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The budding yeast cell cycle :
The budding yeast cell cycle has attracted many experimentalists over the years for its simplicity and facility to manipulate genetically. The regulatory components described in the budding yeast, Saccharomyces cerevisiae, are conserved in higher eukaryotes. The budding yeast is governed by a complex network of chemical reactions controlling the activity of the cyclin-dependent kinases (CDKs), proteins that drive the major events of the cell cycle. The presence of these proteins is required for the transition from G1 to S phase (Start) whereas their absence permits the transition from S/M to G1 phase (Finish). The cell cycle of the budding yeast is based on the alternation between these two states. However, the complexity of this network is such that it requires mathematical tools in order to test the accuracy of the theory based on the experiments. We built and transcribed a hypothetical molecular mechanism of the budding yeast into differential equations and a corresponding parameter set illustrating the main events of the cell cycle such as: the synthesis of cyclins (Cln1,2; Cln3; Clb1,2; Clb5,6) by their transcription factors (SBF, Mcm1, MBF); their association with stoichiometric inhibitors (Sic1, Cdc6); their degradation by SCF and adaptors of the APC (Cdc20, Cdh1). The emphasis was put on mechanisms responsible for the release of Cdc14 from the RENT complex, Cdc14 being the major player in exit from mitosis. The wild type cells and more than 100 mutants showed phenotypes in accordance with the experimental results. From these results, some mutants defective in the Start and Finish transitions and the different ways to rescue them can be simulated as well. An interactive page web describing the model is available at http://mpf.biol.vt.edu/
The model is presented in Molecular Biology of the Cell - [Abstract] [Article]
The drosophila early cell cycles :
Previous studies on modeling of budding yeast (Saccharomyces cerevisiae), fission yeast (Schizosaccharomyces pombe) or mammalian cells have described in details the mechanisms of cell cycle regulation. Drosophila melanogaster cell cycle, although comparable, presents interesting challenges. In Drosophila embryogenesis, different types of cell cycles are observed. One of them, immediately following fertilization, is characterized by thirteen syncytial cycles during which only nuclear divisions occur, rapidly and synchronously. These cycles, driven by maternal genes, are alternating between S and M phases. Although division cycles are observed, almost no oscillation in total level of B-cyclins (CycB) is recorded, suggesting a local degradation of these cyclins. Based on a previous mathematical model of Xenopus cell cycles, a tentative model is built to describe the Drosophila melanogaster division cycles in early developmental stages. This study is in progress.
Modeling in BIOCHAM:
BIOCHAM (the BIOCHemical Abstract Machine) is a programming language for modeling biochemical systems. It is based on two aspects:
(1) the analysis and simulation of boolean, kinetic and stochastic models and (2) the formalization of biological properties in temporal logic (CTL and LTL with constraints).
This language allows to analyze,
verify and query the structure of the model, and find appropriate
values of the parameters to obtain a specific behavior of the system.
For example, it is possible to find one or several parameter values
specific properties (e.g. the system oscillates with a period T or a protein fully activates -
concentration reaches a threshold value), etc
... Coupled with other methods for finding parameter values
(bifurcation diagrams ...), this search assists the modeler/biologist
in the modeling process.
The formalization of biological properties is essential
to learn or verify biochemical reaction rules in an existing model.
1. If the structure of the protein network is known (for example, Kohn, 1999), it is possible to verify that some properties are true or conserved: the molecule X can activate at some point, or a protein X is a checkpoint for the (in)activation of another protein Y, etc ...
2. If the model is incomplete, BIOCHAM can propose ways to complete the model by adding or delete rules such that the model verifies the set of CTL formulae (called specification).
webpage for more details.
Protein dynamics in growth and polarity in fission yeast cells.
In progress ...