Friday, January 29, 2010

William Albert Hugh Rushton

This semester, I am teaching a graduate class at Oakland University on Bioelectric Phenomena (PHY 530). Rather than using a textbook, I require the students to read original papers, thereby providing insights into the history of the subject and many opportunities to learn about the structure and content of original research articles.

We began with a paper by Alan Hodgkin and Bernard Katz (“The Effect of Sodium Ions on the Electrical Activity of the Giant Axon of the Squid,” Journal of Physiology, Volume 108, Pages 37–77, 1949) that tests the hypothesis that the nerve membrane becomes selectively permeable to sodium during an action potential. We then moved on to Alan Hodgkin and Andrew Huxley’s monumental 1952 paper in which they present the Hodgkin-Husley model of the squid nerve axon (“A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve,” Journal of Physiology, Volume 117, Pages 500–544, 1952). In order to provide a more modern view of the ion channels that underlie Hodgkin and Huxley’s model, we next read an article by Roderick MacKinnon and his group (“The Structure of the Potassium Channel: Molecular Basis of K+ Conduction and Selectivity,” Science, Volume 280, Pages 69–77, 1998). Then we read a paper by Erwin Neher, Bert Sakmann and their colleagues that described patch clamp recordings of single ion channels (“Improved Patch-Clamp Techniques for High-Resolution Current Recordings from Cells and Cell-Free Membrane Patches,” Pflugers Archive, Volume 391, Pages 85–100, 1981).

This week I wanted to cover one-dimensional cable theory, so I chose one of my favorite papers, by Alan Hodgkin and William Rushton (“The Electrical Constants of a Crustacean Nerve Fibre,” Proceedings of the Royal Society of London, B, Volume 133, Pages 444–479, 1946). I recall reading this lovely article during my first summer as a graduate student at Vanderbilt University (where my daughter Kathy is now an attending college). My mentor, John Wikswo, had notebook after notebook full of research papers about nerve electrophysiology, and I set out to read them all. Learning a subject by reading the original literature is an interesting experience. It is less efficient than learning from a textbook, but you pick up many insights that are lost when the research is presented in a condensed form. Hodgkin and Rushton’s paper contains the fascinating quote
Electrical measurements were made by applying rectangular pulses of current and recording the potential response photographically. About fifteen sets of film were obtained in May and June 1939, and a preliminary analysis was started during the following months. The work was then abandoned and the records and notes stored for six years [my italics]. A final analysis was made in 1945 and forms the basis of this paper.
During those six years, the authors were preoccupied with a little issue called World War II.

Sometimes I like to provide my students with biographical information about the authors of these papers, and I had already talked about my hero, the Nobel Prize-winning Alan Hodgkin, earlier in the semester. So, I did some research on Rushton, who I was less familiar with. It turns out, he is known primarily for his work on vision. William Albert Hugh Rushton (1901–1980) has only a short Wikipedia entry, which does not even discuss his work on nerves. (Footnote: Several months ago, after reading—or rather listening to while walking my dog Suki—The Wikipedia Revolution: How a Bunch of Nobodies Created the World’s Greatest Encyclopedia by Andrew Lih, I became intensely interested in Wikipedia and started updating articles related to my areas of expertise. This obsession lasted for only about a week or two. I rarely make edits anymore, but I may update Rushton’s entry.) Rushton was a professor of physiology at Trinity College in Cambridge University. He became a Fellow of the Royal Society in 1948, and received the Royal Medal from that society in 1970.

Horace Barlow wrote an obituary for Rushton in the Biographical Memoirs of Fellows of the Royal Society (Volume 32, Pages 423–459, 1986). It begins
William Rushton first achieved scientific recognition for his work on the excitability of peripheral nerve where he filled the gap in the Cambridge succession between Lord Adrian, whose last paper on peripheral nerve appeared in 1922, and Alan Hodgkin, whose first paper was published in 1937. It was on the strength of this work that he was elected as a fellow of the Royal Society in 1948, but then Rushton started his second scientific career, in vision, and for the next 30 years he was dominant in a field that was advancing exceptionally fast. In whatever he was engaged he cut a striking and influential figure, for he was always interested in a new idea and had the knack of finding the critical argument or experiment to test it. He was argumentative, and often an enormously successful showman, but he also exerted much influence from the style of his private discussions and arguments. He valued the human intellect and its skillful use above everything else, and he successfully transmitted this enthusiasm to a large number of students and disciples.
Another of my favorite papers by Rushton is “A Theory of the Effects of Fibre Size in Medullated Nerve” (Journal of Physiology, Volume 115, Pages 101–122, 1951). Here, he correctly predicts many of the properties of myelinated nerve axons, such as the ratio of the inner and outer diameters of the myelin, from first principles.

Both of the Rushton papers I have cited here are also referenced in the 4th edition of Intermediate Physics for Medicine and Biology. Problem 34 in Chapter 6 is based on the Hodgkin-Rushton paper. It examines their analytical solution to the one-dimensional cable equation, which involves error functions. Was it Hodgkin or Rushton who was responsible for this elegant piece of mathematics gracing the Journal of Physiology? I can’t say for sure, but in Hodgkin’s Nobel Prize autobiography he claims he learned about cable theory from Rushton (who was 13 years older than him).

William Rushton provides yet another example of how a scientist with a firm grasp of basic physics can make fundamental contributions to biology.

Friday, January 22, 2010

Summer Internships

Many readers of the 4th edition of Intermediate Physics for Medicine and Biology are undergraduate majors in science or engineering. This time of the year, these students are searching for summer internships. I have a few suggestions.

My first choice is the NIH Summer Internship Program in Biomedical Research. The intramural campus of the National Institutes of Health in Bethesda, Maryland is the best place in the world to do biomedical research. My years working there in the 1990s were wonderful. Apply now. The deadline is March 1.

The National Science Foundation supports Research Experience for Undergraduate (REU) programs throughout the US. Click here for a list (it is long, but probably incomplete). Often NSF requires schools to not just select from their own undergraduates, but also to open some positions in their REU program to students from throughout the country. You might also try to Google “REU” and see what you come up with. Each program has different deadlines and eligibility requirements. For several years Oakland University, where I work, had an REU program run by the physics department. We have applied for funding again, but have not heard yet if we were successful. If lucky, we will run the program this summer, with a somewhat later deadline than most.

Last year, as part of the federal government’s stimulus package, the National Institutes of Health encouraged researchers supported by NIH grants to apply for a supplement to fund undergraduate students in the summer. Most of these supplements were for two years, and this will be the second summer. Therefore, I expect there will be extra opportunities for undergraduate students to do biomedical research in the coming months. Strike while the iron’s hot! The stimulus program is scheduled to end next year.

Finally, one of the best ways for undergraduate students to find opportunities to do research in the summer is to ask around among your professors. Get a copy of your department’s annual report and find out which professors have funding. Attend department seminars and colloquia to find out who is doing research that interests you. Or just show up at a faculty member’s door and ask (first read what you can about his or her research, and have your resume in hand). If you can manage it financially, consider working without pay for the first summer, just to get your foot in the door.

When I look back on my undergraduate education at the University of Kansas, one of the most valuable experiences was doing research in Professor Wes Unruh’s lab. I learned more from Unruh and his graduate students than I did in my classes. But such opportunities don’t just fall into your lap. You need to look for them. Ask around, knock on some doors, and keep your eyes open. And start now, because many of the formal internship programs have deadlines coming up soon.

If, dear reader, you are fortunate enough to get an internship this summer, but it’s far from home, then don’t forget to pack your copy of Intermediate Physics for Medicine and Biology when you go. After working all day in the lab, you can relax with it in the evening!

Good luck.

Friday, January 15, 2010


The TeXbook,
by Donald Knuth.
Russ Hobbie and I wrote the 4th edition of Intermediate Physics for Medicine and Biology using TeX, the typesetting program developed by Donald Knuth. Well, not really. We actually used LaTeX, a document markup language based on TeX. To be honest, “we” didn’t even use LaTeX: Russ did all the typesetting with LaTeX while I merely read pdf files and sent back comments and suggestions.

TeX is particularly well suited for writing equations, of which there are many in Intermediate Physics for Medicine and Biology. I used TeX in graduate school, while working in John Wikswo’s laboratory at Vanderbilt University. This was back in the days before LaTeX was invented, and writing equations in TeX was a bit like programming in machine language. I remember sitting at my desk with Knuth’s TeXbook (blue, spiral bound, and delightful), worrying about arcane details of typesetting some complicated expression. At that time, TeX was new and unique. When I first arrived at Vanderbilt in 1982, Wikswo’s version of TeX did not even have a WYSIWYG editor, and our lab did not have a laser printer, so I would make a few changes in the TeX document and then run down the hall to the computer center to inspect my printout. As you can imagine, after several iterations of this process the novelty of TeX wore off. But, oh, did our papers look good when we shipped them out to the journal (and, yes, we did mail paper copies; no electronic submission back then). Often, I thought our version looked better than what was published. By the way, Donald Knuth is a fascinating man. Check out his website at He pays $2.56 to readers who find an error in his books (according to Knuth, 256 pennies is one hexadecimal dollar). Russ Hobbie used to pay a quarter for errors, and all I give is a few lousy extra credit points to my students.

I must confess, now-a-days I use the equation editor in Microsoft Word for writing equations. Word’s output doesn’t look as nice as TeX’s, but I find it easier to use. The solution manual for the 4th edition of Intermediate Physics for Medicine and Biology is written entirely using Word (email Russ or me for a copy), and so is the errata. But I did reacquaint myself with TeX when writing my Scholarpedia article about the bidomain model. Both Wikipedia and Scholarpedia use some sort of TeX hybrid for equations.

Listen to Donald Knuth describe his work.

Friday, January 8, 2010

In The Beat of a Heart

In the Beat of a Heart: Life, Energy, and the Unity of Nature, by John Whitfield, superimposed on Intermediate Physics for Medicine and Biology.
In the Beat of a Heart:
Life, Energy, and the Unity of Nature,
by John Whitfield.
Over Christmas break, I read In the Beat of a Heart: Life, Energy, and the Unity of Nature, by John Whitfield. I had mixed feelings about the book. I didn’t have much interest in the parts dealing with biodiversity in tropical forests and skimmed through them rather quickly. But other parts I found fascinating. One of the main topics explored in the book is Kleiber’s law (metabolic rate scales as the 3/4th power of body mass), which Russ Hobbie and I discuss in Chapter 2 of the 4th edition of Intermediate Physics for Medicine and Biology. But the book has a broader goal: to compare and contrast the approaches of physicists and biologists to understanding life. The main idea can be summarized by the subtitle of the textbook I studied biology out of when an undergraduate at the University of Kansas: The Unity and Diversity of Life. Intermediate Physics for Medicine and Biology lies on the “unity” side of this great divide, but the interplay of these two views of life makes for a remarkable story.

The book begins with a Prologue about D’Arcy Thompson (Whitfield calls him “the last Victorian scientist”), author of the influential, if out-of-the-mainstream, book On Growth and Form.
This is the story—with some detours—of D’Arcy Thompson’s strand of biology and of a century-long attempt to build a unified theory, based on the laws of physics and mathematics, of how living things work. At the story’s heart is the study of something that Thompson called “a great theme”—the role of energy in life... The way that energy affects life depends on the size of living things. Size is the most important single notion in our attempt to understand energy’s role in nature. Here, again, we shall be following Thompson’s example. After its introduction, On Growth and Form ushers the reader into a physical view of living things with a chapter titled “On Magnitude,” which looks at the effects of body size on biology, a field called biological scaling.
In the Beat of a Heart examines Max Rubner’s idea that metabolism scales with surface area (2/3rd power), and Max Kleiber’s modification of this rule to a 3/4th power. It then describes the attempt of physicist Geoffrey West and ecologist Brian Enquist to explain this rule by modeling the fractal networks that provide the raw materials needed to maintain metabolism. While I was familiar with much of this story before reading Whitfield’s book, I nevertheless found the historical context and biographical background engrossing. Then came the lengthy section on forest ecology (Zzzzzzzzz). I soldiered on and was rewarded by a penetrating final chapter comparing the physicist’s and biologist’s points of view.
Finding a unity of nature would not make studying the details of nature obsolete. Indeed, finding unity depends on understanding the details. The variability of life means that in biology the ability to generalize is not enough. If you've measured one electron, you've measured them all, but, as I saw in Costa Rica, to understand a forest you must be able to see the trees, and that takes a botanist. Thinkers such as Humboldt, Darwin, and Wallace gained their understanding of how nature works from years of intimate experience of nature in the flesh and the leaf. And yet they were not just interested in what their senses told them: they also tried to abstract and unify. The combination of attributes--intrepid and reflective, naturalist and mathematician--strikes me as rather rare, and becoming more so. These days scientific lone wolves such as D’Arcy Thompson are almost extinct, and it would take a truly awesome polymath to acquire the necessary suite of skills in natural history, ecology, mathematics, and physics to devise a theory as complex as fractal networks.
The book ends with a provoking question and answer that sums up the debate nicely:
Is nature beautifully simple or beautifully complex? Yes, it is.
More about In the Beat of a Heart can be found at the book’s website:

Friday, January 1, 2010


2010 is finally here. Happy New Year! Let’s celebrate by discussing the National Research Council report BIO2010.

In 2003 the NRC released the report BIO2010: Transforming Undergraduate Education for Future Research Biologists. If I had to sum up the report in one phrase, it would be “they are signing our song.” In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I incorporate many of the ideas championed in BIO2010. The preface of the report recommends
a comprehensive reevaluation of undergraduate science education for future biomedical researchers. In particular it calls for a renewed discussion on the ways that engineering and computer science, as well as chemistry, physics, and mathematics are presented to life science students. The conclusions of the report are based on input from chemists, physicists, and mathematicians, not just practicing research biologists. The committee recognizes that all undergraduate science education is interconnected. Changes cannot be made solely to benefit future biomedical researchers. The impact on undergraduates studying other types of biology, as well as other sciences, cannot be ignored as reforms are considered. The Bio2010 report therefore provides ideas and options suitable for various academic situations and diverse types of institutions. It is hoped that the reader will use these possibilities to initiate discussions on the goals and methods of teaching used within their own department, institution, or professional society.
The executive summary begins
The interplay of the recombinant DNA, instrumentation, and digital revolutions has profoundly transformed biological research. The confluence of these three innovations has led to important discoveries, such as the mapping of the human genome. How biologists design, perform, and analyze experiments is changing swiftly. Biological concepts and models are becoming more quantitative, and biological research has become critically dependent on concepts and methods drawn from other scientific disciplines. The connections between the biological sciences and the physical sciences, mathematics, and computer science are rapidly becoming deeper and more extensive. The ways that scientists communicate, interact, and collaborate are undergoing equally rapid and dramatic transformations, which are driven by the accessibility of vast computing power and facile information exchange over the Internet.
Readers of this blog will be particularly interested in Recommendation #1.3 of the report, dealing with the physics education required by biologists, reproduced below. In the list of concepts the report considers essential, I have indicated in brackets the sections of the 4th edition of Intermediate Physics for Medicine and Biology that address each topic. (I admit that the comparison of the report’s recommended physics topics to those topics covered in our book may be a bit unfair, because the report was referring to an introductory physics class, not an intermediate one.) Some of the connections between the report’s topics and sections in our book need additional elaboration, which I have included as footnotes.


The principles of physics are central to the understanding of biological processes, and are increasingly important in sophisticated measurements in biology. The committee recommends that life science majors master the key physics concepts listed below. Experience with these principles provides a simple context in which to learn the relationship between observations and mathematical description and modeling.

The typical calculus-based introductory physics course taught today was designed to serve the needs of physics, mathematics, and engineering students. It allocates a major block of time to electromagnetic theory and to many details of classical mechanics. In so doing, it does not provide the time needed for in-depth descriptions of the equally basic physics on which students can build an understanding of biology. By emphasizing exactly solvable problems, the course rarely illustrates the ways that physics can be applied to more recalcitrant problems. Illustrations involving modern biology are rarely given, and computer simulations are usually absent. Collective behaviors and systems far from equilibrium are not a traditional part of introductory physics. However, the whole notion of emergent behavior, pattern formation, and dynamical networks is so central to understanding biology, where it occurs in an extremely complex context, that it should be introduced first in physical systems, where all interactions and parameters can be clearly specified, and quantitative study is possible.

Concepts of Physics

Motion, Dynamics, and Force Laws
  • Measurement1: physical quantities [throughout], units [1.1, symbol list at the end of each chapter], time/length/mass [1.1], precision [none]
  • Equations of motion2: position [Appendix B], velocity [Appendix B], acceleration [Appendix B], motion under gravity [2.7, Problem 1.28]
  • Newton’s laws [1.8]: force [1.2], mass [1.12], acceleration [Appendix B], springs [Appendix F] and related material: stiffness3 [1.9], damping4 [1.14, 2.7, 10.6], exponential decay [2.2], harmonic motion [10.6]
  • Gravitational [3.9] and spring [none] potential energy, kinetic energy [1.8], power [1.8], heat from dissipation [Problem 8.24], work [1.8]
  • Electrostatic forces [6.2], charge [6.2], conductors/insulators [6.5], Coulomb’s law [6.2]
  • Electric potential [6.4], current [6.8], units [6.2, 6.4, 6.6, 6.8], Ohm’s law [6.8]
  • Capacitors [6.6], R [6.9] and RC [6.11] circuits
  • Magnetic forces [8.1] and magnetic fields [8.2]
  • Magnetic induction and induced currents [8.6]
Conservation Laws and Gobal [sic] Constraints
  • Conservation of energy [3.3] and momentum5 [15.4]
  • Conservation of charge [6.9, 7.9]
  • First [3.3] and Second [3.19] Laws of thermodynamics
Thermal Processes at the Molecular Level
  • Thermal motions: Brownian motion [3.10], thermal force (collisions) [none], temperature [3.5], equilibrium [3.5]
  • Boltzmann’s law [3.7], kT [3.5], examples [3.8, 3.9, 3.10]
  • Ideal gas statistical concepts using Boltzmann’s law, pressure [1.11]
  • Diffusion limited dynamics6 [4.6], population dynamics [2.9, Problem 2.34]
Waves, Light, Optics, and Imaging
  • Oscillators and waves [13.1]
  • Geometrical optics: rays, lenses [14.12], mirrors7 [none]
  • Optical instruments: microscopes and microscopy [Problem 14.45]
  • Physical optics: interference [14.6.2] and diffraction [13.7]
  • X-ray scattering [15.4] and structure determination [none]
  • Particle in a box [none]; energy levels [3.2, 14.2]; spectroscopy from a quantum viewpoint [14.2, 14.3]
  • Other microscopies8: electron [none], scanning tunneling [none], atomic force [none]
Collective Behaviors and Systems far from Equilibrium
  • Liquids [1.11, 1.12, 1.14, 1.15], laminar flow [1.14], viscosity [1.14], turbulence [1.18]
  • Phase transitions9 [Problem 3.57], pattern formation10 [10.11.5], and symmetry breaking [none]
  • Dynamical networks11: electrical, neural, chemical, genetic [none]
1. Russ Hobbie and I have not developed a laboratory to go along with our book, so we don’t discuss measurement, the important differences between precision and accuracy, the ideas of random versus systematic error, or error propagation.

2. Some elementary topics—such as position, velocity, and acceleration vectors—are not presented in the book, but are summarized in an Appendix (we assume they would be mastered in an introductory physics class). We analyze Newton’s second law specifically, but do not develop his three laws of motion in general.

3. We describe Young’s modulus, but we never introduce the term “stiffness.” We talk about potential energy, and especially electrical potential energy, but we don’t spend much time on mass-spring systems and never introduce the concept of elastic (or spring) potential energy.

4. The term “damping” is used
only occasionally in our book, but we discuss several types of dissipative phenomena, such as viscosity, exponential decay plus a constant input, and a harmonic oscillator with friction.

5. We use conservation of momentum when we analyze Compton scattering of electrons in Chapter 15, but we never actually present conservation of momentum as a concept.

6. We don’t discuss “diffusion limited dynamics,” but we do analyze diffusion extensively in Chapter 4.

7. We analyze lenses, but not mirrors, and never analyze the reflection of light (although we spend considerable time discussing the reflection of ultrasonic waves in Chapter 13).

8. I have to admit our book is weak on microscopy: the light microscope is relegated to a homework problem, and we don’t talk at all about electron, scanning tunneling, or atomic force microscopies.

9. We discuss thermodynamic phase transitions in a homework problem, but I believe that the report refers more generally to phase transitions that occur in condensed matter physics (e.g., the Ising model), which we do not discuss.

10. We touch on pattern formation in Chapter 10, and in particular in Problems 10.39 and 10.40 that describe wave propagation in the heart using a cellular automaton. But we do not analyze pattern formation (such as Turing patterns) in detail. Symmetry breaking is not mentioned.

11. We don’t discuss neural networks, or other related topics such as emergent behavior. We can only cover so much in one book.

I may be biased, but I believe that the 4th edition of Intermediate Physics for Medicine and Biology does a pretty good job of implementing the BIO2010 report suggestions into a textbook on physics for biologists. With 2010 now here, it’s important to remind aspiring biology students about the importance of physics in their undergraduate education.