A Boolean network model of the cell-cycle regulatory network of fission yeast (Schizosaccharomyces Pombe) is constructed solely on the basis of the known biochemical interaction topology. Simulating the model in the computer faithfully reproduces the known activity sequence of regulatory proteins along the cell cycle of the living cell. Contrary to existing differential equation models, no parameters enter the model except the structure of the regulatory circuitry. The dynamical properties of the model indicate that the biological dynamical sequence is robustly implemented in the regulatory network, with the biological stationary state G1 corresponding to the dominant attractor in state space, and with the biological regulatory sequence being a strongly attractive trajectory. Comparing the fission yeast cell-cycle model to a similar model of the corresponding network in S. cerevisiae, a remarkable difference in circuitry, as well as dynamics is observed. While the latter operates in a strongly damped mode, driven by external excitation, the S. pombe network represents an auto-excited system with external damping.

Computer models are valuable tools towards an understanding of the cell's biochemical regulatory machinery. Possible levels of description of such models range from modelling the underlying biochemical details to top-down approaches, using tools from the theory of complex networks. The latter, coarse-grained approach is taken where regulatory circuits are classified in graph-theoretical terms, with the elements of the regulatory networks being reduced to simply nodes and links, in order to obtain architectural information about the network. Further, considering dynamics on networks at such an abstract level seems rather unlikely to match dynamical regulatory activity of biological cells. Therefore, it came as a surprise when recently examples of discrete dynamical network models based on very simplistic dynamical elements emerged which in fact do match sequences of regulatory patterns of their biological counterparts. Here I will review such discrete dynamical network models, or Boolean networks, of biological regulatory networks. Further, we will take a look at such models extended with stochastic noise, which allow studying the role of network topology in providing robustness against noise. In the end, we will discuss the interesting question of why at all such simple models can describe aspects of biology despite their simplicity. Finally, prospects of Boolean models in exploratory dynamical models for biological circuits and their mutants will be discussed.

Will we ever be able to build predictive models of the complex genetic networks that determine function as well as malfunction of living cells? Studies of small cellular circuits that represent building blocks indicate that there might be a higher level of description that would reduce the vast complexity of genetic network models. In his Perspective, [Bornholdt][1] discusses the results reported in the same issue by [ Brandman et al .][2] who characterize a frequent building block of cellular circuits. Such elements exhibit particularly simple dynamics and the hope is that models of large genetic networks become feasible when based on the dynamics of such simple building blocks. [1]: http://www.sciencemag.org/cgi/content/full/310/5747/449 [2]: http://www.sciencemag.org/cgi/content/short/310/5747/496

Survival of living cells and organisms is largely based on highly reliable function of their regulatory networks. However, the elements of biological networks, e.g., regulatory genes in genetic networks or neurons in the nervous system, are far from being reliable dynamical elements. How can networks of unreliable elements perform reliably? We here address this question in networks of autonomous noisy elements with fluctuating timing and study the conditions for an overall system behavior being reproducible in the presence of such noise. We find a clear distinction between reliable and unreliable dynamical attractors. In the reliable case, synchrony is sustained in the network, whereas in the unreliable scenario, fluctuating timing of single elements can gradually desynchronize the system, leading to nonreproducible behavior. The likelihood of reliable dynamical attractors strongly depends on the underlying topology of a network. Comparing with the observed architectures of gene regulation networks, we find that those 3-node subgraphs that allow for reliable dynamics are also those that are more abundant in nature, suggesting that specific topologies of regulatory networks may provide a selective advantage in evolution through their resistance against noise.

We model the robustness against random failure or an intentional attack of networks with an arbitrary large-scale structure. We construct a block-based model which incorporates\char22{}in a general fashion\char22{}both connectivity and interdependence links, as well as arbitrary degree distributions and block correlations. By optimizing the percolation properties of this general class of networks, we identify a simple core-periphery structure as the topology most robust against random failure. In such networks, a distinct and small ``core'' of nodes with higher degree is responsible for most of the connectivity, functioning as a central ``backbone'' of the system. This centralized topology remains the optimal structure when other constraints are imposed, such as a given fraction of interdependence links and fixed degree distributions. This distinguishes simple centralized topologies as the most likely to emerge, when robustness against failure is the dominant evolutionary force.

Despite being highly interdependent, the major biochemical networks of the living cell—the networks of interacting genes and of metabolic reactions, respectively—have been approached mostly as separate systems so far. Recently, a framework for interdependent networks has emerged in the context of statistical physics. In a first quantitative application of this framework to systems biology, here we study the interdependent network of gene regulation and metabolism for the model organism Escherichia coli in terms of a biologically motivated percolation model. Particularly, we approach the system’s conflicting tasks of reacting rapidly to (internal and external) perturbations, while being robust to minor environmental fluctuations. Considering its response to perturbations that are localized with respect to functional criteria, we find the interdependent system to be sensitive to gene regulatory and protein-level perturbations, yet robust against metabolic changes. We expect this approach to be applicable to a range of other interdependent networks.