Inference of gene regulatory networks from time series by Tsallis entropy

Background: The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed. Results: In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes. Conclusions: A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 <= q <= 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

Synchronous versus asynchronous modeling of gene regulatory networks.

MOTIVATION: In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. RESULTS: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software. Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1-Th2 cellular differentiation process. AVAILABILITY: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.

Modeling stochasticity and robustness in gene regulatory networks.

MOTIVATION: Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. RESULTS: In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. AVAILABILITY: Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

Cognate microRNA-Gene Regulatory Networks Mediating Glioblastoma Oncogenic Properties

Malignant gliomas, including the most common and fatal form glioblastoma (GBM, WHO grade IV astrocytoma), remain a challenge to treat. In the United States and Europe, more than 30,000 patients per year are newly diagnosed with GBM. Despite ongoing trials, the best currently available multimodal treatment approaches include surgical resection followed by concomitant and adjuvant radiation (RT) and temozolomide (TMZ) therapy, resulting in a low median overall survival (OS) rate ranging from 12.2 - 15.9 months. The important role of genetic and epigenetic changes in DNA, RNA, and protein alteration as well as epigenetic changes secondary to the tumor microenvironment and outside selection pressure (therapeutic interventions), are increasingly being recognized. In GBM treatment, the focus is shifting toward a more patient-centered (personalized) therapy. In this regard, in particular, microRNAs are being increasingly studied. MicroRNAs are non¬protein coding small RNAs that serve as negative gene regulators by binding to a specific sequence in the promoter region of a target gene, thus regulating gene expression. A single microRNA potentially targets hundreds of genes; thus, microRNAs and their cognate target genes have important roles as tumor suppressors and oncogenes as well as regulators of various cancer- specific cellular features, such as proliferation, apoptosis, invasion, and metastasis. The identification of distinct microRNA-gene regulatory networks in GBM patients can be expected to provide novel therapeutic insights by identifying candidate patients for targeted therapies. To this end, in this work we identified and validated clinically relevant and meaningful novel gene- microRNA regulatory networks that correlated with MR tumor phenotypes, histopathology, and patient survival and response rates to therapy. - Le traitement des gliomes malins, y compris sous leur forme la plus commune et meurtrière, le glioblastome (GBM, ou astrocytome de grade IV selon l'OMS), demeure à ce jour un défi. Aux États-Unis et en Europe, un nouveau diagnostic de GBM est prononcé dans plus de 30Ό00 cas par an. En dépit de tests en cours, les meilleures approches thérapeutiques combinées actuellement disponibles comprennent la résection chirurgicale de la tumeur, suivie d'une radiothérapie adjuvante ainsi que d'un traitement au temozolomide (RT/TMZ), thérapies dont résulte une médiane de survie globale basse (overall survival, OS), comprise entre 12.2 et 15.9 mois. On reconnaît de plus en plus le rôle majeur de l'ADN, de l'ARN et de l'altération des protéines ainsi que des modifications épigénétiques, secondaires par rapport au microenvironnement de la tumeur et à la pression de sélection extérieure (les interventions thérapeutiques). Dans le traitement du GBM, le centre d'intérêt se déplace vers une thérapie centrée sur le cas individuel du patient. Dans ce but, en particulier les microARN sont de plus en plus analysés. Les microARN sont de petits ARN non-codants (les protéines) qui servent de régulateurs négatifs de gènes en s'attachant à une séquence spécifique dans la région promotrice d'un gène-cible, régulant ainsi l'expression du gène. Un seul microARN cible potentiellement des centaines de gènes; on a ainsi découvert que les microARN et leurs gènes-cibles apparentés ont une fonction importante en tant que suppresseurs de tumeurs et d'oncogènes, ainsi que comme régulateurs de diverses caractéristiques cellulaires spécifiques du cancer, comme la prolifération, l'apoptose, l'invasion et la métastase. On peut s'attendre à ce que l'identification de réseaux microARN régulateurs de gènes, distincts selon les patients de GBM, fournisse une approche thérapeutique inédite par la détermination des patients susceptibles de réagir favorablement à des thérapies ciblées.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

Identifying regulational alterations in gene regulatory networks by state space representation of vector autoregressive models and variational annealing

Background: In the analysis of effects by cell treatment such as drug dosing, identifying changes on gene network structures between normal and treated cells is a key task. A possible way for identifying the changes is to compare structures of networks estimated from data on normal and treated cells separately. However, this approach usually fails to estimate accurate gene networks due to the limited length of time series data and measurement noise. Thus, approaches that identify changes on regulations by using time series data on both conditions in an efficient manner are demanded. Methods: We propose a new statistical approach that is based on the state space representation of the vector autoregressive model and estimates gene networks on two different conditions in order to identify changes on regulations between the conditions. In the mathematical model of our approach, hidden binary variables are newly introduced to indicate the presence of regulations on each condition. The use of the hidden binary variables enables an efficient data usage; data on both conditions are used for commonly existing regulations, while for condition specific regulations corresponding data are only applied. Also, the similarity of networks on two conditions is automatically considered from the design of the potential function for the hidden binary variables. For the estimation of the hidden binary variables, we derive a new variational annealing method that searches the configuration of the binary variables maximizing the marginal likelihood. Results: For the performance evaluation, we use time series data from two topologically similar synthetic networks, and confirm that our proposed approach estimates commonly existing regulations as well as changes on regulations with higher coverage and precision than other existing approaches in almost all the experimental settings. For a real data application, our proposed approach is applied to time series data from normal Human lung cells and Human lung cells treated by stimulating EGF-receptors and dosing an anticancer drug termed Gefitinib. In the treated lung cells, a cancer cell condition is simulated by the stimulation of EGF-receptors, but the effect would be counteracted due to the selective inhibition of EGF-receptors by Gefitinib. However, gene expression profiles are actually different between the conditions, and the genes related to the identified changes are considered as possible off-targets of Gefitinib. Conclusions: From the synthetically generated time series data, our proposed approach can identify changes on regulations more accurately than existing methods. By applying the proposed approach to the time series data on normal and treated Human lung cells, candidates of off-target genes of Gefitinib are found. According to the published clinical information, one of the genes can be related to a factor of interstitial pneumonia, which is known as a side effect of Gefitinib.

Intrinsic noise in gene regulatory networks

Cells are intrinsically noisy biochemical reactors: low reactant numbers can lead to significant statistical fluctuations in molecule numbers and reaction rates. Here we use an analytic model to investigate the emergent noise properties of genetic systems. We find for a single gene that noise is essentially determined at the translational level, and that the mean and variance of protein concentration can be independently controlled. The noise strength immediately following single gene induction is almost twice the final steady-state value. We find that fluctuations in the concentrations of a regulatory protein can propagate through a genetic cascade; translational noise control could explain the inefficient translation rates observed for genes encoding such regulatory proteins. For an autoregulatory protein, we demonstrate that negative feedback efficiently decreases system noise. The model can be used to predict the noise characteristics of networks of arbitrary connectivity. The general procedure is further illustrated for an autocatalytic protein and a bistable genetic switch. The analysis of intrinsic noise reveals biological roles of gene network structures and can lead to a deeper understanding of their evolutionary origin.

Bayesian Methods for Inferring Gene Regulatory Networks

Thesis (Ph.D.)--University of Washington, 2016-08

Conditional mutual inclusive information enables accurate quantification of associations in gene regulatory networks

International audience

Evolution of developmental gene regulatory networks in echinoids

Developmental gene regulatory networks (dGRNs) are assemblages of regulatory genes that direct embryonic development of animal body plans and their morpho-logical structures. dGRNs exhibit recursively-wired circuitry that is encoded in the genome and executed during development. Alteration to the regulatory architecture of dGRNs causes variation in developmental programs both during the development of an individual organism and during the evolution of an individual lineage. The ex-planatory power of these networks is best exemplified by the global dGRN directing early development of the euechinoid sea urchin Strongylocentrotus purpuratus. This network consists of numerous regulatory genes engaging in hundreds of genomic regulatory transactions that collectively direct the delineation of early embryonic domains and the specification of cell lineages. Research on closely-related euechi-noid sea urchins, e.g. Lytechinus variegatus and Paracentrotus lividus, has revealed marked conservation of dGRN architecture in echinoid development, suggesting little appreciable alteration has occurred since their divergence in evolution at least 90 million years ago (mya).

We sought to test whether this observation extends to all sea urchins (echinoids) and undertook a systematic analysis of over 50 regulatory genes in the cidaroid sea urchin Eucidaris tribuloides, surveing their regulatory activity and function in a sea urchin that diverged from euechinoid sea urchins at least 268 mya. Our results revealed extensive alterations have occurred to all levels of echinoid dGRN archi-tecture since the cidaroid-euechinoid divergence. Alterations to mesodermal sub-circuits were particularly striking, including functional di˙erences in specification of non-skeletogenic mesenchyme (NSM), skeletogenic mesenchyme (SM), and en-domesodermal segregation. Specification of endomesodermal embryonic domains revealed that, while their underlying network circuitry had clearly diverged, regu-latory states established in pregastrular embryos of these two groups are strikingly similar. Analyses of E. tribuloides specification leading to the estab-lishment of dorsal-ventral (aboral-oral) larval polarity indicated that regulation of regulatory genes expressed in mesodermal embryonic domains had incurred significantly more alterations than those expressed in endodermal and ectodermal domains. Taken together, this study highlights the ability of dGRN architecture to buffer extensive alterations in the evolution and early development of echinoids and adds further support to the notion that alterations can occur at all levels of dGRN architecture and all stages of embryonic development.

Modeling gene expression regulatory networks with the sparse vector autoregressive model

Abstract Background To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems. Results We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets. Conclusion The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any a priori information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.

Evolution of the gene regulatory network controlling flower dorsoventral asymmetry

Tese de Doutoramento em Biologia de Plantas.

Modularity and evolutionary constraints in a baculovirus gene regulatory network

Abstract Background The 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. Results We 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. Conclusions Albeit 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.

Transient Activation of Meox1 Is an Early Component of the Gene Regulatory Network Downstream of Hoxa2

Hox genes encode transcription factors that regulate morphogenesis in all animals with bilateral symmetry. Although Hox genes have been extensively studied, their molecular function is not clear in vertebrates, and only a limited number of genes regulated by Hox transcription factors have been identified. Hoxa2 is required for correct development of the second branchial arch, its major domain of expression. We now show that Meox1 is genetically downstream from Hoxa2 and is a direct target. Meox1 expression is downregulated in the second arch of Hoxa2 mouse mutant embryos. In chromatin immunoprecipitation (ChIP), Hoxa2 binds to the Meox1 proximal promoter. Two highly conserved binding sites contained in this sequence are required for Hoxa2-dependent activation of the Meox1 promoter. Remarkably, in the absence of Meox1 and its close homolog Meox2, the second branchial arch develops abnormally and two of the three skeletal elements patterned by Hoxa2 are malformed. Finally, we show that Meox1 can specifically bind the DNA sequences recognized by Hoxa2 on its functional target genes. These results provide new insight into the Hoxa2 regulatory network that controls branchial arch identity.