Parameter space exploration for signaling pathway dynamics

Abstract

Computational modeling is a valuable tool for understanding complex biological systems. It has been suggested that mathematical models will soon replace databases as primary means for exchanging biological knowledge. Such models often posses complex topological structures with multiple positive and/or negative feedbacks and a large number of parameters so that perturbation on these parameter values can greatly affect qualitative behaviors of the models. Besides, it is likely that biological parameters such as rate constants and initial concentrations are variable in large ranges depending on the specific cell type and cellular environment. Biological systems are known to be robust against noise and perturbations which can be regarded as the variations of parameter values. Dynamical analyses at a specific point in the parameter space can give only limit understandings of the systems. It is therefore necessary to analyze the dynamical properties of models in a large-scale parametric perturbation scheme. One of the issue in model building is understanding the scope of behaviors that the model can experience and which key parameters controls the model behaviors. Given a computational model of a signaling pathway, this study asks following questions: 1) what kind of qualitative behaviors the model may exhibit if its parameters are perturbed globally? 2) which parameters are the key factors that drive the model to specific behaviors? In searching for the answer, we propose a general framework based on a Monte Carlo simulation approach and data-mining techniques for parameter space exploration and dynamical analysis of the model. Large-scale perturbations of parameters are performed with Latin hypercube sampling technique in combination with a divide-and-conquer strategy that assures to explore the model parameter space in an efficient way. Temporal simulation outputs are then group in to different clusters using a $\It{k}$ -mean clustering algorithm to define qu...