Parameter estimation in systems biology models using spline approximation

Two parameter estimation methods of combining spline theory with Linear Programming (LP) and Nonlinear Programming (NLP) are developed. These methods remove the need for ODE solvers during the identification process. Our analysis shows that the augmented cost function surfaces used in the two proposed methods are smoother; which can ease the optima searching process and hence enhance the robustness and speed of the search algorithm. Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily. Eight system biology models are used for testing the proposed approaches. Our results confirm that the proposed methods are both efficient and robust.The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.In recent years, the rapid development of sophisticated experiment tools in molecular biology allows the acquisition of high qualitative time series data which can significantly improve the ability of revealing the complex dynamics and interactions of biological systems. Profiting from the rapid technological advances, more and more researchers from different disciplines can now utilize such observation data to establish mechanism-based models which can incorporate every possible detail and functioning of biological systems [1]. One common approach is to characterize the biological system with a set of Ordinary Differential Equations (ODEs) [2-7]. Generally, there are two major aspects of building an ODE model for a biological system from experimentally measured time series: (1) to determine the structure of the system through a set of suitable ODEs with unknown parameters; (2) to determine the unknown parameters of this ODE model. The identification of these unknown parameter with fixed model structure from observations is one of the central issues of computational systems biology [8]. This type of approach can be c