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Figure 1. Computational simulations using reported levels of expression variation show a dramatic loss of analog single‐cell transmission accuracy
Schematic of a five‐step analog signaling pathway where the asterisk (*) represents the activated form which is assumed in this model to be a small fraction of the total.The timecourse plots show how relative threefold (red) and ninefold (blue) input changes in R result in analog output responses with different degrees of noise. Random lognormal expression variation was added simultaneously to each pathway component. The accuracy of analog signal transmission is dramatically reduced as the coefficient of variations (CVs) increase from 5% (top), 10% (middle), to 25% (bottom).Example of the output response distributions of unstimulated (black) and stimulated (green) cells at the fold‐Input Detection Limit (fIDL). The fIDL represents the minimal stimulus, R, needed to distinguish the output of stimulated cells from unstimulated cells with 95% accuracy, as marked by the vertical black dashed line. For the system in (A) with a 10% CV in each pathway component, the fIDL is 2.83.Barplot comparing the fIDL values for the system in (A) with CVs of 5, 10, and 25%.Simulation of the pathway model in (A) but now comparing the situation in which the pathway components are all uncorrelated with each other (top) with the situation in which the activating and de‐activating pathway components covary with each other, respectively (bottom). The overlapping output distributions in the right panels show that covariance of components in the same pathway would introduce a marked loss in signal transmission accuracy.
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Figure EV1. Comparison of fIDL and mutual information (MI) analysisMI analysis requires a fold‐output range which we added to the model in Fig 1A by using a saturation term for y4 (see Materials and Methods). As shown for CVs of 5 and 10%, in contrast to MI analysis (top), fIDL analysis (bottom) is largely independent of the fold‐output range.
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Figure EV2. Selected reaction monitoring mass spectrometry approach to measure tens of proteins in parallel in single Xenopus eggs
Schematic of protocol to quantitate the abundance of tens of endogeneous proteins in parallel in a single Xenopus egg.Typical selected reaction monitoring mass spectrometry (SRM‐MS) chromatogram.
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Figure 2. Development of a method to quantitatively measure relative abundances of tens of endogenous proteins in parallel in single Xenopus eggs
Comparison of protein abundance of a set of cell cycle, signaling and control proteins in Xenopus eggs. Abundance measurements are based on SRM‐MS measurements of the combined cell extracts from 5 eggs collected at the same time and before initiation of the first cell cycle. Quantitation of relative protein abundance was carried out by adding heavy isotope‐labeled reference peptides to the egg extracts.Timecourse analysis of changes in Cyclin A and Cyclin B levels during the first Xenopus cell cycle measured in combined cell extracts from 5 eggs per timepoint.Five individual eggs were collected at five timepoints: 0, 20, 40, 60, and 80 min after the addition of calcium ionophore. To minimize variability due to sample handling and instrument sources, the 25 individual eggs were prepared for mass spectrometry analysis at the same time and were then analyzed in sequential runs on the same mass spectrometer. Barplot shows relative abundance changes of the 26 proteins shown in (A) tracked through the first egg cell cycle. Each black dot represents the value from an individual egg.
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Figure 3. Single‐cell variation in relative protein abundance is typically 5–10% in Xenopus eggs
Variation analysis of the relative abundance data from Fig 2C. Each point represents the coefficient of variation (CV) of the relative abundance of a protein between five individual eggs in a batch collected at the same timepoint. Red boxes mark the mean CV of 5 batches, each batch collected either at 0, 20, 40, 60, and 80 minutes after cell‐cycle activation. (Right) The histogram of the measured CVs for all 26 proteins at five timepoints shows that CVs typically range from 5 to 10% with a mean CV of 7%.Variation analysis of a second independent set of 120 eggs. Sixty individual eggs were collected at 60 (blue) and at 80 (red) minutes after the addition of calcium ionophore. The 60 eggs at each timepoint were divided into six batches of 10 eggs analyzed sequentially on the mass spectrometer to minimize technical variation. The CV of the relative abundance of each protein between 10 individual eggs in a batch was calculated and plotted as filled blue and red ovals. The black boxes mark the 25th to 75th percentile of the six batch‐calculated CVs for each protein at either the 60‐ or 80‐min timepoint. (Right) The histogram of the 312 CV measurements (6 CVs of 26 proteins at 2 timepoints) shows the mean CV is 9%.Control scatter plot shows that the CVs of the 26 measured proteins are similar between two independent experiments: the 25‐egg experiment shown in (A) and the 60‐egg, 60‐min experiment shown in (B). Red circles indicate proteins that have both high CV and change their abundance during the cell cycle.CVs for a set of human homologs in HeLa cells. Immunocytochemistry was performed on cells plated in 96‐well wells (representative images are shown in Fig EV5). Each blue dot represents the CV calculated from the ˜5,000 cells in the respective well. Each barplot shows the mean CV of 3–12 wells. Error bars show standard deviation of the wells for that condition. Data shown are representative of three independent experiments.
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Figure EV3. Bootstrap analysis of CVs of the relative abundance of 26 proteins using a 60‐egg set collected at 60 min after egg activationBootstrapping of random samples was performed 2,000 times with replacement. We used the bootstrap analysis to determine CVs for the entire 60‐egg dataset (blue circles) or on six batches of 10 eggs that were sequentially analyzed on the mass spectrometer (red circles). The lower CVs for batches of sequentially analyzed cells (median CV of 9% for the 26 proteins) argues that accurate concentration comparison using SRM analysis is optimally performed in batches of samples analyzed sequentially.
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Figure EV4. Comparison of technical and biological variation in the SRM mass spectrometry measurements
Schematic of the experimental design. To measure technical variation, 30 individual eggs were lysed and mixed together to collapse any biological variability. The lysate mixture was then pipetted into 30 individual tubes and processed individually before carrying out SRM analysis to quantify sample handling variation.The CVs due to technical variation were compared to the CVs measured in Fig 3B.
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Figure EV5. Representative images of immunohistochemistry staining of the proteins studied
Images from HeLa cells. Scale bar is 20 μm.Images from MCF10A cells. Scale bar is 20 μm.
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Figure EV6. siRNA‐mediated depletion experiments
A, B.
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Figure 4. MEK and ERK expression covary in Xenopus eggs and cultured human cells
Heatmap of Pearson's correlation values between the respective proteins in Xenopus eggs. Twenty‐six relative protein abundances were correlated pairwise in 120 single eggs. Only correlations with a P‐value less than 0.05 are shown. P‐values were adjusted for multiple comparison testing using Benjamini‐Hochberg corrections (Table EV4).Two examples of pairwise correlations are shown between MCM5 and MCM7 and between MEK and ERK in Xenopus eggs.Pairwise correlation analysis in HeLa cells, using MCM5 versus MCM7 as a positive control and MCM5 versus GAPDH as an uncorrelated control. Correlations between MEK and ERK concentrations are shown. Each scatter plot shows values from ˜15,000 cells. The bar graphs on the right show correlation coefficients for three separate wells, containing ˜5,000 cells each, for the same three correlation pairs.
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Figure 5. Using a general five‐step model to understand the effect of variation on controlling the fraction of cells in the population that respond to input stimulus
A binary output step was added to the model from Fig 1A. A threshold of 10 was used in each simulation to determine whether a cell was activated or not (y5∗ > 10).Plot of how increasing the CVs in expression of the pathway components in this binary model from 0 to 40% increases the range over which changes in the input stimuli can change the fraction of cells in the population which trigger the binary switch and become activated.Hill coefficients were fit to the data in (B) to quantify the steepness in the curves. The steepness is an inverse measure of how wide the input range is that controls the output.
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Figure 6. Live‐cell imaging experiments and simulations using an established MEK/ERK signaling model show that variation between MEK and ERK expression widens the window over which input stimuli can control the fraction of cells that are activated in the population
MCF10A cells stably expressing the EKAR‐EV FRET sensor were activated with varying concentrations of EGF after being serum starved for at least 48 h. Cells were imaged every 2 min throughout the timecourse. (left) The plots at EGF doses of 0, 62.5, 125, 250, and 500 pg/ml show FRET intensity timecourses from approximately 800, 520, 1,200, 1,000, and 900 individual cells, respectively. (right) Histograms show the corresponding integrated ERK activity of individual cells. Integrated ERK activity was calculated for each timecourse as the area under the curve after the addition of EGF. The dashed line shows the threshold used to distinguish cells with active versus inactive ERK.Plot showing percentage of activated cells (cells to the right of the threshold plotted in (A)) in response to different EGF concentrations.Box‐and‐whisker plots of MEK (left) and ERK (right) concentrations in cells with high (top 15%, magenta) or low (bottom 15%, green) integrated ERK activity in response to EGF stimulation. The high and low conditions represent 162 and 161 cells respectively, out of a total of 1,073 cells, stimulated with 3,000 pg/ml of EGF (MEK plots), and 198 and 197 cells respectively, out of a total of 1,316 cells stimulated with 125 pg/ml of EGF (ERK plots). In the box‐and‐whisker plots, the bold line in the center of the notch represents the median, the ends of the notched box represent the first and third quartiles, the length of the upper whisker shows the largest point no more than 1.5 times the inter‐quartile range (IQR or length of the box), the lower whisker represents the smallest point no more than 1.5 times the inter‐quartile range, and the notches represent 1.58 * IQR/sqrt(n), which approximates the 95% confidence interval of the median. The non‐overlapping notches between the high and low populations, as well as the low P‐values, indicate that the differences between the two populations are statistically significant.Timecourse output from an established MEK/ERK model (Sturm et al, 2010) in response to high, medium, and low concentrations of input (RasGTP) stimulus shows that the output for intermediate stimuli is bimodal with mainly either high pERK or low pERK cells separated by a threshold pERK intensity of approximately 17. Random lognormal noise with 15% CV was applied to MEK and ERK and 10% CV to the input stimulus (RasGTP).Model simulations resulting from applying random lognormal noise with different CVs to MEK and ERK. In all cases, random lognormal noise with 10% CV was applied to the input stimulus (RasGTP).
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Figure 7. Single‐cell imaging experiments and model simulations show that covariation between MEK and ERK expression facilitates control of bimodal ERK activation
Immunohistochemistry experiments in MCF10A cells and pairwise correlation analysis show covariance of MEK and ERK. MCM5 versus MCM7 is used as a positive control and MCM5 versus GAPDH as an uncorrelated control. Each scatter plot shows values from ˜15,000 cells. The bar graphs on the right shows correlation coefficients for 3 separate wells of each correlation pair, containing ˜5,000 cells each.Using the 5‐step binary model from Fig 5A to now look at the effect of covariance in the pathway. The same type of plot as in Fig 5B is shown to compare the output of the binary model if the pathway components vary randomly or covary with each other. The population response when uncorrelated CVs of 10% were applied to the pathway components is shown in red. The blue curve shows the population response when covariation was added to the model. To obtain a maximal effect, the CVs of 10% were applied to all positive and all negative regulators, respectively, such that the positive regulators covaried together and the negative regulators covaried together. Covariation in the pathway broadens the range by which input stimuli can regulate the percent of activated cells, as shown by the decrease in the apparent Hill coefficient from 5.4 to 2.3 and less steep sigmoidal response.Using an established MAPK model (Sturm et al, 2010) to compare the effect of covarying MEK and ERK concentrations. The red curve show the results of simulations in which random lognormal noise with 15% CV was applied independently to the MEK and ERK concentrations. The blue curve shows the results of simulations in which MEK and ERK concentrations were made to covary by applying the same 15% CV lognormal noise term to both MEK and ERK in each simulation. In all cases, lognormal noise with 10% CV was applied to the input stimulus (RasGTP). The shallower slope of the blue curve show that the percent of activated cells can be regulated over a wider range of input stimuli if there is covariance between MEK and ERK.Output of simulations using same MAPK model as in (C). Scatter plot shows output of simulations (cells) colored by whether they had high (magenta) or low (green) ERK activity at the end of the timecourse. Cells shown were stimulated with input doses between 210.5 to 212, a range which results in both active and inactive cells in the population as shown in (C).
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Figure 8. Competing demands on variation and covariation in the control of analog single‐cell versus binary population‐level signaling outputs
A. B–D. E. F. G.
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