Models Of Gene Regulatory Networks Research Articles

Estimation of Ordinary Differential Equation Models for Gene Regulatory Networks Through Data Cloning.

Ordinary differential equations (ODEs) are widely used for elucidating dynamic processes in various fields. One of the applications of ODEs is to describe dynamics of gene regulatory networks (GRNs), which is a critical step in understanding disease mechanisms. However, estimation of ODE models for GRNs is challenging because of inflexibility of the model and noisy data with complex error structures such as heteroscedasticity, correlations between genes, and time dependency. In addition, either a likelihood or Bayesian approach is commonly used for estimation of ODE models, but both approaches have benefits and drawbacks in their own right. Data cloning is a maximum likelihood (ML) estimation method through the Bayesian framework. Since it works in the Bayesian framework, it is free from local optimum problems that are common drawbacks of ML methods. Also, its inference is invariant for the selection of prior distributions, which is a major issue in Bayesian methods. This study proposes an estimation method of ODE models for GRNs through data cloning. The proposed method is demonstrated through simulation and it is applied to real gene expression time-course data.

Robust KALMAN Filter State Estimation for Gene Regulatory Networks.

This paper proposes a revised version of the robust generalized maximum likelihood (GM)-type unscented KALMAN filter (GM-UKF) for the state estimation of gene regulatory networks (GRNs) in the presence of different types of deviations from assumptions. As known, the parameters and the power of the assumed noises within the GRN model may change abruptly as a result of jump behavior and bursting process in transcription and translation phases. Moreover, there may be outlying samples among genomic measurement data. Some other outliers may also occur in the model dynamics. The outliers may be misinterpreted by the filtering method if not detected and downweighted. To deal with all such deviations, a robust GM-UKF is designed that includes some modifications to address the challenges in calculating the projection statistics in GRNs such as the nonlinear behavior and the natural distance of the states. The proposed filter is compared to four Bayesian filters, i.e., the conventional UKF, the H ∞-UKF, the downweighting UKF (DW-UKF), and a modified version of the GM-UKF, the so-called maximum-likelihood UKF(M-UKF). The outcome results demonstrate that the GM-UKF outperforms other methods for all outlier types while the H ∞-UKF is appropriate for the changes in noise powers.

Dynamic modeling of the cellular senescence gene regulatory network

Cellular senescence is a cell fate that prominently impacts physiological and pathophysiological processes. Diverse cellular stresses induce it, and dramatic gene expression changes accompany it. However, determining the interactions comprising the gene regulatory network (GRN) governing senescence remains challenging. Recent advances in signal processing techniques provide opportunities to reconstruct GRNs. Here, we describe a GRN for senescence integrating time-series transcriptome and transcription factor depletion datasets. Specifically, we infer a set of differential equations using the “Sparse Identification of Nonlinear Dynamics” (SINDy) algorithm, discriminate genes with potential hidden regulators, validate the inferred GRN for time-points not included in the training data, and comprehensively benchmark our approach. Our work is a proof of concept for a data-driven GRN reconstruction method, consolidating an iterative, powerful mathematical platform for senescence modeling that can be used to test hypotheses in silico and has the potential for future discoveries of clinical impact.

Integrated regulatory and metabolic networks of the tumor microenvironment for therapeutic target prioritization.

Translation of genomic discovery, such as single-cell sequencing data, to clinical decisions remains a longstanding bottleneck in the field. Meanwhile, computational systems biological models, such as cellular metabolism models and cell signaling pathways, have emerged as powerful approaches to provide efficient predictions in metabolites and gene expression levels, respectively. However, there has been limited research on the integration between these two models. This work develops a methodology for integrating computational models of probabilistic gene regulatory networks with a constraint-based metabolism model. By using probabilistic reasoning with Bayesian Networks, we aim to predict cell-specific changes under different interventions, which are embedded into the constraint-based models of metabolism. Applications to single-cell sequencing data of glioblastoma brain tumors generate predictions about the effects of pharmaceutical interventions on the regulatory network and downstream metabolisms in different cell types from the tumor microenvironment. The model presents possible insights into treatments that could potentially suppress anaerobic metabolism in malignant cells with minimal impact on other cell types' metabolism. The proposed integrated model can guide therapeutic target prioritization, the formulation of combination therapies, and future drug discovery. This model integration framework is also generalizable to other applications, such as different cell types, organisms, and diseases.

The gene regulatory network of Staphylococcus aureus ST239-SCCmecIII strain Bmb9393 and assessment of genes associated with the biofilm in diverse backgrounds.

Staphylococcus aureus is one of the most prevalent and relevant pathogens responsible for a wide spectrum of hospital-associated or community-acquired infections. In addition, methicillin-resistant Staphylococcus aureus may display multidrug resistance profiles that complicate treatment and increase the mortality rate. The ability to produce biofilm, particularly in device-associated infections, promotes chronic and potentially more severe infections originating from the primary site. Understanding the complex mechanisms involved in planktonic and biofilm growth is critical to identifying regulatory connections and ways to overcome the global health problem of multidrug-resistant bacteria. In this work, we apply literature-based and comparative genomics approaches to reconstruct the gene regulatory network of the high biofilm-producing strain Bmb9393, belonging to one of the highly disseminating successful clones, the Brazilian epidemic clone. To the best of our knowledge, we describe for the first time the topological properties and network motifs for the Staphylococcus aureus pathogen. We performed this analysis using the ST239-SCCmecIII Bmb9393 strain. In addition, we analyzed transcriptomes available in the literature to construct a set of genes differentially expressed in the biofilm, covering different stages of the biofilms and genetic backgrounds of the strains. The Bmb9393 gene regulatory network comprises 1,803 regulatory interactions between 64 transcription factors and the non-redundant set of 1,151 target genes with the inclusion of 19 new regulons compared to the N315 transcriptional regulatory network published in 2011. In the Bmb9393 network, we found 54 feed-forward loop motifs, where the most prevalent were coherent type 2 and incoherent type 2. The non-redundant set of differentially expressed genes in the biofilm consisted of 1,794 genes with functional categories relevant for adaptation to the variable microenvironments established throughout the biofilm formation process. Finally, we mapped the set of genes with altered expression in the biofilm in the Bmb9393 gene regulatory network to depict how different growth modes can alter the regulatory systems. The data revealed 45 transcription factors and 876 shared target genes. Thus, the gene regulatory network model provided represents the most up-to-date model for Staphylococcus aureus, and the set of genes altered in the biofilm provides a global view of their influence on biofilm formation from distinct experimental perspectives and different strain backgrounds.

A data-driven optimization method for coarse-graining gene regulatory networks

One major challenge in systems biology is to understand how various genes in a gene regulatory network (GRN) collectively perform their functions and control network dynamics. This task becomes extremely hard to tackle in the case of large networks with hundreds of genes and edges, many of which have redundant regulatory roles and functions. The existing methods for model reduction usually require the detailed mathematical description of dynamical systems and their corresponding kinetic parameters, which are often not available. Here, we present a data-driven method for coarse-graining large GRNs, named SacoGraci, using ensemble-based mathematical modeling, dimensionality reduction, and gene circuit optimization by Markov Chain Monte Carlo methods. SacoGraci requires network topology as the only input and is robust against errors in GRNs. We benchmark and demonstrate its usage with synthetic, literature-based, and bioinformatics-derived GRNs. We hope SacoGraci will enhance our ability to model the gene regulation of complex biological systems.

Identification of Gene Regulatory Networks Using Variational Bayesian Inference in the Presence of Missing Data.

The identification of gene regulatory networks (GRN) from gene expression time series data is a challenge and open problem in system biology. This paper considers the structure inference of GRN from the incomplete and noisy gene expression data, which is a not well-studied issue for GRN inference. In this paper, the dynamical behavior of the gene expression process is described by a stochastic nonlinear state-space model with unknown noise information. A variational Bayesian (VB) framework are proposed to estimate the parameters and gene expression levels simultaneously. One of the advantages of this method is that it can easily handle the missing observations by generating the prediction values. Considering the sparsity of GRN, the smoothed gene data are modeled by the extreme gradient boosting tree, and the regulatory interactions among genes are identified by the importance scores based on the tree model. The proposed method is tested on the artificial DREAM4 datasets and one real gene expression dataset of yeast. The comparative results show that the proposed method can effectively recover the regulatory interactions of GRN in the presence of missing observations and outperforms the existing methods for GRN identification.

The ensemble of gene regulatory networks at mutation-selection balance.

The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation-selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that-across a broad spectrum of selection pressures-the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory-and thus to classical populations genetics-providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules.

Genetic and metabolic engineering of Methanococcus spp

Methanococcus is a genus of well-characterized mesophilic and hydrogenotrophic methanogens with a robust genetic system. Commonly found in tidal marshes, they compete with sulfate- and iron-reducing bacteria for hydrogen gas (H2) and formate, their two major energy sources. They are characterized by rapid growth in mineral medium and requirements for marine levels of salts for optimal growth. Genetic tools developed over the last twenty years include improvements in shuttle vectors for production of recombinant proteins and CRISPR systems for mutagenesis as well as a variety of marker proteins for studies of gene expression. These tools have enabled functional characterization of the genome, including regulation of the transcriptome and proteome, mapping of transcription start and termination sites, and identification of essential genes. Metabolic and gene regulatory network models have been created. This foundation in the basic biology of Methanococcus provides an opportunity for development of biotechnological applications of these hydrogenotrophic methanogens.

Gene Regulatory Network Modeling Using Single-Cell Multi-Omics in Plants.

Single-cell multi-omics technology can be applied to plant cells to characterize gene expression and open chromatin regions in individual cells. In this chapter, we describe a computational pipeline for the analysis of single-cell data to construct gene regulatory networks. The major steps of this pipeline include the following: (1) normalize and integrate scRNA-seq and scATAC-seq data (2) identify cluster maker genes (3) perform motif finding for selected marker genes, and (4) identify regulatory networks with machine learning. The pipeline has been tested using data from the model species Arabidopsis and is generally applicable to other plant and animal species to characterize regulatory networks using single-cell multi-omics data.

Virtual cells in a virtual microenvironment recapitulate early development-like patterns in human pluripotent stem cell colonies.

The mechanism by which morphogenetic signals engage the regulatory networks responsible for early embryonic tissue patterning is incompletely understood. Here, we developed a minimal gene regulatory network (GRN) model of human pluripotent stem cell (hPSC) lineage commitment and embedded it into "cellular" agents that respond to a dynamic morphogenetic signaling microenvironment. Simulations demonstrated that GRN wiring had significant non-intuitive effects on tissue pattern order, composition, and dynamics. Experimental perturbation of GRN connectivities supported model predictions and demonstrated the role of OCT4 as a master regulator of peri-gastrulation fates. Our so-called GARMEN strategy provides a multiscale computational platform to understand how single-cell-based regulatory interactions scale to tissue domains. This foundation provides new opportunities to simulate the impact of network motifs on normal and aberrant tissue development.

Analysis of an extended gene regulatory network model with time delay

Analysis of an extended gene regulatory network model with time delay

Gene regulatory network models for modules of molecular mechanism of the control of the photo-morphogenesis in plants

Plants are dynamic systems able to continuously adapt to changing environmental conditions, showing a remarkable phenotypic plasticity as from transition from germination to vegetative growth then to reproductive development. In this review, effect of light, molecular mechanisms photo-morphogenesis and gene regulatory networks were reviewed. This review provides insight into regulatory mechanisms for phytochrome-mediated light signaling pathway; and the roles of phytochromes and their downstream signaling components, molecular mechanisms light-perceiving photoreceptors and other positive and negative regulators of light signaling as well as interactions between these components during plant growth and development. Light is one of the most important factors regulating plant growth and development (photo-morphogenesis). Photomorphogenesis and skotomorphogenesis are two key events that control plant development, from seed germination to flowering and senescence. A group of wavelength-specific photoreceptors, E3 ubiquitin ligases, and various transcription factors work together to regulate these two critical processes. Phytochromes are the main photoreceptors in plants for perceiving red/far-red light and transducing the light signals to downstream factors that regulate the gene expression network for photomorphogenic development.

Systematic comparison of modeling fidelity levels and parameter inference settings applied to negative feedback gene regulation

Quantitative stochastic models of gene regulatory networks are important tools for studying cellular regulation. Such models can be formulated at many different levels of fidelity. A practical challenge is to determine what model fidelity to use in order to get accurate and representative results. The choice is important, because models of successively higher fidelity come at a rapidly increasing computational cost. In some situations, the level of detail is clearly motivated by the question under study. In many situations however, many model options could qualitatively agree with available data, depending on the amount of data and the nature of the observations. Here, an important distinction is whether we are interested in inferring the true (but unknown) physical parameters of the model or if it is sufficient to be able to capture and explain available data. The situation becomes complicated from a computational perspective because inference needs to be approximate. Most often it is based on likelihood-free Approximate Bayesian Computation (ABC) and here determining which summary statistics to use, as well as how much data is needed to reach the desired level of accuracy, are difficult tasks. Ultimately, all of these aspects-the model fidelity, the available data, and the numerical choices for inference-interplay in a complex manner. In this paper we develop a computational pipeline designed to systematically evaluate inference accuracy for a wide range of true known parameters. We then use it to explore inference settings for negative feedback gene regulation. In particular, we compare a detailed spatial stochastic model, a coarse-grained compartment-based multiscale model, and the standard well-mixed model, across several data-scenarios and for multiple numerical options for parameter inference. Practically speaking, this pipeline can be used as a preliminary step to guide modelers prior to gathering experimental data. By training Gaussian processes to approximate the distance function values, we are able to substantially reduce the computational cost of running the pipeline.

Computational modelling of plasticity-led evolution.

Plasticity-led evolution is a form of evolution where a change in the environment induces novel traits via phenotypic plasticity, after which the novel traits are genetically accommodated over generations under the novel environment. This mode of evolution is expected to resolve the problem of gradualism (i.e., evolution by the slow accumulation of mutations that induce phenotypic variation) implied by the Modern Evolutionary Synthesis, in the face of a large environmental change. While experimental works are essential for validating that plasticity-led evolution indeed happened, we need computational models to gain insight into its underlying mechanisms and make qualitative predictions. Such computational models should include the developmental process and gene-environment interactions in addition to genetics and natural selection. We point out that gene regulatory network models can incorporate all the above notions. In this review, we highlight results from computational modelling of gene regulatory networks that consolidate the criteria of plasticity-led evolution. Since gene regulatory networks are mathematically equivalent to artificial recurrent neural networks, we also discuss their analogies and discrepancies, which may help further understand the mechanisms underlying plasticity-led evolution.

SRGS: sparse partial least squares-based recursive gene selection for gene regulatory network inference

BackgroundThe identification of gene regulatory networks (GRNs) facilitates the understanding of the underlying molecular mechanism of various biological processes and complex diseases. With the availability of single-cell RNA sequencing data, it is essential to infer GRNs from single-cell expression. Although some GRN methods originally developed for bulk expression data can be applicable to single-cell data and several single-cell specific GRN algorithms were developed, recent benchmarking studies have emphasized the need of developing more accurate and robust GRN modeling methods that are compatible for single-cell expression data.ResultsWe present SRGS, SPLS (sparse partial least squares)-based recursive gene selection, to infer GRNs from bulk or single-cell expression data. SRGS recursively selects and scores the genes which may have regulations on the considered target gene based on SPLS. When dealing with gene expression data with dropouts, we randomly scramble samples, set some values in the expression matrix to zeroes, and generate multiple copies of data through multiple iterations to make SRGS more robust. We test SRGS on different kinds of expression data, including simulated bulk data, simulated single-cell data without and with dropouts, and experimental single-cell data, and also compared with the existing GRN methods, including the ones originally developed for bulk data, the ones developed specifically for single-cell data, and even the ones recommended by recent benchmarking studies.ConclusionsIt has been shown that SRGS is competitive with the existing GRN methods and effective in the gene regulatory network inference from bulk or single-cell gene expression data. SRGS is available at: https://github.com/JGuan-lab/SRGS.

Early effects of gene duplication on the robustness and phenotypic variability of gene regulatory networks

BackgroundResearch on gene duplication is abundant and comes from a wide range of approaches, from high-throughput analyses and experimental evolution to bioinformatics and theoretical models. Notwithstanding, a consensus is still lacking regarding evolutionary mechanisms involved in evolution through gene duplication as well as the conditions that affect them. We argue that a better understanding of evolution through gene duplication requires considering explicitly that genes do not act in isolation. It demands studying how the perturbation that gene duplication implies percolates through the web of gene interactions. Due to evolution’s contingent nature, the paths that lead to the final fate of duplicates must depend strongly on the early stages of gene duplication, before gene copies have accumulated distinctive changes.MethodsHere we use a widely-known model of gene regulatory networks to study how gene duplication affects network behavior in early stages. Such networks comprise sets of genes that cross-regulate. They organize gene activity creating the gene expression patterns that give cells their phenotypic properties. We focus on how duplication affects two evolutionarily relevant properties of gene regulatory networks: mitigation of the effect of new mutations and access to new phenotypic variants through mutation.ResultsAmong other observations, we find that those networks that are better at maintaining the original phenotype after duplication are usually also better at buffering the effect of single interaction mutations and that duplication tends to enhance further this ability. Moreover, the effect of mutations after duplication depends on both the kind of mutation and genes involved in it. We also found that those phenotypes that had easier access through mutation before duplication had higher chances of remaining accessible through new mutations after duplication.ConclusionOur results support that gene duplication often mitigates the impact of new mutations and that this effect is not merely due to changes in the number of genes. The work that we put forward helps to identify conditions under which gene duplication may enhance evolvability and robustness to mutations.

Lévy noise-induced phase transition in p53 gene regulatory network near bifurcation points

The dynamics of tumor suppressor p53 is closely related to cell fate decisions in responses to various stress signals, especially p53 oscillation. In this paper, phase transition of p53 dynamics from stable steady state to oscillatory state induced by Lévy noise is investigated numerically in p53 gene regulatory network. First, we carry out bifurcation analysis of p53 protein expression levels with respect to the degradation rate of ataxia telangiectasia mutated (ATM) protein in deterministic model of the p53 gene regulatory network. The bifurcation diagram demonstrates that p53 activities can display a stable steady state, a stable limit cycle and the coexistence of a stable steady state with a stable limit cycle upon varying ATM degradation rate. Then, we investigate the influences of Lévy noise parameters on phase transition from stable steady state to stable limit cycle in stochastic model of the p53 gene regulatory network for control parameters near bifurcation points. Moreover, phase transitions are verified through autocorrelation at lag-1, variance, kurtosis, skewness and potential landscape. Our results reveal that phase transition may occur for an optimal interval of stability index α, and is positive and negative correlation with noise intensity D and skewness parameter β, respectively. Besides, phase transition from low stable steady state to stable limit cycle is sensitive to Lévy noise parameters, but it is the opposite for high one. These results may provide an insight to uncover p53 dynamics in p53 gene regulatory network upon noise.

Exploring the Molecular Mechanism of Sepal Formation in the Decorative Flowers of Hydrangea macrophylla 'Endless Summer' Based on the ABCDE Model.

With its large inflorescences and colorful flowers, Hydrangea macrophylla has been one of the most popular ornamental plants in recent years. However, the formation mechanism of its major ornamental part, the decorative floret sepals, is still not clear. In this study, we compared the transcriptome data of H. macrophylla 'Endless Summer' from the nutritional stage (BS1) to the blooming stage (BS5) and annotated them into the Kyoto Encyclopedia of Genes and Genomes (KEGG) and Gene Ontology (GO) databases. The 347 identified differentially expressed genes (DEGs) associated with flower development were subjected to a trend analysis and a protein-protein interaction analysis. The combined analysis of the two yielded 60 DEGs, including four MADS-box transcription factors (HmSVP-1, HmSOC1, HmAP1-2, and HmAGL24-3) and genes with strong connectivity (HmLFY and HmUFO). In addition, 17 transcription factors related to the ABCDE model were screened, and key candidate genes related to the development of decorative floret sepals in H. macrophylla were identified by phylogenetic and expression pattern analysis, including HmAP1-1, HmAP1-2, HmAP1-3, HmAP2-3, HmAP2-4, and HmAP2-5. On this basis, a gene regulatory network model of decorative sepal development was also postulated. Our results provide a theoretical basis for the study of the formation mechanism of decorative floret sepals and suggest a new direction for the molecular breeding of H. macrophylla.

Convolutional Neural Networks as Summary Statistics for Approximate Bayesian Computation.

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such as time series into a few informative, low-dimensional summary statistics. The quality of those statistics acutely impacts the accuracy of the inference task. Existing methods to select the best subset out of a pool of candidate statistics do not scale well with large pools of several tens to hundreds of candidate statistics. Since high quality statistics are imperative for good performance, this becomes a serious bottleneck when performing inference on complex and high-dimensional problems. This paper proposes a convolutional neural network architecture for automatically learning informative summary statistics of temporal responses. We show that the proposed network can effectively circumvent the statistics selection problem of the preprocessing step for ABC inference. The proposed approach is demonstrated on two benchmark problem and one challenging inference problem learning parameters in a high-dimensional stochastic genetic oscillator. We also study the impact of experimental design on network performance by comparing different data richness and data acquisition strategies.