BackgroundMathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and is still one of the most challenging tasks. Many parameter estimation methods have been developed but none of these methods is effective for all cases and can overwhelm all other approaches. Instead, various methods have their advantages and disadvantages. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints.ResultsTwo 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.ConclusionsThe proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.

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The inverse problem of identifying unknown parameters of known structure dynamical biological systems, which are modelled by ordinary differential equations or delay differential equations, from experimental data is treated in this paper. A two stage approach is adopted: first, combine spline theory and Nonlinear Programming (NLP), the parameter estimation problem is formulated as an optimization problem with only algebraic constraints; then, a new differential evolution (DE) algorithm is proposed to find a feasible solution. The approach is designed to handle problem of realistic size with noisy observation data. Three cases are studied to evaluate the performance of the proposed algorithm: two are based on benchmark models with priori-determined structure and parameters; the other one is a particular biological system with unknown model structure. In the last case, only a set of observation data available and in this case a nominal model is adopted for the identification. All the test systems were successfully identified by using a reasonable amount of experimental data within an acceptable computation time. Experimental evaluation reveals that the proposed method is capable of fast estimation on the unknown parameters with good precision.

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