Boolean network models of cellular regulation: prospects and limitations

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

Testing a Mathematical Model of the Yeast Cell Cycle

We derived novel, testable predictions from a mathematical model of the budding yeast cell cycle. A key qualitative prediction of bistability was confirmed in a strain simultaneously lacking cdc14 and G1 cyclins. The model correctly predicted quantitative dependence of cell size on gene dosage of the G1 cyclin CLN3, but it incorrectly predicted strong genetic interactions between G1 cyclins and the anaphase- promoting complex specificity factor Cdh1. To provide constraints on model generation, we determined accurate concentrations for the abundance of all nine cyclins as well as the inhibitor Sic1 and the catalytic subunit Cdc28. For many of these we determined abundance throughout the cell cycle by centrifugal elutriation, in the presence or absence of Cdh1. In addition, perturbations to the Clb-kinase oscillator were introduced, and the effects on cyclin and Sic1 levels were compared between model and experiment. Reasonable agreement was obtained in many of these experiments, but significant experimental discrepancies from the model predictions were also observed. Thus, the model is a strong but incomplete attempt at a realistic representation of cell cycle control. Constraints of the sort developed here will be important in development of a truly predictive model