Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise

Abstract

Background: Cell-to-cell variability in protein expression can be large, and its propagation through signaling networks affects biological outcomes. Here, we apply deterministic and probabilistic models and biochemical measurements to study how network topologies and cell-to-cell protein abundance variations interact to shape signaling responses.

Results: We observe bimodal distributions of extracellular signal-regulated kinase (ERK) responses to epidermal growth factor (EGF) stimulation, which are generally thought to indicate bistable or ultrasensitive signaling behavior in single cells. Surprisingly, we find that a simple MAPK/ERK-cascade model with negative feedback that displays graded, analog ERK responses at a single cell level can explain the experimentally observed bimodality at the cell population level. Model analysis suggests that a conversion of graded input-output responses in single cells to digital responses at the population level is caused by a broad distribution of ERK pathway activation thresholds brought about by cell-to-cell variability in protein expression.

Conclusions: Our results show that bimodal signaling response distributions do not necessarily imply digital (ultrasensitive or bistable) single cell signaling, and the interplay between protein expression noise and network topologies can bring about digital population responses from analog single cell dose responses. Thus, cells can retain the benefits of robustness arising from negative feedback, while simultaneously generating population-level on/off responses that are thought to be critical for regulating cell fate decisions.

Figure 1

Cell population dose and dynamic response of ppERK to EGF. A-D. Each panel corresponds to a fixed time after EGF stimulations: 2 min (A), 5 min (B), 10 min (C) and 30 min (D). In each panel, the different colors correspond to different EGF doses as indicated by the visual legend. Each distribution is compiled from 10,000 individual HEK293 cell responses as measured by flow cytometry, and is representative of between three and six independent experiments. Events were gated based on forward and side scatter to exclude debris, dead cells, and cell clusters. The x-axis is the magnitude of activated ERK (ppERK) in arbitrary fluorescence units, and the y-axis is the frequency of observing a particular level of fluorescence in a cell. E. Total ERK abundance data. The best-fit gamma distribution curve is depicted by the green line, while the black line shows experimental data. Data are representative of five independent experiments, and were fit to a gamma distribution. Mean and standard deviation of the fit parameters are k = 5.4; θ = 2.7 × 10⁵ [AU]. F-I. Cells were stimulated with either 0.1 nM (F,H) or 1 nM (G,I) EGF for five minutes, and then analyzed by flow cytometry to measure ppERK and total ERK levels simultaneously. In F-G, black curves correspond to ppERK distributions, and green curves correspond to normalized distributions where ppERK levels in each cell were divided by the total ERK signal intensity in the same cell. To compare the green and black curves on the same axis, intensities for each distribution are divided by their respective mean. In the H-I dot plots, ppERK levels are on the x-axis, whereas total ERK levels are on the y-axis.

Figure 2

RasGTP Dynamics. A. HEK293 cells were stimulated with 0.1 nM (low, L), 1 nM (medium, M) or 10 nM (high, H) EGF for the indicated times and then cell lysates were assayed for RasGTP as described in “Materials and Methods” section. IP denotes the pull-down fraction, TCL denotes total cell lysate, and IB denotes immunoblot. Each data point corresponds to the average of three independent experiments, and error bars correspond to 90% confidence intervals. Data were normalized by dividing by basal (no EGF) RasGTP levels. B. A bimodal RasGTP distribution as would be obtained from a bistable RasGTP model for low, medium and high levels of EGF, and how it would map onto a dose–response relationship between RasGTP and ppERK.

Figure 3

Modeling and analysis of single cell characteristics of the ppERK dynamics and dose response. A. Schematic of a mechanistic model of ERK activation and its steady-state response properties. The positive feedback (PF), no-feedback, ultrasensitive (US), and negative feedback (NF) models have the feedback strength F_a set to different values (5, 1 and 0.5, respectively). The input is RasGTP, and the output is ppERK. B-D. Steady-state, deterministic input/output response curves for the PF, US and NF models. E-G. Steady-state, cell population input/output response curves for the PF, US and NF models. In B-G, red denotes increasing input from low levels, while blue denotes decreasing input from high levels. When only one color is shown, there is no difference between the increasing and decreasing input curves. Dashed lines indicate the 95^th percentile of all simulations, and dotted lines indicate the 5^th percentile.

Figure 4

Simulations of ppERK dynamics in cell populations. A. Simulated RasGTP dynamics for different EGF doses. Simulations were done as described in the “Materials and Methods” section. B-D. Simulated dose and dynamic ppERK responses for the PF (B), US (C) and NF (D) models. To facilitate comparison of these simulations with the experimental data, normally distributed noise with mean and standard deviation of 10 nM was added to the raw simulation data. (E-G) Dynamics and dose response of the ERK-on population mean for the PF (E), US (F), and NF (G) models. Simulated population responses were parsed into ERK-on and ERK-off populations based on a cutoff of 100 nM.

Figure 5

Confirming the presence of negative feedback. HEK293 cells were pretreated with 5 μM U0126 or vehicle alone (DMSO) for 30 min prior to stimulation with 0.1 nM, 1 nM or 10 nM of EGF (A) or TGFα (B) for 5 or 30 minutes. Control cells were left unstimulated (−). Total cell lysates were assayed for activated RasGTP as described in “Materials and Methods” section. IP denotes the pull-down fraction, TCL denotes total cell lysate, and IB denotes immunoblot.

Figure 6

Conversion of Analog Inputs Into Bimodal Responses by a Negative Feedback System Combined with Protein Expression Noise. An analog EGF stimulus (blue, green, and red correspond respectively to small, medium, and large stimulation magnitudes) induces variable but dose-dependent RasGTP responses in the cell population due to expression variability in the EGF pathway proteins. RasGTP responses are converted into ppERK responses in single cells according to a threshold-linear response governed by negative feedback (NF model). However, variability in RasGTP levels coupled with variability in ERK activation thresholds creates bimodal active ERK distributions at the population level despite the analog input and linear dose response at the single cell level.