Physical Models of Living Systems

Physical Models of
Living Systems,
by Philip Nelson.

Philip Nelson has a new textbook that came out earlier this year: Physical Models of Living Systems. It’s an excellent book, well written and beautifully illustrated. The target audience is similar to that for the 4th edition of Intermediate Physics for Medicine and Biology: upper-level undergraduates who have studied physics and math at the introductory level. Like IPMB, it stresses the construction of physical and mathematical models of living systems.

At the start of the book, Nelson provides a section labeled “To the Student.” I hope students read this, as it provides much wisdom and advice. In fact, most of this advice applies as well to IPMB. I found his discussion of “skills” to be so valuable that I reproduce it here.

Science is not just a pile of facts for you to memorize. Certainly you need to know many facts, and this book will supply some as background to the case studies. But you also need skills. Skills cannot be gained just by reading through this (or any) book. Instead you’ll need to work through at least some of the exercises, both those at the ends of chapters and others sprinkled throughout the text.

Specifically, this book emphasizes

• Model construction skills: It's important to find an appropriate level of description and then write formulas that make sense at that level. (Is randomness likely to be an essential feature of this system? Does the proposed model check out at the level of dimensional analysis?) When reading others’ work, too, it’s important to be able to grasp what assumptions their model embodies, what approximations are being made, and so on.

• Interconnection skills: Physical models can bridge topics that are not normally discussed together, by uncovering a hidden similarity. Many big advances in science came about when someone found an analogy of this sort.

• Critical skills: Sometimes a beloved physical model turns out to be . . . wrong. Aristotle taught that the main function of the brain was to cool the blood. To evaluate more modern hypotheses, you generally need to understand how raw data can give us information, and then understanding.

• Computer skills: Especially when studying biological systems, it’s usually necessary to run many trials, each of which will give slightly different results. The experimental data very quickly outstrip our abilities to handle them by using the analytical tools taught in math classes. Not very long ago, a book like this one would have to content itself with telling you things that faraway people had done; you couldn’t do the actual analysis yourself, because it was too difficult to make computers do anything. Today you can do industrial-strength analysis on any personal computer.

• Communication skills: The biggest discovery is of little use until it makes it all the way into another person’s brain. For this to happen reliably, you need to sharpen some communication skills. So when writing up your answers to the problems in this book, imagine that you are preparing a report for peer review by a skeptical reader. Can you take another few minutes to make it easier to figure out what you did and why? Can you label graph axes better, add comments to your code for readability, or justify a step? Can you anticipate objections?

You'll need skills like these for reading primary research literature, for interpreting your own data when you do experiments, and even for evaluating the many statistical and pseudostatistical claims you read in the newspapers.

One more skill deserves separate mention. Some of the book’s problems may sound suspiciously vague, for example, “Comment on . . .” They are intentionally written to make you ask, “What is interesting and worthy of comment here?” There are multiple “right” answers, because there may be more than one interesting thing to say. In your own scientific research, nobody will tell you the questions. So it’s good to get the habit of asking yourself such things.

Nelson begins the book by discussing virus dynamics, and specifically analyzes the work of Alan Perelson, who constructs mathematical model of how the human immunodeficinecy virus interacts with our immune system. Here at Oakland University, Libin Rong (a former postdoc of Perelson’s) does similar research, and their work is an excellent case study in using mathematics to model a biological process.

A large fraction of the book examines the role of randomness in biology, leading to a detailed analysis of probability. Nelson provides an elegant discussion of the experiments of Max Delbruck and Salvador Luria.

S. Luria and M. Delbruck set out to explore inheritance in bacteria in 1943. Besides addressing a basic biological problem, this work developed a key mode of scientific thought. The authors laid out two competing hypotheses, and sought to generate testable quantitative predictions from them. But unusually for the time, the predictions were probabilistic in character. No conclusion can be drawn from any single bacterium—sometimes it gains resistance; usually it doesn’t. But the pattern of large numbers of bacteria has bearing on mechanism. We will see how randomness, often dismissed as an unwelcome inadequacy of an experiment, turned out to be the most interesting feature of the data.

Perhaps one way to appreciate the differences between Physical Models of Living Systems and IPMB is to compare how each handles diffusion. Russ Hobbie and I consider diffusion in Chapter 4 of IPMB; we describe diffusion as arising from a concentration gradient (Fick’s first law), and use the continuity equation to derive the diffusion equation (Fick’s second law). These relationships are macroscopic descriptions of diffusion. Then, at the end of the chapter—almost as an afterthought—we show that diffusion can be thought of as a random walk. Nelson, on the other hand, starts by analyzing the random nature of diffusion using probabilistic ideas, and then—almost as an afterthought—derives the diffusion equation (or at least a discrete approximation of it). I think this example reflects the different approaches of the two books: IPMB generally takes a macroscopic approach but sometimes reaches down with an example at the microscopic level, whereas Physical Models in Living Systems typically starts with a microscopic description and then sometimes works its way up to the macroscopic level.

Both books also have an extensive analysis of feedback. The canonical example in IPMB comes from physiology at the organism level: breathing rate controls and is controlled by blood carbon dioxide concentration. In Physical Models in Living Systems, a central example is how bacteria use feedback to regulate the synthesis of the amino acid tryptophan. Both case studies are excellent examples of negative feedback, but at different spatial scales. One example is not better than the other; they’re merely different illustrations of the same idea.

One strength of Physical Models of Living Systems is its emphasis on using computer simulations to describe a system’s behavior. IPMB has a few computer programs (for example, a program is provided to simulate the Hodgkin-Huxley model of a nerve axon), but Physical Models of Living Systems has a much heavier reliance on numerical simulation. Again, one approach isn’t better than the other, just different. One can learn a lot about biology using toy models and analytical analysis, but many more-complicated (often nonlinear) processes need the numerical approach. Anyone who uses, or plans to use, MATLAB for simulations may benefit from the Student’s Guide to Physical Models of Living Systems (available free to all at www.macmillanhighered.com/physicalmodels1e).

In conclusion, Nelson states that Physical Models of Living Systems is about how “physical science and life science illuminate each other,” and I can’t think of a better description of the goal of Intermediate Physics for Medicine and Biology. Students are lucky they have both to choose from. Finally, what is the very best thing about Physical Models of Living Systems? At the end of the “To the Student” section, Nelson lists several other books that complement his, and cites…you guessed it…Intermediate Physics for Medicine and Biology.