We propose a protein interaction network for the regulation of DNA synthesis and mitosis that emphasizes the universality of the regulatory system among eukaryotic cells. The idiosyncrasies of cell cycle regulation in particular organisms can be attributed, we claim, to specific settings of rate constants in the dynamic network of chemical reactions. The values of these rate constants are determined ultimately by the genetic makeup of an organism. To support these claims, we convert the reaction mechanism into a set of governing kinetic equations and provide parameter values (specific to budding yeast, fission yeast, frog eggs, and mammalian cells) that account for many curious features of cell cycle regulation in these organisms. Using one-parameter bifurcation diagrams, we show how overall cell growth drives progression through the cell cycle, how cell-size homeostasis can be achieved by two different strategies, and how mutations remodel bifurcation diagrams and create unusual cell-division phenotypes. The relation between gene dosage and phenotype can be summarized compactly in two-parameter bifurcation diagrams. Our approach provides a theoretical framework in which to understand both the universality and particularity of cell cycle regulation, and to construct, in modular fashion, increasingly complex models of the networks controlling cell growth and division.

A chemical reaction network for the regulation of the quinic acid (qa) gene cluster of Neurospora crassa is proposed. An efficient Monte Carlo method for walking through the parameter space of possible chemical reaction networks is developed to identify an ensemble of deterministic kinetics models with rate constants consistent with RNA and protein profiling data. This method was successful in identifying a model ensemble fitting available RNA profiling data on the qa gene cluster. With genome sequencing projects supplying an almost complete inventory of the building blocks of life, functional genomics is now facing the challenge of ''re-assembling the pieces'' (1, 2). Time-dependent mRNA (3) and protein profiling (4), protein-protein (5-8) and protein-DNA (9) interaction mapping, and the in vitro reconstruction of reaction networks (10, 11) are providing insight into the topology and kinetics of a living cell's full biochemical and gene regulatory circuitry. For the first time, it is now possible to place a particular biological circuit like those describing carbon metabolism, transcription, cell cycle, or the biological clock in simple eukaryotes in a larger context, and to examine the coupling of these circuits (12).New tools in computational biology are needed to identify these reaction networks by using well studied subcircuits like those for carbon metabolism, cell cycle, or the biological clock as a launch point into the entire circuit of a living cell. The qa gene cluster of Neurospora crassa and the GAL gene cluster of Saccharomyces cerevisiae in carbon metabolism have served as early paradigms for eukaryotic gene regulation (13,14) and are prime candidates for taking a genomic perspective on biological circuits. Mechanisms of regulation in the qa and GAL clusters with their transcriptional activator and repressors are also shared with many other regulatory networks. Because of their relative simplicity, they also provide an opportunity to test new genomic approaches to identifying chemical reaction networks or biological circuits that underlie many fundamental biological processes (15). Three opportunities exist now for identifying and refining biological circuits: the accumulation of transcriptional profiling data (3), a growing number of approaches to modeling gene regulation (11,(15)(16)(17)(18)(19)(20)(21), and the ability to carry out the in vitro reconstruction of biological circuits with a diversity of emergent properties including bistable (10) and oscillatory activity (11).However, initially, the profiling data will be scarce and the unknown parameters plentiful. Identification of the parameters in a reaction network is further complicated by the facts that the data are noisy and that our knowledge of the underlying reaction network's topology and of its participating molecular species is incomplete, even in well studied networks like those for the -switch, lac operon, trp operon, or GAL cluster. To circumvent these difficulties, we present a statistical modeling approach called the ensemble m...

A three-component reaction-diffusion model is proposed as the first example to exhibit chemical turbulence with multiaffine fractal structures, the underlying mechanism being the same as for similar turbulence discovered recently in some nonlocally coupled oscillator systems. The role played by the strongly diffusive component can be substituted by a long-wave random force, and this idea leads to our proposal of the second, far simpler reaction-diffusion model given by the randomly driven FitzHugh-Nagumo nerve conduction equation. [S0031-9007(98)07376-1] PACS numbers: 82.20.Fd, 05.45. + b, 47.53. + n

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