Friday, September 25, 2015

Polonium-210, The Perfect Poison

Figure 17.27 in the 5th edition of Intermediate Physics for Medicine and Biology shows the decay series arising from the radioactive isotope radon-222, which itself is produced by the decay of the long-lived isotope uranium-238. The last step in this long chain of reactions is the alpha decay of polonium-210 to the stable isotope lead-206. The half-life of this decay is 138 days. This is not the only isotope of polonium in radon’s decay series. A heavier isotope polonium-214 has a half-life of 160 microseconds, and polonium-218 has a half-life of 3 minutes.

Polonium was discovered by Marie and Pierre Curie in 1898 when analyzing pitchblende, a uranium containing ore. It was named after Marie’s homeland, Poland. Now 210Po is produced by bombarding bismuth-209 with neutrons, forming bismuth-210, which undergoes beta decay to 210Po.

210Po is infamous for being a deadly poison. For a given mass, 210Po is 250,000 times more toxic than hydrogen cyanide. Its toxicity comes from the 5.3-MeV alpha particle it emits. Because alpha particles are easily stopped by clothing and even skin, 210Po is dangerous primarily when breathed or ingested, so that the alpha particles are emitted inside the body. A nearly pure alpha emitter, 210Po rarely emits a gamma ray, making it difficult to detect this poison unless one measures the alpha particles directly. A lethal dose comes from ingesting about a microgram.

210Po was used in the 2006 assassination of Alexander Litvinenko, a former Russian spy who was apparently given some polonium-laced tea by Russian agents (the investigation into this complicated murder continues--see here and here--and the details are still debated). Death by 210Po is slow; the 44-year old Litvinenko needed 22 days for the radiation to eventually take his life.

Polonium was also suspected to play a role in the 2004 death of Palestinian leader Yasser Arafat. Just this month, a French investigation has concluded that there is not enough evidence for pressing charges. The issue is complicated because 210Po is found in cigarette smoke, and Arafat was a heavy smoker. The National Council on Radiation Protection and Measurements reports that the annual effective dose equivalent to a smoker from radiation in tobacco is about 13 mSv, which is over four times the average annual dose of 3 mSv we are all exposed to (see Section 16.12 in IPMB), but is still a tiny dose.

The Environmental Protection Agency has published a report titled Occurrence of 210Po and Biological Effects of Low-Level Exposure: The Need for Research. As with all studies of low-level radiation exposure, the results are difficult to assess, and depend on our assumptions about radiation risks at small doses. But Alexander Litvinenko’s death proves that at high doses 210Po is very dangerous indeed; it is perhaps the perfect poison.

Friday, September 18, 2015

Boltzmann’s Tomb

In Chapter 3 of the 5th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the Boltzmann factor and Boltzmann’s constant. Later in the book, we analyze the Poisson-Boltzmann equation and the Stefan-Boltzmann law. Who was Boltzmann? In Asimov’s Biographical Encyclopedia of Science and Technology (2nd revised edition), Issac Asimov writes
BOLTZMANN, Ludwig Edward (bohlts’mahn)
Austrian physicist
Born: Vienna, February 20, 1844
Died: Duino, near Trieste (then in Austria, now in Italy), September 5, 1906

Boltzmann, the son of a civil servant, received his Ph.D. from the University of Vienna in 1866. His work on the kinetic theory of gases was done independently of Maxwell and they share the credit.

Beginning in 1871, Boltzmann increased the rigor of the mathematical treatment and emphasized the statistical interpretation of the second law of thermodynamics thus founding ‘statistical mechanics.’ He showed that Clausius’ concept of increasing entropy of disorder [could be based on statistical ideas], laying the groundwork for the later achievements of Gibbs.

He was a firm proponent of atomism at a time when Ostwald was mounting the final campaign against it. Boltzmann also advanced a mathematical treatment that explained the manner in which, according to the experimental observations of Stefan (whom Boltzmann, in this college years, served as assistant), quantity of radiation increased as the fourth power of the temperature. This is therefore sometimes called the Stefan-Boltzmann law.

Boltzmann turned down a chance to succeed Kirchhoff at Berlin but in 1894 succeeded to Stefan’s post in Vienna.

Though Boltzmann lived longer than Maxwell, his life too was cut short. In his case it was suicide, brought on by recurrent episodes of severe mental depression accentuated, perhaps, by opposition to his atomistic notions by Oswald and others.

His equation relating entropy and disorder was engraved on the headstone of his grave.
I particularly am intrigued by the last sentence of Asimov’s entry. Who puts an equation on their tombstone? Boltzmann did!


This equation is Eq. 3.20 in IPMB.

S = kB ln Ω ,

where S is the entropy, kB is Boltzmann’s constant, ln is the natural logarithm, and Ω is the number of microstates. The equation says that the entropy increases as the number of possible microstates increases. If there are only one or a few states available, the entropy is small; if there are many states available, the entropy is large. Thus, from a statistical mechanics point-of-view, the thermodynamic concept of entropy (developed well before Boltzmann’s work) is a measure of the number of states. The logarithm is important, because if system A has 10 states available and system B has 20 states available, the total number of states is the product, 200. If the entropy were proportional to Ω, the total entropy of the two systems would not be the sum of the entropy in each system. However, the logarithm property ln(ΩAΩB)=ln(ΩA)+ln(ΩB) ensures that the entropy is indeed additive.

The definition of entropy in terms of the number of states is a fundamental relationship connecting thermodynamics and statistical mechanics. No wonder Boltzmann wanted it on his tombstone.

Friday, September 11, 2015

Meselson, Stahl, and the Most Beautiful Experiment in Biology

In Chapter 17 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I added a new homework problem to the 5th edition about the famous Hershey-Chase experiment. We had two goals: to demonstrate how scientists use radioisotopes as tracers in biological experiments, and to describe a key experiment in modern biology.

A series of homework problems in Chapter 1 of IPMB describe the physics of the ultracentrifuge. Perhaps Russ and I should add a new homework problem in Chapter 1, to demonstrate how the centrifuge provides crucial information about biological mechanisms, and to describe another famous biological experiment. Here is my try at this new problem.
Problem 24 1/2. Suppose you grow E. coli bacteria in a growth medium containing the rare, heavy but stable isotope of nitrogen, N15. At some time t = 0 remove some of the E. coli from this medium and place it into another growth medium containing the normal isotope of nitrogen, N14. Then, at different times place DNA from the E. coli into a density gradient centrifuge (see Problem 23) and measure where along the gradient the DNA settles.
a) Describe qualitatively what you would expect to see at t = 0, before any of the E. coli reproduce.
b) Assume DNA replicates semiconservatively: replication produces two new DNA molecules, each containing two strands: one a strand from the original DNA molecule and another new strand produced from the medium. Describe what you would expect to see at t = t1, where t1 is the time required to produce one new generation of E. coli. Describe what you would expect to see at t = 2 t1
c) Repeat part b) assuming DNA replicates conservatively: each replication produces two DNA molecules, one containing the original two strands and the other containing two new strands. 
d) Repeat part b) assuming DNA replicates dispersively: each replication produces two new DNA molecules, both containing a mix of the original and new DNA. 
This experiment was performed by Meselson and Stahl in 1958, and is one of the central experiments underlying modern biology. It demonstrates the semiconservative replication of DNA.
If you want to learn more about the Meselson-Stahl experiment, I suggest reading Chapter 3 of The Eighth Day of Creation: The Makers of the Revolution in Biology, by Horace Freeland Judson. Below I provide an excerpt.
“I first heard of semiconservative replication on New Year’s Day, 1958, in Chicago—and a bright, windy, iron-cold morning it was. Seven of us who had been undergraduates together at the University of Chicago (we had all overlapped Watson’s last year there) were sitting scratchy-eyed over bacon and eggs and coffee when Matthew Meselson, by then a doctoral candidate with Pauling at Cal Tech, took a photograph from his wallet and passed it around the table. The picture showed a stack of gray stripes, with narrow, dark-gray bands across them—some stripes with one band, some with two or three together near the middle. The photo was the main result of an experiment that Menelson had devised with a post doctoral fellow at Cal Tech, Franklin Stahl.

Their paper was not yet published—not yet written. The work it describes is now recognized as displaying the most rare technical skill, while conceptually its confirmation of the way DNA reproduces itself has become, simply, part of the mainstream. In its place towards the end of the history of the elucidation of the structure and function of DNA, Meselson’s and Stahl’s paper possessed an importance and authority like Oswald Avery’s announcement, fourteen years earlier, of the isolation of the transforming principle and its identification as DNA. 'Classic' was Watson’s epithet for Meselson’s and Stahl’s paper. Watson’s predecessor as director of the Cold Spring Harbor Laboratory, John Cairns, startled me in conversation when he described Meselson’s central demonstration without qualification as ‘the most beautiful experiment in biology.’“

Friday, September 4, 2015

Learning Biology

Suppose you are a physicist, mathematician, or engineer who wants to change your research direction toward biology and medicine. How do you learn biology? Let’s assume you don’t quit your day job, so you have limited time. Here are my suggestions.
  1. Read The Machinery of Life (2nd edition), by David Goodsell. I discussed this book a few weeks ago in this blog. It is visual, easy to read, not too long, cheap, and doesn’t get bogged down in details. It’s a great introduction; this is where I would start.
  2. If you haven’t had an introductory biology class, you might consider taking this online biology class from MIT. It is free, it has homework assignments and quizzes so you can assess your learning, and you can work at your own schedule. For those who prefer an online class to reading a book, this is the thing to do.
  3. If you would prefer reading an introductory biology textbook, a popular one is Campbell Biology by Reece et al., now in its 10th edition. The MIT online course mentioned above and the introductory biology classes here at Oakland University use this book. Its advantages are that it covers all of biology and it is written for introductory students. Its disadvantages are that it is expensive and long. I am not an expert on the different intro biology textbooks; there may be others just as good.
  4. I like to learn a subject by studying its history. If you want to try this, I suggest: The Double Helix by James Watson (of Watson and Crick) and The Eighth Day of Creation by Horace Freeland Judson. Watson’s book is a classic: a first-person account the discovery of the structure of DNA. It is well written, controversial, and should be read by anyone interested in science. The Eighth Day of Creation is longer and more comprehensive, but it is a fantastic book.
  5. The textbook Physical Biology of the Cell by Phillips et al. was written by physicists trying to learn biology. Also from a physicist’s point of view are Biological Physics and Physical Models of Living Systems, both by Philip Nelson. These books do not cover all of biology, but a physicist may like them.
  6. I learned a lot of biology in high school reading Isaac Asimov books. They often take a historical approach, and are qualitative, interesting, clearly written, fairly short, and cheap. I worry about recommending them because biology has progressed so much over the last few decades that these books from the 1960s are out-of-date. However, I suspect they are still useful introductions, and I suggest The Wellsprings of Life, The Genetic Code, The Human Body, The Human Brain, and A Short History of Biology.
  7. Some books from my ideal bookshelf cover parts of biology from the point of view of a physicist: Air and Water by Mark Denny, Scaling: Why is Animal Size so Important? by Knut Schmidt-Nielsen, and Random Walks in Biology by Howard Berg. Steven Vogel has many books you might like, including Life in Moving Fluids, Vital Circuits, and Life’s Devices
  8. Nothing in biology makes sense except in light of evolution. To learn about evolution, read the books of Stephen Jay Gould. I enjoyed his collections of essays from the magazine Natural History. Start with Ever Since Darwin.
  9. Once you have a general biology background, what comes next? When I was in graduate school, I sat in on the Vanderbilt Medical School’s Physiology class and their Biochemistry class. These are the two courses that I encourage Oakland University Medical Physics graduate students to take. Typical textbooks are Guyton and Hall’s Textbook of Medical Physiology, now in its 13th edition, and Nelson and Cox's Lehninger Principles of Biochemistry, now in its 6th edition. Both books are long, expensive, and detailed. If interested in cell and molecular biology, a leading text is Molecular Biology of the Cell by Bruce Alberts and Alexander Johnson. 
  10. If you have the time, you can do what Russ Hobbie did: between 1971 and 1973 he audited all the courses medical students take in their first two years at the University of Minnesota. Finally, you can always purchase a copy of the 5th edition of Intermediate Physics for Medicine and Biology!
If readers of the blog have their own recommendations, please add them in the comments.