Discovering Dynamic Characteristics of Biochemical Pathways using Geometric Patterns among Parameter-Parameter Dependencies in Differential Equations

This paper proposes a novel approach to the analysis and validation of mathematical models using two-dimensional geometrical patterns representing parameter-parameter dependencies (PPD) in dynamic systems. A geometrical pattern is obtained by calculating moment values, such as the area under the curve (AUC), area under the moment curve (AUMC), and mean residence time (MRT), for a series of simulations with a wide range of parameter values. In a mathematical model of the metabolic pathways of the cancer drug irinotecan (CPT11), geometrical patterns can be classified into three major categories: “independent,” “hyperbolic,” and “complex.” These categories characterize substructures arising in differential equations, and are helpful for understanding the behavior of large-scale mathematical models. The Open Bioinformatics Grid (OBIGrid) provides a cyber-infrastructure for users to share these data as well as computational resources.