Models Of Gene Regulatory Networks Research Articles

Modelling of Gene Regulatory Networks by Parent Node Screening-Based Bayesian Method

Modelling of Gene Regulatory Networks by Parent Node Screening-Based Bayesian Method

Overview of Gene Regulatory Network Inference Based on Differential Equation Models.

Reconstruction of gene regulatory networks (GRN) plays an important role in understanding the complexity, functionality and pathways of biological systems, which could support the design of new drugs for diseases. Because differential equation models are flexible androbust, these models have been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates the differential equation models for reverse engineering gene regulatory networks. We introduce three kinds of differential equation models, including ordinary differential equation (ODE), time-delayed differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are utilized to search the optimal structures and parameters of differential equation models. This investigation could provide a comprehensive understanding of differential equation models, and lead to the discovery of novel differential equation models.

Analysis of Single-Cell Gene Pair Coexpression Landscapes by Stochastic Kinetic Modeling Reveals Gene-Pair Interactions in Development.

Single-cell transcriptomics is advancing discovery of the molecular determinants of cell identity, while spurring development of novel data analysis methods. Stochastic mathematical models of gene regulatory networks help unravel the dynamic, molecular mechanisms underlying cell-to-cell heterogeneity, and can thus aid interpretation of heterogeneous cell-states revealed by single-cell measurements. However, integrating stochastic gene network models with single cell data is challenging. Here, we present a method for analyzing single-cell gene-pair coexpression patterns, based on biophysical models of stochastic gene expression and interaction dynamics. We first developed a high-computational-throughput approach to stochastic modeling of gene-pair coexpression landscapes, based on numerical solution of gene network Master Equations. We then comprehensively catalogued coexpression patterns arising from tens of thousands of gene-gene interaction models with different biochemical kinetic parameters and regulatory interactions. From the computed landscapes, we obtain a low-dimensional “shape-space” describing distinct types of coexpression patterns. We applied the theoretical results to analysis of published single cell RNA sequencing data and uncovered complex dynamics of coexpression among gene pairs during embryonic development. Our approach provides a generalizable framework for inferring evolution of gene-gene interactions during critical cell-state transitions.

The Impact of Self-Loops on Boolean Networks Attractor Landscape and Implications for Cell Differentiation Modelling.

Boolean networks are a notable model of gene regulatory networks and, particularly, prominent theories discuss how they can capture cellular differentiation processes. One frequent motif in gene regulatory networks, especially in those circuits involved in cell differentiation, is autoregulation. In spite of this, the impact of autoregulation on Boolean network attractor landscape has not yet been extensively discussed in literature. In this paper we propose to model autoregulation as self-loops, and analyse how the number of attractors and their robustness may change once they are introduced in a well-known and widely used Boolean networks model, namely random Boolean networks. Results show that self-loops provide an evolutionary advantage in dynamic mechanisms of cells, by increasing both number and maximal robustness of attractors. These results provide evidence to the hypothesis that autoregulation is a straightforward functional component to consolidate cell dynamics, mainly in differentiation processes.

Reinforcement Learning Approach to Feedback Stabilization Problem of Probabilistic Boolean Control Networks

In this letter, we study the control of probabilistic Boolean control networks (PBCNs) by leveraging a model-free reinforcement learning (RL) technique. In particular, we propose a Q-learning (QL) based approach to address the feedback stabilization problem of PBCNs, and we design optimal state feedback controllers such that the PBCN is stabilized at a given equilibrium point. The optimal controllers are designed for both finite-time stability and asymptotic stability of PBCNs. In order to verify the convergence of the proposed QL algorithm, the obtained optimal policy is compared with the optimal solutions of model-based techniques, namely value iteration (VI) and semi-tensor product (STP) methods. Finally, some PBCN models of gene regulatory networks (GRNs) are considered to verify the obtained results.

A Hox gene regulatory network for hindbrain segmentation.

In vertebrates, the hindbrain serves as a highly conserved complex coordination center for regulating many fundamental activities of the central nervous system, such as respiratory rhythms, sleep patterns and equilibrium, and it also plays an important role in craniofacial development. The basic ground plan that underlies the diverse functions of the hindbrain and its neural crest derivatives is established and patterned by a process of segmentation. Through a dynamic series of signaling and regulatory interactions the developing hindbrain is transiently compartmentalized into a set of seven segmental units, termed rhombomeres. The nested expression of the Hox family of transcription factors is tightly coupled to the process of segmentation and provides a molecular code for specifying the unique regional properties of the hindbrain and its neural crest derived craniofacial structures. The high degree of similarity in hindbrain architecture between diverse vertebrates has enabled cross-species regulatory analysis. This has facilitated the experimental assembly of the signaling and regulatory interactions, which underlie the process of segmentation, into a Hox-dependent gene regulatory network (GRN) model. This hindbrain GRN is a key regulatory feature of head patterning, conserved to the base of vertebrate evolution. This regulatory framework also serves as a basis for comparing and contrasting GRNs that govern cranial neural crest formation and axial patterning and provide insight into regulatory mechanisms associated with the evolution of novel vertebrate traits. The purpose of this review is to discuss the majorfeatures of the GRN for hindbrain segmentation and its relationship to the broader functional role of the hindbrain in patterning head development.

Double Deep-Q Learning-Based Output Tracking of Probabilistic Boolean Control Networks

In this article, a reinforcement learning (RL)-based scalable technique is presented to control the probabilistic Boolean control networks (PBCNs). In particular, a double deep-Q network (DDQN) approach is firstly proposed to address the output tracking problem of PBCNs, and optimal state feedback controllers are obtained such that the output of PBCNs tracks a constant as well as a time-varying reference signal. The presented method is model-free and offers scalability, thereby provides an efficient way to control large-scale PBCNs that are a natural choice to model gene regulatory networks (GRNs). Finally, three PBCN models of GRNs including a 16-gene and 28-gene networks are considered to verify the presented results.

Construction Method of Probabilistic Boolean Networks Based on Imperfect Information

A probabilistic Boolean network (PBN) is well known as one of the mathematical models of gene regulatory networks. In a Boolean network, expression of a gene is approximated by a binary value, and its time evolution is expressed by Boolean functions. In a PBN, a Boolean function is probabilistically chosen from candidates of Boolean functions. One of the authors has proposed a method to construct a PBN from imperfect information. However, there is a weakness that the number of candidates of Boolean functions may be redundant. In this paper, this construction method is improved to efficiently utilize given information. To derive Boolean functions and those selection probabilities, the linear programming problem is solved. Here, we introduce the objective function to reduce the number of candidates. The proposed method is demonstrated by a numerical example.

Classification-Based Inference of Dynamical Models of Gene Regulatory Networks.

Cell-fate decisions during development are controlled by densely interconnected gene regulatory networks (GRNs) consisting of many genes. Inferring and predictively modeling these GRNs is crucial for understanding development and other physiological processes. Gene circuits, coupled differential equations that represent gene product synthesis with a switch-like function, provide a biologically realistic framework for modeling the time evolution of gene expression. However, their use has been limited to smaller networks due to the computational expense of inferring model parameters from gene expression data using global non-linear optimization. Here we show that the switch-like nature of gene regulation can be exploited to break the gene circuit inference problem into two simpler optimization problems that are amenable to computationally efficient supervised learning techniques. We present FIGR (Fast Inference of Gene Regulation), a novel classification-based inference approach to determining gene circuit parameters. We demonstrate FIGR’s effectiveness on synthetic data generated from random gene circuits of up to 50 genes as well as experimental data from the gap gene system of Drosophila melanogaster, a benchmark for inferring dynamical GRN models. FIGR is faster than global non-linear optimization by a factor of 600 and its computational complexity scales much better with GRN size. On a practical level, FIGR can accurately infer the biologically realistic gap gene network in under a minute on desktop-class hardware instead of requiring hours of parallel computing. We anticipate that FIGR would enable the inference of much larger biologically realistic GRNs than was possible before.

Decentralized gene regulatory networks: An approach to energy efficient node coordination with delay constraints for wireless sensor systems

Wireless sensor networks (WSNs) systems have been used for several applications from target tracking to environment monitoring. Recently, there has been increased interest in the design of WSN protocols for delay-sensitive applications, such as military surveillance, health monitoring, and infrastructure security. However, due to the strict resource constraints of the sensor nodes, WSNs pose critical challenges for network protocol design for reliable communications with delay constraints. Biologically inspired modeling techniques have received considerable attention for their robustness, scalability, and adaptability with simple local interactions and limited information. In this paper, we apply gene regulatory networks (GRNs) principles to the WSN system and propose a new GRN model for decentralized node coordination to achieve energy saving while meeting delay requirements. Using control theory, we provide conditions of system parameters to ensure system convergence and stability. Simulation results indicate that the proposed scheme achieves superior performance with energy savings as well as desirable delay guarantees compared with other wellknown schemes.

Automated inference of gene regulatory networks using explicit regulatory modules

Gene regulatory networks are a popular tool for modelling important biological phenomena, such as cell differentiation or oncogenesis. Efficient identification of the causal connections between genes, their products and regulating transcription factors, is key to understanding how defects in their function may trigger diseases. Modelling approaches should keep up with the ever more detailed descriptions of the biological phenomena at play, as provided by new experimental findings and technical improvements. In recent years, we have seen great improvements in mapping of specific binding sites of many transcription factors to distinct regulatory regions. Recent gene regulatory network models use binding measurements; but usually only to define gene-to-gene interactions, ignoring regulatory module structure. Moreover, current huge amount of transcriptomic data, and exploration of all possible cis-regulatory arrangements which can lead to the same transcriptomic response, makes manual model building both tedious and time-consuming.In our paper, we propose a method to specify possible regulatory connections in a given Boolean network, based on transcription factor binding evidence. This is implemented by an algorithm which expands a regular Boolean network model into a “cis-regulatory” Boolean network model. This expanded model explicitly defines regulatory regions as additional nodes in the network, and adds new, valuable biological insights to the system dynamics. The expanded model can automatically be compared with expression data. And, for each node, a regulatory function, consistent with the experimental data, can be found. The resulting models are usually more constrained (by biologically-motivated metadata), and can then be inspected in in silico simulations.The fully automated method for model identification has been implemented in Python, and the expansion algorithm in R. The method resorts to the Z3 Satisfiability Modulo Theories (SMT) solver, and is similar to the RE:IN application (Yordanov et al., 2016).It is available on https://github.com/regulomics/expansion-network.

Computational Inference of Gene Co-Expression Networks for the identification of Lung Carcinoma Biomarkers: An Ensemble Approach.

Gene Networks (GN), have emerged as an useful tool in recent years for the analysis of different diseases in the field of biomedicine. In particular, GNs have been widely applied for the study and analysis of different types of cancer. In this context, Lung carcinoma is among the most common cancer types and its short life expectancy is partly due to late diagnosis. For this reason, lung cancer biomarkers that can be easily measured are highly demanded in biomedical research. In this work, we present an application of gene co-expression networks in the modelling of lung cancer gene regulatory networks, which ultimately served to the discovery of new biomarkers. For this, a robust GN inference was performed from microarray data concomitantly using three different co-expression measures. Results identified a major cluster of genes involved in SRP-dependent co-translational protein target to membrane, as well as a set of 28 genes that were exclusively found in networks generated from cancer samples. Amongst potential biomarkers, genes and are highlighted due to their implications in a considerable portion of lung and bronchus primary carcinomas. These findings demonstrate the potential of GN reconstruction in the rational prediction of biomarkers.

Changes in students\u2019 mental models from computational modeling of gene regulatory networks

BackgroundComputational modeling is an increasingly common practice for disciplinary experts and therefore necessitates integration into science curricula. Computational models afford an opportunity for students to investigate the dynamics of biological systems, but there is significant gap in our knowledge of how these activities impact student knowledge of the structures, relationships, and dynamics of the system. We investigated how a computational modeling activity affected introductory biology students’ mental models of a prokaryotic gene regulatory system (lac operon) by analyzing conceptual models created before and after the activity.ResultsStudents’ pre-lesson conceptual models consisted of provided, system-general structures (e.g., activator, repressor) connected with predominantly incorrect relationships, representing an incomplete mental model of gene regulation. Students’ post-lesson conceptual models included more context-specific structures (e.g., cAMP, lac repressor) and increased in total number of structures and relationships. Student conceptual models also included higher quality relationships among structures, indicating they learned about these context-specific structures through integration with their expanding mental model rather than in isolation.ConclusionsStudent mental models meshed structures in a manner indicative of knowledge accretion while they were productively re-constructing their understanding of gene regulation. Conceptual models can inform instructors about how students are relating system structures and whether students are developing more sophisticated models of system-general and system-specific dynamics.

On Convergence for Piecewise Affine Models of Gene Regulatory Networks via a Lyapunov Approach

In this paper, we analyse convergence and stability properties for piecewise affine models of gene regulatory networks, by means of piecewise quadratic Lyapunov functions. In the first part, we present the piecewise affine model of a gene regulatory network then, after proving a result on the existence of a minimal, attractive, and positively invariant box, we describe a linear matrix inequalitie framework to construct a Lyapunov function for the system. In the second part of the work, after a characterization of the system solutions when considering also isolated Zeno behavior of the trajectories, a monotonicity property of the so found Lyapunov function is formally proved, together with a result on the convergence of the trajectories, in the sense of measure. Finally, we present two examples, showing the applicability and utility of the main theoretical results previously explained.

Boolean Kalman filter and smoother under model uncertainty

Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear state-space models that provide a rich framework for modeling many complex dynamical systems. The model consists of a hidden Boolean state process, observed through an arbitrary noisy mapping to a measurement space. The optimal minimum mean-square error (MMSE) POBDS state estimators are the Boolean Kalman Filter and Smoother. However, in many practical problems, the system parameters are not fully known and must be estimated. In this paper, for POBDS under model uncertainty, we derive an optimal Bayesian estimator for state and parameter estimation. The exact algorithms are derived for the case of discrete and finite parameter space, and for general parameter spaces, an approximate Markov-Chain Monte-Carlo (MCMC) implementation is introduced. We demonstrate the performance of the proposed methodology by means of numerical experiments with POBDS models of gene regulatory networks observed through noisy measurements.

Cell differentiation: What have we learned in 50 years?

I revisit two theories of cell differentiation in multicellular organisms published a half-century ago, Stuart Kauffman's global genome regulatory dynamics (GGRD) model and Roy Britten's and Eric Davidson's modular gene regulatory network (MGRN) model, in light of newer knowledge of mechanisms of gene regulation in the metazoans (animals). The two models continue to inform hypotheses and computational studies of differentiation of lineage-adjacent cell types. However, their shared notion (based on bacterial regulatory systems) of gene switches and networks built from them have constrained progress in understanding the dynamics and evolution of differentiation. Recent work has described unique write-read-rewrite chromatin-based expression encoding in eukaryotes, as well metazoan-specific processes of gene activation and silencing in condensed-phase, enhancer-recruiting regulatory hubs, employing disordered proteins, including transcription factors, with context-dependent identities. These findings suggest an evolutionary scenario in which the origination of differentiation in animals, rather than depending exclusively on adaptive natural selection, emerged as a consequence of a type of multicellularity in which the novel metazoan gene regulatory apparatus was readily mobilized to amplify and exaggerate inherent cell functions of unicellular ancestors. The plausibility of this hypothesis is illustrated by the evolution of the developmental role of Grainyhead-like in the formation of epithelium.

Computational analysis of viable parameter regions in models of synthetic biological systems

BackgroundGene regulatory networks with different topological and/or dynamical properties might exhibit similar behavior. System that is less perceptive for the perturbations of its internal and external factors should be preferred. Methods for sensitivity and robustness assessment have already been developed and can be roughly divided into local and global approaches. Local methods focus only on the local area around nominal parameter values. This can be problematic when parameters exhibits the desired behavior over a large range of parameter perturbations or when parameter values are unknown. Global methods, on the other hand, investigate the whole space of parameter values and mostly rely on different sampling techniques. This can be computationally inefficient. To address these shortcomings ’glocal’ approaches were developed that apply global and local approaches in an effective and rigorous manner.ResultsHerein, we present a computational approach for ’glocal’ analysis of viable parameter regions in biological models. The methodology is based on the exploration of high-dimensional viable parameter spaces with global and local sampling, clustering and dimensionality reduction techniques. The proposed methodology allows us to efficiently investigate the viable parameter space regions, evaluate the regions which exhibit the largest robustness, and to gather new insights regarding the size and connectivity of the viable parameter regions. We evaluate the proposed methodology on three different synthetic gene regulatory network models, i.e. the repressilator model, the model of the AC-DC circuit and the model of the edge-triggered master-slave D flip-flop.ConclusionsThe proposed methodology provides a rigorous assessment of the shape and size of viable parameter regions based on (1) the mathematical description of the biological system of interest, (2) constraints that define feasible parameter regions and (3) cost function that defines the desired or observed behavior of the system. These insights can be used to assess the robustness of biological systems, even in the case when parameter values are unknown and more importantly, even when there are multiple poorly connected viable parameter regions in the solution space. Moreover, the methodology can be efficiently applied to the analysis of biological systems that exhibit multiple modes of the targeted behavior.

Restricted information in a two-step cascade.

A cell must sense extracellular and intracellular fluctuations and respond appropriately to survive for optimal cellular functioning. Accordingly, a cell builds up biochemical networks which can transduce information of extracellular and intracellular fluctuations accurately. We consider a generic two-step cascade as a model gene regulatory network containing three regulatory proteins S, X, and Y connected as S→X→Y. The intermediate node X is a stochastic variable, acts as an obstacle, and impedes the information flow from S to Y.We quantify the information that is restricted by X using the tools of information theory and term this as restricted information. In this context, we further propose two measurable quantities, restricted efficiency and information transfer efficiency. The former determines how efficiently X restricts the upstream information coming from S, while the latter computes the efficiency of X to pass the upstream information toward Y. We also quantify the information that is being uniquely transferred from X to Y, which determines the extent of the ability of X to act as a source of information. Our analysis shows that when the signal strength (or mean population of S, 〈s〉) is low, the intermediate X can carry forward the upstream information reliably as well, as it acts as a better source of information, thereby increasing the fidelity of the network. But at the high signal strength, X restricts most of the upstream information, and its ability to act as a source of information gets reduced. This leads to a loss of fidelity of the network.

Revisiting the Reduction of Stochastic Models of Genetic Feedback Loops with Fast Promoter Switching

Propensity functions of the Hill type are commonly used to model transcriptional regulation in stochastic models of gene expression. This leads to an effective reduced master equation for the mRNA and protein dynamics only. Based on deterministic considerations, it is often stated or tacitly assumed that such models are valid in the limit of rapid promoter switching. Here, starting from the chemical master equation describing promoter-protein interactions, mRNA transcription, protein translation, and decay, we prove that in the limit of fast promoter switching, the distribution of protein numbers is different than that given by standard stochastic models with Hill-type propensities. We show the differences are pronounced whenever the protein-DNA binding rate is much larger than the unbinding rate, a special case of fast promoter switching. Furthermore, we show using both theory and simulations that use of the standard stochastic models leads to drastically incorrect predictions for the switching properties of positive feedback loops and that these differences decrease with increasing mean protein burst size. Our results confirm that commonly used stochastic models of gene regulatory networks are only accurate in a subset of the parameter space consistent with rapid promoter switching.

From Discrete to Continuous Modeling of Lymphocyte Development and Plasticity in Chronic Diseases.

The molecular events leading to differentiation, development, and plasticity of lymphoid cells have been subject of intense research due to their key roles in multiple pathologies, such as lymphoproliferative disorders, tumor growth maintenance and chronic diseases. The emergent roles of lymphoid cells and the use of high-throughput technologies have led to an extensive accumulation of experimental data allowing the reconstruction of gene regulatory networks (GRN) by integrating biochemical signals provided by the microenvironment with transcriptional modules of lineage-specific genes. Computational modeling of GRN has been useful for the identification of molecular switches involved in lymphoid specification, prediction of microenvironment-dependent cell plasticity, and analyses of signaling events occurring downstream the activation of antigen recognition receptors. Among most common modeling strategies to analyze the dynamical behavior of GRN, discrete dynamic models are widely used for their capacity to capture molecular interactions when a limited knowledge of kinetic parameters is present. However, they are less powerful when modeling complex systems sensitive to biochemical gradients. To compensate it, discrete models may be transformed into regulatory networks that includes state variables and parameters varying within a continuous range. This approach is based on a system of differential equations dynamics with regulatory interactions described by fuzzy logic propositions. Here, we discuss the applicability of this method on modeling of development and plasticity processes of adaptive lymphocytes, and its potential implications in the study of pathological landscapes associated to chronic diseases.