Modeling the action of drugs on cellular enzymes by means of optimal control techniques

In this paper we apply Optimal Control techniques, based on the solution of Hamilton-Jacobi-Bellman equations, to simulate the action of a drug on some sub-networks of an intracellular signal transduction network. The cost functional to be minimized is chosen in order to take into account, in the models, different factors, like the toxicity of some reactants, the drug action and the costs of the drug itself. Numerical results are also shown, to test the model.