Characterization of heterogeneity among signaling species in the ensemble model.

<p>All error bars are 95% confidence intervals. (A) Visual depiction of our simulation method. An initial state was defined (red; all monomeric protein agents with one exception) and a number of trajectories were simulated to represent a set of untreated, homeostatic yeast cells (green). Pheromone was then added and each steady-state cell was simulated for a number of independent 1-hour trajectories (blue). Drift values were then calculated pairwise for all simulations that were derived from the same original homeostatic cell. The same procedure was also performed without adding pheromone as a control. (B) Average drift on a log time scale (n = 45). All simulations in this case (both with and without pheromone) start from <i>identical</i> steady-state initial conditions, so we have <i>d</i> = 0 at time <i>t</i> = 0. Simulations with pheromone (red) show a greater overall increase in drift as compared with simulations without pheromone (black). Peak levels of drift (∼0.8) occur around 100–300 seconds into simulations with pheromone. The ultimate decline in drift (<i>t</i> = 3600 s) is due to the presence of negative feedback in the cascade, returning the MAPK network to homeostasis. (C) Density of drift among scaffold-based complexes with randomized parameters (black, n = 9000) and the parameters that reproduce the experimental data (blue, n = 450). 1000 parameter sets were randomly generated and simulated, and we employed kernel density estimators to produce the density curves (Section 2.4 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003278#pcbi.1003278.s002" target="_blank">Text S1</a>). Though the mean drift values of the two distributions are significantly different (<i>p</i><10⁻⁵, Section 2.4 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003278#pcbi.1003278.s002" target="_blank">Text S1</a>), the vast majority of drift values in the models with both randomized and fixed parameters are above 0.8, demonstrating the robustness of high drift in the model, regardless of rate parameters. (D) Autodrift occurs on two different timescales as indicated by statistical analysis of our double-exponential fit (n = 10, Section 3.3 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003278#pcbi.1003278.s002" target="_blank">Text S1</a>). Signaling events induce rapid divergence within one second (inset) from identical initial states within a particular simulation starting at the time of peak signal output (<i>t</i> = 300 s, Section 3.3 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003278#pcbi.1003278.s002" target="_blank">Text S1</a>) <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003278#pcbi.1003278-Creamer1" target="_blank">[47]</a>. Also of note is the blue dashed line, which is the average drift between simulations at the 360 second time point (the blue dotted lines are the 95% confidence interval).