Digital signaling decouples activation probability and population heterogeneity.

Digital signaling enhances robustness of cellular decisions in noisy environments, but it is unclear how digital systems transmit temporal information about a stimulus. To understand how temporal input information is encoded and decoded by the NF-κB system, we studied transcription factor dynamics and gene regulation under dose- and duration-modulated inflammatory inputs. Mathematical modeling predicted and microfluidic single-cell experiments confirmed that integral of the stimulus (or area, concentration × duration) controls the fraction of cells that activate NF-κB in the population. However, stimulus temporal profile determined NF-κB dynamics, cell-to-cell variability, and gene expression phenotype. A sustained, weak stimulation lead to heterogeneous activation and delayed timing that is transmitted to gene expression. In contrast, a transient, strong stimulus with the same area caused rapid and uniform dynamics. These results show that digital NF-κB signaling enables multidimensional control of cellular phenotype via input profile, allowing parallel and independent control of single-cell activation probability and population heterogeneity.

Introduction

Cells must make decisions in noisy environments and have to decrease the chance of an errant response. One way cells can reduce sensitivity to noise is through digital or switch-like activation, such that only sufficiently strong signal exceeds an internal threshold and initiates a response. Switch-like activation occurs through diverse mechanisms (Shah and Sarkar, 2011). For example, observations in Xenopus oocytes showed that the MAPK pathway converted graded progesterone input to digital output in p42 MAPK that determined oocyte maturation (Petty et al., 1998). Subsequently, similar observations were seen for the JNK pathway (Bagowski and Ferrell, 2001). The scaffolding protein Spe5 was found to mediate digital MAPK activation of mating in yeast (Malleshaiah et al., 2010). More recently, it was found that inflammasome signaling leads to all-or-none caspase1 activation that mediates apoptosis (Liu et al., 2013). Both amplitude (dose) and duration of input signals provide information that regulates cellular decisions. The duration of Epidermal Growth Factor (EGF) stimulation modulates ERK dynamics and controls differentiation (Santos et al., 2007; von Kriegsheim et al., 2009; Ahmed et al., 2014). Glucose sensing in plants showed that cells have gene regulatory network mechanisms to allow similar responses to a short, intense or sustained, moderate stimulus (Fu et al., 2014). Lymphocytes must precisely measure both antigen affinity and frequency to decide differentiation and proliferation (Iezzi et al., 1998; Gottschalk et al., 2012; Miskov-Zivanov et al., 2013). Although digital pathway activation allows robust cellular decision across a wide range of systems, it is not clear how digital signaling impacts processing of dose and duration information.

NF-κB is a critical regulator of phenotype in immunity and disease (Hayden and Ghosh, 2008) and responds digitally to Tumor Necrosis Factor (TNF) stimulation (Tay et al., 2010; Turner et al., 2010). NF-κB activation occurs for a multitude of cell stress and inflammatory signals that converge on the IKK (IκB Kinase) signaling hub, which induces degradation of the cytoplasmic inhibitor IκB and liberates NF-κB to enter the nucleus and regulate gene expression (Hayden and Ghosh, 2008). Multi-layered negative and positive feedback lead to complex pathway dynamics including oscillations (Hoffmann et al., 2002; Nelson et al., 2004; Tay et al., 2010; Kellogg and Tay, 2015). Although it is not fully resolved how NF-κB coordinates gene and phenotype regulation, it is known that dynamic NF-κB activation is involved in input–output specificity and information transmission (Werner et al., 2005; Ashall et al., 2009; Behar and Hoffmann, 2013; Selimkhanov et al., 2014). The core IκB-NF-κB regulatory module is well-studied and appears largely consistent across multiple stimulation contexts (Hoffmann et al., 2002; Nelson et al., 2004; Tay et al., 2010; Hughey et al., 2014); however, the role of module upstream of IKK activation including receptor-ligand binding and adaptor protein assembly in input-encoding remains unclear.

To probe how diverse IKK-upstream signaling architectures impact NF-κB processing of pathogen- and host-associated inflammatory inputs, we used microfluidic cell culture to precisely modulate dose and duration of LPS and TNF stimuli and measured NF-κB dynamics using live cell imaging (Figure 1) (Junkin and Tay, 2014; Kellogg et al., 2014). We found that lipopolysaccharide (LPS) induces NF-κB activation in a digital way where cells respond in an all-or-none fashion, but in a distinct manner from TNF, with greater ultrasensitivity and pronounced input-dependent activation delay. Computational modeling predicted and experiments confirmed that LPS integral over the stimulus or ‘area’ (concentration × duration) controls the percentage of cells that activate in the population. Importantly, dynamics of NF-κB activation depend on input temporal profile, so that a long duration, low-dose (LL) signal induces delayed, heterogeneous activation timing in the population while a short duration, strong amplitude (SS) signal with the same area causes rapid activation without cell-to-cell timing variability (Figure 1). These results reveal a function for digital signaling beyond simple noise filtering: digital activation controls fate along a two dimensional space by allowing an input signal to independently control the population response (percentage of responding cells) and single-cell response (transcription factor dynamics and gene expression phenotype) though modulation of signal area and shape.

Figure 1.

How does input profile determine digital signaling response?

Since the amplitude and time profile of input signals depends on biological context, such as distance to an infection site or pathogen loading, we use microfluidics to manipulate dose (A) and duration (B) of LPS and TNF input signals, which induces digital activation of NF-κB. (C) Switch-like digital NF-κB responses are analyzed in terms of fraction of cells that activate in the population and heterogeneity in the dynamic responses in activating cells.

DOI: http://dx.doi.org/10.7554/eLife.08931.003

Results

NF-κB switch dynamics distinguish pathogen (LPS) and host (TNF) signals

To initially evaluate the behavior of the LPS/NF-κB pathway, we stimulated 3T3 NF-κB reporter cells (Lee et al., 2009; Tay et al., 2010) with different concentrations of LPS in a microfluidic system (Gómez-Sjöberg et al., 2007; Kellogg et al., 2014) and performed time-lapse live microscopy to record NF-κB nucleus-cytoplasm translocation over time (Figure 2A). Each experimental condition is measured in duplicate chambers on the chip. We found that LPS-exposed cells activated NF-κB in an ultrasensitive, digital fashion. The population consisted of cells either responding or ignoring the LPS input, with the percentage of responding cells in the population scaling with LPS concentration, from 5% at 0.25 ng/ml to 100% at 500 ng/ml (Figure 2B,D). Amplitude is highly variable across doses. Median amplitude increases gradually with dose though this change is statistically less significant than change in response time (Figure 2—figure supplement 2). NF-κB dynamics in activating cells showed small oscillations beyond the first peak. When ligand is flowed continuously through the chamber to replace ligand loss due to cellular internalization, oscillations sustain for the duration of the stimulus (Figure 2—figure supplement 1A). Under low intensity LPS stimulation, most cells did not respond (Figure 2C,D). This was a similar effect as previously observed under TNF (Tay et al., 2010; Turner et al., 2010). While both LPS and TNF are digital in preserving first peak area, the TNF-induced NF-κB initial peak becomes flatter and wider with increasing response time but unchanging onset time for decreasing input dose, while LPS experiences greater dose-dependent onset delay and timing variability and maintains a consistent peak shape (Figure 2C and Figure 2—figure supplement 1B). The dose-response curve for LPS was steeper than that for TNF (fitted to Hill dynamics reveals Hill coefficients of 2.3 and 1.5, respectively) (Figure 2C, Figure 2—figure supplement 1C, Figure 5—figure supplement 1B). These results indicate that the LPS pathway activates in a switch-like manner, with increasing fraction of cells in the population responding as dose is increased, but with distinct activation dynamics compared to TNF input.

Figure 2.

Digital, time-delayed NF-κB activation under varied LPS dose stimulation.

(A) Cells process pathogen signal dose and duration to dynamically activate NF-κB, which induces gene expression and coordinates the innate immune response. We test the role of pathogen load by varying LPS concentration from 0.25 ng/ml to 500 ng/ml using microfluidic cell culture. (B) Time series images of NF-κB activation following LPS treatment. Top row: high LPS dose causes nearly 100% of cells to respond synchronously. Bottom row: at low LPS concentration, less than 5% of cells respond and initiate NF-κB activation with variable, delayed timing. The cells respond digitally, with nearly all cytoplasmic NF-κB moving into the nucleus. The response amplitude (indicated by peak intensity of nuclear p65-dsRed fluorescence) depends on the initial NF-κB abundance in the nucleus and exhibits high variability across doses. (C) Trajectories of NF-κB activation (intensity of nuclear p65-dsRed) tracked in single cells over time for LPS doses ranging from 500 to 0.25 ng/ml. As the LPS dose decreases, response timing becomes delayed and variable, and the percent of responding cells in the population drops. (D) Across the LPS doses tested: top panel, dose-response curve of the fraction of active cells (plotted is the mean of two duplicate cell chambers in the chip for each condition), middle panel, the intensity of nuclear NF-κB at the peak of the response, and lower panel, time until the peak of the response. Peak nuclear NF-κB amplitude is highly variable across doses. The dose response shows a sharp drop in fraction of active cells between 1 and 5 ng/ml concentration, indicating that the activation threshold is within this range for most cells. With lower dose, the response time increases in both median duration and variability. In middle and lower panels, data points and error bars represent median and interquartile range, respectively. (E) NF-κB dependent gene expression dynamics under varied LPS concentrations (blue: 500 ng/ml, green: 100 ng/ml, red: 50 ng/ml). With lower LPS concentration, several genes show delayed induction. TNF dose-modulated expression of the same genes can be found in Figure 3 of Tay et al. (2010) and Figure 2A of Pękalski et al. (2013).

DOI: http://dx.doi.org/10.7554/eLife.08931.004

(A) Sustained NF-κB oscillations for continuously perfused LPS achieving constant LPS concentration. Bolded blue line: example cell. (B) Analysis of the LPS induced NF-κB nuclear localization peak. Lower LPS doses induce a pronounced onset delay, but the peak shape is mostly conserved across different doses. Data points and error bars are median and interquartile range, respectively. (C) Cartoon illustrating activation curves for LPS vs TNF. (D) Cartoon illustrating first peak time profile for LPS vs TNF. LPS leads to greater dose-dependent delay than TNF and a more conserved peak shape. (E) Area under the NF-κB localization curve show little change across all doses tested. Data are plotted as median and interquartile range.

DOI: http://dx.doi.org/10.7554/eLife.08931.005

Each table contains p-values of two-sample T-test for each dose combination. Red denotes statistical significance (p < 0.05).

DOI: http://dx.doi.org/10.7554/eLife.08931.006

Figure 2—figure supplement 2.

Statistical analysis for NF-κB peak amplitude and timing measurements under LPS dose modulation (corresponding to Figure 2D).

Each table contains p-values of two-sample T-test for each dose combination. Red denotes statistical significance (p < 0.05).

DOI: http://dx.doi.org/10.7554/eLife.08931.006

Figure 2—figure supplement 1.

Digital, time-delayed NF-κB activation under continuous LPS stimulation.

(A) Sustained NF-κB oscillations for continuously perfused LPS achieving constant LPS concentration. Bolded blue line: example cell. (B) Analysis of the LPS induced NF-κB nuclear localization peak. Lower LPS doses induce a pronounced onset delay, but the peak shape is mostly conserved across different doses. Data points and error bars are median and interquartile range, respectively. (C) Cartoon illustrating activation curves for LPS vs TNF. (D) Cartoon illustrating first peak time profile for LPS vs TNF. LPS leads to greater dose-dependent delay than TNF and a more conserved peak shape. (E) Area under the NF-κB localization curve show little change across all doses tested. Data are plotted as median and interquartile range.

DOI: http://dx.doi.org/10.7554/eLife.08931.005

Figure 5—figure supplement 1.

NF-κB dynamics under pulsed stimulation with TNF at 10 ng/ml concentration.

(A) Single-cell NF-κB trajectories for TNF pulse durations of 1, 5, 10, 20, 40, and 60 s. The number and percent of activated cells is indicated in the plot. (B) Comparison of active NF-κB cell fraction (top), response amplitude (middle), and response time (bottom) under LPS vs TNF pulses. The fraction-active curve is less steep under TNF than LPS. Fraction of active cells is plotted as mean for two duplicate cell chambers for each condition. In middle and lower panels, data points and error bars represent median and interquartile range, respectively. LPS data are duplicated from main Figure 5C for comparison.

DOI: http://dx.doi.org/10.7554/eLife.08931.013

Response timing and single-cell heterogeneity depends on stimulus intensity

We next analyzed dynamics of the NF-κB response in those cells that activate. Notably, there were differences in the timing of the response for high versus low dose. High-dose long duration input caused a rapid response with the response peak occurring at approximately 35 min after stimulation. In contrast, low-dose long duration (LL) input led to a pronounced statistically significant delay in the response (Figure 2C,D and Figure 2—figure supplement 2). At lowest doses, the median delay until the peak of the response exceeded 80 min with heterogeneity in the response timing between cells (Figure 2C,D).

We next asked whether this delayed response impacted LPS and NF-κB-mediated gene expression. We explored how the increase in delay for 500 ng/ml LPS versus 50 ng/ml LPS impacted gene regulation. Notably, gene expression of early and intermediate genes exhibited a dose-dependent delay (Figure 2E). The extent and magnitude of the dose-dependent delay and heterogeneity differs from TNF stimulation of the same cell type (Tay et al., 2010). While decreasing TNF dose altered the response slope, LPS response maintained a stereotypical peak shape that shifts later in time with lower dose (Figure 2E). Delayed gene expression observed under LPS stimulation contrasts with TNF-α input that does not induce delayed induction of these genes (Tay et al., 2010; Pękalski et al., 2013). For early genes IκBα and A20, gene expression peak is shifted from 30 min to 1 hr after stimulation. IκBϵ expression shifts from maximum expression at 1 hr–2 hr and from 30 min to 2 hr for TNF mRNA under LPS input. Intermediate genes Ccl2 and Icam shift expression peaks from 1 hr to 2 hr and from 1 hr to 3 hr (Figure 2E), respectively. Late genes Ccl5 and Casp4 do not reflect the delayed NF-κB activation due to slower induction kinetics. Both NF-κB dynamics in microfluidics and mRNA responses in tissue culture may be affected by autocrine signaling loops (Pękalski et al., 2013). Overall, these results indicate that LPS induces digital NF-κB activation with an input dose-dependent delay that carries through to gene expression dynamics.

Cooperative IKK activation underlies dose-dependent response delay

To study how various pathway components upstream of IKK influence input information transfer to NF-κB, we developed a model of LPS-induced NF-κB switch activation. LPS activates NF-κB by TLR4 engagement via CD14, leading to TLR4 dimerization. TLR4 dimers recruit MyD88, IRAK2/4, and other adaptor proteins leading to clustering and higher order assembly of Myddosome and TRAF6 lattice structures, which cooperatively activates IKK (Yin et al., 2009; Lin et al., 2010; Zanoni et al., 2011). Following IKK activation, nuclear NF-κB induces expression of IκBα, which negatively regulates NF-κB and IKK, respectively (Hayden and Ghosh, 2008). Experimental IκBα expression kinetics were similar for LPS and TNF, despite induction delay under LPS (Figure 2E). Multiple efforts have modeled NF-κB pathway dynamics under TNF stimulation (Hoffmann et al., 2002; Lipniacki et al., 2007; Ashall et al., 2009; Paszek et al., 2010; Tay et al., 2010; Pękalski et al., 2013). Extrinsic noise including variation in receptor-level and pathway components contributes to cell-to-cell heterogeneity in cell sensitivity and response dynamics (Snijder et al., 2009; Tay et al., 2010). We based our mathematical model on the core IKK-NF-κB regulatory module (Tay et al., 2010), which has been extensively validated experimentally.

To extend the NF-κB core model for LPS, we added species for LPS, TLR4, and TRAF6 (Appendix 1) (Figure 3A). To introduce variability in the model, we allowed fluctuation in the number of TLR4 receptor molecules between cells. TLR4 is expressed at relatively low level compared to CD14 and furthermore varies significantly between cells in the population (Zanoni et al., 2011). To account for cooperative activation due to Myddosome assembly and TRAF6 lattice formation, we model IKK phosphorylation by TRAF6 using Hill kinetics. The model reproduced the observed LPS induced NF-κB dynamics in single cells for different LPS doses (Figure 3B–D and Figure 3—figure supplement 1), though showed more dose-dependent first peak amplitude variation than observed in experiments. The distinct feature of the proposed LPS model is the Myddosome formation leading to cooperative activation of IKK (coopertivity coefficient = 4, note this value is distinct from the slope of the active cell fraction response curve), which simultaneously assures delay in activation observed experimentally for low doses, and steeper response curve than in the case of TNF stimulation (Figure 3 and Figure 2—figure supplement 1).

Figure 3.

Model scheme and simulation of LPS dose modulation.

(A) The scheme of the model. LPS binds TLR4 leading to TRAF6 activation, which cooperatively activates IKK. Active IKK induces IκB degradation, which allows NF-κB to enter the nucleus and upregulate expression of IκB and A20. New IκB sequesters NF-κB in the cytoplasm and A20 inhibits upstream pathway activation by IKK and TRAF6. (B) Simulated versus experimental LPS dose response. (C) NF-κB peak intensities (expressed as proportion of total NF-κB molecules in the nucleus). (D) NF-κB response time as function of LPS dose. (E) Sample simulated curves of nuclear NF-κB fractions under LPS treatment. In box and whisker plots (C, D), the central red line is the median, the edges of the box are the 25th and 75th percentiles, and the whiskers extend to the most extreme data points.

DOI: http://dx.doi.org/10.7554/eLife.08931.007

(A–H) LPS concentration decreases over time due to cellular internalization in sealed microfluidic chambers, leading to damped oscillations. (Note: y-scale changes between plots.)

DOI: http://dx.doi.org/10.7554/eLife.08931.008

(A) Extrinsic noise is generated by selecting the number of TLR4 molecule for each cell from a lognormal distribution. Fraction of active cells was analyzed for increased TLR4 variability (parameter Sigma). With higher TLR4 number variability, the change in fraction of active cells becomes more gradual with changing LPS concentration. (B) Simulation response delay under varied LPS dose with and without clustering. Clustering mediating cooperative IKK activation is required to reproduce the experimentally observed response delay with decreasing LPS dose. Central point and error bars represent median and interquartile range, respectively.

DOI: http://dx.doi.org/10.7554/eLife.08931.009

Figure 3—figure supplement 1.

Simulated NF-κB trajectories for various doses of LPS treatment.

(A–H) LPS concentration decreases over time due to cellular internalization in sealed microfluidic chambers, leading to damped oscillations. (Note: y-scale changes between plots.)

DOI: http://dx.doi.org/10.7554/eLife.08931.008

Input duration controls activation probability independent of response heterogeneity

Cellular environments like infected tissue encode information in both amplitude and duration of input signals (Gottschalk et al., 2012; Fu et al., 2014). To understand how pathogen input signal duration and input integral or area (concentration × duration) impact digital NF-κB signaling, we performed a simulated screen across a large range of LPS concentration and duration combinations using our model. We first observed that just as LPS concentration modulates fraction of active cells so does duration. Simulations keeping concentration high and changing input duration on a short, sub-minute timescale altered the percent of activating cells (Figure 4). Nearly, all cells respond for durations exceeding 1 min at 500 ng/ml. Notably, in contrast to changing concentration under constant long duration, which introduces timing delay and heterogeneity (Figures 2C, 3D), changing sub-minute duration of a high-amplitude signal in simulation controlled fraction of active cells while maintaining uniformly timed, rapid NF-κB responses (Figure 4B,D and Figure 4—figure supplement 1).

Figure 4.

Model simulation predicts that stimulus duration controls fraction of activating cells and response timing variability.

(A) Simulated fractions of activated cells under increasing duration of 500 ng/ml LPS pulse. (B) Sample simulated curves of NF-κB under 5- to 40-s duration LPS (500 ng/ml) pulse. (C) Distributions of nuclear NF-κB amplitude and (D) response times of activating cells under various durations of LPS treatment. In box and whisker plots (C, D), the central red line is the median, the edges of the box are the 25th and 75th percentiles, and the whiskers extend to the most extreme data points.

DOI: http://dx.doi.org/10.7554/eLife.08931.010

The concentration of LPS is 500 ng/ml. Color: activated cells. Gray: inactivated cells. (Note: y-scale changes between plots.)

DOI: http://dx.doi.org/10.7554/eLife.08931.011

Figure 4—figure supplement 1.

(A–F) Simulated NF-κB single-cell trajectories with randomly sampled numbers of TLR4 and NF-κB for 1- to 60-s durations of LPS exposure.

The concentration of LPS is 500 ng/ml. Color: activated cells. Gray: inactivated cells. (Note: y-scale changes between plots.)

DOI: http://dx.doi.org/10.7554/eLife.08931.011

We experimentally provided pulsed LPS at 500 ng/ml for sub-minute durations using microfluidic cell culture (Figure 5A). In agreement with simulation predictions, we found that precisely controlled stimulus duration regulated the activation of cells in the population in a strongly all-or-none manner, with 1- to 40-s duration LPS exposure (500 ng/ml) activating ∼3–88% of the population (Figure 5B and Supplementary Videos 1, 2). Short duration (i.e., 1 s) stimulation, mimicking very brief exposure to bacteria, activated a small percentage of cells in the population. Moreover, under short duration, strong amplitude (SS) input, responses were fast and uniform (Figure 5B, top row) in contrast to low, long (LL) stimulation that led to delayed, variable responses (Figure 2C). For example, 3–5% activation occurred for both a 1-s short pulse at 500 ng/ml LPS (SS signal) and a 0.25 ng/ml constant input signal (LL signal) (Figure 5B, Figure 2D). However, modulating duration of the SS signal from 1 s to 40 s (activating 3.3% and 87.5% the population, respectively) changes median response timing by less than 2 min (Figure 5B,C). Statistical analysis indicates no significant difference in response time under varied pulse durations (Figure 5—figure supplement 2). In contrast, modulating concentration of the LL signal from 0.25 to 500 ng/ml (activating 4.9% and 98% of the population, respectively) changes the response time more than 35 min (reduced from 80 to 43 min). Moreover, while the variability in the response time scales with dose under LL stimulation, timing variability remains low under duration-modulated SS stimulation (Figures 4D, 5C). From an immunological perspective, this experiment indicates that brief but high pathogen load leads to uniform and strong NF-κB response in the population, while chronic low-grade pathogen exposure leads to population variability and delay.

Figure 5.

Short duration LPS pulse stimulation modulates responding cell fraction and fast, uniformly timed response.

(A) LPS duration is manipulated using microfluidic cell culture in the range of 1–40 s. Dose is held constant at 500 ng/ml. (B) Single-cell NF-κB trajectories for 1- to 40-s duration LPS pulse stimulation. Short pulse LPS reduces variation in timing in the start of NF-κB activation. (C) Top panel: fraction of active cells as a function of LPS pulse duration. (Plotted points are the mean of two duplicate chambers in chip.) Middle panel: NF-κB nuclear response intensity as a function of LPS pulse duration. Lower panel: time of the NF-κB response peak as a function of LPS pulse duration. Timing variability is dramatically reduced under short-pulsed stimulation (see Figure 2D for comparison to constant stimulation). In middle and lower panels, data points and error bars represent median and interquartile range, respectively.

DOI: http://dx.doi.org/10.7554/eLife.08931.012

(A) Single-cell NF-κB trajectories for TNF pulse durations of 1, 5, 10, 20, 40, and 60 s. The number and percent of activated cells is indicated in the plot. (B) Comparison of active NF-κB cell fraction (top), response amplitude (middle), and response time (bottom) under LPS vs TNF pulses. The fraction-active curve is less steep under TNF than LPS. Fraction of active cells is plotted as mean for two duplicate cell chambers for each condition. In middle and lower panels, data points and error bars represent median and interquartile range, respectively. LPS data are duplicated from main Figure 5C for comparison.

DOI: http://dx.doi.org/10.7554/eLife.08931.013

Each table contains p-values of two-sample T-test comparing each duration combination. Red denotes statistical significance (p < 0.05).

DOI: http://dx.doi.org/10.7554/eLife.08931.014

Each table contains p-values of two-sample T-tests comparing each duration combination. Overall, amplitude is affected to a greater extent than response time under changing TNF duration. Red denotes statistical significance (p < 0.05).

DOI: http://dx.doi.org/10.7554/eLife.08931.015

Figure 5—figure supplement 2.

Statistical analysis for NF-κB peak amplitude and timing measurements under LPS duration modulation (corresponding to Figure 5B).

Each table contains p-values of two-sample T-test comparing each duration combination. Red denotes statistical significance (p < 0.05).

DOI: http://dx.doi.org/10.7554/eLife.08931.014

Digital NF-κB response unders 1 second duration LPS exposure (500 ng/ml).

This video shows fibroblast cells expressing NF-κB p65-dsRed responding in a digital fashion to brief (1-s duration) stimulus in a microfluidic chamber. Only 3–4% of cells show a response.

DOI: http://dx.doi.org/10.7554/eLife.08931.016

Digital NF-κB response under 10 second duration LPS exposure (500 ng/ml).

This video shows fibroblast cells expressing NF-κB p65-dsRed responding in a digital fashion to 20-s duration stimulus in a microfluidic chamber, activating more than half (∼55%) of cells in the population.

DOI: http://dx.doi.org/10.7554/eLife.08931.017

We next changed the stimulus type to TNF instead of LPS. In vivo, TNF is secreted from immune cells that come in contact with pathogenic signals like LPS. Again, we observed the phenomena that the fraction of active cells changed while the response timing did not (Figure 5—figure supplement 1), though amplitude is more significantly affected (Figure 5—figure supplement 3). Together, these results indicated that SS input achieves control over the fraction of cells activating without affecting the dynamics in the response. Therefore, duration sensing allows control of percentage of cells that produce a response without affecting response timing or heterogeneity. This contrasts to amplitude (concentration) sensing, where response dynamics in activating cells differs for high versus low amplitude. Since NF-κB dynamics influence gene expression, duration modulation to control percent population activation is therefore a strategy to achieve more homogeneous gene expression and phenotype outcomes between cells.

Figure 5—figure supplement 3.

Statistical analysis for NF-κB peak amplitude and timing measurements under TNF (10 ng/ml) duration modulation (corresponding to Figure 5—figure supplement 1).

Each table contains p-values of two-sample T-tests comparing each duration combination. Overall, amplitude is affected to a greater extent than response time under changing TNF duration. Red denotes statistical significance (p < 0.05).

DOI: http://dx.doi.org/10.7554/eLife.08931.015

Integral of stimulus determines fraction of active cells in the population

We sought to fully characterize the relationship between signal amplitude and duration in NF-κB switch activation. Since modulating either amplitude or duration was able to change the percentage of activating cells, we hypothesized that the fraction of activation may depend on the integral of the input (concentration × duration). Indeed, mathematical analytical analysis suggested that percent activating cells should scale with the input area (Appendix 1).

To validate our mathematical analysis and clarify how digital activation integrates stimulus dose and duration, we performed simulations. Each simulation series fixed the LPS stimulus dose and varied duration from 1 to 500 s. The output of these simulations as a function of stimulus duration shows multiple dose-response curves that do not coincide, indicating that duration is not the only predictor of switching probability or fraction of active cells (Figure 6A). However, when instead plotted as a function of stimulus area (concentration × duration), all simulation series closely coincide, indicating that stimulus area clearly determines the percentage of cells that activate in the population (Figure 6A).

Figure 6.

Simulations demonstrating an ‘Area Rule’, that is, the relationship between LPS stimulus area and fraction of active cells.

(A) The simulated fractions of activated cells for pulsed inputs of LPS with various doses and durations. Each fraction is estimated by 500 independent simulations. When the points are plotted as a function of stimulus area (rather than duration), all points fall on the same curve, indicating that stimulus area tightly controls the fraction of active cells. (B) The minimal duration for certain fractions of activation as a function of dose. The minimal duration is determined by searching for the first tested time point where the estimated fractions of activation are above the threshold. The doses for which the threshold level cannot be achieved are not shown in the figure. Blue: 10% activation, green: 50% activation, red: 90% activation. (C) Further verification of the relationship between stimulus area and active cell fraction using square wave input profiles. Equal area input was generated using either a single pulse (top left), square wave with 10-s period (lower left), or square wave with 20-s period (top right). Regardless of input shape, all simulated points fall on the same curve when plotted as a function of stimulus area. For square wave inputs, one input begins high (blue) while another input (green) begins low. Note that the curves intersect for durations 10 s, 20 s, 30 s (or 20 s, 40 s, 0 s, … for the input with 20-s period) when area under the two signals is the same.

DOI: http://dx.doi.org/10.7554/eLife.08931.018

(A) Simulated fractions of activated cells for pulsed inputs of TNF with various doses and durations. (B) The minimal duration for certain fractions of activation as a function of dose. (C) Verification of the relationship between stimulus area and active cell fraction using square wave input profiles. Equal area input was generated using either a single pulse (top left), square wave with 10-s period (lower left), or square wave with 20-s period (top right).

DOI: http://dx.doi.org/10.7554/eLife.08931.019

To illustrate further the relationship between stimulus area and percentage of active cells, we plotted for each simulation dose the minimum duration needed to achieve 10%, 50%, and 90% activation (Figure 6B). This analysis revealed a reciprocal relationship between dose and duration in NF-κB switch activation (high dose requires less duration to achieve activation and vice versa). Simulations therefore supported analytical derivation of an ‘Area Rule’ in which concentration × duration determines the percentage of cells that activate in the population for a given stimulus.

Importantly, for concentrations that achieve less that 100% activation, increasing the duration infinitely will not further increase the active fraction (Figure 6B). Once duration is sufficiently long to activate the maximal potential cell fraction for a given dose, further increases in area by lengthening duration do not further increase percentage of active cells, indicating a limitation in the Area Rule.

We next simulated whether the Area Rule holds for fluctuating signals. When we compared a constant input signal to square wave input signals, with one square wave that ‘starts high’ and another that ‘starts low’, simulation revealed an equal percentage of activating cells when the two opposing square waves have equal area (i.e., the duration is a multiple of the square wave period) (Figure 6C). Further, the fraction of active cells matched that for a constant input signal with the same area (Figure 6C). Performing identical simulations using a model of TNF-induced NF-κB activation (Tay et al., 2010), we found that the Area Rule held also for the TNF network (Figure 6—figure supplement 1).

Figure 6—figure supplement 1.

Stimulus area simulation using a TNF model (Tay et al., 2010) revealed that the ‘Area Rule’ holds also for TNF.

(A) Simulated fractions of activated cells for pulsed inputs of TNF with various doses and durations. (B) The minimal duration for certain fractions of activation as a function of dose. (C) Verification of the relationship between stimulus area and active cell fraction using square wave input profiles. Equal area input was generated using either a single pulse (top left), square wave with 10-s period (lower left), or square wave with 20-s period (top right).

DOI: http://dx.doi.org/10.7554/eLife.08931.019

We found that in both the LPS amplitude-modulated and duration-modulated microfluidic experiments, stimulus area is an accurate predictor of fraction of active cells in the population (Figure 7A), as predicted by the model simulations. To experimentally verify that the integral over time of the input signal determines the fraction of activating cells, we performed microfluidic experiments varying temporal profile while maintaining the same integrated area. We observed 500 ng/ml LPS pulsed for 10 s activated approximately half the population (Figure 5C). Therefore, we tested two additional input profiles having the same area (5000 ng ml−1*s): 50 ng/ml for 100 s and 100 ng/ml for 50 s. In agreement with model prediction, each of these conditions also activates a similar fraction of the population (51% and 54%, respectively) (Figure 7C). Together, experimental findings, simulations, and mathematical analysis demonstrate how cells integrate amplitude and duration of input signals in switch-like pathway activation. Stimulus integral (or area) determines the effective ‘probability’ that a given cell activates NF-κB (based on the percentage that activate in the population). These results indicate that the pathogen load (i.e., LPS dose) and duration of exposure (i.e., LPS pulse duration) are integrated by NF-κB system and together determine the population response.

Figure 7.

Stimulus area determines NF-κB population response.

(A) Stimulus area determines fraction of active cells. The experimentally tested dose and duration inputs fall on the same hill-like activation curve when plotted as a function of stimulus area, as predicted by model simulations, indicating that total integrated ligand concentration (stimulus area) controls the probability of cell activation. These results show that pathogen load (i.e., LPS dose) and duration of exposure (i.e., LPS pulse duration) are integrated by NF-κB system and together determine the population response. (B) Response time discriminates between sustained, low intensity (blue) and transient, high intensity (red) stimulus. Data points and error bars represent median and interquartile range, respectively. (C) Experimental verification that stimulus integral over time determines the fraction of active cells. A pulse of either LPS 50 ng/ml for 100-s duration or 100 ng/ml for 50-s duration generated approximately the same responding cell percentage as a, 51% and 54% for the two inputs, respectively. (D) Input profile controls digital responses along two axes: integral over stimulus (area) controls the fraction of activated cells in the population. Input temporal profile (shape) controls dynamic heterogeneity in responding cells. In (B), data points and error bars represent median and interquartile range.

DOI: http://dx.doi.org/10.7554/eLife.08931.020

(A) Comparison of cell-to-cell dynamic heterogeneity for different fractions of active cells for either constant or pulsed input (Figures 2 and 5). Pulsed (duration-modulated) LPS input (red) achieves lower response time variability than constant (dose-modulated) input for the same fraction of active cells. (B) Unlike response delay, response intensity does not provide sufficient information to distinguish between pulsed LPS and constant LPS signals. Data points and error bars represent median and interquartile range, respectively.

DOI: http://dx.doi.org/10.7554/eLife.08931.021

Amplitude and duration information transfer via digital NF-κB activation

We showed that modulating stimulus amplitude altered response dynamics by changing the amount of activation delay. In contrast, modulating stimulus duration did not affect activation delay but changed the population variability. These findings indicate tradeoffs in dose versus duration sensing. Duration sensing allows for controlling only the population response while not affecting the single-cell response, so that it is possible to achieve homogeneous dynamics and uniform phenotype in a desired proportion of cells. In contrast, it may be useful to transmit information that can instruct different dynamics and phenotype, which is achieved by modulating dose. While dose information is transmitted through the NF-κB digital response, duration information is lost at the single-cell level.

However, transmitting information using only dose modulation necessarily changes the percentage of cells in the population that respond. In physiological settings, it may be desirable to transmit information without affecting population response, that is, for a signal to affect response dynamics in activating cells without impacting the proportion that activate. To achieve this requires modulating both dose and duration to maintain input area, leading to a shift in input temporal profile from a SS to a LL signal. Cells distinguish an SS versus LL signal profile based on NF-κB and gene expression dynamics. We show that an intense, brief (SS) signal induces distinct dynamics than a weak, sustained (LL) signal, but the percentage of cells responding is the same in both cases (Figure 2C, Figure 5B). Response timing and intensity are dynamic features that provide information for discriminating input temporal profile. Indeed, plotting response delay as a function of stimulus area shows that SS and LL signals can be distinguished on the basis of response delay (Figure 7B). Cells can discern the category of the signal (whether SS or LL) for a given input area based on whether the response time falls above or below a separation line (Figure 7B). Modulating input amplitude associated with higher timing variability than input duration modulation for controlling the fraction of active cells (Figure 7—figure supplement 1A). Because response amplitude exhibits high variability between cells, amplitude alone does not provide sufficient information to discriminate an SS versus LL signal (Figure 7—figure supplement 1B). Physiological cues are in fact commonly transmitted by changing from an SS to an LL input profile (Iezzi et al., 1998; Fu et al., 2014). Biological systems therefore appear to take advantage of the unique ability of digital signaling to separate control of population and single-cell dynamics, by modulating input area to determine the proportion of cells that activate in the population and input shape to instruct to determine phenotype outcomes in the activating subset of cells (Figure 7).

Figure 7—figure supplement 1.

LPS response heterogeneity under pulsed and continuous input.

(A) Comparison of cell-to-cell dynamic heterogeneity for different fractions of active cells for either constant or pulsed input (Figures 2 and 5). Pulsed (duration-modulated) LPS input (red) achieves lower response time variability than constant (dose-modulated) input for the same fraction of active cells. (B) Unlike response delay, response intensity does not provide sufficient information to distinguish between pulsed LPS and constant LPS signals. Data points and error bars represent median and interquartile range, respectively.

DOI: http://dx.doi.org/10.7554/eLife.08931.021

Discussion

This study asked how stimulus amplitude and duration determine NF-κB digital activation. Modeling and experiments showed that NF-κB activation is achieved by integrating the input: stimulus integral or area (concentration × duration) controlled the percentage of cells that activated for both a ‘foreign’ pathogen signal LPS and a ‘self’ immune signal TNF (population response). However, switch dynamics and gene expression phenotype varied depending on the input dose (single-cell response), with rapid homogeneous responses at high dose and delayed heterogeneous responses at low dose. Dynamics of transcription factor activation determine the timing and specificity of gene expression and phenotype responses (Werner et al., 2005; Kobayashi et al., 2009; Purvis et al., 2012). Therefore, intercellular signaling systems may achieve distinct phenotype outcomes by controlling the input shape or temporal profile (whether SS or LL), while input area determines percentage of cells that respond (Figure 7B). Greater heterogeneity with decreasing dose and decreased heterogeneity under short duration input is measured by coefficient of variation (Figure 7—figure supplement 1).

In lymphocyte signaling, T- and B-cells' cell fate depends on both antigen quality (affinity) and quantity (amount of presented antigen). Antigen quality is encoded in the duration of receptor-antigen contact, with characteristic interaction times on the order of seconds (Altan-Bonnet and Germain, 2005; Gottschalk et al., 2012; Miskov-Zivanov et al., 2013). T- and B-cell receptor binding with antigen-MHC triggers digital activation and cell fate control via NF-κB (Kingeter et al., 2010; Oh and Ghosh, 2013; Gerondakis et al., 2014; Shinohara et al., 2014). A reciprocal relationship is observed between antigen quality and quantity in lymphocyte activation: Higher antigen affinity requires lower dose of antigen to trigger T-cell proliferation, and inversely, lower affinity requires higher dose (Gottschalk et al., 2012). Moreover, an intense, transient compared to a weak, sustained signal induces positive versus negative selection of naive thymic T cells (Iezzi et al., 1998) and T helper cell differentiation into alternatively CD4 or CD8 status (Adachi and Iwata, 2002). Therefore, analogous to our findings, while a combination of antigen dose and contact duration determines the probability of activation, input profile determined by relationship between antigen quality and quantity decides the phenotypic outcome of lymphocyte activation.

We show that switch-like signaling enables parallel and independent control over response probability and response dynamics: while stimulus area (concentration × duration or antigen quantity × quality) regulates the percentage of cells that respond, the stimulus temporal profile or shape (for example, whether short-strong or low-long or antigen quality/quantity ratio) determines the response timing and gene expression phenotype in responding cells. Dose and duration sensing may be beneficial in different contexts. Dose information is encoded in the delay timing and heterogeneity of NF-κB response. On the other hand, modulating duration on the sub-minute timescale does not regulate response dynamics. Indeed, achieving control of percentage active in a population without introducing heterogeneity requires modulating duration of a high-dose input (Figure 4). It was shown that signaling dynamics mediates transfer of input dose information (Selimkhanov et al., 2014). We find that while dose information is transmitted through dynamics of NF-κB activation, on short (minute) time scales duration, information is lost in the single-cell response but retained in the population response (fraction of activated cells).

Between the innate immune signals TNF and LPS, we found that LPS exhibits greater ultrasensitivity (a steeper stimulus-response curve) and more pronounced activation delay than TNF. Both of these features are explained by higher coopertivity in IKK activation for LPS than for TNF (Figure 3—figure supplement 2B). Distinct higher order adapter protein architectures may activate IKK with different effective coopertivities (Kazmierczak and Lipniacki, 2010). We note that the LPS-signaling response in macrophages may differ from that in 3T3 cells, including effects due to stronger auto and paracrine TNF signaling.

Figure 3—figure supplement 2.

Modelling predictions for the LPS pathway.

(A) Extrinsic noise is generated by selecting the number of TLR4 molecule for each cell from a lognormal distribution. Fraction of active cells was analyzed for increased TLR4 variability (parameter Sigma). With higher TLR4 number variability, the change in fraction of active cells becomes more gradual with changing LPS concentration. (B) Simulation response delay under varied LPS dose with and without clustering. Clustering mediating cooperative IKK activation is required to reproduce the experimentally observed response delay with decreasing LPS dose. Central point and error bars represent median and interquartile range, respectively.

DOI: http://dx.doi.org/10.7554/eLife.08931.009

While TNF signaling activates formation of a filamentous amyloid complex involving RIP1 and RIP3 kinases, LPS signaling is mediated through helical assembly of the Myddosome complex (Lin et al., 2010), which interfaces with a TRAF6 lattice structure to activate IKK (Yin et al., 2009). Heterogeneity in switching threshold between cells may arise from cell-to-cell expression differences in signalosome components such as RIP1/3, MyD88, IRAK2/4, and TRAF6, leading to altered kinetics of signalosome assembly and IKK activation. Because the IKK hub mediates NF-κB responses for a multitude of input types and coordinates cross-talk with other signaling pathways, understanding how different signalosome architectures induce specific responses paves the way to interventions directed at switch-like signaling to modulate population and individual cell dynamics towards therapeutic outcomes (Negro et al., 2008; Behar et al., 2013). In this study, we have shown that the switch-like character of NF-κB activation enables orthogonal control over two critical aspects of the response—probability of activation (fraction of active cells) and the heterogeneity of response—through the integral and temporal profile of the input. Secretion of signaling molecules often occurs in discrete or quantized way in the form of secretory bursts, and particularly in the case of short range paracrine signaling, cells may produce brief but intense secretion to achieve, for example, low probability but high predictability responses (non-heterogeneous dynamics). Overall, these results expand the repertoire of functions for digital signaling beyond increasing robustness to also facilitate multidimensional phenotype control based on temporal information in input signals.

Materials and methods

Cell lines

We used p65-knockout 3T3 fibroblasts (courtesy Markus Covert) modified using lentiviral vectors to express p65-DsRed under its endogenous promoter along with an H2B-GFP nuclear reporter, as described previously (Lee et al., 2009). The cell line was clonally derived to express at p65-DsRed at lowest detectable level to preserve near endogenous expression.

Automated microfluidic cell culture system

Automated microfluidic cell culture was performed as previously described (Gómez-Sjöberg et al., 2007; Tay et al., 2010; Kellogg et al., 2014). Briefly, microfluidic chambers were fibronectin treated and seeded with cells at approximately 200 cells/chamber. Cells were allowed to grow for 1 day with periodic media replenishment until 80% confluence. To stimulate cells, media equilibrated to 5% CO2 and containing the desired LPS amount was delivered to chambers, leading to a step increase in LPS concentration. All LPS doses were tested in parallel in a single chip. To produce LPS and TNF pulses, chambers were washed with media after incubation with ligand for the desired duration. Stimulations were applied in duplicate chambers on the chip. Following stimulation, chambers were sealed and imaged at 5- to 6-min intervals.

Image acquisition and data analysis

DsRed and GFP channels were acquired using a Leica Microsystems (Wetzlar, Germany) DMI6000B widefield microscope at 20× magnification with a Retiga-SRV CCD camera (QImaging - Surrey, BC, Canada) using Leica L5 and Y3 filters to acquire GFP and DsRED signals, respectively, and a Leica EL6000 mercury metal halide light source. One or two images were acquired per chamber and stitched if required using ImageJ (Pairwise stitching plugin). CellProfiler software (www.cellprofiler.org) and custom Matlab software was used to automatically track cells and quantify NF-κB translocation, and automated results were manually compared with images to ensure accuracy prior to further analysis. Mitotic cells were excluded from analysis. NF-κB activation was quantified as mean nuclear fluorescence intensity normalized by mean cytoplasm intensity. Area of the first peak was integrated after baseline correction from the time of LPS stimulation to the first minimum for each cell using Matlab function trapz. For peak analysis, data were smoothed (Matlab function smooth) followed by peak detection (Matlab function mspeaks) to extract NF-κB peak properties (intensity, area, delay) with manual verification using a custom interface in Matlab. Statistical analysis of NF-κB peak amplitude and timing data was performed by unpaired two-sample T-test (Matlab function ttest2).

Gene expression

Cells were seeded at 10,000 cells/well in a 96-well plate and left to attach overnight before stimulation with LPS (1–500 ng/ml). Cells were stimulated with LPS and then lysed, the RNA reverse-transcribed and cDNA pre-amplified (specific target amplification with the set of 24 primers) using the One-Step RT-PCR kit from Invitrogen (San Diego, CA, United States). Quantitative PCR with technical duplicates was carried out on 48.48 dynamic arrays from Fluidigm according to manufacturer instructions, and expression was normalized to GAPDH.

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Thank you for submitting your work entitled “Digital signaling decouples activation probability and population heterogeneity” for peer review at eLife. Your submission has been favorably evaluated by Naama Barkai (Senior editor) and three reviewers, one of whom is a member of our Board of Reviewing Editors.

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This is an interesting study of digital signaling dynamics using LPS-stimulated NF-kB activation in 3T3 cells as a model system. Microfluidic analysis is used to follow the behavior of single cells. The authors report the analysis of a dose response (under non-pulse conditions) and a pulse-length study with a high LPS dose together with simulation studies based on a mathematical model. The authors conclude that the fractional digital response to LPS is increased with both dose and pulse length. Please address the following points in a revised submission:

A) The experimental data requires statistical analysis. Error bars are missing in some Figure panels (or are present, but not defined in some other panels) and the number of biological replicates is not stated. Moreover, conclusions based on the experimental data are not supported by statistical tests.

B) The term “full response” should be to be clarified. A “full response” implies that most, if not all, NF-κB translocates to the nucleus (as in high dose stimulation), yet Figure 2C (0.25ng/ml LPS) does not appear to show this. In addition, the authors state that the Nuc-NF-κB is constant on average, yet the single-cell traces clearly gives the impression that the amplitude increases with respect to the concentration. Figure 3C and E (model) predicts quite striking amplitude changes as the dose is varied. Moreover, the simulation (Figure 3–figure supplement 1) uses different scales for different treatments (showing the amplitude decreasing with lowering the dose). In addition, the pulse-length study with TNF (Figure 5–figure supplement 1A) appears to show a graded response, but this is not represented in Figure 5–figure supplement 1B).

C) The conclusion of a Hill coefficient of 2 (Figure 2D) is problematic because of the absence of data between 1 and 5ng/ml. Moreover, if the Hill coefficient is 2, why is a Hill coefficient of 4 used in the model?

D) The criteria for inclusion/exclusion of NF-kB pathway characteristics in the model are unclear. Is variable TLR4/CD14 expression the mechanism of NF-κB dynamics variability? Is MyD88 the mechanism of non-linearity? What justifies the focus on these features of the NF-kB pathway?

E) The model simulation data are interesting, but the usefulness of the model is to generate hypotheses concerning signaling network behavior. The authors need to experimentally test a model-based prediction. In this case, the model is used to predict the response to different pulse length variations for intermediate LPS doses (Figure 6). However, the experimental data shown is limited to a dose response (under non-pulse conditions) and a pulse-length study with a high LPS dose.

A) The experimental data requires statistical analysis. Error bars are missing in some Figure panels (or are present, but not defined in some other panels) and the number of biological replicates is not stated. Moreover, conclusions based on the experimental data are not supported by statistical tests.

We performed statistical analysis of all amplitude and timing data and included this in as additional supplementary figures associated with Figures 2 and 5. These new figures are Figure 2–figure supplement 2, Figure 5–figure supplement 2, and Figure 5–figure supplement 3. We now refer to this analysis in the claims in the main text (subsections “NF-κB switch dynamics distinguish pathogen (LPS) and host (TNF) signals”, “Response timing and single-cell heterogeneity depends on stimulus intensity” and “Input duration controls activation probability independent of response heterogeneity”). Error bars are included in all places applicable and we clarify the meaning of error bars in the figure captions. Data are plotted as median with interquartile range. The manuscript text is updated to reflect the number of biological replicates, two duplicate microfluidic chambers per condition (subsections “NF-κB switch dynamics distinguish pathogen (LPS) and host (TNF) signals” and “Automated microfluidic cell culture system”).

B) The term “full response” should be to be clarified. A “full response” implies that most, if not all, NF-κB translocates to the nucleus (as in high dose stimulation), yet (0.25ng/ml LPS) does not appear to show this. In addition, the authors state that the Nuc-NF-κB is constant on average, yet the single-cell traces clearly gives the impression that the amplitude increases with respect to the concentration. (model) predicts quite striking amplitude changes as the dose is varied. Moreover, the simulation () uses different scales for different treatments (showing the amplitude decreasing with lowering the dose). In addition, the pulse-length study with TNF () appears to show a graded response, but this is not represented in ).

We have revised the text to clarify these points. We do observe responses at lowest doses where nearly all NF-κB enters the nucleus (see Figure 2B). Amplitude is highly variable across doses, and while median amplitude increases gradually with dose the change is statistically less significant than changes in response time (Figure 2–figure supplement 2) (subsection “NF-κB switch dynamics distinguish pathogen (LPS) and host (TNF) signals”). We acknowledge greater amplitude dependence on dose in the model (subsection “Cooperative IKK activation underlies dose-dependent response delay”) and add notes to indicate the changing y-scale in Figure 3–figure supplement 1 and Figure 4–figure supplement 1. Figure 5–figure supplement 1B represents analysis of the traces presented in Figure 5–figure supplement 1A. Statistical analysis shows overall that amplitude does modulate significantly with duration change (Figure 5–figure supplement 3; subsection “Input duration controls activation probability independent of response 151 heterogeneity”).

C) The conclusion of a Hill coefficient of 2 () is problematic because of the absence of data between 1 and 5ng/ml. Moreover, if the Hill coefficient is 2, why is a Hill coefficient of 4 used in the model?

The experimental hill coefficient refers to the steepness in increase in fraction of activating cells with increasing input level. We incorporated analysis of 3ng/ml LPS into Figure 2, which activated 40.6% of the population. Refitting the Hill curve led to a steepness coefficient of 2.3, which we updated in the main text (subsection “NF-κB switch dynamics distinguish pathogen (LPS) and host (TNF) signals”).

The comment about hill coefficient of 4 in the model (subsection “Cooperative IKK activation underlies dose-dependent response delay”, last paragraph) refers to the cooperativity in IKK activation by TRAF6 (distinct from the slope in the fraction of activation as a function of dose). We now term this value cooperativity coefficient and add a note to avoid this confusion.

D) The criteria for inclusion/exclusion of NF-kB pathway characteristics in the model are unclear. Is variable TLR4/CD14 expression the mechanism of NF-κB dynamics variability? Is MyD88 the mechanism of non-linearity? What justifies the focus on these features of the NF-kB pathway?

Inclusion/exclusion of NF-κB pathway characteristics in the model is based on the available information about LPS-NF-κB signaling, maintaining model simplicity, and following methodology consistent with currently accepted NF-κB models. The mathematical supplement sections 1 and 2 contain substantial discussion of our process and decisions in constructing the model.

To explain observed heterogeneity in cell responses it is enough to assume that cells have different sensitivities to the signal, which can result from broad distribution of receptors. Receptor level variation is a major source of heterogeneity between cells, though we acknowledge that other sources of heterogeneity could contribute (subsection “Cooperative IKK activation underlies dose-dependent response delay”). The nonlinearity results from clustering and oligomerization of receptors and adapter proteins including MyD88 and TRAF6. Multiple studies support that clustering mediates digital activation in NF-κB signaling (discussed in the aforementioned subsection) though we discuss other cases where additional factors may contribute (Introduction, first paragraph). We have updated the supplemental mathematical materials for clarity and with additional details of the methodology and justification in building the model.

E) The model simulation data are interesting, but the usefulness of the model is to generate hypotheses concerning signaling network behavior. The authors need to experimentally test a model-based prediction. In this case, the model is used to predict the response to different pulse length variations for intermediate LPS doses (). However, the experimental data shown is limited to a dose response (under non-pulse conditions) and a pulse-length study with a high LPS dose.

We use the model to generate the hypothesis that integral of the input determines the fraction of activating cells, which is supported by the experimental dose response and high-dose pulse data. We now test this prediction in new experiments further by comparing inputs with different temporal profiles but equal integral (area). We observed 500ng/ml LPS pulsed for 10 s activated approximately half the population (Figure 5C). Therefore we tested two additional input profiles having the same area (5000 ngml-1/s): 50ng/ml for 100s and 100ng/ml for 50s. In agreement with model prediction, each of these conditions also activates a similar fraction of the population (51% and 54%, respectively). This is discussed in the main text (subsection “Integral of stimulus determines fraction of active cells in the population”, last paragraph) and Figure 7 has been updated with trajectories and images from these experiments.

Appendix table 1.

The reactions in the TLR4-MyD88-dependent branch

DOI: http://dx.doi.org/10.7554/eLife.08931.023

Reaction/Description	Rate laws
LPS → ∅	ld[LPS]
Degradation of LPS
LPS + CD14 → LPS.CD14	lb,CD14[LPS][CD14]
Association of LPS and CD14
LPS.CD14 → LPS + CD14	lf,CD14[LPS.CD14]
Dissociation of LPS.CD14
LPS.CD14 → LPS.CD14.int	lin,CD14[LPS.CD14]
Internalization of LPS.CD14
LPS.CD14.int → LPS.CD14	lout,CD14[LPS.CD14.int]
Externalization of LPS.CD14.int
LPS.CD14 + TLR4 → LPS.CD14.TLR4	lb[LPS.CD14][TLR4]
Association of LPS.CD14 and TLR4
LPS.CD14.TLR4 → LPS.CD14 + TLR4	lf[LPS.CD14.TLR4]
Dissociation of LPS.CD14.TLR4
TRAF6 → TRAF6a	l_a[LPS.CD14.TLR4][TRAF6]k_M,A20k_M,A20+[A20]
Activation of TRAF6 by LPS.CD14.TLR4
TRAF6a → TRAF6	li[TRAF6a]
Inactivation of TRAF6
IKKn → IKKa	c_1[TRAF6a]^n[TRAF6a]^n+KIKKKn[IKKn]
Activation of IKK by TRAF6a

Appendix table 2.

The additional reactions in the TLR4-TRIF-dependent branch

DOI: http://dx.doi.org/10.7554/eLife.08931.024

Reaction/Description	Rate laws
LPS.CD14.TLR4 → LPS.CD14.TLR4.int	lin[LPS.CD14.TLR4]
Internalization of LPS.CD14.TLR4
LPS.CD14.TLR4.int → LPS.CD14.TLR4	lout[LPS.CD14.TLR4.int]
Externalization of LPS.CD14.TLR4.int
TRAF6 → TRAF6a	l_a,int[LPS.CD14.TLR4.int][TRAF6]k_M,A20k_M,A20+[A20]
Activation of TRAF6 by LPS.CD14.TLR4.int

Appendix table 3.

The reactions upstream of IKK activation in the final model

DOI: http://dx.doi.org/10.7554/eLife.08931.025

Reaction/Description	Rate laws
LPS → ∅	ld[LPS]
Degradation of LPS
LPS + TLR4 → LPS.TLR4	lb[LPS][TLR4]
Association of LPS and TLR4
LPS.TLR4 → LPS + TLR4	lf[LPS.TLR4]
Dissociation of LPS and TLR4
TRAF6 → TRAF6a	l_a[LPS.TLR4][TRAF6]k_M,A20k_M,A20+[A20]
Activation of TRAF6 by LPS.TLR4
TRAF6a → TRAF6	li[TRAF6a]
Inactivation of TRAF6a
IKKn → IKKa	c_1[TRAF6a]^n[TRAF6a]^n+KIKKKn[IKKn]
Activation of IKKn by TRAF6a

Appendix table 4.

The conversion table of LPS between concentrations and molecular numbers

DOI: http://dx.doi.org/10.7554/eLife.08931.027

Concentrations (/ng⋅ml^−1)	Molecular numbers
500	1.2 × 107
100	2.4 × 106
50	1.2 × 106
10	2.4 × 105
5	1.2 × 105
1	2.4 × 104
0.5	1.2 × 104
0.25	6.0 × 103

Appendix table 5.

The parameter values used in the model

DOI: http://dx.doi.org/10.7554/eLife.08931.028

Parameters	Biological meanings	Values	Remarks
ld	Degradation rate of LPS	5 × 10−4	Fitted
lb	Binding rate of LPS and TLR4	5 × 10−9	Fitted
lf	Unbinding rate of LPS.TLR4	4.5 × 10−4	Fitted
la	Activation rate of TRAF6	1 × 10−7	Fitted
kM,A20	Constant for repressed TRAF6 activation	1 × 105	Assume same as Tay et al. (2010)
li	Inactivation rate of TRAF6a	1 × 10−2	Assume same as Tay et al. (2010)
c1	Activation rate of IKK	2 × 10−2	Fitted
KIKKK	Dissociation constant for IKK activation	3.5 × 103	Fitted
n	Hill coefficient	4	Fitted, with support from Yin et al. (2009)
MIKKK	Total number of TRAF6	105	Assume same as Tay et al. (2010)