Synthesis of optimal control of complex biological pathways enabled by global sensitivity analysis

The past few years have witnessed growth in the number of system biological models corresponding to several different pathways and have shed light on biological processes governing vital functions such as signal transduction, cell-proliferation and cell-apoptosis. Among several challenges in modeling and verification, significant efforts have been made in system identification including model parameter estimation and key component identification. In a practical or experimental setting, the effects of various control strategies, are usually associated with costs including enzyme consumption or the desired levels of output transcription. In this work we address the problem of designing an optimal control law via a combination of computational tools such as sensitivity analysis, Pontryagin maximum principle and steepest descent technique. We find that, in the presence of limitation of enzyme concentration level control, optimal control law can be developed only by choosing enzyme with dominant effect on dynamical behavior of biological pathway. In this work, we study JAK/STAT signal transduction pathway, and by simulation analysis, we investigate the effectiveness of Sobol values in developing optimal control law.