Population robustness arising from cellular heterogeneity

Abstract

Heterogeneity between individual cells is a common feature of dynamic cellular processes, including signaling, transcription, and cell fate; yet the overall tissue level physiological phenotype needs to be carefully controlled to avoid fluctuations. Here we show that in the NF-kappaB signaling system, the precise timing of a dual-delayed negative feedback motif [involving stochastic transcription of inhibitor kappaB (IkappaB)-alpha and -epsilon] is optimized to induce heterogeneous timing of NF-kappaB oscillations between individual cells. We suggest that this dual-delayed negative feedback motif enables NF-kappaB signaling to generate robust single cell oscillations by reducing sensitivity to key parameter perturbations. Simultaneously, enhanced cell heterogeneity may represent a mechanism that controls the overall coordination and stability of cell population responses by decreasing temporal fluctuations of paracrine signaling. It has often been thought that dynamic biological systems may have evolved to maximize robustness through cell-to-cell coordination and homogeneity. Our analyses suggest in contrast, that this cellular variation might be advantageous and subject to evolutionary selection. Alternative types of therapy could perhaps be designed to modulate this cellular heterogeneity.

Fig. 1.

Transcriptional regulation of dual negative IκB feedback. (A) Schematic representation of the dual negative IκB feedback motif showing the time delay between activation of IκBα and IκBε transcription. (B–D) Quantitative RT-PCR analysis of IκBα and IκBε mRNA levels in mouse embryonic fibroblasts (MEF) cells stimulated with (B) 10 ng/mL TNFα, (C), 10 ng/mL IL-1β and (D) 100 μM PMA. Thick lines depict stimulation over a 480-min time course. Results (1 replicate) were normalized to unstimulated controls (in triplicates). Error bars (1 SD) were calculated by propagating the error from the unstimulated controls. Thin lines represent stimulation over 60-min time course (two replicates) normalized to the former at the 60-min time point.

Fig. 2.

Delay-induced heterogeneity of NF-κB oscillation timing. (A) Simulated nuclear NF-κB kinetics following chronic TNFα stimulation of WT and IκBε knock-out (IκBε^−/−) cells. Three single cell trajectories are shown with colored lines. The population average constructed from 500 cells is shown with a thick black line. (B) Analysis of single cell oscillation timing based on data in A. Variability is represented by Fano factor (variance normalized by average) of peak-to-peak timing.

Fig. 3.

IκBε transcriptional delay maximizes heterogeneity between individual cells. (A) Effect of the altered delay time. Fano-factor for nuclear NF-κB peak3-to-peak4 timing, based on 200 single cells simulated for 5-, 15-, 30-, 45- (WT), 60-, 75-, and 90-min transcriptional delay and IκBε-deficient cells (Fig. S12). (B) Effect of the distributed delay time. Fano-factor for nuclear NF-κB peak3-to-peak4 timing, based on 2,000 single cells simulated for distributed IκBε delay time vs. IκBε knock-out. The delay time was randomized according to a normal distribution with mean μ (min.) and SD σ, N (μ, σ²), in a population, but constant per cell (Fig. S13).

Fig. 4.

IκBε feedback decreases single cell sensitivity to parameter variation. (A) Correlation between the NF-κB expression level and peak2-to-peak3 oscillation timing. Model simulations (500 single cells) for WT (Left) and IκBε^−/− (Right) with the cellular NF-κB expression level uniformly distributed on the interval from 10,000–180,000 molecules. (B and C) Average sensitivity of nuclear NF-κB timing and amplitudes in WT and IκBε^−/−. Shown are averages of individual sensitivity coefficients normalized by the number of model parameters, Eq. S8, calculated for amplitudes (peak1, peak2, peak3) and peak timings (peak1 timing, peak2 timing, peak3 timing) of nuclear NF-κB. Forty-seven system parameters (in WT) and 33 parameters in IκBε^−/− were independently changed twofold in both directions with respect to the nominal value (500 simulated cells per parameter change). (B) Average first-order (mean) sensitivity of peak amplitudes (Left) and timing (Right). (C) Average second-order (variability of) sensitivity of peak amplitudes (Left) and timing (Right).

Fig. 5.

Cellular heterogeneity minimizes fluctuations in tissue-level paracrine secretion (A) Schematic representation of a putative feedback loop due to paracrine signaling. (B–E) Analysis of paracrine signaling in the open loop (dashed line in A disconnected in the model). The model incorporates regulation of a putative diploid paracrine gene using parameters that match the dynamics of TNFα transcription and translation. The simulations shown are based on 500 cells. (B) Average nuclear NF-κB levels for 45-min delay (in black) and 5-min delay (in red) in IκBε transcription as well as IκBε^−/− (in blue). (C) Average levels of paracrine protein, color-coded as in B. Ten-minute mRNA and protein half-life assumed. (D) Average levels of paracrine protein, color-coded as in B. The mRNA and protein half-lives are assumed to be 10 min and 45 min, respectively. (E) Distribution of peak timing and amplitude of paracrine protein, for data in C (color coding as in B).