XS-systems: eXtended S-Systems and Algebraic Differential Automata for Modeling Cellular Behavior

Several biological and biochemical mechanisms can be modeled with relatively simple sets of differential algebraic equations (DAE). The numerical solution to these differential equations provide the main investigative tool for biologists and biochemists. However, the set of numerical traces of very complex systems become unwieldy to wade through when several variables are involved. To address this problem, we propose a novel way to query large sets of numerical traces by combining in a new way well known tools from numerical analysis, temporal logic and verification, and visualization.In this paper we describe XS-systems: computational models whose aim is to provide the users of S-systems with the extra tool of an automaton modeling the temporal evolution of complex biochemical reactions. The automaton construction is described starting from both numerical and analytic solutions of the differential equations involved, and parameter determination and tuning are also considered. A temporal logic language for expressing and verifying properties of XS-systems is introduced and a prototype implementation is presented.