Cruz_Diss_2012

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<ul><li><p> AN APPROACH TO MECHANISM RECOGNITION FOR MODEL BASED ANALYSIS </p><p>OF BIOLOGICAL SYSTEMS </p><p>AN APPROACH TO MECHANISM RECOGNITION </p><p>FOR MODEL BASED ANALYSIS OF BIOLOGICAL SYSTEMS </p><p>vorgelegt von Master of Science in Process Engineering </p><p>Mariano Nicols Cruz Bournazou aus Mexiko City, Mexiko </p><p>von der Fakultt III- Prozesswissenschaften der Technischen Universitt Berlin </p><p>zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften </p><p>- Dr.-Ing. - </p><p>genehmigte Dissertation </p><p>Promotionsausschuss: Vorsitzender: Prof. Dr.-Ing. G. Tsatsaronis Gutachter: Prof. Dr.-Ing. G. Wozny Gutachter: Prof. Dr. P. Neubauer Gutachter: Prof. G. Lyberatos Tag der wissenschaftlichen Aussprache 24.01.2012 </p><p>Berlin 2012 </p><p>D 83 </p></li><li><p>dedicada a Heberto y Helig </p></li><li><p>ACKNOWLEDGEMENTS </p><p>I want to express my gratitude to my supervisor, Professor Gnter Wozny, for his </p><p>constant support and useful advice on a professional and personal level and to my co-</p><p>supervisor, Professor Peter Neubauer, for finding a perfect application for MR and for </p><p>his intellectual input to this work. </p><p>I would also like to thank Professor Kravaris and Professor Lyberatos at the University </p><p>of Patras for his collaboration and hospitality. </p><p>Special thanks go to Dr. Harvey Arellano-Garcia, Dr. Stefan Junne and Dr. Tilman Barz </p><p>for interesting discussions and support during the critical phases of this project (which </p><p>were quite numerous). </p><p>I must of course thank all my other friends and colleagues in the Chair of Process </p><p>Dynamics and Operations and in the Chair of Bioprocesses. </p><p>I would also like to thank my second family, conformed of all my friends spread around </p><p>the world, who have always motivated me to follow my goals and offered a shoulder to </p><p>console my sorrows. </p><p>Finally, I would like to thank my parents, Mariano and Effi, and my family for always </p><p>being at my side despite the distance and especially to Alexis Cruz, who one day might </p><p>realize his great contribution to each one of the achievements in my life. </p><p>M. Nicols Cruz B. </p></li><li><p> Ich Mariano Nicolas Cruz Bournazou erklre an Eides Statt, dass die vorliegende Dissertation in allen Teilen von mir selbstndig angefertigt wurde und die benutzten Hilfsmittel vollstndig angegeben worden sind. </p><p>Mariano Nicolas Cruz Bournazou Berlin, 1. Februar 2012 </p></li><li><p>Content </p><p>i </p><p>CONTENT </p><p>Zusammenfassung ....................................................................................................................... v </p><p>Abstract ....................................................................................................................................... vii </p><p>Figure content ............................................................................................................................. ix </p><p>Table content............................................................................................................................... xi </p><p>List of Abbreviations ................................................................................................................ xii </p><p>List of symbols ......................................................................................................................... xvii </p><p>1 Introduction ......................................................................................................................... 1 </p><p>1.1 The gap between research and industry ................................................................. 1 </p><p>1.2 Hierarchical modeling ............................................................................................... 3 </p><p>1.3 Understanding process dynamics ............................................................................ 4 </p><p>1.4 The bridge between industry and research ............................................................ 5 </p><p>1.5 Related work............................................................................................................... 7 </p><p>1.6 Project Goal ............................................................................................................... 9 </p><p>1.7 Advantages of Mechanism Recognition............................................................... 10 </p><p>1.8 The good, the bad, and the useful model ............................................................ 11 </p><p>2 Modeling ............................................................................................................................. 13 </p><p>2.1 Definition ................................................................................................................. 13 </p><p>2.2 Model complexity .................................................................................................... 14 </p><p>2.3 Engineering approach to complex systems ......................................................... 15 </p><p>2.4 Modeling in systems biology .................................................................................. 16 </p><p>2.4.1 Systems biology ................................................................................................... 16 </p><p>2.4.2 Modeling of genetic regulatory systems ........................................................... 17 </p><p>2.5 Mathematical model for a batch biochemical reactor ........................................ 19 </p><p>3 Model Reduction ............................................................................................................... 21 </p><p>3.1 Introduction ............................................................................................................. 21 </p><p>3.2 Basic approaches to Model Reduction ................................................................. 22 </p><p>3.2.1 Reaction invariants.............................................................................................. 22 </p><p>3.2.2 Switching functions and the reaction invariant .............................................. 24 </p><p>3.2.3 Sensitivity analysis ............................................................................................... 25 </p></li><li><p>Content </p><p>ii </p><p>3.2.4 Lumping................................................................................................................ 26 </p><p>3.2.5 Perturbation theory ............................................................................................. 27 </p><p>3.2.6 Time scale analysis .............................................................................................. 28 </p><p>4 Optimal Experimental Design ......................................................................................... 31 </p><p>4.1 The experiment ........................................................................................................ 33 </p><p>4.1.1 The Maximum Likelihood ................................................................................. 34 </p><p>4.1.2 Model identifiability ............................................................................................ 35 </p><p>4.2 The Fisher Information Matrix.............................................................................. 37 </p><p>4.2.1 The confidence Interval ..................................................................................... 37 </p><p>4.2.2 Approximation of parameter variance-covariance matrix ............................. 39 </p><p>4.2.3 Limitations of the Fisher Information Matrix ................................................ 40 </p><p>4.3 Model discrimination............................................................................................... 42 </p><p>4.3.1 Model discrimination in Mechanism Recognition .......................................... 44 </p><p>5 Code generation, simulation and optimization ............................................................. 47 </p><p>5.1 Code generation ....................................................................................................... 47 </p><p>5.1.1 MOSAIC .............................................................................................................. 47 </p><p>5.1.2 SBPD..................................................................................................................... 48 </p><p>5.2 Simulation ................................................................................................................. 49 </p><p>5.2.1 sDACL .................................................................................................................. 49 </p><p>5.3 Optimization............................................................................................................. 50 </p><p>6 An approach to Mechanism Recognition ...................................................................... 51 </p><p>6.1 A short introduction to Mechanism Recognition ............................................... 51 </p><p>6.1.1 Illustrative Example ............................................................................................ 53 </p><p>6.2 Methodology for Mechanism Recognition .......................................................... 56 </p><p>6.3 Program steps ........................................................................................................... 57 </p><p>6.3.1 Submodels ............................................................................................................ 57 </p><p>6.3.2 General structure ................................................................................................. 57 </p><p>6.3.3 Submodel distinguishability ............................................................................... 58 </p><p>6.3.4 Initial interval ....................................................................................................... 59 </p><p>6.3.5 MR initialization .................................................................................................. 59 </p><p>6.3.6 Detection of switching points ........................................................................... 60 </p><p>6.3.7 Initial conditions of the interval k+1 ............................................................... 62 </p><p>6.3.8 Detection of the next switching point ............................................................. 62 </p></li><li><p>Content </p><p>iii </p><p>6.3.9 Flow diagram ....................................................................................................... 63 </p><p>7 Mechanism Recognition applied on Sequencing Batch Reactors .............................. 65 </p><p>7.1 Introduction ............................................................................................................. 65 </p><p>7.1.1 Activated Sludge .................................................................................................. 65 </p><p>7.1.2 Sequencing Batch Reactor ................................................................................. 66 </p><p>7.1.3 Nitrate Bypass Generation ................................................................................ 67 </p><p>7.1.4 Monitoring of wastewater processes ................................................................ 68 </p><p>7.2 Submodel building ................................................................................................... 68 </p><p>7.3 A proposed 9state model ....................................................................................... 69 </p><p>7.3.1 Storage .................................................................................................................. 69 </p><p>7.3.2 Reduction of the extended ASM3 model to a 9state model ......................... 70 </p><p>7.3.3 Mathematical representation of the 9state model .......................................... 71 </p><p>7.3.4 Stoichiometric matrix ......................................................................................... 73 </p><p>7.3.5 Limitations of the reduced models ................................................................... 74 </p><p>7.4 A proposed 6state model ....................................................................................... 74 </p><p>7.5 A proposed 5state model ....................................................................................... 75 </p><p>7.6 Results ....................................................................................................................... 75 </p><p>7.6.1 Simulations Results ............................................................................................. 77 </p><p>7.7 Mechanism Recognition in SBR processes .......................................................... 78 </p><p>7.8 Recognition of organic matter depletion ............................................................. 79 </p><p>7.8.1 Conditions for proper process description with Mechanism Recognition 79 </p><p>7.8.2 Conditions for accurate switching point detection ........................................ 80 </p><p>7.8.3 MR initialization .................................................................................................. 82 </p><p>7.8.4 Detection of switching points ........................................................................... 82 </p><p>7.9 Conclusions .............................................................................................................. 83 </p><p>8 Mechanism Recognition in Escherichia coli cultivations ................................................. 85 </p><p>8.1 Escherichia coli cultivations ....................................................................................... 85 </p><p>8.2 Models for the description of Escherichia coli cultivations .................................. 86 </p><p>8.2.1 Division of physiological states ........................................................................ 87 </p><p>8.3 Modeling Escherichia coli batch fermentations with Mechanism Recognition . 90 </p><p>8.3.1 General model ..................................................................................................... 90 </p><p>8.3.2 Submodels for dividing metabolic states ......................................................... 92 </p><p>8.4 Material and methods ............................................................................................. 96 </p></li><li><p>Content </p><p>iv </p><p>8.4.1 Strain and culture conditions ............................................................................. 96 </p><p>8.4.2 Online analysis ..................................................................................................... 97 </p><p>8.4.3 Offline analysis .................................................................................................... 99 </p><p>8.4.4 Data treatment ................................................................................................... 103 </p><p>8.5 Experimental validation ........................................................................................ 104 </p><p>8.5.1 Conditions for proper process description with MR ................................... 104 </p><p>8.5.2 Conditions for accurate switching point detection ...................................... 105 </p><p>8.5.3 Data set ............................................................................................................... 106 </p><p>8.5.4 Recognition of overflow and substrate limitation regimes ......................... 109 </p><p>8.5.5 Simulations vs. experimental data ................................................................... 110 </p><p>8.5.6 Results ..........................................</p></li></ul>