TRANSIENT IKK ACTIVITY MEDIATES NF- κ B TEMPORAL DYNAMICS IN RESPONSE TO A WIDE RANGE OF TNF α DOSES

Dynamic properties of signaling control function.

cytoplasm; phosphorylated IκBs are rapidly polyubiquitinated and proteasomally degraded, releasing free NF-κB which translocates to the nucleus and modulates gene expression (2).
Detailed biochemical and genetic analysis over the past 25 years have helped elucidate the components that connect TNFα to NF-κB. However, relatively little is known about how these molecular players act together as a signaling system, whose complex dynamics control time variable activity of NF-κB and subsequent gene expression (3)(4)(5)(6). Recently, it has become apparent that analysis of the systems properties of complex biochemical pathways can benefit from an integrated approach combining systematic experimental perturbations with associated computational analysis of molecular interactions (7)(8)(9)(10)(11)(12)(13). This type of analysis applied to TNFαinduced NF-κB activity demonstrated that the α, β, and ε isoforms of IκB cooperate to produce a biphasic NF-κB response (5). Varying the duration of the TNFα stimulus had no effect on the duration of the initial response, thus ensuring expression of some NF-κB-regulated genes even in response to very short stimuli (5). This analysis, however, did not address the question of how other types of signaling inputs are processed.
In this study, we analyze in detail a different type of inputs -constant stimulations at different TNFα doses -and experimentally and computationally analyze the resulting pathway characteristics. Surprisingly, we find that both the duration and dose of TNFα stimulus have little effect on the duration of the initial NF-κB response and that NF-κB responds sensitively to extremely wide range of TNFα concentrations. Analysis of a computational model of the pathway predicts that these signal transduction properties are crucially dependent on a transient nature of IKK activity. The experimental confirmation of this prediction underscores the importance of the mechanisms rapidly downregulating IKK following its activation. Based on further model analysis, we suggest that the observed dynamic properties of IKK activity are well-suited to offset limitations imposed by ligand diffusion, thereby ensuring robust TNFα-induced NF-κB activity in cells of infected tissues.

MATERIALS AND METHODS
Cell Lines and Tissue Culture --Immortalized 3T3 mouse embryonic fibroblasts (MEFs) were grown in DMEM with 10% bovine calf serum. Confluent, serum-starved (0.5% serum) cells were stimulated with murine TNFα (Roche). In the experiments shown in Fig. 3B, cells were pretreated with 10µg/ml cycloheximide (CHX; Sigma Chemicals) for 30 min prior to TNFα stimulation.

Electrophoretic Mobility Shift Assay (EMSA) --
After TNFα stimulation, cells were washed with ice cold Phosphate Buffered Saline (PBS) + 1mM EDTA, and were scraped and collected into a microcentrifuge tube and pelleted at 2000x g. Cells (about 10 6 ) were resuspended in 100µL CE Buffer [10mM HEPES-KOH (pH 7.9), 60mM KCl, 1mM EDTA, 0.5% NP-40, 1mM DTT, 1mM PMSF], and vortexed for lysis. Nuclei were pelleted at 4000x g, resuspended in 30µL NE Buffer [250mM Tris (pH 7.8), 60mM KCl, 1mM EDTA, 1mM DTT, 1mM PMSF], and lysed by 3 freeze-thaw cycles. Nuclear lysates were cleared by 14000x g centrifugation and the Bradford assay was used to determine protein concentrations, which rarely varied by more than 30% from sample to sample. Protein concentrations were normalized by diluting the more concentrated samples in NE buffer. 2.5µL of these samples was reacted at room temperature for 15 minutes with 0.01 pmol of 32 P-labeled 38bp double-stranded oligonucleotide containing two consensus κB sites: (GCTACAAGGGACTTTCCGCTGGGGACTT TCCAGGGAGG) in binding buffer [10mM Tris-Cl (pH 7.5), 50mM NaCl, 10% glycerol, 1% NP-40, 1mM EDTA, 0.1µg/µL polydIdC], for a total reaction volume of 6 µL. Complexes were resolved on a non-denaturing 5% acrylamide (30:0.8) gel containing 5% glycerol and 1X TGE [24.8mM Tris, 190mM glycine, 1mM EDTA], and were visualized using a Phosphoimager (Molecular Dynamics). The gel images were quantitated by drawing and integrating, for each lane, equally sized boxes around the NF-κBspecific DNA-protein complex, around the background above it, and around the unbound probe. The unbound probe was at >20 fold excess and was used as a loading control by taking the value of the signal minus the background then dividing by the unbound probe value. The resulting specific EMSA signal was multiplied by 1000 or some constant to provide convenient arbitrary units. For input reconstruction, we assumed an activation rate of the form shown in Eq. 1 and a constant inactivation rate. We also assumed that changes in TNFα concentration uniformly and directly affect the activation rate function. The parameter space was exhaustively sampled within biochemically plausible ranges (10 -3 ≤ k init ≤ 10 -1 µM/min, 10 0.25 ≤ k init /k final ≤ 10 2 , 5 ≤ τ ≤ 30 min., 10 -2 ≤ k inact ≤ 10 1 min -1 ) and results were filtered for resemblance to  (16,17). The parameter k = 0.0275 min -1 , corresponding to a half life of 25 min, and represents loss of TNFα due to degradation and adherence to extracellular matrix proteins. TNFα secretion was modeled as a spherically symmetric flux of TNFα from a sphere of radius 10 µm, with the flux magnitude set so that the concentration at the source surface was about 10 ng/mL. With respect to time, TNFα secretion was modeled as a rectangular pulse of 10 minute duration. Finally, we imposed the boundary condition that C 0 as |r| ∞. The simulation was performed in Femlab 3.1 (Comsol, Burlington, MA). Simulations were run for different values of D, k, pulse length, and flux magnitude, which did not qualitatively affect any of the conclusions reported in the body of the paper. See Section 3 of the Supplementary Information for extrapolation of the IKK response to arbitrary TNFα time-courses.

NF-κB is sensitive to a wide range of TNFα concentrations --
To investigate the response of NF-κB to different TNFα doses, we exposed murine embryonic fibroblasts (MEFs) to TNFα over a concentration range spanning three orders of magnitude (0.01-10 ng/mL). NF-κB in these experiments was found to respond robustly and sensitively throughout this range, including the lowest dose of TNFα, as measured by EMSA (Figs. 1A,B). This experiment, in which the duration of TNFα stimulation is held fixed (chronic) while altering the amplitude, complements our previous work in which the amplitude of TNFα was held fixed (10 ng/mL) while the duration was altered (5). Remarkably, in both cases, cells show a stereotypical response of an initial peak of NF-κB activity lasting 60-75 minutes (Figs. 1A,B). These results show that the NF-κB pathway is sensitive to a wide range of TNFα concentrations, which may help ensure a response to local TNFα signals in innate immune response (see below).

Transient IKK activity generates observed dynamics in the computational model --
To investigate the molecular basis underlying the robust dynamics of NF-κB activation, we attempted to recapitulate the dose response in our computational model of the NF-κB pathway. The model included detailed interactions between IKK, IκB, and NF-κB, and reflecting contemporary uncertainty about the mechanisms of IKK regulation (18), assumed an exponential decay curve for IKK during chronic TNFα stimulation. The model was previously validated for TNFα doses of 10 ng/mL, so to simulate lower TNFα concentrations we decreased the initial level of IKK. However, our simulation results did not adequately fit the measured responses as even a ten-fold reduction in IKK greatly delayed the onset of predicted NF-κB activity ( Fig. 2A), suggesting that the model requires modification to recapitulate the experiment.
As a control, we first addressed whether the discrepancy between model prediction and experiment is due to a simple mis-estimation of rate constants described by the parameters in the model. Out of 10,000 parameter sets generated by random sampling within ± 2 orders of the nominal values, none fit the dose response while maintaining previously validated properties of the model (5). Sampling parameters in a way biased toward producing a fit, such as with evolutionary algorithms (19), also generated no fits. The results obtained by these naïve sampling methods were then confirmed by rational analysis of the model. Systematic dissection of how parameters influence key conserved features of the NF-κB temporal profile (peak timing and amplitude) revealed two independent effects neither of which could be employed to reconcile the model and experiment without sacrificing previously validated properties of the model (see Supplementary Information, Section 1). This rules out simple mis-estimation in parameter values as the source of discrepancy and suggests that the model should be extended to more fully describe the signaling pathway (20).
Since the model has successfully recapitulated several dynamic properties of the pathway (5), we surmised that the core model is essentially correct but that interactions with external components should be re-evaluated. One such component is the dynamic profile of IKK activity in response to TNFα stimulation, which serves as input for the core model of the IκB-NF-κB signaling module (Fig. 2B). Thus we used the computational model to identify the temporal profiles of IKK activity that produce the observed NF-κB dynamics, essentially reverse-engineering the input from the known output.
In order to screen for IKK profiles that could produce the NF-κB response, we created a generator of IKK temporal profiles and linked the generator to the model. This is shown schematically in Fig. 2B. Active IKK is generated through new protein synthesis or by activation from an inactive state according to some timevarying activation rate, then removed by protein degradation or inactivation according to some time-varying inactivation rate (Fig. 2B, gray box). One or both of these steps may be dependent on TNF receptor activation by TNFα. Additionally, IKK provides input into the core model (Fig. 2B, yellow box) by interacting with IκB, whose negative feedback to NF-κB is the central feature of the core model.
With the IKK profile generator written in this general form, our task is to identify activation and inactivation rate functions that produce the observed NF-κB dynamics. When both functions are temporally constant, no pair of rates can reproduce the response to high TNFα (Fig. 2C), suggesting that the regulation of IKK activity is nonlinear. To understand the nature of this nonlinearity, we examined the distribution of constant rates for which either the peak (Fig. 2C, dark gray) or the trough fit (Fig. 2C, light gray). Since all TNFα doses produce NF-κB temporal profiles that contain a peak between 15 and 45 min. followed by a trough between 60 and 90 min. (Fig.  1B), we concluded that the IKK activation rate may begin in the regime where the peak fits then decrease in time to the regime where the trough fits (as if to follow the arrow in Fig. 2C).
To test this possibility, we assumed a simple functional form (Eq. 1) for an activation rate that decreases exponentially from a high initial value (k init ) to low final value (k final ) in about time τ, while holding the inactivation rate (k inact ) constant.
This functional form, combined with a simple method for representing different TNFα concentrations (see Materials and Methods), allowed us to fully specify the IKK profile in response to a range of TNFα with only 4 parameters. An exhaustive grid-based search of the parameter space (see Supplementary  Information, Section 2) uncovered exactly 1 parameter set out of 5,615 tested that reproduces the response to different TNFα concentrations while maintaining previously validated properties of the model, suggesting that the observed output can only be produced by a very specific IKK activity profile. The activation rate functions thus identified (Fig. 2D) produce transient IKK activity at all TNFα doses (Fig. 2E), and result in NF-κB profiles (Fig. 2F) whose initial duration is fixed but amplitude varies with TNFα concentration, as desired. Thus, the model strongly suggests that the IKK activity profile has to be transient at all TNFα doses.

Predicted transient IKK activity profile is verified experimentally --
The model-based reconstruction of IKK activity gives rise to an experimentallytestable prediction: in response to a wide range of TNFα concentrations, IKK activity should peak at around 10 minutes and decrease over the next 20 minutes to a low level above basal activity (Fig.  2E). To further gauge the strength of this prediction, we chose other activation and inactivation rate functions in order to systematically test similarly shaped IKK profiles but with different peak timings and peak widths. The results showed that the specific profiles in Fig.  2E gave a near optimal fit with the experimentally by guest on March 24, 2020 http://www.jbc.org/ Downloaded from measured NF-κB time courses (data not shown). Therefore, the dynamics of IKK activity are highly constrained. To validate this prediction, we measured the actual IKK activity in MEFs (Fig.  3A), revealing a very close agreement with the model predictions, especially in terms of the timing of the activation peak. Also, consistent with the idea that the IKK profile is highly constrained, IKK profiles display similar shape and timing when measured in multiple other cell types at 10 ng/mL TNFα or higher (21)(22)(23)(24)(25)(26), though the significance of these IKK kinetics was not previously interpreted. The unexpected insight provided by our model-validated experimentally-is that a rapid decrease in IKK activity is required to explain the dependence of the amplitude, duration and timing of the initial peak of NF-κB activity in response to a wide range of TNFα concentrations.
Given the requirement for fast IKK downregulation in eliciting NF-κB activity in response to TNFα, we considered the question of what biochemical mechanisms could mediate it. The computational model does not strongly constrain the mechanism, because the activation and inactivation rate functions can be coordinately changed (equivalent to different biochemical mechanisms) without changing the overall IKK activity profile, resulting in the same NF-κB dynamics (data not shown). Instead, we considered this question in the context of known IKK inhibitors. One possible mediator of IKK downregulation is A20, an inhibitor of RIP (27), which is transcriptionally upregulated by NF-κB within 30 minutes (6), thus potentially forming a negative feedback loop. We explored if, as previously suggested (15), A20 is essential for the control of dynamics of early IKK and NF-κB activation.
However, IKK activity is downregulated at 30 min. following onset of stimulation even with very low concentrations of TNFα making it unlikely that feedback via A20 is solely responsible for regulating the dynamics of the IKK activity profile. Consistent with this, in cells exposed to cycloheximide, an inhibitor of new protein synthesis, IKK activity is still high at 10 min. and low at 60 min (Fig. 3B). Furthermore, IKK activity in A20-deficient cells still shows a peak at around 10 min. though attenuation at later times is defective (24,28). We also considered that if A20 negative feedback was solely responsible for early downregulation of IKK, it would be difficult to infer IKK activity profiles from the NF-κB activity profile, as feedbacks generally preclude one-to-one input-output mapping. Although NF-κB regulated IKK inhibitors like A20 may play a late role in IKK regulation, our results suggest that early IKK inhibition is likely not mediated by NF-κB upregulation of A20 or similar feedback mechanism. High sensitivity of NF-κB to TNFα may provide robust signaling at a distance --Finally, we attempted to understand the dynamic properties of the pathway in a physiologic context. The primary physiological function of TNFα is to mediate innate immune responses in response to infection (29). The effects of TNFα are local, as enforced by multiple mechanisms. TNFα expression by pathogen-activated macrophages is brief and selflimited, since phagocytosis of pathogens rapidly removes the inciting stimulus, and prolonged exposure to TNFα can both lead to quick apoptosis of TNFα-secreting macrophages (30) and inappropriately induce systemic responses (31,32). Several post-induction repression and autocrine inhibition mechanisms have been described for TNFα expression (33), and both TNFα mRNA and secreted protein have a short half-life (34)(35)(36). At the same time, TNFα's affinity to its receptors is similar to its affinity to extracellular matrix proteins (37) and the molecular weight of TNFα is high (51 kDa as active trimer), impeding diffusion and increasing buffering through non-specific binding. All of these mechanisms serve to limit the effects of TNFα to a local tissue environment.
To model the local spread of TNFα in an infected tissue in a way consistent with the above, we considered the simple scenario in which a TNFα-secreting cell (or cluster of cells) produces a transient pulse of TNFα which then diffuses into the surroundings, where it is subject to degradation and buffering. The real tissue environment is intricate and probably involves the presence of additional cytokines and more complex spatiotemporal patterns of TNFα secretion, but these simplifying assumptions can be viewed as a limiting case designed to investigate if weak TNFα signaling can still be effective. Our simulations show that in this scenario nearby cells would experience a pulse of TNFα whose duration and amplitude both decrease rapidly with distance (Figs. 4A,B, Supplementary Movie S1). We then considered how target cells might respond to such local changes in TNFα concentration by coupling the TNFα diffusion simulation (Fig. 4A) to the NF-κB pathway model (Fig. 2B).
At various distances from the model TNFα source cell (e.g., a macrophage), we determined the local kinetic TNFα profiles due to diffusive spread, related them to the corresponding IKK activities (Supplementary Information, Section 3) and the resulting outputs of the NF-κB pathway. The simulations reveal that the NF-κB response amplitude (Fig. 4C) depends linearly on the distance from the TNFα source, whereas the duration of the response remains approximately constant (Fig. 4D). Furthermore, this qualitative behavior does not depend on the precise concentration or duration of the TNFα pulse (Figs.  4C,D), nor on precise value of diffusivity or degradation rate/buffering strength (not shown). Rather, this signaling behavior is essentially due to the exponential drop of the maximum TNFα concentration with distance (Fig. 4B) coupled with logarithmic variation of the maximum NF-κB activity with TNFα input (Fig. 1B), and the remarkable independence of the duration of the initial NF-κB response on both the duration and the amplitude of the TNFα stimulus.
Importantly, the duration of NF-κB activity remains approximately constant even at distances (~500 µm) where the activity amplitude becomes negligible (Figs. 4C,D). In comparison, the theoretical limit for cell-cell signaling has been estimated to be a few hundred microns (16). Thus, our results suggest that one function of the dynamic properties of the IKK/NF-κB pathway illuminated in this study is to provide a reliable and immediate response to TNFα even at limiting distances in infected tissue.

DISCUSSION
Here we undertook an iterative computational and experimental study of the dynamics of NF-κB in response to different TNFα doses. We present experimental data that shows that NF-κB responds sensitively to TNFα over a concentration range of three orders of magnitude. Interestingly, the duration of the initial response is constant with respect to TNFα dose, a dynamic property without an obvious mechanistic or teleologic explanation.
Computational modeling of NF-κB signaling helped suggest both the mechanistic basis and possible physiological significance of the dynamic properties of the pathway. We found, by reconstructing the input into the IκB-NF-κB module, that one property mechanistically required for the observed NF-κB activity profiles is highly transient IKK activity with a peak at around 10 min. following TNFα stimulation at different doses. Such reverse engineering may be useful in investigating other systems, but it is often difficult due to nonlinearities present in signaling systems and the large number of permissible input functions (38). We overcame these obstacles by starting with a simple linear case and using the results to guide the choice of nonlinear assumptions as well as by keeping the parameter space small to allow for exhaustive testing of all reasonable possibilities. Systematic perturbation of the revised model then indicated that the IKK activity was highly constrained by the observed output and this strong prediction was confirmed by kinase assays of IKKβ activity.
The molecular mechanism for fast inactivation of IKK remains mysterious. It is unlikely that post-induction attenuation of IKK activity is solely dependent on NF-κB-regulated IKK inhibitors like A20. Other IKK inhibitors like PP2Cβ, PP2A, CYLD, hTid-1, and Hsp70 might be involved (25,(39)(40)(41)(42)(43)(44), or regulation of the conformational state of IKKβ via hyperautophosphorylation of its C-terminus can lead to IKK inactivation (22). Importantly, the disruption of the C-terminal sites in IKKβ leads to persistently active IKK upon stimulation (22), suggesting inhibitory autophosphorylation as the major source of fast IKK downregulation. High basal activity of IKK phosphorylation mutants prohibited us from easily testing this mechanism (22), but highlights the need for additional study into the mechanisms of IKK regulation.
The computational model also suggested how the characteristic NF-κB pathway dynamics might facilitate innate immunity in tissues during infection. TNFα may be secreted by a cell or a small cluster of cells (e.g., macrophages) thereby signaling to target cells located nearby. TNFα is a poor signaling agent because it is secreted briefly at low levels and diffuses slowly, but our results paint an intuitively appealing picture of why the local action of TNFα in innate immunity, acting through activation of NF-κB, can be both robust and efficient. TNFα can effectively activate NF-κB for prolonged periods in cells, possibly to ensure efficient triggering of gene transcription, even at near-limiting distances. The spatially graded nature of the response amplitude (Fig. 4E) also may ensure that cells respond commensurate with their distance from the source of danger (45), which could provide an economical result in which every responsive cell is neither excessively nor inadequately stimulated. These dynamic properties, in combination with information provided by other extracellular cues, could help prime and coordinate tissue responses to local infection. As such, IKK regulatory mechanisms may represent sensitive clinical targets in diseases with aberrant innate immune system activity.   Fig. 1B. B, Generalized model input scheme. A generator of IKK profiles was created (gray box) using arbitrary functions f act (t) and f inact (t) to represent the IKK activation and inactivation rates, respectively. The symbol "∅" represents a source or sink for active IKK. The output of this profile generator feeds into the core model, influencing the behavior of the IκB-NF-κB negative feedback loop (yellow box). C, Distribution of fits under a linear model of IKK regulation. The rate functions from B are assumed to be constant, and for each pair of rates tested the corresponding square is colored if the initial peak in NF-κB activity is high and timely (dark gray) or if the trough in NF-κB activity is low and timely (light gray). The regions do not overlap, showing that no pair of constant rates gives a complete fit to experiment, and suggesting that a time-varying rate is needed (arrow). D, Activation rate functions identified by exhaustive screening. Activation rates corresponding to high (red), medium (green), and low (blue) levels of TNFα are shown. E, The IKK and F, NF-κB activity timecourses predicted by the model using the functions in D and an inactivation rate of k inact = 0.1 min -1 . Colors correspond to D.

Fig. 3. Experiment validates prediction of transient IKK activity.
A, Dose response of IKK activity. MEFs were stimulated with TNFα for the indicated time and dose, and kinase activity of immunoprecipitated IKK complex was measured against a GST-IκBα substrate. Bottom panel shows an example control for IKK complex immunoprecipitation efficiency. Timing of transient IKK activity matches the prediction in Fig. 2E. B, IKK activity profile in MEFs following stimulation with 1 ng/mL TNFα for the indicated times in the presence or absence of 10 µg/mL cycloheximide. Immunoprecipitation controls are shown.