INFERENCE OF LARGE-SCALE GENE REGULATORY NETWORKS USING REGRESSION-BASED NETWORK APPROACH

SLIVER: Unveiling large scale gene regulatory networks of single-cell transcriptomic data through causal structure learning and modules aggregation

Inferring transcriptional gene regulatory networks from transcriptomic datasets is a key challenge of systems biology, with potential impacts ranging from medicine to agronomy. There are several techniques used presently to experimentally assay transcription factors to target relationships, defining important information about real gene regulatory networks connections. These techniques include classical ChIP-seq, yeast one-hybrid, or more recently, DAP-seq or target technologies. These techniques are usually used to validate algorithm predictions. Here, we developed a reverse engineering approach based on mathematical and computer simulation to evaluate the impact that this prior knowledge on gene regulatory networks may have on training machine learning algorithms. First, we developed a gene regulatory networks-simulating engine called FRANK (Fast Randomizing Algorithm for Network Knowledge) that is able to simulate large gene regulatory networks (containing 104 genes) with characteristics of gene regulatory networks observed in vivo. FRANK also generates stable or oscillatory gene expression directly produced by the simulated gene regulatory networks. The development of FRANK leads to important general conclusions concerning the design of large and stable gene regulatory networks harboring scale free properties (built ex nihilo). In combination with supervised (accepting prior knowledge) support vector machine algorithm we (i) address biologically oriented questions concerning our capacity to accurately reconstruct gene regulatory networks and in particular we demonstrate that prior-knowledge structure is crucial for accurate learning, and (ii) draw conclusions to inform experimental design to performed learning able to solve gene regulatory networks in the future. By demonstrating that our predictions concerning the influence of the prior-knowledge structure on support vector machine learning capacity holds true on real data (Escherichia coli K14 network reconstruction using network and transcriptomic data), we show that the formalism used to build FRANK can to some extent be a reasonable model for gene regulatory networks in real cells.

Recently, nonlinear vector autoregressive (NVAR) model based on Granger causality was proposed to infer nonlinear gene regulatory networks from time series gene expression data. Since NVAR requires a large number of parameters due to the basis expansion, the length of time series microarray data is insufficient for accurate parameter estimation and we need to limit the size of the gene set strongly. To address this limitation, we employ L1 regularization technique to estimate NVAR. Under L1 regularization, direct parents of each gene can be selected efficiently even when the number of parameters exceeds the number of data samples. We can thus estimate larger gene regulatory networks more accurately than those from existing methods. Through the simulation study, we verify the effectiveness of the proposed method by comparing its limitation in the number of genes to that of the existing NVAR. The proposed method is also applied to time series microarray data of Human hela cell cycle.

S-system model has been proposed to identify gene regulatory network in the past years. However, due to the computation complexity, this model is only used for reconstruction of small-scale networks. In this paper, the restricted additive tree model (RAT) is proposed to infer the large-scale gene regulatory networks. In the method, restricted additive tree model is used to encode the S-system model, and the hybrid evolution approach is used to optimize the structure and parameters of restricted additive tree. The large-scale gene regulatory network containing 30 genes is used to test the performance of our method. The results reveal that our method could identify the large-scale gene regulatory network correctly.

Plants respond to stresses like drought and heat through complex gene regulatory networks (GRNs). To improve resilience, understanding these is crucial, but large-scale GRNs (>100 genes) are difficult to model using ordinary differential equations (ODEs) due to the high number of parameters that have to be estimated. Here we solve this problem by introducing BADDADAN, which uses machine learning to identify gene modules—groups of co-expressed and/or co-regulated genes—and constructs an ODE model that predicts gene module dynamics under stress. By integrating time-series gene expression data with prior co-expression data it finds modules that are both coherent and interpretable. We demonstrate BADDADAN on heat and drought datasets of A. thaliana, modelling over 1,000 genes, recovering known mechanistic insights, and proposing new hypotheses. By combining machine learning with mechanistic modelling, BADDADAN deepens our understanding of stress-related GRNs in plants and potentially other organisms.

In this chapter, a novel gene regulatory network gene regulatory network inference algorithm based on the fuzzy logic network fuzzy logic network is proposed and tested. The algorithm is intuitive and robust. The key motivation for this algorithm is that genes with regulatory relationships can be modeled via fuzzy logic, and the degrees of regulations can be represented as the accumulated distance during a period of time intervals. One unique feature of this algorithm is that it makes very limited prior assumptions concerning the modeling; hence the algorithm is categorized as a data-driven algorithm data-driven algorithm. As a non-parametric model, the algorithm is very useful when only limited a priori knowledge on the target microarray exists. Another characteristic of this algorithm is that the time-series microarray data have been treated as a dynamic gene regulatory network gene regulatory network, and the fuzzification of gene expression values makes the algorithm more agreeable to reality. We have deduced the dynamic properties of the FLN using the anneal approximation, and dynamic equations of the FLN have been analyzed. Based upon previous investigation results that in yeast protein-protein networks, as well as in the Internet and social networks, the distribution of connectivity follows the Zipf’s law, the criteria of parameter quantifications for the algorithm have been achieved. The algorithm was applied on the yeast cell-cycle dataset from Stanford Saccharomyces cerevisiae database which produced pleasing results. The computation also showed that a triplet search is suitable and efficient for the inference of gene regulatory networks. The chapter is organized as follows: first, the broader context of gene regulatory networks research is addressed. Then the definition of the FLN is given, and the dynamic properties of the FLN are deduced using the annealed approximation annealed approximation in Sect. FLNTheory. Combined with the Zipf’s law, the parameter quantification guidelines are achieved at the end of this section. In Sect. AlgorithmDesign, the algorithm is illustrated in detail with its data-driven rationale. Then, the algorithm’s inference results on Saccharomyces cerevisiae dataset are presented and analyzed in Sect. ComputationResults. Future research work with the algorithm is discussed at the end of this chapter.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

Genes encode proteins, some of which in turn regulate other genes. Such interactions make up a gene regulatory network. The understanding and unraveling of gene regulatory networks have been proven very useful in disease diagnosis and genomic drug design. Due to the complexity of gene regulatory networks, the completely understanding of their dynamics is difficult to achieve only through biological experiments without any computational aids. As a consequence, computational models for gene regulatory networks are indispensable. Recently a wide variety of different computational models have been proposed for inferring gene regulatory networks. This paper surveys some of computational models for inferring large gene regulatory networks, in particular, Boolean network model, differential/ difference equation models, and state-space models. Some advantages and disadvantages of these models are commented on. Some criteria for validating the inferred gene regulatory networks are also discussed from the bioinformatics perspective. Finally, several directions of the future work for modeling gene regulatory networks are proposed.

Mathematical modeling gene regulatory networks is important for understanding and controlling them, with various drugs and their dosage regimens. The ordinary differential equations approach is sensible but also very difficult. Our reverse engineering algorithm (RODES), based on neural networks feedback linearization and genetic programming, takes as inputs high-throughput (e.g., microarray) time series data and automatically infer an accurate ordinary differential equations model. The algorithm decouples the systems of differential equations, reducing the problem to that of revere engineering individual algebraic equations, and is able to deal with missing information, reconstructing the temporal series of the transcription factors or drug related compounds which are usually missing in microarray experiments. It is also able to incorporate common a priori knowledge. To our knowledge, this is the first realistic reverse engineering algorithm, based on genetic programming and neural networks, applicable to large gene networks.

The inference of genetic regulatory networks (GRNs) reveals how genes interact with each other. A few genes can regulate many genes as targets to control cell functions. We present new methods based on the order-1 vector autoregression (VAR1) for inferring GRNs from gene expression time series. The methods use the automatic relevance determination (ARD) to incorporate the regulatory hub structure into the estimation of VAR1 in a Bayesian framework. Several sparse approximation schemes are applied to the estimated regression weights or VAR1 model to generate the sparse weighted adjacency matrices representing the inferred GRNs. We apply the proposed and several widespread reference methods to infer GRNs with up to 100 genes using simulated, DREAM4 in silico and experimental E. coli gene expression time series. We show that the proposed methods are efficient on simulated hub GRNs and scale-free GRNs using short time series simulated by VAR1s and outperform reference methods on small-scale DREAM4 in silico GRNs and E. coli GRNs. They can utilize the known major regulatory hubs to improve the performance on larger DREAM4 in silico GRNs and E. coli GRNs. The impact of nonlinear time series data on the performance of proposed methods is discussed.

Many studies exist for reconstructing gene regulatory networks (GRNs). In this paper, we propose a method based on an advanced neuro-fuzzy system, for gene regulatory network reconstruction from microarray time-series data. This approach uses a neural network with a weighted fuzzy function to model the relationships between genes. Fuzzy rules, which determine the regulators of genes, are very simplified through this method. Additionally, a regulator selection procedure is proposed, which extracts the exact dynamic relationship between genes, using the information obtained from the weighted fuzzy function. Time-series related features are extracted from the original data to employ the characteristics of temporal data that are useful for accurate GRN reconstruction. The microarray dataset of the yeast cell cycle was used for our study. We measured the mean squared prediction error for the efficiency of the proposed approach and evaluated the accuracy in terms of precision, sensitivity, and F-score. The proposed method outperformed the other existing approaches.

Specification of endoderm is the prerequisite for gut formation in the embryogenesis of bilaterian organisms. Modern lineage labelling studies have shown that in the sea urchin embryo model system, descendants of the veg1 and veg2 cell lineages produce the endoderm, and that the veg2 lineage also gives rise to mesodermal cell types. It is known that Wnt/β-catenin signalling is required for endoderm specification and Delta/Notch signalling is required for mesoderm specification. Some direct cis-regulatory targets of these signals have been found and various phenomenological patterns of gene expression have been observed in the pre-gastrular endomesoderm. However, no comprehensive, causal explanation of endoderm specification has been conceived for sea urchins, nor for any other deuterostome. Here we propose a model, on the basis of the underlying genomic control system, that provides such an explanation, built at several levels of biological organization. The hardwired core of the control system consists of the cis-regulatory apparatus of endodermal regulatory genes, which determine the relationship between the inputs to which these genes are exposed and their outputs. The architecture of the network circuitry controlling the dynamic process of endoderm specification then explains, at the system level, a sequence of developmental logic operations, which generate the biological process. The control system initiates non-interacting endodermal and mesodermal gene regulatory networks in veg2-derived cells and extinguishes the endodermal gene regulatory network in mesodermal precursors. It also generates a cross-regulatory network that specifies future anterior endoderm in veg2 descendants and institutes a distinct network specifying posterior endoderm in veg1-derived cells. The network model provides an explanatory framework that relates endoderm specification to the genomic regulatory code.

Correct inference of genetic regulations inside a cell from the biological database like time series microarray data is one of the greatest challenges in post genomic era for biologists and researchers. Recurrent Neural Network (RNN) is one of the most popular and simple approach to model the dynamics as well as to infer correct dependencies among genes. Inspired by the behavior of social elephants, we propose a new metaheuristic namely Elephant Swarm Water Search Algorithm (ESWSA) to infer Gene Regulatory Network (GRN). This algorithm is mainly based on the water search strategy of intelligent and social elephants during drought, utilizing the different types of communication techniques. Initially, the algorithm is tested against benchmark small and medium scale artificial genetic networks without and with presence of different noise levels and the efficiency was observed in term of parametric error, minimum fitness value, execution time, accuracy of prediction of true regulation, etc. Next, the proposed algorithm is tested against the real time gene expression data of Escherichia Coli SOS Network and results were also compared with others state of the art optimization methods. The experimental results suggest that ESWSA is very efficient for GRN inference problem and performs better than other methods in many ways.

BackgroundA genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data.ResultsThe structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification.ConclusionA statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

A vector autoregressive (VAR) model is a widely used parametric method that captures linear interdependencies between multivariate time series data. However, conventional VAR models are frequently constrained by some assumptions of linearity and stationarity, limiting their ability to capture complex and nonlinearity dynamic observed in real life data. This research aims to develop Multivariate Random Forest Technique for VAR model. Augmented Dickey Fuller (ADF) was applied to test the stationarity of the time series data. Simulated stationary time series data and real time series dataset were applied for modeling VAR model in order to compare their forecast performance. The forecast performance for the proposed technique and existing technique for VAR models were based on Mean Absolute Error and Root Mean Square Error. The proposed multivariate Random Forest technique for VAR model has been developed. The results for unit root test for real life data indicate that all the variables are stationary at level. The result for simulated data in term of forecast performance indicated that the proposed multivariate Random Forest techniques for VAR model outperform existing technique (conventional VAR model) in long term forecasting, while the conventional VAR model outperform proposed multivariate Random Forest technique in short term forecast based on MAE and RMSE. The results for real dataset indicated that the proposed multivariate Random Forest technique for VAR model is superior in terms of forecast performance than that of conventional VAR model in short-term and long-term forecast based on MAE and RMS since the proposed technique has the least value of MAE and RMSE in short and long-term forecasting than the conventional VAR model.