Friday, March 30, 2012


I recently discovered iBioMagazine, which I highly recommend. The iBioMagazine website describes its goals.
“iBioMagazine offers a collection of short (<15 min) talks that highlight the human side of research. iBioMagazine goes 'behind-the-scenes' of scientific discoveries, provides advice for young scientists, and explores how research is practiced in the life sciences. New topics will be covered in each quarterly issue. Subscribe to be notified when a new iBioMagazine is released.”
Here are some of my favorites:

Bruce Alberts, Editor-in-Chief of Science magazine and coauthor of The Molecular Biology of the Cell, tells about how he learned from failure.

Former NIH director Harold Varmus explains why he became a scientist.

Young researchers participating in a summer course at the Marine Biological Laboratory at Woods Hole explain why they became scientists.

Hugh Huxley discusses his development of the sliding filament theory of muscle contraction. Of particular interest is that Huxley began his career as a physics student, and then changed to biology. Andrew Huxley (no relation), of Hodgkin and Huxley fame, independently developed a similar model.

Finally, readers of Intermediate Physics for Medicine and Biology should be sure to listen to Rob Phillips’ wonderful talk about the role of quantitative thinking and mathematical modeling in biology. Phillips is coauthor of the textbook Physical Biology of the Cell, which I have discussed earlier in this blog.

Friday, March 23, 2012

Saltatory Conduction

Action potential propagation along a myelinated nerve axon is often said to occur by “saltatory conduction.” The 4th edition of Intermediate Physics for Medicine and Biology follows this traditional explanation.
“We have so far been discussing fibers without the thick myelin sheath. Unmyelinated fibers constitute about two-thirds of the fibers in the human body . . . Myelinated fibers are relatively large, with outer radii of 0.5 – 10 μm. They are wrapped with many layers of myelin between the nodes of Ranvier . . . In the myelinated region the conduction of the nerve impulse can be modeled by electrotonus because the conductance of the myelin sheath is independent of voltage. At each node a regenerative Hodgkin-Huxley-type (HH-type) conductance change restores the shape of the pulse. Such conduction is called saltatory conduction because saltare is the Latin verb ‘to jump.’ ”
I have never liked the physical picture of an action potential jumping from one node to the next. The problem with this idea is that the action potential is in fact distributed over many nodes simultaneously as it propagates along the axon. Consider an action potential with a rise time of about half a millisecond. Let the radius of the axon be 5 microns. Table 6.2 in Intermediate Physics for Medicine and Biology indicates that the speed of propagation for this axon is 85 m/s, which implies that the upstroke of the action potential is spread over (0.5 ms) x (85 mm/ms) = 42.5 mm. But the distance between nodes for this fiber (again, from Table 6.2) is 1.7 mm. Therefore, the action potential upstroke is distributed over 25 nodes! The action potential is not rising at one node and then jumping to the next, but it propagates in a nearly continuous way along the myelinated axon. I grant that in other cases, when the speed is slower or the rise time is briefer, you can observe behavior that begins to look saltatory (e.g., Huxley and Stampfli, 1949, J. Physiol, 108:315-339), but even then the action potential upstroke is distributed over many nodes (see their Fig. 13).

If saltatory conduction is not the best description of propagation along a myelinated axon, then what is responsible for the speedup compared to unmyelinated axons? Primarily, the action potential propagates faster because of a reduction of the membrane capacitance. Along the myelinated section of the membrane, the capacitance is low because of the many layers of myelin (N capacitors C in series result in a total capacitance of C/N). At a node of Ranvier, the capacitance per unit area of the membrane is normal, but the area of the nodal membrane is small. Adding these two contributions together leads to a very small average, or effective, capacitance, which allows the membrane potential to increase very quickly, resulting in fast propagation.

In summary, I don’t find the idea of an action potential jumping from node to node to be the most useful image of propagation along a myelinated axon. Instead, I prefer to think of propagation as being nearly continuous, with the reduced effective capacitance increasing the speed. This is not the typical explanation found in physiology books, but I believe it is closer to the truth. Rather than using the term salutatory conduction, I suggest we use curretory conduction, for the Latin verb currere, “to run.”

Friday, March 16, 2012

Henry Moseley

Henry Moseley is an English physicist who developed X-ray methods to assign a unique atomic number Z to each element. He appears in Problem 3 of Chapter 16 in the 4th edition of Intermediate Physics for Medicine and Biology.
Problem 3 Henry Moseley first assigned atomic numbers to elements by discovering that the square root of the frequency of the Kα photon is linearly related to Z. Solve Eq. 16.2 for Z and show that this is true. Plot Z vs the square root of the frequency and compare it to data you look up.
Asimov’s Biographical Encyclopedia of Science & Technology (Second Revised Edition) describes Moseley:
“For a time [Moseley] did research under Ernest Rutherford where he was the youngest and most brilliant of Rutherford’s brilliant young men . . .

This discovery [that each element could be assigned an atomic number] led to a major improvement of Mendeleev’s periodic table. Mendeleev had arranged his table of elements in order of atomic weight, but this order had had to be slightly modified in a couple of instances to keep the table useful. Moseley showed that if it was arranged in order of nuclear charge (that is, according to the number of protons in the nucleus, a quantity that came to be known as the atomic number) no modifications were necessary . . . Furthermore, Moseley’s X-ray technique could locate all the holes in the table representing still-undiscovered elements, and exactly seven such holes remained in 1914, the year Moseley developed the concept of the atomic number.”
Moseley died when he was only 28 years old. Asimov tells the story:
World War I had broken out at this time and Moseley enlisted at once as a lieutenant of the Royal Engineers. Nations were still naïve in their understanding of the importance of scientists to human society and there seemed no reason not to expose Moseley to the same chances of death to which millions of other soldiers were being exposed. Rutherford tried to get Moseley assigned to scientific labors but failed. On June 13, 1915, Moseley shipped to Turkey and two months later he was killed at Gallipoli as part of a thoroughly useless and badly bungled campaign, his death having brought Great Britain and the world no good . . . In view of what he might still have accomplished (he was only twenty-seven when he died), his death might well have been the most costly single death of the war to mankind generally.

Had Moseley lived it seems as certain as anything can be in the uncertain world of scientific history, that he would have received a Nobel Prize in physics . . .”
To learn more about Moseley, I recommend Chapter 4 (“The Long Grave Already Dug”) in Richard Rhodes’ classic The Making of the Atomic Bomb. Rhodes writes that “When he heard of Moseley’s death, the American physicist Robert A. Millikan wrote in public eulogy that his loss alone made the war ‘one of the most hideous and most irreparable crimes in history.’ ”

Friday, March 9, 2012

Glimpses of Creatures in Their Physical Worlds

I have recently finished reading Steven Vogel’s book Glimpses of Creatures in Their Physical Worlds, which is a collection of twelve essays previously published in the Journal of Biosciences. The Preface begins
“The dozen essays herein look at bits of biology, bits that reflect the physical world in which organisms find themselves. Evolution can do wonders, but it cannot escape its earthy context—a certain temperature range, a particular gravitational acceleration, the physical properties of air and water, and so forth. Nor can it tamper with mathematics. Thus the design of organisms—the level of organization at which natural selection acts most directly as well as the focus here—must reflect that physical context. The baseline it provides both imposes constraints and affords opportunities, the co-stars in what follows….”
The first essay is titled “Two Ways to Move Material,” and the two ways it discusses are diffusion and flow. To compare the two quantitatively, Vogel uses the Péclet number, Pe, defined as Pe = VL/D, where V is the flow speed, L the distance, and D the diffusion coefficient. As I read his analysis I suddenly got a sinking feeling: Russ Hobbie and I discussed just such a dimensionless number in Problem 37 of Chapter 4 in the 4th edition of Intermediate Physics for Medicine and Biology, but we called it the Sherwood Number, not the Péclet number. Were we wrong?

Edward Purcell, in his well-known article Life at Low Reynolds Number, introduced the quantity VL/D, which he called simply “S” with no other name. However, in a footnote at the end of the article he wrote “I’ve recently discovered that its official name is the Sherwood number, so S is appropriate after all!” Mark Denny, in his book Air and Water, states that VL/D is the Sherwood number, but in his Encyclopedia of Tide Pools and Rocky Shores he calls it the Péclet number. Vogel, in his earlier book Life in Moving Fluids, introduces VL/D as the Péclet number but adds parenthetically “sometimes known as the Sherwood number”

Some articles report a more complicated relationship between the Péclet and Sherwood number, implying they cannot be the same. For instance, consider the paper Nutrient Uptake by a Self-Propelled Steady Squirmer, by Vanesa Magar, Tomonobu Goto, and T. J. Pedley (Quarterly Journal of Mechanics and Applied Mathematics, Volume 56, Pages 65-91, 2003), in which they write “We find the relationship between the Sherwood number (Sh), a measure of the mass transfer across the surface, and the Péclet number (Pe), which indicates the relative effect of convection versus diffusion”. Similarly, Fumio Takemura and Akira Yabe (Gas Dissolution Process of Spherical Rising Gas Bubbles, Chemical Engineering Science, Volume 53, Pages 2691-2699, 1998) define the Péclet number as VL/D, but define the Sherwood number as αL/D, where α is the mass transfer coefficient at an interface (having, by necessity, the same units as speed, m/s). After reviewing these and other sources, I conclude that Vogel is probably right: VL/D should properly be called the Péclet number and not the Sherwood number, although the distinction is not always clear in the literature.

Now that we have cleared up this Péclet/Sherwood unpleasentness, let’s return to Vogel’s lovely essay about two ways to move material. He calculated the Péclet number for capillaries, using a speed of 0.7 mm/s (close to the 1 mm/s listed in Table 1.4 of Intermediate Physics for Medicine and Biology), a capillary radius of 3 microns (we use 4 microns in Table 1.4), and a oxygen diffusion constant of 1.8 × 10-9 m/s2 (2 × 10-9 m/s2 in Intermediate Physics for Medicine and Biology), and finds a Péclet number of 1.2 (if you use the data in our book, you would get 2). Vogel then argues that the optimum size for capillaries is when the Péclet number is approximately one, so that evolution has created a nearly optimized system. The argument, in my words, is that oxygen transport changes from convection to diffusion in the capillaries. If the Péclet number were much smaller than one, diffusion would dominate and we would be better off with larger capilarries that are farther apart and faster blood flow to improve convection. If the Péclet number were much larger than one, convection would dominate and our circulatory system would be improved by using smaller capilarries closer together, even if that means slower blood flow, to improve diffusion. A Péclet number of about one seems to be the happy medium.

The third essay, “Getting Up to Speed” is also relevant to readers of Intermediate Physics for Medicine and Biology. Our Problem 43 of Chapter 2 is about how high animals can jump.
Problem 43 Let’s examine how high animals can jump [Schmidt-Nielsen (1984), pp. 176-179]. Assume that the energy output of the jumping muscle is proportional to the body mass, M. The gravitational potential energy gained upon jumping to a height h is Mgh (g=9.8 m s-2). If a 3 g locust can jump 60 cm, how high can a 70 kg human jump? Use scaling arguments.
In the next problem, number 44, Russ and I ask the reader to calculate the acceleration of the jumper, which if you solve the problem you will find varies inversely with length.

Vogel analyzes this same topic, but digs a little deeper. Here examines all sorts of jumpers, including seeds and spores that are hurled upward without the help of muscles at all. He finds that the scaling laws from Problems 43 and 44 do indeed hold, but the traditional reasoning behind the law is flawed.
“The diversity of cases for which the scaling rule works ought to raise a flag of suspicion. Why should an argument based on muscle work for systems that do their work with other engines? . . . Something else must be afoot—again, the original argument presumed isometrically built muscle-powered jumpers. In short, the fit of the far more diverse projectiles demands a more general argument for the scaling of projectile performance. . .”
Vogel goes on to show that for small animals, muscles would have to work unrealistically fast in order to produce the accelerations required to jump to a fixed height.
“The old argument has crashed and burned. The work relative to mass of a contracting muscle deteriorates as animals get smaller rather than holding constant—a consequence of the requisite rise in intrinsic speed. Muscle need not and commonly does not power jumps in real time—elastic energy storage in tendons of collagen, in apodemes of chitin, and in pads of resilin provides power amplification. Finally, muscle powers none of those seed and tiny fungal projectiles. Yet acceleration persists in scaling as the classic argument anticipates. . ."
So how does Vogel explain the scaling law?
“A possible alternative emerges if we reexamine the relationship between force and acceleration defined by Newton’s second law. If acceleration indeed scales inversely with length and mass directly with the cube of length, then force should scale with the square of the length. Or, put another way, force divided by the square of the length should remain constant. Force over the square of length corresponds to stress, so we’re saying that stress should be constant. Perhaps our empirical finding that acceleration varies with length tells us that stress in some manner limits the systems.”
Vogel’s book is full of these sorts of physical insights. I recommend it as supplemental reading for those studying from Intermediate Physics for Medicine and Biology.

Friday, March 2, 2012

Odds and Ends

It’s time to catch up on topics discussed previously in this blog.

Several times I have written about the Technetium-99m shortage facing the United States (see here, here, here, and here). Russ Hobbie and I discuss 99mTc in Chapter 17 of the 4th edition of Intermediate Physics for Medicine and Biology.
“The most widely used isotope is 99mTc. As its name suggests, it does not occur naturally on earth, since it has no stable isotopes. We consider it in some detail to show how an isotope is actually used. Its decay scheme has been discussed above. There is a nearly monoenergetic 140-keV γ ray. Only about 10% of the energy is in the form of nonpenetrating radiation. The isotope is produced in the hospital from the decay of its parent, 99Mo, which is a fission product of 235U and can be separated from about 75 other fission products. The 99Mo decays to 99mTc.”
An interesting article by Matthew Wald about the supply of 99mTc appeared in the February 6 issue of the New York Times. Wald writes
“For years, scientists and policy makers have been trying to address two improbably linked problems that hinge on a single radioactive isotope: how to reduce the risk of nuclear weapons proliferation, and how to assure supplies of a material used in thousands of heart, kidney and breast procedures a year. . .

The isotope is technetium 99m, or tech 99 for short. It is useful in diagnostic tests because it throws off an easy-to-detect gamma ray; also, because it breaks down very quickly, it gives only a small dose of radiation to the patient.

But the recipe for tech 99 requires another isotope, molybdenum 99, that is now made in nuclear reactors using weapon-grade uranium. In May 2009, a Canadian reactor that makes most of the North American supply of moly 99 was shut because of a safety problem. A second reactor, in the Netherlands, was simultaneously closed for repairs.

The 54-year-old Canadian reactor, Chalk River in Ontario, is running now, but its license expires in four years. Canada built two replacement reactors, but even though they turned out to be unusable, their construction discouraged potential competitors ...”
One solution to the 99mTc shortage may be to produce 99Mo in a cyclotron. The New York Times article discussed this solution briefly, and more detail is supplied by a report written by Hamish Johnston and published on the website (all readers of Intermediate Physics for Medicine and Biology should become familiar with The gist of the method is to bombard 100Mo with protons in a cyclotron. Recently, researchers have made progress in developing this method. Johnston writes
“Scientists in Canada are the first to make commercial quantities of the medical isotope technetium-99m using medical cyclotrons. The material is currently made in just a few ageing nuclear reactors worldwide, and recent reactor shutdowns have highlighted the current risk to the global supply of this important isotope.”
See also an article in the Canadian newspaper, The Globe and Mail.

Another topic addressed recently in this blog is the risk of low levels of radiation, discussed in Chapter 16 of Intermediate Physics for Medicine and Biology.
“In dealing with radiation to the population at large, or to populations of radiation workers, the policy of the various regulatory agencies has been to adopt the linear-nonthreshold (LNT) model to extrapolate from what is known about the excess risk of cancer at moderately high doses and high dose rates, to low doses, including those below natural background.”
On February 21, published an article asking “Does LNT model overestimate cancer risk?” Science writer Jude Dineley reports
“An in vitro study has demonstrated that DNA repair mechanisms respond more effectively when exposed to low doses of ionizing radiation, compared to high doses. The observations potentially contradict the benchmark for radiation-induced cancer risk estimation, the linear-no-threshold (LNT) model, and if so, could have large implications for cancer risk estimation (PNAS 109 443).”
The Proceedings of the National Academy of Sciences paper that Dineley cites is titled “Evidence for formation of DNA repair centers and dose-response nonlinearity in human cells,” and is written by a team of researchers at the Lawrence Berkeley National Laboratory. The abstract is given below.
“The concept of DNA 'repair centers' and the meaning of radiation-induced foci (RIF) in human cells have remained controversial. RIFs are characterized by the local recruitment of DNA damage sensing proteins such as p53 binding protein (53BP1). Here, we provide strong evidence for the existence of repair centers. We used live imaging and mathematical fitting of RIF kinetics to show that RIF induction rate increases with increasing radiation dose, whereas the rate at which RIFs disappear decreases. We show that multiple DNA double-strand breaks (DSBs) 1 to 2 μm apart can rapidly cluster into repair centers. Correcting mathematically for the dose dependence of induction/resolution rates, we observe an absolute RIF yield that is surprisingly much smaller at higher doses: 15 RIF/Gy after 2 Gy exposure compared to approximately 64 RIF/Gy after 0.1 Gy. Cumulative RIF counts from time lapse of 53BP1-GFP in human breast cells confirmed these results. The standard model currently in use applies a linear scale, extrapolating cancer risk from high doses to low doses of ionizing radiation. However, our discovery of DSB clustering over such large distances casts considerable doubts on the general assumption that risk to ionizing radiation is proportional to dose, and instead provides a mechanism that could more accurately address risk dose dependency of ionizing radiation.”
PNAS published an editorial by Lynn Hlatky, titled “Double-Strand Break Motions Shift Radiation Risk Notions,” accompanying the article. Also, see the Lawrence Berkeley lab press release.

Finally, my coauthor Russ Hobbie is now on iTunes! His video "Photon Interactions: A Simulation Study with MacDose" can be downloaded free from iTunes, and provides much insight into how radiation interacts with tissue. The description on iTunes states
“This 26-minute video uses a computer simulation to demonstrate how x-ray photons interact in the body through coherent scattering, the photoelectric effect, Compton scattering, and pair production. It emphasizes the statistical nature of photon attenuation and energy absorption. The viewer should be able to distinguish between the quantities energy transferred, energy absorbed, Kerma, and absorbed dose, describe the effect of secondary photons on energy transferred and absorbed dose, and understand the effect of photons of different energy when used for radiation therapy.”