A computational framework for gene regulatory network inference that combines multiple methods and datasets

Background  

Reverse engineering in systems biology entails inference of gene regulatory networks from observational data. This data typically include gene expression measurements of wild type and mutant cells in response to a given stimulus. It has been shown that when more than one type of experiment is used in the network inference process the accuracy is higher. Therefore the development of generally applicable and effective methodologies that embed multiple sources of information in a single computational framework is a worthwhile objective.     

Integrative inference of gene-regulatory networks in Escherichia coli using information theoretic concepts and sequence analysis

Background  

Although Escherichia coli is one of the best studied model organisms, a comprehensive understanding of its gene regulation is not yet achieved. There exist many approaches to reconstruct regulatory interaction networks from gene expression experiments. Mutual information based approaches are most useful for large-scale network inference.     

Influence of statistical estimators of mutual information and data heterogeneity on the inference of gene regulatory networks

The inference of gene regulatory networks from gene expression data is a difficult problem because the performance of the inference algorithms depends on a multitude of different factors. In this paper we study two of these. First, we investigate the influence of discrete mutual information (MI) estimators on the global and local network inference performance of the C3NET algorithm. More precisely, we study 4 different MI estimators (Empirical, Miller-Madow, Shrink and Schürmann-Grassberger) in combination with 3 discretization methods (equal frequency, equal width and global equal width discretization). We observe the best global and local inference performance of C3NET for the Miller-Madow estimator with an equal width discretization. Second, our numerical analysis can be considered as a systems approach because we simulate gene expression data from an underlying gene regulatory network, instead of making a distributional assumption to sample thereof. We demonstrate that despite the popularity of the latter approach, which is the traditional way of studying MI estimators, this is in fact not supported by simulated and biological expression data because of their heterogeneity. Hence, our study provides guidance for an efficient design of a simulation study in the context of network inference, supporting a systems approach.     

Function approximation approach to the inference of reduced NGnet models of genetic networks

Background  

The inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.     

Inference of the Xenopus tropicalis embryonic regulatory network and spatial gene expression patterns

Background

During embryogenesis, signaling molecules produced by one cell population direct gene regulatory changes in neighboring cells and influence their developmental fates and spatial organization. One of the earliest events in the development of the vertebrate embryo is the establishment of three germ layers, consisting of the ectoderm, mesoderm and endoderm. Attempts to measure gene expression in vivo in different germ layers and cell types are typically complicated by the heterogeneity of cell types within biological samples (i.e., embryos), as the responses of individual cell types are intermingled into an aggregate observation of heterogeneous cell types. Here, we propose a novel method to elucidate gene regulatory circuits from these aggregate measurements in embryos of the frog Xenopus tropicalis using gene network inference algorithms and then test the ability of the inferred networks to predict spatial gene expression patterns.

Results

We use two inference models with different underlying assumptions that incorporate existing network information, an ODE model for steady-state data and a Markov model for time series data, and contrast the performance of the two models. We apply our method to both control and knockdown embryos at multiple time points to reconstruct the core mesoderm and endoderm regulatory circuits. Those inferred networks are then used in combination with known dorsal-ventral spatial expression patterns of a subset of genes to predict spatial expression patterns for other genes. Both models are able to predict spatial expression patterns for some of the core mesoderm and endoderm genes, but interestingly of different gene subsets, suggesting that neither model is sufficient to recapitulate all of the spatial patterns, yet they are complementary for the patterns that they do capture.

Conclusion

The presented methodology of gene network inference combined with spatial pattern prediction provides an additional layer of validation to elucidate the regulatory circuits controlling the spatial-temporal dynamics in embryonic development.     

Integrated cellular network of transcription regulations and protein-protein interactions

Background  

With the accumulation of increasing omics data, a key goal of systems biology is to construct networks at different cellular levels to investigate cellular machinery of the cell. However, there is currently no satisfactory method to construct an integrated cellular network that combines the gene regulatory network and the signaling regulatory pathway.     

From knockouts to networks: establishing direct cause-effect relationships through graph analysis

Background

Reverse-engineering gene networks from expression profiles is a difficult problem for which a multitude of techniques have been developed over the last decade. The yearly organized DREAM challenges allow for a fair evaluation and unbiased comparison of these methods.

Results

We propose an inference algorithm that combines confidence matrices, computed as the standard scores from single-gene knockout data, with the down-ranking of feed-forward edges. Substantial improvements on the predictions can be obtained after the execution of this second step.

Conclusions

Our algorithm was awarded the best overall performance at the DREAM4 In Silico 100-gene network sub-challenge, proving to be effective in inferring medium-size gene regulatory networks. This success demonstrates once again the decisive importance of gene expression data obtained after systematic gene perturbations and highlights the usefulness of graph analysis to increase the reliability of inference.     

DREAM4: Combining genetic and dynamic information to identify biological networks and dynamical models

Background

Current technologies have lead to the availability of multiple genomic data types in sufficient quantity and quality to serve as a basis for automatic global network inference. Accordingly, there are currently a large variety of network inference methods that learn regulatory networks to varying degrees of detail. These methods have different strengths and weaknesses and thus can be complementary. However, combining different methods in a mutually reinforcing manner remains a challenge.

Methodology

We investigate how three scalable methods can be combined into a useful network inference pipeline. The first is a novel t-test–based method that relies on a comprehensive steady-state knock-out dataset to rank regulatory interactions. The remaining two are previously published mutual information and ordinary differential equation based methods (tlCLR and Inferelator 1.0, respectively) that use both time-series and steady-state data to rank regulatory interactions; the latter has the added advantage of also inferring dynamic models of gene regulation which can be used to predict the system''s response to new perturbations.

Conclusion/Significance

Our t-test based method proved powerful at ranking regulatory interactions, tying for first out of methods in the DREAM4 100-gene in-silico network inference challenge. We demonstrate complementarity between this method and the two methods that take advantage of time-series data by combining the three into a pipeline whose ability to rank regulatory interactions is markedly improved compared to either method alone. Moreover, the pipeline is able to accurately predict the response of the system to new conditions (in this case new double knock-out genetic perturbations). Our evaluation of the performance of multiple methods for network inference suggests avenues for future methods development and provides simple considerations for genomic experimental design. Our code is publicly available at http://err.bio.nyu.edu/inferelator/.     

Bayesian Orthogonal Least Squares (BOLS) algorithm for reverse engineering of gene regulatory networks

Background  

A reverse engineering of gene regulatory network with large number of genes and limited number of experimental data points is a computationally challenging task. In particular, reverse engineering using linear systems is an underdetermined and ill conditioned problem, i.e. the amount of microarray data is limited and the solution is very sensitive to noise in the data. Therefore, the reverse engineering of gene regulatory networks with large number of genes and limited number of data points requires rigorous optimization algorithm.     

Integrative approach for inference of gene regulatory networks using lasso-based random featuring and application to psychiatric disorders

Background

Inferring gene regulatory networks is one of the most interesting research areas in the systems biology. Many inference methods have been developed by using a variety of computational models and approaches. However, there are two issues to solve. First, depending on the structural or computational model of inference method, the results tend to be inconsistent due to innately different advantages and limitations of the methods. Therefore the combination of dissimilar approaches is demanded as an alternative way in order to overcome the limitations of standalone methods through complementary integration. Second, sparse linear regression that is penalized by the regularization parameter (lasso) and bootstrapping-based sparse linear regression methods were suggested in state of the art methods for network inference but they are not effective for a small sample size data and also a true regulator could be missed if the target gene is strongly affected by an indirect regulator with high correlation or another true regulator.

Results

We present two novel network inference methods based on the integration of three different criteria, (i) z-score to measure the variation of gene expression from knockout data, (ii) mutual information for the dependency between two genes, and (iii) linear regression-based feature selection.Based on these criterion, we propose a lasso-based random feature selection algorithm (LARF) to achieve better performance overcoming the limitations of bootstrapping as mentioned above.

Conclusions

In this work, there are three main contributions. First, our z score-based method to measure gene expression variations from knockout data is more effective than similar criteria of related works. Second, we confirmed that the true regulator selection can be effectively improved by LARF. Lastly, we verified that an integrative approach can clearly outperform a single method when two different methods are effectively jointed. In the experiments, our methods were validated by outperforming the state of the art methods on DREAM challenge data, and then LARF was applied to inferences of gene regulatory network associated with psychiatric disorders.

     

The impact of measurement errors in the identification of regulatory networks

Background  

There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise.     

Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information

Abstract

The extended Kalman filter (EKF) has been applied to inferring gene regulatory networks. However, it is well known that the EKF becomes less accurate when the system exhibits high nonlinearity. In addition, certain prior information about the gene regulatory network exists in practice, and no systematic approach has been developed to incorporate such prior information into the Kalman-type filter for inferring the structure of the gene regulatory network. In this paper, an inference framework based on point-based Gaussian approximation filters that can exploit the prior information is developed to solve the gene regulatory network inference problem. Different point-based Gaussian approximation filters, including the unscented Kalman filter (UKF), the third-degree cubature Kalman filter (CKF₃), and the fifth-degree cubature Kalman filter (CKF₅) are employed. Several types of network prior information, including the existing network structure information, sparsity assumption, and the range constraint of parameters, are considered, and the corresponding filters incorporating the prior information are developed. Experiments on a synthetic network of eight genes and the yeast protein synthesis network of five genes are carried out to demonstrate the performance of the proposed framework. The results show that the proposed methods provide more accurate inference results than existing methods, such as the EKF and the traditional UKF.

     

Reverse engineering gene regulatory networks from measurement with missing values

Background

Gene expression time series data are usually in the form of high-dimensional arrays. Unfortunately, the data may sometimes contain missing values: for either the expression values of some genes at some time points or the entire expression values of a single time point or some sets of consecutive time points. This significantly affects the performance of many algorithms for gene expression analysis that take as an input, the complete matrix of gene expression measurement. For instance, previous works have shown that gene regulatory interactions can be estimated from the complete matrix of gene expression measurement. Yet, till date, few algorithms have been proposed for the inference of gene regulatory network from gene expression data with missing values.

Results

We describe a nonlinear dynamic stochastic model for the evolution of gene expression. The model captures the structural, dynamical, and the nonlinear natures of the underlying biomolecular systems. We present point-based Gaussian approximation (PBGA) filters for joint state and parameter estimation of the system with one-step or two-step missing measurements. The PBGA filters use Gaussian approximation and various quadrature rules, such as the unscented transform (UT), the third-degree cubature rule and the central difference rule for computing the related posteriors. The proposed algorithm is evaluated with satisfying results for synthetic networks, in silico networks released as a part of the DREAM project, and the real biological network, the in vivo reverse engineering and modeling assessment (IRMA) network of yeast Saccharomyces cerevisiae.

Conclusion

PBGA filters are proposed to elucidate the underlying gene regulatory network (GRN) from time series gene expression data that contain missing values. In our state-space model, we proposed a measurement model that incorporates the effect of the missing data points into the sequential algorithm. This approach produces a better inference of the model parameters and hence, more accurate prediction of the underlying GRN compared to when using the conventional Gaussian approximation (GA) filters ignoring the missing data points.

     

Boolean networks using the chi-square test for inferring large-scale gene regulatory networks

Background  

Boolean network (BN) modeling is a commonly used method for constructing gene regulatory networks from time series microarray data. However, its major drawback is that its computation time is very high or often impractical to construct large-scale gene networks. We propose a variable selection method that are not only reduces BN computation times significantly but also obtains optimal network constructions by using chi-square statistics for testing the independence in contingency tables.