Fig. 6: Bayesian mulitmodel inference suggests that subcellular differences in ERK activity depend on both Rap1 activity and ERK negative feedback.
From: Increasing certainty in systems biology models using Bayesian multimodel inference
a EKAR4 measurements from ref. 27 Figure 3C, D normalized to the average maximum EKAR4 emission ratio in each location separately. Mean and standard deviation for EKAR4-only (black) and EKAR4 with Rap1 inhibition measurements (+Rap1GAP; red). b Posterior predictions for the best and worst models indicated by ELPD, i.e., O' 2009 with location differences in Rap1 and negative feedback (O' 2009 Rap1 & (−)FB diff.) and S' 2014 with location differences in negative feedback (S' 2014 (−)FB diff.), respectively. Predictions from all models are shown in Supplementary Fig. 11. Error bars show the 95% posterior credible interval. c ELPD values for all models. d MMI weights assigned to all models using pseudo-BMA, stacking, and BMA. e Marginal posterior densities for the Rap1 activation/deactivation and ERK negative feedback parameters in each location for the O' 2009 and R' 2015 models with Rap1 and negative feedback location differences selected by MMI. Cytoplasm densities (CYTO) are blue, and those for the plasma membrane (PM) are black. All densities are statistically independent between locations (p < 0.005 by the Kolmogorov–Smirnov test with a two-sided hypothesis). f Posterior predictions for selected models with negative feedback inhibition alone ((−)FB inhib.) and simultaneous Rap1 and negative feedback inhibition (Rap1 inhibition + (−)FB inhib.). Error bars show the 95% posterior credible interval. g The proposed mechanism of subcellular differences in ERK activity discovered using MMI. Rap1 activation is stronger at the plasma membrane, while negative feedback is stronger in the cytoplasm.
