Models Of Gene Regulatory Networks Research Articles

A Review of Computational Approach for S-system-based Modeling of Gene Regulatory Network.

Inference of gene regulatory network (GRN) from time series microarray data remains as a fascinating task for computer science researchers to understand the complex biological process that occurred inside a cell. Among the different popular models to infer GRN, S-system is considered as one of the promising non-linear mathematical tools to model the dynamics of gene expressions, as well as to infer the GRN. S-system is based on biochemical system theory and power law formalism. By observing the value of kinetic parameters of S-system model, it is possible to extract the regulatory relationships among genes. In this review, several existing intelligent methods that were already proposed for inference of S-system-based GRN are explained. It is observed that finding out the most suitable and efficient optimization technique for the accurate inference of all kinds of networks, i.e., in-silico, in-vivo, etc., with less computational complexity is still an open research problem to all. This paper may help the beginners or researchers who want to continue their research in the field of computational biology and bioinformatics.

ILSGRN: inference of large-scale gene regulatory networks based on multi-model fusion.

Gene regulatory networks (GRNs) are a way of describing the interaction between genes, which contribute to revealing the different biological mechanisms in the cell. Reconstructing GRNs based on gene expression data has been a central computational problem in systems biology. However, due to the high dimensionality and non-linearity of large-scale GRNs, accurately and efficiently inferring GRNs is still a challenging task. In this article, we propose a new approach, iLSGRN, to reconstruct large-scale GRNs from steady-state and time-series gene expression data based on non-linear ordinary differential equations. Firstly, the regulatory gene recognition algorithm calculates the Maximal Information Coefficient between genes and excludes redundant regulatory relationships to achieve dimensionality reduction. Then, the feature fusion algorithm constructs a model leveraging the feature importance derived from XGBoost (eXtreme Gradient Boosting) and RF (Random Forest) models, which can effectively train the non-linear ordinary differential equations model of GRNs and improve the accuracy and stability of the inference algorithm. The extensive experiments on different scale datasets show that our method makes sensible improvement compared with the state-of-the-art methods. Furthermore, we perform cross-validation experiments on the real gene datasets to validate the robustness and effectiveness of the proposed method. The proposed method is written in the Python language, and is available at: https://github.com/lab319/iLSGRN.

Bifurcation control of a novel fractional-order gene regulatory network with incommensurate order and time delay

Gene regulatory networks play an extremely important role in human life activities. This paper presents a novel fractional-order gene regulatory network model (NFGRNM). The model employs incommensurate fractional orders and introduces time delay arising from the binding of miRNAs to RNA. Time delay often triggers instability such as oscillation and bifurcation, so in this paper we introduce a generalized hybrid control to control the unstable dynamical behavior induced by time delay. First we derive the NFGRNM using fractional order theory, after which the equilibrium point of the network model is calculated. Next, a systematic dynamics analysis of the NFGRNM is performed to derive sufficient conditions to generate the Hopf bifurcation. Most importantly, we introduce the extended hybrid control for the periodic oscillations generated by the time delay in the NFGRNM. Finally, numerical simulation results show that the order of the fractional order can have a great impact on the dynamical behavior of the network model and that the hybrid control has a significant role in delaying (or advancing) the Hopf bifurcation. Since infectious diseases such as SARS-Cov-2, influenza A, and HIV are still prevalent today, the study of gene regulatory networks not only promotes the study of the dynamics of complex networks but also has profound implications for the study of virus transmission in the host and various life activities in humans.

Automated pattern generation for swarm robots using constrained multi-objective genetic programming

Swarm robotic systems (SRSs), which are widely used in many fields, such as search and rescue, usually comprise a number of robots with relatively simple mechanisms collaborating to accomplish complex tasks. A challenging task for SRSs is to design local interaction rules for self-organization of robots that can generate adaptive patterns to entrap moving targets. Biologically inspired approaches such as gene regulatory network (GRN) models provide a promising solution to this problem. However, the design of GRN models for generating entrapping patterns relies on the expertise of designers. As a result, the design of the GRN models is often a laborious and tedious trial-and-error process. In this study, we propose a modular design automation framework for GRN models that can generate entrapping patterns. The framework employs basic network motifs to construct GRN models automatically without requiring expertise. To this end, a constrained multi-objective genetic programming is utilized to simultaneously optimize the structures and parameters of the GRN models. A multi-criteria decision-making approach is adopted to choose the preferred GRN model for generating the entrapping pattern. Comprehensive simulation results demonstrate that the proposed framework can obtain novel GRN models with simpler structures than those designed by human experts yet better performance in complex and dynamic environments. Proof-of-concept experiments using e-puck robots confirmed the feasibility and effectiveness of the proposed GRN models.

Dynamic network-guided CRISPRi screen identifies CTCF-loop-constrained nonlinear enhancer gene regulatory activity during cell state transitions.

Comprehensive enhancer discovery is challenging because most enhancers, especially those contributing to complex diseases, have weak effects on gene expression. Our gene regulatory network modeling identified that nonlinear enhancer gene regulation during cell state transitions can be leveraged to improve the sensitivity of enhancer discovery. Using human embryonic stem cell definitive endoderm differentiation as a dynamic transition system, we conducted a mid-transition CRISPRi-based enhancer screen. We discovered a comprehensive set of enhancers for each of the core endoderm-specifying transcription factors. Many enhancers had strong effects mid-transition but weak effects post-transition, consistent with the nonlinear temporal responses to enhancer perturbation predicted by the modeling. Integrating three-dimensional genomic information, we were able to develop a CTCF-loop-constrained Interaction Activity model that can better predict functional enhancers compared to models that rely on Hi-C-based enhancer-promoter contact frequency. Our study provides generalizable strategies for sensitive and systematic enhancer discovery in both normal and pathological cell state transitions.

Quantum gene regulatory networks

In this work, we present a quantum circuit model for inferring gene regulatory networks (GRNs) from single-cell transcriptomic data. The model employs qubit entanglement to simulate interactions between genes, resulting in competitive performance and promising potential for further exploration. We applied our quantum GRN modeling approach to single-cell transcriptomic data from human lymphoblastoid cells, focusing on a small set of genes involved in innate immunity regulation. Our quantum circuit model successfully predicted the presence and absence of regulatory interactions between genes, while also estimating the strength of these interactions. We argue that the application of quantum computing in biology has the potential to provide a better understanding of single-cell GRNs by more effectively approaching the relationship between fully interconnected genes compared to conventional statistical methods such as correlation and regression. Our results encourage further investigation into the creation of quantum algorithms that utilize single-cell data, paving the way for future research into the intersection of quantum computing and biology.

Self-Organization and Genomic Causality in Models of Morphogenesis.

The debate about what causes the generation of form and structure in embryological development goes back to antiquity. Most recently, it has focused on the divergent views as to whether the generation of patterns and form in development is a largely self-organized process or is mainly determined by the genome, in particular, complex developmental gene regulatory processes. This paper presents and analyzes pertinent models of pattern formation and form generation in a developing organism in the past and the present, with a special emphasis on Alan Turing's 1952 reaction-diffusion model. I first draw attention to the fact that Turing's paper remained, at first, without a noticeable impact on the community of biologists because purely physical-chemical models were unable to explain embryological development and often also simple repetitive patterns. I then show that from the year 2000 and onwards, Turing's 1952 paper was increasingly cited also by biologists. The model was updated to include gene products and now seemed able to account for the generation of biological patterns, though discrepancies between models and biological reality remained. I then point out Eric Davidson's successful theory of early embryogenesis based on gene-regulatory network analysis and its mathematical modeling that not only was able to provide a mechanistic and causal explanation for gene regulatory events controlling developmental cell fate specification but, unlike reaction-diffusion models, also addressed the effects of evolution and organisms' longstanding developmental and species stability. The paper concludes with an outlook on further developments of the gene regulatory network model.

Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics.

Modern biological science is trying to solve the fundamental complex problems of molecular biology, which include protein folding, drug discovery, simulation of macromolecular structure, genome assembly, and many more. Currently, quantum computing (QC), a rapidly emerging technology exploiting quantum mechanical phenomena, has developed to address current significant physical, chemical, biological issues, and complex questions. The present review discusses quantum computing technology and its status in solving molecular biology problems, especially in the next-generation computational biology scenario. First, the article explained the basic concept of quantum computing, the functioning of quantum systems where information is stored as qubits, and data storage capacity using quantum gates. Second, the review discussed quantum computing components, such as quantum hardware, quantum processors, and quantum annealing. At the same time, article also discussed quantum algorithms, such as the grover search algorithm and discrete and factorization algorithms. Furthermore, the article discussed the different applications of quantum computing to understand the next-generation biological problems, such as simulation and modeling of biological macromolecules, computational biology problems, data analysis in bioinformatics, protein folding, molecular biology problems, modeling of gene regulatory networks, drug discovery and development, mechano-biology, and RNA folding. Finally, the article represented different probable prospects of quantum computing in molecular biology.

A Holistic Approach from Systems Biology Reveals the Direct Influence of the Quorum-Sensing Phenomenon on Pseudomonas aeruginosa Metabolism to Pyoverdine Biosynthesis.

Computational modeling and simulation of biological systems have become valuable tools for understanding and predicting cellular performance and phenotype generation. This work aimed to construct, model, and dynamically simulate the virulence factor pyoverdine (PVD) biosynthesis in Pseudomonas aeruginosa through a systemic approach, considering that the metabolic pathway of PVD synthesis is regulated by the quorum-sensing (QS) phenomenon. The methodology comprised three main stages: (i) Construction, modeling, and validation of the QS gene regulatory network that controls PVD synthesis in P. aeruginosa strain PAO1; (ii) construction, curating, and modeling of the metabolic network of P. aeruginosa using the flux balance analysis (FBA) approach; (iii) integration and modeling of these two networks into an integrative model using the dynamic flux balance analysis (DFBA) approximation, followed, finally, by an in vitro validation of the integrated model for PVD synthesis in P. aeruginosa as a function of QS signaling. The QS gene network, constructed using the standard System Biology Markup Language, comprised 114 chemical species and 103 reactions and was modeled as a deterministic system following the kinetic based on mass action law. This model showed that the higher the bacterial growth, the higher the extracellular concentration of QS signal molecules, thus emulating the natural behavior of P. aeruginosa PAO1. The P. aeruginosa metabolic network model was constructed based on the iMO1056 model, the P. aeruginosa PAO1 strain genomic annotation, and the metabolic pathway of PVD synthesis. The metabolic network model included the PVD synthesis, transport, exchange reactions, and the QS signal molecules. This metabolic network model was curated and then modeled under the FBA approximation, using biomass maximization as the objective function (optimization problem, a term borrowed from the engineering field). Next, chemical reactions shared by both network models were chosen to combine them into an integrative model. To this end, the fluxes of these reactions, obtained from the QS network model, were fixed in the metabolic network model as constraints of the optimization problem using the DFBA approximation. Finally, simulations of the integrative model (CCBM1146, comprising 1123 reactions and 880 metabolites) were run using the DFBA approximation to get (i) the flux profile for each reaction, (ii) the bacterial growth profile, (iii) the biomass profile, and (iv) the concentration profiles of metabolites of interest such as glucose, PVD, and QS signal molecules. The CCBM1146 model showed that the QS phenomenon directly influences the P. aeruginosa metabolism to PVD biosynthesis as a function of the change in QS signal intensity. The CCBM1146 model made it possible to characterize and explain the complex and emergent behavior generated by the interactions between the two networks, which would have been impossible to do by studying each system's individual components or scales separately. This work is the first in silico report of an integrative model comprising the QS gene regulatory network and the metabolic network of P. aeruginosa.

Being noisy in a crowd: Differential selective pressure on gene expression noise in model gene regulatory networks.

Expression noise, the variability of the amount of gene product among isogenic cells grown in identical conditions, originates from the inherent stochasticity of diffusion and binding of the molecular players involved in transcription and translation. It has been shown that expression noise is an evolvable trait and that central genes exhibit less noise than peripheral genes in gene networks. A possible explanation for this pattern is increased selective pressure on central genes since they propagate their noise to downstream targets, leading to noise amplification. To test this hypothesis, we developed a new gene regulatory network model with inheritable stochastic gene expression and simulated the evolution of gene-specific expression noise under constraint at the network level. Stabilizing selection was imposed on the expression level of all genes in the network and rounds of mutation, selection, replication and recombination were performed. We observed that local network features affect both the probability to respond to selection, and the strength of the selective pressure acting on individual genes. In particular, the reduction of gene-specific expression noise as a response to stabilizing selection on the gene expression level is higher in genes with higher centrality metrics. Furthermore, global topological structures such as network diameter, centralization and average degree affect the average expression variance and average selective pressure acting on constituent genes. Our results demonstrate that selection at the network level leads to differential selective pressure at the gene level, and local and global network characteristics are an essential component of gene-specific expression noise evolution.

Correlated stabilizing selection shapes the topology of gene regulatory networks.

The evolution of gene expression is constrained by the topology of gene regulatory networks, as co-expressed genes are likely to have their expressions affected together by mutations. Conversely, co-expression can also be an advantage when genes are under joint selection. Here, we assessed theoretically whether correlated selection (selection for a combination of traits) was able to affect the pattern of correlated gene expressions and the underlying gene regulatory networks. We ran individual-based simulations, applying a stabilizing correlated fitness function to three genetic architectures: a quantitative genetics (multilinear) model featuring epistasis and pleiotropy, a quantitative genetics model where each genes has an independent mutational structure, and a gene regulatory network model, mimicking the mechanisms of gene expression regulation. Simulations showed that correlated mutational effects evolved in the three genetic architectures as a response to correlated selection, but the response in gene networks was specific. The intensity of gene co-expression was mostly explained by the regulatory distance between genes (largest correlations being associated to genes directly interacting with each other), and the sign of co-expression was associated with the nature of the regulation (transcription activation or inhibition). These results concur to the idea that gene network topologies could partly reflect past selection patterns on gene expression.

Gene regulatory networks with binary weights

An evolutionary computation framework to learn binary threshold networks is presented. Inspired by the recent trend of binary neural networks, where weights and activation thresholds are represented using 1 and -1 such that they can be stored in 1-bit instead of full precision, we explore this approach for gene regulatory network modeling. We test our method by inferring binary threshold networks of two regulatory network models: Quorum sensing systems in bacterium Paraburkholderia phytofirmans PsJN and the fission yeast cell-cycle. We considered differential evolution and particle swarm optimization for the simulations. Results for weights having only 1 and -1 values, and different activation thresholds are presented. Full binary threshold networks were found with minimum error (2 bits), whereas when the binary restriction is relaxed for the activation thresholds, networks with 0 bit error were found.

Network Biology Analyses and Dynamic Modeling of Gene Regulatory Networks under Drought Stress Reveal Major Transcriptional Regulators in Arabidopsis.

Drought is one of the most serious abiotic stressors in the environment, restricting agricultural production by reducing plant growth, development, and productivity. To investigate such a complex and multifaceted stressor and its effects on plants, a systems biology-based approach is necessitated, entailing the generation of co-expression networks, identification of high-priority transcription factors (TFs), dynamic mathematical modeling, and computational simulations. Here, we studied a high-resolution drought transcriptome of Arabidopsis. We identified distinct temporal transcriptional signatures and demonstrated the involvement of specific biological pathways. Generation of a large-scale co-expression network followed by network centrality analyses identified 117 TFs that possess critical properties of hubs, bottlenecks, and high clustering coefficient nodes. Dynamic transcriptional regulatory modeling of integrated TF targets and transcriptome datasets uncovered major transcriptional events during the course of drought stress. Mathematical transcriptional simulations allowed us to ascertain the activation status of major TFs, as well as the transcriptional intensity and amplitude of their target genes. Finally, we validated our predictions by providing experimental evidence of gene expression under drought stress for a set of four TFs and their major target genes using qRT-PCR. Taken together, we provided a systems-level perspective on the dynamic transcriptional regulation during drought stress in Arabidopsis and uncovered numerous novel TFs that could potentially be used in future genetic crop engineering programs.

Computing Minimal Boolean Models of Gene Regulatory Networks

Computing Minimal Boolean Models of Gene Regulatory Networks

Abstract 4313: A novel gene regulatory network model identifies master regulators in cancer

Abstract Small-scale regulatory networks can model known biological processes; while large-scale genome-wide datasets can identify novel mechanisms. We developed a biophysical modeling framework that combines the accuracy of small-scale networks with the power of large-scale datasets. As a proof of principle, we implemented this framework on a cohort of 844 multiple myeloma (MM) patients’ (and 1092 TCGA breast cancer patients) z-normalized RNAseq data using t-Distributed Stochastic Neighbor Embedding to construct a disease-specific transcriptomic map, where genes closer to each other co-express within the cohort. Fuzzy c-means clustering is carried out to identify clusters of genes that are likely regulated by a common transcription factor (TF). We construct a gene regulatory network (GRN) for each cluster of co-expressing genes on a disease-specific transcriptomic map by identifying upstream TFs for each cluster using publicly available databases ENCODE and ChEA, and kinases that phosphorylate these TFs using PhosphoSitePlus and PhosphoPoint. An exhaustive list of TFs and kinases are reduced to a few key predictor variables using regression tree modeling for each gene in that cluster. This leads to a cascading network of kinases that phosphorylate TFs, which regulate expression of genes in a cluster. We derived a mechanistic model from first-principles to define functional relationships governing the GRN; where transcription, translation, and post-translational modifications are modeled using first-order reversible reaction kinetic equations. The patient-specific rate constants of the model are parametrized by single sample gene set enrichment analysis scores of key KEGG pathways like ribosome, protein synthesis, RNA degradation, etc. The system of differential equations, under steady-state, reduce to an algebraic equation that can predict the expression of every gene in a cluster from the expression of its upstream TFs and kinases alone, which is fitted to RNAseq data of 422 MM patients to estimate undetermined parameters. The remaining patients’ data is used to estimate the accuracy of the model using Pearson’s correlation (model predicted vs actual) coefficient, r. Out of 16,738 genes, 7,936 were predicted accurately (r>0.5), while the remaining genes were shown to have a significant overlap (hypergeometric test; p-value<1e-48 and representation factor = 7.27) with genes that have high variability in chromatin accessibility across patients. A reduced GRN with only accurately predicted genes is obtained for each cluster, followed by linking GRNs to each other through TFs and kinases that are featured in other GRNs; where betweenness centrality measures of the resulting directed graph identifies disease-specific master regulators. MYC, STAT3, CREB1, POLR2A, PLK1, and TP53 are found to be key hubs in MM network; similar analyses are being conducted for other cancers featured in TCGA. Citation Format: Praneeth Reddy Sudalagunta, Rafael Renatino Canevarolo, Mark Meads, Maria Coelho Silva, Xiaohong Zhao, Raghunandan Reddy Alugubelli, Joon-hyun Song, Erez Persi, Mehdi Damaghi, Kenneth H. Shain, Ariosto Silva. A novel gene regulatory network model identifies master regulators in cancer. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 4313.

A multiscale hybrid model for exploring the effect of Resolvin D1 on macrophage polarization during acute inflammation

Dysregulated inflammation underlies various diseases. Specialized pro-resolving mediators (SPMs) like Resolvin D1 (RvD1) have been shown to resolve inflammation and halt disease progression. Macrophages, key immune cells that drive inflammation, respond to the presence of RvD1 by polarizing to an anti-inflammatory type (M2). However, RvD1’s mechanisms, roles, and utility are not fully understood.This paper introduces a gene-regulatory network (GRN) model that contains pathways for RvD1 and other SPMs and proinflammatory molecules like lipopolysaccharides. We couple this GRN model to a partial differential equation–agent-based hybrid model using a multiscale framework to simulate an acute inflammatory response with and without the presence of RvD1. We calibrate and validate the model using experimental data from two animal models.The model reproduces the dynamics of key immune components and the effects of RvD1 during acute inflammation. Our results suggest RvD1 can drive macrophage polarization through the G protein-coupled receptor 32 (GRP32) pathway. The presence of RvD1 leads to an earlier and increased M2 polarization, reduced neutrophil recruitment, and faster apoptotic neutrophil clearance.These results support a body of literature that suggests that RvD1 is a promising candidate for promoting the resolution of acute inflammation. We conclude that once calibrated and validated on human data, the model can identify critical sources of uncertainty, which could be further elucidated in biological experiments and assessed for clinical use.

The transcriptional mechanism responding to air particulate matter in Laurus nobilis (L.)

Air levels of particulate matter (PM) are dangerously increasing in urban environment due to high levels of industrialization. The use of plants to reduce pollutants is well-known although molecular mechanisms underlying this phenomenon have been scarcely investigated. The aim of this work was to shed lights into the molecular physiological responses of leaves of a typical plant ornamental species (Laurus nobilis L.), to identify key PM-modulated genes of early leaf responses and to optimize phylloremediation strategies in polluted areas. The transcriptome and the PM accumulation in leaf tissues were analysed in plants grown in pots for three months under two different areas: rural and traffic. Differentially expressed genes in common between different pairwise comparisons were highly effective in discriminating leaves at high PM levels after three months of exposure. Thirty of these genes showed contrasting trend of expression between rural and traffic conditions. Higher PM levels highlighted significant repression of genes and gene set categories involved in cell wall and membrane modification. In addition, a repression of genes involved in photosynthesis reactions, glycolysis, gluconeogenesis, TCA, fermentation was observed. Some key members of C2H2, WRKYs and CCAAT-HAP2 were induced as well as downstream defense response genes. The results allowed to develop a general model of gene regulatory networks in response to particulate matter in plants and innovative biotechnological approaches for phylloremediation strategies.

Gene Self-Expressive Networks as a Generalization-Aware Tool to Model Gene Regulatory Networks

Self-expressiveness is a mathematical property that aims at characterizing the relationship between instances in a dataset. This property has been applied widely and successfully in computer-vision tasks, time-series analysis, and to infer underlying network structures in domains including protein signaling interactions and social-networks activity. Nevertheless, despite its potential, self-expressiveness has not been explicitly used to infer gene networks. In this article, we present Generalizable Gene Self-Expressive Networks, a new, interpretable, and generalization-aware formalism to model gene networks, and we propose two methods: GXN•EN and GXN•OMP, based respectively on ElasticNet and OMP (Orthogonal Matching Pursuit), to infer and assess Generalizable Gene Self-Expressive Networks. We evaluate these methods on four Microarray datasets from the DREAM5 benchmark, using both internal and external metrics. The results obtained by both methods are comparable to those obtained by state-of-the-art tools, but are fast to train and exhibit high levels of sparsity, which make them easier to interpret. Moreover we applied these methods to three complex datasets containing RNA-seq informations from different mammalian tissues/cell-types. Lastly, we applied our methodology to compare a normal vs. a disease condition (Alzheimer), which allowed us to detect differential expression of genes' sub-networks between these two biological conditions. Globally, the gene networks obtained exhibit a sparse and modular structure, with inner communities of genes presenting statistically significant over/under-expression on specific cell types, as well as significant enrichment for some anatomical GO terms, suggesting that such communities may also drive important functional roles.

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.