A Computational Approach to Reconstructing Gene Regulatory Networks.

Motivation: Many modeling frameworks have been applied to infer regulatory networks from gene expression data sets. Linear Additive Models (LAMs), as one large category of models, have been gaining more and more popularity. One problem associated with this kind of models is that the system is often under-determined because of excessive number of unknown parameters. In addition, the practical utility of these models has remained unclear. Methods: Based on LAMs, we developed an improved method to infer gene regulatory networks from time-series gene expression data sets. The method includes an incremental connectivity model with indexed regulatory elements and a linear time complexity fitting algorithm embedded with genetic algorithm. Comparing to previous LAMs, where a fully connected model is used, the new technique reduces the number of parameters by O(N), therefore increasing the chance of recovering the underlying regulatory network. The fitting algorithm increment the connectivity during the fitting process until a satisfactory fit is obtained. Results: We performed a systematic study to explore the data mining availability of LAMs. A guideline to use LAMs is provided: If the system is small (3-20 elements), more than 90% regulation pathways can be correctly determined. For a large scale system, either a clustering is needed or it is necessary to integrate other information besides expression profile only. Coupled with clustering method, we applied our method to Rat Central Nervous System development (CNS) data with 112 genes. We were able to efficiently generate regulatory networks with statistically significant pathways which have been previously predicted

Inferring Regulatory Networks by Combining Perturbation Screens and Steady State Gene Expression Profiles

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or are expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network. The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each obtained causal ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in reconstructing the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.Comment: 24 pages, 4 figures, 6 table

High-Dimensional Bayesian Network Inference From Systems Genetics Data Using Genetic Node Ordering

Studying the impact of genetic variation on gene regulatory networks is essential to understand the biological mechanisms by which genetic variation causes variation in phenotypes. Bayesian networks provide an elegant statistical approach for multi-trait genetic mapping and modelling causal trait relationships. However, inferring Bayesian gene networks from high-dimensional genetics and genomics data is challenging, because the number of possible networks scales super-exponentially with the number of nodes, and the computational cost of conventional Bayesian network inference methods quickly becomes prohibitive. We propose an alternative method to infer high-quality Bayesian gene networks that easily scales to thousands of genes. Our method first reconstructs a node ordering by conducting pairwise causal inference tests between genes, which then allows to infer a Bayesian network via a series of independent variable selection problems, one for each gene. We demonstrate using simulated and real systems genetics data that this results in a Bayesian network with equal, and sometimes better, likelihood than the conventional methods, while having a significantly higher overlap with groundtruth networks and being orders of magnitude faster. Moreover our method allows for a unified false discovery rate control across genes and individual edges, and thus a rigorous and easily interpretable way for tuning the sparsity level of the inferred network. Bayesian network inference using pairwise node ordering is a highly efficient approach for reconstructing gene regulatory networks when prior information for the inclusion of edges exists or can be inferred from the available data

Inferring Gene Regulatory Networks from Time Series Microarray Data

The innovations and improvements in high-throughput genomic technologies, such as DNA microarray, make it possible for biologists to simultaneously measure dependencies and regulations among genes on a genome-wide scale and provide us genetic information. An important objective of the functional genomics is to understand the controlling mechanism of the expression of these genes and encode the knowledge into gene regulatory network (GRN). To achieve this, computational and statistical algorithms are especially needed. Inference of GRN is a very challenging task for computational biologists because the degree of freedom of the parameters is redundant. Various computational approaches have been proposed for modeling gene regulatory networks, such as Boolean network, differential equations and Bayesian network. There is no so called golden method which can generally give us the best performance for any data set. The research goal is to improve inference accuracy and reduce computational complexity. One of the problems in reconstructing GRN is how to deal with the high dimensionality and short time course gene expression data. In this work, some existing inference algorithms are compared and the limitations lie in that they either suffer from low inference accuracy or computational complexity. To overcome such difficulties, a new approach based on state space model and Expectation-Maximization (EM) algorithms is proposed to model the dynamic system of gene regulation and infer gene regulatory networks. In our model, GRN is represented by a state space model that incorporates noises and has the ability to capture more various biological aspects, such as hidden or missing variables. An EM algorithm is used to estimate the parameters based on the given state space functions and the gene interaction matrix is derived by decomposing the observation matrix using singular value decomposition, and then it is used to infer GRN. The new model is validated using synthetic data sets before applying it to real biological data sets. The results reveal that the developed model can infer the gene regulatory networks from large scale gene expression data and significantly reduce the computational time complexity without losing much inference accuracy compared to dynamic Bayesian network

Application of new probabilistic graphical models in the genetic regulatory networks studies

This paper introduces two new probabilistic graphical models for reconstruction of genetic regulatory networks using DNA microarray data. One is an Independence Graph (IG) model with either a forward or a backward search algorithm and the other one is a Gaussian Network (GN) model with a novel greedy search method. The performances of both models were evaluated on four MAPK pathways in yeast and three simulated data sets. Generally, an IG model provides a sparse graph but a GN model produces a dense graph where more information about gene-gene interactions is preserved. Additionally, we found two key limitations in the prediction of genetic regulatory networks using DNA microarray data, the first is the sufficiency of sample size and the second is the complexity of network structures may not be captured without additional data at the protein level. Those limitations are present in all prediction methods which used only DNA microarray data.Comment: 38 pages, 3 figure