This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Dynamic disease pathways are a combination of complex dynamical processes among bio-molecules in a cell that leads to diseases. Network modeling of disease pathways considers disease-related bio-molecules (e.g. DNA, RNA, transcription factors, enzymes, proteins, and metabolites) and their interaction (e.g. DNA methylation, histone modification, alternative splicing, and protein modification) to study disease progression and predict therapeutic responses. These bio-molecules and their interactions are the basic elements in the study of the misregulation in the disease-related gene expression that lead to abnormal cellular responses. Gene regulatory networks, cell signaling networks, and metabolic networks are the three major types of intracellular networks for the study of the cellular responses elicited from extracellular signals. The disease-related cellular responses can be prevented or regulated by designing control strategies to manipulate these extracellular signals. The paper reviews the regulatory mechanisms, the dynamic models, and the control strategies for each intracellular network. The applications, limitations and the prospective for modeling and control are also discussed.

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Objective: We designed three new controllers: a sigmoid-based controller, a polynomial dynamic inversion-based controller, and a proportional-integral-derivative (PID) impulsive controller for cancer differentiation therapy. We compared these three controllers to existing control strategies to show the improvement in performance and compare their robustness. Methods: The sigmoid-based controller adds a sigmoid term associated with the error of the controlled state and a selected observed state. The sigmoid term is multiplied by a control gain, thereby decreasing the control effort for state transition can decrease. The polynomial dynamic inversion-based controller adds a cubic error term in the error dynamic to achieve a shorter convergence time to the desired value of the controlled state. The PID impulsive controller considers the accumulated controlled state error and the rate of change of the controlled state error, thereby forcing the controlled state to converge to the desired value and alleviating the damping effect in the steady state. Results: For the considered cancer network, the sigmoid-based controller can reduce the amount of drug dosage to complete state transition compared to existing domain control. The polynomial dynamic inversion-based controller uses less time for differentiation therapy compared to the domain controller. The PID impulsive controller can increase the time interval between each drug dosage and show better robustness compared to vanilla impulsive control. Conclusion: The 3 new cancer control strategies exhibit superior and robust performance. Significance: The PID impulsive controller has a significant improvement in robustness compared to the impulsive controller and has greater potential for cancer differentiation therapy.