Model Discrimination of Polynomial Systems via Stochastic Inputs

Systems biologists are often faced with competing models for a given experimental system. Unfortunately, performing experiments can be time-consuming and expensive. Therefore, a method for designing experiments that, with high probability, discriminate between competing models is desired. In particular, biologists often employ models comprised of polynomial ordinary differential equations that arise from biochemical networks. Within this setting, the discrimination problem is cast as a finite-horizon, dynamic, zero-sum game in which parameter uncertainties in the model oppose the effort of the experimental conditions. The resulting problem, including some of its known relaxations, is intractable in general. Here, a new scalable relaxation method that yields sufficient conditions for discrimination is developed. If the conditions are met, the method also computes the associated random experiment that can discriminate between competing models with high probability, regardless of the actual system behavior. The method is illustrated on a biochemical network with an unknown structure.