Browsing by Author "Battogtokh, D."
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- Analysis of a generic model of eukaryotic cell-cycle regulationCsikasz-Nagy, A.; Battogtokh, D.; Chen, Katherine C.; Novak, Bela; Tyson, John J. (CELL PRESS, 2006-06)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.
- Bifurcation analysis of a model of the budding yeast cell cycleBattogtokh, D.; Tyson, John J. (American Institute of Physics, 2004-09-01)We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable steady states of high or low kinase activity). The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity (two stable oscillatory states), we explore possible effects of extrinsic fluctuations on cell cycle progression. (C) 2004 American Institute of Physics.
- A Bistable Switch Mechanism for Stem Cell Domain Nucleation in the Shoot Apical MeristemBattogtokh, D.; Tyson, John J. (Frontiers, 2016-05-23)
- Comparison of Domain Nucleation Mechanisms in a Minimal Model of Shoot Apical MeristemBattogtokh, D.; Tyson, John J. (2016-04-20)Existing mathematical models of the shoot apical meristem (SAM) explain nucleation and confinement of a stem cell domain by Turing's mechanism, assuming that the diffusion coefficients of the activator (WUSCHEL) and inhibitor (CLAVATA) are significantly different. As there is no evidence for this assumption of differential diffusivity, we recently proposed a new mechanism based on a bistable switch model of the SAM. Here we study the bistable-switch mechanism in detail, demonstrating that it can be understood as localized switches of WUSHEL activity in individual cells driven by a non-uniform field of a peptide hormone. By comparing domain formation by Turing and bistable-switch mechanisms on a cell network, we show that the latter does not require the assumptions needed by the former, which are not supported by biological evidences.
- Turbulence near cyclic fold bifurcations in birhythmic mediaBattogtokh, D.; Tyson, John J. (American Physical Society, 2004-08-01)