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キーワード:
Quantitative Biology, Molecular Networks, q-bio.MN,Mathematics, Dynamical Systems, math.DS
要旨:
This paper is a mathematical study of some aspects of the signalling pathway
leading to the activation of the transcription factor NFAT (nuclear factor of
activated T cells). Activation takes place by dephosphorylation at multiple
sites. This has been modelled by Salazar and H\"ofer using a large system of
ordinary differential equations depending on many parameters. With the help of
chemical reaction network theory we show that for any choice of the parameters
this system has a unique stationary solution for each value of the conserved
quantity given by the total amount of NFAT and that all solutions converge to
this stationary solution at late times. The dephosphorylation is carried out by
calcineurin, which in turn is activated by a rise in calcium concentration. We
study the way in which the dynamics of the calcium concentration influences
NFAT activation, an issue also considered by Salazar and H\"ofer with the help
of a model arising from work of Somogyi and Stucki. Criteria are obtained for
convergence to equilibrium of solutions of the model for the calcium
concentration.
