Friday, May 25, 2018

The Constituents of Blood

Intermediate Physics for Medicine and Biology: The Constituents of BloodI’m a big supporter of blood donation. This week I gave another pint to the Red Cross, which brings my total to 8 gallons. As I lay there with a needle stuck in my arm, I began to wonder “what’s in this blood they’re squeezing out of me?”

Table 3.1 in Intermediate Physics for Medicine and Biology lists some constituents of blood. I reproduce the table below, with revisions.

Constituent Density in mg/cm3 Number in 1 μm3
Water 1000 33,000,000,000
Sodium 3 83,000,000
Glucose 1 3,300,000
Cholesterol 2 3,100,000
Hemoglobin 150 1,400,000
Albumin 45 390,000

This version of the table highlights several points. Water molecules outnumber all others by a factor of four hundred. Sodium ions are sixty times more common than hemoglobin molecules, but the mass density of hemoglobin is over fifty times that of sodium. In other words, if judged by number of molecules (and therefore the osmotic effect) sodium is most important, but if judged by mass or volume fraction, hemoglobin dominates. Glucose and cholesterol are intermediate cases. Albumin has a surprisingly small number of molecules, given that I thought it was one of the main contributors to osmotic pressure. It is a big molecule, however, so by mass it contributes nearly a third as much as hemoglobin.

Are other molecules in blood important? You can find a comprehensive list of blood constituents beautifully illustrated here. When judged by number, sodium is the most important small ion, but the chloride ion contributes nearly as much. Carbon dioxide and bicarbonate are also significant, and potassium has about the same number of molecules as glucose. If you drive drunk, you may have twice as many ethyl alcohol molecules as potassium ions (if the number of ethanol molecules reaches the level of sodium or chloride ions, you die). Urea has a similar number of molecules as hemoglobin.

Judged by mass, you get an entirely different picture. Large protein molecules dominate. Hemoglobin is by far the largest contributor to blood by mass (after water, of course), followed by albumin and another group of proteins called globulins. Next are glycoproteins such as the clotting factor fibrinogen and iron-binding transferrin.

Many trace constituents hardly affect the osmotic pressure or density of blood, but are excellent biomarkers for diagnosing diseases.

If you’re starting to think that blood is awfully crowded, you’re right. The picture below is by David Goodsell. No scale bar is included, but each candy-apple-red hemoglobin molecule in the lower left has a diameter of about 6 nm. The water, ions, and other small molecules such as glucose are not shown; if they had been they would produce a fine granular appearance (water has diameter of about 0.3 nm) filling in the spaces between the larger macromolecules.

Blood. Illustration by David S. Goodsell, the Scripps Research Institute.
Blood. Serum is in the upper right and a red blood cell is in the lower left. In the serum, the Y-shaped molecules are antibodies (an immunoglobulin), the long thin light-red molecules are fibrinogen (a glycoprotein), and the numerous potato-like yellow proteins are albumin. The red blood cell is filled with red hemoglobin molecules. The cell membrane is in purple. The illustration is by David S. Goodsell of the Scripps Research Institute.

In another eight weeks I will get free juice and cookies be eligible to give blood again. It doesn’t hurt (much) or take (too) long. If you want to donate, contact the American Red Cross. Give the gift of life.

Friday, May 18, 2018

A Biological Constant

Intermediate Physics for Medicine and Biology: A Biological Constant
Membranes, Ions and Impulses, by Kenneth Cole, shelved alongside Intermediate Physics for Medicine and Biology.
Membranes, Ions
and Impulses
by Kenneth Cole
Physics has many famous constants: Planck’s constant, the speed of light, and the gravitational constant, to name a few. Biology has few such constants. Life is so full of variety that almost any parameter can vary between species or tissues. In fact, physicists differ from biologists by their focus on the unity rather than the diversity of life.

There is, however, one parameter that comes close to being a biological constant. All cells are surrounded by a membrane whose thickness and composition varies little among species. Therefore, the capacitance per unit area, Cm, of a membrane is as close to being a biological constant as you are likely to find.

In Section 6.17 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I calculate the capacitance of a lipid bilayer, and find that Cm is about 0.01 farads per square meter. Many of the key papers during the “golden age” of classical biophysics didn’t use standard SI units. Instead of measuring distance in meters, they used centimeters. If you express Cm as per square centimeter, and if you use microfarads instead of farads, you get the easy-to-remember value of Cm = 1 μF/cm2. Kenneth Cole wrote in his book Membranes, Ions and Impulses: A Chapter of Classical Biophysics
This figure of about 1 μF/cm2 has been so confirmed and refined, extended and approximated for membranes of red cells and almost all other living cells, as to become a biophysical constant.
Are there other biological constants? I suppose some constants governing the structure of key biological molecules, such as the distance between adjacent base pairs of the DNA double helix (0.34 nm), are conserved throughout biology. But these parameters belong more to the realm of biochemistry than biophysics. If you restrict your selection to parameters discussed in IPMB, Cm is one of the few biological constants.

Membranes, Ions and Impuses: A Chapter of Classical Biophysics, by Kenneth Cole, superimposed on Intermediate Physics for Medicine and Biology.
Membranes, Ions and Impulses, by Kenneth Cole.

Membrane Capacitance, as discussed in Membranes, Ions and Impulses

Table of Contents for Membranes, Ions and Impulses, by Kenneth Cole

Friday, May 11, 2018

The Curie Temperature

Intermediate Physics for Medicine and Biology: The Curie Temperature In Chapter 8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss magnetic materials, including ferromagnets (permanent magnets in which electron spins are aligned even in the absence of an external magnetic field). We write
If the temperature of the sample is raised above a critical temperature called the Curie temperature, the magnetism is destroyed.
When seeing such a sentence, my first inclination is to write a homework problem that uses a toy model to illustrate the physics behind the concept. Unfortunately, analyzing the Curie temperature is difficult, so no new homework problem appears in this post (readers are encouraged to try their hand at writing one).

Solid State Physics,  by Ashcroft and Mermin, superimposed on Intermediate Physics for Medicine and Biology.
Solid State Physics,
by Ashcroft and Mermin.
When faced with a difficult concept in material physics, I reach for a copy of Solid State Physics by Neil Ashcroft and N. David Mermin. Regular readers of this blog may recall that I am a big fan of Mermin (for instance, see here and here). Everything I know about solid state physics (which isn’t much) I learned from Solid State Physics. When Ashcroft and Mermin describe magnetic ordering of spins, they explain that
Quantitative theories of magnetic ordering have proved most difficult to construct near the critical temperature Tc at which ordering disappears. The difficulty is not peculiar to the problem of magnetism. The critical points of liquid-vapor transitions, superconducting transitions (Chapter 34), the superfluid transition in liquid He4, and order-disorder transitions in alloys, to name just a few, present quite strong analogies and give rise to quite similar theoretical difficulties.
They settle for a phenomenological description of the Curie temperature.
The critical temperature Tc above which magnetic ordering vanishes is known as the Curie temperature in ferromagnets… As the critical temperature is approached from below, the spontaneous magnetization…drops continuously to zero. The observed magnetization just below Tc is well described by a power law.

M(T) ∼ (TcT)β,

where β is typically between 0.33 and 0.37.
Below I plot of the spontaneous magnetization M versus the absolute temperature T for β=1/3.

magnetization versus temperature

The Curie temperature is interesting for two reasons. First, it is not named after Marie Curie, who plays such a big role in medical physics for isolating some of the first radioactive elements including radium and polonium. Instead, it is named after her husband Pierre Curie, who did important research on magnetism. Second, the ferromagnetic material that Russ and I discuss most in IPMB is magnetite (Fe3O4), which is found in magnetosomes, small magnetic particles that cause magnetotactic bacteria to align with the earth's magnetic field. The Curie temperature for magnetite is 585 °C, or 858 K, which is too hot to support life. Perhaps other substances exist for which the Curie temperature plays a role in biology and medicine, but I don’t know what they are.

I conclude with a quote from Mermin’s delightful essay “Writing Physics” in which he talks about writing Solid State Physics with Ashcroft. Enjoy!
The striking exception to my inability to write collaboratively is my eight-year collaboration with Neil Ashcroft on our 800 page book on solid state physics. We have very different prose styles. Yet the book has a clear and distinctive uniform tone, which can't be identified as belonging to either of us. I think the reason this worked was that Neil knows solid state physics much better than I do. So he would produce the first drafts. Characteristically, I would not understand them. So I would try to make sense of what he was saying, and then produce my typical kind of irritating second draft. Neil, however, would now have to correct all my mistakes in a massively rewritten third draft. I would then have to root out any new obscurities he had introduced in a fourth draft. By this kind of tennis-playing, we would go through five or six drafts, and emerge with something that was clear, correct, and sounded like a human voice. That voice, however, was neither of ours.

Friday, May 4, 2018

Strange Glow

Intermediate Physics for Medicine and Biology: Strange Glow
Strange Glow by Timothy Jorgensen on top of Intermediate Physics for Medicine and Biology.
Strange Glow,
by Timothy Jorgensen.
I recently read Strange Glow: The Story of Radiation, by Timothy Jorgensen. This book overlaps many of the topics Russ Hobbie and I discuss in Intermediate Physics for Medicine and Biology, particularly in Section 16.12 (The Risk of Radiation). Jorgensen writes
The common denominator of most radiation exposure scenarios is fear. Just mention the word radiation, and you instill fear—a perfectly understandable response given the images of mushroom clouds and cancerous tumors that immediately come to mind. Those images would justifiably cause anyone to be anxious. Nevertheless, some people have also become highly afraid of diagnostic x-rays, luggage scanners, cell phones, and microwave ovens. This extreme level of anxiety is unwarranted, and potentially dangerous.

When people are fearful, they tend to exaggerate risk. Research has shown that people’s perception of risk is tightly linked to their fear level. They tend to overestimate the risk of hazards that they fear, while underestimating the risk of hazards they identify as being less scary. Often their risk perception has little to do with the facts, and the facts might not even be of interest to them. For example, many Americans are terrified of black widow spiders, which are found throughout the United States. They are uninterested in the reality that fewer than two people die from black widow bites each year, while over 1,000 people suffer serious illness and death annually from mosquito bites. Mosquitoes are just too commonplace to worry about. Likewise, the risk of commercial airplane crashes is tiny compared to motorcycle crashes, but many a biker is afraid to fly.

The point is that risk perception drives our decision making, and these perceptions often do not correspond to the real risk levels, because irrational fear is taking our brains hostage. When irrational fear enters the picture, it is difficult to objectively weigh risks. Ironically, health decisions driven by fear may actually cause us to make choices that increase, rather than decrease, our risks.
Strange Glow is written for a general audience. Those who have studied from IPMB will already have a stronger quantitative background in math and physics than is needed for Strange Glow’s qualitative discussion. However, as Jorgensen writes in the preface, “These highly quantitative approaches have proved to be largely ineffective in communicating the essence of risk to the public.” I can’t argue with that. I recommend IPMB for a technical background, but Strange Glow for appreciating the broader impact of radiation on society.

Like Gaul, Strange Glow is divided into three parts. Part 1 describes how radiation was discovered, Part 2 discusses the effects of radiation on human health, and Part 3 focuses on risk assessment. I liked the third part best. Jorgensen emphasizes the human stories behind the science. For instance, he begins the chapter about radon by telling the tale of the Watras house.
On December 2, 1984, Stanley J. Watras, an engineer working on construction of the new Limerick nuclear power plant near Portstown, Pennsylvania, arrived at work. The plant, just seven miles from his home in Boyertown, was scheduled to begin generating power within three weeks, and the construction crew had just installed radiation detectors at the plant doors—a standard safeguard to ensure that nuclear workers don’t exit the plant with any radioactive contamination on their bodies. When Watras arrived that day, he set off the alarms on the detectors as he walked into the plant. Over the following two weeks he would set off the alarms every morning. Further investigation revealed that his clothes were contaminated with radioactivity that he had picked up at his home!

When radiation safety personnel from the plant visited Watras’s home, they discovered what they didn’t think possible. There was more radon gas in the Watras split-level house than was found in a typical uranium mine . . . about 20 times as much! Surprised, the radiation safety technicians checked the radon levels in the neighboring houses. “Our house,” Watras remarked in consternation, “had perhaps the highest contamination level in the world, but our next door neighbors had none.” How could this be?
Jorgensen then describes how the Environmental Protection Agency publicized—and perhaps exaggerated—the risks of radon. But by trying to err on the side of safety, their efforts became a case study in the challenges of risk assessment.
This is one of the trade-offs of using multiple, highly conservative assumptions in risk assessment. It may seem prudent to inflate the risk in order not to underestimate it. Nevertheless, by adopting high-end estimates for every uncertain risk parameter, the cascade of high-end risk assumptions can compound to the point where the final predicted risk levels become incredulous and may even defy common sense.
I find Jorgensen’s evidence-based, unemotional discussion of risk assessment to be a breath of fresh air. Far too often public fears are driven by emotions and ignorance, rather than a balancing of risks and benefits. I highly recommend Strange Glow to anyone wondering or worrying about the danger of radiation. Sometimes the danger is real and sometimes it is not, and you need to know which is which.

Below are some videos about the book and its author. Enjoy!