Allosteric Regulation of the Transcription FactorNFAT1 by Multiple Phosphorylation Sites:A Mathematical Analysis

Carlos Salazar and Thomas Hofer*

Theoretische BiophysikInstitut fur BiologieHumboldt-Universitat BerlinInvalidenstrasse 42D-10115 Berlin, Germany

NFAT transcription factors are activated through dephosphorylation bythe phosphatase calcineurin. Experimental data show that 13 conservedphosphorylation sites conspire to control the transition between an in-active and an active conformation. We propose a quantitative model ofthe underlying molecular mechanisms that may generally apply to highlyphosphorylated proteins. Mathematical analysis shows that multiplephosphorylation sites result in a threshold for protein activation. Itssharpness increases with the number of sites, thus providing a rationalefor the involvement of the large number of serine residues in NFAT acti-vation. The model predicts that nuclear kinases exert a larger control onthe activation threshold than cytoplasmic kinases, and that the NFAT acti-vation kinetics can discriminate between input signals of differentamplitude.

q 2003 Elsevier Science Ltd. All rights reserved

Keywords: signal transduction; calcineurin; kinases; conformational switch;nuclear transport*Corresponding author

Introduction

Phosphorylation and dephosphorylation areubiquitous modes of the regulation of protein func-tion. Phosphate groups can alter the local environ-ment of a functional structure such as a catalyticcenter or a binding site and thereby determinethe enzymatic activity or affinity of a protein.1

Phosphorylation sites distant from such func-tional motifs may regulate the activity of a proteinby inducing changes in its global conformation.2,3

A recent study of the highly phosphorylated tran-scription factor NFAT1 has led to the proposal ofa specific model for such conformational controlby phosphorylation.4 NFAT transcription factorsregulate cytokine expression in T lymphocytesand gene expression in a variety of developmentalprocesses.5 – 8 The main NFAT members, NFAT1-4,

reside in the cytoplasm in phosphorylated formand are imported into the nucleus after dephos-phorylation by the calcium-calmodulin-dependentphosphatase calcineurin. In T lymphocytes, NFATsare thought to be critical decoders of antigensignals.9 – 11

In a detailed study of NFAT1 phosphorylationstates, Okamura et al. found that the inactiveprotein is phosphorylated on a large number ofserine residues in its regulatory domain.4 Thirteenof these residues are located in sequence motifsconserved in the NFAT family, and their dephos-phorylation is required for nuclear import andtranscriptional activity. Dephosphorylation favorsthe exposure of a nuclear localization signal (NLS)and probably also the masking of a nuclear exportsignal (NES). The binding of the NLS to thetransport machinery of the nuclear pore complexmediates nuclear import, while the masking ofthe NES prevents nuclear export.12 Strikingly, theregulatory serine residues have been mapped toregions outside the actual NLS.4 Moreover, it wasfound that the NLS is accessible to proteasecleavage in the dephosphorylated but not in thephosphorylated form of the protein.

On the basis of these data, Okamura et al.suggested a molecular mechanism that links thephosphorylation state of NFAT1 with its activity

0022-2836/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved

E-mail address of the corresponding author:thomas.hoefer@rz.hu-berlin.de

Abbreviations used: CK-I, casein kinase I; CRACchannel, calcium released-activated calcium channel;GSK-3, glycogen synthase kinase-3; MAP kinase,mitogen-activated protein kinase; NFAT, nuclear factorof activated T-cells; NES, nuclear export signal; NLS,nuclear localization signal; SP region, serine and proline-rich region; SRR region, serine-rich region; TCR, T-cellreceptor.

doi:10.1016/S0022-2836(03)00085-8 J. Mol. Biol. (2003) 327, 31–45

through a conformational switch.4 Specifically, theyproposed that: (i) NFAT1 can exist in two globalconformations, an active conformation in whichthe NLS exposed, the NES is masked, and NFAT1is imported into the nucleus, and an inactive con-formation in which the NLS masked, the NES isexposed, and NFAT1 is exported from the nucleus.(ii) The switching between the two conformationsis regulated by the phosphorylation state in such away that the probability of the active conformationis high in the dephosphorylated state and low inthe phosphorylated state.

The switching between active and inactiveconformations is a basic property of the classicmodels of allosteric control described by Monodet al.13 and by Koshland et al.14 Mathematical analy-sis of these models13 – 15 has been instrumental inunderstanding how oligomeric proteins regulatedby reversible ligand binding can exhibit cooper-ative behavior.16,17 However, these theories cannotbe applied to study the regulation of NFAT1,which is based on covalent modifications of asingle regulatory domain. In particular, it is notclear whether a comparable cooperativity mayresult from the presence of multiple phosphoryl-ation sites.

In the present work, we will formulate theconformational switch model described by Okamuraet al.4 in mathematical terms on the basis of plaus-ible physical assumptions. These assumptions arephrased in general form such that the analysiswill also apply to other proteins exhibiting allo-steric regulation by covalent modification. Themodel will allow us to establish how the functionof such a protein is controlled by the activitiesof the kinases and phosphatases acting on it.By including conformation-dependent nuclearimport and export, we will address the regulationof NFAT1 nuclear localization and transcriptionalactivity.

The main findings of the theoretical analysis canbe summarized as follows. The conformationalcontrol mechanism based on phosphorylationstate of multiple residues gives rise to a thresholdfor protein activation. The sharpness of thethreshold increases with the number of phos-phorylation sites involved, such that NFATproteins (with 13 conserved serine residues) canexhibit a binary off–on response to calcineurinactivity. Inclusion of transport through the nuclearpore complex in the model shows that completenuclear localization of NFATs requires phosphataseactivity of calcineurin both in the cytoplasm and inthe nucleus. Accordingly, cytoplasmic and nuclearkinases may counteract NFAT activation, and themodel shows that their activities set the thresholdcalcineurin activity for NFAT activation. However,changing the kinase activities in the two compart-ments may have different effects, depending onthe ratio of their basal activities. When the basalactivity of the kinases is higher in the nucleusthan in the cytoplasm, the nuclear kinases aloneset the threshold for NFAT1 activation by calci-

neurin. Otherwise, both cytoplasmic and nuclearkinases exert control. The model correctly repro-duces the kinetics of NFAT1 activation and deacti-vation observed under different experimentalconditions. The simulations of the kinetics showthat there is a kinetic threshold effect; partial calci-neurin stimulation is predicted to result in con-siderably slower NFAT activation than maximalcalcineurin stimulation. Taken together, our resultsshow that NFATs may serve as critical switchesin the T-cell antigen receptor (TCR) pathway thatcan be regulated at multiple levels.

Model

Phosphorylation states andconformational equilibria

The conformational switch model proposed byOkamura et al.4 can be restated as follows:

(1) NFAT1 can assume two different struc-tures, an active (A) conformation and an in-active (J) conformation.

(2) The phosphorylation state of certain resi-dues (the 13 identified serine residues in theregulatory domain) affects the global confor-mation of the protein. Therefore the probabilitiesof assuming the A and J conformations dependon the phosphorylation state.

(3) The A conformation is favored in thedephosphorylated state, while the J confor-mation is favored in the phosphorylated state.

(4) The A conformation is imported into thenucleus; the J conformation is exported fromthe nucleus.

Clearly, the first three assumptions may moregenerally apply to proteins exhibiting confor-mational control by covalent modification, where Aand J in assumption (3) could be interchanged.3,18

(In particular, it should be applicable to NFAT2-4,as suggested by the conservation of the 13 regu-latory serine motifs in the NFAT family.) We willtherefore give a general formulation of the modelthat can be adapted to other proteins as well.However, to be concrete we will relate our findingsprimarily to the experimental results for NFAT1.

Let us assume that the protein in questioncontains N regulatory phosphorylation sites,which we number consecutively by n ¼ 1;…;N:A particular phosphorylation state can be symbol-ized by a string of 0s and Ps, denoting unphos-phorylated and phosphorylated sites, respectively;e.g. [0 P 0 P P …]. The number of different phos-phorylation states is 2N; for NFAT1, we have N ¼13 serine residues and thus 8192 states (cf. alsoJeffery et al.19 for a random multiple phosphoryl-ation model). Although it is feasible to construct amodel accounting for all these states, a more man-ageable description is suggested by two obser-vations. First, calcineurin cleaves the phosphate

32 Conformational Switch Model for NFAT

groups in the NFAT1 regulatory domain in asequential order, proceeding from the serine-richregion 1 (SRR-1) to the more C-terminal SP motifs2 and 3.4 Second, the main kinases so far identifiedto phosphorylate NFAT proteins, glycogensynthase kinase-3 (GSK-3) and casein kinase I(CK-I) sequentially process SP motifs and theSRR-1, respectively (H. Okamura, unpublishedresults).20,21 Moreover, sequential phosphorylationhas also been reported for other proteins,22,23 andsequential rephosphorylation of NFAT2 from theSP to the SRR-1 motifs has been suggested.20 Thuswe make the simplifying assumption that dephos-phorylation and phosphorylation are sequentialand proceed in the reverse order. The changesof phosphorylation state can be written as, e.g.for the fifth residue:

½0 0 0 0 P P P P P P P P P� Ocalcineurin

kinases½0 0 0 0 0 P P P P P P P P�

In this sequential model the phosphorylation statescan be labeled by the number of phosphorylatedresidues; An and Jn will be used to symbolize theactive and inactive conformations, respectively,with n phosphorylated residues.

The A and J conformations correspond to localminima of the Gibbs free energy of the protein.According to assumption (2), the difference of

their energy values under standard conditions:

DGn ¼ GðJnÞ2 GðAnÞ ð1Þ

depends on the phosphorylation state of the pro-tein. The equilibrium constant of the conforma-tional transition:

An Olþn

l2nJn

with the forward and backward rate constantslþn and l2n ; respectively, is given by the thermo-dynamic relation:

Ln ¼ lþn =l2n ¼ e2DGn=RT ð2Þ

where DGn denotes the standard free energy dif-ference between the active and inactive confor-mations as defined by equation (1).

For NFAT1, assumption (3) implies that in thefully dephosphorylated state DG0 . 0 and in thefully phosphorylated state DGN , 0: For inter-mediate phosphorylation states, it is natural toassume that DGn decreases with the number ofphosphorylated residues: DG0 . DG1 . · · · . DGN:Thus we can depict the possible states in aschematic energy diagram (Figure 1(a)). In thisdiagram we have indicated schematically that thevarious energy differences, DGn; may result from a

Figure 1. Conformational switch model for the activation of NFAT1. (a) Schematic energy diagram of the NFAT1conformations and phosphorylation states. The active A conformation is favored in the dephosphorylated state,as indicated by a lower conformational energy than the inactive J conformation. However, the J conformation isstabilized by phosphorylation and eventually has a lower energy than A conformation in the fully phosphorylatedstate. For simplicity, only five of the 13 phosphorylation sites are indicated. (b) Model scheme. Cytoplasmic NFAT1in the A and J conformations with n phosphorylated residues are denoted by an and in, respectively, n ¼ 1; 2;…;N).The corresponding nuclear symbols are An and In. Cytoplasmic NFAT1 in the A conformation is imported into thenucleus with rate constant d. Conversely, nuclear molecules in the J conformation are exported with rate constant f.Conformational transitions, phosphorylation, and dephosphorylation can take place both in the cytoplasm and in thenucleus. For further explanation, see the text.

Conformational Switch Model for NFAT 33

direct interaction of the NLS with the phosphategroups (e.g. by electrostatic attraction between thephosphate groups and the basic amino acids ofthe NLS). However, the interaction could also beindirect and be propagated through the confor-mation of the protein.

Phosphorylation and dephosphorylation

Both A and J conformations can be dephos-phorylated and phosphorylated. For the A con-formation, we assume the first-order kineticsAnþ1 !

cnAn and An !

knAnþ1 for dephosphorylation

and phosphorylation, respectively. cn is theactivity of calcineurin with respect to cleavingthe phosphate group n þ 1: kn is the kinaseactivity with respect to adding the same phosphategroup (note that kn is proportional to the ATPconcentration which will be assumed constant).This formulation implies that there is a certainprobability of calcineurin and kinase moleculesdissociating and rebinding while processing thephosphate groups. Such a distributive mode ofphosphorylation has been found, for example,for dual phosphorylation in the MAP kinasepathway.24,25

For NFATs, there appear to be different kinaseswhich may act on different serine residues.This effect can be accounted for in the modelbecause a specific kinase activity can be assignedto each residue. Similarly, we can define calci-neurin and kinase activities for the covalentmodifications of the Jn states, c0n and k0n;respectively.

In the following analysis, cytoplasmic andnuclear enzyme activities will be distinguishedby writing lower-case symbols (kn and cn) for thecytoplasm and upper-case symbols (Kn and Cn) forthe nucleus.

Nuclear import and export

We assume that cytoplasmic NFAT1 in the Aconformation is imported into the nucleus withthe rate constant d and nuclear NFAT1 in the Jconformation is exported with the rate constant f;d and f are determined by the transport machineryof the nuclear pore complex.

The processes regulating the nuclear localiz-ation of NFAT1 are summarized in Figure 1(b).Based on this scheme, kinetic equations for thevarious fractions of the protein can be derived.We denote the nuclear fractions of the mol-ecules in the An and Jn states by An and In;respectively. The corresponding cytoplasmicfractions are denoted by an and in (see Figure1(b)). Assuming that all species occur at suffi-ciently high concentrations to justify a deter-ministic description, and employing linearmass-action kinetics, we obtain the kineticequations for the fractions of active and inactive

states in the nucleus as:

dAn

dt¼ Kn21An21 2 KnAn|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

phosphorylation

þ CnAnþ1 2 Cn21An|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}dephosphorylation

þ l2n In 2 lþn An|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}conform: switch

þ dan|{z}import

ð3Þ

dIn

dt¼ K0

n21In21 2 K0nIn|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}

phosphorylation

þ C0nInþ1 2 C0

n21In|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}dephosphorylation

þ lþn An 2 l2n In|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}conform: switch

þ fIn|{z}export

ð4Þ

where 1 , n , N: Analogous kinetic equationscan be given for A0; I0; AN; IN; and for the cyto-plasmic fractions an and in:

Basic implications of the model equations fromwhich the steady-state equations given in Resultscan be derived are as follows. On the time-scaleof interest, we assume that the total number ofNFAT1 molecules remains constant, such that weobtain, by summing over all fractions:

XN

n¼0

An þ In þ an þ in ¼ 1 ð5Þ

When the conformational transitions are in equi-librium, we have:

In

An¼

inan

¼ Ln ð6Þ

When the phosphorylation and dephosphorylationrates are equal, one obtains for the fractions of theactive conformations:

anþ1

an¼

kn

cn;

Anþ1

An¼

Kn

Cnð7Þ

For the inactive conformations, one finds fromequations (6) and (7):

inþ1

in¼

k0nc0n

¼Lnþ1

Ln

kn

cn;

Inþ1

In¼

K0n

C0n

¼Lnþ1

Ln

Kn

Cn

ð8Þ

Clearly, phosphorylation favors the inactive con-formation, such that Lnþ1=Ln . 1: This implies that:

k0

c0.

k

cð9Þ

that is, the J conformation is more readily phos-phorylated than the A conformation or the Aconformation is more readily dephosphorylatedthan the J conformation, or both.

Simplifying assumptions

To gain insight into the behavior of the model, itis useful to make simplifying assumptions. In the

34 Conformational Switch Model for NFAT

following, we will assume that each phosphategroup contributes a constant free energy incre-ment dGP , 0; such that we obtain the free energydifference of the J and A conformations as DGn ¼DG0 þ ndGP: This assumption of additivity ofthe individual contributions may not be entirelycorrect, owing to interactions between the phos-phate groups, but serves as a useful first approxi-mation. It results in an exponential distribution ofthe conformational equilibrium constants:

Ln ¼ L0ln ð10Þ

with the increment factor l ¼ e2dGP=RT . 1:According to our assumptions on the con-formational energy differences (Figure 1(a)), wehave L0 p 1 and LN q 1: Moreover, we will assumethat the calcineurin and kinase activities do notdiffer between phosphorylation sites:

cn ¼ c; Cn ¼ C; kn ¼ k; Kn ¼ K ð11Þ

As a result, the model behavior is determined bythe nine parameters listed in Table 1.

Experimental data indicate that the time-scalefor dephosphorylation is considerably faster(,1 minute)26 than the time-scale for nuclearimport/export (<15 minutes).4 The conformationaltransition may be yet faster than dephosphoryla-tion (e.g. conformational changes in hemoglobinare observed on a subsecond time-scale17). Thuson the time-scale of several minutes which is rele-vant for a change in nuclear localization ofNFAT1, we can assume that the conformationaltransitions and the phosphorylation and dephos-phorylation reactions will rapidly approach theequilibria given by equations (6)–(8). The appli-cation of such a rapid-equilibrium approximationwill simplify the analysis of the kinetic behavior ofthe model.27

Results

Multiple dephosphorylation creates a sharpthreshold for the conformational transition

For a single NFAT1 molecule, the model predictsits probability to be in the active conformation,

given a certain phosphorylation state. In a largeensemble of molecules, we will find a distributionof phosphorylation states. What percentage ofmolecules is then in the active conformation?Clearly, this frequency of occurrence of the activeconformation, f, is given by the number ofmolecules in the active conformation divided bythe total number of molecules in the compartmentconsidered (to be specific, the calculations willrefer to the cytoplasmic fraction of NFAT1, but theresults are independent of the compartment andhold equally for the nucleus). From the modelequations, we obtain:

f ¼

XN

n¼0

an

XN

n¼0

an þ in

¼

1 þXN

n¼1

Yn21

j¼0

kj=cj

0@

1A

1 þ L0 þXN

n¼1

ð1 þ LnÞYn21

j¼0

kj=cj

ð12Þ

This equation expresses the frequency of the activeconformation as a function of the conformationalequilibrium constants, Ln; and of the kinase andcalcineurin activities, kn and cn, respectively. Tomake the following arguments more transparent,we assume that the kinase and calcineurin activi-ties are the same for each residue (kn ¼ k; cn ¼ c;see Model) and that the equilibrium constants Ln

follow the exponential distribution, equation (10).Then the expression for f simplifies to:

f ¼ 1= 1 þ L0ðlk=cÞNþ1 2 1

lk=c 2 1

k=c 2 1

ðk=cÞNþ1 2 1

� ð13Þ

Using this equation we can plot the stimulus-response curve of the frequency of NFAT1 in theA conformation versus the calcineurin activity(Figure 2(a)); note that a frequency of unity is thesame as 100% activation. From this curve, we canalso infer the frequency of the inactive confor-mation, 1 2 f:

Arguably the most conspicuous feature of theproposed model is the involvement of a highnumber of conserved phosphorylation sitesðN ¼ 13Þ: The model allows a comparison of

Table 1. Parameters of the simplified model

Parameter Symbol

Number of phosphorylation sites involved in the conformational switch NCalcineurin activity in the cytoplasma cCalcineurin activity in the nucleusa CKinase activity in the cytoplasma kKinase activity in the nucleusa KConformational equilibrium constant in the fully unphosphorylated state L0

Increment factor in the conformational equilibrium constant per phosphorylated residue lNuclear import rate constant of the active conformation dNuclear export rate constant of the inactive conformation f

a These parameters are related to the A conformation.

Conformational Switch Model for NFAT 35

(hypothetical) proteins that contain different num-bers of phosphorylation sites. Growing values ofN result in an increasingly sharp threshold in thestimulus-response curve (Figure 2(b)). The pro-nounced threshold behavior seen for N ¼ 13renders random input (calcineurin activity) fluctu-ations and small input ineffectual while respond-ing with maximal activation to any suprathresholdinput.

The stimulus-response curves can be characterizedby four parameters: the calcineurin concentrationat threshold (EC50), the steepness of the curve atthreshold, and the minimum and maximum valuesof the response. The threshold (EC50) value for thecalcineurin stimulus, in the following denotedby Q, can be calculated exactly in a special case(symmetric energy profile DGN ¼ 2DG0). Onefinds:

Q ¼ kffiffiffil

pð14Þ

Indeed, it holds generally that the EC50 value isproportional to the kinase activity k. Thus, thekinase activity can effectively set the activationthreshold. This can be seen even more clearlyby realizing that equation (14) is equivalent to(see equation (8)): ffiffiffiffiffi

cc0p

¼ffiffiffiffiffiffikk0

pð15Þ

Here c0 and k0 denote the calcineurin and kinaseactivities for dephosphorylation and phosphoryl-ation, respectively, of the inactive conformation.These will generally be different from those forthe active conformation, c and k, because the acces-sibility of the serine residues will be different in thetwo conformations (see Relation (9)). Equation (15)then states that half-maximal activation of NFAT1is achieved when the calcineurin activity averagedover both conformations, as expressed by the geo-metric mean, equals the averaged kinase activity.

To define the steepness, it is useful to considerthe prototypical sigmoid function, the Hillfunction:

f ¼cn

un þ cnð16Þ

The Hill coefficient n is a measure of the steepnessof the threshold and u is the half-saturation con-stant. We find that for large enough N, the Hillfunction yields excellent fits to the stimulus-response curves (Figure 2(b), broken lines for N ¼4 and N ¼ 13). The Hill coefficients obtained bythese fits are of the same magnitude as the numberof phosphorylation sites (Table 2). This result is

Figure 2. Steady-state response of NFAT1 to calci-neurin stimulation. (a) Frequency of occurrence of theA conformation, f, for N ¼ 13: The J conformationequals 1 2 f; as indicated. (b) Comparison of the stimu-lus-response curves for different numbers of phosphoryl-ation sites (continuous lines, N indicated at the curves):larger N result in sharper thresholds. The broken linesfor N ¼ 4 and N ¼ 13 are best fits to the Hill function(see Table 2). The calcineurin activity, c, is given in unitsrelative to the kinase activity, k (i.e. at c ¼ 1 bothare equal). Parameter values: L0 ¼ 102N=2; l ¼ 10:(c) Maximal response range fmax –fmin as a function ofthe energy increment per phosphate group (fmin andfmax are the frequencies of the A conformation at zeroand saturating calcineurin activities, respectively.)Curves are given for N ¼ 1; 2 and 13 phosphorylationsites. For N ¼ 13; the maximal response range isachieved above a critical energy increment of only about1RT; the energy of thermal fluctuations.

Table 2. Apparent Hill coefficients of stimulus-responsecurves ðl ¼ 10Þ

Phosphorylationsites (N)

4 5 7 9 11 13

Fitted Hill coefficient(n)

2.90 3.94 6.01 8.04 10.05 12.06

36 Conformational Switch Model for NFAT

remarkable when compared to the Hill coefficientsof oligomeric proteins regulated by reversiblebinding of allosteric effectors. Those are generallysmaller than the number of protein subunits andtypically range between 2 and 4. By contrast, themodel predicts an apparent Hill coefficient forNFAT1 activation by calcineurin of the order often. Such steep responses have been referred to asultrasensitive.28

For the threshold value u, we get u < Q in thespecial symmetric case, and the more generalestimate u < kl

ffiffiffiffiffiL0

Np

otherwise.The minimum and the maximum of the response

curve can be calculated as:

fmin ¼1

1 þ LN; fmax ¼

1

1 þ L0ð17Þ

They depend on only the conformational equi-librium constants of the fully phosphorylated anddephosphorylated proteins, respectively. A maxi-mal range of response, with fmin < 0 and fmax <1; is obtained when L0 is very small and LN

very large. However, this requires a certain dif-ference in Gibbs free energy, DG0 2 DGN ¼RTðln LN 2 ln L0Þ; that must be supplied by inter-actions of the protein structure with the phosphate

groups. Let us suppose that each phosphate groupcontributes a fixed increment in interaction energy,dGP: Then the total energetic difference achievedis proportional to the number of phosphate groups.In other words, to obtain a maximal responserange, fmax 2 fmin < 1; with a large number ofphosphorylation sites requires each site to make asmaller energetic contribution than when thisresponse range is to be achieved with a small num-ber of sites (Figure 2(c)). For N ¼ 13; it is sufficientwhen the energy increment contributed per phos-phate group is in the range of the energy of ther-mal fluctuations.

Switch-like activation of NFATs results frommultiple dephosphorylation in both cytoplasmand nucleus

We can now relate the phosphorylation state ofNFAT1 to its nuclear localization. Nuclear locali-zation is determined by the balance of the nuclearimport rate, nþ; and the nuclear export rate, n2:At steady state, these rates are equal.

In analogy to the frequency of active cytoplasmicmolecules (f), we define the frequency of inactivenuclear molecules, c. This is obtained by:

c ¼ 1 2 fðC;KÞ ð18Þ

where fðC;KÞ is the expression given in equation(13), but calculated with the nuclear calcineurinand kinase activities, C and K, respectively. Thusfðc; kÞ expresses the percentage of importablemolecules in the cytoplasm, while cðC;KÞ givesthe percentage of exportable molecules in thenucleus.

We focus on the total nuclear fraction of NFAT1,as this can be measured in the experimental systemby fluorescent labeling of the protein. Denotingthe nuclear fraction by Z, we clearly have Z ¼PN

n¼0 An þ In: Because the nuclear and cytoplasmicfractions sum to unity, the cytoplasmic fraction is1 2 Z: The rates of nuclear import and export canthen be expressed as:

nþ ¼ dfð1 2 ZÞ and n2 ¼ fcZ ð19Þ

respectively. In the steady state ðnþ ¼ n2Þ; weobtain the total nuclear fraction:

Z ¼df

dfþ fcð20Þ

Within the nuclear fraction, different phosphoryl-ation states will generally be present. Of these,the fully dephosphorylated state is transcription-ally active.4 From the model, the fraction offully dephosphorylated NFAT1 in the nucleus, Z0,is found as a subfraction of Z according to:

Z0 ¼ A0 þ I0

¼Zð1 þ L0Þ

ðK=CÞNþ1 2 1

K=C 2 1þ L0

ðlK=CÞNþ1 2 1

lK=C 2 1

ð21Þ

Figure 3. Activation of NFAT1 requires cytoplasmicand nuclear dephosphorylation. (a) Total nuclear fraction(Z, continuous line) and transcriptionally active fraction(Z0, broken line) in response to calcineurin activation incytoplasm and nucleus. (b) Total nuclear fraction andtranscriptionally active fraction in response to calci-neurin activation in cytoplasm only. Parameters: C ¼ cfor (a), C ¼ 0 for (b); K ¼ k; d ¼ f; L0 and l as in Figure 2.

Conformational Switch Model for NFAT 37

Clearly, when the calcineurin activity far exceedsthe kinase activity, all nuclear NFAT1 is dephos-phorylated (with K=C ! 0; Z0 ! Z).

Calcineurin appears to reside predominantlyin the cytoplasm in unstimulated cells and isco-transported with NFATs to the nucleus afterstimulation.29 Indeed, when comparing thebehavior predicted by equations (20) and (21)with the experimental data, one can immediatelyconclude that dephosphorylation is required tooccur both in the cytoplasm and in the nucleusto get NFAT1 activation in the model (Figure 3(a)).In this case, the computed response curves ofZ and Z0 versus the calcineurin activity showcomplete nuclear localization for suprathresholdcalcineurin activity (Z, continuous line), and con-comitant transcriptional activity (Z0, broken line).Such complete nuclear localization of NFAT is com-monly observed after calcineurin activation.

An alternative view would be that phosphataseactivity of calcineurin is required only in thecytoplasm.30 However, cytoplasmic dephosphoryl-ation alone results in partial nuclear localization in

the model (Figure 3(b); Z, continuous line). Thereason for this phenomenon is that nuclear exportremains active while nuclear import becomes acti-vated (owing to the action of the constitutivekinases in the nucleus). Thus import and exportcompete, and maximal calcineurin activationresults in a nuclear fraction of Z ¼ d=ðd þ f Þ: Thiswould come close to unity only if the export rateconstant f were much smaller than the import rateconstant d. This is clearly contradicted by theobserved transport kinetics, which indicates that dand f are of the same order of magnitude. An evenmore stringent argument against a merely cyto-plasmic phosphatase activity of calcineurin is theresponse of the transcriptionally active fraction,which remains near zero throughout (Z0, brokenline). Thus, because of the lack of activedephosphorylation in the nucleus, fully dephos-phorylated NFAT1 entering the nucleus wouldbecome rephosphorylated. Thus all the followingcalculations will be done with calcineurin acti-vation both in the cytoplasm and in the nucleus.For simplicity, we will take the nuclear calcineurinactivity proportional to the cytoplasmic activity.

As shown above for the frequency of the activeconformation, the model also predicts that thenumber of phosphorylation sites is crucial increating a threshold behavior for the responseof transcriptionally active NFAT1 (Figure 4(a)).The switch-like response for large N can be viewedas the result of linking the probabilities of manyphosphorylation events. Thus for subthresholdcalcineurin activities, the fully phosphorylatedfraction and, to a lesser degree, the N 2 1 timesphosphorylated fraction dominate, and are, ofcourse, found in the cytoplasm (Figure 4(b); iN

and iN21; broken gray lines). Conversely, forhigh calcineurin activities, almost all moleculesare fully dephosphorylated or phosphorylated justonce and located in the nucleus (A0 and A1; con-tinuous black lines). Only around the threshold doother forms occur at a noticeable frequency, suchas the fully dephosphorylated cytoplasmic mol-ecules (a0; continuous gray line) and the fully phos-phorylated nuclear molecules (IN; broken blackline).

Nuclear and cytoplasmic kinases can controlthreshold and shape of the NFAT responseto calcineurin

In the previous calculations, we have tacitlyassumed that the calcineurin activities in thecytoplasm and nucleus increase equally upon cellstimulation, c ¼ C; and that the kinase activities inthe cytoplasm and the nucleus are equal, k ¼ K:This symmetry yields easily interpretable results,but may of course not be realized in cells. Indeed,kinases targeting NFATs are also subject to regu-lation by TCR signals and can be differentiallyregulated in the cytoplasm and in the nucleus.6

Moreover, the cytoplasmic and nuclear calcineurinconcentrations need not be equal in stimulated

Figure 4. Threshold response for NFAT1 activation.(a) Transcriptionally active fraction in the nucleus fordifferent numbers of phosphorylation sites (N indicatedat the curves). (b) The dominant NFAT1 substates forN ¼ 13: Cytoplasmic states: J conformation, fully phos-phorylated and N 2 1 times phosphorylated (iN andiN21; broken gray lines); A conformation, fully dephos-phorylated (a0; continuous gray line). Nuclear states:A conformation, fully dephosphorylated and oncephosphorylated (A0 and A1; continuous black lines); Jconformation, fully phosphorylated (IN; broken blackline). Parameters as in Figure 3(a).

38 Conformational Switch Model for NFAT

cells. In the model, the steady-state level of thenuclear NFAT fraction depends on the ratios ofkinase to calcineurin activities in the cytoplasmand the nucleus. Thus there are two asymmetriccases: the nuclear ratio being higher, or lower,than the cytoplasmic ratio. To avoid overloadingthe following arguments, we will discuss thesetwo cases by considering different kinase activitiesðk – KÞ and equal calcineurin activities ðc ¼ CÞ:

To obtain the NFAT response curves to calci-neurin activation for different cytoplasmic andnuclear kinase activities, we compute the frequen-cies of the active (importable) conformation in thecytoplasm, fðc; kÞ; and of the inactive (exportable)conformation in the nucleus, cðC;KÞ; (Figure 5).Because of the differences in kinase activities inthe two compartments, the conformational switchoccurs at different calcineurin activities, Qf ¼ k

ffiffiffil

p

in the cytoplasm and Qc ¼ Kffiffiffil

pin the nucleus.

If the nuclear kinases have a higher activitythan the cytoplasmic kinases, we have Qf , Qc;(Figure 5(a1)). This yields a stimulus responsecurve for nuclear NFAT with a “double threshold”(Figure 5(a2), continuous line). Below the cyto-plasmic threshold, Qf; import is inactive andexport is active, such that NFAT is in the cytoplasmðZ < 0Þ: In between the cytoplasmic thresholdand the nuclear threshold, Qc; import becomesactivated and export remains active, leading topartial nuclear localization ðZ < 0:5Þ: Once calci-neurin activity crosses the nuclear threshold,export is inhibited and NFAT becomes completelylocalized to the nucleus ðZ < 1Þ: The calcineurinactivity of half-maximal nuclear localization is thegeometric mean of the cytoplasmic and nuclear

thresholds:

Q0:5 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiQfQc

pð22Þ

(like equation (14), this equation can be interpretedin terms of equal geometric means of calcineurinand kinase activities:

ffiffiffiffifficc0

p¼

ffiffiffiffiffiffiffiffiffiffiffiffiffikk0KK04

p). However,

nuclear phosphorylation persists up to the nuclearthreshold, and therefore the transcriptionally activefraction, Z0, rises only when calcineurin activitygets above the nuclear threshold (Figure 5(a2),broken line). As a consequence, the nuclear kinasesset the threshold for NFAT1 activation. Changingthe activity of the cytoplasmic kinases has no effectas long as they remain less active than the nuclearkinases.

Control of NFAT1 activation is different whenthe cytoplasmic kinases are more active than thenuclear kinases. Then the nuclear threshold isbelow the cytoplasmic threshold and export isinhibited before import becomes activated (Figure5(b1)). Thus, however small the activation ofimport may initially be when calcineurin activityrises, it will lead to an immediate accumulation ofNFAT in the nucleus, because export is alreadyshut off. Moreover, most of the NFAT entering thenucleus will remain in the dephosphorylatedstate. As a result, the total nuclear and tran-scriptionally active fractions rise simultaneously(Figure 5(b2), continuous and broken lines, respec-tively). Indeed, half-maximal activation of NFAT1nearly coincides with its half-maximal nuclearlocalization at Q0:5: Therefore, both the cytoplasmicand the nuclear kinases set the threshold for NFATactivation in this case.

Figure 5. NFAT1 activation withdifferent kinase activitities inthe cytoplasm and the nucleus.(a) Nuclear kinase activityexceeds cytoplasmic kinaseactivity; (b) nuclear kinase activityis smaller than cytoplasmic kinaseactivity. (a1, b1) Frequencies ofactive cytoplasmic (f; continuousline) and inactive nuclear (c; bro-ken line) NFAT1 molecules. (a2,b2) Total nuclear NFAT1 (Z, con-tinuous line) and transcriptionallyactive nuclear NFAT1 (Z0, brokenline). The threshold values Qf;Qc; and Q0:5 are explained in thetext. Parameter values: (a) K ¼ 5(relative units), k ¼ 1; (b) K ¼ 1;k ¼ 5: Other parameters as inFigure 3(a).

Conformational Switch Model for NFAT 39

These results imply that there are two differentregimes with respect to the control of NFAT acti-vation by kinases. As a measure of control, wetake the threshold calcineurin activity for theresponse of the transcriptionally active fraction,Z0. When the nuclear kinases are dominant ðK .kÞ; this threshold approximately equals Qc ¼ K

ffiffiffil

p:

Therefore, the threshold is controlled by thenuclear kinases and changing the cytoplasmickinases has no effect (Figure 6(a)). However, ifthe cytoplasmic dominate ðk . KÞ; the thresholdis approximately Q0:5 ¼ l

ffiffiffiffiffiffikK

p—both cytoplasmic

and nuclear kinases exert the same degree ofcontrol (Figure 6(b), dotted and broken lines). Oneconsequence of this fact is that the effect on thethreshold is stronger if the kinase activities in bothcompartments are changed in a coordinatedfashion (Figure 6(b), continuous line).

GSK-3, which is thought to be involved innuclear export of NFATs, indeed appears to bedifferentially regulated in the cytoplasm and thenucleus. It is constitutively active in resting T cells

in both compartments,11 but the nuclear fractionis preferentially inhibited in response to TCRstimulation,31 which may point to dominantcontrol of the nuclear GSK-3 fraction.

The observed kinetics of translocation can beexplained by the model

The activation kinetics of NFATs have beenmeasured under various conditions, thus provid-ing a critical test for the model. (i) On stimulationof calcium entry, NFATs get translocated tothe nucleus on a time-scale of 5–15 minutes.4,29

(ii) Interestingly, Okamura et al. have reported thata small fraction of NFAT1 accumulates in thenucleus even in unstimulated cells when nuclearexport is inhibited.4 This nuclear import proceedsmore slowly, on a time-scale of hours. Arguablythe simplest explanation for this observation isthat even phosphorylated NFAT1 is imported at alow rate, which, however, can be seen only whenthe much faster export is blocked. (iii) Dolmetschet al. found that the kinetics of NFAT translocationto the nucleus depend sensitively on the temporalpattern of calcium mobilization.9 A single calciumspike gives rise to transient NFAT translocation,whereas continuous, plateau-like, calcium eleva-tions cause sustained nuclear localization of NFAT.The higher the amplitude of the calcium plateau,the faster NFAT translocation will be. As shownin the following, all three sets of data can beexplained by the model.

So far, we have considered the model at thesteady state that results when the rate of nuclearimport and export become equal ðnþ ¼ n2Þ: If con-ditions are changed, e.g. calcineurin is activated ornuclear export is inhibited, the rate of change ofthe nuclear NFAT fraction is given by:

dZ

dt¼ nþ 2 n2 ¼ df2 ðdfþ fcÞZ ð23Þ

From this equation, we can calculate the transientkinetics of the nuclear fraction Z (and, usingequation (21), also of the transcriptionally activefraction Z0). Choosing reasonable values of theimport and export rate constants (d ¼ f ¼0.2 min21), NFAT1 accumulation follows supra-threshold calcineurin activation within about15 minutes (Figure 7(a)). After the calcineurinactivity subsides, NFAT1 leaves the nucleus on thesame time-scale.

From equation (23), we infer that the charac-teristic time of a change in NFAT1 nuclear locali-zation is:

t ¼1

dfþ fcð24Þ

If calcineurin is activated, we have f < 1 and c <0; such that t < 1=d—under stimulated conditionsthe characteristic time is determined by the importrate constant, d. Conversely, it can be shown thatunder unstimulated conditions, the characteristic

Figure 6. Change in the threshold calcineurin activityresulting from variations of kinase activities. (a) Whenthe basal kinase activity is larger in the nucleus than inthe cytoplasm, variation of nuclear kinases changes thethreshold (broken line), whereas cytoplasmic kinaseshave no effect (dotted line). Reference parameters asin Figure 5(a). (b) When the basal kinase activity islarger in the cytoplasm than in the nucleus, variationsof nuclear kinases (broken line) and cytoplasmic kinases(dotted line) have the same effect on the threshold.Concomitant variation of both potentiates this effect(continuous line). Reference parameters as in Figure 5(b).

40 Conformational Switch Model for NFAT

time is set by the export rate constant, f ðt < 1=f Þ:Thus for d < f ; nuclear localization of NFAT1 andits clearance from the nucleus require a similarperiod of time.

The very same argument implies that theinhibition of nuclear export in unstimulated cells(i.e. a substantial decrease of f) leads to a residualnuclear accumulation of NFAT with a very largecharacteristic time. This very slow entry is illus-trated by the model simulation of Figure 7(b). Thisfinding is in remarkable agreement with theexperimental observations by Okamura et al.4

Above, we pointed out that the phosphorylationreactions, the dephosphorylation reactions, andthe conformational transitions can be assumed tobe much faster than the nuclear transport pro-cesses. Therefore, a so-called rapid-equilibriumapproximation was applied to these processes(this was indeed used to derive equation (23) forthe kinetics of nuclear translocation from themodel equations (3), (4) etc. in a formal manner).A detailed comparison with the solutions of thefull model equations shows the validity of therapid-equilibrium approximation for calcineurinactivities either sufficiently below or above thethreshold, Q0:5: In these cases, the characteristictimes of changes in NFAT1 distribution are indeeddetermined by the nuclear import and exportsteps. However, we found that in the vicinity ofthe threshold the approximation fails and thephosphorylation and dephosphorylation reactionshave a noticeable effect on the characteristic time.

To expose this kinetic threshold effect, wecomputed numerically the characteristic time forNFAT1 activation, t; as a function of the ratio ofcalcineurin to kinase activity for different fixedvalues of kinase activity, k (Figure 7(c)). For easeof comparison, k can be used to define a charac-teristic time, T ¼ 1=k; for the processing of a singlephosphate group. T can thus be expected to bewell below one minute. Nevertheless, near thethreshold calcineurin activity, even small T canlead to a collective effect of the many phosphoryl-ation and dephosphorylation steps significantlyslowing the overall nuclear translocation (Figure7(c)). This appears to be due to the fact that nearthe threshold, calcineurin and kinases compete toa significant degree, while below and above thethreshold kinases and calcineurin, respectively,dominate. This remarkable kinetic property wouldallow a very effective discrimination of near-threshold signals by their duration. This effectcould be used for an additional kinetic filtering ofTCR signals acting on calcineurin.

Evidence for such a kinetic effect is provided bythe data of Dolmetsch et al. showing that the timefor NFAT translocation increases when the ampli-tude of the triggering calcium signal decreases.9

In fact, this work studied the effect on NFAT acti-vation of three types of calcium signals: singlespike, spike followed by plateau, and low-ampli-tude plateau. With a basic model of calciumdynamics, incorporating calcium release from theendoplasmic reticulum and activation-dependentcalcium entry through CRAC channels,32 we wereable to generate these three calcium patterns(Figure 8(a)), which are transduced in different

Figure 7. Kinetic behavior of the model. (a) NFAT1activity closely follows step-wise activation of calci-neurin (broken line, saturating suprathreshold stimulusc/k ¼ 10, d ¼ f ¼ 0.2 min21). (b) Block of nuclear exportleads to slow residual nuclear accumulation of NFAT1(c/k ¼ 0, d ¼ 0.2 min21, f ¼ 0.01 min21, l ¼ 5). (c) Forcalcineurin stimuli near the threshold, the characteristictime t of NFAT1 activation is substantially increasedand depends on the rates of the individual phosphoryl-ation and dephosphorylation steps (indicated as charac-teristic reaction times T at the broken curves). As areference, the characteristic time of NFAT1 activation inthe rapid-equilibrium approximation for (de)phosphoryl-ation is indicated by the continuous line ðT ! 0Þ: Par-ameters are as in Figure 5(a). Specifically, we have setk ¼ 1=T and c ¼ S=T: The characteristic time t for thebroken lines is estimated numerically according to thedefinition given by Llorens et al.37

Conformational Switch Model for NFAT 41

patterns of NFAT1 activation (Figure 8(b)). Fora single spike, NFAT1 activation transientlyapproaches 100% and declines again more slowly.Rapid and sustained activation of NFAT1 in themodel is seen when the spike is followed by acalcium plateau, whereas a low calcium plateauleads to slow and submaximal activation ofNFAT1. Thus our comparatively simple model(with identical parameters for all phosphorylationsites) qualitatively reproduces the three differentactivation patterns described experimentally.9 How-ever, a fully quantitative match will require moredetailed modeling.

Discussion

Allosteric control of protein activity by multiplephosphorylation sites

Here, we have proposed a plausible mechanismof how multiple phosphorylation sites control pro-tein activity and analyzed it mathematically. Thefundamental feature of this mechanism is that the

phosphorylation state determines the likelihoodof the protein to assume either an active or aninactive global conformation. Following the experi-mental data of Okamura et al.4 the multiple phos-phorylation sites are assumed to conspire indetermining the equilibrium distribution betweenactive and inactive conformations. We find thatthis property can result in a binary response to anactivating signal, if the number of phosphorylationsites involved is moderately large. Application ofthe model to NFAT, with 13 conserved serine resi-dues involved in the conformational transition,shows that such proteins can practically switchbetween an off-state and an on-state at a thresholdvalue of an activation signal.

However, it must be kept in mind that theanalysis was done under the simplifying assump-tion that the 13 conserved serine residues in theNFAT regulatory domain are equivalent withrespect to their effect on conformation. This isprobably not the case, as the work of Okamuraet al. shows that the five serine residues located inthe SRR-1 motif of the regulatory domain exert alarger control on the conformation of NFAT1 than

Figure 8. Differential NFAT activation according to duration and amplitude of the calcium/calcineurin stimulus.(a) Different types of calcineurin stimuli reflecting the types of calcium signals studied by Dolmetsch et al.: singlespike (broken line), spike followed by plateau (continuous line), and low-amplitude plateau (dotted line).9 Thesethree patterns were obtained from a basic model of calcium dynamics, incorporating calcium release from the endo-plasmic reticulum and activation-dependent calcium entry through CRAC channels.38 The model contains the threevariables calcium concentration in the cytoplasm, ½Cacyt�; calcium concentration in the endoplasmic reticulum,½CaER�; and active calcineurin concentration (½CaN� ¼ c; in relative units), and reads:

d½Cacyt�

dt¼ C10 þ C1a

½IP3�

KIP3þ ½IP3�

2 ðC2 þ C3Þ½Cacyt� þ C40 þ C4a

½Cacyt�2

K2Ca þ ½Cacyt�

2

½IP3�2

K2p þ ½IP3�

2

" #ðCaER 2 CacytÞ

d½CaER�

dt¼ r C3½Cacyt�2 C40 þ C4a

½Cacyt�2

K2Ca þ ½Cacyt�

2

½IP3�2

K2p þ ½IP3�

2

" #ðCaER 2 CacytÞ

" #

d½CaN�

dt¼ kþCaNð½CaNtotal�2 ½CaN�Þ½Cacyt�2 k2CaN½CaN�

The parameters are: C10 ¼ 0:05 mM/minute, C1a ¼ 0:5 mM/minute, C2 ¼ 1 min21, C3 ¼ 1 min21 (continuous and bro-ken lines), C3 ¼ 0:1 min21 (dotted line), C40 ¼ 0:001 min21, C4a ¼ 0:2 min21, KIP3

¼ KCa ¼ Kp ¼ 0:5 mM, r ¼ 10;kþCaN ¼ k2CaN ¼ 5 min21, ½CaN�total ¼ 25 (continuous and broken lines), ½CaN�total ¼ 10 (dotted line); the IP3 concen-tration reflecting the stimulus is set to 1 mM for two minutes (broken line) and 20 minutes (continuous and dottedlines). (b) Kinetics of nuclear NFAT localization for the stimulus patterns of Figure 8(a): transient for calcineurinspike broken line), rapid and sustained for calcineurin spike and plateau (continuous line) and slow sustained forlow-amplitude calcineurin plateau (dotted line). Parameters of NFAT model: l ¼ 5; T ¼ 0:1 minute, d ¼ 0:4 min21,f ¼ 0:1 min21.

42 Conformational Switch Model for NFAT

the calcineurin-targeted serine residues in other(SP) regions.4 The control of each phosphorylationsite should in principle be quantifiable in terms ofthe energetic contribution to the conformationalenergy made by a phosphate group bound to it.Our calculations show that if fewer than 13 serineresidues made the dominant energetic contri-butions, the activation threshold would be lesssteep.

For obtaining an activation threshold, it is crucialthat the kinases and calcineurin rebind severaltimes to achieve complete phosphorylation anddephosphorylation, respectively, of the substrate.For simplicity, we have assumed in the model thatbinding and dissociation of the enzymes proceedmuch more rapidly than the catalytic steps. How-ever, the principal conclusions of the model remainvalid for a modest degree of processivity of theenzymes (i.e. the processing of several phosphategroups by one bound enzyme before dissociationand rebinding events occur). In such a case, thethreshold would become less steep (unpublishedresults). It will thus be interesting to experi-mentally study the kinetics of phosphorylationand dephosphorylation of highly phosphorylatedproteins as has been done for the doubly phos-phorylated MAP kinase.24,25,33

On the level of the entire calcium/calcineurin/NFAT pathway, Dolmetsch et al. indeed observeda threshold behavior when target gene expressionwas plotted against calcium concentration,34 forwhich they reported an apparent Hill coefficientof 4.7. It is not clear at present how this thresholdis generated by the various steps of the pathway,including NFAT binding to the target gene.However, our analysis shows that the thresholdcould be primarily due to the mechanism of NFATactivation through multiple dephosphorylation.

Order of phosphate processing

In the model, we assumed that the phosphoryl-ation and dephosphorylation of the sites proceedin a sequential fashion and that the sites are other-wise independent of one another. The generationof the threshold can be seen as a probabilisticeffect. If the likelihood for a single site to bephosphorylated is low, then the likelihood for nindependent sites all to be phosphorylateddecreases practically exponentially with n andthus is entirely negligible for large n (exact analysisshows that the conformational equilibria betweenA and J conformations also play some role).The converse holds for a large single-site proba-bility of phosphorylation. As a result, partiallyphosphorylated molecules occupy an appreciablefraction of the total protein number only whenthe kinase and phosphatase activities are well-balanced. This point of balance defines thethreshold for activation.

A sequential mechanism of phosphate process-ing will therefore be more efficient at creatinga conformational switch than non-sequential, or

random, processing. With a random mechanism,the fraction of molecules in partially phosphoryl-ated states generally would be much largerthan with a sequential mechanism, because therewould be more possible partially phosphorylatedstates available (e.g. the state [0 0 P 0 0 P 0 0 P 0 0 P 0]is compatible with a random processing mechan-ism but not the sequential mechanism). We alsocarried out analysis of random phosphate proces-sing and found that it indeed results in moregraded dose-response curves, as compared to thesharp dose–response curves obtained with thesequential mechanism. Because the number ofintermediate states grows exponentially with ran-dom processing order and only linearly withsequential order, this difference between randomand sequential phosphate processing becomesmore pronounced when the number of phos-phorylation sites is large. Thus the extent to whichphosphate processing follows a fixed order couldbe important in determining the regulatory proper-ties of the protein.

Experimentally, random multisite phosphoryl-ation has been reported for the oligomeric CheYprotein.35 By contrast, several kinases are knownto sequentially phosphorylate serine/threonineresidues within single protein domains.21 – 23 Theregulatory domain of NFAT proteins containssequential phosphorylation motifs for GSK-3 andfor CK-I in the SP and SRR-1 motifs, respectively,such that the mechanism of phosphorylation issequential for these subgroups of the phosphoryl-ation sites (H. Okamura, unpublished results).20

For dephosphorylation, there is also an orderbetween the subgroups, with the SRR-1 regionbecoming dephosphorylated first.4 Thus therewill be at least partially sequential phosphateprocessing in NFATs that keeps the number ofintermediate phosphorylation states limited.

It must be noted that there are a number ofpresently unresolved questions on the mechanismsof phosphate processing. In particular, is the bind-ing of calcineurin and kinases mutually exclusiveor can both associate with an NFAT moleculeat the same time? Moreover, what is the exactsequence of NFAT phosphorylation and whichkinases are required? Experimental data on theseissues should lead to a considerable refinement ofthe mathematical model and its predictions.

Kinetics of NFAT activation

In agreement with experimental data, we find inthe model that the kinetics of NFAT activation anddeactivation occur on a similar time-scale. Therapid activation and deactivation make NFAT aprime candidate for tracing TCR occupancy,11 incontrast to more permanently elevated T-cell tran-scription factors linked to differentiation state.36

Moreover, the data also indicate that the activationtime depends on the amplitude of the stimulus:activation time increases significantly when theamplitude of the triggering calcium signal

Conformational Switch Model for NFAT 43

decreases.9 The model offers a rationale forthis observation. We find that the characteristictime for NFAT activation attains a maximum atthe threshold calcineurin activity. At this point,the activities of calcineurin and kinases arevery similar, so that dephosphorylation iscounteracted by phosphorylation, and this com-petition results in a long activation time. Bycontrast, when the calcineurin activity is wellabove threshold and thus much larger than thekinase activity, activation is much faster. Themodel shows that this phenomenon is morepronounced the more phosphorylation sites areinvolved.

This attenuation of near-threshold stimulimay be of importance for T-cell activation as itcould create an additional kinetic threshold forsignals coming from the T-cell receptor. Thuslow-amplitude, suprathreshold signals could beeffectively discriminated with respect to theirduration. By contrast, large-amplitude signalsresult in much shorter activation times ofNFAT and could thus effectively trace the time-course of the T-cell receptor signal, as has beensuggested previously.11

Model predictions

Our analysis of the conformational switchmechanism leads to several conclusions that haveso far not been assessed experimentally. Besidesthe predicted threshold behavior of NFAT activa-tion, we were able to analyze the contributions ofcalcineurin and the kinases located in the cyto-plasmic and nuclear compartments. The modelclearly shows that phosphatase activity of calci-neurin is required both in the cytoplasm and inthe nucleus to cause effective nuclear translocationof NFAT proteins. This is consistent with thefinding that calcineurin is cotransported to thenucleus with NFATs,29 where it can be kept activeby elevated calcium levels.

The kinases acting on NFATs form a secondtarget for regulation. According to the model,basal kinase activity in both cytoplasm andnucleus is required to keep NFATs inactive andlocalized in the cytoplasm in the absence of cal-cineurin stimulation. Strikingly, the kinases inthe two compartments may have differentialcontrol on the NFAT activitation characteristics.If the nuclear kinases have larger activity thanthe cytoplasmic kinases, they alone control thedegree of calcineurin stimulation required tocause NFAT transcriptional activity. By contrast,if the cytoplasmic kinases have larger activity,both cytoplasmic and nuclear kinases controlNFAT activation by calcineurin. Thus, in anysituation the nuclear kinases are predicted tobe effective regulators of NFATs, and this couldbe a rationale for the observation that GSK-3targeting NFATs is preferentially regulated inthe nucleus.31

Acknowledgements

We thank A. Rao, A. Radbruch, and R. Baumgrassfor stimulating discussions. The work was sup-ported by a grant from the German AcademicExchange Sevice to C.S. and by the DeutscheForschungsgemeinschaft through SFB 618 (to T.H.).

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Edited by M. Levitt

(Received 18 October 2002; received in revised form 18 December 2002; accepted 21 December 2002)

Conformational Switch Model for NFAT 45