Friday, June 26, 2009

Physics Meets Biology

Readers of the 4th Edition of Intermediate Physics for Medicine and Biology may find a news feature by Jonathan Knight published in the September 19, 2002 issue of Nature interesting. The article “Physics Meets Biology: Bridging the Culture Gap” (Volume 419, Page 244-246) begins:
“In late July, several dozen physicists with an interest in biology gathered at the Colorado mountain resort of Snowmass for a birthday celebration. Hans Frauenfelder, a physicist who began studying proteins decades ago, turned 80 this year. But unofficially, the physicists were celebrating something else — a growing feeling that their discipline's mindset will be crucial to reaping the harvest of biology's postgenomic era.”
It continues:
"’Biology today is where physics was at the beginning of the twentieth century,’ observes José Onuchic, who is the co-director of the new Center for Theoretical Biological Physics (CTBP) at the University of California, San Diego. ‘It is faced with a lot of facts that need an explanation.’

Physicists believe that they can help, bringing a strong background in theory and the modeling of complexity to nudge the study of molecules and cells in a fresh direction. 'What has been all too rare in biology is the symbiosis between theory and experiment that is routine in physics,' says Laura Garwin, director of research affairs at Harvard University's Bauer Center for Genomics Research, who has made her own transition to biology — she was once Nature's physical-sciences editor.”
The article concludes
“Onuchic believes that immersing young physicists in the culture of biology is the key. At the CTBP, postdocs train in both disciplines simultaneously, developing projects that involve two labs, one in biology and one in physics. They attend two sets of group meetings, and so learn the language and mentality of both disciplines at the same time. 'They get inside the culture of the two fields,' Onuchic says. ‘They get comfortable with the vocabulary and the journals. Life in both labs is more important than any classes you can take.’

Time will tell whether the new generation of biological physicists avoid becoming the lonely children of biology. But for now, the prospects look bright. ‘We have always been the odd kids in the playground,’ says Onuchic. ‘But we never gave up, and now we are becoming very popular.’”

Friday, June 19, 2009

Resource Letter PFBi-1: Physical Frontiers in Biology

Eugenie Mielczarek of George Mason University published Resource Letter PFBi-1: Physical Frontiers in Biology in the American Journal of Physics (Volume 74, Pages 375-381, 2006). The fourth edition of Intermediate Physics for Medicine and Biology was one of 39 books listed in the letter.

What are Resource Letters? They are collections of references that are published periodically by the American Journal of Physics.
"Resource Letters are guides for college and university physicists, astronomers, and other scientists to literature, websites, and other teaching aids. Each Resource Letter focuses on a particular topic and is intended to help teachers improve course content in a specific field of physics or to introduce nonspecialists to this field."
Mielczarek's Resource Letter discusses topics that will be of interest to readers of Intermediate Physics for Medicine and Biology.
"This Resource Letter provides a guide to the literature on physical frontiers in biology. Books and review articles are cited as well as journal articles for the following topics: cells and cellular mats; conformational dynamics/folding; electrostatics; enzymes, proteins, and molecular machines; material-biomineralization; miscellaneous topics; nanoparticles and nanobiotechnology; neuroscience; photosynthesis; quantum mechanics theory; scale and energy; spectroscopy and microscopy: experiments and instrumentation; single-molecule dynamics; and water and hydrogen-bonded solvents. A list of web resources and videotapes is also given."
The letter begins with a fascinating 3-page overview of the role of physics in biology. For instance, Mielczarek asks the question
"Which principles govern life? Dutifully the physicist might answer—the organizing of electrons into their lowest energy states, forcing molecules and groups of molecules into specific configurations. But be cautious: this simplistic answer implies an isolated system in equilibrium. It conceals the dynamics of life, which require a continuous input of matter and energy. Cells, tissues and organisms are dependent upon energy refreshment."
Readers who enjoy Intermediate Physics for Medicine and Biology will probably find Mielczarek's Resource Letter to be a valuable...well, resource. They may also enjoy her book Iron, Nature's Universal Element: Why People Need Iron & Animals Make Magnets .

Friday, June 12, 2009

The Magnetic Field of a Single Axon

When I was in graduate school, working in John Wikswo's lab at Vanderbilt University, I calculated and measured the magnetic field of a single nerve axon. The calculation makes a nice, although slightly advanced, homework problem for Chapter 8 of the 4th Edition of Intermediate Physics for Medicine and Biology.

Section 8.2

Problem 14.5 Use Ampere's law to calculate the magnetic field produced by a nerve axon.

(a) First, solve Problem 30 of Chapter 7 to obtain the electrical potential inside (V_i) and outside (V_o) an axon
[this blog does not do math well; an underscore "_" means subscript]. The solution will be in terms of the modified Bessel functions I_0(kr) and K_0(kr), where k is a spatial frequency and r is the radial distance from the center of the axon. Assume the axon has a radius a.

(b) Find the axial component of the current density, J, both inside and outside the axon using J_iz = - sigma_i dV_i/dz and J_oz = - sigma_o dV_o/dz, where sigma_i and sigma_o are the intracellular and extracellular conductivities (Eqs. 6.16b and 6.26)
["sigma" of course means the Greek letter sigma].

(c) Integrate J_iz over the axon cross-section to get the total intracellular current. Then integrate J_oz over an annulus from a to the radius r, to get the "return current".

(d) Use Ampere's law (Eq. 8.9) to calculate the magnetic field. Take the line integral of Ampere's law as a closed loop of radius r concentric with the axon (r > a). The current enclosed by this loop is simply the sum of the intracellular and return currents calculated in (c).

In part (c), you will need the following Bessel function integrals
["int" stands for the integral sign]:

int I_0(x) x dx = x I_1(x)
int K_0(x) x dx = - x K_1(x) .

To check your solution, see Eq. A13 of "The Magnetic Field of a Single Axon" (Roth and Wikswo, Biophysical Journal, Volume 48, Pages 93-109, 1985). However, that paper uses complex exponentials whereas Problem 30 of Chapter 7 uses sines and cosines, introducing a slight difference between your expression and that in Eq. A13 of the Roth and Wikswo paper.

I recall the day I derived this expression for the magnetic field. I was puzzled because another graduate student in Wikswo's lab, James Woosley, had derived a different expression for the magnetic field of an axon using the Biot-Savart law (Sec. 8.2.3). How could there be two seemingly different expressions for the magnetic field? Previous discussions with Prof. John Barach had given me a hint. He had derived two expressions for the magnetic field produced by a battery in a bucket of saline, using either Ampere's law or the Biot-Savart law, and showed that they were the same (he eventually published this in "The Effect of Ohmic Return Current on Biomagnetic Fields", Journal of Theoretical Biology, Volume 125, Pages 187-191, 1987). I worried about this problem for some time, until one evening (September 22, 1983; Wikswo insisted that I keep careful records in my lab notebook) I was working on my electricity and magnetism homework and found the solution staring at me: Eq. 3.147 in Jackson's famous textbook Classical Electrodynamics (here I quote the current 3rd Edition, but at the time I was using my now tattered 2nd Edition with the red cover). This equation defines the Wronskian condition for Bessel functions:

I_0(x) K_1(x) + K_0(x) I_1(x) = 1/x .

I didn't have all my work at home, so I remember riding my bike (I didn't yet own a car) back to the lab in the rain so I could check if the Wronskian would resolve the difference between my expression and Woosley's. It did; the two expressions were equivalent (in my usually dry notebook, I wrote "HA! It works"). You can calculate the magnetic field using either Ampere's law or the Biot-Savart law, and you get the same result. To see how these two equations predict the same magnetic field in a slightly easier case (like that considered by Barach), solve Problem 13 of Chapter 8 in the 4th Edition of Intermediate Physics for Medicine and Biology.

For those of you interested in Woosley's expression, you can find its derivation in "The Magnetic Field of a Single Axon: A Volume Conductor Model" (Woosley, Roth, and Wikswo, Mathematical Biosciences, Volume 76, Pages 1-36, 1985). In particular, they state on page 13
"If we ... rearrange terms, and use a relation which can be derived from the Wronskian...we can show that...Equation (45), derived from Ampere's law, is identical to...Equation (36), derived from the law of Biot and Savart."

Friday, June 5, 2009

Ichiji Tasaki (1910-2009)

Ichiji Tasaki (1910-2009) died January 4 in Bethesda, Maryland. Tasaki was known for his discovery in 1939 of saltatory conduction of action potentials in a myelinated nerve axon. You can learn more about myelinated fibers and saltatory conduction in the 4th Edition of Intermediate Physics for Medicine and Biology.

Tasaki had a long and fascinating career in science. His life is described in an obituary published in the May 2009 issue of Neuroscience Research. He is also featured in an article of the NIH Record, the weekly newsletter for employees of the National Institutes of Health.

I knew Tasaki when I was working at NIH in the 1990s. Late in his career he worked with my friend Peter Basser in the National Institute of Child Health and Human Development. I recall him working every day in his laboratory, despite being in his 80s, with his wife as his assistant. He led a fascinating life. His best known research on saltatory conduction was performed in Japan just before and during World War II. After the war, he spent over 50 years at NIH.

Basser describes Tasaki as "a scientist’s scientist, never afraid to question current dogma, always digging deeper to discover the truth." Congressman Chris van Hollen of Maryland paidtribute to Tasaki a few months before he died, beginning "Madam Speaker, I rise today to recognize the outstanding achievements of my constituent Dr. Ichiji Tasaki. Dr. Tasaki has worked at the National Institutes of Health for 54 years, since November 1953, and has made invaluable contributions to the scientific community."