Abstract
This paper proposes a new system representation called a positive quadratic system for analysis and synthesis of molecular interaction in a cell, which includes a signal transduction pathway and a gene expression transcriptional regulation. One of the features of the proposed model is that it can capture the quadratic property of molecular interaction as well as the positivity properties of the state variables in terms of a rather simple form. Based on this model, we derive a sufficient condition of the stability of the origin in the sense of Lyapunov, and present a method for estimating an invariant set depending on the initial state and a positive invariant set. We show that the proposed method is effective by numerical simulations of two fundamental biological models.
