No Arabic abstract
Inferring genetic networks from gene expression data is one of the most challenging work in the post-genomic era, partly due to the vast space of possible networks and the relatively small amount of data available. In this field, Gaussian Graphical Model (GGM) provides a convenient framework for the discovery of biological networks. In this paper, we propose an original approach for inferring gene regulation networks using a robust biological prior on their structure in order to limit the set of candidate networks. Pathways, that represent biological knowledge on the regulatory networks, will be used as an informative prior knowledge to drive Network Inference. This approach is based on the selection of a relevant set of genes, called the molecular signature, associated with a condition of interest (for instance, the genes involved in disease development). In this context, differential expression analysis is a well established strategy. However outcome signatures are often not consistent and show little overlap between studies. Thus, we will dedicate the first part of our work to the improvement of the standard process of biomarker identification to guarantee the robustness and reproducibility of the molecular signature. Our approach enables to compare the networks inferred between two conditions of interest (for instance case and control networks) and help along the biological interpretation of results. Thus it allows to identify differential regulations that occur in these conditions. We illustrate the proposed approach by applying our method to a study of breast cancers response to treatment.
We introduce the notion of non-oscillation, propose a constructive method for its robust verification, and study its application to biological interaction networks (also known as, chemical reaction networks). We begin by revisiting Muldowneys result on non-existence of periodic solutions based on the study of the variational system of the second additive compound of the Jacobian of a nonlinear system. We show that exponential stability of the latter rules out limit cycles, quasi-periodic solutions, and broad classes of oscillatory behavior. We focus then on nonlinear equations arising in biological interaction networks with general kinetics, and we show that the dynamics of the aforementioned variational system can be embedded in a linear differential inclusion. We then propose algorithms for constructing piecewise linear Lyapunov functions to certify global robust non-oscillatory behavior. Finally, we apply our techniques to study several regulated enzymatic cycles where available methods are not able to provide any information about their qualitative global behavior.
One of the outstanding challenges in comparative genomics is to interpret the evolutionary importance of regulatory variation between species. Rigorous molecular evolution-based methods to infer evidence for natural selection from expression data are at a premium in the field, and to date, phylogenetic approaches have not been well-suited to address the question in the small sets of taxa profiled in standard surveys of gene expression. We have developed a strategy to infer evolutionary histories from expression profiles by analyzing suites of genes of common function. In a manner conceptually similar to molecular evolution models in which the evolutionary rates of DNA sequence at multiple loci follow a gamma distribution, we modeled expression of the genes of an emph{a priori}-defined pathway with rates drawn from an inverse gamma distribution. We then developed a fitting strategy to infer the parameters of this distribution from expression measurements, and to identify gene groups whose expression patterns were consistent with evolutionary constraint or rapid evolution in particular species. Simulations confirmed the power and accuracy of our inference method. As an experimental testbed for our approach, we generated and analyzed transcriptional profiles of four emph{Saccharomyces} yeasts. The results revealed pathways with signatures of constrained and accelerated regulatory evolution in individual yeasts and across the phylogeny, highlighting the prevalence of pathway-level expression change during the divergence of yeast species. We anticipate that our pathway-based phylogenetic approach will be of broad utility in the search to understand the evolutionary relevance of regulatory change.
Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be used to adequately describe this complex process. In this paper, we investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher-order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments as well as the global features of actomyosin networks. We first map the networks into local graph representations and then, using principles from network-theory order parameters, combine properties from these representations to gain insight on the heterogeneous morphologies of actomyosin networks at a global level. We find that ABPs with a valency greater than two promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosin-like motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosin detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape.
We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and fast variables are made, or necessary.We apply the theoretical results to chemical reaction networks with mass action kinetics admitting slow and fast reactions. For some relevant classes of such systems there exist canonical parameterizations of the variety of stationary points, hence the theory is applicable in a natural manner. In particular we obtain a closed form expression for the reduced system when the fast subsystem admits complex balanced steady states.
A multilayer network approach combines different network layers, which are connected by interlayer edges, to create a single mathematical object. These networks can contain a variety of information types and represent different aspects of a system. However, the process for selecting which information to include is not always straightforward. Using data on two agonistic behaviors in a captive population of monk parakeets (Myiopsitta monachus), we developed a framework for investigating how pooling or splitting behaviors at the scale of dyadic relationships (between two individuals) affects individual- and group-level social properties. We designed two reference models to test whether randomizing the number of interactions across behavior types results in similar structural patterns as the observed data. Although the behaviors were correlated, the first reference model suggests that the two behaviors convey different information about some social properties and should therefore not be pooled. However, once we controlled for data sparsity, we found that the observed measures corresponded with those from the second reference model. Hence, our initial result may have been due to the unequal frequencies of each behavior. Overall, our findings support pooling the two behaviors. Awareness of how selected measurements can be affected by data properties is warranted, but nonetheless our framework disentangles these efforts and as a result can be used for myriad types of behaviors and questions. This framework will help researchers make informed and data-driven decisions about which behaviors to pool or separate, prior to using the data in subsequent multilayer network analyses.