Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities

Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for a course taken simultaneously by students majoring in mathematics or computer science and those in the life sciences. The cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modelling, readers will learn to value the approach and develop confidence and competencies to apply them in other settings. The case studies in this book focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected.

Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities solves the problem of putting together in a single volume, the mathematics, biological examples with data and wet lab experiences suitable for non-experts. The latter provides a valuable practical experience of actually designing experiments with a model in mind, collecting data and using it to determine parameters, test the original hypothesis and make new ones.

• Presents a single volume containing the mathematics and biological examples with data and wet lab experiences suitable for non-experts
• Each chapter contains three real-world biological Case Studies and one wet lab for application of the mathematical models
• Includes R code templates throughout the text, which are also available through an online repository, along with the necessary data files to complete all projects and labs

Students and researchers in biomedical engineering, computational biology, mathematics, computer science and life sciences who are interested in understanding and applying mathematical modelling

1 Discrete-Time Models and an Introduction to the Modeling Process
1.1 Case Study 1: Pharmacokinetics Model
1.2 Case Study 2: Breathing Model
1.3 Case Study 3: Island Biogeography
1.4 Wet Lab: Population Dynamics
2 Differential Equations: Model Formulation and Curve Fitting
2.1 Biological Background
2.2 Mathematical and R Background
2.2.1 Differential Equation Model Formulation
2.2.2 Nonlinear Fitting
2.3 Model Validation
2.4 Case Study 1: How Leaf Decomposition Rates Vary with Anthro- pogenic Nitrogen Deposition
2.4.1 Background
2.4.2 The Data
2.4.3 Model Formulation
2.4.4 Parameter Estimation
2.4.5 Model Evaluation
2.5 Case Study 2: Exploring Models to Describe Tumor Growth Rates
2.5.1 Background
2.5.2 The Data
2.5.3 Model Formulation
2.5.4 Parameter Estimation
2.5.5 Model Evaluation: Descriptive Power
2.5.6 Model Evaluation: Predictive Power
2.6 Case Study 3: Photosynthesis
2.7 Wet Lab: Enzyme Kinetics of Catechol Oxidase
2.7.1 Overview of Activities:
2.7.2 Introduction to Enzyme Catalyzed Reaction Kinetics
2.7.3 Deriving the model
2.7.4 Our Enzyme: Catechol Oxidase
2.7.5 Experiment: Collecting Initial Rates for the Michaelis- Menten Model
2.7.6 Analysis using R
2.7.7 Effects of Inhibitors on Enzyme Kinetics
2.7.8 Experiment: Measuring the Effects of Two Catechol Oxidase Inhibitors, Phenylthiourea and Benzoic Acid