Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities - 1st Edition - ISBN: 9780128195956

Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities

1st Edition

Authors: Rebecca Sanft Anne Walter
Paperback ISBN: 9780128195956
Imprint: Academic Press
Published Date: 1st March 2020
Page Count: 270
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Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's 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 modeling, readers will learn to value the approach and apply competencies in other settings.

Included case studies 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.

Key Features

  • Presents a single volume on mathematics and biological examples, with data and wet lab experiences suitable for non-experts
  • 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

Table of Contents

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


No. of pages:
© Academic Press 2020
1st March 2020
Academic Press
Paperback ISBN:

About the Author

Rebecca Sanft

Dr. Sanft received her Ph.D. in applied mathematics from the University of Arizona. She then worked at Bryn Mawr College as a Howard Hughes Medical Institute Postdoctoral Fellow. During this time, she developed courses in mathematical modelling and worked with biology faculty to incorporate more quantitative training throughout their curriculum. Following this appointment, Dr. Sanft was an Assistant Professor of Mathematics at St. Olaf College where she led a team of faculty in mathematics and biology to develop a concentration (interdisciplinary minor) in Mathematical Biology. She is passionate about designing interdisciplinary classroom experiences. Her research interests are at the interface of mathematics, biology, and mechanics, with an emphasis on modelling growth in soft tissues.

Affiliations and Expertise

Assistant Professor of Mathematics, University of North Carolina Asheville, USA

Anne Walter

Dr. Walter received her Ph.D. in Physiology and Pharmacology from Duke University. Dr. Walter was a Fellow at the National Institutes of Health where she first worked collaboratively with mathematicians in the Laboratory of Mathematical Biology. Her research areas have included transport physiology, physical properties of biological membranes and their lipids and proteins. During her 30 years of teaching, she has taught courses in renal physiology, comparative animal physiology, cell physiology and neuroscience as well as general education. Dr. Walter has been at the forefront of interdisciplinary course development including an integrated introduction to chemistry and biology program, writing and science literacy, and the mathematics of biology. She also enjoys opportunities to guide students in international study to take interdisciplinary approaches to problems related to human and environmental health in India, evolution, ecology and conservation in Ecuador and water and climate change in Morocco.

Affiliations and Expertise

Professor of Biology, St. Olaf College, USA

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