Threshold-dominated regulation hides genetic variation in gene expression networks

Background  

In dynamical models with feedback and sigmoidal response functions, some or all variables have thresholds around which they regulate themselves or other variables. A mathematical analysis has shown that when the dose-response functions approach binary or on/off responses, any variable with an equilibrium value close to one of its thresholds is very robust to parameter perturbations of a homeostatic state. We denote this threshold robustness. To check the empirical relevance of this phenomenon with response function steepnesses ranging from a near on/off response down to Michaelis-Menten conditions, we have performed a simulation study to investigate the degree of threshold robustness in models for a three-gene system with one downstream gene, using several logical input gates, but excluding models with positive feedback to avoid multistationarity. Varying parameter values representing functional genetic variation, we have analysed the coefficient of variation (CV) of the gene product concentrations in the stable state for the regulating genes in absolute terms and compared to the CV for the unregulating downstream gene. The sigmoidal or binary dose-response functions in these models can be considered as phenomenological models of the aggregated effects on protein or mRNA expression rates of all cellular reactions involved in gene expression.     

Robust stability of stochastic delayed genetic regulatory networks

Gene regulation is an intrinsically noisy process, which is subject to intracellular and extracellular noise perturbations and environment fluctuations. In this paper, we consider the robust stability analysis problem of genetic regulatory networks with time-varying delays and stochastic perturbation. Different from other papers, the genetic regulate system considers not only stochastic perturbation but also parameter disturbances, it is in close proximity to the real gene regulation process than determinate model. Based on the Lyapunov functional theory, sufficient conditions are given to ensure the stability of the genetic regulatory networks. All the stability conditions are given in terms of LMIs which are easy to be verified. Illustrative examples are presented to show the effectiveness of the obtained results.     

Dizzy: stochastic simulation of large-scale genetic regulatory networks

We describe Dizzy, a software tool for stochastically and deterministically modeling the spatially homogeneous kinetics of integrated large-scale genetic, metabolic, and signaling networks. Notable features include a modular simulation framework, reusable modeling elements, complex kinetic rate laws, multi-step reaction processes, steady-state noise estimation, and spatial compartmentalization.     

On the robustness of complex heterogeneous gene expression networks

We analyze a continuous gene expression model on the underlying topology of a complex heterogeneous network. Numerical simulations aimed at studying the chaotic and periodic dynamics of the model are performed. The results clearly indicate that there is a region in which the dynamical and structural complexity of the system avoid chaotic attractors. However, contrary to what has been reported for Random Boolean Networks, the chaotic phase cannot be completely suppressed, which has important bearings on network robustness and gene expression modeling.     

Effect of feedback regulation on stochastic gene expression

Stochastic noise in gene expression arises as a result of species in small copy number undergoing transitions between discrete chemical states. Here the noise in a single gene network is investigated using the Omega-expansion techniques. We show that the linear noise approximation implies an invariant relationship between the normalized variances and normalized covariance in steady-state statistics. This invariant relationship provides an exactly statistical interpretation for why the stochastic noise in gene expression should be measured by the normalized variance. The nature of the normalized variance reveals the basic relationship between the stochasticity and system size in gene expression. The linear noise approximation implies also that for both mRNA and protein, the total noise can be decomposed into two basic components, one concerns the contribution of average number of molecules, and other the contribution of interactions between mRNA and protein. For the situation with linear feedback, our results clearly show that for two genes with the same average number of protein molecules, the gene with negative feedback will have a small protein noise, i.e., the negative feedback will reduce the protein noise. For the effect of the burst size on the protein noise, we show also that the protein intrinsic noise will decrease with the increase of the burst size, but the protein extrinsic noise is independent of the burst size.     

Signal propagation in nonlinear stochastic gene regulatory networks

The ability to build genetic circuits with a reproducible response to external stimuli depends on the experimental and theoretical methods used in the process. A theoretical formalism that describes the response of a nonlinear stochastic genetic network to the external stimuli (input signals), is proposed. Two applications are studied in detail: the design of a logic pulse and the interference of three signal generators in the E2F1 regulatory element. The gene interactions are presented using molecular diagrams that have a precise mathematical structure and retain the biological meaning of the processes.     

Effective temperature in stochastic kinetics and gene networks

The fluctuation-dissipation theorem, one of the central theorems in thermal dynamics, breaks down in out-of-equilibrium systems. The idea of effective temperature coming from the extensions of that theorem has been recently introduced to study glasses and has proved to be a key concept for out-of-equilibrium systems. Gene networks involve stochastic chemical kinetics and are far from equilibrium. This leads us to try to use the notion of effective temperature to study them. To develop this idea, we study a simple birth-death process and a general two-species interacting process using the language of effective temperature. Furthermore, a model of a nonregulatory gene is studied as an example. The effective temperature may serves as an alternative and somewhat more fundamental language to describe the intrinsic-extrinsic noise distinction that has already provided a tool for qualifying gene networks.     

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.     

On the complexity measures of genetic sequences

MOTIVATION: It is well known that the regulatory regions of genomes are highly repetitive. They are rich in direct, symmetric and complemented repeats, and there is no doubt about the functional significance of these repeats. Among known measures of complexity, the Ziv-Lempel complexity measure reflects most adequately repeats occurring in the text. But this measure does not take into account isomorphic repeats. By isomorphic repeats we mean fragments that are identical (or symmetric) modulo some permutation of the alphabet letters. RESULTS: In this paper, two complexity measures of symbolic sequences are proposed that generalize the Ziv-Lempel complexity measure by taking into account any isomorphic repeats in the text (rather than just direct repeats as in Ziv-Lempel). The first of them, the complexity vector, is designed for small alphabets such as the alphabet of nucleotides. The second is based on a search for the longest isomorphic fragment in the history of sequence synthesis and can be used for alphabets of arbitrary cardinality. These measures have been used for recognition of structural regularities in DNA sequences. Some interesting structures related to the regulatory region of the human growth hormone are reported.     

NetAtlas: a Cytoscape plugin to examine signaling networks based on tissue gene expression

Graphical methods are useful for visualizing signaling networks derived from the synthesis of large bodies of literature information or large-scale experimental measurements. Software tools to filter and organize these networks allow the exploration of their inherent biological and structural properties. We have developed NetAtlas, an open-source, Java-based Cytoscape plugin for examining signaling networks in the context of tissue gene expression patterns. The tissue gene expression data available through NetAtlas consists of 79 human tissues, 61 mouse tissues, and 44 combined tissues from 3 rat strains. Users may also import their own tissue gene expression data. The NetAtlas plugin allows the creation of tissue-defined signaling networks by identifying which components are expressed in particular tissues, which components show tissue-specific expression, and which components within the network are coordinately expressed across tissues. The NetAtlas plugin is available at http://sourceforge.net/projects/netatlas/.     

A graphical model approach for inferring large-scale networks integrating gene expression and genetic polymorphism

Background  

Graphical models (e.g., Bayesian networks) have been used frequently to describe complex interaction patterns and dependent structures among genes and other phenotypes. Estimation of such networks has been a challenging problem when the genes considered greatly outnumber the samples, and the situation is exacerbated when one wishes to consider the impact of polymorphisms (SNPs) in genes.     

Colored extrinsic fluctuations and stochastic gene expression

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise’, is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored’). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high‐throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.     

Anomalous phylogenies based on bacterial catalase gene sequences

Phylogenies based on nine prokaryotic catalase sequences demonstrate no relationship to phylogenies based on rDNA sequences or other known criteria. When this observation is considered together with the monophyletic relationship observed for eukaryotic catalase sequences, it seems likely that the catalase gene sequence has migrated repeatedly from eukaryotes to prokaryotes.     

Functional gene networks based on the gene neighborhood in metagenomes

The gene neighborhood in prokaryotic genomes has been effectively utilized in inferring co-functional networks in various organisms. Previously, such genomic context information has been sought among completely assembled prokaryotic genomes. Here, we present a method to infer functional gene networks according to the gene neighborhood in metagenome contigs, which are incompletely assembled genomic fragments. Given that the amount of metagenome sequence data has now surpassed that of completely assembled prokaryotic genomes in the public domain, we expect benefits of inferring networks by the metagenome-based gene neighborhood. We generated co-functional networks for diverse taxonomical species using metagenomics contigs derived from the human microbiome and the ocean microbiome. We found that the networks based on the metagenome gene neighborhood outperformed those based on 1748 completely assembled prokaryotic genomes. We also demonstrated that the metagenome-based gene neighborhood could predict genes related to virulence-associated phenotypes in a bacterial pathogen, indicating that metagenome-based functional links could be sufficiently predictive for some phenotypes of medical importance. Owing to the exponential growth of metagenome sequence data in public repositories, metagenome-based inference of co-functional networks will facilitate understanding of gene functions and pathways in diverse species.