Qualitative modeling in computational systems biology Citation for published version (APA): Musters, M. W. J. M. (2007). Qualitative modeling in computational systems biology. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR629275 DOI: 10.6100/IR629275 Document status and date: Published: 01/01/2007 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 26. Sep. 2021 Qualitative Modeling in Computational Systems Biology Applied to Vascular Aging PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magni¯cus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op dinsdag 18 september 2007 om 16.00 uur door Mark Wilhelmus Johannes Maria Musters geboren te Breda Dit proefschrift is goedgekeurd door de promotor: prof.dr.ir. P.P.J. van den Bosch Copromotor: dr.ir. N.A.W. van Riel CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Musters, Mark W.J.M. Qualitative modeling in computational systems biology : applied to vascular aging / by Mark Wilhelmus Johannes Maria Musters. - Eindhoven : Technische Universiteit Eindhoven, 2007. Proefschrift. - ISBN 978-90-386-1564-6 NUR 954 Trefw.: nietlineaire di®erentiaalvergelijkingen / kunstmatige intelligentie / regelsystemen ; parameterschatting / fysieke veroudering. Subject headings: nonlinear di®erential equations / piecewise linear techniques / parameter estimation / ageing. This thesis was prepared by using the LATEX typesetting system. Cover design by Christoph Brach [email protected], http://www.nutsdesign.net Printed by Gildeprint drukkerijen, Enschede. Qualitative Modeling in Computational Systems Biology Applied to Vascular Aging Samenstelling kerncommissie: prof. dr. ir. P.P.J. van den Bosch promotor TU/e dr. ir. N.A.W. van Riel copromotor TU/e prof. dr. P.A.J. Hilbers lid kerncommissie TU/e dr. ir. H. de Jong lid kerncommissie INRIA Rh^one-Alpes prof. dr. ir. C. Th. Verrips lid kerncommissie UU Contents 1 Introduction 1 1.1 Challenges in Systems Biology . 2 1.1.1 Top-Down versus Bottom-Up . 4 1.2 Aging of the Vascular System . 5 1.2.1 Extending Longevity in Mythology . 5 1.2.2 Understanding Aging: the Scienti¯c Approach . 5 1.2.3 Changes in Biochemical Networks during Vascular Aging . 6 1.3 Problem Statement . 7 1.3.1 Project Description . 7 1.3.2 Research Goals . 8 1.4 Related Work . 9 1.5 Thesis Outline . 10 2 Analysis of Bistable Systems 11 2.1 Basic Knowledge about Feedback Loops, Circuits and Systems . 11 2.2 Nonlinear Dynamics in Biology . 12 2.3 Mathematical Model of ECM Remodeling . 14 2.4 Graphical Study of Bistability . 14 2.4.1 Breaking the Feedback Loop . 16 2.4.2 Solving the Steady-States Symbolically . 16 2.4.3 Deriving Restrictions on Parameter Values . 17 2.5 Discussion . 17 3 Qualitative Analysis of Nonlinear Biochemical Networks 19 3.1 General Description of the Procedure . 19 3.1.1 Approximation of Nonlinear Function with PWA Functions . 20 3.1.2 Selection of PWA Parameters . 25 3.1.3 Detection of Equilibrium Points and Performing Stability Analysis . 27 3.1.4 Construction of Qualitative Transition Graphs . 29 3.2 Example: an Arti¯cial Biochemical Network . 29 3.2.1 PWA Approximation . 30 3.2.2 Determination of the Equilibrium Points . 31 3.2.3 Dynamical Behavior at the Equilibrium Points and Stability Analysis 33 v CONTENTS 3.3 Transition Analysis . 33 3.4 Discussion . 36 4 Analysis of the Transforming Growth Factor-¯1 pathway 41 4.1 Physiology of the TGF-¯1 Signaling Pathway . 41 4.1.1 Isolation of the R-SMAD Loop . 42 4.2 Qualitative Analysis of the Transforming Growth Factor-¯1 Pathway . 44 4.2.1 Model Reduction of the TGF-¯1 Pathway . 44 4.2.2 Quasi-Steady-State Approximation of the TGF-¯1 Model . 48 4.2.3 From Nonlinear to Piecewise-A±ne . 51 4.2.4 Equilibria and Stability Analysis . 52 4.2.5 Transition Analysis . 56 4.3 Discussion . 63 5 Signal Transduction of the Unfolded Protein Response 65 5.1 Introduction . 65 5.2 Protein Folding of the von Willebrand Factor . 65 5.2.1 Translation and Translocation . 66 5.2.2 Protein Folding . 66 5.3 The Unfolded Protein Response . 67 5.3.1 Signal Transduction in the UPR . 67 5.4 Mathematical Model of Signal Transduction during the UPR . 69 5.5 Qualitative Analysis . 72 5.5.1 From Nonlinear to Piecewise-A±ne . 72 5.5.2 Equilibrium Points in the UPR Model . 74 5.5.3 Transition Analysis . 78 5.5.4 Comparison with Experimental Data . 80 5.6 Discussion . 86 6 System Identi¯cation with Parameter Constraints 87 6.1 The Biochemical Oscillator . 87 6.2 Qualitative Phase Space Analysis . 90 6.2.1 Nonlinear to PWA Conversion . 90 6.2.2 Transition Analysis . 90 6.2.3 Constrained Nonlinear Parameter Estimation . 92 6.3 Discussion . 95 7 Hybrid System Identi¯cation 97 7.1 General Identi¯cation Procedure . 97 vi Contents 7.1.1 Model Class . 97 7.1.2 Identi¯cation and Classi¯cation of a Hybrid Model . 98 7.2 PWA Identi¯cation of the Biochemical Oscillator . 99 7.2.1 Methods . 100 7.2.2 Results . 100 7.3 Discussion . 102 8 Conclusion and Discussion 103 8.1 Conclusions . 103 8.2 Future Perspectives . 106 A Nomenclature 107 A.1 List of Abbreviations . 107 A.2 Symbols . 108 A.2.1 Latin . 108 A.2.2 Greek . 109 Summary 127 Samenvatting 129 Dankwoord 131 About the Author 133 vii Contents viii 1 Introduction NOWLEDGE of health and the need of solutions for addressing diseases have K always fascinated humanity. Understanding the biochemical processes within cells,\the building blocks of life", has become indispensable. During the 20th century, our understanding of cellular biology has increased at an astonishing rate. Over the last decades, it can mainly be attributed to breakthroughs in the research ¯eld of molecular biology. This research ¯eld deals with the use of techniques from various research areas on solving biological problems. For example, molecular biology provided the necessary high throughput methods for unraveling the complete human genome in 2001 [96, 173]. This was an important step towards a better comprehension of the \blueprint of life" at that time, but it has recently become clear that dynamical information provides more insights about human physiology and pathological phenomena. A human can be viewed as a system with 1014 cells [72], each containing approximately 25; 000 genes [96, 173] and intertwined signaling networks operating over distinct spatio-temporal scales [132]. These data emphasize that comprehension of life's complexity is impossible by intuitive reasoning alone; computational approaches that integrate the available information into a single framework have therefore become indispensable [15, 91]. A mathematical model is a description of a system in terms of mathematical equa- tions [25]. A plethora of mathematical formalisms exists to describe physiological pro- cesses: discrete, continuous, deterministic, stochastic and combinations of these model- ing frameworks. Some of these frameworks are suitable for speci¯c situations. For in- stance, stochastic models are used for processes that are in essence dominated by random events [156], e.g. binding of a substrate to a receptor; it can result in di®erent outcomes for the same initial conditions. Since the deterministic approximation of the biochemical reaction systems becomes more di±cult for reactions with a few number of molecules, stochastic models are therefore more appropriate for describing these biochemical reac- tions. They provide a thorough description, based on several fundamental properties from physics. Unfortunately, computational complexity increases exponentially for sys- 1 Chapter 1 tems with more substrates. For a detailed overview of the wide variety of computational methods, the reader is referred to a review of de Jong [26]. At a cellular level, mathematical models are frequently deterministic descriptions as they provide a good balance between computational e®ort and accuracy. Tools from system identi¯cation enable building mathematical models of a dynamic system based on measured data [170]. The parameters of a given model are subsequently adjusted until the predicted dynamics coincide as good as possible with the measured signals.