Mathematics of the NFAT signalling pathway

TL;DR

This paper provides a mathematical analysis of the NFAT signalling pathway, demonstrating unique stationary solutions and convergence properties using chemical reaction network theory, and exploring calcium dynamics influence on NFAT activation.

Contribution

The study applies chemical reaction network theory to prove convergence and uniqueness of solutions in a detailed NFAT pathway model, enhancing understanding of its mathematical properties.

Findings

Unique stationary solution for NFAT activation system.

All solutions converge to equilibrium over time.

Calcium concentration dynamics influence NFAT activation.

Abstract

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.