Mathematical Methods for Inferring Regulatory Networks Interactions: Application to Genetic Regulation

This paper deals with the problem of reconstruction of the intergenic interaction graph from the raw data of genetic co-expression coming with new technologies of bio-arrays (DMA-arrays, protein-arrays, etc.). These new imaging devices in general only give information about the asymptotical part (fixed configurations of co-expression or limit cycles of such configurations) of the dynamical evolution of the regulatory networks (genetic and/or proteic) underlying the functioning of living systems. Extracting the casual structure and interaction coefficients of a gene interaction network from the observed configurations is a complex problem. But if all the fixed configurations are supposedly observed and if they are factorizable into two or more subsets of values, then the interaction graph possesses as many connected components as the number of factors and the solution is obtained in polynomial time. This new result allows us for example to partly solve the topology of the genetic regulatory network ruling the flowering in Arabidopsis thaliana .     

Interactions between Financial and Environmental Networks in OECD Countries

We analysed a multiplex of financial and environmental networks between OECD countries from 2002 to 2010. Foreign direct investments and portfolio investment showing the flows in equity securities, short-term, long-term and total debt, these securities represent the financial layers; emissions of NO _x, PM10, SO ₂, CO ₂ equivalent and the water footprint associated with international trade represent the environmental layers. We present a new measure of cross-layer correlations between flows in different layers based on reciprocity. For the assessment of results, we implement a null model for this measure based on the exponential random graph theory. We find that short-term financial flows are more correlated with environmental flows than long-term investments. Moreover, the correlations between reverse financial and environmental flows (i.e. the flows of different layers going in opposite directions) are generally stronger than correlations between synergic flows (flows going in the same direction). This suggests a trade-off between financial and environmental layers, where, more financialised countries display higher correlations between outgoing financial flows and incoming environmental flows than from lower financialised countries. Five countries are identified as hubs in this finance-environment multiplex: The United States, France, Germany, Belgium-Luxembourg and United Kingdom.     

基因调控网络的生物信息学研究

调控网络的研究对于深入理解细胞的决定和分化、多细胞生物的生长发育至关重要。在调控网络中调控元件、基序(motif)、组件(module)、网络整体的拓扑学结构等4个结构层次进行的研究已经发展出了几类主要方法,但仍然有些问题需要解决。用理论方法及基于生物工程技术和合成生物学中研究成果的方法,建立调控网络Circuit的可计算模型的标准和数据库也在不断发展中。新近的研究还显示,高拟真度的Circuit模型与Circuit重建的研究方法联用,可以切实地解决许多调控网络研究中的重要问题。     

Regulatory Interactions between a Bacterial Tyrosine Kinase and Its Cognate Phosphatase

The cyclic process of autophosphorylation of the C-terminal tyrosine cluster (YC) of a bacterial tyrosine kinase and its subsequent dephosphorylation following interactions with a counteracting tyrosine phosphatase regulates diverse physiological processes, including the biosynthesis and export of polysaccharides responsible for the formation of biofilms or virulence-determining capsules. We provide here the first detailed insight into this hitherto uncharacterized regulatory interaction at residue-specific resolution using Escherichia coli Wzc, a canonical bacterial tyrosine kinase, and its opposing tyrosine phosphatase, Wzb. The phosphatase Wzb utilizes a surface distal to the catalytic elements of the kinase, Wzc, to dock onto its catalytic domain (Wzc_CD). Wzc_CD binds in a largely YC-independent fashion near the Wzb catalytic site, inducing allosteric changes therein. YC dephosphorylation is proximity-mediated and reliant on the elevated concentration of phosphorylated YC near the Wzb active site resulting from Wzc_CD docking. Wzb principally recognizes the phosphate of its phosphotyrosine substrate and further stabilizes the tyrosine moiety through ring stacking interactions with a conserved active site tyrosine.     

Regulatory Networks and Complex Interactions between the Insulin and Angiotensin II Signalling Systems: Models and Implications for Hypertension and Diabetes

The cross-talk between insulin and angiotensin II signalling pathways plays a significant role in the co-occurrence of diabetes and hypertension. We developed a mathematical model of the system of interactions among the biomolecules that are involved in the cross-talk between the insulin and angiotensin II signalling pathways. We have identified several feedback structures that regulate the dynamic behavior of the individual signalling pathways and their interactions. Different scenarios are simulated and dominant steady-state, dynamic and stability characteristics are revealed. The proposed mechanistic model describes how angiotensin II inhibits the actions of insulin and impairs the insulin-mediated vasodilation. The model also predicts that poor glycaemic control induced by diabetes contributes to hypertension by activating the renin angiotensin aystem.     

A Developmental Systems Perspective on Epistasis: Computational Exploration of Mutational Interactions in Model Developmental Regulatory Networks

The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/− feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.     

Discovering Study-Specific Gene Regulatory Networks

Microarrays are commonly used in biology because of their ability to simultaneously measure thousands of genes under different conditions. Due to their structure, typically containing a high amount of variables but far fewer samples, scalable network analysis techniques are often employed. In particular, consensus approaches have been recently used that combine multiple microarray studies in order to find networks that are more robust. The purpose of this paper, however, is to combine multiple microarray studies to automatically identify subnetworks that are distinctive to specific experimental conditions rather than common to them all. To better understand key regulatory mechanisms and how they change under different conditions, we derive unique networks from multiple independent networks built using glasso which goes beyond standard correlations. This involves calculating cluster prediction accuracies to detect the most predictive genes for a specific set of conditions. We differentiate between accuracies calculated using cross-validation within a selected cluster of studies (the intra prediction accuracy) and those calculated on a set of independent studies belonging to different study clusters (inter prediction accuracy). Finally, we compare our method''s results to related state-of-the art techniques. We explore how the proposed pipeline performs on both synthetic data and real data (wheat and Fusarium). Our results show that subnetworks can be identified reliably that are specific to subsets of studies and that these networks reflect key mechanisms that are fundamental to the experimental conditions in each of those subsets.     

Evolving Robust Gene Regulatory Networks

Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of ‘parts’ and ‘devices’. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.     

Modeling of Hysteresis in Gene Regulatory Networks

Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.     

Gene Regulatory Networks in the Genomics Era

<正>The precise regulation of gene expression is critical to the normal development and biological function of all organisms. Dysregulation of gene expression during early development can result in a spectrum of failures ranging from minor defects to the termination of development. In adult life, dysregulation ncan lead to     

Variable Interactions between Sucrose Non-fermented 1-Related Protein Kinases and Regulatory Proteins in Higher Plants

WPK4 is a sucrose non-fermented 1 (SNF1)-related wheat protein kinase, and was previously reported to interact with 14-3-3 proteins. We identified four Arabidopsis thaliana WPK4-like genes, and designated them AtWL1 through AtWL4. Yeast two-hybrid analysis, however, indicated that none of the AtWLs interacted with any of A. thaliana 14-3-3 (At14-3-3) proteins, although WPK4 itself interacted with six of them. Structurally, AtWLs were classified into a subfamiliy of AtCIPK, which generally interacts with calucineurin B-like proteins (CBL). This was also the case for AtWL1 and AtWL2, showing an efficient interaction with AtCBL2. In contrast, WPK4 interacted with none of the CBLs. In addition, to ascertain the possible interaction in vivo, expression of those genes was examined with a promoter-GUS assay. These results suggested that the interacting partner of SNF1-related protein kinases varies among plant species, and that, in the case of A. thaliana, it was CBLs, some of which were predicted to broadly regulate multiple CIPKs.     

Recent Advances in Intervention in Markovian Regulatory Networks

Markovian regulatory networks constitute a class of discrete state-space models used to study gene regulatory dynamics and discover methods that beneficially alter those dynamics. Thereby, this class of models provides a framework to discover effective drug targets and design potent therapeutic strategies. The salient translational goal is to design therapeutic strategies that desirably modify network dynamics via external signals that vary the expressions of a control gene. The objective of an intervention strategy is to reduce the likelihood of the pathological cellular function related to a disease. The task of finding an effective intervention strategy can be formulated as a sequential decision making problem for a pre-defined cost of intervention and a cost-per-stage function that discriminates the gene-activity profiles. An effective intervention strategy prescribes the actions associated with an external signal that result in the minimum expected cost. This strategy in turn can be used as a treatment that reduces the long-run likelihood of gene expressions favorable to the disease. In this tutorial, we briefly summarize the first method proposed to design such therapeutic interventions, and then move on to some of the recent refinements that have been proposed. Each of these recent intervention methods is motivated by practical or analytical considerations. The presentation of the key ideas is facilitated with the help of two case studies.Key Words: Regulatory networks, markovian decision processes, translational genomics, systems biology.