Graphical Construction of Stability Certificates for Biomolecular Interaction Networks

Abstract

—We study robust stability of Biological Interaction Networks (BINs) by constructing stability certificates in the form of Robust Lyapunov Functions (RLFs) using graphical methods. Previous works have mainly constructed RLFs by utilizing linear programs or iterative algorithms. Such algo- rithms become tedious or computationally infeasible for large networks. In addition, they do not identify motifs or graph modifications that maintain stability. In this work, we provide several graphical criteria for constructing stability certificates. We characterize a set of stability-preserving graph modifications which include, in particular, the enzymatic catalysis motif. Hence, stability of a class of arbitrarily large networks can be examined by simple visual inspection. We present applications of this technique to Post-Translational Modification (PTM) cycles, Ribosome Flow Model (RFM), and T -cell kinetic proofreading. Index Terms —Nonlinear Systems, Systems Biology, Petri-nets, Lyapunov Functions, Robust Stability, Reaction Networks.