TNF-α induced oscillations of endogenous NF-κB are sustained in single cells expressing GFP-tagged p65 knocked into the native locus
To observe real time dynamics, we monitored the localization of NF-κB in single living cells, which are the basic unit for pathway operations and are the definitive context for probing pathway dynamics unambiguously. We used fibroblasts derived from knock-in mice where the endogenous p65 gene was replaced by GFP-p65 () 
. This approach allows live cell imaging of the endogenous p65, without any of the potential problems associated with over-expressed proteins. The protein expression level of GFP-p65 in our knock-in fibroblasts was comparable to that in wild-type fibroblasts (
and data not shown). Activation profiles of p65 target genes in response to TNF-α were also very similar to wild-type cells (
and data not shown). Together with the normal phenotype of the knock-in mice 
, these data indicate that the GFP-p65 is functional and the NF-κB regulatory network is physiological. Since the expression of GFP-p65 was as low as the endogenous level, a microscope with a special optical scanner was necessary to visualize and quantify the GFP signal (see Materials and Methods
, Fig. S1
, Videos S1
(C, center plot in D) shows an example of a time lapse experiment after TNF-α stimulation where we quantify the nuclear:total ratio of GFP-p65. The long-term dynamics of p65 in individual single cells ranged from 1~2 cycles to dramatic oscillations with 6~7 cycles. A minority of cells had a single cycle with subsequent minor and irregular fluctuations (8 oscillating cells and 2 non-oscillators are shown in ). Most cells showed multiple striking peaks; later peaks had gradually decreasing amplitudes but were clearly discernible. Often the p65 flux out of the nucleus between the periodic cycles was so efficient as to reduce the nuclear level to a basal state. We subjected the time course data from 95 cells to Fourier analysis () and found that the majority of the cells (79%) oscillated with a somewhat variable period with a median value of 2.2 hours (n
75, ). Cells that were not treated with TNF-α had no nuclear translocation of p65 as expected ( bottom panel). Although we classified the time courses into two categories by the presence/absence of a strong periodic component, we cannot rule out the possibility that even the ‘non-oscillating’ cells may have weak oscillations which can nevertheless mediate some signaling effect.
Periodic cycles in TNF-α induced NF-κB oscillations are sustained in most cells.
Computer simulations suggest that NF-κB oscillations are selected by fine-tuning network dynamics through the relative strengths of negative feedback loops
To gain systems-level insight on the parameters that influence the observed NF-κB behavior in different cells after TNF-α stimulation, we explored variability and robustness properties of a minimal mathematical model that captures some essential pathway components (see and Supplementary Information, Fig. S2
. Parameter analysis is often done by varying one parameter at a time, fixing all the other parameter values. While computationally manageable, this results in an extremely limited investigation of the system properties 
(). Instead, we employed an extensive multi-parameter sampling approach, where a large set of random parameter combinations was chosen for model simulations. Exploration of a range of possible parameter values is necessary because of the uncertainty in the model parameter values that were inferred or compiled from reported experiments 
. In fact, individual cells are likely to have slightly variable rate constants for each molecular process in the model.
Computer simulations suggest that NF-κB dynamic profiles are mostly controlled by kinetic parameters for negative feedback.
Our computer simulations revealed several possible patterns of response for the NF-κB network after activation (). Distinct patterns were readily identifiable when the K-means clustering algorithm was applied to group similar time courses. Numerous optimizations of K-means with different numbers of clusters indicated that these eight clusters were reproducible and representative. The patterns that closely represent the experimentally observed oscillatory profiles (clusters 5, 7, and 8, ; , left 8 plots) were from parameter values that occupy a significantly broad region in the 18-dimensional parameter space. This implies that oscillation is a robust feature of this network.
Our multi-parameter variation analysis also shows a pattern with non-oscillating, one-peak responses (cluster 2), which is similar to the experimentally observed profile of non-oscillating cells (, right 2 plots). This pattern resulted from parameter values for hyperactive IκBα induction and/or fast IKK inactivation. Thus, with an appropriate choice of feedback parameter values, the NF-κB system could operate in a non-oscillating mode, which may be embodied by the non-oscillating cells. The absence of some computationally predicted scenarios (clusters 1, 3, 4, and 6) from the experimentally observed time course profiles could be partly due to some unrealistic combinations of parameter values in our variation analysis. Alternatively, it might reflect a preference of the NF-κB regulatory network for oscillations, suggestive of functional advantage.
Next we extensively examined the correlation of these distinct responses with the underlying parameter values, and found that 16 out of 18 parameters had no clear influence on system dynamics (Fig. S2E
), while inducible synthesis of IκBα and post-stimulus IKK inactivation are the major processes that determine the kinetic behavior (). Notably, these are precisely the mechanisms that represent the two classes of negative feedback loops in the regulatory network. For example, low IκBα synthesis rate and/or persistent IKK activity explain the aberrant response pattern with no post-stimulus attenuation (cluster 3).
Taken together, observed dynamic patterns and modeling indicate that diverse behaviors, including non-oscillatory responses, are possible from the NF-κB network, and indeed a small fraction of cells do not oscillate. The above multi-parameter variations suggest that the relative strengths of the two classes of negative feedback is a strong determinant of NF-κB dynamics and that the oscillatory behavior represents a robust but selective pattern of the network dynamics. The prevalence of the oscillatory pattern, over other possible behaviors, suggests that it might be chosen for specific function and adaptive value, rather than imposed by the system design and thus inevitable.
LMB or CHX co-treatment with TNF-α produces one cycle of nuclear NF-κB localization
Next we wished to investigate the functional role of NF-κB dynamics by altering the natural oscillations. Some commonly used perturbation methods, however, presented serious problems for our systems approach. For example, siRNA, widely used for specific down-regulation of genes, would be impossible to model at the single cell level because silencing action takes effect over a long time (~hours) with its own kinetics, and cell-to-cell heterogeneity is invariably significant. Similarly, genetically disrupted cells settle into altered steady states long before the experiments by compensatory mechanisms, complicating model-based comparison of mutant behavior to that of wild-type. Thus, we chose to use nearly instantaneous inhibitors that interfere with key steps in the NF-κB network, using Leptomycin B (LMB), an inhibitor of nuclear protein export, and Cycloheximide (CHX), an inhibitor of protein synthesis.
LMB blocks nuclear export of p65 into the cytoplasm, an enabling mechanism behind NF-κB oscillation. When cells are simultaneously treated with TNF-α and LMB, a single pulse of free nuclear NF-κB is expected to be followed by the formation of the NF-κB
IκBα complex in the nucleus. This is also predicted by model simulations (, upper panel; Parameter values were from cluster 5, 7, 8 in , and all export rates were reduced by 105
-fold at t
0; An example decomposition plot for TNF-α alone is shown in Fig. S2C
for comparison). Time lapse imaging confirmed that total nuclear p65 accumulates in the nucleus (, upper panel). The nuclear retention of IκBα-bound inactive NF-κB by LMB matches previous reports well 
Two contrasting perturbations of NF-κB oscillations decouple nucleocytoplasmic shuttling from feedback-driven long-term dynamics.
On the other hand, co-treatment of CHX together with TNF-α inhibits IκBα re-synthesis, a dominant mechanism that drives the system dynamics toward oscillatory regimes. Live imaging showed that CHX constrains p65 in the nucleus for hours, as expected (, lower panel). Nuclear p65 is predicted to be active (free of IκBα) under this condition (, bottom panel; Parameter values were from cluster 5, 7, 8 in , and s was reduced by 100-fold at t
The two contrasting perturbations of NF-κB oscillations reveal reverse nucleus-to-cytoplasm flux
We noticed an unexpected difference between the time lapse imaging data from TNF-α only, TNF-α/LMB co-treated, and TNF-α/CHX co-treated cells: The temporal profiles of nuclear GFP-p65 in cells treated with TNF-α and LMB showed significantly higher peak translocation, in comparison to cells treated with TNF-α alone or with CHX (Fig. S3
). This suggests the existence of the reverse-translocating (nucleus-to-cytoplasm) p65 molecules even during the early activation phase of NF-κB after TNF-α treatment, which had not been appreciated previously. It also implies that the nuclear p65 level at a given moment is simply the net result of the constituent fluxes.
We therefore asked whether p65 molecules may be exported from the nucleus independently of IκB. First, we ran model simulations with the IκBα synthesis rate set to zero (at t
0), and also all nuclear import rates were reduced to zero when nuclear NF-κB level is maximal (at t
90 min). If there was no export, blockade of nuclear import at this time would not have any effect on the nuclear p65 level. The simulation results showed gradual efflux of p65 into the cytoplasm that is appreciable within minutes for a wide range of parameter values (). This was due to the slow export of free NF-κB that was allowed in the mathematical model, which was masked by the dominant IκBα-mediated export during the normal TNF-α induced dynamics (Fig. S2
We then experimentally validated this somewhat neglected possibility by fluorescence loss in photobleaching (FLIP) (). When cells are treated with TNF-α and CHX together, no IκB molecules are present because their re-synthesis is blocked after their TNF-α-dependent degradation. When p65 nuclear translocation was apparently complete (30 to 60 minutes after co-treatment), a cytoplasmic spot was bleached repeatedly. This caused a decrease in nuclear GFP-p65 signal, indicating the presence of p65 export into the cytoplasm. The observed time course is in agreement with the predicted loss of nuclear p65 (), implying that NF-κB continuously exports out to the cytoplasm in an IκBα-independent manner. The retrograde flux of p65 was detectable only when the nuclear p65 level was maximal. When p65 was still accumulating in the nucleus 10 to 25 minutes after TNF-α and CHX, the same FLIP protocol did not produce a reduction in nuclear GFP-p65 level, most likely due to the import flux canceling out the loss by the export flux (Fig. S4
). We note that a putative nuclear export signal within p65 has been reported 
The extent of FLIP in the presence of IκBα (TNF-α alone) was slightly faster than that observed in cells treated with TNF-α and CHX, which suggests that p65 export is indeed enhanced by IκBα (). As a negative control, FLIP was applied to cells co-treated with TNF-α and LMB, which resulted in little or no reduction in nuclear GFP signal (). These data indicate an inherent tendency of NF-κB to shuttle out to the cytoplasm independently of IκB. We also confirmed that IκBα increases p65 export efficiency upon TNF-α stimulation.
Taken together these results demonstrate that the nucleocytoplasmic shuttling of NF-κB is bi-directional and does not require oscillations or IκBα. This implies that NF-κB shuttles continuously, sampling the full intracellular environment, with or without concurrent oscillations in the level of nuclear p65.
The characteristic genome-scanning activity of NF-κB is maintained through sustained oscillation
We predicted that the functional consequences of CHX and LMB perturbations would be extremely different on p65 activity, despite the similar effect on its nuclear localization. LMB would render NF-κB bound to IκBα, thus unable to bind chromatin, whereas CHX would maintain its ability to bind chromatin. To address this experimentally and compare perturbed conditions with the unperturbed behavior, we first evaluated features of the distinct p65 cycles in the nucleus using an assay with the temporal precision to resolve the asynchronous cycles in single cells. We note that a functional transcription factor scans the genome by binding and dissociating to chromatin repeatedly, and by diffusing within the nucleus 
. This activity is indicated by a fast recovery of signal from the GFP fusion protein during fluorescence recovery after photobleaching (FRAP), a widely utilized assay. We recently discovered that functional NF-κB binds to target chromatin sites, with fast exchange kinetics on the timescale of seconds 
. The chromatin residence time of p65, and its mobility measured by FRAP, are affected by its DNA binding affinity: a higher affinity mutant p65 has a slower mobility and lower affinity mutants have faster mobility 
, . Of note, the reported numbers of p65 molecules per cell and NF-κB binding sites in the genome are within an order of magnitude (60,000 
and 14,000 
, respectively). Such comparable numbers suggest that FRAP measurements from the nucleus of our GFP-p65 knock-in cells reflect some binding activity of endogenous p65 in living cells.
We used a non-invasive optimized line FRAP technique 
() in conjunction with real time monitoring, and found that p65 mobility during peak of nuclear translocation did not change from early to late cycles of TNF-α induced oscillations (, top panel). This result implies that p65 in the late translocation cycles is capable of diffusing on and interacting with the genome as effectively as the first p65 molecules activated after TNF-α. This is remarkable given the numerous feedback and post-translational mechanisms that act upon p65 to attenuate its activity following stimuli.
Perturbations of NF-κB oscillations by inhibiting either shuttling or IκBα re-synthesis cause opposite defects in characteristic genome-scanning activity of p65.
In contrast, when oscillations were blocked by either LMB or CHX, intranuclear p65 mobility measured by line FRAP was progressively altered with time. LMB induced faster mobility of GFP-p65, which is consistent with unproductive interaction of p65 with the chromatin (, bottom left panel). CHX, however, effectively slowed down p65 mobility in the nucleus, indicative of prolonged binding of p65 with target chromatin and inefficient genome scanning (, bottom right). These opposite outcomes are in line with the predicted differences in terms of free NF-κB. It is equally important to note that p65 mobility is still rather fast despite the absence of IκB in this condition, indicating that IκBα is not necessary for ‘displacing’ NF-κB from target promoters 
. Our data suggest that p65 detaches from target chromatin without IκBα intervention, and IκBα might simply capture displaced p65, either in the nucleus or in the cytoplasm. Together with the FLIP data in , the FRAP results support the idea that NF-κB has an inherent tendency to dissociate from the chromatin and shuttle out to the cytoplasm, as a feature of its dynamic behavior.
NF-κB oscillations ensure a balanced gene expression program in response to TNF-α
The dynamical systems analysis and the mobility data from line FRAP suggest that even the late periodic cycles of NF-κB oscillations may contribute significantly to the functional response induced by TNF-α. To assess the role of oscillations on transcription, we measured by qRT-PCR the gene expression kinetics of representative NF-κB targets. ‘Early’ genes were maximally transcribed within half an hour after TNF-α stimulation, while ‘intermediate’ and ‘late’ primary target genes were activated later and highly expressed only after 1.5 and 3 hours, respectively ().
TNF-α induced gene expression programs are quantitatively modulated by perturbations of NF-κB dynamics that alter the number of signaling cycles or peak durations.
LMB co-treatment with TNF-α strongly inhibited the induction of all genes examined, leaving only a transient pulse of expression for immediate early genes. This is in complete agreement with the predicted single cycle of p65 activity followed by nuclear sequestration of p65 by IκBα, and the reduced genomic interaction observed in the line FRAP assay.
On the contrary, CHX co-treatment dramatically exaggerated the induction profiles of most genes, with its strongest effect on early genes for which the transcriptional output increased by 5~50 fold (). The enhanced transcription is again consistent with the model prediction and increased chromatin residence time of p65 in living cells for this condition.
Thus, one signaling cycle or constant action of NF-κB from LMB or CHX, respectively, induced opposite functional consequences: premature termination or uncontrolled accumulation of target gene transcripts. Our data also imply that oscillatory activity of NF-κB strongly constrains the expression of the immediate early genes. The dramatic difference between TNF-α and TNF-α/CHX co-treatment suggests that transcription of NF-κB dependent genes may not occur continuously after TNF-α treatment, but rather in bursts with intermittent ‘off’ periods, echoing periodic p65 cycles.