The inference of large-scale gene regulatory networks from high-throughput data sets has revealed a diverse picture of only partially overlapping descriptions. Nevertheless, several properties in the organization of these networks are recurrent, such as hubs, a modular structure and certain motifs. Several authors have recently claimed cell systems to be stable against perturbations and random errors, but still able to rapidly switch between different states from specific stimuli. Since inferred mathematical models of large-scale systems need to be extremely simple to avoid overfitting, these two features are hard to attain simultaneously for a model. Here we review and discuss possible measures of how system stability and flexibility may be manifested and measured for linearized models based on systems of ordinary differential equations. Furthermore, we review how the network properties mentioned above together with the nature of the interactions contribute to these systems level properties. It turns out that the presence of repressed hubs, together with other phenomena of topological nature such as motifs and modules, contribute to the overall stability and/or flexibility of the model.

Background: To predict gene expressions is an important endeavour within computational systems biology. It can both be a way to explore how drugs affect the system, as well as providing a framework for finding which genes are interrelated in a certain process. A practical problem, however, is how to assess and discriminate among the various algorithms which have been developed for this purpose. Therefore, the DREAM project invited the year 2008 to a challenge for predicting gene expression values, and here we present the algorithm with best performance.

Methodology/Principal Findings: We develop an algorithm by exploring various regression schemes with different model selection procedures. It turns out that the most effective scheme is based on least squares, with a penalty term of a recently developed form called the “elastic net”. Key components in the algorithm are the integration of expression data from other experimental conditions than those presented for the challenge and the utilization of transcription factor binding data for guiding the inference process towards known interactions. Of importance is also a cross-validation procedure where each form of external data is used only to the extent it increases the expected performance.

Conclusions/Significance: Our algorithm proves both the possibility to extract information from large-scale expression data concerning prediction of gene levels, as well as the benefits of integrating different data sources for improving the inference. We believe the former is an important message to those still hesitating on the possibilities for computational approaches, while the latter is part of an important way forward for the future development of the field of computational systems biology.

Recently, important insights into static network topology for biological systems have been obtained, but still global dynamical network properties determining stability and system responsiveness have not been accessible for analysis. Herein, we explore a genome-wide gene-to-gene regulatory network based on expression data from the cell cycle in Saccharomyces cerevisae (budding yeast). We recover static properties like hubs (genes having several out-going connections), network motifs and modules, which have previously been derived from multiple data sources such as whole-genome expression measurements, literature mining, protein-protein and transcription factor binding data. Further, our analysis uncovers some novel dynamical design principles; hubs are both repressed and repressors, and the intra-modular dynamics are either strongly activating or repressing whereas inter-modular couplings are weak. Finally, taking advantage of the inferred strength and direction of all interactions, we perform a global dynamical systems analysis of the network. Our inferred dynamics of hubs, motifs and modules produce a more stable network than what is expected given randomised versions. The main contribution of the repressed hubs is to increase system stability, while higher order dynamic effects (e.g. module dynamics) mainly increase system flexibility. Altogether, the presence of hubs, motifs and modules induce few flexible modes, to which the network is extra sensitive to an external signal. We believe that our approach, and the inferred biological mode of strong flexibility and stability, will also apply to other cellular networks and adaptive systems.

In this chapter we outline a methodology to reverse engineer GRNs from various data sources within an ODE framework. The methodology is generally applicable and is suitable to handle the broad error distribution present in microarrays. The main effort of this chapter is the exploration of a fully data driven approach to the integration problem in a “soft evidence” based way. Integration is here seen as the process of incorporation of uncertain a priori knowledge and is therefore only relied upon if it lowers the prediction error. An efficient implementation is carried out by a linear programming formulation. This LP problem is solved repeatedly with small modifications, from which we can benefit by restarting the primal simplex method from nearby solutions, which enables a computational efficient execution. We perform a case study for data from the yeast cell cycle, where all verified genes are putative regulators and the a priori knowledge consists of several types of binding data, text-mining and annotation knowledge.

The quest to determine cause from effect is often referred to as reverse engineering in the context of cellular networks. Here we propose and evaluate an algorithm for reverse engineering a gene regulatory network from time-series kind steady-state data. Our algorithmic pipeline, which is rather standard in its parts but not in its integrative composition, combines ordinary differential equations, parameter estimations by least angle regression, and cross-validation procedures for determining the in-degrees and selection of nonlinear transfer functions. The result of the algorithm is a complete directed net-work, in which each edge has been assigned a score front it bootstrap procedure. To evaluate the performance, we submitted the outcome of the algorithm to the reverse engineering assessment competition DREAM2, where we used the data corresponding to the InSillico1 and InSilico2 networks as input. Our algorithm outperformed all other algorithms when inferring one of the directed gene-to-gene networks.

Using deep sequencing (deepCAGE), the FANTOM4 study measured the genome-wide dynamics of transcription-start-site usage in the human monocytic cell line THP-1 throughout a time course of growth arrest and differentiation. Modeling the expression dynamics in terms of predicted cis-regulatory sites, we identified the key transcription regulators, their time-dependent activities and target genes. Systematic siRNA knockdown of 52 transcription factors confirmed the roles of individual factors in the regulatory network. Our results indicate that cellular states are constrained by complex networks involving both positive and negative regulatory interactions among substantial numbers of transcription factors and that no single transcription factor is both necessary and sufficient to drive the differentiation process.

The concept of controllability of linear systems from control theory is applied to networks inspired by biology. A node is in this context controllable if an external signal can be applied which can adjust the level (e.g., protein concentration) of the node in a finite time to an arbitrary value, regardless of the levels of the other nodes. The property of being downstream of the node to which the input is applied turns out to be a necessary but not a sufficient condition for being controllable. An interpretation of the controllability matrix, when applied to networks, is also given. Finally, two case studies are provided in order to better explain the concepts, as well as some results for a gene regulatory network of fission yeast.