Single-cell NF-κB dynamics reveal digital activation and analogue information processing

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Cells operate in dynamic environments using extraordinary communication capabilities that emerge from the interactions of genetic circuitry. The mammalian immune response is a striking example of the coordination of different cell types1. Cell-to-cell communication is primarily mediated by signalling molecules that form spatiotemporal concentration gradients, requiring cells to respond to a wide range of signal intensities2. Here we use high-throughput microfluidic cell culture3 and fluorescence microscopy, quantitative gene expression analysis and mathematical modelling to investigate how single mammalian cells respond to different concentrations of the signalling molecule tumour-necrosis factor (TNF)-α, and relay information to the gene expression programs by means of the transcription factor nuclear factor (NF)-κB. We measured NF-κB activity in thousands of live cells under TNF-α doses covering four orders of magnitude. We find, in contrast to population-level studies with bulk assays2, that the activation is heterogeneous and is a digital process at the single-cell level with fewer cells responding at lower doses. Cells also encode a subtle set of analogue parameters to modulate the outcome; these parameters include NF-κB peak intensity, response time and number of oscillations. We developed a stochastic mathematical model that reproduces both the digital and analogue dynamics as well as most gene expression profiles at all measured conditions, constituting a broadly applicable model for TNF-α-induced NF-κB signalling in various types of cells. These results highlight the value of high-throughput quantitative measurements with single-cell resolution in understanding how biological systems operate.

At a glance


  1. NF-[kgr]B single-cell microscopy measurements.
    Figure 1: NF-κB single-cell microscopy measurements.

    a, Representative real-time fluorescent images of cells during stimulation with 10ngml−1 (top row) and 0.25ngml−1 (bottom row) TNF-α. Arrows show the activated cell nuclei. At the high dose, all cells except one respond, whereas only two out of five respond at the lower dose. b, Fraction of activated cells versus TNF-α concentration for four different experiments (N = number of quantified active cells). The mean of four experiments fit to a Hill function with n = 1.5. cf, Representative traces for active single cells. Also shown (f) are population means at 0.01ngml−1 TNF-α stimulation, when only active cells are included (black squares), and when both active and non-active cells are included (red squares). The population traces averaged over all cells (N = ~80) misleadingly shows reduced activity. g, The integrated area under the first peak versus TNF-α concentration for a single experiment, showing that the total NF-κB nuclear activity in the first peak remains constant across all concentrations. h, NF-κB nuclear intensity versus TNF-α concentration. i, NF-κB response time versus TNF-α concentration. Error bars in gi are the standard deviation from the mean, and show the natural variation in single-cell responses. jl, Representative traces for the low-dose, short-pulsed stimulation experiment. Cells were stimulated with two consecutive 20-min-long pulses of 0.1ngml−1 TNF-α. The pulses were separated by 180min, allowing the cells to reset. Ten per cent respond to only the first pulse (j), 9% respond only to the second pulse (k), and 11% of the cells in the chamber respond to both pulses (l). The existence of cells responding to only one of the pulses indicates that NF-κB activation is partly governed by a stochastic process, whereas the high percentage of cell responding to both pulses indicates pre-existing high sensitivity to TNF-α in this subpopulation.

  2. Time-dependent expression profiles of NF-[kgr]B target genes.
    Figure 2: Time-dependent expression profiles of NF-κB target genes.

    Cells were stimulated with various doses of TNF-α ranging from 10ngml−1 to 0.01ngml−1. a, Relative expression levels of each gene were quantified using approximately 500 cells by qPCR, and digital-PCR was used to calibrate expression levels to the total number of mRNAs per cell. The expression levels shown in a are population averages of all cells (active and non-active) in the PCR reaction. Genes cluster in three groups with early (left column), intermediate (middle) and late term (right) activation dynamics. b, c, Expression levels of a representative early (b) and late (c) gene normalized to the fraction of active cells at each TNF-α concentration. mRNA levels were normalized to a single active cell level by dividing with the active fraction of cells at that concentration (see Fig. 1). Normalized expression of the early gene Il6 does not vary in response to a 1,000-fold change in TNF-α concentration. The late gene RANTES is expressed only at the highest TNF-α concentrations.

  3. Mathematical model development and simulations.
    Figure 3: Mathematical model development and simulations.

    Where applicable, error bars show standard deviation from the mean. a, Model architecture is based on stochastic description of receptor and gene activity, quadratic representation of IKK activation, and negative feedback via IκBα and A20. b, Simulated (blue) and measured (red) fraction of activated cells. c, d, Simulated single-cell NF-κB nuclear localization traces at the experimentally measured TNF-α concentration range. The low dose (0.01ngml−1) stimulated cells show clear separation between active and non-active cells similar to experiments. Among 200 simulated cells, only 10 were activated. The model faithfully reproduces important aspects of experimental means and distributions (shown with error bars) across all concentrations. e, Simulated NF-κB nuclear intensity versus TNF-α concentration (see Fig. 1h). f, Simulated NF-κB response time versus TNF-α concentration (see Fig. 1i).

  4. Model predictions: stochastic and variable cell switching and target gene expression dynamics.
    Figure 4: Model predictions: stochastic and variable cell switching and target gene expression dynamics.

    a, Simulated single-cell traces for low-dose, short-pulsed stimulation. Cells were stimulated with two consecutive 20-min-long pulses of 0.1ngml−1 TNF-α. The pulses were separated by 180min. Ten per cent respond to only the first pulse (top), 10% respond only to the second pulse (middle) and 11% of the cells in the chamber respond to both pulses (bottom), showing excellent agreement with experimental results shown in Fig. 1j–l. b, Simulations of early (top), intermediate (middle) and late (bottom) term NF-κB target genes under various doses of TNF-α. The model reproduces basic features of the expression profiles shown in Fig. 2a by varying only the transcript degradation times (Tdeg).


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Author information

  1. These authors contributed equally to this work.

    • Savaş Tay &
    • Jacob J. Hughey


  1. Department of Bioengineering, Stanford University, Stanford, California 94305, USA

    • Savaş Tay,
    • Jacob J. Hughey,
    • Timothy K. Lee,
    • Stephen R. Quake &
    • Markus W. Covert
  2. Howard Hughes Medical Institute, Stanford, California 94305, USA

    • Savaş Tay &
    • Stephen R. Quake
  3. Institute of Fundamental Technological Research, Warsaw 02-106, Poland

    • Tomasz Lipniacki


S.T. and J.J.H. performed the experiments, S.T. and T.L. developed the mathematical models and performed the simulations, T.K.L. developed the image processing methods and all authors contributed to analysis of the data and to writing the manuscript.

Competing financial interests

S.R.Q. is a founder, shareholder and consultant for Fluidigm.

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Supplementary information

PDF files

  1. Supplementary Information 1 (1.4M)

    This file contains Supplementary Figures 1-13 with legends and Supplementary Tables 1-3.

  2. Supplementary Information 2 (3.1M)

    This file contains Supplementary Mathematical Methods and Data, Supplementary Figures M1-M6 with legends, Supplementary Tables 1-3 and References.


  1. Supplementary Movie 1 (9.9M)

    This file contains a time-lapse fluorescent microscopy video of a single microfluidic chamber during stimulation with 10 ng/ml TNF-α, showing p65-DsRed nuclear localization oscillations in single-cells.

  2. Supplementary Movie 2 (6M)

    This file contains a time-lapse fluorescent microscopy video of a single microfluidic chamber during stimulation with 0.1 ng/ml TNF-α, showing p65-DsRed nuclear localization oscillations in single-cells.

Zip files

  1. Supplementary Information 3 (17K)

    This zipped file contains the stochastic and deterministic model files. All code was written in Matlab. Deterministic model files are denoted with D, i.e. ModelD.m. The files include the following: (1) Main file that calls appropriate modeling functions (Mainfile.m, MainfileD.m). Start here to perform simulations, as this file calls all the other functions in the model. This file contains some commonly changed parameters such as the TNF-α dose; (2) Parameters file (Parameters.m, ParametersD.m). This file contains most of the biochemical parameters used in the simulations; (3) Model equations (Model.m, ModelD.m). ODE's corresponding to biochemical reactions; (4) Status change file (StatusChange.m): Calculates receptor and gene binding propensities in the stochastic version of the model; (5) Plotting files: AllCellPlotting.m and AllCellPlottingD.m plot individual cell traces and related parameters, while AverageCellPlotting.m and AverageCellPlottingD.m plot the population averages of the same simulated cells.

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