Calibration of stochastic biochemical models against behavioral temporal logic specifications

Abstract

Calibrating stochastic biochemical models against experimental insights remains a critical challenge in biological design automation. Stochastic biochemical models incorporate the uncertainty inherent in the system being modeled, thus demanding meticulous calibration techniques. We present an approach for calibrating stochastic biochemical models such that the calibrated model satisfies a given behavioral temporal logic specification with a given probability. Model calibration is defined as an optimization problem that aims to minimize a cost function that computes either a qualitative or a quantitative measure of distance between the parameterized stochastic biochemical model and the expected behavioral specification. To minimize this distance, our approach combines various statistical hypothesis testing methods with automated runtime monitoring of high-level temporal logic specifications against time-series data obtained by simulating stochastic models. We apply sequential probability ratio test (SPRT) and Bayesian statistical model checking (BSMC) when the distance between the model and the behavioral specification is a qualitative value. Alternatively, when the distance is a quantitative value describing how well a specification is satisfied by the model, we use a hypothesis test to sequentially select between two distributions of the distance metric that has the larger mean. Such tests describe the stopping condition to reduce the number of samples required for discovering the correct parameter values. We demonstrate the potential of our approach on two examples using agent-based models implemented in SPARK and rule-based models implemented in BioNetGen modeling languages. The distance between a candidate biochemical model and an expected behavior encoded in temporal logic can be used to drive a local or global search technique during the model calibration process. Our approach follows Simulated Annealing as the global search algorithm that avoids local minima by accepting inferior solutions, at high temperatures, with a very low probability. The problem of stochastic model calibration against behavioral temporal logic specifications has numerous applications in science and engineering and has been widely studied. Our algorithmic approach towards this problem may be an important component of future biological design automation software suite.