Decision-Tree Based Model Analysis for Efficient Identification of Parameter Relations Leading to Different Signaling States

Abstract

In systems biology, a mathematical description of signal transduction processes is used to gain a more detailed mechanistic understanding of cellular signaling networks. Such models typically depend on a number of parameters that have different influence on the model behavior. Local sensitivity analysis is able to identify parameters that have the largest effect on signaling strength. Bifurcation analysis shows on which parameters a qualitative model response depends. Most methods for model analysis are intrinsically univariate. They typically cannot consider combinations of parameters since the search space for such analysis would be too large. This limitation is important since activation of a signaling pathway often relies on multiple rather than on single factors. Here, we present a novel method for model analysis that overcomes this limitation. As input to a model defined by a system of ordinary differential equations, we consider parameters for initial chemical species concentrations. The model is used to simulate the system response, which is then classified into pre-defined classes (e.g., active or not active). This is combined with a scan of the parameter space. Parameter sets leading to a certain system response are subjected to a decision tree algorithm, which learns conditions that lead to this response. We compare our method to two alternative multivariate approaches to model analysis: analytical solution for steady states combined with a parameter scan, and direct Lyapunov exponent (DLE) analysis. We use three previously published models including a model for EGF receptor internalization and two apoptosis models to demonstrate the power of our approach. Our method reproduces critical parameter relations previously obtained by both steady-state and DLE analysis while being more generally applicable and substantially less computationally expensive. The method can be used as a general tool to predict multivariate control strategies for pathway activation and to suggest strategies for drug intervention.