AN APPROACH TO MECHANISM RECOGNITION FOR MODEL BASED ANALYSIS

OF BIOLOGICAL SYSTEMS

AN APPROACH TO MECHANISM RECOGNITION

FOR MODEL BASED ANALYSIS OF BIOLOGICAL SYSTEMS

vorgelegt von Master of Science in Process Engineering

Mariano Nicols Cruz Bournazou aus Mexiko City, Mexiko

von der Fakultt III- Prozesswissenschaften der Technischen Universitt Berlin

zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften

- Dr.-Ing. -

genehmigte Dissertation

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

Berlin 2012

D 83

dedicada a Heberto y Helig

ACKNOWLEDGEMENTS

I want to express my gratitude to my supervisor, Professor Gnter Wozny, for his

constant support and useful advice on a professional and personal level and to my co-

supervisor, Professor Peter Neubauer, for finding a perfect application for MR and for

his intellectual input to this work.

I would also like to thank Professor Kravaris and Professor Lyberatos at the University

of Patras for his collaboration and hospitality.

Special thanks go to Dr. Harvey Arellano-Garcia, Dr. Stefan Junne and Dr. Tilman Barz

for interesting discussions and support during the critical phases of this project (which

were quite numerous).

I must of course thank all my other friends and colleagues in the Chair of Process

Dynamics and Operations and in the Chair of Bioprocesses.

I would also like to thank my second family, conformed of all my friends spread around

the world, who have always motivated me to follow my goals and offered a shoulder to

console my sorrows.

Finally, I would like to thank my parents, Mariano and Effi, and my family for always

being at my side despite the distance and especially to Alexis Cruz, who one day might

realize his great contribution to each one of the achievements in my life.

M. Nicols Cruz B.

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.

Mariano Nicolas Cruz Bournazou Berlin, 1. Februar 2012

Content

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CONTENT

Zusammenfassung ....................................................................................................................... v

Abstract ....................................................................................................................................... vii

Figure content ............................................................................................................................. ix

Table content............................................................................................................................... xi

List of Abbreviations ................................................................................................................ xii

List of symbols ......................................................................................................................... xvii

1 Introduction ......................................................................................................................... 1

1.1 The gap between research and industry ................................................................. 1

1.2 Hierarchical modeling ............................................................................................... 3

1.3 Understanding process dynamics ............................................................................ 4

1.4 The bridge between industry and research ............................................................ 5

1.5 Related work............................................................................................................... 7

1.6 Project Goal ............................................................................................................... 9

1.7 Advantages of Mechanism Recognition............................................................... 10

1.8 The good, the bad, and the useful model ............................................................ 11

2 Modeling ............................................................................................................................. 13

2.1 Definition ................................................................................................................. 13

2.2 Model complexity .................................................................................................... 14

2.3 Engineering approach to complex systems ......................................................... 15

2.4 Modeling in systems biology .................................................................................. 16

2.4.1 Systems biology ................................................................................................... 16

2.4.2 Modeling of genetic regulatory systems ........................................................... 17

2.5 Mathematical model for a batch biochemical reactor ........................................ 19

3 Model Reduction ............................................................................................................... 21

3.1 Introduction ............................................................................................................. 21

3.2 Basic approaches to Model Reduction ................................................................. 22

3.2.1 Reaction invariants.............................................................................................. 22

3.2.2 Switching functions and the reaction invariant .............................................. 24

3.2.3 Sensitivity analysis ............................................................................................... 25

Content

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3.2.4 Lumping................................................................................................................ 26

3.2.5 Perturbation theory ............................................................................................. 27

3.2.6 Time scale analysis .............................................................................................. 28

4 Optimal Experimental Design ......................................................................................... 31

4.1 The experiment ........................................................................................................ 33

4.1.1 The Maximum Likelihood ................................................................................. 34

4.1.2 Model identifiability ............................................................................................ 35

4.2 The Fisher Information Matrix.............................................................................. 37

4.2.1 The confidence Interval ..................................................................................... 37

4.2.2 Approximation of parameter variance-covariance matrix ............................. 39

4.2.3 Limitations of the Fisher Information Matrix ................................................ 40

4.3 Model discrimination............................................................................................... 42

4.3.1 Model discrimination in Mechanism Recognition .......................................... 44

5 Code generation, simulation and optimization ............................................................. 47

5.1 Code generation ....................................................................................................... 47

5.1.1 MOSAIC .............................................................................................................. 47

5.1.2 SBPD..................................................................................................................... 48

5.2 Simulation ................................................................................................................. 49

5.2.1 sDACL .................................................................................................................. 49

5.3 Optimization............................................................................................................. 50

6 An approach to Mechanism Recognition ...................................................................... 51

6.1 A short introduction to Mechanism Recognition ............................................... 51

6.1.1 Illustrative Example ............................................................................................ 53

6.2 Methodology for Mechanism Recognition .......................................................... 56

6.3 Program steps ........................................................................................................... 57

6.3.1 Submodels ............................................................................................................ 57

6.3.2 General structure ................................................................................................. 57

6.3.3 Submodel distinguishability ............................................................................... 58