Tags:Conservative approximation, Differential equations, Evolution systems, Polymers and Rule-based modelling
Abstract:
We propose a systematic approach to approximate the behaviour of models of polymers synthesis/degradation. Our technique consists in discovering time-dependent lower and upper bounds for the concentration of some patterns of interest. These bounds are obtained by approximating the state of the system by a hyper-box, with differential equations defining the evolution of the coordinates of each hyper-face. The equation of each hyper-face is obtained by pessimistically bounding the derivative with respect to the corresponding coordinate when the system state ranges over this hyper-face.
In order to synthesise these bounds, we use Kappa to describe our models of polymers. This provides symbolic equalities and inequalities which intentionally may be understood as algebraic constructions over patterns, and extensionally as sound properties about the concentration of the bio-molecular species that contain these patterns.