Inference of S-system models of gene regulatory networks using immune algorithm

The S-system model is one of the nonlinear differential equation models of gene regulatory networks, and it can describe various dynamics of the relationships among genes. If we successfully infer rigorous S-system model parameters that describe a target gene regulatory network, we can simulate gene expressions mathematically. However, the problem of finding an optimal S-system model parameter is too complex to be solved analytically. Thus, some heuristic search methods that offer approximate solutions are needed for reducing the computational time. In previous studies, several heuristic search methods such as Genetic Algorithms (GAs) have been applied to the parameter search of the S-system model. However, they have not achieved enough estimation accuracy. One of the conceivable reasons is that the mechanisms to escape local optima. We applied an Immune Algorithm (IA) to search for the S-system parameters. IA is also a heuristic search method, which is inspired by the biological mechanism of acquired immunity. Compared to GA, IA is able to search large solution space, thereby avoiding local optima, and have multiple candidates of the solutions. These features work well for searching the S-system model. Actually, our algorithm showed higher performance than GA for both simulation and real data analyses.     

Inferring gene networks from time series microarray data using dynamic Bayesian networks

Dynamic Bayesian networks (DBNs) are considered as a promising model for inferring gene networks from time series microarray data. DBNs have overtaken Bayesian networks (BNs) as DBNs can construct cyclic regulations using time delay information. In this paper, a general framework for DBN modelling is outlined. Both discrete and continuous DBN models are constructed systematically and criteria for learning network structures are introduced from a Bayesian statistical viewpoint. This paper reviews the applications of DBNs over the past years. Real data applications for Saccharomyces cerevisiae time series gene expression data are also shown.     

Reconstruction of gene networks using Bayesian learning and manipulation experiments

MOTIVATION: The analysis of high-throughput experimental data, for example from microarray experiments, is currently seen as a promising way of finding regulatory relationships between genes. Bayesian networks have been suggested for learning gene regulatory networks from observational data. Not all causal relationships can be inferred from correlation data alone. Often several equivalent but different directed graphs explain the data equally well. Intervention experiments where genes are manipulated can help to narrow down the range of possible networks. RESULTS: We describe an active learning algorithm that suggests an optimized sequence of intervention experiments. Simulation experiments show that our selection scheme is better than an unguided choice of interventions in learning the correct network and compares favorably in running time and results with methods based on value of information calculations.     

Gene networks inference using dynamic Bayesian networks

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.     

Bayesian learning of sparse gene regulatory networks

Differential equations (DEs) have been the most widespread formalism for gene regulatory network (GRN) modeling, as they offer natural interpretation of biological processes, easy elucidation of gene relationships, and the capability of using efficient parameter estimation methods. However, an important limitation of DEs is their requirement of O(d(2)) parameters where d is the number of genes modeled, which often causes over-parameterization for large d, leading to the over-fitting of data and dense parameter sets that are hard to interpret. This paper presents the first effort to address the over-parameterization problem by applying the sparse Bayesian learning (SBL) method to sparsify the GRN model of DEs. SBL operates on the parsimony principle, with the objective to reduce the number of effective parameters by driving the redundant parameters to zero. The resulting sparse parameter set offers three important advantages for GRN inference: first, the inferred GRNs are more plausible, since the biological counterparts are known to be sparse; second, gene relationships can be more easily elucidated from sparse sets than from dense sets; and third, the solutions become more optimal and consistent, due to the reduction in the volume of solution space. Experiments are conducted on the yeast Saccharomyces cerevisiae time-series gene expression data, in which known regulatory events related to the cell cycle G1/S phase are reliably reproduced.     

Inference reasoning on fishers' knowledge using Bayesian causal maps

Scientists and managers are not the only holders of knowledge regarding environmental issues: other stakeholders such as farmers or fishers do have empirical and relevant knowledge. Thus, new approaches for knowledge representation in the case of multiple knowledge sources, but still enabling reasoning, are needed. Cognitive maps and Bayesian networks constitute some useful formalisms to address knowledge representations. Cognitive maps are powerful graphical models for knowledge gathering or displaying. If they offer an easy means to express individual judgments, drawing inferences in cognitive maps remains a difficult task. Bayesian networks are widely used for decision making processes that face uncertain information or diagnosis. But they are difficult to elicitate. To take advantage of each formalism and to overcome their drawbacks, Bayesian causal maps have been developed. In this approach, cognitive maps are used to build the network and obtain conditional probability tables. We propose here a complete framework applied on a real problem. From the different views of a group of shellfish dredgers about their activity, we derive a decision facilitating tool, enabling scenarios testing for fisheries management.     

Bayesian Phylogenetic Inference using Relaxed-clocks and the Multispecies Coalescent

The multispecies coalescent (MSC) model accommodates both species divergences and within-species coalescent and provides a natural framework for phylogenetic analysis of genomic data when the gene trees vary across the genome. The MSC model implemented in the program bpp assumes a molecular clock and the Jukes–Cantor model, and is suitable for analyzing genomic data from closely related species. Here we extend our implementation to more general substitution models and relaxed clocks to allow the rate to vary among species. The MSC-with-relaxed-clock model allows the estimation of species divergence times and ancestral population sizes using genomic sequences sampled from contemporary species when the strict clock assumption is violated, and provides a simulation framework for evaluating species tree estimation methods. We conducted simulations and analyzed two real datasets to evaluate the utility of the new models. We confirm that the clock-JC model is adequate for inference of shallow trees with closely related species, but it is important to account for clock violation for distant species. Our simulation suggests that there is valuable phylogenetic information in the gene-tree branch lengths even if the molecular clock assumption is seriously violated, and the relaxed-clock models implemented in bpp are able to extract such information. Our Markov chain Monte Carlo algorithms suffer from mixing problems when used for species tree estimation under the relaxed clock and we discuss possible improvements. We conclude that the new models are currently most effective for estimating population parameters such as species divergence times when the species tree is fixed.     

Inference of scale-free networks from gene expression time series

Quantitative time-series observation of gene expression is becoming possible, for example by cell array technology. However, there are no practical methods with which to infer network structures using only observed time-series data. As most computational models of biological networks for continuous time-series data have a high degree of freedom, it is almost impossible to infer the correct structures. On the other hand, it has been reported that some kinds of biological networks, such as gene networks and metabolic pathways, may have scale-free properties. We hypothesize that the architecture of inferred biological network models can be restricted to scale-free networks. We developed an inference algorithm for biological networks using only time-series data by introducing such a restriction. We adopt the S-system as the network model, and a distributed genetic algorithm to optimize models to fit its simulated results to observed time series data. We have tested our algorithm on a case study (simulated data). We compared optimization under no restriction, which allows for a fully connected network, and under the restriction that the total number of links must equal that expected from a scale free network. The restriction reduced both false positive and false negative estimation of the links and also the differences between model simulation and the given time-series data.     

Experimental design for efficient identification of gene regulatory networks using sparse Bayesian models

Background  

Identifying large gene regulatory networks is an important task, while the acquisition of data through perturbation experiments (e.g., gene switches, RNAi, heterozygotes) is expensive. It is thus desirable to use an identification method that effectively incorporates available prior knowledge – such as sparse connectivity – and that allows to design experiments such that maximal information is gained from each one.     

Bayesian nonparametric meta-analysis using Polya tree mixture models

Summary .   A common goal in meta-analysis is estimation of a single effect measure using data from several studies that are each designed to address the same scientific inquiry. Because studies are typically conducted in geographically disperse locations, recent developments in the statistical analysis of meta-analytic data involve the use of random effects models that account for study-to-study variability attributable to differences in environments, demographics, genetics, and other sources that lead to heterogeneity in populations. Stemming from asymptotic theory, study-specific summary statistics are modeled according to normal distributions with means representing latent true effect measures. A parametric approach subsequently models these latent measures using a normal distribution, which is strictly a convenient modeling assumption absent of theoretical justification. To eliminate the influence of overly restrictive parametric models on inferences, we consider a broader class of random effects distributions. We develop a novel hierarchical Bayesian nonparametric Polya tree mixture (PTM) model. We present methodology for testing the PTM versus a normal random effects model. These methods provide researchers a straightforward approach for conducting a sensitivity analysis of the normality assumption for random effects. An application involving meta-analysis of epidemiologic studies designed to characterize the association between alcohol consumption and breast cancer is presented, which together with results from simulated data highlight the performance of PTMs in the presence of nonnormality of effect measures in the source population.     

A Bayesian mixture model for partitioning gene expression data

In recent years there has been great interest in making inference for gene expression data collected over time. In this article, we describe a Bayesian hierarchical mixture model for partitioning such data. While conventional approaches cluster the observed data, we assume a nonparametric, random walk model, and partition on the basis of the parameters of this model. The model is flexible and can be tuned to the specific context, respects the order of observations within each curve, acknowledges measurement error, and allows prior knowledge on parameters to be incorporated. The number of partitions may also be treated as unknown, and inferred from the data, in which case computation is carried out via a birth-death Markov chain Monte Carlo algorithm. We first examine the behavior of the model on simulated data, along with a comparison with more conventional approaches, and then analyze meiotic expression data collected over time on fission yeast genes.     

Bayesian infinite mixture model based clustering of gene expression profiles

MOTIVATION: The biologic significance of results obtained through cluster analyses of gene expression data generated in microarray experiments have been demonstrated in many studies. In this article we focus on the development of a clustering procedure based on the concept of Bayesian model-averaging and a precise statistical model of expression data. RESULTS: We developed a clustering procedure based on the Bayesian infinite mixture model and applied it to clustering gene expression profiles. Clusters of genes with similar expression patterns are identified from the posterior distribution of clusterings defined implicitly by the stochastic data-generation model. The posterior distribution of clusterings is estimated by a Gibbs sampler. We summarized the posterior distribution of clusterings by calculating posterior pairwise probabilities of co-expression and used the complete linkage principle to create clusters. This approach has several advantages over usual clustering procedures. The analysis allows for incorporation of a reasonable probabilistic model for generating data. The method does not require specifying the number of clusters and resulting optimal clustering is obtained by averaging over models with all possible numbers of clusters. Expression profiles that are not similar to any other profile are automatically detected, the method incorporates experimental replicates, and it can be extended to accommodate missing data. This approach represents a qualitative shift in the model-based cluster analysis of expression data because it allows for incorporation of uncertainties involved in the model selection in the final assessment of confidence in similarities of expression profiles. We also demonstrated the importance of incorporating the information on experimental variability into the clustering model. AVAILABILITY: The MS Windows(TM) based program implementing the Gibbs sampler and supplemental material is available at http://homepages.uc.edu/~medvedm/BioinformaticsSupplement.htm CONTACT: medvedm@email.uc.edu     

Network Plasticity as Bayesian Inference

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.     

Bayesian Inference on Proportional Elections

Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software.