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Most features of NF-κB activation dynamics vary significantly with respect to ligand type and concentration. The distribution of the time between two nuclear entries is an invariant feature in populations but not individual cells, suggesting an additional level of control, which regulates the overall distribution of translocation timing.

The activation dynamics of nuclear factor (NF)-κB have been shown to affect downstream gene expression. On activation, NF-κB shuttles back and forth across the nuclear envelope. Many dynamic features of this shuttling have been characterized, and most features vary significantly with respect to ligand type and concentration. Here, we report an invariant feature with regard to NF-κB dynamics in cellular populations: the distribution—the average, as well as the variance—of the time between two nuclear entries (the period). We find that this period is conserved, regardless of concentration and across several different ligands. Intriguingly, the distributions observed at the population level are not observed in individual cells over 20-h time courses. Instead, the average period of NF-κB nuclear translocation varies considerably among single cells, and the variance is much smaller within a cell than that of the population. Finally, analysis of daughter-cell pairs and isogenic populations indicates that the dynamics of the NF-κB response is heritable but diverges over multiple divisions, on the time scale of weeks to months. These observations are contrary to the existing theory of NF-κB dynamics and suggest an additional level of control that regulates the overall distribution of translocation timing at the population level.

The nuclear factor (NF)-κB signaling network plays a critical role in innate immune signaling (

Although the oscillations of NF-κB have been observed in multiple types of cultured mammalian cells, they have only been well characterized in response to a single stimulus—tumor necrosis factor (TNF). Signaling to NF-κB can be activated by many different stimuli, and it is unclear how different stimuli might change the oscillations. Recent theoretical work suggests that the period of the oscillations may be stimulus independent (

In earlier work, we measured the nuclear localization of a fluorescent protein fused to NF-κB subunit p65 in response to TNF concentrations spanning five orders of magnitude and for thousands of individual cells (

The time between p65-dsRed nuclear localization peaks is constant across stimuli and concentration. (A) The fraction of active cells (top row), as well as the time to (second row) and amplitude of (third row) the first peak, vary, depending on stimulus and concentration, whereas the time between the first and second peaks (bottom row) is constant. (B) Distributions of all interpeak times for five different environmental conditions: TNF and LPS (concentrations as shown in A), LPS (concentrations as shown in A), together with soluble TNF receptor II (sTNFR; 5 μg/ml), Pam3CSK4 (1 μg/ml), and Sendai virus (10 and 100 U/ml). See also Supplemental Figure S1.

The aim of this study was to quantitatively characterize the oscillations of NF-κB localization across stimuli and individual cells and over generations. We report that not only the mean, but also the entire distribution of the interpeak times is conserved—across concentrations and several stimuli. By making substantial improvements in our ability to observe and track single cells, we further show that the conservation of interpeak times holds only at the population level and not for individual cells. This finding is not explained by existing computational models of NF-κB, which focus on transcriptional variability within cells as opposed to variability across cellular populations. Finally, we show that over time and many generations, the clonal population derived from a single cell largely recapitulates the conserved distribution of interpeak time.

In previous work, we found that the time between two subsequent p65 nuclear translocations was conserved across concentrations of TNF (

We and others previously reported that cells stimulated with certain preparations of LPS may secrete TNF, which can activate NF-κB in a paracrine and autocrine manner (

To determine whether the interpeak time distribution was the same for other stimuli, we measured the period of nuclear localization in response to Pam3CSK4 and Sendai virus, which activate NF-κB through different receptors from those that are bound by either TNF (TNFR) or LPS (TLR4). Pam3CSK4, a synthetic triacylated lipoprotein that mimics bacterial lipopeptides, is believed to activate NF-κB through a complex of TLR1 and TLR2 (

Although Pam3CSK4 and Sendai virus activate NF-κB via distinct molecular pathways, the distribution of interpeak times of p65 nuclear localization was similar to our previous measurements (

The distribution of interpeak times was constant, but it was also broad, with a coefficient of variation of ∼40%. Part of that large variability comes from a cell's first interpeak time, which tended to be longer and more variable than later interpeak times (Supplemental Figure S1, B and C). However, even including only the later oscillations, the distribution in interpeak times showed marked variability. Of importance, our results so far have been based on data pooled from many cells, which means the variability we measured was a property of the population of cells, not a property of NF-κB signaling in single cells. Given the cell-to-cell variability that we have observed in cells’ responsiveness to low concentrations of TNF (

The variability in the population must arise from a combination of two sources—one intracellular and the other intercellular (

The distribution of interpeak times within individual cells varies from one cell to another. (A) Schematic illustrating variation within cells and between cells. (B) Nuclear localization traces and (C) interpeak time distributions of three cells (selected from 199 total across two experiments) monitored for 20 h upon stimulation with 10 ng/ml TNF. (D) Mean interpeak time for each cell plotted against CV. (E) Mean and SDs of interpeak time for each individual cell plotted together with the distribution that would be expected without intercellular variability (black). (F) Ratio of variance between cells to variance within cells (

The other possible source of variability is intercellular (also referred to as cell-to-cell), that is, between cells in the population. If intercellular variability were at least partly responsible for the variability in the interpeak time that we observed across the population, the distribution of interpeak times would be different from one cell to another (

Which type of variability is responsible for the interpeak time distributions we observed? To quantify accurately the intracellular and intercellular variability of the dynamics of p65 translocation, we needed to determine the distribution of interpeak time for many individual cells. This required measuring many more oscillations for each cell than had previously been reported. A number of technical improvements (see

Our results showed that the individual cells varied considerably in their distributions of interpeak time (^{2} = 2 × 10^{−5}).

Finally, we tested for intercellular variability. We pooled all the interpeak times from all the cells and then randomly and repeatedly drew 10 interpeak times from that pool (with replacement) to create a null distribution corresponding to no intercellular variability. This randomization of the interpeak times produced a significantly different distribution than was actually observed in single cells (^{−9} by two-sample Kolmogorov–Smirnov [KS] test), and the variance between cells was found to be about sixfold higher than that within cells (

Given the intercellular variability in p65 oscillations that we observed, we next sought to examine the sources of variability in a computational model of the NF-κB signaling network. To represent the heterogeneity in single cells, a model must contain a stochastic or variable element. The model we used represents the binding of NF-κB to the promoters of its inhibitors (A20, IκBα, and IκBε) as a stochastic process, which leads to stochastic transcription of the corresponding mRNAs (

Using this model, we ran 500 simulations of a 20-h stimulation with 10 ng/ml TNF. Each simulation corresponds to the dynamics of the signaling network in an individual cell. These simulated cells show sustained oscillations of p65 localization (

Computational modeling captures variability within, but not between, cells. (A) Three model simulations of p65 nuclear localization. (B) Interpeak time distributions of three model simulations. (C) CV vs. mean interpeak time for each simulation (orange) and for each experimentally observed cell (blue). Ratio of variability between cells to variability within all simulations, as determined using bootstrap analysis. (D) Mean and SDs of interpeak time for each individual simulation, plotted together with the distribution that would be expected without any intercellular variability (black). (E) Ratio of variance between simulations to variance within all simulations (

We then calculated the intracellular and intercellular variability by comparing interpeak times within and between individual simulations. A typical simulated cell had a mean interpeak time of between 66.5 and 71.1 min and a CV between 15 and 20% (interquartile ranges; ^{2} = 0.08).

Finally, to test statistically for intercellular (i.e., intersimulation) variability, we performed the same randomization procedure that we did for the experimentally observed cells. We found that the distribution of mean interpeak times from the simulations differed only slightly from the null distribution corresponding to no intercellular variability (

Besides stochastic processes, another way to produce heterogeneity in a model is to vary the parameters from one simulation to another. With that in mind, we explored how varying the model parameters affected the oscillations of NF-κB. We independently varied each model parameter up and down twofold. For each set of parameters, we ran 50 simulations of a 12-h stimulation with TNF, then calculated the mean and CV of the interpeak time for those simulations. Finally, we calculated the sensitivity of the mean and CV of the interpeak time to each parameter (Supplemental Figure S3). Intriguingly, the results suggest that parameters can have widely varying effects on the oscillations of NF-κB. For example, an increase in A20's translation rate (parameter c2) increases the oscillatory period and strongly reduces the variability of the oscillations, whereas an increase in A20 mRNA's degradation rate (parameter c3) strongly reduces the oscillatory period but has no effect on the variability.

Our simulation results therefore suggest that many parameters could produce the intercellular variability that we observe if the parameters vary from one cell to another. Such parameters might be considered epigenetic factors, which could drift over time and generations.

The finding that the individual cell interpeak time distributions were so different from each other, especially given that the overall population distribution is so constant across stimuli and concentrations, led to questions about time scales. In particular, how long does it take for the progeny of an individual cell to generate the variability seen in the population? To answer this question, we considered cells at generations 0 (the founding cell) and 1 (the daughter cells), as well as after development of a clonal population (∼4–8 wk).

First, we considered the founding cell. Because our cells were actively growing during the experiment, it seemed possible that the cell cycle might affect the oscillations of NF-κB. However, we found that the average period of the population did not change significantly over time (

Analysis of the time scale on which the period changes. (A) For every 50-min interval from 100 to 1100 min after TNF stimulation, the mean (black) and SD (gray) of all observed interpeak times whose left peak occurs in that interval. (B) Distribution, along with mean and SD, of the Spearman rank correlation of interpeak time with time for every cell. (C) Two examples of cell division that occurred during TNF stimulation: mother cell (black) and two daughter cells (light and dark blue). (D) Distribution of absolute difference in mean interpeak time between two daughter cells with the same mother and between any two daughter cells. (E) Distribution of interpeak times, in response to 10 ng/ml TNF stimulation, for each clonal cell line. (F) Same calculation as in D. Distribution of all pairwise comparisons of mean interpeak time within cells of a clone compared with the distribution of all pairwise comparisons across cells of any clone. See also Supplemental Figure S2.

Next we investigated whether the distribution of interpeak time was affected by cell division. To do this, we analyzed the oscillations of p65 in cells that divided during our experiments (

Finally, to study how the period of NF-κB oscillations change on a longer time scale, we created multiple clonal lines of cells derived from our original cells. At the time of our experiments, we estimate that the cells of each clonal line were separated from their respective founding cell by at least 30 cell divisions. For each clonal cell line, we analyzed the dynamics of p65 nuclear localization in response to 10 ng/ml TNF and quantified interpeak times as before. We found that the interpeak time distributions for each clone resembled each other (

We then calculated the absolute differences between mean interpeak times within clones and for all cells in the clone data sets and compared the distributions for each (

In summary, we have identified an invariant property in the dynamic response of NF-κB to multiple stimuli and concentrations: the period of oscillation of p65 between the cytoplasm and the nucleus. In addition, the distribution of oscillation periods is conserved across concentrations and for a variety of ligands, namely a cytokine, a virus, and bacterial wall components. These experimental results are consistent with recent theoretical work (

Whether the TNF-induced dynamics of p65 localization is oscillatory on time scales longer than a few hours has been controversial. Extending the results of others (

Much effort has gone into uncovering the forms and mechanisms of stimulus specificity in immune signaling, of which NF-κB is just one of several transcription factors involved (

Surprisingly, we also found that the invariance we observed in the population depends on variability created as single cells diverge over time. Although we previously explored the sources of variability affecting whether a cell responds to intermediate concentrations of TNF (

Most intriguingly, although the distribution of the period is conserved within the cell population, this conservation does not extend to individual cells. Our long time courses enabled us to measure accurately the distributions of oscillation period in single cells, and we found the intercellular variability to be significantly greater than the intracellular variability. These findings indicate that, although the population distribution of the period is not influenced by the multiple stimuli we tested, there are intracellular parameters that can vary among cells to tune the period. Previous work suggested that these parameters might relate to the expression of IkBa (

Moreover, these data raise the possibility that the interpeak time is at least partially determined by epigenetic factors (e.g., protein levels or chromatin modifications), in that it is conserved for at least one division cycle but shifts over longer time scales. This phenomenon resembles what has been observed for cells undergoing apoptosis (

As dynamic, single-cell data continue to be collected for other signaling networks, we expect that further invariant or recurrent features will be identified, providing new insight into the networks’ essential biological mechanisms and functions.

Cell culture was performed as previously described (^{−/−} mouse 3T3s infected with lentivirus to express p65-dsRed and H2B-GFP. Where specified, cells were stimulated with LPS-EB Ultrapure (tlrl-pelps; Invivogen, San Diego, CA), recombinant mouse TNF (11271156001; Roche, Indianapolis, IN), Pam3CSK4 (tlrl-pms; Invivogen), or Sendai virus (600503; Charles River, San Diego, CA). Solutions were prepared in imaging media (DMEM prepared without riboflavin, folic acid, or phenol red, with 1% fetal bovine serum [FBS]) and kept on ice, and then warmed to 37°C just before stimulation. Soluble TNF Receptor II (426-R2; R & D Systems, Minneapolis, MN) was used at 5 μg/ml. Clonal lines were derived from the parental strain by limiting dilution into a 96-well plate at a concentration of 1 cell/5 wells. Cells grew in 19 of the 96 wells, and based on a Poisson distribution, ∼17 (91%) of these 19 outgrowths should be derived from a single cell, that is, be clonal. We measured p65 nuclear localization in the clonal cell lines that expressed both p65-dsRed and H2B-GFP.

_{2} (5%), and humidity were held constant. For the 20-h time courses, Breathe-Easy film was used to minimize evaporation from the wells. In addition, for some wells in the plate, two-by-two grids of fields of view overlapping by ∼15% were imaged, to be stitched together later. Because our cells move around during the experiment, this was designed to decrease the perimeter:area ratio and thereby decrease the proportion of cells lost due to their moving out of the field of view.

Flat-fielding (correcting for uneven illumination of the field of view) and time-lapse registration (correcting for small imprecision of the stage movement) of images were performed with custom Matlab code. Image stitching was performed with custom Matlab code, using an iterative algorithm to stitch together adjacent fields of view. For each grid of fields of view at each time point, the stitching program first calculated the overlaps using the FITC (H2B-GFP) image and then applied those overlaps to the FITC and TRITC (p65-dsRed) images. Segmentation of nucleus and cytoplasm was performed in Matlab and in CellProfiler (

Except for the data in

We used the stochastic model of the NF-κB pathway as described. We first ran the model without any TNF to find the median initial conditions and then ran the 500 simulations using those initial conditions. To calculate the sensitivity of the interpeak time to the model parameters, each parameter was independently increased or decreased twofold, and 50 simulations of 20-h stimulation with TNF were run. For each parameter, the sensitivity of the mean interpeak time was calculated as the difference between the mean interpeak time (across all simulations) for the twofold increase and mean interpeak time for the twofold decrease, divided by the mean interpeak time for the baseline value of the parameter. The sensitivity of the CV was calculated analogously.

This article was published online ahead of print in MBoC in Press (

*These authors contributed equally to this work.

We are grateful for support from the National Institutes of Health, including a Director's Pioneer Award (5DP1LM01150), a National Cancer Institute Pathway to Independence Award (R00CA125994), an R21 grant (1R21AI104305), and a Systems Biology Center grant (P50 GM107615), in addition to a Paul Allen Family Foundation Distinguished Investigator Award to M.W.C., Bio-X and ARCS Fellowships to J.J.H., and Weiland and Rensselaer Engineering Fellowships to M.V.G. We thank Derek Macklin and Harendra Guturu for developing the interactive figure and thank the Covert lab for helpful discussions and advice.

inhibitor of κB

lipopolysaccharide

melanoma differentiation-associated protein 5

myeloid differentiation primary response 88

nuclear factor κB

retinoic acid-inducible gene 1

Toll-like receptor

tumor necrosis factor (receptor)

TIR (Toll/Interleukin-1 receptor)-domain-containing adapter-inducing interferon-β.

Boldface names denote co–first authors.