No abstract

The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides a rigorous and reliable tool for unraveling the complexities of molecular regulatory networks. The budding yeast cell cycle is a challenging test case for this approach, because the control system is known in exquisite detail and its function is constrained by the phenotypic properties of >100 genetically engineered strains. We show that a mathematical model built on a consensus picture of this control system is largely successful in explaining the phenotypes of mutants described so far. A few inconsistencies between the model and experiments indicate aspects of the mechanism that require revision. In addition, the model allows one to frame and critique hypotheses about how the division cycle is regulated in wild-type and mutant cells, to predict the phenotypes of new mutant combinations, and to estimate the effective values of biochemical rate constants that are difficult to measure directly in vivo.

The molecular machinery of cell cycle control is known in more detail for budding yeast, Saccharomyces cerevisiae, than for any other eukaryotic organism. In recent years, many elegant experiments on budding yeast have dissected the roles of cyclin molecules (Cln1-3 and Clb1-6) in coordinating the events of DNA synthesis, bud emergence, spindle formation, nuclear division, and cell separation. These experimental clues suggest a mechanism for the principal molecular interactions controlling cyclin synthesis and degradation. Using standard techniques of biochemical kinetics, we convert the mechanism into a set of differential equations, which describe the time courses of three major classes of cyclin-dependent kinase activities. Model in hand, we examine the molecular events controlling "Start" (the commitment step to a new round of chromosome replication, bud formation, and mitosis) and "Finish" (the transition from metaphase to anaphase, when sister chromatids are pulled apart and the bud separates from the mother cell) in wild-type cells and 50 mutants. The model accounts for many details of the physiology, biochemistry, and genetics of cell cycle control in budding yeast.

Cells progressing through the cell cycle must commit irreversibly to mitosis without slipping back to interphase before properly segregating their chromosomes. A mathematical model of cell-cycle progression in cell-free egg extracts from frog predicts that irreversible transitions into and out of mitosis are driven by hysteresis in the molecular control system. Hysteresis refers to toggle-like switching behavior in a dynamical system. In the mathematical model, the toggle switch is created by positive feedback in the phosphorylation reactions controlling the activity of Cdc2, a protein kinase bound to its regulatory subunit, cyclin B. To determine whether hysteresis underlies entry into and exit from mitosis in cell-free egg extracts, we tested three predictions of the NovakTyson model. (i) The minimal concentration of cyclin B necessary to drive an interphase extract into mitosis is distinctly higher than the minimal concentration necessary to hold a mitotic extract in mitosis, evidence for hysteresis. (ii) Unreplicated DNA elevates the cyclin threshold for Cdc2 activation, indication that checkpoints operate by enlarging the hysteresis loop. (iii) A dramatic ''slowing down'' in the rate of Cdc2 activation is detected at concentrations of cyclin B marginally above the activation threshold. All three predictions were validated. These observations confirm hysteresis as the driving force for cell-cycle transitions into and out of mitosis.

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.

Intraperitoneal injection of epidermal growth factor (EGF) into mice resulted in the appearance in liver nuclei of three tyrosine phosphorylated proteins (84, 91, and 92 kilodaltons) within minutes after administration of EGF. Administration of interferon-gamma (IFN-gamma) resulted in the appearance in liver nuclei of two tyrosine phosphorylated proteins (84 and 91 kilodaltons). The 84- and 91-kilodalton proteins detected after either EGF or IFN-gamma administration were identified as the IFN-gamma activation factors (GAF). Furthermore, gel shift analysis revealed that these GAF proteins, detected after either EGF or IFN-gamma administration, specifically bound to the sis-inducible element of the c-fos promoter. Thus, GAF proteins participate in nuclear signaling in both IFN-gamma and EGF pathways.

Intraperitoneal injection of epidermal growth factor into mice results in the appearance of multiple tyrosine-phosphorylated proteins in liver nuclei within minutes after administration. We have previously identified three of these proteins as Stat la, Stat 113 (p91, p84), and Stat 3 (p89). In the present report we demonstrate that Stat 5 (p92), the recently described prolactin inducible transcription factor detected in mammary glands, is the major tyrosinephosphorylated protein translocated to the nucleus in mouse liver in response to epidermal growth factor. Furthermore, gel-shift analysis and affinity purification revealed that Stat 5, Stat la, and Stat 1p specifically bind to the prolactin inducible element upstream of the p-casein promoter.Epidermal growth factor (EGF) elicits a variety of biological responses when administered either to intact animals or added to cells growing in culture (1-3). These responses are mediated at the cell surface by the EGF receptor. Upon ligand binding, the intrinsic tyrosine kinase activity of the EGF receptor is augmented, resulting in its autophosphorylation, as well as the phosphorylation, of specific intracellular protein substrates (4-6). Some of these tyrosine-phosphorylated proteins are responsible for initiating signal transduction from the cell membrane to the nucleus and have been termed Stat (signal transducers and activators of transcription) proteins (7).The Stat proteins are members of a growing family of transcription factors that reside in the cytosol, are activated by tyrosine phosphorylation, and are translocated to the nucleus in response to various growth factors and cytokines. Stat la/1f3 (p91, p84) was shown to be tyrosine-phosphorylated and form specific binding complexes with the sis-conditioned medium inducible element (SIE) upstream of the c-fos promoter in response to both interferon y and EGF (8,9). Similarly, Stat 3 (p89) was shown to be tyrosine-phosphorylated and bind the SIE in response to both EGF and interleukin 6 or lipopolysaccharide (10,11). Recently, several reports have appeared that describe the induction in sheep mammary glands of DNA-binding activity specific for a prolactin (PRL)-inducible element (PIE). This PRL-induced DNA-binding activity was attributed to a 92-kDa protein that has been termed Stat 5 (or mammary gland factor) due to sequence homologies with conserved regions of known Stat proteins (12, 13).We previously reported that injection of EGF into mice leads to a rapid increase in the level of tyrosine phosphorylation of many proteins in all organs examined (14). Using this in situ system we were able to detect at least four tyrosinephosphorylated proteins (p92, p91, p89, and p84) in nuclear extracts from the livers of mice treated with EGF. Three of these proteins, p91, p89, and p84, were identified as Stat la, Stat 3, and Stat 1/3, respectively (8, 11). However, the identity of the major tyrosine-phosphorylated protein detected in the nucleus in response to EGF, p92, was unknown. In this report, we identify p92 ...

In the cell division cycle of budding yeast, START refers to a set of tightly linked events that prepare a cell for budding and DNA replication, and FINISH denotes the interrelated events by which the cell exits from mitosis and divides into mother and daughter cells. On the basis of recent progress made by molecular biologists in characterizing the genes and proteins that control START and FINISH, we crafted a new mathematical model of cell cycle progression in yeast. Our model exploits a natural separation of time scales in the cell cycle control network to construct a system of differential-algebraic equations for protein synthesis and degradation, post-translational modifications, and rapid formation and dissociation of multimeric complexes. The model provides a unified account of the observed phenotypes of 257 mutant yeast strains (98% of the 263 strains in the data set used to constrain the model). We then use the model to predict the phenotypes of 30 novel combinations of mutant alleles. Our comprehensive model of the molecular events controlling cell cycle progression in budding yeast has both explanatory and predictive power. Future experimental tests of the model’s predictions will be useful to refine the underlying molecular mechanism, to constrain the adjustable parameters of the model, and to provide new insights into how the cell division cycle is regulated in budding yeast.