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1.
Figure 1

Figure 1. The TRAIL-induced signaling network.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A) Schematic diagram of the TRAIL-induced cell death signaling network including live-cell imaging reporters for MOMP, the inter-membrane space reporter protein (IMS-RP), and for initiator or effector caspase activity (IC-RP or EC-RP, respectively). The features tPARP, fPARP, and tswitch can all be evaluated based on EC-RP dynamics and tMOMP can be measured in live cells using IMS-RP. IC-RP enables measurement of the threshold of cleaved initiator caspase substrate required for MOMP and of an initial rate of caspase activity (kIC). See also Figure 2 and Table Box 1 for description of how reporter dynamics were modeled and for precise definitions of features.

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.
2.
Figure 8

Figure 8. Variability in cell fate and time-to-death depends on the interplay between multiple factors.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A) Plots of tMOMP as a function of Bcl-2 level for three levels of Bax (0.3X [Bax]0, left, 1X [Bax]0, center, and 3X [Bax]0, right) and Bid (0.1X [Bid]0, blue, 1X [Bid]0, green, and 10X [Bid]0, red). Orange shading represents the 5th and 95th percentiles of the measured distribution of endogenous Bcl-2 in HeLa cells. (B) Histograms of the tMOMP distributions in the range of endogenous Bcl-2 (indicated by the orange shading) for varying Bid and Bax levels. For panels A and B, initial concentrations of Bcl-2 were sampled uniformly in the exponent between 102 to 107 molecules per cell and all other proteins concentrations were set at their default mean values (Table S2 in Text S3).

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.
3.
Figure 6

Figure 6. Predictability of death time is improved by knowledge of key protein concentrations.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A) Scatter plot of predicted tMOMP as a function of Bid initial concentration when no other initial protein concentrations are known (left) or when the initial concentrations of the next seven most influential proteins as ranked by R2 of tMOMP are also known with precision within ±12.5% (right). Simulations shown were selected from a series of 105 simulations sampling from a joint distribution for Bax, Bcl-2, Bid, caspase-3 and XIAP (as measured) and independently for all other proteins with non-zero initial concentration. To mimic knowledge of a protein concentration, simulations were randomly selected from those with an initial concentration of mean value ±12.5% for this protein. Black points represent the predicted death times given perfect knowledge of the concentrations of all model species. MSE is the mean squared error relative to perfect knowledge (black points). (B) Graph of the mean squared error in tMOMP (relative to perfect knowledge, black points in (A)) as a function of the number of proteins whose concentration is “known”; values are the averages from different runs and error bars represent the standard deviations (n = 10). “Known” proteins were added either randomly (blue), by high-to-low R2 for tMOMP (gray; Figure S10) or tPARP (yellow; Figure 5E), or by high-to-low CV for tPARP (brown; Figure 4C).

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.
4.
Figure 2

Figure 2. Feature-based description and sensitivity of apoptosis dynamics.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A) Plot showing the simulated time courses of cleaved PARP (blue; an effector caspase substrate), total cytosolic Smac (green) and total cleaved Bid (tBid, yellow; an initiator caspase substrate). Cleaved PARP corresponds to model species 23. Total cytosolic Smac is the sum of Smac_r (species 47), Smac (species 45) and Smac:XIAP (species 57). Total cleaved Bid is the sum of tBid (species 26), tBid:Bax (species 28), and tBid:Mcl1 (species 30). The four model features under investigation are indicated (tMOMP, tPARP, fPARP, and tswitch), as well as two features used to classify proteins in Figures 4 and 7 (the initiator caspase rate, kIC, and threshold). (B) Schematic representations of three classes of changes in the cPARP trajectory and the corresponding time-integrated value of the parameter sensitivity (gray). Changes that are quantitatively similar in terms of conventional sensitivity are distinct by feature sensitivity. The same qualitative distinctions apply to sensitivities calculated in the limit of an infinitesimal change in parameter values. Therefore the curves in panel B are related to feature sensitivities (and to Equation 1) as shown by the expressions on the right.

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.
5.
Figure 4

Figure 4. The impact of variability in protein initial concentrations is feature-specific.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A) Histograms showing the distributions of initial concentrations of Bcl-2 and XIAP used as inputs to the model (left) and the model output distributions for tMOMP and tswitch (right). Input distributions were generated by sampling 10,000 times from a log-normal distribution parameterized with measured or assumed mean and CV as listed in Table S2 in Text S3. Output distributions were calculated from104 simulations where the initial concentration of the indicated protein was sampled from the distributions shown on the left; all others protein concentrations were set to their default value (Table S2 in Text S3). (B–E) Bar graph showing the coefficients of variation (CV) obtained for model output distributions of tMOMP (B), tPARP (C), fPARP (D), and tswitch (E) from series of 104 simulations where the indicated protein initial concentration is sampled from a log-normal distribution and all other concentrations set to their default value (Table S2 in Text S3). Proteins were classified as affecting the pre-MOMP rate of initiator caspase activity (Rate; gray), the MOMP threshold (Threshold; purple) or post-MOMP processes (Post-MOMP; green) based on their position in the TRAIL-induced signaling network (Figure 1). In panels B–E, the black bar (“All”) indicates the variability observed in a series of 104 simulations where all non-zero initial conditions were independently sampled from log-normal protein distributions using the measured CV where available or else CV = 0.25 (as listed in Table S2 in Text S3).

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.
6.
Figure 3

Figure 3. Sensitivity of tMOMP to changes in protein initial concentrations and measurements of protein variance and co-variance in HeLa cells.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A) Scatter plots show the simulated relationship between initial protein concentration and tMOMP (green) or numerically calculated tMOMP sensitivity (blue; tMOMP sensitivity is unitless and is calculated using finite-difference approximations of the derivatives, or slopes, of the green curves) following TRAIL addition, for the indicated proteins. The initial concentration for the indicated protein was uniformly sampled in the exponent for values between 102 to 107 proteins per cell while all other initial protein concentrations and rate constants were set at their default value. Vertical bars represent the 5th and 95th percentiles of the measured (orange, see panel B–D and Table S2) or assumed (gray) distributions in endogenous protein concentrations for untreated HeLa cells. Shaded regions in the plot for Bid show an example of concentration ranges that were attained experimentally using RNAi knockdown and GFP-fusion protein overexpression [15], [23], [29]. (B) Overlays of endogenous Bcl-2 concentration distributions in untreated HeLa cells as measured by flow cytometry (FACS, blue), or immunofluorescence (IF, green). The FACS data are well fit by a log-normal distribution (Fit, red); a.u., arbitrary units. (C) Scatter plot of anti-Bcl-2 vs. GFP-Bcl-2 signal in GFP-Bcl-2-transfected HeLa cells measured by 2-color flow cytometry. (D) Histograms of the endogenous Bcl-2 concentration distribution in wildtype HeLa cells measured with an anti-Bcl-2 antibody (left) and of the off-diagonal noise distribution for the scatter plot in (B) (right). Both distributions are for mean-centered data to allow comparison of variability; std is the standard deviation and IQR is the interquartile range.

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.
7.
Figure 7

Figure 7. Overexpression of Bcl-2 in HeLa cells shows a region of variable fate before a threshold is reached where all cells survive.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A–B) Scatter plots showing the relationship between tMOMP and total Bcl-2 amount as measured in HeLa cells treated with 50 ng/ml TRAIL and 2.5 µg/ml cycloheximide (left) or simulated in EARM1.3, sampling linearly in the exponent for GFP-Bcl-2 levels and from a joint distribution for Bax, Bcl-2, Bid, caspase-3 and XIAP and independently for all other non-zero initial protein concentrations (right). Quantitative immunoblotting (Figure S5 in Text S1) and single-cell fluorescence quantification were combined to derive the absolute levels of GFP-Bcl-2 for each cell, to which the average endogenous Bcl-2 amount (30,000 molecules/cell; experimentally unobservable) was added to convert the x-axis to units of total Bcl-2 molecules per cell. Cells that did not undergo MOMP by 12 hr were assumed to have survived. (C) Boxplots of initial protein concentration distributions for surviving (green) or dying (gray) simulated cells selected for having a range of total Bcl-2 expression where ∼50% died (∼53,000–57,000 molecules/cell). Box edges show the 25th and 75th percentiles, notches show the 95% confidence interval for the median (horizontal line), and whiskers extend to the most extreme data points that are not considered outliers. Asterisks indicate proteins for which the surviving and dying simulated cells show significantly different medians for initial concentration (p<0.05), double asterisks mark the distributions for [Bax]0 which have the most significant difference. (D) Bar graph showing the coefficients of variation (CV) obtained for model output distributions of tMOMP when using 3×104 Bcl-2/cell as the mean [Bcl-2]0 (striped bars; reproduced from Figure 4B), or when the average [Bcl-2]0 was changed to 6×104 Bcl-2/cell (solid bars). As in Figure 4, proteins were classified as affecting the pre-MOMP rate of initiator caspase activity (Rate; gray), the MOMP threshold (Threshold; purple) or post-MOMP processes (Post-MOMP; green).

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.
8.
Figure 5

Figure 5. Correlations in protein levels affect the distribution of death times and the rank ordering of the most sensitive species.. From: Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis.

(A) Scatter plots showing joint measurements of the levels of pairs of proteins in a population of HeLa cells by flow cytometry (least correlated pair, Bcl-2 and caspase-3 (C3), left; most correlated pair, Bcl-2 and Bax, right). (B) Bar graph showing the measured Pearson correlation coefficients (calculated by linear regression) in the level of ten protein pairs. Error bars show the standard error of the mean. For all protein pairs, measurements were on cells that were size-selected by stringent gating for forward and side scatter. (C) Bar graph of the CVs of tMOMP distributions measured by monitoring IMS-RP translocation via time-lapse microscopy in HeLa cells treated with 50 ng/ml TRAIL with 2.5 µg/ml cycloheximide (green) or obtained from 104 simulations using independent sampling of all initial conditions (independent, blue), or sampling from the experimentally determined joint distributions for Bax, Bcl-2, Bid, caspase-3 and XIAP (allowing all other proteins to vary independently; correlated, brown). Error bars represent standard deviations obtained by bootstrapping (n = 1000). Sampling for joint distributions reduced the predicted variability in tPARP from a CV = 0.23 to CV = 0.19, a statistically significant improvement in the match to experimental data: an Ansari-Bradley test for equal variability on median-corrected data yielded p = 0.006 for experimental data vs. independent sampling simulation, and p = 0.137 for experimental data vs. sampling with correlated distributions, rejecting the equal variance hypothesis only for data vs. independent sampling. (D) Heat map showing the effect of pairwise correlations on tPARP variability. Above the diagonal (gray), color indicates the ratio of the CV of tPARP for 104 simulations with sampling from correlated vs. independent distributions for the indicated pair (all other proteins were sampled independently from log-normal distributions parameterized as in Table S2 in Text S3). Below the diagonal, the most significant p-value from a two-sample Kolmogov-Smirnov test is indicated in green (p = 0.04). (E) Bar graph of the Pearson correlation coefficients (R-values) of tPARP with the indicated protein initial concentration for simulations sampling from fully independent distributions (blue), from joint distribution for Bax, Bcl-2, Bid, caspase-3 and XIAP (brown), or from a joint distribution for the same five proteins where the Bcl-2-Bax correlation was set to zero (yellow bar). Scatter plots of tPARP as a function of initial protein levels for the same simulation sets are presented in Figure S9 in Text S1.

Suzanne Gaudet, et al. PLoS Comput Biol. 2012 April;8(4):e1002482.

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