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This paper is a mathematical study of some aspects of the signalling pathwayleading to the activation of the transcription factor NFAT (nuclear factor ofactivated T cells). Activation takes place by dephosphorylation at multiplesites. This has been modelled by Salazar and H\"ofer using a large system ofordinary differential equations depending on many parameters. With the help ofchemical reaction network theory we show that for any choice of the parametersthis system has a unique stationary solution for each value of the conservedquantity given by the total amount of NFAT and that all solutions converge tothis stationary solution at late times. The dephosphorylation is carried out bycalcineurin, which in turn is activated by a rise in calcium concentration. Westudy the way in which the dynamics of the calcium concentration influencesNFAT activation, an issue also considered by Salazar and H\"ofer with the helpof a model arising from work of Somogyi and Stucki. Criteria are obtained forconvergence to equilibrium of solutions of the model for the calciumconcentration.

Mathematics of the NFAT signalling pathway