Constraint Minimization for Efficient Modeling of Gene Regulatory Network

This study was carried out to evaluate the advantage of preselecting SNP markers using Markov blanket algorithm regarding the accuracy of genomic prediction for carcass and meat quality traits in Nellore cattle. This study considered 3675, 3680, 3660 and 524 records of rib eye area (REA), back fat thickness (BF), rump fat (RF), and Warner-Bratzler shear force (WBSF), respectively, from the Nellore Brazil Breeding Program. The animals have been genotyped using low-density SNP panel (30 k), and subsequently imputed for arrays with 777 k SNPs. Four Bayesian specifications of genomic regression models, namely Bayes A, Bayes B, Bayes Cπ and Bayesian Ridge Regression methods were compared in terms of prediction accuracy using a five folds cross-validation. Prediction accuracy for REA, BF and RF was all similar using the Bayesian Alphabet models, ranging from 0.75 to 0.95. For WBSF, the predictive ability was higher using Bayes B (0.47) than other methods (0.39 to 0.42). Although the prediction accuracies using Markov blanket of SNP markers were lower than those using all SNPs, for WBSF the relative gain was lower than 13%. With a subset of informative SNPs markers, identified using Markov blanket, probably, is possible to capture a large proportion of the genetic variance for WBSF. The development of low-density and customized arrays using Markov blanket might be cost-effective to perform a genomic selection for this trait, increasing the number of evaluated animals, improving the management decisions based on genomic information and applying genomic selection on a large scale.

BackgroundThe emergent dynamics of complex gene regulatory networks govern various cellular processes. However, understanding these dynamics is challenging due to the difficulty of parameterizing the computational models for these networks, especially as the network size increases. Here, we introduce a simulation library, Gene Regulatory Interaction Network Simulator (GRiNS), to address these challenges.ResultsGRiNS integrates popular parameter-agnostic simulation frameworks, RACIPE and Boolean Ising formalism, into a single Python library capable of leveraging GPU acceleration for efficient and scalable simulations. GRiNS extends the ordinary differential equations (ODE) based RACIPE framework with a more modular design, allowing users to choose parameters, initial conditions, and time-series outputs for greater customisability and accuracy in simulations. For large networks, where ODE-based simulation formalisms do not scale well, GRiNS implements Boolean Ising formalism, providing a simplified, coarse-grained alternative, significantly reducing the computational cost while capturing key dynamical behaviours of large regulatory networks.ConclusionGRiNS enables parameter-agnostic modeling of gene regulatory networks to study their dynamic and steady-state behaviors in a scalable and efficient manner. The documentation and installation instructions for GRiNS can be found at https://moltenecdysone09.github.io/GRiNS/.

Detecting genetic interactions associated with complex disease is a major issue in genetic studies. Although a number of methods to detect gene-gene interactions for population-based Genome-Wide Association Studies (GWAS) have been developed, the statistical methods for family-based GWAS have been limited. In this study, we propose a new Bayesian approach called MB-TDT to find high-order genetic interactions for pedigree data. The MB-TDT method combines the Markov blanket algorithm with classical Transmission Disequilibrium Test (TDT) statistic. The Incremental Association Markov Blanket (IAMB) algorithm was adopted for large-scale Markov blanket discovery. We evaluated the proposed method using both real and simulated data sets. In a simulation study, we compared the power of MB-TDT with conditional logistic regression, Multifactor Dimensionality Reduction (MDR) and MDR-pedigree disequilibrium test (MDR-PDT). We demonstrated the superior power of MB-TDT in many cases. To demonstrate the approach, we analysed the Korean autism disorder GWAS data. The MB-TDT method can identify a minimal set of causal SNPs associated with a specific disease, thus avoiding an exhaustive search.

Gene regulatory network is a set of genes which interact with each other indirectly and thereby rates of gene expression to mRNA are controlled. DNA microarrays can measure the expression levels of thousands of genes. Because of noise in microarray data and probabilistic nature of Bayesian networks (BN), we used them to model causal relations between genes. One difficulty with this technique is that learning the BN structure is an NP-hard problem, as the number of possible structures is superexponential in the number of genes. So in this paper, genes are clustered based on gene ontology and then BN is applied to model relationships between co-clustered genes. On the other hand since time delay information exists in a real regulatory network and BN is a static network, we proposed a novel method that uses cross-correlation between co-clustered genes to incorporate time information in BN. This method is applied to reconstruct the regulatory network of 84 yeast genes from Saccharomyces cerevisiae cell cycle dataset. Comparing the simulations results with the KEGG pathway map show that using cross-correlation increases accuracy from 66% to 72%. Sensitivity of model is improved too, as the number of inferred links is increased from 70 to 101.

DNA microarray technology plays an important role in advancing the analysis of gene expression and gene functions. However, gene expression data often contain missing values, which cause problems as most of the analysis methods of gene expression data require a complete matrix. Several missing value imputation methods have been developed to overcome the problems. In this paper, effects of the missing value imputation methods in modeling of gene regulatory network are investigated. Three missing value imputation methods are used, which are k-Nearest Neighbor (kNN), Iterated Local Least Squares (ILLsimpute), and Fixed Rank Approximation Algorithm (FRAA). Dataset used in this paper is E. coli. The results suggest that the performance of each missing value imputation method is influenced by the percentage and distribution of the missing values in the dataset, which subsequently affect the modeling of gene regulatory network using Dynamic Bayesian network.

Application of high-throughput data from microarray experiments is a promising way of finding regulatory relationships between genes. Recently, a causal model approach was presented for learning gene regulatory networks from microarray data. The paper investigates and extends this model by identifying the way in which the causal structure can be best exploited computationally to make inference faster and closer to the underlying model. We examine the influence of various hypotheses about the sub-model space on the discovery of causal models. We develop scoring algorithms to learn V-structure, Y- structure and the Markov blanket of every node, by the efficient application of conditional independence (CI) tests of increasing orders on the data. Data from artificial networks as well as real-world S.cerevisiae cellcycle measurements (Spellman et al) were used to evaluate the confidence in our scoring algorithms. The Markov blanket algorithm demonstrated better structural correctness, computational efficiency along with accuracy improvement compared to V-structure and Y-structure learning algorithms.

A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

Living cells can be observed as complex dynamical systems that are constantly remodelling themselves as response to changes in their environment (Zak et al., 2005). The cell metabolism includes number of reactions and products of reactions which interact forming a metabolic network. Due to the fact that large amount of date about processes in living cells are being collected every day, it become necessary to use computers for data processing and analysis. Introducing computer technologies into biology new discipline has been develop, systems biology or computational biology. The aim of system biology is describing and understanding how parts of organism interact in one complex system ; systems biology aims to develop mathematical model of biological systems by integrating experimental and theoretical techniques (Hecker et al., 2009, Albert, 2004). Systems biology studies biological systems by systematically perturbating them (biologically, genetically or chemically) monitoring the genes, proteins and informational pathway response (Strizh et al., 2007). Progress in molecular biology led to development of complete maps of genomes of many organisms ; it is also possible to identify and classify proteins. Although the number of completely sequenced genomes is mounting rapidly, our knowledge of transcription regulation is limited to a few model organisms (Janga and Collado-Vides, 2007). The interactive regulation of genes, working together to create gene networks has been considered the origin of many functions of organism (Mochizuki, 2008). According to Bruggeman and Westerholl, a complete systems biology approach requires (i) characterisation of organism molecular composition, (ii) components dynamics (spatial and temporal) and (iii) detail analysis of molecular response to internal and external stimuli. All these facts are included in development of gene regulatory network. In this chapter the theory of gene regulatory networks will be presented. The chapter will start with ideas how gene regulatory networks are constructed. There will be data on different types of gene regulatory networks and approaches for modeling those systems. This chapter will try to explain why is the modeling of complex regulatory networks important for genetic engineering and how can the mathematical analysis of gene regulatory networks be used for genetic engineering experiments planning and results interpretation.

Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization

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.

Towards efficient and effective discovery of Markov blankets for feature selection

Acute myeloid leukemia (AML) is characterized by uncontrolled proliferation of poorly differentiated myeloid cells, with a heterogenous mutational landscape. Mutations in IDH1 and IDH2 are found in 20% of the AML cases. Although much effort has been made to identify genes associated with leukemogenesis, the regulatory mechanism of AML state transition is still not fully understood. To alleviate this issue, here we develop a new computational approach that integrates genomic data from diverse sources, including gene expression and ATAC-seq datasets, curated gene regulatory interaction databases, and mathematical modeling to establish models of context-specific core gene regulatory networks (GRNs) for a mechanistic understanding of tumorigenesis of AML with IDH mutations. The approach adopts a new optimization procedure to identify the top network according to its accuracy in capturing gene expression states and its flexibility to allow sufficient control of state transitions. From GRN modeling, we identify key regulators associated with the function of IDH mutations, such as DNA methyltransferase DNMT1, and network destabilizers, such as E2F1. The constructed core regulatory network and outcomes of in-silico network perturbations are supported by survival data from AML patients. We expect that the combined bioinformatics and systems-biology modeling approach will be generally applicable to elucidate the gene regulation of disease progression.

Background and Objectives: Gene regulatory networks model the interactions among the genes and provide a decision rule describing activation and repression of each gene via various proteins. In order to be able to capture the complex gene interactions efficiently, it is imperative to develop algorithms that model the nonlinear interactions among the genes. This work considers the problem of inferring gene regulatory networks using time series data. A nonlinear model is assumed for the gene expression profiles, whereas the microarray data follows a linear Gaussian model. Methods: A particle filter based approach is proposed to estimate the gene expression profiles and the parameters are estimated online using the Kalman filter. In order to capture the inherent sparsity of gene networks, a least squares shrinkage selection operator (LASSO) based regression and model selection algorithm is proposed. Results: The performance of the aforementioned algorithm is rigorously evaluated for synthetic as well as real biological data sets arising from Drosophila melanogaster time series gene expression profiles. The results are contrasted with those reported in the literature. The performance of the proposed algorithm is compared with the extended Kalman filter (EKF) algorithm using mean square error (MSE) as the fidelity criterion. The proposed algorithm is observed to outperform the EKF in the scenarios considered. Conclusions: This work considered the problem of modeling and learning of gene regulatory networks using a nonlinear dynamical model. This represents a quite general modeling set-up. The gene network is modeled using a state space approach, and particle filtering is used for state estimation. The parameters regulating the interaction among genes are supplied by an online Kalman filter. Since the parameter vector is sparse, LASSO identifies the subset of these parameters pertaining to the relevant system coefficients. Extensive performance evaluations demonstrate that the proposed particle filter based approach outperforms EKF in terms of MSE.

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.

Models of Gene Regulatory Networks (GRNs) capture the dynamics of the regulatory processes that occur within the cell as a means to understand the variability observed in gene expression between different conditions. Arguably the simplest mathematical construct used for modeling is the Boolean network, which dictates a set of logical rules for transition between states described as Boolean vectors. Due to the complexity of gene regulation and the limitations of experimental technologies, in most cases knowledge about regulatory interactions and Boolean states is partial. In addition, the logical rules themselves are not known a-priori. Our goal in this work is to create an algorithm that finds the network that fits the data optimally, and identify the network states that correspond to the noise-free data. We present a novel methodology for integrating experimental data and performing a search for the optimal consistent structure via optimization of a linear objective function under a set of linear constraints. In addition, we extend our methodology into a heuristic that alleviates the computational complexity of the problem for datasets that are generated by single-cell RNA-Sequencing(scRNA-Seq). We demonstrate the effectiveness of these tools using a public scRNA-Seq dataset and the GRN that is associated with it. Our methodology wm enable researchers to obtain a better understanding of the dynamics of gene regulatory networks and their biological role.