Dynamic sensitivity analysis of oscillating biochemical systems using modified collocation method

Sensitivity analysis plays an important role in the study of biological systems. Biochemical systems theory (BST) as well as metabolic control analysis (MCA) has had great success in describing the control and regulation of biological systems at steady state. However, there are notable exceptions, such as signal transduction or cell cycle regulation systems where the transient or oscillatory behavior of interest is often found in the temporal response. Some extensions of BST and MCA to non-steady behavior have appeared in the literature. However, there requires to have a unified methodology to efficiently solve biological system models described by the BST or MCA formulation. In this work, the modified collocation method is applied to solve transient responses and its corresponding dynamic sensitivities for the non-linear biological systems described by the GMA formulation. The method could simultaneously compute both solutions and dynamic sensitivities of the system equations element-by-element. Any MCA formulations could be recast into a GMA model so the Jacobian matrix and the partial derivatives with respect to the model parameters could be analytically evaluated while the solution is in progress. In this study, we have presented three biological systems to illustrate the efficiency of the proposed algorithm.