Clustering Parameter Values for Differential Equation Models of Biological Pathways

Dynamics of many biological systems can be modeled in the form of nonlinear differential equations, where variables represent concentrations of participating molecular species, and parameters specify dynamics coefficients such as reaction rates and activity levels. It has been one of the hardest problems to determine right parameters even after we have acceptable model equations for a particular biological pathway. In this study, we propose a parameter space clustering method based on top-down refinement. The whole parameter space of a given model is explored by means of randomized comparison and top-down stepwise refinement. After the process, we come up with clusters of parameter values, each of which shows similar dynamics of a particular model. We expect that each of the clusters may be associated to a distinct phenotypical state of a given biological pathway. A simplified model of the well-known JAK-STAT pathway is used to illustrate the clustering process, and show the applicability of this technique.