Ensembles of signal transduction models using Pareto Optimal Ensemble Techniques (POETs).

Mathematical modeling of complex gene expression programs is an emerging tool for understanding disease mechanisms. However, identification of large models sometimes requires training using qualitative, conflicting or even contradictory data sets. One strategy to address this challenge is to estimate experimentally constrained model ensembles using multiobjective optimization. In this study, we used Pareto Optimal Ensemble Techniques (POETs) to identify a family of proof-of-concept signal transduction models. POETs integrate Simulated Annealing (SA) with Pareto optimality to identify models near the optimal tradeoff surface between competing training objectives. We modeled a prototypical-signaling network using mass-action kinetics within an ordinary differential equation (ODE) framework (64 ODEs in total). The true model was used to generate synthetic immunoblots from which the POET algorithm identified the 117 unknown model parameters. POET generated an ensemble of signaling models, which collectively exhibited population-like behavior. For example, scaled gene expression levels were approximately normally distributed over the ensemble following the addition of extracellular ligand. Also, the ensemble recovered robust and fragile features of the true model, despite significant parameter uncertainty. Taken together, these results suggest that experimentally constrained model ensembles could capture qualitatively important network features without exact parameter information.