Determinants of Cell-to-Cell Variability in Protein Kinase Signaling
Figure 1
Cell-to-cell variability in a minimal model of a gradual kinase cascade.
A 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 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 Table S1). 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). C The variabilities of
and
respond inversely to changes in kinetic parameter values. Cell-to-cell variability simulations (similar to panel 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). 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 (Figure S1). D 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 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.