Multiscale binarization of gene expression data for reconstructing Boolean networks.

Network inference algorithms can assist life scientists in unraveling gene-regulatory systems on a molecular level. In recent years, great attention has been drawn to the reconstruction of Boolean networks from time series. These need to be binarized, as such networks model genes as binary variables (either "expressed" or "not expressed"). Common binarization methods often cluster measurements or separate them according to statistical or information theoretic characteristics and may require many data points to determine a robust threshold. Yet, time series measurements frequently comprise only a small number of samples. To overcome this limitation, we propose a binarization that incorporates measurements at multiple resolutions. We introduce two such binarization approaches which determine thresholds based on limited numbers of samples and additionally provide a measure of threshold validity. Thus, network reconstruction and further analysis can be restricted to genes with meaningful thresholds. This reduces the complexity of network inference. The performance of our binarization algorithms was evaluated in network reconstruction experiments using artificial data as well as real-world yeast expression time series. The new approaches yield considerably improved correct network identification rates compared to other binarization techniques by effectively reducing the amount of candidate networks.

Network modeling of signal transduction: establishing the global view.

Embryonic development and adult tissue homeostasis are controlled through activation of intracellular signal transduction pathways by extracellular growth factors. In the past, signal transduction has largely been regarded as a linear process. However, more recent data from large-scale and high-throughput experiments indicate that there is extensive cross-talk between individual signaling cascades leading to the notion of a signaling network. The behavior of such complex networks cannot be predicted by simple intuitive approaches but requires sophisticated models and computational simulations. The purpose of such models is to generate experimentally testable hypotheses and to find explanations for unexpected experimental results. Here, we discuss the need for, and the future impact of, mathematical models for exploring signal transduction in different biological contexts such as for example development.

Extended analyses of the Wnt/beta-catenin pathway: robustness and oscillatory behaviour.

The Wnt/beta-catenin signalling pathway is evolutionarily conserved across many species and plays important roles during embryogenesis. The Lee-Heinrich model (to recognize the contributions of R. Heinrich we will refer to the work proposed by Lee et al. [Lee, E., Salic, A., Krüger, R., Heinrich, R., Kirschner, M.W. (2003) The roles of APC and axin derived from experimental and theoretical analysis of the Wnt pathway. PloS Biol. 1, 116-132] as the Lee-Heinrich model) describes this pathway by use of coupled ordinary differential equations. Here, we extend this model by introducing negative feedback loops of the pathway using time-delay differential equations. Single- and multiple-parameter perturbations suggest a very robust behaviour of this pathway that can also demonstrate oscillatory behaviour. These findings are of biological significance as Wnt pathway components show oscillations during vertebrate somitogenesis.