What is remarkable about Dynamic Models in Biology is that it truly speaks to students of the biological sciences. It puts biology first, and then tries to explain how mathematical tools can explain biological phenomena. Nothing else I’ve seen does this anywhere near as well. The authors (a biologist and a mathematician) have combined their experience and talents to produce an excellent textbook.
There are several identifiable elements that combine to create a success. The authors’ use of case studies focuses on doing a few well-chosen examples in depth. There is no attempt to be comprehensive. The applications range across the areas of biology where dynamic models have made compelling contributions. The authors introduce just enough mathematics to understand the modeling results — and no more. This keeps biology in the forefront and can perhaps inspire students to follow up with more in-depth investigations on their own or through a related mathematics course. The authors spend a significant amount of time on the modeling process itself. In part this is because the complexity of biological problems requires a more subtle approach to the concept of modeling. Questions like ‘What is a model?’, ‘What data are available to estimate model parameters or to validate a model?’, and ‘How much simplification is acceptable to keep a model tractable?’ can be much harder to answer than, for example, in the modeling of a mechanical system.
Computation is well-integrated throughout. The authors rely on high level languages such as MATLAB or R for calculations or to implement the models. (MATLAB is probably well-known to readers, and R is an object-oriented scripting language appropriate for simulating dynamical models.) The authors provide a website with supplementary materials including lab manuals for both MATLAB and R as well as MATLAB files and R scripts. Computation and simulation are viewed simply as tools that are available to explore a model and identify biologically significant results, especially when the phenomena are so complex that extensive computation or simulation are the only means of getting predictions from the model.
The authors explore dynamic models exclusively, and focus more on deterministic than stochastic systems. It would be wonderful to see a companion volume on genomics, bioinformatics, and structural biology, but the authors’ interests and experience are on the dynamics side.
There are four primary case studies. They are: matrix models and structured population dynamics, membrane channels and action potentials, cellular dynamics, and infectious disease. The models that the authors choose to investigate are either time-tested and more traditional (the population and infectious disease models, for example) or models of more prominent current interest, For example, the case study on cellular dynamics includes a discussion of one recently constructed gene network that acts like a clock and another that acts like a switch.
A chapter on spatial models in biology explores reaction-diffusion models as well as stationary patterns (e.g., animal coats and insect markings) or moving patterns (e.g., chemical waves or heartbeats). Another chapter takes a quick look at other computational approaches including agent-based models and artificial life models such as Tierra.
The authors do not discuss prerequisites, but the book presumes some level of familiarity with differential calculus and very basic differential equations. Although its primary audience consists of biology students, mathematics students would benefit considerably from exposure to deeper and more tangible applications than they would typically see in mathematics courses.
Bill Satzer (email@example.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.