an interaction among information sources in a probabilistic fashion. Our extensive computational studies on KEGG signaling pathways as well as on gene expression data from breast cancer and yeast heat shock response reveal that both approaches can significantly enhance the reconstruction accuracy of Bayesian Networks compared to other competing methods as well as to the situation without any prior. Our framework allows for using diverse information sources, like pathway databases, GO terms and protein domain data, etc. and is flexible enough to integrate new sources, if available.     

Logos: a modular bayesian model for de novo motif detection

The complexity of the global organization and internal structure of motifs in higher eukaryotic organisms raises significant challenges for motif detection techniques. To achieve successful de novo motif detection, it is necessary to model the complex dependencies within and among motifs and to incorporate biological prior knowledge. In this paper, we present LOGOS, an integrated LOcal and GlObal motif Sequence model for biopolymer sequences, which provides a principled framework for developing, modularizing, extending and computing expressive motif models for complex biopolymer sequence analysis. LOGOS consists of two interacting submodels: HMDM, a local alignment model capturing biological prior knowledge and positional dependency within the motif local structure; and HMM, a global motif distribution model modeling frequencies and dependencies of motif occurrences. Model parameters can be fit using training motifs within an empirical Bayesian framework. A variational EM algorithm is developed for de novo motif detection. LOGOS improves over existing models that ignore biological priors and dependencies in motif structures and motif occurrences, and demonstrates superior performance on both semi-realistic test data and cis-regulatory sequences from yeast and Drosophila genomes with regard to sensitivity, specificity, flexibility and extensibility.     

Integrating external biological knowledge in the construction of regulatory networks from time-series expression data

ABSTRACT: BACKGROUND: Inference about regulatory networks from high-throughput genomics data is of great interest in systems biology. We present a Bayesian approach to infer gene regulatory networks from time series expression data by integrating various types of biological knowledge. RESULTS: We formulate network construction as a series of variable selection problems and use linear regression to model the data. Our method summarizes additional data sources with an informative prior probability distribution over candidate regression models. We extend the Bayesian model averaging (BMA) variable selection method to select regulators in the regression framework. We summarize the external biological knowledge by an informative prior probability distribution over the candidate regression models. CONCLUSIONS: We demonstrate our method on simulated data and a set of time-series microarray experiments measuring the effect of a drug perturbation on gene expression levels, and show that it outperforms leading regression-based methods in the literature.     

Continuous hidden process model for time series expression experiments

MOTIVATION: When analyzing expression experiments, researchers are often interested in identifying the set of biological processes that are up- or down-regulated under the experimental condition studied. Current approaches, including clustering expression profiles and averaging the expression profiles of genes known to participate in specific processes, fail to provide an accurate estimate of the activity levels of many biological processes. RESULTS: We introduce a probabilistic continuous hidden process Model (CHPM) for time series expression data. CHPM can simultaneously determine the most probable assignment of genes to processes and the level of activation of these processes over time. To estimate model parameters, CHPM uses multiple time series datasets and incorporates prior biological knowledge. Applying CHPM to yeast expression data, we show that our algorithm produces more accurate functional assignments for genes compared to other expression analysis methods. The inferred process activity levels can be used to study the relationships between biological processes. We also report new biological experiments confirming some of the process activity levels predicted by CHPM. AVAILABILITY: A Java implementation is available at http:\\www.cs.cmu.edu\~yanxins\chpm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Automated refinement and inference of analytical models for metabolic networks

The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.     

Probabilistic segmentation and intensity estimation for microarray images

We describe a probabilistic approach to simultaneous image segmentation and intensity estimation for complementary DNA microarray experiments. The approach overcomes several limitations of existing methods. In particular, it (a) uses a flexible Markov random field approach to segmentation that allows for a wider range of spot shapes than existing methods, including relatively common 'doughnut-shaped' spots; (b) models the image directly as background plus hybridization intensity, and estimates the two quantities simultaneously, avoiding the common logical error that estimates of foreground may be less than those of the corresponding background if the two are estimated separately; and (c) uses a probabilistic modeling approach to simultaneously perform segmentation and intensity estimation, and to compute spot quality measures. We describe two approaches to parameter estimation: a fast algorithm, based on the expectation-maximization and the iterated conditional modes algorithms, and a fully Bayesian framework. These approaches produce comparable results, and both appear to offer some advantages over other methods. We use an HIV experiment to compare our approach to two commercial software products: Spot and Arrayvision.     

Detecting and Removing Inconsistencies between Experimental Data and Signaling Network Topologies Using Integer Linear Programming on Interaction Graphs

Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely available toolbox SigNetTrainer making it an appealing approach for various applications.     

Gene ordering in partitive clustering using microarray expressions

A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering and ordering the genes using gene expression data into homogeneous groups was shown to be useful in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on gene ordering in hierarchical clustering framework for gene expression analysis, there is no work addressing and evaluating the importance of gene ordering in partitive clustering framework, to the best knowledge of the authors. Outside the framework of hierarchical clustering, different gene ordering algorithms are applied on the whole data set, and the domain of partitive clustering is still unexplored with gene ordering approaches. A new hybrid method is proposed for ordering genes in each of the clusters obtained from partitive clustering solution, using microarray gene expressions.Two existing algorithms for optimally ordering cities in travelling salesman problem (TSP), namely, FRAG_GALK and Concorde, are hybridized individually with self organizing MAP to show the importance of gene ordering in partitive clustering framework. We validated our hybrid approach using yeast and fibroblast data and showed that our approach improves the result quality of partitive clustering solution, by identifying subclusters within big clusters, grouping functionally correlated genes within clusters, minimization of summation of gene expression distances, and the maximization of biological gene ordering using MIPS categorization. Moreover, the new hybrid approach, finds comparable or sometimes superior biological gene order in less computation time than those obtained by optimal leaf ordering in hierarchical clustering solution.     

Microarray missing data imputation based on a set theoretic framework and biological knowledge

Gene expressions measured using microarrays usually suffer from the missing value problem. However, in many data analysis methods, a complete data matrix is required. Although existing missing value imputation algorithms have shown good performance to deal with missing values, they also have their limitations. For example, some algorithms have good performance only when strong local correlation exists in data while some provide the best estimate when data is dominated by global structure. In addition, these algorithms do not take into account any biological constraint in their imputation. In this paper, we propose a set theoretic framework based on projection onto convex sets (POCS) for missing data imputation. POCS allows us to incorporate different types of a priori knowledge about missing values into the estimation process. The main idea of POCS is to formulate every piece of prior knowledge into a corresponding convex set and then use a convergence-guaranteed iterative procedure to obtain a solution in the intersection of all these sets. In this work, we design several convex sets, taking into consideration the biological characteristic of the data: the first set mainly exploit the local correlation structure among genes in microarray data, while the second set captures the global correlation structure among arrays. The third set (actually a series of sets) exploits the biological phenomenon of synchronization loss in microarray experiments. In cyclic systems, synchronization loss is a common phenomenon and we construct a series of sets based on this phenomenon for our POCS imputation algorithm. Experiments show that our algorithm can achieve a significant reduction of error compared to the KNNimpute, SVDimpute and LSimpute methods.     

Identification of protein complexes by comparative analysis of yeast and bacterial protein interaction data.

Mounting evidence shows that many protein complexes are conserved in evolution. Here we use conservation to find complexes that are common to the yeast S. cerevisiae and the bacteria H. pylori. Our analysis combines protein interaction data that are available for each of the two species and orthology information based on protein sequence comparison. We develop a detailed probabilistic model for protein complexes in a single species and a model for the conservation of complexes between two species. Using these models, one can recast the question of finding conserved complexes as a problem of searching for heavy subgraphs in an edge- and node-weighted graph, whose nodes are orthologous protein pairs. We tested this approach on the data currently available for yeast and bacteria and detected 11 significantly conserved complexes. Several of these complexes match very well with prior experimental knowledge on complexes in yeast only and serve for validation of our methodology. The complexes suggest new functions for a variety of uncharacterized proteins. By identifying a conserved complex whose yeast proteins function predominantly in the nuclear pore complex, we propose that the corresponding bacterial proteins function as a coherent cellular membrane transport system. We also compare our results to two alternative methods for detecting complexes and demonstrate that our methodology obtains a much higher specificity.     

Discriminative motifs.

This paper takes a new view of motif discovery, addressing a common problem in existing motif finders. A motif is treated as a feature of the input promoter regions that leads to a good classifier between these promoters and a set of background promoters. This perspective allows us to adapt existing methods of feature selection, a well-studied topic in machine learning, to motif discovery. We develop a general algorithmic framework that can be specialized to work with a wide variety of motif models, including consensus models with degenerate symbols or mismatches, and composite motifs. A key feature of our algorithm is that it measures overrepresentation while maintaining information about the distribution of motif instances in individual promoters. The assessment of a motif's discriminative power is normalized against chance behaviour by a probabilistic analysis. We apply our framework to two popular motif models and are able to detect several known binding sites in sets of co-regulated genes in yeast.     

Probabilistic Approach to Predicting Substrate Specificity of Methyltransferases

We present a general probabilistic framework for predicting the substrate specificity of enzymes. We designed this approach to be easily applicable to different organisms and enzymes. Therefore, our predictive models do not rely on species-specific properties and use mostly sequence-derived data. Maximum Likelihood optimization is used to fine-tune model parameters and the Akaike Information Criterion is employed to overcome the issue of correlated variables. As a proof-of-principle, we apply our approach to predicting general substrate specificity of yeast methyltransferases (MTases). As input, we use several physico-chemical and biological properties of MTases: structural fold, isoelectric point, expression pattern and cellular localization. Our method accurately predicts whether a yeast MTase methylates a protein, RNA or another molecule. Among our experimentally tested predictions, 89% were confirmed, including the surprising prediction that YOR021C is the first known MTase with a SPOUT fold that methylates a substrate other than RNA (protein). Our approach not only allows for highly accurate prediction of functional specificity of MTases, but also provides insight into general rules governing MTase substrate specificity.     

MetaReg: a platform for modeling, analysis and visualization of biological systems using large-scale experimental data

MetaReg http://acgt.cs.tau.ac.il/metareg/application.html is a computational tool that models cellular networks and integrates experimental results with such models. MetaReg represents established knowledge about a biological system, available today mostly in informal form in the literature, as probabilistic network models with underlying combinatorial regulatory logic. MetaReg enables contrasting predictions with measurements, model improvements and studying what-if scenarios. By summarizing prior knowledge and providing visual and computational aids, it helps the expert explore and understand her system better.