Note: "Das Verbundprojekt "KOGGE: Kommunale Gewässer gemeinschaftlich entwickeln" wurde vom Bundesministerium für Bildung und Forschung (BMBF) im Rahmen der Fördermaßnahme "Regionales Wasserressourcen-Management für den nachhaltigen Gewässerschutz in Deutschland" (ReWaM) gefördert (Förderkennzeichen: 033W032A). Laufzeit: 01.04.2015-30.09.2018" - Seite 3 , Verbundnummer 01157605

Note: Front Cover -- Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities -- Copyright -- Contents -- Preface -- Tips for using this text - instructors -- Tips for using this text - students -- Online resources -- Acknowledgments -- 1 Preliminaries: models, R, and lab techniques -- 1.1 Bringing mathematics and biology together through modeling -- 1.2 R basics -- 1.2.1 RStudio layout -- 1.2.2 Simple calculations -- 1.2.3 Data structures -- Vectors -- Matrices -- Data frames -- 1.2.4 Basic plotting -- 1.2.5 Reading data from les -- 1.2.6 Iteration -- 1.2.7 Fitting a linear regression model -- 1.3 Prelab lab: practicing the fundamentals -- Introduction -- Materials -- Using the micropipettes -- Serial dilution with dye solutions and water -- Measuring absorbance -- Graphing and data analysis -- 2 Introduction to modeling using difference equations -- 2.1 Discrete-time models -- 2.1.1 Solutions to rst-order difference equations -- 2.1.2 Using linear regression to estimate parameters -- 2.2 Putting it all together: the whooping crane -- 2.3 Case study 1: Island biogeography -- 2.3.1 Background -- 2.3.2 Model formulation -- 2.3.3 Rakata story -- Data -- Parameter estimation -- Model analysis -- 2.3.4 Modern approach: lineage data -- Model -- Parameter estimation -- Model analysis -- 2.3.5 Back to MacArthur and Wilson: effects of distance and area -- 2.4 Case study 2: Pharmacokinetics model -- 2.4.1 Background -- Pharmacokinetics: basic concepts and terminology -- Caffeine -- 2.4.2 Formulating the model -- 2.4.3 Understanding the model -- 2.4.4 Parameter estimation -- 2.4.5 Model evaluation/analysis -- 2.4.6 Further exploration -- 2.5 Case study 3: Invasive plant species -- 2.5.1 Background -- 2.5.2 Model formulation -- 2.5.3 Parameter estimation -- 2.5.4 Model predictions -- 2.5.5 Management strategies. , 2.6 Wet lab: logistic growth model of bacterial population dynamics -- 2.6.1 Introduction -- 2.6.2 Modeling populations -- 2.6.3 The experiment -- Preparation -- Measuring growth rates by optical density -- Measuring growth rate by serial dilution and plate count -- 2.6.4 Model calibration and analysis -- 2.6.5 Experiment part 2: effect of changing media -- 3 Differential equations: model formulation, nonlinear regression, and model selection -- 3.1 Biological background -- 3.2 Mathematical and R background -- 3.2.1 Differential equation-based model formulation -- Constant ow rate -- Relative rates -- Mass action -- Feedback -- 3.2.2 Solutions to ordinary differential equations -- 3.2.3 Investigating parameter space -- 3.2.4 Nonlinear tting -- 3.3 Model selection -- 3.4 Case study 1: How leaf decomposition rates vary with anthropogenic nitrogen deposition -- 3.4.1 Background -- 3.4.2 The data -- 3.4.3 Model formulation -- 3.4.4 Parameter estimation -- 3.4.5 Model evaluation -- 3.5 Case study 2: Exploring models to describe tumor growth rates -- 3.5.1 Background -- 3.5.2 The data -- 3.5.3 Model formulation -- 3.5.4 Parameter estimation -- 3.5.5 Model evaluation: descriptive power -- 3.5.6 Model evaluation: predictive power -- 3.6 Case study 3: Predator responses to prey density vary with temperature -- 3.6.1 Background -- Can predator-prey interactions predict invasive behavior? -- 3.6.2 Analysis of functional response data: determining the parameters -- 3.6.3 Exploring functional responses as a function of temperature -- 3.7 Wet lab: enzyme kinetics of catechol oxidase -- 3.7.1 Overview of activities -- 3.7.2 Introduction to enzyme catalyzed reaction kinetics -- 3.7.3 Deriving the model -- 3.7.4 Estimating KM and Vmax -- 3.7.5 Our enzyme: catechol oxidase -- 3.7.6 Experiment: collecting initial rates for the Michaelis-Menten model. , Overview of the procedure -- Materials -- Enzyme preparation -- Running the reactions -- Analysis in R -- 3.7.7 Effects of inhibitors on enzyme kinetics -- 3.7.8 Experiment: measuring the effects of two catechol oxidase inhibitors, phenylthiourea and benzoic acid -- Analysis in R -- 4 Differential equations: numerical solutions, model calibration, and sensitivity analysis -- 4.1 Biological background -- 4.2 Mathematical and R background -- 4.2.1 Numerical solutions to differential equations -- Example: logistic growth (one variable) -- Example: tumor growth model (a system of two differential equations) -- 4.2.2 Calibration: tting models to data -- Example: calibrating the logistic growth model -- 4.2.3 Sensitivity analysis -- Global sensitivity -- Local sensitivity analysis -- Local sensitivity example: logistic model -- 4.2.4 Putting it all together: the dynamics of Ebola virus infecting cells -- Numerical solution for the Ebola model -- Fitting parameters to the Ebola model: calibrating the model -- Local sensitivity analysis: assessing key parameters in the Ebola virus-cell system -- 4.3 Case study 1: Modeling the 2009 in uenza pandemic -- 4.3.1 Background -- 4.3.2 The SIR model -- Model simulations -- 4.3.3 Cumulative number of cases -- 4.3.4 Epidemic threshold -- 4.3.5 Public health interventions -- 4.3.6 2009 H1N1 in uenza pandemic -- Estimating parameters -- Taking action -- 4.4 Case study 2: Optimizing immunotherapy in prostate cancer -- 4.4.1 Background -- 4.4.2 Model formulation -- 4.4.3 Model implementation -- 4.4.4 Parameter estimation -- 4.4.5 Vaccination protocols and model predictions -- 4.4.6 Sensitivity analysis -- 4.4.7 Simulating other treatment strategies -- 4.5 Case study 3: Quorum sensing -- 4.5.1 Introduction -- 4.5.2 Model formulation -- 4.5.3 Parameter estimation -- 4.5.4 Model simulations -- 4.5.5 Sensitivity analysis. , The temporal response -- 4.6 Wet lab: hormones and homeostasis-keeping blood glucose concentrations stable -- 4.6.1 Overview of activities -- 4.6.2 Introduction to blood glucose regulation and its importance -- 4.6.3 Developing a model -- 4.6.4 Experiment: measuring blood glucose concentrations following glucose ingestion -- Introduction to the procedure -- Experimental procedure -- 4.6.5 Analysis -- 4.6.6 Thoughts to consider for potential follow-up experiments -- 5 Technical notes for laboratory activities -- 5.1 Introduction -- 5.2 Population growth -- Bacterial growth media and tips -- Optional plate counts and converting optical density to numbers of bacteria -- Alternate organisms -- 5.3 Enzyme kinetics -- Tips and solution preparation for catechol oxidase -- Notes on data analysis -- 5.3.1 Notes on other enzymes or similar experiments -- Predator-prey or the enzyme game -- Other enzymes -- 5.4 Blood glucose monitoring -- 5.4.1 Tips for glucose monitoring -- Example of a subject consent form -- 5.4.2 Other lab activities -- Bibliography -- Index -- Back Cover.