DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems ...

DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems BiologyList of Figures1.1 Organization of the toolbox code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1 Scheme of the solution of the resulting dynamic optimization problem with sensitivity equationsapproach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.1 Optimal solution from DOTcvp for the van der Pol oscillator. . . . . . . . . . . . . . . . . . . . . 225.1 The optimal control profiles obtained by mesh refinement algorithm for the van der Pol oscillatorproblem for 10, 30, 90, and 270 time intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.1 The presented figure shows the dynamical behavior of the cdc2-cyclin model. The figure is generatedby the simulation module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287.1 GUI for a van der Pol oscillator: introduction screen. . . . . . . . . . . . . . . . . . . . . . . . . 307.2 GUI for a van der Pol oscillator: NLP definition. . . . . . . . . . . . . . . . . . . . . . . . . . . 307.3 GUI for a van der Pol oscillator: settings related to the initialization, NLP, and IVP. . . . . . . . . 317.4 GUI for a van der Pol oscillator: problem definition. . . . . . . . . . . . . . . . . . . . . . . . . . 317.5 GUI for a van der Pol oscillator: equality and inequality constraints. . . . . . . . . . . . . . . . . 327.6 GUI for a van der Pol oscillator: ODE and sensitivities initialization. . . . . . . . . . . . . . . . . 327.7 GUI for a van der Pol oscillator: output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337.8 GUI for a van der Pol oscillator: MATLAB output. . . . . . . . . . . . . . . . . . . . . . . . . . 338.1 Optimal solution for the drug displacement problem without the path constraint. . . . . . . . . . . 368.2 Optimal solution for the drug displacement problem wit the path constraint. . . . . . . . . . . . . 368.3 Simulation of the system with no inhibition and with the constant maximum inhibition of thePMCA of calcium oscillator problem for the calcium oscillator problem. . . . . . . . . . . . . . . 378.4 Optimal control profiles for the calcium oscillator problem. . . . . . . . . . . . . . . . . . . . . . 388.5 Optimal state and control trajectories for the calcium oscillator problem. . . . . . . . . . . . . . . 398.6 The problem simulation to longer times without more stimuli for the calcium oscillator problem. . 409.1 Optimal solution for the Lee-Ramirez bioreactor. . . . . . . . . . . . . . . . . . . . . . . . . . . 429.2 Optimal solution for the fed-batch reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439.3 Optimal solution for the fed-batch fermenter for penicillin production. . . . . . . . . . . . . . . . 449.4 Optimal solution for the fed-batch reactor for ethanol production. . . . . . . . . . . . . . . . . . . 4510.1 Optimal control trajectories for the simple batch reactor. . . . . . . . . . . . . . . . . . . . . . . 4710.2 Optimal solution for the van der Pol oscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Page – 5