Modeling stochasticity and variability in gene regulatory networks

A stochastic genetic toggle switch model that consists of two identical, mutually repressive genes is built using the Gillespie algorithm with time delays as an example of a simple stochastic gene regulatory network. The stochastic kinetics of this model is investigated, and it is found that the delays for the protein productions can highly weaken the global fluctuations for the expressions of the two genes, making the two mutually repressive genes coexist for a long time. Starting from this model, we propose a practical modeling strategy for more complex gene regulatory networks. Unlike previous applications of the Gillespie algorithm to simulate specific genetic networks dynamics, this modeling strategy is proposed for an ensemble approach to study the dynamical properties of these networks. The model allows any combination of gene expression products, forming complex multimers, and each one of the multimers is assigned to a randomly chosen gene promoter site as an activator or inhibitor. In addition, each gene, although it has only one promoter site, can have multiple regulatory sites and distinct rates of translation and transcription. Also, different genes have different time delays for transcription and translation and all reaction constant rates are initially randomly chosen from a range of values. Therefore, the general strategy here proposed may be used to simulate real genetic networks.

Revealing gene regulation-based neural network computing in bacteria

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/.

The Gene Regulatory Networks (GRNs) ensure the stability of cellular states, preserving specific phenotypes and functions throughout the differentiation process. However, current tools still need improvement to effectively integrate multi-omics data and infer GRNs for particular cell types. We introduce CLMOGRI, a multi-omics TF-gene regulatory network inference framework based on heterogeneous networks and contrastive learning, designed to integrate multi-omics data for GRN inference. Through random walk techniques, CLMOGRI embeds multi-omics data into a unified feature space and extracts similar features between nodes. It then measures node similarity and predicts node relationships by contrastive learning. Finally, it includes a regulatory network interpreter to identify critical nodes and modules in GRNs, offering an analytical method for understanding complex interactions within biological systems. CLMOGRI surpasses existing baseline methods in terms of Area Under the Precision-Recall Curve (AUPR) and F-Score metrics, indicating its efficacy in capturing multi-omics information for GRN inference. It also reveals vital nodes and modules within the gene regulatory network, improving the interpretability of CLMOGRI and the utility of GRNs.

Modulators (Ms) are proteins that modify the activity of transcription factors (TFs) and influence expression of their target genes (TGs). To discover modulators of NF-κB/RelA, we first identified 365 NF-κB/RelA-binding proteins using liquid chromatography-tandem mass spectrometry (LC-MS/MS). We used a probabilistic model to infer 8349 (M, NF-κB/RelA, TG) triplets and their modes of modulatory action from our combined LC-MS/MS and ChIP-Seq (ChIP followed by next generation sequencing) data, published RelA modulators and TGs, and a compendium of gene expression profiles. Hierarchical clustering of the derived modulatory network revealed functional subnetworks and suggested new pathways modulating RelA transcriptional activity. The modulators with the highest number of TGs and most non-random distribution of action modes (measured by Shannon entropy) are consistent with published reports. Our results provide a repertoire of testable hypotheses for experimental validation. One of the NF-κB/RelA modulators we identified is STAT1. The inferred (STAT1, NF-κB/RelA, TG) triplets were validated by LC-selected reaction monitoring-MS and the results of STAT1 deletion in human fibrosarcoma cells. Overall, we have identified 562 NF-κB/RelA modulators, which are potential drug targets, and clarified mechanisms of achieving NF-κB/RelA multiple functions through modulators. Our approach can be readily applied to other TFs.

Comparing to neural networks, genetic regulatory networks (GRNs) have two variables, mRNA and proteins, interacting in a very complex way. This special structure of GRNs promises better adaptive performance. In this chapter, cooperative controllers inspired by GRNs are proposed. First, the robust H ∞ state estimation problem is investigated for a class of discrete-time stochastic GRNs with probabilistic measurement delays. Then, a bio-inspired cooperative controller via evolution of GRN is presented to make the performance index of each stage stable over the whole study horizon and the overall performance index close to the desired value against vibrations simultaneously.

BackgroundMaize (Zea mays L.) is one of the most important crops worldwide. Although sophisticated maize gene regulatory networks (GRNs) have been constructed for functional genomics and phenotypic dissection, a multi-omics GRN connecting the translatome and transcriptome is lacking, hampering our understanding and exploration of the maize regulatome.ResultsWe collect spatio-temporal translatome and transcriptome data and systematically explore the landscape of gene transcription and translation across 33 tissues or developmental stages of maize. Using this comprehensive transcriptome and translatome atlas, we construct a multi-omics GRN integrating mRNAs and translated mRNAs, demonstrating that translatome-related GRNs outperform GRNs solely using transcriptomic data and inter-omics GRNs outperform intra-omics GRNs in most cases. With the aid of the multi-omics GRN, we reconcile some known regulatory networks. We identify a novel transcription factor, ZmGRF6, which is associated with growth. Furthermore, we characterize a function related to drought response for the classic transcription factor ZmMYB31.ConclusionsOur findings provide insights into spatio-temporal changes across maize development at both the transcriptome and translatome levels. Multi-omics GRNs represent a useful resource for dissection of the regulatory mechanisms underlying phenotypic variation.

Inferring biosynthetic and gene regulatory networks from Artemisia annua RNA sequencing data on a credit card-sized ARM computer

In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results.

Inferring gene regulatory network from single-cell transcriptomic data by integrating multiple prior networks

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.

Molecular fingerprinting of the podocyte reveals novel gene and protein regulatory networks

Genes regulate each other and form a gene regulatory network (GRN) to realise biological functions. Elucidating GRN from experimental data remains a challenging problem in systems biology. Numerous techniques have been developed and sparse linear regression methods become a promising approach to infer accurate GRNs. However, most linear methods are either based on steady-state gene expression data or their statistical properties are not analysed. Here, two sparse penalties, adaptive least absolute shrinkage and selection operator and smoothly clipped absolute deviation, are proposed to infer GRNs from time-course gene expression data based on an auto-regressive model and their Oracle properties are proved under mild conditions. The effectiveness of those methods is demonstrated by applications to in silico and real biological data.

BackgroundThe structure of regulatory networks remains an open question in our understanding of complex biological systems. Interactions during complete viral life cycles present unique opportunities to understand how host-parasite network take shape and behave. The Anticarsia gemmatalis multiple nucleopolyhedrovirus (AgMNPV) is a large double-stranded DNA virus, whose genome may encode for 152 open reading frames (ORFs). Here we present the analysis of the ordered cascade of the AgMNPV gene expression.ResultsWe observed an earlier onset of the expression than previously reported for other baculoviruses, especially for genes involved in DNA replication. Most ORFs were expressed at higher levels in a more permissive host cell line. Genes with more than one copy in the genome had distinct expression profiles, which could indicate the acquisition of new functionalities. The transcription gene regulatory network (GRN) for 149 ORFs had a modular topology comprising five communities of highly interconnected nodes that separated key genes that are functionally related on different communities, possibly maximizing redundancy and GRN robustness by compartmentalization of important functions. Core conserved functions showed expression synchronicity, distinct GRN features and significantly less genetic diversity, consistent with evolutionary constraints imposed in key elements of biological systems. This reduced genetic diversity also had a positive correlation with the importance of the gene in our estimated GRN, supporting a relationship between phylogenetic data of baculovirus genes and network features inferred from expression data. We also observed that gene arrangement in overlapping transcripts was conserved among related baculoviruses, suggesting a principle of genome organization.ConclusionsAlbeit with a reduced number of nodes (149), the AgMNPV GRN had a topology and key characteristics similar to those observed in complex cellular organisms, which indicates that modularity may be a general feature of biological gene regulatory networks.

The divergence of regulatory regions and gene regulatory network (GRN) rewiring is a key driver of cichlid phenotypic diversity. However, the contribution of miRNA-binding site turnover has yet to be linked to GRN evolution across cichlids. Here, we extend our previous studies by analyzing the selective constraints driving evolution of miRNA and transcription factor (TF)–binding sites of target genes, to infer instances of cichlid GRN rewiring associated with regulatory binding site turnover. Comparative analyses identified increased species-specific networks that are functionally associated to traits of cichlid phenotypic diversity. The evolutionary rewiring is associated with differential models of miRNA- and TF-binding site turnover, driven by a high proportion of fast-evolving polymorphic sites in adaptive trait genes compared with subsets of random genes. Positive selection acting upon discrete mutations in these regulatory regions is likely to be an important mechanism in rewiring GRNs in rapidly radiating cichlids. Regulatory variants of functionally associated miRNA- and TF-binding sites of visual opsin genes differentially segregate according to phylogeny and ecology of Lake Malawi species, identifying both rewired, for example, clade-specific and conserved network motifs of adaptive trait associated GRNs. Our approach revealed several novel candidate regulators, regulatory regions, and three-node motifs across cichlid genomes with previously reported associations to known adaptive evolutionary traits.