Intro -- Supervisor -- Co-Supervisors -- Faculty Opponent -- Abstract -- Svensk sammanfattning -- Publications and Manuscripts -- Abbreviations -- Mathematical symbols -- Table of Contents -- 1 Introduction -- 1.1 Complexity -- 1.2 The Book of Life: from DNA to protein -- 1.3 Omics -- 1.4 Personalized medicine -- 1.5 Systems biology -- 1.6 Aim and scope -- 1.7 Outline of thesis -- 2 Science Through Hypothesis Testing -- 2.1 Facts, hypotheses, and theories -- 2.2 Verifications and falsifications -- 3 Mathematical Modeling -- 3.1 Modelling definitions and concepts -- 3.1.1 Model properties -- 3.1.2 Modeling frameworks -- 3.2 Ordinary differential equations -- 3.3 Black box modeling and regression models -- 3.4 Networks and data-driven modeling -- 3.5 Partial differential equations -- 3.6 Stochastic modeling -- 4 ODE Modeling Methods -- 4.1 The minimal model and modeling cycle approach -- 4.2 Model construction -- 4.2.1 Hypothesis and data -- 4.2.2 Scope and simplifications -- 4.2.3 Reaction kinetics and measurement equations -- 4.2.4 Units -- 4.3 Model simulation -- 4.3.1 Runge-Kutta, forward Euler, and tolerance -- 4.3.2 Adams-Bashforth -- 4.3.3 Adams-Moulton -- 4.3.4 Backward Differentiation Formulas -- 4.3.5 On Stiffness and software -- 4.4 Parameter estimation and goodness of fit -- 4.4.1 Objective function -- 4.4.2 Cost landscape -- 4.4.3 Local optimization -- Steepest descent, Newton, and quasi-Newton -- Nelder-Mead downhill simplex -- 4.4.4 Global Optimization -- Multi-start optimization -- Simulated annealing -- Evolutionary algorithms -- Particle swarm optimization -- 4.5 Statistical assessment of goodness of fit -- 4.5.1 The χ2-test -- 4.5.2 Whiteness, run, and Durbin-Watson test -- 4.5.3 Interpretation of rejections -- 4.6 Uncertainty analysis -- 4.6.1 Model uncertainty -- 4.6.2 Parameter uncertainty -- Sensitivity analysis.

Fisher information matrix -- Identifiability and the profile likelihood -- 4.6.3 Prediction uncertainty -- 4.7 Testing predictions -- 4.7.1 Core predictions -- 4.7.2 Validation data -- 4.7.3 Overfitting -- 4.8 Model selection -- 4.8.1 Experimental design and testing -- 4.8.2 Ranking methods and tests -- Information criterion -- The likelihood ratio test -- 4.9 Bootstrapping and empirical distributions -- 5 Model Systems -- 5.1 Insulin signaling system in human adipocytes -- 5.2 Cell-to-cell variability in yeast -- 5.3 Facilitation in murine nerve cells -- 6 Results -- 6.1 Modeling of dominant negative inhibition data -- 6.2 Quantification of nuclear transport rates in yeast cells -- 6.3 Quantitative modeling of facilitation in pyramidal neurons -- 6.4 A novel method for hypothesis testing using bootstrapping -- 7 Concluding Remarks -- 7.1 Summary of results and conclusions -- 7.1.1 DN data should be analyzed using mathematical modeling -- 7.1.2 A single-cell modeling method for quantification of nuclear transport -- 7.1.3 Facilitation can be explained by a single mechanism -- 7.1.4 A novel 2D bootstrap approach for hypothesis testing -- 7.2 Relevancy of mathematical modeling -- 7.2.1 Hypothesis testing -- 7.2.2 Mechanistic understanding -- 7.2.3 Design of experiments -- 7.2.4 Data analysis -- 7.2.5 Healthcare -- 7.3 Outlook -- Acknowledgements -- References -- Endnotes.