Understanding NF-jB Signaling Via Mathematical Modeling

Molecular Systems Biology 4; Article number 192; doi:10.1038/msb.2008.30Citation: Molecular Systems Biology 4:192& 2008 EMBO and Nature Publishing Group All rights reserved TIVEUnderstanding NF-jB signaling via mathematicalmodelingRaymond Cheong1, Alexander Hoffmann2and Andre Levchenko1,*1Department of Biomedical Engineering, Johns Hopkins University, Baltimore,MD, USA and2Signaling Systems Laboratory, Department of Chemistry and Biochemistry,University of California, San Diego, La Jolla, CA, USA* Corresponding author. Department of Biomedical Engineering, Johns HopkinsUniversity, 208C Clark Hall, 3400 N Charles St, Baltimore, MD 21208, USA.Tel.: þ 1 410 516 5584; Fax: þ 1 410 516 6240; E-mail: alev@jhu.eduReceived 8.1.08; accepted 1.4.08Mammalian inflammatory signaling, for which NF-jB is aprincipal transcription factor, is an exquisite example ofhow cellular signaling pathways can be regulated toproduce different yet specific responses to different inflammatory insults. Mathematical models, tightly linked toexperiment, have been instrumental in unraveling theforms of regulation in NF-jB signaling and their underlyingmolecular mechanisms. Our initial model of the IjB–NF-jBsignaling module highlighted the role of negative feedbackin the control of NF-jB temporal dynamics and geneexpression. Subsequent studies sparked by this workhave helped to characterize additional feedback loops, theinput–output behavior of the module, crosstalk betweenmultiple NF-jB-activating pathways, and NF-jB oscillations. We anticipate that computational techniques willenable further progress in the NF-jB field, and the signaltransduction field in general, and we discuss potentialupcoming developments.Molecular Systems Biology 6 May 2008;doi:10.1038/msb.2008.30Subject Categories: simulation and data analysis; signal transductionKeywords: NF-kB; signal transduction; systems biologyThis is an open-access article distributed under the terms of theCreative Commons Attribution Licence, which permitsdistribution and reproduction in any medium, provided theoriginal author and source are credited. Creation of derivativeworks is permitted but the resulting work may be distributed onlyunder the same orsimilar licence to this one. This licence does notpermit commercial exploitation without specific permission.IntroductionThe transcription factor NF-kB is a central inflammatorymediator, as it is essential for the majority of gene inductionevents in response to inflammatory cytokines as well aspathogen-derived substances. In unstimulated cells, NF-kB isbound to IkB proteins which hold it latent in the cytoplasm.Cellular stimulation with inflammatory agents results in& 2008 EMBO and Nature Publishing GroupIKK-mediated phosphorylation of IkB proteins, their ubiquitination, and proteasome-mediated proteolysis, allowing freeNF-kB to accumulate in the nucleus and bind the cognate kBelements in target gene promoters (Box 1; reviewed in Haydenand Ghosh, 2008). Regulation of NF-kB is important for thephysiology of inflammation and immune activation, andmisregulation of NF-kB activity has been identified as a majorculprit of chronic inflammatory diseases and cancer. As suchunderstanding NF-kB regulation has been a major focus ofbiochemical, mouse genetic, and human disease studiessince its discovery more than 20 years ago (Sen andBaltimore, 1986).Major components of many signaling pathways that activateNF-kB have been mapped, and this information is oftensummarized in pathway diagrams (e.g. Box 1). However, thedynamics of molecular level regulation are insufficientlycaptured by the static representation inherent in suchdiagrams. Mathematical models, on the other hand, canquantitatively describe how changes in signaling occur inspace and time, enabling exploration of signaling pathways insilico (Box 2). The resulting insights can provide a theoreticalframework and generate testable predictions for subsequentexperimental studies. Experimental results likewise inform thedevelopment and refinement of mathematical models withpredictive power. In this way, our understanding of cellsignaling processes can be progressively advanced (Kearnsand Hoffmann, 2008).Here, we review how mathematical modeling has impactedour understanding of signaling through NF-kB pathways. First,we summarize our original mathematical model, which is thepredecessor of many models used to study the regulation ofNF-kB dynamics (Table I). Then, we describe how mathematical and computational models have been instrumental inincreasing our understanding of the control of NF-kB signaling. We also discuss the emerging areas of research in whichmathematical models may shed light.The original mathematical modelof the IjB–NF-jB signaling moduleNF-kB activation involves stimulus-induced degradation of itsinhibitor IkB, which allows for its translocation to the nucleus.The earliest attempt to capture the dynamics of these events inmathematical equations was aimed at understanding howNF-kB translocation and IkB association/dissociation rateconstants keep the majority of NF-kB in an inactive state inresting cells (Carlotti et al, 2000). However, this work did notresult in a model that allowed for computational simulations ofthe full NF-kB activation and attenuation process.Our interest was to understand the differential functions, ifany, of the three IkB isoforms (IkBa, IkBb, and IkBe) thatmodulate inflammatory activation of NF-kB. BiochemicalMolecular Systems Biology 2008 1

Understanding NF-kB signaling via mathematical modelingR Cheong et alBox 1 Primer on TNFa signaling to NF-kBUpon binding of TNFa (1), TNF receptor (TNFR) is activated, leadingto activation of the IkB kinase (IKK) (2). IKK dually phosphorylates inhibitorof NF-kB (IkB) (3), which in a basal state holds NF-kB latent in thecytoplasm. Phosphorylated IkB is targeted for ubiquitination (4) andsubsequently proteosome-mediated degradation (5). NF-kB, no longerbound to IkB, enters the nucleus (6) where it may modulate genetranscription. The genes for IkB are among the genes that are upregulatedby NF-kB (7). Newly synthesized IkBenters the nucleus, binds to NF-kB,and promotes its export to the cytoplasm (8), thereby forming a negativefeedback loop that terminates the response. New IkB–NF-kB complexesmay enter the feedback loop, beginning with phosphorylation by IKK, ifTNF stimulation persists (9). There are three typical isoforms of IkB: IkBa,IkBb, and IkBe. As discussed in the main text, expression of IkBa isrobustly induced by NF-kB and was a focus of initial modeling studies ofthe pathway, whereas NF-kB-induced expression of IkBb and IkBe was atopic of later investigations.studies had shown that all three sequester p65–p50, thepredominant NF-kB dimer, are degraded in response tostimulation with tumor necrosis factor alpha (TNFa) (Ghoshet al, 1998). Nevertheless, mice deficient in any one of thesethree IkB proteins have distinct phenotypes, indicating that theIkBs have different and non-overlapping functions (Beg et al,1995; Klement et al, 1996; Memet et al, 1999; Mizgerd et al,2002). As time-course data, derived from electrophoreticmobility shift assays (EMSAs), indicated that the three IkBproteins had differential dynamic control, we set out toconstruct a mathematical model of NF-kB signaling to studythe specific roles of each IkB isoform in regulating the temporalcontrol of NF-kB (Hoffmann et al, 2002).We defined the scope of the model to be that of the IkB–NFkB signaling module, in which the IKK activity as an input tothe model determines the NF-kB activity over time. The modelconsisted of a system of differential equations based onmass action kinetics of the association/dissociation,synthesis/degradation, and translocation of IKK, IkB, andNF-kB species. Of the 34 independent model parameters,about one-third were derived from the extensive biochemicalliterature on NF-kB, especially for the parameters of theMichaelis–Menten reactions of IKK-mediated IkB phosphorylation. A further third, especially those parameters relatingto species half-lives, transport rates, and IkB–NF-kBaffinities, was constrained by published time-course data.We used a genetic approach to reduce the complexity of thesignaling module to obtain the data used to fit the remaining2 Molecular Systems Biology 2008parameters (primarily mRNA and protein synthesis).By mouse reverse genetics, we obtained cells deficientin any two of the three IkB isoforms, thereby enabling us toparameter fit three reduced models each containing only oneIkB isoform that were then combined into a wild-typecell model.Exploration of the model with computational simulationsresulted in two major insights. First, it described howdifferential functions of the IkB isoforms could give rise tostrikingly different NF-kB dynamics in genetically reducedcells. The role of IkBa, whose expression is induced by NF-kB,was to provide negative feedback. This was aptly demonstrated by pronounced oscillations in NF-kB activity in cellslacking the other isoforms (Figure 1A). The role of IkBb andIkBe was to dampen these oscillations. When all threeisoforms were present, the NF-kB response was biphasic, withan initial NF-kB activity rising and falling within B1 h,followed by a late activation phase characterized by a steadyintermediate level of activity (Figure 1B). Second, we exploredthe ‘temporal dose–response’ characteristics of the NF-kBsignaling module by simulating the NF-kB response durationfor different stimulus durations. The model predicted that themodule would generate the initial phase of 60 min of NF-kBactivity even with much shorter stimuli, while only for longerlasting stimuli (41 h) did the responses have durationsproportional to the input duration. This predictionwas confirmed by using EMSA on wild-type cells. Moreover,we found experimentally that the initial phase of NF-kBactivity is sufficient to drive the expression of a subsetof inflammatory genes, while others require longer lastingNF-kB activity. Hence, the functions of IkBa, IkBb, and IkBecombine to allow the signaling module to distinguish betweenshort and longer lasting stimuli. A subsequent study of geneexpression in single cells also found that some targetgenes require longer lasting TNFa stimulation than others(Nelson et al, 2004).Two of the more significant advances provided by our studywere that temporal dynamics of NF-kB help control theexpression of inflammatory genes, and that mathematicalmodeling could be extremely useful in understanding themolecular mechanisms that regulate NF-kB dynamics. Thisspurred a number of subsequent modeling studies designedto further understand the regulation of NF-kB dynamics, whichwe review below. Some of these studies were primarilytheoretical in nature and pointed to interesting potentialdynamical properties of NF-kB signaling, whereas in others,modeling was tightly integrated with experiment leading to aplethora of unexpected insights into the mechanisms that controlNF-kB dynamics.Mechanisms that control NF-jB dynamicsrevealed by mathematical modelsIn this section, we highlight how mathematical and computational models have been applied with impressive success todirect or illuminate experimental studies to characterizeadditional feedback loops involving NF-kB, IKK dynamics,crosstalk between inflammatory and non-inflammatoryinducers of NF-kB activity, and NF-kB oscillations.& 2008 EMBO and Nature Publishing Group