Recurrent neural network-based modeling of gene regulatory network using elephant swarm water search algorithm.

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

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/.

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.

BackgroundInferring a gene regulatory network (GRN) from high throughput biological data is often an under-determined problem and is a challenging task due to the following reasons: (1) thousands of genes are involved in one living cell; (2) complex dynamic and nonlinear relationships exist among genes; (3) a substantial amount of noise is involved in the data, and (4) the typical small sample size is very small compared to the number of genes. We hypothesize we can enhance our understanding of gene interactions in important biological processes (differentiation, cell cycle, and development, etc) and improve the inference accuracy of a GRN by (1) incorporating prior biological knowledge into the inference scheme, (2) integrating multiple biological data sources, and (3) decomposing the inference problem into smaller network modules.ResultsThis study presents a novel GRN inference method by integrating gene expression data and gene functional category information. The inference is based on module network model that consists of two parts: the module selection part and the network inference part. The former determines the optimal modules through fuzzy c-mean (FCM) clustering and by incorporating gene functional category information, while the latter uses a hybrid of particle swarm optimization and recurrent neural network (PSO-RNN) methods to infer the underlying network between modules. Our method is tested on real data from two studies: the development of rat central nervous system (CNS) and the yeast cell cycle process. The results are evaluated by comparing them to previously published results and gene ontology annotation information.ConclusionThe reverse engineering of GRNs in time course gene expression data is a major obstacle in system biology due to the limited number of time points. Our experiments demonstrate that the proposed method can address this challenge by: (1) preprocessing gene expression data (e.g. normalization and missing value imputation) to reduce the data noise; (2) clustering genes based on gene expression data and gene functional category information to identify biologically meaningful modules, thereby reducing the dimensionality of the data; (3) modeling GRNs with the PSO-RNN method between the modules to capture their nonlinear and dynamic relationships. The method is shown to lead to biologically meaningful modules and networks among the modules.

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.

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.

Interaction among the gene products contributes to the regulation of gene expression.

A reverse-problem in modern systems biology focuses on modeling and simulation of gene regulatory networks, metabolic networks from time-course data. With the depth of research, not only the network structures but also its dynamics are paid more attention. We proposed a method to model the gene regulatory networks in Escherichia coli by using Immune Memory Particle Swarm Optimization(IM-PSO) and Ordinary differential equations (ODEs). This method successfully inferred the dynamics of a small regulation networks for 7 genes using only 4 time-course data of gene expression.

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.

Due to various complexities, as well as noise and high dimensionality, reconstructing a gene regulatory network (GRN) from a high-throughput microarray data becomes computationally intensive.In our earlier work on causal model approach for GRN reconstruction, we had shown the superiority of Markov blanket (MB) algorithm compared to the algorithm using the existing Y and V causal models. In this paper, we show the MB algorithm can be enhanced further by application of the proposed constraint logic minimization (CLM) technique. We describe a framework for minimizing the constraint logic involved (condition independent tests) by exploiting the Markov blanket learning methods developed for a Bayesian network (BN). The constraint relationships are represented in the form of logic using K-map and with the aid of CLM increase the algorithm efficiency and the accuracy. We show improved results by investigations on both the synthetic as well as the real life yeast cell cycle data sets.KeywordsCausal modelMarkov blanketConstraint minimizationGene regulatory network

This paper reviews the information theoretic methods used for inferring gene regulatory networks. Mutual information has been widely used as a dependency measure to estimate the undirected interactions between genes using steady state data. However, employing time-series data results in a directed graph. Since two genes may be interacting with each other via an intermediate gene, their mutual information may show a direct dependency. To resolve this issue, data processing inequality and conditional mutual information have been employed. Mutual information, being a symmetric measure, is unable to predict directed edges using the steady-state data alone, while algorithms using time-series data can be computationally complex as more data is involved. Therefore, non-symmetric measures such as φ mixing coefficients have recently been proposed in the literature. The algorithms using these techniques are also discussed in this article. Estimation of information-theoretic metrics is explained which is a core component of all the methods. Performance metrics that are frequently used to test the robustness and accuracy of the algorithms are also described and some avenues of future research are proposed.

Mathematical modeling has become increasingly indispensable for scientists who study the dynamics of gene regulatory networks (GRN) that underlie cell differentiation and pattern formation in animal development including Xenopus embryogenesis. Here I outline a step-by-step procedure for constructing a mathematical model of GRN based on ordinary differential equations (ODE), using the network of Activin and its downstream target genes Xenopus Brachyury (Xbra) and Goosecoid (Gsc) as an example. I also briefly explain methods to analyse the dynamics described by an ODE model.