Foundations of a Query and Simulation System for the Modeling of Biochemical and Biological Processes

The analysis of large amounts of data, produced as (numerical) traces of in vivo, in vitro and in silico experiments, has become a central activity for many biologists and biochemists. Recent advances in the mathematical modeling and computation of biochemical systems have moreover increased the prominence of in silico experiments; such experiments typically involve the simulation of sets of Differential Algebraic Equations (DAE), e.g., Generalized Mass Action systems (GMA) and S-systems. In this paper we reason about the necessary theoretical and pragmatic foundations for a query and simulation system capable of analyzing large amounts of such trace data. To this end, we propose to combine in a novel way several well-known tools from numerical analysis (approximation theory), temporal logic and verification, and visualization. The result is a preliminary prototype system: simpathica/xssys. When dealing with simulation data simpathica/xssys exploits the special structure of the underlying DAE, and reduces the search space in an efficient way so as to facilitate any queries about the traces. The proposed system is designed to give the user possibility to systematically analyze and simultaneously query different possible timed evolutions of the modeled system.