Fig 2: Mechanisms regulating TNF receptor turnover and signaling control the oscillatory content in TNF‐induced NFκB dynamics AParameter scan (left) of listed reaction parameters (right) in the TNF receptor module (white background) of the NFκB signaling network model and simplified depiction of the NFκB core module (yellow background). Graphs depict nuclear NFκB dynamics over 8 h with increased (blue, 100.1× to 101×) and decreased (red, 10–0.1× to 10−1×) parameter values in 10 steps each (linear on log scale) from the original model parameters (1×). Parameter indices that allow a shift of simulated TNF‐induced NFκB oscillations to less oscillatory dynamics are labeled in red.BSimulated single‐cell nuclear NFκB dynamics upon TNF stimulation over 8 h (heatmaps) sorted by maximum amplitude in “WT” and “Tnf −/−” cells (row 1, row 2). Parameters determined in (A) to allow decrease in oscillatory character of NFκB dynamics were distributed for sampling (sampled parameter indicated in heatmap heading). NFκB dynamics in simulated Tnf −/− cells were modeled by shifting the mean of the parameter distributions by 100.1 or 10–0.1 (see Fig EV3A). Indicated pairs of parameters were also sampled. Percentage of cells with oscillatory NFκB trajectories among all simulated responder cells (row 3) and oscillation power of simulated NFκB trajectories (row 4) are shown below. A total of 2,000 cells were simulated. Marker indicates median of distribution. Statistical significance was evaluated by Kolmogorov–Smirnov test. Number indicates log10(P‐value). Results for other parameters and parameter combinations that can mediate less oscillatory responses are shown in Fig EV3C.CSimulated average IKK activity over 8 h in mathematical models of TNF‐induced NFκB dynamics in “WT” and “Tnf −/−” cells, as in (B).DSimulated mean TNF receptor levels at steady state in mathematical models of TNF‐induced NFκB dynamics in “WT” and “Tnf −/−” cells, as in (B).ETNF receptor 1 (TNFR1, left), TNF receptor 2 (TNFR2, center), and CD11b (right) cell surface expression in Tnf −/− compared to WT BMDMs unstimulated or stimulated for 30 min with 10 ng/ml TNF, measured by flow cytometry. Per experiment, median fluorescence intensity average of three culture replicates in Tnf −/− cells is expressed as percent of expression in WT cells. Data are represented as mean ± SD of three biological replicates. Statistical significance was determined by two‐tailed one‐sample t‐test using a hypothesis mean of 100.F(Left) TNF receptor 1 (TNFR1) cell surface expression at baseline in BMDMs pre‐treated with TNFR1 siRNA, control (ctrl) siRNA, or untreated (−). Median fluorescence intensity is expressed as percent of expression in untreated WT cells. (Right) Percentage of cells with oscillatory NFκB activity (measured by fluorescence microscopy) among all responder cells upon indicated siRNA pre‐treatment and stimulation with 10 ng/ml TNF. Per condition, 1,032–1,484 responding cells were analyzed. (Left, right) Data are represented as mean ± SD of three biological replicates. Statistical significance was determined by one‐tailed paired‐sample t‐test. Heatmaps of NFκB trajectories from one biological replicate are show in Fig EV3G. Source data are available online for this figure.

Fig 3: Mechanisms regulating TNF receptor turnover and signaling control oscillatory content in TNF‐induced NFκB dynamics A, BDistribution of parameters and parameter combinations that can mediate less oscillatory responses used to simulate heterogeneous single‐cell NFκB trajectories in “WT” and “Tnf −/−” models in Fig 3B (A) or Fig EV3C (B). The “Tnf −/−” population was modeled by shifting the mean of the parameter distributions by 100.1× or 10–0.1×.CSimulated single‐cell NFκB dynamics upon TNF stimulation over 8 h (heatmaps) in “WT” and “Tnf −/−” models (row 1, row 2) as in Fig 3B. Results using parameters and parameter combinations that can mediate less oscillatory responses not shown in Fig 3B are shown here. Percentage of cells with oscillatory NFκB trajectories among all simulated responder cells (row 3) and oscillation power of simulated NFκB trajectories (row 4) are shown below. A total of 2,000 cells were simulated. Marker indicates median of distribution. Statistical significance was evaluated by Kolmogorov–Smirnov test. Number indicates log10(P‐value).DSimulated average IKK activity over 8 h in mathematical models of TNF‐induced NFκB dynamics in “WT” and “Tnf −/−” cells, as in (C).ESimulated mean TNF receptor levels at steady state in mathematical models of TNF‐induced NFκB dynamics in “WT” and “Tnf −/−” cells, as in (C).FTNF receptor 1 (TNFR1, left), TNF receptor 2 (TNFR2, center), and CD11b (right) cell surface expression in WT and Tnf −/− BMDMs unstimulated or stimulated for 30 min with 10 ng/ml TNF, measured by flow cytometry. Data are represented as mean ± SD of three culture replicates. One of three biological replicates is shown. Statistical significance was determined by unpaired two‐tailed t‐test. MFI, median fluorescence intensity.GNuclear localization of mVenus‐RelA upon stimulation with 10 ng/ml TNF was measured over time by fluorescence microscopy in BMDMs of indicated genotypes pre‐treated with TNFR1 siRNA, control (ctrl) siRNA, or untreated (−). Nuclear mVenus‐RelA was quantified by automated image analysis. Each row of the heatmap represents the NFκB signaling trajectory of one cell. Trajectories are filtered for responding cells and sorted by maximum amplitude. Data from one of three biological replicates are depicted.