The Pardee and Riley Experiment and the Discovery of mRNA

Today I want to discuss an experiment that led to the discovery of messenger RNA (mRNA). Why did I choose to focus on one specific experiment? First, because of its importance in the history of molecular biology. Second, the experiment highlights the use of radioisotopes like those Russ Hobbie and I describe in Chapter 17 of Intermediate Physics for Medicine and Biology. Third, the recent development and of mRNA vaccines for Covid and other diseases makes this a good time to review how our knowledge of mRNA was established.  

A crucial experiment was performed by Arthur Pardee and Monica Riley at the University of California, Berkeley, and published in 1960. Let me provide some context and set the stage. The structure of DNA had been discovered by Watson and Crick in 1953. By 1960, scientists knew that individual genes in DNA coded for individual proteins. The question was how the genetic information got from DNA to the protein. RNA was suspected to be involved, in part because ribosomes—the stable cellular macromolecules where DNA was produced—are made from RNA. Were the ribosomes the messenger, or was there something else? Many key experiments in biology, like the one by Pardee and Riley, are performed using a simple model system: E coli bacteria. Another important tool of early modern biology was radioisotopes, a product of modern physics from the first half of the twentieth century that was essential for biology during the second half of the century. 

Since I’m neither a molecular biologist nor a historian of science, I’ll let Horace Freeland Judson—author of one of my favorite history of science books, The Eight Day of Creation: The Makers of the Revolution in Biology—tell you about Pardee and Riley’s work.

The experiment Pardee and Riley had done in Berkeley was new, technically amusing, and persuasive. It amounted to removal of the gene from the cell after it had begun to function. They had grown… bacteria… carrying [a specific gene to produce the protein enzyme beta-galactosidase]… in a broth where the available phosphorus [an important element in DNA] was the radioactive isotope ³²P. The bacteria, with their DNA heavily labeled, were then centrifuged out... [and] resuspended in a nonradioactive broth… [Next] they added glycerol [a type of antifreeze]. Then they took one sample to test for enzyme activity [to check if beta-galactosidase was produced]. They put other samples into small glass ampules, sealed the ampules by fusing the glass at the neck, and lowered them into a vacuum-insulated flask of liquid nitrogen. The bacteria were frozen almost instantly at 196 degrees below zero centigrade. Protected from bursting by the glycerol, the bacteria were not killed, but their vital processes were arrested while the radiophosphorus in the DNA… continued to decay… From day to day, Riley raised ampules of the frozen bacterial suspension from the liquid nitrogen and thawed them… For comparison, they ran the whole [experiment] in parallel without the radioactivity [this was their control].

Before telling you the result, let me digress a bit about phosphorus-32. It’s an unstable isotope that undergoes beta decay to stable sulfur-32. This means the ³²P ejects an electron (and an antineutrino) and transforms to ³²S. In many cases (such as in sodium-24 examined in Fig. 17.9 of IPMB), beta decay occurs to an excited state that then emits gamma rays. But ³²P is “pure” meaning there are no gamma rays, or even different competing beta decay paths. The book MIRD: Radionuclide Data and Decay Schemes by Eckerman and Endo, often cited in IPMB, shows this simple process with this figure and table. 

Note the half-life of ³²P is two weeks, and the average energy of the ejected electron is 695 keV.

What happens when ³²P decays? First, the electron can damage the cells. An electron of this energy has a range of about a millimeter, so that damage would not be localized to an individual bacterium (with a size on the order of 0.001 mm). However, when the ³²P isotope decays, it will recoil, which could eject it from the DNA molecule, causing a strand break. Even if the recoil is not strong enough remove the atom from DNA, there would now be a sulfur atom where a phosphorus atom should be, and these two atoms, being in different columns of the periodic table, will have different chemical properties which surely would disrupt the DNA structure and function. As Judson says

An atom of ³²P decays by emitting a beta particle, which is a high-speed electron, whereupon it is transformed into an atom of sulphur. The transformation, and the recoil of the atom as the electron leaves, breaks the bonds of the backbone of the DNA at that point… Half of those decayed in fourteen days. The [beta-galactosidase] genes were being killed.

So, what was the result? Judson summarizes,

The nonradioactive bacteria sampled before freezing were synthesizing enzyme copiously. So were the radioactive ones before freezing… Thawed after ten days, samples of nonradioactive bacteria synthesized beta-galactosidase just as vigorously as those never frozen. But the bacteria whose [beta-galactosidase] genes had suffered ten days of radioactive decay made the enzyme at less than half the rate they had before. Inactivation of the gene… abolished protein synthesis without delay. Stable intermediates between the gene and its protein—in other words, ribosomes whose RNA carried information to specify the sequence of amino acids—were ruled out. Continual action of the gene was necessary, either directly or by way of an intermediate that was unstable and so had to be steadily renewed.

When Francis Crick and Sydney Breener learned of Pardee and Riley’s results, they combined their knowledge of this experiment with a previous one by Elliot Volkin and Lazarus Astrachan using bacteriophages [a virus that infects bacteria] to hypothesize that a new type of RNA, called messenger RNA, was the unstable intermediary connecting DNA and protein. And the rest is history.

The Pardee and Riley experiment (which made up Monica Riley’s PhD dissertation… wow, what a dissertation topic!) is beautiful and important. It is also relevant today. Why do mRNA vaccines (like the Pfizer and Moderna Covid vaccines) have to be kept so cold when being transported and stored before use? As Pardee and Riley showed, the mRNA is unstable. It will decay quickly if not kept ultra-cold. Can mRNA change the DNA in your cells? No, the mRNA is simply a messenger that transfers the stored genetic information in DNA to the proteins formed on ribosomes. Moreover, one difference between E coli bacteria and human cells is that in humans the DNA is located inside the cell nucleus (bacteria don’t have nuclei) and the ribosomes are in the cytoplasm outside the nucleus. DNA can’t leave the nucleus, and mRNA can only go out of, not into, the nucleus. So an mRNA vaccine will cause human cells to make virus proteins (for the covid vaccine, it will produce the spike protein) that will be detected by your immune system, but the mRNA will only be present a short time before it decays and will not affect your DNA. Finally, the vaccine contains mRNA for only the spike protein, not for the entire virus. So, no actual intact viruses are produced by the vaccine. The spike protein simply activates your immune system, without exposing you to an infection.

Isn’t science great?

Madison Spach (1926–2025)

Madison Stockton Spach died recently. An Instagram post by the account for the Duke Pediatric Cardiology Fellowship stated

Very sad to report the passing of Dr. Madison Spach. Dr. Spach was the first Division Chief of Pediatric Cardiology at Duke and the founder of our program. He was a legend in the field and mentored others who also went on to become preeminent in the field. His impact through innovations, the patients he cared for, those he mentored, and the program he built is immeasurable.

I have not been able to find an obituary about Spach (I hope one is published eventually). However, here’s a picture and bio published in the IEEE Transactions of Biomedical Engineering in 1971. 

His wife Cecilia passed away seven years ago. Her obituary said

Cecilia Goodson Spach, 92, died peacefully in her sleep on Oct 20, 2018, after a short illness. Madison Spach, her loving husband of nearly 70 years, was with her when she passed away…

Cecilia Goodson was born and raised in Winston-Salem. She was a star athlete at Reynolds High School, where she met her perfect match in Madison Spach. Cecilia earned a nursing degree from Presbyterian Hospital School of Nursing in Charlotte. When Madison returned from the service, they married and moved to Durham, where Madison attended Duke University.

Madison Spach was born in 1926. This would mean if he entered the service right out of high school, he may have fought in the last year of World War II. He was 98 when he died this year. It’s sad that we are losing so many of our veterans of the greatest generation these days, when we need them most. 

Russ Hobbie and I didn’t mention Spach in Intermediate Physics for Medicine and Biology, although we do discuss his field: cardiac electrophysiology. However, I described his contributions briefly in my unpublished review and history of the bidomain model of cardiac tissue. I wrote

In the 1980s, Duke was the center for research about the electrical behavior of the heart. Not only was Plonsey there, along with his collaborator Barr and his student Henriquez, but also it hosted several other leading scientists. Barr was a long-time collaborator with Madison Spach, a Duke medical doctor known for his electrophysiological experiments on cardiac tissue. Some of their analyses foreshadowed key features of the bidomain model (Spach et al. 1978).

The citation was to Spach’s paper with long-time collaborator Roger Barr and others published in the journal Circulation Research.

Spach MS, Miller WT III, Miller-Jones E, Warren RB, Barr RC (1978) Extracellular potentials related to intracellular action potentials during impulse conduction in anisotropic canine cardiac muscle. Circ Res 45:188–204.

In addition, when reviewing Craig Henriquez and Robert Plonsey’s work on cardiac wave fronts propagating through cardiac tissue surrounded by a perfusing bath, I wrote

The bidomain model represents cardiac tissue as a continuous syncytium, so Henriquez and Plonsey’s mathematical simulations provided a new interpretation of earlier experimental data that had been used to argue that cardiac tissue acted like a discrete collection of cells (Spach et al. 1981).

This citation was to Spach’s hugely influential article 

Spach MS, Miller WT, Geselowitz DB, Barr RC, Kootsey JM, Johnson EA (1981) The discontinuous nature of propagation in normal cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents. Circ Res 48:39–54.

It’s no secret that, like Henriquez and Plonsey, I disagreed with Spach’s interpretation of his data as implying discontinuous propagation in cardiac tissue. But I’ve told that story before and this isn’t the time or place to rehash it. Suffice to say, according to Google Scholar Spach’s paper has been cited about 950 times. Another paper on the same topic (Spach’s most highly cited article) with Paul Dolber has over a thousand citations.

Spach MS, Dolber PC (1986) Relating extracellular potentials and their derivatives to anisotropic propagation at a microscopic level in human cardiac muscle. Evidence for electrical uncoupling of side-to-side fiber connections with increasing age. Circ Res 58:356–371.

Duke now has a scholarship named jointly for Roger Barr and Madison Spach. Here’s what the Duke scholarship website says about Spach’s contributions.

Madison S. Spach is a James B. Duke Professor Emeritus of medicine and Professor Emeritus of pediatrics in the School of Medicine. A renowned pediatric cardiologist and scientist, his research examined electrophysiology and the mechanisms behind cardiac dysrhythmias. On the faculty from 1960–1996, Spach developed Duke's training program in pediatric cardiology.

As I said in last week’s post, one goal I have for this blog is to support scientists, and that includes  retired ones who’ve made important contributions. Madison Spach helped us advance our knowledge of cardiac electrophysiology. His was a life worth living.

Science Under Siege

Science Under Siege,
by Michael Mann
and Peter Hotez.

I recently finished reading Science Under Siege: How to Fight the Five Most Powerful Forces That Threaten Our World, by Michael Mann and Peter Hotez. Mann is a climate scientist and Hotez develops vaccines. Both have been active in the fight against antiscience. Readers of this blog may recall my review of Hotez’s previous book The Deadly Rise of Antiscience. The authors state their purpose in the final paragraph of their preface.

In Science Under Siege we seek to provide a succinct yet detailed delineation of the five forces behind the modern-day antiscience movement (the five p’s, as we call them—the plutocrats, the petrostates, the pros, the propagandists, and our press). We draw upon our respective experiences on two different fronts of the war on science to identify and delineate the drivers and their financial backers. We provide a road map for dismantling the antiscience machine, through stories that at times are quite personal but speak to challenges and threats that are broad and sweeping. This book is a warning. But it is also a call to arms. While there is urgency—unlike any we’ve ever known—there is still agency. We can still avert disaster if we can understand the nature of the mounting antiscience threat and formulate a strategy to counter it.

In their first chapter they write

We find ourselves facing not just a one-two punch of pandemics and the climate crisis, but a one-two-three punch, with that third punch, antiscience, obstructing the needed response from governments and civil society. The future of humankind and the health of our planet now depend on surmounting the dark forces of antiscience.

My favorite chapter was their last one, titled “The Path Forward.” They present a Venn diagram for winning the war against antiscience.

 

About it they write

One circle describes ways to expand the visibility of scientists, while providing the tools for scientists to better engage with the public. Another characterizes efforts to protect scientists. And the remaining circle emphasizes the battle against the intensifying flow of antiscience disinformation. We propose a framework for accomplishing this tripartite mission.

I’m going to adopt this Venn diagram as a guide for my future posts. 1) I will continue to communicate constructively about Intermediate Physics for Medicine and Biology, but in addition I’ll stress how important science is in our society and oppose the forces of antiscience. I also will try to fulfill this role in my “Bob Park’s What’s New” series that I also publish weekly here. 2) I will search out and attempt to debunk and defeat disinformation. I’ve been trying to do this all along, but this goal is more urgent now. 3) I’ll support scientists. I can’t do much to support them financially or materially, but in this blog I can take on the role of cheerleader-in-chief and provide moral support, especially to those who are attacked by the forces of antiscience.

Mann and Hotez adopt a strident and pugnacious tone in Science Under Siege. Is it justified? It is. I truly believe that there is a Republican War on Science. I believe the forces of antiscience are currently winning this war. And I am certain we must oppose antiscience with all our resources. Particularly as a retired scientist, I have an obligation to fight antiscience for the sake of the next generation of scientists. And as a new grandfather, I must oppose antiscience for the sake of my grandson and all the others of his generation.

I’m going to end by repeating some inspiring words that Mann and Hotez feature. They’re from a commentary in the Journal of Virology titled “The Harms of Promoting the Lab Leak Hypothesis for SARS-CoV-2 Origins Without Evidence” (Volume 98, Article Number e01240–24, 2024). I suggest you read the entire article (it’s not long), but below is the excerpt Mann and Hotez quote.

Science is humanity’s best insurance against threats from nature, but it is a fragile enterprise that must be nourished and protected. What is now happening to virology is a stark demonstration of what is happening to all of science. It will come to affect every aspect of science in a negative and possibly dangerous way, as has already happened with climate science. It is the responsibility of scientists, research institutions, and scientific organizations to push back against the anti-virology attacks, because what we are seeing now may be the tip of the proverbial iceberg.

Book Talk: Michael E. Mann and Peter J. Hotez — Science Under Siege

https://www.youtube.com/watch?v=-foS1FIkK3g

John Clarke Shares the Nobel Prize in Physics

John Clarke
UC Berkeley, CC BY 4.0 , via Wikimedia Commons

This year the Nobel Prize in Physics was awarded to John Clarke, Michel Devoret, and John M. Martinis “for the discovery of macroscopic quantum mechanical tunnelling and energy quantization in an electric circuit.”

I will focus on one member of this trio, John Clarke. Russ Hobbie and I mention Clarke in Intermediate Physics for Medicine and Biology in our chapter on biomagnetism.

Sensitive detectors are constructed from superconducting materials. Some compounds, when cooled below a certain critical temperature, undergo a sudden transition and their electrical resistance falls to zero. A current in a loop of superconducting wire persists for as long as the wire is maintained in the superconducting state. The reason there is a superconducting state is a well-understood quantum-mechanical effect that we cannot go into here. It is due to the cooperative motion of many electrons in the superconductor (Eisberg and Resnick 1985, Sect. 14.1; Clarke 1994). The [line integral of the electric field] around a superconducting ring is zero, which means that [the change in magnetic flux] is zero, and the magnetic flux through a superconducting loop cannot change. If one tries to change the magnetic field with some external source, the current in the superconducting circuit changes so that the flux remains the same.

The detector is called a superconducting quantum interference device (SQUID). The operation of a SQUID and biological applications are described in the Scientific American article by Clarke (1994).

This was not the first Nobel Prize related to the SQUID. In 1973 Brian Josephson shared the Nobel Prize “for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects.” Now, over fifty years later, it’s Clarke’s turn.

A Lawrence Berkeley Laboratory announcement stated

Clarke joined Berkeley Lab in 1969 and retired as a faculty senior scientist in the Materials Sciences Division in 2010. At the time of their prize-winning research, Martinis worked as a graduate student researcher, and Devoret as a postdoctoral scholar, in the Clarke group at Berkeley Lab and UC Berkeley…. 

[Clarke’s circuit using a tunnel barrier] is the foundation for an ultrasensitive detector called a SQUID or a superconducting quantum interference device. Clarke has pioneered and used SQUIDs in many applications, including detection of nuclear magnetic resonance (NMR) signals at ultralow frequencies; geophysics; nondestructive evaluation of materials; biosensors; detection of dark matter; and observing qubits, the fundamental unit of information in a quantum computer.

Clarke describes his first SQUID-like circuit in his Scientific American article that Russ and I cite.

In my early days as a research student at Cambridge, my supervisor, Brian Pippard, proposed that I use a SQUID to make a highly sensitive voltmeter. In those days, procedures for making Josephson junctions were in their infancy and not practicable for manufacturing instruments. One day early in 1965, over the traditional afternoon tea at the Cavendish Laboratory, I was discussing this problem with Paul C. Wraight, a fellow student. He suggested that a molten blob of solder (an alloy of lead and tin that becomes superconducting in liquid helium) deposited onto a niobium wire might just conceivably make a Josephson junction. His rationale was that niobium has a native oxide layer that might behave as a suitable tunnel barrier.

We rushed back to the laboratory, begged a few inches of niobium wire from a colleague, melted a blob of solder onto it, attached some leads and lowered it into liquid helium. As we hoped, Josephson tunneling! The fact that Wraight’s idea worked the first time was important. If it had not, we would never have bothered to try again. Because of its appearance, we christened the device the SLUG. Later I was able to make a voltmeter that could measure 10 femtovolts (10^-14 volt), an improvement over conventional semiconductor voltmeters by a factor of 100,000.

Clarke’s article goes on to describe many of the biological applications of SQUIDs, including for measuring the magnetocardiogram (magnetic field of the heart) and the magnetoencephalogram (magnetic field of the brain).

Congratulations to John Clarke and this colleagues on their Nobel Prize. It’s another wonderful example of physics applied to biology and medicine. 

UC Berkeley press conference 10/7/2025: Professor Emeritus John Clarke 2025 Nobel Prize in Physics

https://www.youtube.com/watch?v=VnL-1VTSp7s

The Physics of Hearing

Physics of the Body.

My hearing is not what it used to be. It’s not terrible now; I still get along okay. But I find myself asking my wife “what?” a lot. So, I borrowed a copy of Physics of the Body—by John Cameron, James Skofronick, and Roderick Grant (1999)— and read Section 11.9: Deafness and Hearing Aids. It covers much of the information that Russ Hobbie and I discuss in Chapter 13 of Intermediate Physics for Medicine and Biology, and more. Below I quote a paragraph from Physics of the Body, with references removed and my comments in brackets.

In 1985 it was estimated that 21 million persons in the United States were either deaf or hard of hearing. The frequency range most important for understanding conversational speech is from about 250 to 3000 Hz. [The figure below shows the hearing response curve for a young adult from IPMB, with the range from 0.25 to 3 kHz shaded.] A person who is “deaf” above 4000 Hz but who has normal hearing in the speech frequencies is not considered deaf or even hard of hearing. [I was taking a walk with my daughter Kathy a few months ago. As we passed one house she grimaced said “what is that terrible high-pitched noise?” I said “what noise?”] However, that person should not spend a lot of money on good stereo equipment. [Music sounds the same now as I remember it back when I was a teenager. Nevertheless, I need no additional encouragement to not spend money; I’m a cheapskate.] Hearing handicaps are classified according to the average hearing threshold at 500, 1000, and 2000 Hz in the better ear [I haven’t noticed any difference between my left and right ears]. A person with a hearing threshold 30 dB above normal would probably not have a hearing problem. People with hearing thresholds of 90 dB are considered deaf or stone deaf. [According to Table 13.1 in IPMB, 30 dB is the “maximum background sound level tolerable in a broadcast studio” and 90 dB is the sound “inside a motor bus.” I am definitely not stone deaf. Is my threshold below 30 dB? I don’t know.] About 1% of the population have thresholds for speech frequencies greater than 55 dB [IPMB says 55 dB is between “office” sounds and “speech at 1 m.” I definitely can hear speech at 1 m. It’s speech from my wife calling from another room that I have trouble with.] and should use hearing aids [Both my mom and dad used hearing aids when they got older. My health has generally parallels my father’s. I fear it is just a matter of time]. About 1.7% have a slight hearing handicap; they have problems with normal speech but have no difficulty with loud speech [I think I am better than that]. Hearing problems increase with age [Yes, that’s the problem. I’m getting old.]

The average sound level of speech is about 60 dB. We adjust the sound level of our speech unconsciously according to the noise level of our surroundings. Speech sound levels in a quiet room may be as low as 45 dB; at a noisy party they may be 90 dB. A person with a hearing loss of 45 dB in the 500 to 2000 Hz range may do all right (hearing-wise) at a cocktail party but hear very little of speech in a quiet room. [I don’t know. It seems to me that I have more of a problem distinguishing speech from background sounds than just hearing speech. I suspect I would do worse at the cocktail party even with people speaking at 90 dB than chatting at 45 dB in the quiet room.]

Now that I’m on Medicare, my wife is encouraging me to have my hearing checked. I suppose I should.

Trident Production

The Study of
Elementary Particles
by the Photographic
Method.

In the 5th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I include two figures showing particle tracks in photographic emulsions: Fig. 15.27, tracks of 22 MeV alpha particles; and Fig. 15.28, tracks of an electron-positron pair. Both figures are reproduced from The Study of Elementary Particles by the Photographic Method. When preparing the 6th edition of IPMB, I obtained a copy of that book through interlibrary loan.

The book is fascinating. It was published in 1959, the year before I was born. All three coauthors are British, and are famous enough to have Wikipedia pages. Cecil Frank Powell was a particle physicist who received the Nobel Prize in 1950 for developing the photographic method for studying nuclear processes, and for using this method to discover the pion. He was trained at the Cavendish Laboratory working with Rutherford. He died in 1969. Peter Howard Fowler was a student of Powell’s who worked on cosmic radiation. He was a radar officer with the Royal Air Force during World War II, and was able to detect German radar jamming and identify its source, leading to a destruction of the responsible German radar station. He was married to physicist Rosemary Fowler, who discovered the kaon. His grandfather was Ernest Rutherford. Fowler died in 1996. Donald Hill Perkins discovered the negative pion. He studied proton decay, and found early evidence of neutrino oscillations. Perkins and Fowler were the first to suggest using pion beams as therapy for cancer in 1961 (The use of pions in medicine hasn't panned out). Perkins died at the ripe old age of 97 in 2022.

When skimming through the book, I noticed an interesting illustration of a trident track produced by high energy electrons. It looks something like this: 

A trident arises from the process of bremsstrahlung followed by pair production; both of which are described in IPMB. A fast electron interacts with an atomic nucleus, decelerating the electron and emitting a bremsstrahlung photon. This photon, if it has high enough energy, can then interact with an atomic nucleus to create an electron-positron pair. The intermediate photon can be “virtual,” existing only fleetingly. The end result is three particles: the original electron plus the pair. I gather that this requires a very high energy electron, and its cross-section is small, so it seems to contribute little to the dose in medical physics. The authors talk about the production of tridents for energies of more than a BeV, which is an old-fashioned way of saying a GeV, equivalent to 1000 MeV.

I’m glad Russ and I included figures from The Study of Elementary Particles by the Photographic Method. I hope I can figure out the permissions situation (the authors are all dead, and the publisher was sold to another company) and we can continue to include the figures in the 6th edition.

The Dollar and Dime Game

Most mornings I take a walk to keep myself in shape. Usually I listen to an audiobook while walking, but for some reason my earbuds didn’t recharge properly overnight and this morning they didn’t work right. So, I had to take my constitutional in silence.

It so happens that yesterday I was revising Appendix H (The Binomial Probability Distribution) for the 6th edition of Intermediate Physics for Medicine and Biology. (Yes, you’re right, Gene Surdutovich and I are getting close to being done if we’re already up to the appendices.) As I was reviewing the material, I thought “it sure would be nice to have some more nontrivial but not too complicated word problems for this appendix.” So, as I hiked I came up with this:

Appendix H

Problem 6. You are a young college student who wants to make a little extra cash for living expenses. You also are an occasional Dungeons and Dragons player, so you have a twenty-sided die in the top drawer of your desk. You decide to set up what you call the “Dollar and Dime” game. Any student in your dormitory can come to you and pay you a dollar and a dime, and you will take out your twenty-sided die and roll it once. If it gives a one, you hand the student a crisp, new twenty dollar bill. If it it rolls a two through twenty, the student walks away empty handed. You’re pretty happy with the game. On average, the dollars earned cover the required payouts, and the dimes are all profit. The game becomes popular among your dormmates, and people stop by to play dozens of times each day.

A page from the Rodgers and
Hammerstein Song Book.

John comes to you late one Friday afternoon. He has invited Jane to attend the school musical Oklahoma! with him that evening (Jame loves musicals, especially those by Rodgers and Hammerstein), but two tickets will cost him $40, and all he has is $11. It’s too late to find a part-time job or to beg funds from his parents. His only chance to avoid reneging on the theater date is to get the needed cash by playing the Dollar and Dime game. John slaps the eleven bucks down on your desk and says “I wanna play ten times.”

Your first thought is to tell John to go to the bank and exchange the ten dollar bill for ten ones and the one dollar bill for ten dimes, so he can play the game properly. But John is on the school wrestling team, is six foot three, and weighs 270 pounds, so you decide to waive this technicality. You accept his $11, get out the twenty-sided die, and start rolling.

Ordinarily when playing this game you relax, knowing that in the long run you will make a profit. However, today you’re a bit nervous because you only have three portraits on Andrew Jackson in the envelope where you store the cash for your game. Earlier in the day, you told your wealthy roommate Peter about your situation, hoping he could cover you if needed (he declined). Now, if John wins the game four or more times, he’s gonna to be upset that you can’t pay him what you owe him, and John is not the kind of guy you want to make mad.

(a) What is the probability that John wins enough money to take Jane to Oklahoma!?

(b) What is the probability that you get clobbered by John?

(c) How do all these results change if Peter (who is annoyed that you converted your dorm room to a casino with people coming and going and noisily rolling that silly icosahedron at all hours of the night) loans John an extra $22, interest free?

The first step in solving this problem is to realize that this, indeed, can be modeled using the binomial probability distribution. In the 5th edition of IPMB, Russ Hobbie and I wrote

Consider an experiment with two mutually exclusive outcomes, which is repeated N times, with each repetition being independent of every other one. One of the outcomes is labeled “success”, the other is called “failure.”

The binomial distribution is given by Eq. H.2,

where N is the number of tries (John has $11 so he can play the game ten times, N = 10), p is the probability of success for each try (it is a twenty sided die, so p = 0.05), and n is the number of successes (rolling a one). John will make 20n dollars by playing the Dollar and Dime game. The key question is, what’s the probability P that John gets n wins.

The odds of John never rolling a one and leaving broke is

Yikes! He has 3:2 odds of losing everything. Next, the probability that John wins only once are 

Only one win will make John twenty bucks, so after paying $11 to play he’ll be nine dollars ahead, but that still isn’t enough to take Jane to see Curly give Laurey that ride in his surrey which, as you will recall, costs $40. He needs at least two wins for that. We now have enough information to answer part (a). The probability that John takes Jane to the show is one minus the probability that he doesn’t earn at least $40. So, John can avoid an unpleasant call to Jane (or, worse, escape being a no show) with a probability of 1 – 0.599 – 0.315 = 0.086. That means the odds are about 11:1 against making Jane happy. Looks like John’s in trouble.

John’s best chance is to win the Dollar and Dime game twice and earn the $40 needed for tickets. The odds are

Boy, that would be great. But if John is really lucky, he’ll win enough for the tickets plus some extra cash for a large popcorn and two medium soft drinks (which costs $18.49).  

There’s only a one percent chance of Jane getting her popcorn.

But wait. If John wins four or more times, you won’t have the cash to cover his winnings. Either he’ll thrash you, or (more likely) you’ll be forced to make a deal where you pay John all that you have, $60, and promise to return his original investment of $11, and grovel before him begging for mercy. That would be good news for John. He would walk away with at least $71, and perhaps more if he knows how to drive a hard bargain (after all, you don’t want to end up daid, like poor Jud). What are the odds he’ll bust the bank? 

We should also add in the chance that John will win five times, or six, or more, but those will be very small (calculate them yourself if you don’t believe me). So, the probability of a disaster (for you, not for John) is about one part per thousand, or a tenth of a percent. The odds are small, but the consequences would be dire (with you possibly ending up in the hospital), so you’re still nervous until John finishes all ten of his rolls.

Now, consider the final twist to the story. Imagine that when your so-called “friend” Peter sees John arrive, he pulls him aside, gives him a wink, and loans him another $22. (Pete could have easily just lent $29 so John would have enough to cover the cost of his date with Jane, but that would defeat his purpose, wouldn’t it?). Now John has $33 to spend on the Dollar and Dime game. The only thing that changes is N increases from ten to thirty. How does that change the probabilities? You can work out the details. I’ll just state the results.

n        P 

  0     0.215 

  1     0.339 

  2     0.259 

  3     0.127 

 4     0.045

The chances of John taking Jane to the musical is now 0.446, so the odds are approaching 50-50. Still not great odds, but much better than before. John’s starting to dream that after he takes Jane to Oklahoma! “people will say we’re in love.” More importantly for you (and for that evil Peter), the odds of busting the bank are now 6%. So, at no cost to himself, Peter just increased the odds of shutting down the hated casino by a factor of sixty. Win or lose, you vow to start looking for another roommate; one who doesn’t know as much math.

By the time I came up with this homework problem, I had just about finished my walk. The problem has no biology or medicine in it, so it probably won’t make it into the revised sixth edition. With any luck, tomorrow I’ll be back to the audio book (and, oh, what a beautiful morning that will be). By the way, our goal is to submit the 6th edition of IPMB to our publisher, Springer, before the end of the year. It’s gonna be close, but we just might make it.

Oklahoma!

https://www.youtube.com/watch?v=ZbrnXl2gO_k&list=RDZbrnXl2gO_k

 

 Oh, What a Beautiful Morning

https://www.youtube.com/watch?v=O5APc0z49wg&list=RDO5APc0z49wg

 

People Will Say We're in Love

 

https://www.youtube.com/watch?v=VEwVAV3VPw4

The Surrey with the Fringe on Top

https://www.youtube.com/watch?v=BIG_GVE-KiE&list=RDBIG_GVE-KiE

Kansas City

https://www.youtube.com/watch?v=M6pmZE1Qtyw&list=RDBIG_GVE-KiE

 

The Farmer and the Cowman

https://www.youtube.com/watch?v=G85aEsgMDwA&list=RDG85aEsgMDwA 

I Cain't Say No

https://www.youtube.com/watch?v=aExjjv2Klrs&list=RDaExjjv2Klrs&start_radio=1

 

Poor Jud is Daid

https://www.youtube.com/watch?v=Euq8Z4l6Iwk&t=171s

Maxwell's Spot

One of my scientific heroes is James Clerk Maxwell. Maxwell (1831–1879) was a Scottish physicist known for developing Maxwell’s equations of electricity and magnetism, and for his work on statistical mechanics. But Maxwell also studied the eye and was an early researcher of color vision.

One of Maxwell’s interesting but not staggeringly important discoveries was Maxwell’s Spot. If for no other reason that I am a big Maxwell fan, today I want to examine his spot. I’ll base my discussion on a 2003 article titled “The Differential Contribution of Macular Pigments and Foveal Anatomy to the Perception of Maxwell’s Spot and Haidinger’s Brushes” by Gary Misson, Rebekka Heitmar, Richard Armstrong, and Stephen Anderson in the journal Vision. I will quote from it with references removed. The article begins

Normally sighted individuals can perceive a short-lived darkened spot at the point of fixation while viewing a plain white surface through a dichroic filter transmitting a mixture of long- and short-wavelength lights. This entoptic phenomenon, known as Maxwell’s spot (MS), was first described in detail by James Clerk Maxwell in 1856.

One of my goals today will be to merely explain what unfamiliar words mean. First, what is a “dichroic filter”? A dichroic filter uses interference rather than absorption to filter light. Interference was discussed only briefly in Intermediate Physics for Medicine and Biology, when Russ Hobbie and I described optical coherence tomography. A dichroic filter is typically made up of many thin layers, each which can reflect light. It creates colors in a similar way that a thin film of oil on the surface of water reflects some colors and not other. It depends on if the reflected or transmitted light from different layers interfere constructively or destructively. One advantage of a dichroic filter is that it can be very selective about what light is transmitted.

Next is “entoptic.” An entoptic phenomenon is a visual effect that arises from a source or structure within the eye itself. Examples of vision phenomena that are NOT entoptic include hallucinations (arising in the brain) and mirages (arising in the optical refraction of light in the environment). Entoptic phenomena would include floaters arising from the shadow of tiny objects in the vitreous humor of the eye, and phosphenes arising from mechanical or electrical excitation of the retina. Whatever Maxwell’s Spot is, it happens because of something within the eye itself. Misson et al. continue

The most widely accepted hypothesis proposed for the origin of the peripheral zones in [Maxwell’s Spot], and its documented perceptual variations, is absorption of blue light by macular pigments that result in a reduction of foveal photoreceptor illumination.

First, what is the “macula?” It is an oval-shaped region in the center of the retina with a diameter of about 5 mm where there is a high density of cone cells responsible for color vision. At the center of the macula is a region of about 1.5 mm diameter that has the highest density of cone cells called the fovea.

To fully understand the vision, you need to realize that humans have what’s called an inverted retina. That is, the light-sensing rods and cones are at the back of the retina, behind the retina’s neurons and capillaries, so light must pass through these other structures before reaching the light-sensing cells. You may ask, why does the retina have this seemingly backwards structure? I’ll tell you. I don’t know. But it does.

The macula also contains pigments that absorb light. Like the neurons and capillaries, these pigments (at least some of them) are located in front of the rods and cones. Pigments are molecules that absorb certain wavelengths of light. Two of the main macular pigments are called lutein and zeaxanthin. These are carotenoids, which are the pigments that give color to pumpkins, carrots, and daffodils. In general, carotenoids absorb blue and violet light. So, the reason a carrot is orange is that when white light shines on it the caretenoids absorb much of the blue light, so the light reflected by the carrot (which is the light you see) is mainly the red and orange light that was not absorbed. This is also why the macula itself looks yellow when viewed with a ophthalmoscope. 

Figure 3 from Misson et al. (2003). The image was obtained
using optical coherence tomography. Light comes in from above.
The bright areas on the top left and right are the macular
pigments. There is also a lot of pigment below the retina,
but that does play a key role in producing Maxwell’s Spot.

So, now we get to the cause of Maxwell’s Spot. Misson and his coauthors write

The results of this study support the theory that the principal mechanism of [Maxwell’s Spot] generation is pre-receptoral screening by macular pigment.

In other words, the pigments in front of the macula (through which the incoming light must pass to reach the rods and cones) filters out some of the blue light. As white light enters the eye, the macular pigments remove some of the blue, but the rest of the retina which does not have these pigments lets all the light through. So, a white screen appears white except at the center spot right where the eye is fixated on with highest spatial resolution and best color vision, and that spot is darker and redish. That, dark red region is Maxwell’s Spot. Note that this phenomenon arises because of the distribution of pigments within the eye; it is entoptic. Because everybody’s pigment distribution and macula arrangement can vary, so can everyone’s perception of Maxwell’s Spot.

Maxwell’s Spot was not Maxwell’s only contribution to vision physiology. He was one of the founders of the theory of trichromatic color vision, which states that there are three types of cone cells in the retina (red, green, and blue) that are responsible for our perception of color. There is no telling how much more Maxwell might have contributed to both physics and physiology if he had not died of cancer at the tragically young age of 48.

Why Are There So Few Aerial Plankton?

Air and Water,
by Mark Denny.

In his book Air and Water, Mark Denny asks an oddball question: Why are there so few aerial plankton? In my mind, this question transforms into: Why are there no flying blue whales, sucking in mouthfuls of air and filtering out tiny organisms for food? Here is what Denny says:

A general characteristic of aquatic (especially marine) environments is the presence of planktonic life. A cubic meter of water taken from virtually anywhere in a stream, lake, or ocean is teeming with small, suspended organisms. In fact, the concentration of these plants and animals is such that many kinds of invertebrates, including clams, mussels, anemones, polychaete worms, and bryozoans, can reliably use planktonic particles as their sole source of food. In contrast, air is relatively devoid of suspended matter. A cubic meter of air might contain a few bacteria, a pollen grain or two, and very occasionally a flying insect or wind-borne seed. Air is so depauperate compared to the aquatic ‘soup’ that few terrestrial animals manage to make a living by straining their food from the surrounding fluid. Web-building spiders are the only example that comes to mind.

To understand why, my first inclination is to examine the balance between gravity, thermal motion, and concentration. You can use a Boltzmann factor, e^–mgh/k_BT, to determine how the concentration changes with height h, assuming particles of mass m are in contact with a fluid at temperature T (g is the acceleration of gravity and k_B is Boltzmann’s constant). But there’s one problem: the Peclet number is often large, meaning advection dominates diffusion. In other words, air or water currents are more effective than diffusion for mixing (like in a blender). In many cases the problem is even worse: the flow is turbulent, which tends to mix materials much more rapidly than diffusion does. In some ways the analysis of turbulent mixing is similar to the case of diffusion. The flux of particles is proportional to the concentration gradient, but the constant of proportionality is not the diffusion constant but instead the turbulent diffusivity. Denny does the analysis in more detail than I can go into here (turbulent flow is always complex). But he states his conclusion clearly and simply

The sinking rates of particles in air are just too high to allow them to remain passively suspended and as a result, aerial plankton are sparse. In water, slow sinking speeds insure that many particles are suspended, and the plankton is plentiful. The abundance of aquatic suspension feeders and the scarcity of terrestrial ones, can therefore be thought of as a direct consequence of the differences in density and viscosity between air and water.

One other factor plays a role here: buoyancy. If the small organisms have a density approximately that of water, then tiny aquatic animals would be almost neutrally buoyant, so they’d be easy to suspend. In air, however, buoyancy plays almost no roll, so these little animals “seem” to be much denser.

It looks like I should abandon my search for a giant flying suspension feeder, resembling a blimp with a big mouth to suck in large amounts of air that it filters to extract food. Too bad. I was looking forward to befriending one, if the physics had only allowed it.

 https://www.youtube.com/watch?v=NivDXM88oCo

Does Stokes’ Law Hold for a Bubble?

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss Stokes’ law. When a small sphere, of radius a, moves with speed U through a fluid having a viscosity η, the drag force D is 6πηaU. This result is well known, but does it apply to a gas bubble moving in water?

Life in Moving Fluids,
by Steven Vogel.

I was reading through Life in Moving Fluids, by Steven Vogel, when I came across the answer. Vogel considers a fluid sphere moving in a fluid medium. His Eq. 15.8 is

Here, η_ext is the viscosity of the external fluid and η_int is the viscosity of the internal fluid.

Suppose you have a sphere of water in air (say, a raindrop falling from the sky toward earth). Then η_int = η_water = 10^–3 Pa s and η_ext = η_air = 2 × 10^–5 Pa s. Thus η_ext/η_int = 0.02. For our purposes, this is nearly zero, and the drag force reduces to Stokes’ law, D = 6πη_extaU.

Now, consider a sphere of air in water (say, a bubble rising toward the surface of a lake). Then η_int = η_air = 2 × 10^–5 Pa s and η_ext = η_water = 10^–3 Pa s. Thus η_ext/η_int = 50. For our purposes, this is nearly infinity, and the drag force becomes D = 4πη_extaU. Yikes! Stokes’ law does not hold for a bubble. Who knew? (Vogel knew.)

Apparently when the sphere is a fluid, internal motion occurs, as shown in Vogel’s picture below.

 

Note that at the edge of the sphere, the internal and external flows are in the same direction. This changes the boundary condition at the surface. A rigid sphere would obey the no-slip condition, but a fluid sphere does not because the internal fluid is moving.

Although Vogel doesn’t address this, I wonder what the drag force is on a sphere of water in water? Does this even make sense? Perhaps we would be better off considering a droplet of some liquid that has the same viscosity as water moving through water (I can imaging this might happen in a microfluidics apparatus). In that case the drag force becomes D = 5πη_extaU. I must confess, I’m not sure if the derivation of the general equation is valid in this case, but I don’t see why it shouldn’t be.

There are all kinds of little jewels inside Vogel’s book. I sure wish he were still around.