Reverse engineering highlights potential principles of large gene regulatory network design and learning

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.

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

The gene regulatory network modeling plays a key role in search for relationships among genes. Many modeling approaches have been introduced to find the causal relationship between genes using time series microarray data. However, they have been suffering from high dimensionality, overfitting, and heavy computation time. Further, the selection of a best model among several possible competing models is not guaranteed that it is the best one. In this study, we propose a simple procedure for constructing large scale gene regulatory networks using a regression-based network approach. We determine the optimal out-degree of network structure by using the sum of squared coefficients which are obtained from all appropriate regression models. Through the simulated data, accuracy of estimation and robustness against noise are computed in order to compare with the vector autoregressive regression model. Our method shows high accuracy and robustness for inferring large-scale gene networks. Also it is applied to Caulobacter crescentus cell cycle data consisting of 1472 genes. It shows that many genes are regulated by two transcription factors, ctrA and gcrA, that are known for global regulators.

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/.

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.

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.

Perturbation avalanches and criticality in gene regulatory networks

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.

The ability to measure the transcriptional response of cells has drawn much attention to the underlying transcriptional networks. To untangle the network, numerous models with corresponding reverse engineering methods have been applied. In this work, we propose a non-linear model with adjustable degrees of complexity. The corresponding reverse engineering method uses a probabilistic scheme to reduce the reconstruction problem to subnetworks. Adequate models for gene regulatory networks must be anchored on sufficient biological knowledge. Here, the cI auto-inhibition circuit (cI circuit) is used to validate our reverse engineering method. Simulations of the cI circuit are used for the reconstruction, whereas a simplified cI circuit model assists the modeling phase. Several levels of complexity are evaluated, subsequently the reconstructed models show different properties. As a result, we reconstruct an abstract model, capturing the dynamic behavior of the cI circuit to a high degree.

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.

BackgroundGenetic canalization reflects the capacity of an organism’s phenotype to remain unchanged in spite of mutations. As selection on genetic canalization is weak and indirect, whether or not genetic canalization can reasonably evolve in complex genetic architectures is still an open question. In this paper, we use a quantitative model of gene regulatory network to describe the conditions in which substantial canalization is expected to emerge in a stable environment.ResultsThrough an individual-based simulation framework, we confirmed that most parameters associated with the network topology (complexity and size of the network) have less influence than mutational parameters (rate and size of mutations) on the evolution of genetic canalization. We also established that selecting for extreme phenotypic optima (nil or full gene expression) leads to much higher canalization levels than selecting for intermediate expression levels. Overall, constrained networks evolve less canalization than networks in which some genes could evolve freely (i.e. without direct stabilizing selection pressure on gene expression).ConclusionsTaken together, these results lead us to propose a two-fold mechanism involved in the evolution of genetic canalization in gene regulatory networks: the shrinkage of mutational target (useless genes are virtually removed from the network) and redundancy in gene regulation (so that some regulatory factors can be lost without affecting gene expression).Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-016-0801-2) contains supplementary material, which is available to authorized users.

A Generalized Gene-Regulatory Network Model of Stem Cell Differentiation for Predicting Lineage Specifiers

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.

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

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.