Probabilistic Boolean Networks: a rule-based uncertainty model for gene regulatory networks

MOTIVATION: Our goal is to construct a model for genetic regulatory networks such that the model class: (i) incorporates rule-based dependencies between genes; (ii) allows the systematic study of global network dynamics; (iii) is able to cope with uncertainty, both in the data and the model selection; and (iv) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes. RESULTS: We introduce Probabilistic Boolean Networks (PBN) that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. We show how the dynamics of these networks can be studied in the probabilistic context of Markov chains, with standard Boolean networks being special cases. Then, we discuss the relationship between PBNs and Bayesian networks--a family of graphical models that explicitly represent probabilistic relationships between variables. We show how probabilistic dependencies between a gene and its parent genes, constituting the basic building blocks of Bayesian networks, can be obtained from PBNs. Finally, we present methods for quantifying the influence of genes on other genes, within the context of PBNs. Examples illustrating the above concepts are presented throughout the paper.     

Collective animal behavior from Bayesian estimation and probability matching

Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is mainly based on empirical fits to observations, with less emphasis in obtaining first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching. In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability equal to the Bayesian-estimated probability that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior.     

A neural network model of metaphor understanding with dynamic interaction based on a statistical language analysis: targeting a human-like model

The purpose of this paper is to construct a model that represents the human process of understanding metaphors, focusing specifically on similes of the form an "A like B". Generally speaking, human beings are able to generate and understand many sorts of metaphors. This study constructs the model based on a probabilistic knowledge structure for concepts which is computed from a statistical analysis of a large-scale corpus. Consequently, this model is able to cover the many kinds of metaphors that human beings can generate. Moreover, the model implements the dynamic process of metaphor understanding by using a neural network with dynamic interactions. Finally, the validity of the model is confirmed by comparing model simulations with the results from a psychological experiment.     

Estimating gene regulatory networks and protein-protein interactions of Saccharomyces cerevisiae from multiple genome-wide data

MOTIVATION: Biological processes in cells are properly performed by gene regulations, signal transductions and interactions between proteins. To understand such molecular networks, we propose a statistical method to estimate gene regulatory networks and protein-protein interaction networks simultaneously from DNA microarray data, protein-protein interaction data and other genome-wide data. RESULTS: We unify Bayesian networks and Markov networks for estimating gene regulatory networks and protein-protein interaction networks according to the reliability of each biological information source. Through the simultaneous construction of gene regulatory networks and protein-protein interaction networks of Saccharomyces cerevisiae cell cycle, we predict the role of several genes whose functions are currently unknown. By using our probabilistic model, we can detect false positives of high-throughput data, such as yeast two-hybrid data. In a genome-wide experiment, we find possible gene regulatory relationships and protein-protein interactions between large protein complexes that underlie complex regulatory mechanisms of biological processes.     

Prediction of protein functions with gene ontology and interspecies protein homology data

Accurate computational prediction of protein functions increasingly relies on network-inspired models for the protein function transfer. This task can become challenging for proteins isolated in their own network or those with poor or uncharacterized neighborhoods. Here, we present a novel probabilistic chain-graph-based approach for predicting protein functions that builds on connecting networks of two (or more) different species by links of high interspecies sequence homology. In this way, proteins are able to "exchange" functional information with their neighbors-homologs from a different species. The knowledge of interspecies relationships, such as the sequence homology, can become crucial in cases of limited information from other sources of data, including the protein-protein interactions or cellular locations of proteins. We further enhance our model to account for the Gene Ontology dependencies by linking multiple but related functional ontology categories within and across multiple species. The resulting networks are of significantly higher complexity than most traditional protein network models. We comprehensively benchmark our method by applying it to two largest protein networks, the Yeast and the Fly. The joint Fly-Yeast network provides substantial improvements in precision, accuracy, and false positive rate over networks that consider either of the sources in isolation. At the same time, the new model retains the computational efficiency similar to that of the simpler networks.     

On the origin of distribution patterns of motifs in biological networks

Background

Data from high-throughput experiments of protein-protein interactions are commonly used to probe the nature of biological organization and extract functional relationships between sets of proteins. What has not been appreciated is that the underlying mechanisms involved in assembling these networks may exhibit considerable probabilistic behaviour.

Results

We find that the probability of an interaction between two proteins is generally proportional to the numerical product of their individual interacting partners, or degrees. The degree-weighted behaviour is manifested throughout the protein-protein interaction networks studied here, except for the high-degree, or hub, interaction areas. However, we find that the probabilities of interaction between the hubs are still high. Further evidence is provided by path length analyses, which show that these hubs are separated by very few links.

Conclusion

The results suggest that protein-protein interaction networks incorporate probabilistic elements that lead to scale-rich hierarchical architectures. These observations seem to be at odds with a biologically-guided organization. One interpretation of the findings is that we are witnessing the ability of proteins to indiscriminately bind rather than the protein-protein interactions that are actually utilized by the cell in biological processes. Therefore, the topological study of a degree-weighted network requires a more refined methodology to extract biological information about pathways, modules, or other inferred relationships among proteins.     

Probabilistic model of the human protein-protein interaction network

A catalog of all human protein-protein interactions would provide scientists with a framework to study protein deregulation in complex diseases such as cancer. Here we demonstrate that a probabilistic analysis integrating model organism interactome data, protein domain data, genome-wide gene expression data and functional annotation data predicts nearly 40,000 protein-protein interactions in humans-a result comparable to those obtained with experimental and computational approaches in model organisms. We validated the accuracy of the predictive model on an independent test set of known interactions and also experimentally confirmed two predicted interactions relevant to human cancer, implicating uncharacterized proteins into definitive pathways. We also applied the human interactome network to cancer genomics data and identified several interaction subnetworks activated in cancer. This integrative analysis provides a comprehensive framework for exploring the human protein interaction network.     

Rich probabilistic models for gene expression

Clustering is commonly used for analyzing gene expression data. Despite their successes, clustering methods suffer from a number of limitations. First, these methods reveal similarities that exist over all of the measurements, while obscuring relationships that exist over only a subset of the data. Second, clustering methods cannot readily incorporate additional types of information, such as clinical data or known attributes of genes. To circumvent these shortcomings, we propose the use of a single coherent probabilistic model, that encompasses much of the rich structure in the genomic expression data, while incorporating additional information such as experiment type, putative binding sites, or functional information. We show how this model can be learned from the data, allowing us to discover patterns in the data and dependencies between the gene expression patterns and additional attributes. The learned model reveals context-specific relationships, that exist only over a subset of the experiments in the dataset. We demonstrate the power of our approach on synthetic data and on two real-world gene expression data sets for yeast. For example, we demonstrate a novel functionality that falls naturally out of our framework: predicting the "cluster" of the array resulting from a gene mutation based only on the gene's expression pattern in the context of other mutations.     

Reconstruction of a functional human gene network, with an application for prioritizing positional candidate genes

Most common genetic disorders have a complex inheritance and may result from variants in many genes, each contributing only weak effects to the disease. Pinpointing these disease genes within the myriad of susceptibility loci identified in linkage studies is difficult because these loci may contain hundreds of genes. However, in any disorder, most of the disease genes will be involved in only a few different molecular pathways. If we know something about the relationships between the genes, we can assess whether some genes (which may reside in different loci) functionally interact with each other, indicating a joint basis for the disease etiology. There are various repositories of information on pathway relationships. To consolidate this information, we developed a functional human gene network that integrates information on genes and the functional relationships between genes, based on data from the Kyoto Encyclopedia of Genes and Genomes, the Biomolecular Interaction Network Database, Reactome, the Human Protein Reference Database, the Gene Ontology database, predicted protein-protein interactions, human yeast two-hybrid interactions, and microarray co-expressions. We applied this network to interrelate positional candidate genes from different disease loci and then tested 96 heritable disorders for which the Online Mendelian Inheritance in Man database reported at least three disease genes. Artificial susceptibility loci, each containing 100 genes, were constructed around each disease gene, and we used the network to rank these genes on the basis of their functional interactions. By following up the top five genes per artificial locus, we were able to detect at least one known disease gene in 54% of the loci studied, representing a 2.8-fold increase over random selection. This suggests that our method can significantly reduce the cost and effort of pinpointing true disease genes in analyses of disorders for which numerous loci have been reported but for which most of the genes are unknown.     

The statistical inevitability of stability-diversity relationships in community ecology

In this article, we explain an often overlooked process that may significantly contribute to positive correlations between measures of species diversity and community stability. Empirical studies showing positive stability-diversity relationships have, for the most part, used a single class of stability (or, more accurately, instability) measures: the temporal variation in aggregate community properties such as biomass or productivity. We show that for these measures, stability will essentially always rise with species diversity because of the statistical averaging of the fluctuations in species' abundances. This simple probabilistic process will operate in the absence of any strong species interactions, although its strength is driven by the relative abundances of species, as well as by the existence of positive or negative correlations in the fluctuations of species. To explore the possible importance of this effect in real communities, we fit a simple simulation model to Tilman's grassland community. Our results indicate that statistical averaging might play a substantial role in explaining stability-diversity correlations for this and other systems. Models of statistical averaging can serve as a useful baseline for predictions of community stability, to which the influences of both negative and positive species interactions may then be added and tested.     

Global mapping of pharmacological space

We present the global mapping of pharmacological space by the integration of several vast sources of medicinal chemistry structure-activity relationships (SAR) data. Our comprehensive mapping of pharmacological space enables us to identify confidently the human targets for which chemical tools and drugs have been discovered to date. The integration of SAR data from diverse sources by unique canonical chemical structure, protein sequence and disease indication enables the construction of a ligand-target matrix to explore the global relationships between chemical structure and biological targets. Using the data matrix, we are able to catalog the links between proteins in chemical space as a polypharmacology interaction network. We demonstrate that probabilistic models can be used to predict pharmacology from a large knowledge base. The relationships between proteins, chemical structures and drug-like properties provide a framework for developing a probabilistic approach to drug discovery that can be exploited to increase research productivity.     

Elastic network modeling of cellular networks unveils sensor and effector genes that control information flow

The high-level organization of the cell is embedded in indirect relationships that connect distinct cellular processes. Existing computational approaches for detecting indirect relationships between genes typically consist of propagating abstract information through network representations of the cell. However, the selection of genes to serve as the source of propagation is inherently biased by prior knowledge. Here, we sought to derive an unbiased view of the high-level organization of the cell by identifying the genes that propagate and receive information most effectively in the cell, and the indirect relationships between these genes. To this aim, we adapted a perturbation-response scanning strategy initially developed for identifying allosteric interactions within proteins. We deployed this strategy onto an elastic network model of the yeast genetic interaction profile similarity network. This network revealed a superior propensity for information propagation relative to simulated networks with similar topology. Perturbation-response scanning identified the major distributors and receivers of information in the network, named effector and sensor genes, respectively. Effectors formed dense clusters centrally integrated into the network, whereas sensors formed loosely connected antenna-shaped clusters and contained genes with previously characterized involvement in signal transduction. We propose that indirect relationships between effector and sensor clusters represent major paths of information flow between distinct cellular processes. Genetic similarity networks for fission yeast and human displayed similarly strong propensities for information propagation and clusters of effector and sensor genes, suggesting that the global architecture enabling indirect relationships is evolutionarily conserved across species. Our results demonstrate that elastic network modeling of cellular networks constitutes a promising strategy to probe the high-level organization and cooperativity in the cell.     

Genome-genome interactions: bacterial communities in initial dental plaque

The usual context for genome-genome interactions is DNA-DNA interactions, but the manifestation of the genome is the cell. Here we focus on cell-cell interactions and relate them to the process of building multi-species biofilm communities. We propose that dental plaque communities originate as a result of intimate interactions between cells (genomes) of different species and not through clonal growth of genetically identical cells. Although DNA exchange might occur between cells within these communities, we limit our opinions to discussions of the spatiotemporal and metabolic relationships that exist here. We believe the multi-species interactions occurring during the early stages of biofilm formation determine the species composition and nature of the mature biofilm. The human oral cavity provides easy access to natural biofilms on a retrievable enamel chip, which is an excellent model for the study of genome-genome interactions.     

Systematic interpretation of genetic interactions using protein networks

Genetic interaction analysis,in which two mutations have a combined effect not exhibited by either mutation alone, is a powerful and widespread tool for establishing functional linkages between genes. In the yeast Saccharomyces cerevisiae, ongoing screens have generated >4,800 such genetic interaction data. We demonstrate that by combining these data with information on protein-protein, prote in-DNA or metabolic networks, it is possible to uncover physical mechanisms behind many of the observed genetic effects. Using a probabilistic model, we found that 1,922 genetic interactions are significantly associated with either between- or within-pathway explanations encoded in the physical networks, covering approximately 40% of known genetic interactions. These models predict new functions for 343 proteins and suggest that between-pathway explanations are better than within-pathway explanations at interpreting genetic interactions identified in systematic screens. This study provides a road map for how genetic and physical interactions can be integrated to reveal pathway organization and function.     

Duplication models for biological networks.

Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit power-law graphs (number of nodes with degree k, N(k) approximately k(-beta)), yet the exponents, beta, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce power-law graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.     

H-CORE: enabling genome-scale Bayesian analysis of biological systems without prior knowledge

The Bayesian network is a popular tool for describing relationships between data entities by representing probabilistic (in)dependencies with a directed acyclic graph (DAG) structure. Relationships have been inferred between biological entities using the Bayesian network model with high-throughput data from biological systems in diverse fields. However, the scalability of those approaches is seriously restricted because of the huge search space for finding an optimal DAG structure in the process of Bayesian network learning. For this reason, most previous approaches limit the number of target entities or use additional knowledge to restrict the search space. In this paper, we use the hierarchical clustering and order restriction (H-CORE) method for the learning of large Bayesian networks by clustering entities and restricting edge directions between those clusters, with the aim of overcoming the scalability problem and thus making it possible to perform genome-scale Bayesian network analysis without additional biological knowledge. We use simulations to show that H-CORE is much faster than the widely used sparse candidate method, whilst being of comparable quality. We have also applied H-CORE to retrieving gene-to-gene relationships in a biological system (The 'Rosetta compendium'). By evaluating learned information through literature mining, we demonstrate that H-CORE enables the genome-scale Bayesian analysis of biological systems without any prior knowledge.