A mathematical model of NFATc1 autoregulation
To analyze how the expression of the NFATc1/a and NFATc1/b proteins is regulated in T cells through the multiple signals affecting P1 activity, we have developed a mathematical model. The inducible promoter P1 responds to two types of input: (i) calcium/calcineurin-mediated stimuli that switch on positive feedback of NFATc1, and (ii) activators that are stimulated by feedforward pathways (such as NF-kB and cAMP-regulated factors). Following the experimental data, we modeled synergistic activation of P1 through these inputs and constitutive transcription from P2. The induction of transcription from P1 requires both calcineurin activity and further activators (FigureS1a). Our theoretical analysis shows that the resulting NFATc1/a induction exhibits a switch-like dependence on calcineurin activity that is due to autoactivation. By contrast, feedforward activators A exert a graded effect on NFATc1/a levels (FigureS1b). This complex regulation of P1 activity is illustrated in FigureS1c: supra-threshold calcineurin activity allows P1 to become active, whereas A determines the actual level of expression. In agreement with the experimental data (see Figure1 in the main text), the induction of transcription from P1 suppresses basal expression of NFATc1/b from P2 (FigureS1d).
The model focuses on the expression of the NFATc1/a and NFATc1/b isoforms from the P1 and P2 promoters, respectively, whereas the regulation by polyadenylation has not been considered. The balance equations for the concentrations of NFATc1/a () and NFATc1/b () have the form:
, ,
where and denote the rates of expression from P1 and P2, respectively. The experimental data indicate that . The parameters are the degradation rate constants of the two NFATc1 isoforms (). The probability that, at any given time, P1 is induced is ; consequently, expression from P2 is reduced by the factor . The synergistic induction of P1 by an activator A (such as NF-kB or proteins binding to the CRE-elements) and by NFATc1 autoregulation is modeled by
,
where gives the fraction of active nuclear NFATc1 as a function of the calcineurin activity Cn [1]. The various K values denote half-saturation constants. Other NFAT members, such as NFATc2, have been neglected here for clarity but can be added to the model. The presence of NFATc2 will make P1 induction more sensitive to calcineurin activity.
We computed the steady-state level of the inducible isoform NFATc1/a as a function of both calcineurin activity (Cn) and feedforward activator (A) for a specific choice of kinetic parameters (FigureS1b,c). A sharp threshold response with respect to calcineurin activity arises from the positive feedback loop. Once calcineurin activity has crossed the threshold, the activator concentration will determine the NFATc1/a concentration. These properties are typical for the model, holding true in a wide range of parameter values.
FigureS1
A mathematical model of NFATc1 autoregulation in T cells. (a) Regulation of the P1 promoter. (b) Response in NFATc1/a expression to calcineurin activity, Cn, and feedforward activator, A. (c) Different cuts through the surface depicted in (b) at constant activator concentrations. (d) The constitutive isoform NFATc1/b decreases as P1 is induced. Parameters: , , , , , (the parameters were made dimensionless with respect to the concentration scale set by the half-saturation constants KA and K1/2).
References
1 Neal, J.W. and Clipstone, N.A. (2001) Glycogen synthase kinase-3 inhibits the DNA binding activity of NFATc. J. Biol. Chem. 276, 3666–3673