Cell-to-cell variability in a minimal model of a gradual kinase cascade.

<p><b>A</b> Schematic representation of a five-step kinase cascade (S…extracellular stimulus; and …active and inactive kinases, respectively; …phosphatases; and …phosphorylation and dephosphorylation rate constants, respectively). <b>B</b> Cell-to-cell variability simulations confirm strong heterogeneity in the gradual kinase cascade. Nine signaling protein concentrations (5 kinases, 4 phosphatases) were sampled from log-normal distributions (; coefficient of variation = ), and the dose-response curve was simulated using Eqs. 3 and 4 for a set of 1000 sampled protein concentrations. Low phosphatase activities were chosen to model a low activation resistance: (Supplemental <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003357#pcbi.1003357.s010" target="_blank">Table S1</a>). The blue and orange areas are enclosed by the dose-response curves which yielded the minimal/maximal and , respectively. Box plots at the top and right side represent the distributions of and , respectively (normalized by the population medians). These box plots indicate the median (middle of box), the first and third quartile (box edges), the data points that lie within a distance of 1.5 interquartile ranges from the lower and higher quartiles (whiskers) and extreme outliers (crosses). <b>C</b> The variabilities of and respond inversely to changes in kinetic parameter values. Cell-to-cell variability simulations (similar to panel <b>B</b>) were repeated for various activation resistances in the cascade which were tuned by simultaneously changing the phosphatase rate constants (x-axis). The variabilities of and were analyzed for each parameter configuration (y-axis) and expressed as inter-quartile ratios (IQRatio = = ratio of the third quartile and the first quartile; related to the width of the box plots shown in <b>B</b>). High inter-quartile ratios imply high cell-to-cell variability while an IQRatio of 1 corresponds to no variability. Similar results are obtained when using the coefficient of variation as a measure of variability (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003357#pcbi.1003357.s001" target="_blank">Figure S1</a>). <b>D</b> Upstream signaling protein fluctuations determine the pathway sensitivity () while downstream fluctuations control the maximal pathway activation (). and were calculated for each simulation run in panel <b>B</b> and related to the concentrations of the first and the terminal kinase in the same simulation. Each dot represents a simulation of a single cell, and the solid lines are linear fits to all points.