Exact reconstruction of gene regulatory networks using compressive sensing.

BackgroundWe consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network's sparseness.ResultsFor the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented.ConclusionsThe method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies

Control Theory: On the Way to New Application Fields

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently, deep interactions are emerging with new application areas, such as systems biology, quantum control and information technology. In order to address the new challenges posed by the new application disciplines, a special focus of this workshop has been on the interaction between control theory and mathematical systems biology. To complement these more biology oriented focus, a series of lectures in this workshop was devoted to the control of networks of systems, fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control

Systems biology approaches to the dynamics of gene expression and chemical reactions

Systems biology is an emergent interdisciplinary field of study whose main goal is to understand the global properties and functions of a biological system by investigating its structure and dynamics [74]. This high-level knowledge can be reached only with a coordinated approach involving researchers with different backgrounds in molecular biology, the various omics (like genomics, proteomics, metabolomics), computer science and dynamical systems theory. The history of systems biology as a distinct discipline began in the 1960s, and saw an impressive growth since year 2000, originated by the increased accumulation of biological information, the development of high-throughput experimental techniques, the use of powerful computer systems for calculations and database hosting, and the spread of Internet as the standard medium for information diffusion [77]. In the last few years, our research group tried to tackle a set of systems biology problems which look quite diverse, but share some topics like biological networks and system dynamics, which are of our interest and clearly fundamental for this field. In fact, the first issue we studied (covered in Part I) was the reverse engineering of large-scale gene regulatory networks. Inferring a gene network is the process of identifying interactions among genes from experimental data (tipically microarray expression profiles) using computational methods [6]. Our aim was to compare some of the most popular association network algorithms (the only ones applicable at a genome-wide level) in different conditions. In particular we verified the predictive power of similarity measures both of direct type (like correlations and mutual information) and of conditional type (partial correlations and conditional mutual information) applied on different kinds of experiments (like data taken at equilibrium or time courses) and on both synthetic and real microarray data (for E. coli and S. cerevisiae). In our simulations we saw that all network inference algorithms obtain better performances from data produced with \u201cstructural\u201d perturbations (like gene knockouts at steady state) than with just dynamical perturbations (like time course measurements or changes of the initial expression levels). Moreover, our analysis showed differences in the performances of the algorithms: direct methods are more robust in detecting stable relationships (like belonging to the same protein complex), while conditional methods are better at causal interactions (e.g. transcription factor\u2013binding site interactions), especially in presence of combinatorial transcriptional regulation. Even if time course microarray experiments are not particularly useful for inferring gene networks, they can instead give a great amount of information about the dynamical evolution of a biological process, provided that the measurements have a good time resolution. Recently, such a dataset has been published [119] for the yeast metabolic cycle, a well-known process where yeast cells synchronize with respect to oxidative and reductive functions. In that paper, the long-period respiratory oscillations were shown to be reflected in genome-wide periodic patterns in gene expression. As explained in Part II, we analyzed these time series in order to elucidate the dynamical role of post-transcriptional regulation (in particular mRNA stability) in the coordination of the cycle. We found that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates. Moreover, the cascade of events which occurs during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses or stimuli. The concepts of network and of systems dynamics return also as major arguments of Part III. In fact, there we present a study of some dynamical properties of the so-called chemical reaction networks, which are sets of chemical species among which a certain number of reactions can occur. These networks can be modeled as systems of ordinary differential equations for the species concentrations, and the dynamical evolution of these systems has been theoretically studied since the 1970s [47, 65]. Over time, several independent conditions have been proved concerning the capacity of a reaction network, regardless of the (often poorly known) reaction parameters, to exhibit multiple equilibria. This is a particularly interesting characteristic for biological systems, since it is required for the switch-like behavior observed during processes like intracellular signaling and cell differentiation. Inspired by those works, we developed a new open source software package for MATLAB, called ERNEST, which, by checking these various criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results of this analysis can be used, for example, for model discrimination: if for a multistable biological process there are multiple candidate reaction models, it is possible to eliminate some of them by proving that they are always monostationary. Finally, we considered the related property of monotonicity for a reaction network. Monotone dynamical systems have the tendency to converge to an equilibrium and do not present chaotic behaviors. Most biological systems have the same features, and are therefore considered to be monotone or near-monotone [85, 116]. Using the notion of fundamental cycles from graph theory, we proved some theoretical results in order to determine how distant is a given biological network from being monotone. In particular, we showed that the distance to monotonicity of a network is equal to the minimal number of negative fundamental cycles of the corresponding J-graph, a signed multigraph which can be univocally associated to a dynamical system

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Identification of Piecewise Linear Models of Complex Dynamical Systems

The paper addresses the realization and identification problem or a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an identification algorithm for this subclass of hybrid systems. The considered system class and the identification problem are motivated by applications in systems biology

Network Identification: A Passivity and Network Optimization Approach

The theory of network identification, namely identifying the interaction topology among a known number of agents, has been widely developed for linear agents over recent years. However, the theory for nonlinear agents remains less extensive. We use the notion maximal equilibrium-independent passivity (MEIP) and network optimization theory to present a network identification method for nonlinear agents.We do so by introducing a specially designed exogenous input, and exploiting the properties of networked MEIP systems. We then specialize on LTI agents, showing that the method gives a distributed cubic-time algorithm for network reconstruction in that case. We also discuss different methods of choosing the exogenous input, and provide an example on a neural network model.Comment: 8 Pages, 3 Figure

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn