Theoretical Biology: Modeling and Simulation of Biological Systems and Laboratory Methods INAUGURAL-DISSERTATION zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.) eingereicht im Fachbereich Biologie, Chemie, Pharmazie der Freien Universität Berlin vorgelegt von CHRISTOPH WIERLING aus Münster, Deutschland November, 2008 Die vorliegende Arbeit wurde in der Zeit von August 1999 bis November 2008 am Max- Planck-Institut für molekulare Genetik in Berlin-Dahlem in der Abteilung von Herrn Prof. Dr. Hans Lehrach in der Arbeitsgruppe von Herrn Dr. Ralf Herwig angefertigt. 1. Gutachter: Prof. Dr. Hans Lehrach Max-Planck-Institut für Molekulare Genetik 2. Gutachter: Prof. Dr. Volker Erdmann Freie Universität Berlin Disputation am 26. Mai 2009 ii Contents Contents........................................ iii ListofFigures..................................... vi ListofTables .....................................viii Summary ....................................... 1 Zusammenfassung(GermanSummary) . .. 2 1 Introduction 3 1.1 Outline ..................................... 5 1.2 BiologicalSystems ............................... 6 1.2.1 Somitogenesis ............................. 7 1.2.2 Cell-cell Communication and Signal Transduction . ....... 11 1.2.2.1 NotchSignaling . 11 1.2.2.2 WntSignaling . .. .. .. .. .. .. 12 1.2.2.3 FGFSignaling. .. .. .. .. .. .. 14 1.3 ComputationalModelingofBiologicalSystems . ........ 16 1.3.1 Mathematical Modeling of Biological Systems Using Ordinary Dif- ferentialEquations . 17 1.3.1.1 ModelingofBiochemicalReactions . 17 1.3.1.2 ModelingofGeneExpression. 20 1.3.2 DataResourcesforSystemsBiology. .. 21 1.3.2.1 Pathwayandinteractiondatabases . 22 1.3.3 Software Applications for Modeling and Simulation . ....... 24 1.3.4 MathematicalModelsofSomitogenesis . ... 27 1.4 Experimental Techniques for Gene Expression Analysis . ........... 30 1.4.1 cDNAArrayTechnology. 30 1.4.2 ImageAnalysis............................. 32 1.5 Objectives.................................... 35 2 Results 37 2.1 PyBioS-ModelingandSimulationPlatform . ...... 37 iii Contents 2.1.1 OverviewofPyBioS .. .. .. .. .. .. .. 38 2.1.2 Modelstructure............................. 40 2.1.3 ModelConstruction .. .. .. .. .. .. .. 42 2.1.4 QuantitativeSimulation . 46 2.1.5 Visualization .............................. 49 2.1.6 AnalysisModules ........................... 50 2.1.7 System’sPerformance . 52 2.1.8 SummaryoftheInventions. 54 2.2 ModelingofBiologicalSystems-Somitogenesis . ........ 56 2.2.1 ModelingOscillatoryNotchSignaling . .... 57 2.2.2 ModelingOscillatoryWntSignaling . ... 59 2.2.3 CouplingWnt,Notch,andFGFsignaling . .. 62 2.3 Modeling of Laboratory Methods - DNA Array Experiments . ........ 66 2.3.1 ImplementationoftheSimulationTool . ... 67 2.3.2 DataSets ................................ 68 2.3.2.1 DesignofArtificialSampleSets . 68 2.3.3 SimulationModel ........................... 70 2.3.3.1 GenerationofSignalIntensities . 70 2.3.3.2 FilterModel ......................... 72 2.3.3.3 LocalDistortions . 72 2.3.3.4 SpotShape.......................... 72 2.3.3.5 BackgroundNoise. 73 2.3.4 DataEvaluationandQualityMeasurement . ... 74 2.3.4.1 ImageAnalysis .. .. .. .. .. .. 74 2.3.4.2 Evaluation of Gridfind and Quantification Quality . ... 74 2.3.4.3 Statistical Evaluation of Differential Expression ...... 74 2.3.5 SimulationofLocalDistortions . .. 75 2.3.5.1 SpotShifting. .. .. .. .. .. .. 75 2.3.5.2 PinShifting ......................... 77 2.3.6 SimulationofDifferentSpotShapes . ... 77 2.3.7 SimulationofBackgroundNoise. 80 2.3.7.1 GlobalBackgroundNoise . 80 2.3.7.2 Localbackgroundnoise . 80 2.3.8 Simulation of the Influence of Background Noise on the Expression Analysis ................................ 80 2.3.8.1 SummaryoftheFindings . 83 iv Contents 3 Discussion 86 3.1 PyBioS - a Modeling and Simulation Platform for Cellular Reaction Networks 87 3.1.1 PredictionintheFaceofUncertainty . ... 89 3.1.2 Applications .............................. 91 3.2 ModelingBiologicalSystems. ... 92 3.3 Modeling of Laboratory Methods - DNA Array Experiments . ........ 92 Bibliography 95 A Appendix 115 A.1 Concepts, Tools, and Methods used for the setup of the computational simu- lationplatforms .................................115 A.1.1 Object-orientedprogramming . 115 A.1.2 Python .................................116 A.1.3 ZopeWebApplicationServer . .116 A.1.4 NumericalSolversforODEsandDAEs . 116 A.1.5 ComputationofConservationRelations . .117 A.2 ModelingofSomitogenesis. 119 A.2.1 KinticsUsedWithintheSomitogenesisModel . .119 A.3 ModelingofDNAArrays. .. .. .. .. .. .. .. .120 A.3.1 cDNAArrayDataUsedforModeling . .120 A.3.2 DataacquisitioninDNAarrayexperiments . .121 A.3.3 MathematicalDescriptionofaCraterSpot . .122 Publications 125 Acknowledgments 127 v List of Figures 1.1 Overviewofthethesis ............................. 6 1.2 Schematicillustrationofsomitogenesis . ........ 9 1.3 CanonicalNotchsignalingpathway . .... 12 1.4 Canonical Wnt/β-cateninsignalingpathway . 13 1.5 Overview:FGFsignaling. 15 1.6 Kineticlawsforbiochemicalreactions . ....... 19 1.7 Kineticlawsforgeneregulation . .... 21 1.8 Modelsof her1 and Hes7 autoinhibition . 29 2.1 PyBioSWebiterface .............................. 39 2.2 UML-diagramofthePyBioSontology . ... 41 2.3 Descriptionofanaction. .. 43 2.4 ManualmodelgenerationinPyBioS . ... 45 2.5 Genericdatabaseinterface(part1) . ...... 47 2.6 Genericdatabaseinterface(part2) . ...... 48 2.7 Elementsfor graphical representationinPyBioS . .......... 50 2.8 Parameterscan ................................. 53 2.9 ScalingofPyBioS................................ 55 2.10Notchmodel................................... 57 2.11 ModelofHes7autoinhibiton . ... 60 2.12 Wntsignalingmodule. 61 2.13 WntsignalingmodelwithinPyBioS . .... 63 2.14 Wntsignaling:Simulationresults . ...... 64 2.15FGFmodel ................................... 65 2.16 Simulationpipelineandarraylayout . ....... 68 2.17 Experimentalreferenceforsimulationdata. .......... 71 2.18Spotshifting. .................................. 76 2.19Pinshifting.................................... 78 2.20 Experimentalblockcenterdeviation. ........ 79 vi List of Figures 2.21 Spotshapeexamples. 79 2.22 Backgroundnoiseexamples. ... 81 2.23 Localbackgroundnoisecorrelation. ....... 82 2.24 Statisticaltestsfor simulatedfold-changes . ............ 85 3.1 Booleannetwork. ............................... 89 vii List of Tables 1.1 Speciescharacteristicsinsomiteformation . .......... 7 1.2 Cyclicgenesofsomitogenesis . ... 10 1.3 Databases useful for modeling of cellular systems. ........... 23 1.4 Statisticsonreactionsinpathwaydatabases . ......... 24 1.5 Modeling toolsfrequently used in systems biology. .......... 25 2.1 Definition, modeling, and critical effects of simulationparameters. 69 3.1 ProjectsinwhichPyBioSisused. .. 91 viii Summary Mathematical modeling and simulation techniques have turned out to be valuable toolsfor the understanding of complex systems in different areas of research and engineering. In recent years this approach came to application frequently also in biology resulting in the establish- ment of the research area systems biology. Systems biology tries to understand the behavior of complex biological systems by means of mathematical approaches. This requires the in- tegration of qualitative and quantitative experimental data into coherent models. Currently, systems biology usually investigates biochemical reaction networks of cellular systems. A challenging task is the construction of large models that requires computer-assisted data in- tegration, simulation and evaluation. In this work I have elaborated technical bases for the computer-assisted modeling of bio- logical systems and experimental techniques. For this I have developed the program PyBioS that provides a user-friendly Web application (http://pybios.molgen.mpg.de) and brings in automation for several important tasks required for the development, implemen- tation, and simulation of cellular models. For the description of cellular reaction systems PyBioS makes use of object-oriented programming, well established methods for the mathe- matical description of biochemical reaction systems based on ordinary differential equation systems, and novel interfaces to biochemical pathway databases (e.g., Reactome, KEGG). In addition PyBioS provides several different functions for the analysis and visualization. The benefit obtained by mathematical modeling of biological systems using PyBioS is il- lustrated for segmentation of the body (somitogenesis) as, e.g., taking place during embryo- genesis. The parameterized somitogenesis model I have developed comprises three signaling pathways, namely Notch, Wnt, and FGF that are known to be relevant for somitogenesis. The model shows a regular oscillation controlled by extracellular Wnt3a. Below a critical thresh- old concentration of Wnt3a the oscillation that is controlled by Wnt signaling arrests and approaches a steady state. These findings are conform to experimental observations found during determination of somite boundaries. Besides the analysis of biological systems, modeling strategies can also be used for the evaluation of biotechnological experimental techniques. To study this I have perfomed sim- ulations of DNA array hybridization experiments for the evaluation of critical parameters during subsequent image and data analysis. Therefore I have carried out simulation stud- ies on several error parameters arising in complex hybridization experiments, such