rsif.royalsocietypublishing.org

ReportCite this article: Fagerlund R, Behar M,Fortmann KT, Lin YE, Vargas JD, Hoffmann A.

2015 Anatomy of a negative feedback loop:

the case of IkBa. J. R. Soc. Interface 12:20150262.

http://dx.doi.org/10.1098/rsif.2015.0262

Received: 25 March 2015

Accepted: 3 August 2015

Subject Areas:systems biology

Keywords:negative feedback, gene regulation,

NFkB, IkBa, oscillation

Author for correspondence:Alexander Hoffmann

e-mail: ahoffmann@ucla.edu

†Present address: Department of Biomedical

Engineering, The University of Texas at Austin,

Austin, TX 78712, USA.

Electronic supplementary material is available

at http://dx.doi.org/10.1098/rsif.2015.0262 or

via http://rsif.royalsocietypublishing.org.

& 2015 The Author(s) Published by the Royal Society. All rights reserved.

Anatomy of a negative feedback loop:the case of IkBa

Riku Fagerlund1, Marcelo Behar1,†, Karen T. Fortmann1, Y. Eason Lin1,2,3,Jesse D. Vargas1,2,3 and Alexander Hoffmann1,2,3

1Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093, USA2Department of Microbiology, Immunology, and Molecular Genetics, and 3Institute for Quantitative andComputational Biosciences, University of California, Los Angeles, CA 90095, USA

The magnitude, duration and oscillation of cellular signalling pathwayresponses are often limited by negative feedback loops, defined as an‘activator-induced inhibitor’ regulatory motif. Within the NFkB signallingpathway, a key negative feedback regulator is IkBa. We show here that,contrary to current understanding, NFkB-inducible expression is not sufficientfor providing effective negative feedback. We then employ computationalsimulations of NFkB signalling to identify IkBa molecular properties thatare critical for proper negative feedback control and test the resulting predic-tions in biochemical and single-cell live-imaging studies. We identifiednuclear import and nuclear export of IkBa and the IkBa–NFkB complex, aswell as the free IkBa half-life, as key determinants of post-induction repressionof NFkB and the potential for subsequent reactivation. Our work emphasizesthat negative feedback is an emergent systems property determined bymultiple molecular and biophysical properties in addition to the required‘activator-induced inhibitor’ relationship.

1. IntroductionNegative feedback control is a ubiquitous regulatory motif in many biologicalsystems, critical to the maintenance of proper homeostasis, dynamic control inresponse to perturbations, or oscillatory patterns [1]. The defining feature of a nega-tive feedback motif is an activator–inhibitor pair in which the activator inducesexpression or activity of the inhibitor. Indeed, many studies focus on the molecularmechanism(s) that provide(s) inducibility, often characterized by the fold changeand any intrinsic delay. However, actual molecular circuits within cells are incom-pletely described by the activator-inducible inhibitor paradigm, as they may needto contend with physical realities within the cell such as the biochemistry of mol-ecular interactions, sub-cellular compartmentalization or protein half-life. Thus,proper functioning of a negative feedback circuit may depend on biochemicalproperties other than the activator-responsive control of the inhibitor.

IkBa is a prominent negative feedback regulator in the NFkB signalling system[2,3]. IkBa directly controls the dynamics of the transcription factor NFkB, a centralregulator of inflammatory and immune response gene expression [4,5]. Through itsreversible sequestration of NFkB in the cytoplasm, IkBa not only controls the dur-ation of NFkB activity [4,6] but also enables reactivation that can result in oscillatorydynamics observed both in population studies [4] and in single cells [7].Mathematical models were shown to recapitulate these dynamic features [8,9],and reduced models have identified NFkB-responsive expression of IkBa as a keydeterminant of oscillatory dynamics [10–12]. The dynamics of NFkB signallingare stimulus-specific, and a critical determinant of inflammatory and immunegene expression programmes [13,14], prompting pioneering work to focusdrug-targeting strategies on dynamical features to achieve superior specificity [15].

Here, we examine the molecular properties that confer IkBa’s ability to con-trol NFkB dynamics. We find that while inducible expression of IkBa isrequired for proper NFkB dynamics [16], inducible expression is not sufficientas inducible expression of another IkB family member, IkBb, is unable to

http://crossmark.crossref.org/dialog/?doi=10.1098/rsif.2015.0262&domain=pdf&date_stamp=2015-08-26mailto:ahoffmann@ucla.edu

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support normal dynamical control of NFkB. This findingprompts us to characterize other IkBa properties that arerequired for proper negative feedback control of NFkB. Our

study delineates how several molecular properties combineto produce the emergent systems property of dynamicnegative feedback control of NFkB.

Figure 1. (Overleaf.) NFkB-dependent transcriptional control is not sufficient for IkB negative functions. (a) Schematic diagram of pBabe and 5xkB retroviralexpression constructs consisting of a tandem repeat of 5xkB sites driving the expression of IkBa. (b) Electrophoretic mobility shift assay (EMSA) and immunoblotanalysis of wt, IkBa2/2, IkBa2/2þ pBabe_IkBa, and IkBa2/2þ 5xkB_ IkBa murine embryo fibroblast (MEF) cell lines. EMSA indicates NFkB activityover a 120 min time course after stimulation with 1 ng ml21 of TNF; NFY binding was used as an EMSA control. Western blot shows protein abundances for IkBa,IkBb and IkBe with a-tubulin as a loading control. (c) IkBa2/2 MEFs reconstituted with NFkB-inducible IkBa or IkBb were treated with 1 ng ml21 of TNFand nuclear extracts analysed by EMSA for NFkB binding activity; NFY binding was used as an EMSA control. Immunoblots of corresponding cytoplasmic fractionswere probed with antibodies specific for IkBa, IkBb and IkBe ; a-tubulin was used as a loading control. Densitometric quantification of NFkB is presented as abar graph below. (d ) EMSA and immunoblot analysis of wild-type MEFs and MEFs that have the endogenous coding region for IkBa replaced by IkBb knock-in(AKBI). Cells were treated with 1 ng ml21 of TNF and nuclear extracts analysed by EMSA for NFkB-binding activity; NFY binding was used as an EMSA control.Immunoblots of corresponding cytoplasmic fractions were probed with antibodies specific for IkBa, IkBb and IkBe ; a-tubulin was used as a loading control.Densitometric quantification of NFkB is presented as a bar graph below. (e,f ) NFkB nuclear localization at the single-cell level. IkBa2/2b2/2e2/2RelA2/2

MEFs reconstituted with AcGFP1-RelA and NFkB-inducible IkBs. (e) IkBa cells were treated with 10 ng of TNF and fluorescent images were captured every 5 minand cellular localization of AcGFP1-RelA was measured and plotted as a normalized nuclear to cytoplasmic ratio individually (bottom left colour traces) and as acombined average (bottom right black trace). ( f ) IkBb cells were treated with 10 ng of TNF and fluorescent images were captured every 5 min and cellularlocalization of AcGFP1-RelA was measured and plotted as a normalized nuclear to cytoplasmic ratio individually (bottom left colour traces) and as a combinedaverage (bottom right black trace).

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2. Results2.1. NFkB-responsive transcriptional control

is necessary but not sufficient for IkBanegative feedback

Studies of NFkB dynamic control by IkB family membershave identified IkBa as the key negative feedback regulatordue to its highly inducible NFkB-responsive promoter [2–4].To characterize the role of NFkB-inducible expression, we com-plemented IkBa-deficient murine embryo fibroblasts (MEFs)with retroviral plasmids that express IkBa from either a constitu-tive (pBabe) or an NFkB-inducible (5xkB) promoter (figure 1a).Unlike pBabe-reconstituted cells, 5xkB_IkBa reconstituted cellsshowed dynamic resynthesis profiles similar to endogenousIkBa in wild-type cells following stimulation with tumour necro-sis factor (TNF) (figure 1b). Importantly, when we examined thecontrol of NFkB activity by electrophoretic mobility shift assay(EMSA), we found that 5xkB cells showed post-induction repres-sion and the transient trough of NFkB activity characteristic ofwild-type cells, correcting the misregulation in IkBa-deficientcells, whereas cells constitutively expressing IkBa were unableto capture this response (figure 1b).

To test whether NFkB-inducible control was not onlyrequired but also sufficient for NFkB dynamic control, wecomplemented IkBa-deficient cells with a 5xkB retrovirusexpressing IkBb, a highly homologous IkB family membercapable of inhibiting NFkB but not normally providing nega-tive feedback. Interestingly, these cells did not show properdynamic control of NFkB even though IkBb expression wasunder NFkB control similar to IkBa (figure 1c; electronic sup-plementary material, figure S1A). However, when anotherknown IkB negative feedback regulator, IkBe [17], was linkedto this promoter, NFkB activity did show post-inductionrepression (electronic supplementary material, figure S1B).These results indicate that, despite the high degree of sequencehomology, IkBa and IkBb have distinct molecular propertiesthat, along with differential gene expression control, renderIkBa an effective negative feedback regulator but not IkBb.In order to confirm the validity of this conclusion, we obtainedfibroblasts from a genetic knock-in mouse in which the IkBbcoding region was engineered to replace the IkBa open readingframe such that IkBb expression was under the control of theendogenous IkBa promoter [18]. Remarkably, these so-calledAKBI cells also failed to show proper NFkB post-induction

attenuation despite highly inducible IkBb expression(figure 1d; electronic supplementary material, figure S1c).

In order to examine translocation dynamics in singlecells, and without the confounding contributions of other IkBfamily members, we generated IkBa2/2b2/2e2/2RelA2/23T3 cells that lack all three classical NFkB inhibitors and RelA,and reconstituted them with a constitutively expressed fluor-escent GFP-RelA and NFkB-responsively expressed IkBa orIkBb. Whereas reconstitution with IkBa resulted in transientNFkB activation in response to TNF treatment, defined by atrough at about 60 min, followed by a second phase insome cells (figure 1e), reconstitution with NFkB-inducibleIkBb resulted in sustained NFkB activation showing only slowand incomplete post-induction repression (figure 1f ). Of note,in both conditions, the mean RelA nuclear localization profileof the collection of individual cells (figure 1e,f, black trace) clo-sely resembled the population level in biochemical studies(figure 1c,d). These data clearly indicate that when expressionof IkBa or IkBb is driven by the same NFkB-responsive promo-ter, resulting in ostensibly similar expression profiles, only IkBacan provide effective dynamic negative feedback control onNFkB. Thus, inducible inhibitor expression in and of itself isnot sufficient for proper negative feedback control of NFkB.

2.2. Mathematical modelling identifies multiplemolecular properties of IkBa contributingto the negative feedback control of NFkB

IkBa has several characteristics—other than NFkB-dependentsynthesis—that in principle may contribute to its negative feed-back function, e.g. its nuclear import and export properties, aswell as constitutive and signal-induced degradation of free andNFkB-bound IkBa (figure 2a). Here, we use a previously estab-lished in silico model of NFkB regulation to investigate thecontributions of each of these processes to the control ofdynamic NFkB signals. When normalized for maximumactivity, we confirmed that partial inhibition of the NFkB-dependent synthesis of IkBa potently impaired post-inductionattenuation, with 10% inhibition resulting in a 30% increase inthe signalling level at 70 min (figure 2b, row 1, and 2c). How-ever, we also found that partial inhibition of IkBa nuclearimport had a similar effect with a 10% inhibition causing an11% increase in signalling at 70 min (figure 2b, row 3). Weakinhibition of the degradation of free IkBa had little effect onpost-attenuation induction, whereas stronger inhibition shifted

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Figure 2. Modelling IkBa properties contributing to negative feedback control of NFkB. (a) Schematic illustrates negative feedback control of NFkB by IkBs.Numbers indicate potential reactions that may contribute to dynamic regulation of NFkB. (b) Normalized nuclear NFkB concentration is shown for unperturbedmodels (black) and models in which the indicated reactions are partially inhibited (blue-red lines reflect various degrees of inhibition). Reaction numbers as in (a).(c) Sensitivity analysis of three temporal phases of the NFkB with respect to changes in IkBa regulation. ((i) – (iii)) Sensitivity ratio (nucNFkBperturbed 2 nucNFkBunperturbed)/nucNFkBunperturbed in per cent units for each reaction (numbers as in (a)). (iv) Global sensitivity (RMSD) integrated over 120 min. Results are shown forthree levels of inhibition (10%, twofold and 10-fold).

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the peak of NFkB to later times resulting in a modest increase inlate activity (90% inhibition caused 14% increase in signallingat 120 min, figure 2b, row 2). Partial inhibition of nuclearexport or of signal-induced degradation of NFkB-bound IkBaalso reduced the post-attenuation reactivation, with a 10% inhi-bition causing 1% and 9.5% decreased signalling at 120 min,respectively (figure 2b, rows 4 and 5).

To compare the contribution of these processes, we deter-mined the sensitivity of NFkB activity at three specific timesrepresenting early, post-induction attenuation and late partsof the signal to various perturbations (figure 2c). We also quan-tified the global sensitivity to each perturbation as the rootmean square deviation (RMSD) of the perturbed and unper-turbed signals over 120 min, sampled at 1 min intervals

(figure 2c(iv)). This analysis posits that IkBa-mediatedpost-induction attenuation of NFkB activity (figure 2c(ii)) is afunction not only of the NFkB-dependent synthesis ratebut also of IkBa’s nuclear import, as well as its constitutivedegradation. It also predicts that nuclear export and IKK-dependent degradation of NFkB-bound IkBa are importantfor late post-attenuation signalling (figure 2c(iii)).

2.3. Experimental testing of model predictions: multipleIkBa properties contribute distinct characteristicsto NFkB dynamic control

To test the computational predictions, we pursued a geneticperturbation approach. Previous work showed nuclear

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import of IkBa to be mediated by an unconventional NLSsequence [19,20]. Using this information, we reconstitutedIkBa-deficient cells with an IkBa NLS mutant (IkBaNLSm:L110A,L115A,L117A,L120A). In DNA binding studies ofIkBaNLSm cells, TNF induced NFkB activation comparableto that of wild-type IkBa cells (figure 3a), and although theresynthesis of IkBaNLSm protein was effectively inducedby NFkB, the IkBaNLSm cells were defective for the rapidpost-induction repression of NFkB. At 70 min, the signalin IkBaNLSm cells was 2.9-fold higher than in wild-typeIkBa cells (considering the different basal levels). This is con-sistent with the threefold increase predicted by the modelwhen the corresponding parameter is reduced to 35% of itswild-type value (figure 3a; electronic supplementary material,figure S2a). Consistent with population-level biochemicalstudies, IkBa2/2b2/2e2/2RelA2/2 cells expressing GFP-RelAshowed that IkBaNLSm was defective in post-inductionrepression and cytoplasmic relocalization of NFkB in singlecells (figure 3b). Despite the substantial heterogeneity inRelA cytoplasmic re-localization, the population mean closelyresembles the population-level results obtained by EMSA.These data clearly show that the nuclear localization of IkBais indispensable for proper termination of NFkB activity.

IkBa also relies on a nuclear export sequence (NES) forthe efficient nuclear export of NFkB [21,22]. Mathematicalmodelling suggested strong inhibition of nuclear exportwould result in reduced late NFkB activity. To assess therole of IkBa nuclear export on the sub-cellular localizationcontrol of NFkB, we generated an NES mutant (IkBaNESm;L45A,L49A,I52A). Reconstituted cells expressing IkBaNESmwere unable to produce the post-repression reactivation ofNFkB characteristic of wild-type protein-controlled NFkB sig-nalling (figure 3c; electronic supplementary material, figureS2b). The activity is qualitatively similar to the model predic-tion for a fivefold attenuation in the correspondingparameter. These results indicate that the nuclear export func-tion of IkBa is crucial for the post-repression activation ofNFkB signalling. Interestingly, the single-cell studies withthe NES mutant revealed seemingly contradictory results(figure 3d ), as most cells displayed sustained RelA nuclearlocalization. This apparent discrepancy is resolved by recog-nizing that: (1) the mutant localizes to the nucleus causinginhibition of NFkB activity but does not allow for NFkBexport and reactivation, and (2) the biochemical assay detectsDNA binding activity of free NFkB, whereas the single-cellimaging is a readout of NFkB localization only.

IkBa is known to have a very short half-life that is exten-ded approximately twofold by an IkBa5M mutant (S283A,S288,T291A,S293A,T296A) [23,24]. When expressed inIkBa2/2 cells from an NFkB-responsive promoter, IkBa5Machieved effective post-induction repression of NFkB activity(figure 3e; electronic supplementary material, figure S2c). How-ever, the re-activation of NFkB was undetectable, consistent withcomputational predictions that indicated a signal close to basallevel at 120 min when the corresponding parameter was reducedto 35% of its wild-type value. Similarly, in single live-cell studies,IkBa5M mediated efficient relocalization of RelA to the cyto-plasm with a complete absence of late-phase activity (figure 3f ).

3. DiscussionGiven the well-documented role of NFkB activity in vitalcellular processes, a number of mechanisms have evolved

to ensure precise regulation of its activity. The IkBa nega-tive feedback loop is a prominent NFkB regulatorymechanism, allowing for both post-induction repressionand repeated or oscillatory bursts of activity, and is criticalfor providing complex dynamic control which is thoughtto mediate specificity in NFkB’s pleiotropic physiologicalfunctions. Prior studies have established that the NFkB-responsive IkBa promoter is critical for this negative feedbackcontrol [16], but it has remained unclear whether specific charac-teristics of the IkBa protein may be important as well. Indeed,biochemical studies presented here using MEFs derived frommice in which IkBb was engineered into the IkBa locus to(AKBI MEFs) clearly demonstrate that, even when IkBb isunder NFkB-transcriptional induction, it is unable to provideproper negative feedback. These data motivated our characteriz-ation of IkBa protein properties that contribute to propernegative feedback function. Our strategy was to complementIkBa2/2 cells with retroviral transgenes providing for kB-responsive expression of engineered IkBa variants defective inspecific molecular characteristics.

In addition to traditional biochemical approaches to studyNFkB response and regulation, we examined NFkB responsedynamics in single cells. Recent studies have characterizedNFkB dynamics in single cells, but, to date, no studies haveemployed gene knock-out cells to probe underlying molecu-lar mechanisms. Thus, regulatory control mechanismsidentified at the biochemical/population level have yet tobe reconciled with single-cell microscopy tracking studiesthat boast high temporal resolution and individual cellularhistories. In this work, we employed a cell line lackingRelA and all canonical IkB proteins (IkBa2/2IkBb2/2

IkBe2/2RelA2/2 cells), which we then reconstituted withNFkB-inducible IkB variants and fluorescent RelA repor-ter in order to examine the contributions of specific IkBprotein characteristics.

Although the IkB proteins were first identified as cyto-plasmic inhibitors, it has become clear that they play amajor role in regulating nuclear NFkB. IkBa has beenshown to be efficiently transported into the nucleus whereit binds active NFkB dimers on the promoters of NFkB-activated genes and facilitates the dissociation of thetranscription factor from DNA. Comparing mutants withwild-type IkB proteins, we were able to show the contri-butions of IkB inducible synthesis, nucleo-cytoplasmictransport and degradation control to the various aspectsof the prototypical NFkB response; namely, duration andamplitude of initial NFkB activation, post-activation repres-sion and post-repression re-activation of NFkB signalling.Our biochemical assays, together with single-cell studies,demonstrated that IkBa nuclear localization is indispensablefor the rapid termination of NFkB activity. Specifically, weshowed that an NES-deficient form of IkBa supported effi-cient induction and post-induction repression of NFkBDNA binding activity, but not the characteristic re-activationand second phase NFkB activity. The deficiency in NES func-tion prevents the protein from efficiently returning NFkB tothe cytoplasm for the next round of activation, maintainingan inactive IkBaNESm-bound pool of NFkB in the nucleus.Finally, by employing an IkBa harbouring five mutationsthat confer stability, increasing the half-life of the normallyrapidly turned over uncomplexed/free protein, we wereable to show the importance of such rapid turnover ingenerating characteristic NFkB temporal profiles. In cells

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Figure 3. Multiple IkBa properties contribute distinct characteristics to NFkB control. Nuclear localization of IkBa is required for the termination of NFkB activity (a,b).Nuclear export function of IkBa is required for post-repression activation of NFkB activity (c,d ). IkBa protein half-life control is critical for sustained NFkB dynamics (e,f ).IkBa2/2 MEFs were reconstituted with NFkB-inducible wild-type or NLS mutant (a,b), NES mutant (c,d ) or the 5M mutant (e,f ) form of IkBa. The cells were treatedwith 1 ng ml21 of TNF and nuclear extracts were analysed by EMSA for NFkB activity and corresponding cytoplasmic extracts subjected to western blotting with indicatedantibodies (a,c,e). Bar graphs show quantification of EMSA; curves are modelling the result of NFkB activity in single cells upon stimulation with 10 ng ml21 of TNF.Real-time fluorescent images of IkBa2/2b2/2e2/2RelA2/2 MEFs reconstituted with AcGFP1-RelA and NFkB-inducible IkBa NLS mutant (b), NES mutant (d ) orthe 5M mutant ( f ) IkBa (showing cellular localization of RelA at indicated time points). Below the fluorescent images, single-cell traces show the ratio of nuclear tocytoplasmic localization of AcGFP1-RelA in fluorescent images (left) as well as the average curve and standard deviation of the single-cell traces (right).

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expressing this IkBa5M form, we found a complete absenceof second-phase activation, indicating that a low level offree IkBa protein (ensured by a short half-life) is requiredfor this aspect of the response.

Our results demonstrate not only that IkBa feedbackis dependent on NFkB-inducible synthesis but also thatseveral other processes dependent on the molecular charac-teristics of the protein itself, for example import, exportand half-life control, must be tuned in a coordinatedmanner to generate the hallmark features of NFkB signal-ling, namely post-induction repression and reactivation.By contrast, the IkBb protein does not support proper nega-tive feedback control even when expressed from IkBa’spromoter; we speculate that substantially reduced nucleo-cytoplasmic transport [25,26] may be a key underlyingreason; a second characteristic that may play a role isIkBa’s but not IkBb’s ability to strip NFkB off the DNA[27]. Indeed, these properties are not required for theNFkB dimer stabilization/chaperone function recentlyascribed to IkBb [28]. Our results illustrate the more generalpoint: that negative feedback regulation in cells is a complexprocess that depends on multiple molecular propertiesbeyond activator-induced expression [29,30]. These findingsmay well extend to other transcriptional networks asnuclear transport is a defining feature of many gene regulat-ory networks. Understanding the specific contributions ofeach process as well as their characteristic time scales isan important step for identifying effective druggable targetsthat may allow for correction of dynamic misregulation incells associated with pathology [15].

4. Material and methods4.1. Computational modellingThe response of the NFkB regulatory module was simulated usingthe computational ODE-based model described in [31]. In order tofocus on regulatory mechanisms involving IkBa, the other IkBfamily members were removed. Following equilibration, TNFresponses were simulated as in [31]. Time-course curves infigure 2 were generated by applying multipliers to the kinetic par-ameters corresponding to the reactions in figure 2a. The multipliervalues were: 223,22.5,22,21.5,21,20.5 (reactions 1, 2, 3 and 5) and226,25,24,23,22,21 (reaction 4), reflecting different sensitivities forreaction 4. NFkB time courses are normalized to their peakvalue. Sensitivity ratios sr(t) at a particular time ti are definedas: (nucNFkBperturbed 2 nucNFkBunperturbed)/nucNFkBunperturbed,where nucNFkBperturbed/unperturbed are the normalized nuclearconcentrations of NFkB at time ti obtained with a model with/without a multiplicative factor (0.9, 0.5, 0.1) for the indicatedkinetic rate parameter (values shown in per cent units). Theglobal average sensitivity in figure 2c was calculated as the RMSof the sr(t) sampled at 1 min intervals between 1 and 120 minpost-stimulation.

4.2. DNA constructsNFkB-inducible IkBa and IkBb constructs were generated in theself-inactivating (SIN) retrovirus backbone (HRSpuro) modifiedto express the IkBa or IkBb transgene under the control of fivetandem kB sites upstream of a minimal promoter. IkBa mutantforms were produced using site-directed mutagenesis. For live-cell studies, AcGFP1 was fused to the N-terminus of RelA andthe resulting construct was sub-cloned into the constitutivelyexpressing retroviral plasmid pBabe-Hygro.

4.3. Cells and cell cultureImmortalized IkBa2/2 MEFs were previously described [4] andIkBa2/2b2/2e2/2RelA2/2 MEFs were produced by interbreed-ing of the four individual mouse knock-out strains andharvesting E13.5 embryos, subjecting primary MEFs to the 3T3protocol of repeated passage until a stably proliferating cell cul-ture emerged. AKBI MEFs were a generous gift from BingBingJiang (Boston University). MEFs were cultured in Dulbecco’smodified Eagle’s medium supplemented with 100 U penicillin/streptomycin (10378016; Life Technologies), 0.3 mg ml21 gluta-mine and 10% fetal calf serum (complete medium). Plat-E cells[32] were maintained in complete medium containing blasticidin(10 mg ml21) and puromycin (1 mg ml21).

4.4. Retrovirus-mediated gene transductionNFkB-inducible IkB and AcGFP1-RelA constructs were trans-fected into Plat-E packaging cells pre-conditioned in antibiotic-free complete medium using poly(ethylenimine). Supernatantwas collected 48 h post-transfection, filtered and used to infecttarget cells with 4 mg ml21 polybrene to enhance infection effi-ciency (Sigma). Infected cells were selected with puromycinhydrochloride (Sigma) for IkBs and/or with hygromycin B (Invi-voGen) for the AcGFP1-RelA. Murine TNF (Roche) was used at 1or 10 ng ml21.

4.5. Biochemical analysesWhole-cell extracts were prepared in radioimmunoprecipitationassay buffer with protease inhibitors and normalized for totalprotein before immunoblot analyses. Cytoplasmic and nuclearextracts for immunoblot analyses and EMSA, respectively, wereprepared as previously described [4,24]. IkBa was probed withsc-371, IkBb with sc-945 and a-tubulin with sc-5286. Allantibodies were from Santa Cruz Biotechnology.

4.6. MicroscopyCells were plated onto 35 mm glass bottom dishes (MatTek) oriBidi eight-well chambers (iBidi) 24 h prior to stimulation andimmediate imaging. Images were acquired on an Axio ObserverZ1 inverted microscope (Carl Zeiss Microscopy GmbH,Germany) with a 40�, 1.3 NA oil-immersion, or 20�, 0.8 NAair-immersion objective to a Coolsnap HQ2 CCD camera (Photo-metrics, Canada) using ZEN imaging software (Carl ZeissMicroscopy GmbH, Germany). Environmental conditions weremaintained in a humidified chamber at 378C, 5% CO2 (Pecon,Germany). Quantitative image processing was performed usingthe FIJI distribution of IMAGE J (NIH). All cells of each frame inthe microscope imaging experiments were measured for totalfluorescence intensity. Time-course data were normalized bythe minimum and maximum values to account for the varyingoverall intensities of different cells. The single-cell traces wereaveraged and error bars in the mean curves are the standarddeviation from the mean.

Authors’ contributions. R.F. performed the experimental work, assisted byK.T.F., Y.E.L. and J.D.V. M.B. performed the computational model-ling. R.F., J.D.V. and A.H. wrote the manuscript.Competing interests. We have no competing interests.Funding. The work was supported by grants to A.H. from the NIH: R01GM071573 and P01 GM071862. R.F. was a Sigrid Juselius Foundationand Saatioiden postdoctoral fellow and M.B. was a Cancer ResearchInstitute postdoctoral fellow.Acknowledgements. We thank Bingbing Jiang (Boston University) for thegenerous gift of AKBI MEFs and acknowledge Santa Cruz Biotech-nology for their support.

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References

rsif.royalsocietypublishing.orgJ.R.Soc.Interface

12:20150262

1. Alon U. 2007 An introduction to systems biology:design principles of biological circuits. Boca Raton,FL: Chapman and Hall/CRC.

2. Scott ML, Fujita T, Liou HC, Nolan GP, Baltimore D.1993 The p65 subunit of NF-kappa B regulates Ikappa B by two distinct mechanisms. Genes Dev. 7,1266 – 1276. (doi:10.1101/gad.7.7a.1266)

3. Chiao PJ, Miyamoto S, Verma IM. 1994 Autoregulationof I kappa B alpha activity. Proc. Natl Acad. Sci. USA 91,28 – 32. (doi:10.1073/pnas.91.1.28)

4. Hoffmann A, Levchenko A, Scott ML, Baltimore D.2002 The IkappaB-NF-kappaB signaling module:temporal control and selective gene activation.Science 298, 1241 – 1245. (doi:10.1126/science.1071914)

5. Hoffmann A, Baltimore D. 2006 Circuitry of nuclearfactor kappaB signaling. Immunol. Rev. 210,171 – 186. (doi:10.1111/j.0105-2896.2006.00375.x)

6. Shih VF, Kearns JD, Basak S, Savinova OV, Ghosh G,Hoffmann A. 2009 Kinetic control of negativefeedback regulators of NF-kappaB/RelA determinestheir pathogen- and cytokine-receptor signalingspecificity. Proc. Natl Acad. Sci. USA 106, 9619 – 9624.(doi:10.1073/pnas.0812367106)

7. Nelson DE et al. 2004 Oscillations in NF-kappaBsignaling control the dynamics of gene expression.Science 306, 704 – 708. (doi:10.1126/science.1099962)

8. O’Dea E, Hoffmann A. 2010 The regulatory logic ofthe NF-kappaB signaling system. Cold Spring Harb.Perspect. Biol. 2, a000216. (doi:10.1101/cshperspect.a000216)

9. Basak S, Behar M, Hoffmann A. 2012 Lessons frommathematically modeling the NF-kappaB pathway.Immunol. Rev. 246, 221 – 238. (doi:10.1111/j.1600-065X.2011.01092.x)

10. Krishna S, Jensen MH, Sneppen K. 2006 Minimalmodel of spiky oscillations in NF-kappaB signaling.Proc. Natl Acad. Sci. USA 103, 10 840 – 10 845.

11. Hayot F, Jayaprakash C. 2006 NF-kappaB oscillationsand cell-to-cell variability. J. Theor. Biol. 240,583 – 591. (doi:10.1016/j.jtbi.2005.10.018)

12. Mothes J, Busse D, Kofahl B, Wolf J. 2015 Sourcesof dynamic variability in NF-kappaB signaltransduction: a mechanistic model. BioEssays 37,452 – 462. (doi:10.1002/bies.201400113)

13. Werner SL, Barken D, Hoffmann A. 2005 Stimulusspecificity of gene expression programs determined

by temporal control of IKK activity. Science 309,1857 – 1861. (doi:10.1126/science.1113319)

14. Behar M, Hoffmann A. 2010 Understanding thetemporal codes of intra-cellular signals. Curr. Opin.Genet. Dev. 20, 684 – 693. (doi:10.1016/j.gde.2010.09.007)

15. Behar M, Barken D, Werner SL, Hoffmann A. 2013The dynamics of signaling as a pharmacologicaltarget. Cell 155, 448 – 461. (doi:10.1016/j.cell.2013.09.018)

16. Werner SL, Kearns JD, Zadorozhnaya V, Lynch C, O’DeaE, Boldin MP, Ma A, Baltimore D, Hoffmann A. 2008Encoding NF-kappaB temporal control in responseto TNF: distinct roles for the negative regulatorsIkappaBalpha and A20. Genes Dev. 22, 2093 – 2101.(doi:10.1101/gad.1680708)

17. Kearns JD, Basak S, Werner SL, Huang CS, HoffmannA. 2006 IkappaBepsilon provides negative feedbackto control NF-kappaB oscillations, signalingdynamics, inflammatory gene expression. J. CellBiol. 173, 659 – 664. (doi:10.1083/jcb.200510155)

18. Cheng JD, Ryseck RP, Attar RM, Dambach D, BravoR. 1998 Functional redundancy of the nuclear factorkappa B inhibitors I kappa B alpha and I kappa Bbeta. J. Exp. Med. 188, 1055 – 1062. (doi:10.1084/jem.188.6.1055)

19. Sachdev S, Bagchi S, Zhang DD, Mings AC, HanninkM. 2000 Nuclear import of IkappaBalpha isaccomplished by a ran-independent transportpathway. Mol. Cell Biol. 20, 1571 – 1582. (doi:10.1128/MCB.20.5.1571-1582.2000)

20. Sachdev S, Hoffmann A, Hannink M. 1998 Nuclearlocalization of IkappaB alpha is mediated by thesecond ankyrin repeat: the IkappaB alpha ankyrinrepeats define a novel class of cis-acting nuclearimport sequences. Mol. Cell Biol. 18, 2524 – 2534.

21. Huang TT, Kudo N, Yoshida M, Miyamoto S. 2000 Anuclear export signal in the N-terminal regulatorydomain of IkappaBalpha controls cytoplasmiclocalization of inactive NF-kappaB/IkappaBalphacomplexes. Proc. Natl Acad. Sci. USA 97,1014 – 1019. (doi:10.1073/pnas.97.3.1014)

22. Huang TT, Miyamoto S. 2001 Postrepressionactivation of NF-kappaB requires the amino-terminal nuclear export signal specific toIkappaBalpha. Mol. Cell Biol. 21, 4737 – 4747.(doi:10.1128/MCB.21.14.4737-4747.2001)

23. Mathes E, O’Dea EL, Hoffmann A, Ghosh G. 2008NF-kappaB dictates the degradation pathway ofIkappaBalpha. EMBO J. 27, 1357 – 1367. (doi:10.1038/emboj.2008.73)

24. O’Dea EL, Kearns JD, Hoffmann A. 2008 UV as anamplifier rather than inducer of NF-kappaB activity.Mol. Cell 30, 632 – 641. (doi:10.1016/j.molcel.2008.03.017)

25. Chen Y, Wu J, Ghosh G. 2003 KappaB-Ras binds tothe unique insert within the ankyrin repeat domainof IkappaBbeta and regulates cytoplasmic retentionof IkappaBbeta�NF-kappaB complexes. J. Biol.Chem. 278, 23 101 – 23 106. (doi:10.1074/jbc.M301021200)

26. Malek S, Chen Y, Huxford T, Ghosh G. 2001IkappaBbeta, but not IkappaBalpha, functionsas a classical cytoplasmic inhibitor of NF-kappaBdimers by masking both NF-kappaB nuclearlocalization sequences in resting cells. J. Biol.Chem. 276, 45 225 – 45 235. (doi:10.1074/jbc.M105865200)

27. Bergqvist S, Alverdi V, Mengel B, Hoffmann A,Ghosh G, Komives EA. 2009 Kinetic enhancement ofNF-kappaBxDNA dissociation by IkappaBalpha. Proc.Natl Acad. Sci. USA 106, 19 328 – 19 333.

28. Tsui R, Kearns JD, Lynch C, Vu D, Ngo KA, Basak S,Ghosh G, Hoffmann A. 2015 IkappaBbeta enhancesthe generation of the low-affinity NFkappaB/RelAhomodimer. Nat. Commun. 6, 7068. (doi:10.1038/ncomms8068)

29. Nguyen LK, Kulasiri D. 2009 On the functionaldiversity of dynamical behaviour in genetic andmetabolic feedback systems. BMC Syst. Biol. 3, 51.(doi:10.1186/1752-0509-3-51)

30. Nguyen LK. 2012 Regulation of oscillation dynamicsin biochemical systems with dual negative feedbackloops. J. R. Soc. Interface 9, 1998 – 2010. (doi:10.1098/rsif.2012.0028)

31. Mukherjee SP, Behar M, Birnbaum HA, Hoffmann A,Wright PE, Ghosh G. 2013 Analysis of the RelA:CBP/p300 interaction reveals its involvement inNF-kappaB-driven transcription. PLoS Biol. 11,e1001647. (doi:10.1371/journal.pbio.1001647)

32. Morita S, Kojima T, Kitamura T. 2000 Plat-E: anefficient and stable system for transient packagingof retroviruses. Gene Ther. 7, 1063 – 1066. (doi:10.1038/sj.gt.3301206)

http://dx.doi.org/10.1101/gad.7.7a.1266http://dx.doi.org/10.1073/pnas.91.1.28http://dx.doi.org/10.1126/science.1071914http://dx.doi.org/10.1126/science.1071914http://dx.doi.org/10.1111/j.0105-2896.2006.00375.xhttp://dx.doi.org/10.1073/pnas.0812367106http://dx.doi.org/10.1126/science.1099962http://dx.doi.org/10.1101/cshperspect.a000216http://dx.doi.org/10.1101/cshperspect.a000216http://dx.doi.org/10.1111/j.1600-065X.2011.01092.xhttp://dx.doi.org/10.1111/j.1600-065X.2011.01092.xhttp://dx.doi.org/10.1016/j.jtbi.2005.10.018http://dx.doi.org/10.1002/bies.201400113http://dx.doi.org/10.1126/science.1113319http://dx.doi.org/10.1016/j.gde.2010.09.007http://dx.doi.org/10.1016/j.gde.2010.09.007http://dx.doi.org/10.1016/j.cell.2013.09.018http://dx.doi.org/10.1016/j.cell.2013.09.018http://dx.doi.org/10.1101/gad.1680708http://dx.doi.org/10.1083/jcb.200510155http://dx.doi.org/10.1084/jem.188.6.1055http://dx.doi.org/10.1084/jem.188.6.1055http://dx.doi.org/10.1128/MCB.20.5.1571-1582.2000http://dx.doi.org/10.1128/MCB.20.5.1571-1582.2000http://dx.doi.org/10.1073/pnas.97.3.1014http://dx.doi.org/10.1128/MCB.21.14.4737-4747.2001http://dx.doi.org/10.1038/emboj.2008.73http://dx.doi.org/10.1038/emboj.2008.73http://dx.doi.org/10.1016/j.molcel.2008.03.017http://dx.doi.org/10.1016/j.molcel.2008.03.017http://dx.doi.org/10.1074/jbc.M301021200http://dx.doi.org/10.1074/jbc.M301021200http://dx.doi.org/10.1074/jbc.M105865200http://dx.doi.org/10.1074/jbc.M105865200http://dx.doi.org/10.1038/ncomms8068http://dx.doi.org/10.1038/ncomms8068http://dx.doi.org/10.1186/1752-0509-3-51http://dx.doi.org/10.1098/rsif.2012.0028http://dx.doi.org/10.1098/rsif.2012.0028http://dx.doi.org/10.1371/journal.pbio.1001647http://dx.doi.org/10.1038/sj.gt.3301206http://dx.doi.org/10.1038/sj.gt.3301206

Anatomy of a negative feedback loop: the case of I[kappa]B[alpha]IntroductionResultsNF[kappa]B-responsive transcriptional control is necessary but not sufficient for I[kappa]B[alpha] negative feedbackMathematical modelling identifies multiple molecular properties of I[kappa]B[alpha] contributing to the negative feedback control of NF[kappa]BExperimental testing of model predictions: multiple I[kappa]B[alpha] properties contribute distinct characteristics to NF[kappa]B dynamic control

DiscussionMaterial and methodsComputational modellingDNA constructsCells and cell cultureRetrovirus-mediated gene transductionBiochemical analysesMicroscopyAuthors’ contributionsCompeting interestsFunding

AcknowledgementsReferences