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

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DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems BiologyModel Parameters (Reaction Coefficients) Weighted Coefficients Initial Values Desired Valuesk 1 = 0.09 k 8 = 32.24 K 15 = 0.16 w 1 = 5.0 x 1 (0) = 0.03966 x s 1 = 6.78677k 2 = 2.30066 K 9 = 29.09 k 16 = 4.85 w 2 = 5.0 x 2 (0) = 1.09799 x s 2 = 22.65836k 3 = 0.64 k 10 = 5.0 K 17 = 0.05 w 3 = 15.0 x 3 (0) = 0.00142 x s 3 = 0.38431K 4 = 0.19 K 11 = 2.67 t F = 22.0 w 4 = 25.0 x 4 (0) = 1.65431 x s 4 = 0.28977k 5 = 4.88 k 12 = 0.7 w 5 = 50.0k 6 = 1.18 k 13 = 13.58 w 6 = 5.0k 7 = 2.08 k 14 = 153.0Table 8.1 – The table with the time-fixed parameters, weighted coefficients, initial, and desired values of the statevariables for a calcium oscillator problem.1 ______________2 Final results [single-optimization; case A]:3 ............. Problem name: DrugDisplacementProblemA4 ...... NLP or MINLP solver: IPOPT5 . Number of time intervals: 56 ... IVP relative tolerance: 1.000000e-0087 ... IVP absolute tolerance: 1.000000e-0088 . Sens. absolute tolerance: 1.000000e-0089 ............ NLP tolerance: 1.000000e-00510 ....... Final state values: 2.000012e-002 2.000044e+000 2.212415e+00211 ...... 1th optimal control: ...12 ..... Final size of the dt: 1.000999e-002 1.000999e-002 1.000998e-002 1.888941e+002 3.231729e+00113 ..... Final time [sum(dt)]: 2.212415e+00214 ______________15 ............ Final CPUtime: ... seconds16 . Cost function [min(J_0)]: 221.241466261 ____________________________2 Final results [stochastic part - hybrid-strategy; case B]:3 ............. Problem name: DrugDisplacementProblemB4 ...... NLP or MINLP solver: DE5 . Number of time intervals: 106 ... IVP relative tolerance: 1.000000e-0057 ... IVP absolute tolerance: 1.000000e-0058 . Sens. absolute tolerance: none9 ............ NLP tolerance: 1.000000e-00310 ....... Final state values: 2.024236e-002 2.002572e+000 2.660897e+00211 ...... 1th optimal control: ...12 ..... Final size of the dt: 2.494448e+001 1.456665e+001 1.030967e+001 1.819885e+001 2.766473e+001 1.751853e+001 4.522449e+00113 9.229657e+000 6.555467e+001 3.287798e+00114 ..... Final time [sum(dt)]: 2.660897e+00215 . 1th inequality constrain violation [without the penalty coefficient]: 1.883506e-00816 ____________________________17 ............ Final CPUtime: ... seconds18 . Cost function [min(J_0)]: 0.843533601920 ____________________________21 Final results [deterministic part - hybrid-strategy; case B]:22 ............. Problem name: DrugDisplacementProblemB23 ...... NLP or MINLP solver: MISQP24 . Number of time intervals: 1025 ... IVP relative tolerance: 1.000000e-00726 ... IVP absolute tolerance: 1.000000e-00727 . Sens. absolute tolerance: 1.000000e-00728 ............ NLP tolerance: 1.000000e-00529 ....... Final state values: 1.999999e-002 2.000000e+000 2.660897e+00230 ...... 1th optimal control: ...31 ..... Final size of the dt: 2.494448e+001 1.456665e+001 1.030967e+001 1.819885e+001 2.766473e+001 1.751853e+001 4.522449e+00132 9.229657e+000 6.555467e+001 3.287798e+00133 ..... Final time [sum(dt)]: 2.660897e+00234 . 1th inequality constrain violation [without the penalty coefficient]: 2.318316e-00935 ____________________________36 ............ Final CPUtime: ... seconds37 . Cost function [min(J_0)]: 0.798502728.2 PHASE RESETTING OF A CALCIUM OSCILLATOR PROBLEMThe state oscillations are possible to observe in the systems biology very frequently. This behavour iscaused by instabilities of the steady-states. These oscillations can be removed temporarily with the help of theexternal stimuli, usually binaries. The strength and timing of these control variables have a smoothing effect onthe behavior of the system. Without further influences of the stimuli the oscillations occur again. It appears fromthis that we can talk about the phase reseting.For the demonstrative purposes of our toolbox with the CVP approach, the calcium oscillator model describingintracellular calcium spiking in hepatocytes induced by an extracellular increase in adenosine triphosphatePage – 35
DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems Biology0.034x 18x 20 50 100 150 20076State Variable0.0252State VariableControl variable543210.0200 50 100 150 200Time0TimeFigure 8.1 – Optimal state trajectories (left) and the control profile (right) for the drug displacement problemwithout the path constraint.x 148x 20 50 100 150 200 2503.570.02736State Variable0.0260.0250.0240.0232.521.5State VariableControl variable5430.0220.0210.0210.52100.0190 50 100 150 200 250Time0TimeFigure 8.2 – Optimal state trajectories (left) and the control profile (right) for the drug displacement problem withthe path constraint.Page – 36
Page 1 and 2: TECHNICAL REPORTDOTcvpSB: a Matlab
Page 3 and 4: Main Web PageIt is possible to get
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Page 13 and 14: CHAPTER 2Optimal control problem2.1
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Page 30 and 31: CHAPTER 7GUI for DOTcvp7.1 STEP BY
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Page 50 and 51: CHAPTER 11Default settingsThe user
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