Modeling Cellular Noise Underlying Heterogeneous Cell Responses in the Epidermal Growth Factor Signaling Pathway

<div><p>Cellular heterogeneity, which plays an essential role in biological phenomena, such as drug resistance and migration, is considered to arise from intrinsic (i.e., reaction kinetics) and extrinsic (i.e., protein variability) noise in the cell. However, the mechanistic effects of these types of noise to determine the heterogeneity of signal responses have not been elucidated. Here, we report that the output of epidermal growth factor (EGF) signaling activity is modulated by cellular noise, particularly by extrinsic noise of particular signaling components in the pathway. We developed a mathematical model of the EGF signaling pathway incorporating regulation between extracellular signal-regulated kinase (ERK) and nuclear pore complex (NPC), which is necessary for switch-like activation of the nuclear ERK response. As the threshold of switch-like behavior is more sensitive to perturbations than the graded response, the effect of biological noise is potentially critical for cell fate decision. Our simulation analysis indicated that extrinsic noise, but not intrinsic noise, contributes to cell-to-cell heterogeneity of nuclear ERK. In addition, we accurately estimated variations in abundance of the signal proteins between individual cells by direct comparison of experimental data with simulation results using Apparent Measurement Error (AME). AME was constant regardless of whether the protein levels varied in a correlated manner, while covariation among proteins influenced cell-to-cell heterogeneity of nuclear ERK, suppressing the variation. Simulations using the estimated protein abundances showed that each protein species has different effects on cell-to-cell variation in the nuclear ERK response. In particular, variability of EGF receptor, Ras, Raf, and MEK strongly influenced cellular heterogeneity, while others did not. Overall, our results indicated that cellular heterogeneity in response to EGF is strongly driven by extrinsic noise, and that such heterogeneity results from variability of particular protein species that function as sensitive nodes, which may contribute to the pathogenesis of human diseases.</p></div

Effects of protein variability of each species on heterogeneity in nuclear ERK.

<p>CV of nuclear ERK with changes in protein variability of each species at (A) low (0.05 ng/mL) and (B) high (50 ng/mL) concentrations of EGF. Circle size represents CV of nuclear ERK. (C) CV of nuclear ERK at various concentrations of EGF when changing protein variability of each species. The patterns of CV were classified into three types. CV of 25% was used as protein variability of each species. The gray region represents the area from EC10 (0.02 ng/mL) to EC90 (0.12 ng/mL) calculated from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005222#pcbi.1005222.g001" target="_blank">Fig 1D</a>.</p

Direct comparison of simulation results with experimental data.

<p>(A) CV of simulated nuclear ERK without/with AME are shown. Points represent experimental data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005222#pcbi.1005222.ref014" target="_blank">14</a>]. (B) The residual sum of squares between simulation results with AME and experimental data. (C) Mutual information between EGF concentration and nuclear ERK was calculated from simulation results and experimental data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005222#pcbi.1005222.ref014" target="_blank">14</a>]. (D) Distributions of nuclear ERK in simulation results at 25% CV of protein variability and experimental data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005222#pcbi.1005222.ref014" target="_blank">14</a>].</p

Validation of EGF signaling pathway model.

<p>The time courses of changes in (A) phosphorylated and (B) nuclear ERK levels at different concentrations of EGF (0–50 ng/mL) are shown. EGF dose response of peak levels at (C) phosphorylated and (D) nuclear ERK were calculated from deterministic simulations. Points and lines represent observed data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005222#pcbi.1005222.ref014" target="_blank">14</a>] and simulation results, respectively. The effects of ERK-mediated regulation of NPC on the dose response of (E) phosphorylated and (F) nuclear ERK are shown. The Hill coefficients were obtained by curve fitting of simulation results.</p

Effects of covariation among initial proteins on heterogeneity in ERK.

<p>(A) An example of the relationship among proteins under initial conditions with and without covariation. Points represent different simulation data. (B) The distributions of steady-state levels of nuclear ERK at 25% CV of initial proteins under conditions of no stimulation with and without covariation. (C) CV of peak levels of nuclear ERK with and without covariation with or without application of AME.</p

Simplified reaction network of EGF signaling pathway model.

<p>Details of reactions are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005222#pcbi.1005222.s002" target="_blank">S1 Fig</a>.</p

Optical configurations.

<p>(A) TIRFM simulation module. (B) LSCM simulation modules. Grey arrows represent direction of photon propagation.</p

Simple models (A) 100 stationary HaloTag-TMR molecules are distributed on a glass surface. (B) 19,656 HaloTag-TMR molecules are distributed in a 30 × 30 × 6 <i>μ</i>m³ box of aqueous solution (= 5 nM), and rapidly diffuse at 100 <i>μ</i>m²/sec.

<p>Simple models (A) 100 stationary HaloTag-TMR molecules are distributed on a glass surface. (B) 19,656 HaloTag-TMR molecules are distributed in a 30 × 30 × 6 <i>μ</i>m³ box of aqueous solution (= 5 nM), and rapidly diffuse at 100 <i>μ</i>m²/sec.</p

Schematic overview of the computational framework.

<p>Direction of photon propagation is presented by thick blue arrows.</p

Using HaloTag-TMR molecules distributed on a glass surface to evaluate the performance of TIRFM simulation module.

<p>(A) Expected images of the simple particle model at various beam flux densities (20,30,40 and 50 W/cm²). The expected images are obtained by averaging 100 images over 3 sec exposure period. Intensity histograms are also shown below each expected images and presented with black-colored bars. Each histograms are logarithmically scaled and presented with grey-colored bars. (B) Simulated digital images of the simple particle model are shown at various beam flux densities (20,30,40 and 50 W/cm²). Size of each images is 152 × 156 pixel. Orange scalebar represents 3.15 <i>μ</i>m. Intensity histograms are also shown below each simulated images. (C) Real captured images obtained from <i>in vitro</i> experiment are shown at various beam flux densities (20,30,40 and 50 W/cm²). The maximum value of the grayscale is adjusted to improve visualization of each image. Intensity histograms are also shown below each actual images.</p