Region of attraction estimation of biological continuous Boolean models

Quantitative analysis of biological systems has become an increasingly important research field as scientists look to solve current day health and environmental problems. The development of modeling and model analysis approaches that are specifically geared toward biological processes is a rapidly growing research area. Continuous approximations of Boolean models, for example, have been identified as a viable method for modeling such systems. This is because they are capable of generating dynamic models of biochemical pathways using inferred dependency relationships between components. The resulting nonlinear equations and therefore nonlinear dynamics, however, can present a challenge for most system analysis approaches such as region of attraction (ROA) estimation. Continued progress in the area of biosystems modeling will require that computational techniques used to analyze simple nonlinear systems can still be applied to nonlinear equations typically used to model the dynamics associated with biological processes. In this paper, we assess the applicability of a state of the art ROA estimation technique based on interval arithmetic to a subnetwork of the Rb-E2F signaling pathway modeled using continuous Boolean functions. We show that this method can successfully be used to provide an estimate of the ROA for dynamic models described using Hillcube continuous Boolean approximations.