From Parameter Exploration to Robustness Analysis of Stochastic Biochemical Systems

In my talk, I will present our novel framework for exploring kinetic parameters of stochastic biochemical systems. The main question addressed is how the validity of an a priori hypothesis expressed as a Continuous Stochastic Logic property depends on kinetic parameters. First I will show, how to effectively compute an evaluation function that, for each parameter point from the inspected parameter space, returns the quantitative model checking result for the respective continuous time Markov chain (CTMC). We have designed a parametrized uniformization (a novel modification of the standard uniformization technique) that allows us to iteratively approximate the lower and upper bounds of the evaluation function with respect to a given accuracy. Further I will show, how the evaluation function can be used to adapt the general concept of robustness by Kitano to the class of stochastic systems modeled by CTMCs. We have considered several interpretations of the evaluation function allowing for different ways to capture the stochastic robustness. We have applied our framework to two biologically relevant case studies to demonstrate that our concept of robustness can adequately capture and quantify the ability of the stochastic systems to maintain their functionality. The case studies show that our framework provides deeper understanding of how the validity of the inspected hypotheses depends on reaction rate parameters and initial conditions.