Abstract
Stochastic rule-based models serve as natural and compact representations for biochemical reactions. The Gillespie stochastic simulation algorithm and its variants are employed to predict the behavior of biochemical systems modeled by such stochastic rule-based models. However, it is often not feasible to create a complete stochastic rule-based model from first principles. Instead, our knowledge of the biochemical system is used to obtain the set of chemical reactions of the stochastic rule-based model. The lack of knowledge about the rate constants of biochemical reactions is readily modeled by using unknown parameters in stochastic rule-based models.A primary challenge in the use of such a parameterized stochastic rule-based model for predicting the behavior of a biological system is the determination of the parameters of the model from multiple experimental observations. However, the focus of many earlier efforts has been on discovering parameter values of a parameterized stochastic biological model from a single specification written down in a computer-readable language such as probabilistic temporal logic.In practice, a biological model must satisfy multiple experimental observations made on the biological system being modeled. Hence, it is important to synthesize a single set of parameter values that cause a parameterized stochastic model to satisfy multiple probabilistic temporal logic specifications simultaneously.We present a new approach for estimating parameter values of stochastic biochemical models so that a single parameterized model satisfies all the given probabilistic temporal logic behavioral specifications simultaneously. Our approach first computes a quantitative metric describing how well a stochastic biochemical model satisfies a given specification. It then utilizes a multiple hypothesis testing based statistical model checking method to simultaneously validate the model against multiple probabilistic temporal logic behavioral specifications.We demonstrate the usefulness of our method by estimating the parameters of two stochastic rule-based models of biochemical receptors with 26 and 29 parameters against three probabilistic temporal logic behavioral specifications each. Our computational experiments are performed on an AMD Ryzen Threadripper 1900X 8-Core 3.8 GHz processor with 16 GB of RAM operating under Ubuntu 16.04, and obtained a set of parameter values for each model within one day.