BACKGROUND: Network motifs within biological networks show non-random abundances in systems at different scales. Large directed protein networks at the cellular level are now well defined in several diverse species. We aimed to compare the nature of significantly observed two- and three-node network motifs across three different kingdoms (Arabidopsis thaliana for multicellular plants, Saccharomyces cerevisiae for unicellular fungi and Homo sapiens for animals). RESULTS: 'Two-node feedback' is the most significant motif in all three species. By considering the sign of each two-node feedback interaction, we examined the enrichment of the three types of two-node feedbacks [positive-positive (PP), negative-negative (NN) and positive-negative (PN)]. We found that PN is enriched in the network of A.thaliana, NN in the network of S.cerevisiae and PP and NN in the network of H.sapiens. Each feedback type has characteristic features of robustness, multistability and homeostasis. CONCLUSIONS: We suggest that amplification of particular network motifs emerges from contrasting dynamical and topological properties of the motifs, reflects the evolutionary design principles selected by the characteristic behavior of each species and provides a signature pointing to their behavior and function.

MOTIVATION: Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. RESULTS: A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. AVAILABILITY: The software used in this article is available from http://sbie.kaist.ac.kr/software

MOTIVATION: Gene regulatory networks (GRNs) govern cellular differentiation processes and enable construction of multicellular organisms from single cells. Although such networks are complex, there must be evolutionary design principles that shape the network to its present form, gaining complexity from simple modules. RESULTS: To isolate particular design principles, we have computationally evolved random regulatory networks with a preference to result either in hysteresis (switching threshold depending on current state), or in multistationarity (having multiple steady states), two commonly observed dynamical features of GRNs related to differentiation processes. We have analyzed the resulting evolved networks and compared their structures and characteristics with real GRNs reported from experiments. CONCLUSION: We found that the artificially evolved networks have particular topologies and it was notable that these topologies share important features and similarities with the real GRNs, particularly in contrasting properties of positive and negative feedback loops. We conclude that the structures of real GRNs are consistent with selection to favor one or other of the dynamical features of multistationarity or hysteresis. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. RESULTS: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-kappaB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. CONCLUSION: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks.

Stable and robust oscillations in the concentration of adenosine 3', 5'-cyclic monophosphate (cAMP) are observed during the aggregation phase of starvation-induced development in Dictyostelium discoideum. In this paper we use mathematical modelling together with ideas from robust control theory to identify two factors which appear to make crucial contributions to ensuring the robustness of these oscillations. Firstly, we show that stochastic fluctuations in the molecular interactions play an important role in preserving stable oscillations in the face of variations in the kinetics of the intracellular network. Secondly, we show that synchronisation of the aggregating cells through the diffusion of extracellular cAMP is a key factor in ensuring robustness of the oscillatory waves of cAMP observed in Dictyostelium cell cultures to cell-to-cell variations. A striking and quite general implication of the results is that the robustness analysis of models of oscillating biomolecular networks (circadian clocks, Ca(2+) oscillations, etc.) can only be done reliably by using stochastic simulations, even in the case where molecular concentrations are very high.