A Temporal Logic Inference Approach for Model Discrimination

We propose a method for discriminating among competing models for biological systems. Our approach is based on learning temporal logic formulas from data obtained by simulating the models. We apply this method to find dynamic features of epidermal growth factor induced extracellular signal-regulated kinase (ERK) activation that are strictly unique to positive versus negative feedback models. We first search for a temporal logic formula from a training set that can eliminate ERK dynamics observed with both models and then identify the ERK dynamics that are unique to each model. The obtained formulas are tested with a validation sample set and the decision rates and classification rates are estimated using the Chernoff bound. The results can be used in guiding and optimizing the design of experiments for model discrimination.