How does free convection work? If water is heated from below, it expands as it becomes hotter, reducing its density. Less dense water is buoyant and rises. As the water moves away from the source of heat, it cools, becomes denser, and sinks. The process then repeats. The fluid flow caused by all this rising, sinking, heating, and cooling is what’s known as free convection. One reason Russ and I don’t dwell on this topic is that our body is isothermal. You need a temperature gradient to drive convection.
Many scientists believe early life was based on ribonucleic acid, or RNA, rather than DNA and proteins. RNA replication is aided by temperature oscillations, which allow the double-stranded RNA to separate and make complementary copies (hot), and then accumulate without being immediately degraded (cold). Molecules moving with water during free convection undergo such a periodic heating and cooling. One more process is needed, called thermophoresis, which causes long strands of RNA to move from hot to cold regions preferentially compared to short strands. Salditt et al. write
The interplay of convective and thermophoretic transport resulted in a
length-dependent net transport of molecules away from
the warm temperature spot. The efficiency of this transport
increased for longer RNAs, stabilizing them against cleavage
that would occur at higher temperatures.
Where does free convection happen? Around hydrothermal vents at the bottom of the ocean.
A natural
setting for such a heat flow could be the dissipation of heat across
volcanic or hydrothermal rocks. This leads to temperature
differences over porous structures of various shapes and lengths.
The authors conclude
The search for the origin of life implies
finding a location for informational molecules to replicate
and undergo Darwinian evolution against entropic
obstacles such as dilution and spontaneous degradation.
The experiments described here demonstrate how a heat
flow across a millimeter-sized, water-filled porous rock can
lead to spatial separation of molecular species resulting in
different reaction conditions for different species. The
conditions inside such a compartment can be tuned
according to the requirements of the partaking molecules
due to the scalable nature of this setting. A similar setting
could have driven both the accumulation and RNA-based
replication in the emergence of life, relying only on thermal
energy, a plausible geological energy source on the early
Earth. Current forms of RNA polymerase ribozymes can
only replicate very short RNA strands. However, the
observed thermal selection bias toward long RNA strands
in this system could guide molecular evolution toward
longer strands and higher complexity.
The first page of “Tests for Human Perception
of 60 Hz Moderate Strength Magnetic Fields,”
by Tucker and Schmitt (IEEE Trans. Biomed. Eng.
25:509-518, 1978).
Foster (1996) reviewed many of the laboratory studies and described
cases where subtle cues meant the observers were not making truly
“blind” observations. Though not directly relevant to the issue under
discussion here, a classic study by Tucker and Schmitt (1978) at the
University of Minnesota is worth noting. They were seeking to detect
possible human perception of 60-Hz magnetic fields. There appeared
to be an effect. For 5 years they kept providing better and better isolation
of the subject from subtle auditory clues. With their final isolation
chamber, none of the 200 subjects could reliably perceive whether the
field was on or off. Had they been less thorough and persistent, they
would have reported a positive effect that does not exist.
In this blog, I like to revisit articles that we cite in IPMB.
After preliminary experiments that pointed out the extreme cleverness with which perceptive individuals unintentionally used subtle auxiliary clues to develop impressive records of apparent magnetic field detection, we developed a heavy, tightly sealed subject chamber to provide extreme isolation against such false detection. A large number of individuals were tested in this isolation system with computer randomized sequences of 150 trials to determine whether they could detect when they were, and when they were not, in a moderate (7.5-15 gaussrms) alternating magnetic field, or could learn to detect such fields by biofeedback training. In a total of over 30,000 trials on more than 200 persons, no significantly perceptive individuals were found, and the group performance was compatible, at the 0.5 probability level, with the hypothesis that no real perception occurred.
The Tucker-Schmitt study illustrates how observing small effects can be a challenge. Their lesson is valuable, because many weak-field experiments are subject to systematic errors that provide an illusion of a positive result. Near the start of their article, Tucker and Schmitt write
We quickly learned that some individuals are incredibly
skillful at sensing auxiliary non-magnetic clues, such as coil
hum associated with field, so that some “super perceivers”
were found who seemed to sense the fields with a statistical
probability as much as 10–30 against happening by chance.
A vigorous campaign had then to be launched technically to
prevent the subject from sensing “false” clues while leaving
him completely free to exert any real magnetic perceptiveness
he might have.
Few authors are as forthright as Tucker and Schmitt when recounting early, unsuccessful experiments. Yet, their tale shows how experimental scientists work.
Early experiments, in which an operator visible to the test
subject controlled manually, according to a random number
table, whether a field was to be applied or not, alerted us to
the necessity for careful isolation of the test subject from
unintentional clues from which he could consciously, or subconsciously,
deduce the state of coil excitation. No poker face
is good enough to hide, statistically, knowledge of a true
answer, and even such feeble clues as changes in building light,
hums, vibrations and relay clatter are converted into low but
significant statistical biases.
IPMB doesn’t teach experimental methods, but all scientists must understand the difference between systematic and random errors. Uncertainty from random errors is suppressed by taking additional data, but eliminating systematic errors may require you to redesign your experiment.
In a first round of efforts to prevent utilization of such clues,
the control was moved to a remote room and soon given over
to a small computer. A “fake” air-core coil system, remotely
located but matched in current drain and phase angle to the
real large coil system was introduced as a load in the no-field
cases. An acoustically padded cabinet was introduced to house
the experimental subject, to isolate him from sound and vibration.
Efforts were also made to silence the coils by clamping
them every few centimeters with plastic ties and by supporting
them on air pocket packing material. We tried using masking
sound and vibrations, but soon realized that this might also
mask real perception of magnetic fields.
Designing experiments is fun; you get to build stuff in a machine shop! I imagine Tucker and Schmitt didn’t expect they would have this much fun. Their initial efforts being insufficient, they constructed an elaborate cabinet to perform their experiments in.
This cabinet was fabricated with four layers of 2 in plywood,
full contact epoxy glued and surface coated into a monolithic
structure with interleaved corners and fillet corner reinforcement
to make a very rigid heavy structure weighing, in total,
about 300 kg. The structure was made without ferrous metal
fastening and only a few slender brass screws were used. The
door was of similar epoxyed 4-ply construction but faced with
a thin bonded melamine plastic sheet. The door was hung on
two multi-tongue bakelite hinges with thin brass pins. The
door seals against a thin, closed-cell foam-rubber gasket, and
is pressure sealed with over a metric ton of force by pumping a
mild vacuum inside the chamber of means of a remote
acoustically silenced hose-connected large vacuum-cleaner
blower. The subject received fresh air through a small acoustic filter inlet leak that also assures sufficient air flow to cool the
blower. The chosen “cabin altitude” at about 2500 ft above
ambient presented no serious health hazard and was fail-safe
protected.
An experimental scientist must be persistent. I remember learning that lesson as a graduate student when I tried for weeks to measure the magnetic field of a single nerve axon. I scrutinized every part of the experiment and fixed every problem I could find, but I still couldn’t measure an action current. Finally, I realized the coaxial cable connecting the nerve to the stimulator was defective. It was a rookie mistake, but I was tenacious and ultimately figured it out. Tucker and Schmitt personify tenacity.
As still more isolation seemed necessary to guarantee practically
complete exclusion of auxiliary acoustic and mechanical
clues, an extreme effort was made to improve, even further,
the already good isolation. The cabinet was now hung by aircraft “Bungee” shock cord running through the ceiling to roof
timbers. The cabinet was prevented from swinging as a pendulum
by four small non-load-bearing lightly inflated automotive
type inner tubes placed between the floor and the cabinet
base. Coils already compliantly mounted to isolate intercoil
force vibration were very firmly reclamped to discourage
intracoil “buzzing.”
The cabinet was draped inside with sound
absorbing material and the chair for the subject shock-mounted
with respect to the cabinet floor. The final experiments, in
which minimal perception was found, were done with this
system.
Once Tucker and Schmitt heroically eliminated even the most subtle cues about the presence of a magnetic field, subjects could no longer detect whether or not a magnetic field was present. People can’t perceive 60-Hz, 0.0015-T magnetic fields.
Russ and I relegate this tale to a footnote, but it’s an important lesson when analyzing the effects of weak electric and magnetic fields. Small systematic errors abound in these experiments, both when studying humans and when recording from cells in a dish. Experimentalists must ruthlessly design controls that can compensate for or eliminate confounding effects. The better the experimentalist, the more doggedly they root out systematic errors. One reason the literature on the biological effects of weak fields is so mixed may be that few experimentalists take the time to eradicate all sources of error.
Tucker and Schmitt’s experiment is a lesson for us all.
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The introduction is two short paragraphs (a mere hundred words). The first puts the work in context.
Successive stimulation (S1, then S2) of cardiac tissue can induce
reentry. In many cases, an S1 stimulus triggers a propagating action potential that creates a gradient of refractoriness. The S2 stimulus then
interacts with this S1 refractory gradient, causing reentry. Many theoretical
and experimental studies of reentry induction are variations on
this theme [1]–[9].
When I wrote this communication, the critical point hypothesis was a popular explanation for how to induce reentry in cardiac tissue. I cited nine papers discussing this hypothesis, but I associate it primarily with the books of Art Winfree and the experiments of Ray Ideker.
The critical point hypothesis.
The figure above illustrates the critical point hypothesis. A first (S1) stimulus is applied to the right edge of the tissue, launching a planar wavefront that propagates to the left (arrow). By the time of the upper snapshot, the tissue on the right (purple) has returned to rest and recovered excitability, while the tissue on the left (red) remains refractory. The green line represents the boundary between refractory and excitable regions: the line of critical refractoriness.
The lower snapshot is immediately after a second (S2) stimulus is applied through a central cathode (black dot). The tissue near the cathode experiences a strong stimulus above threshold (yellow), while the remaining tissue experiences a weak stimulus below threshold. The green curve represents the boundary between the above-threshold and below-threshold regions: the circle of critical stimulus. S2 only excites tissue that is excitable and has a stimulus above threshold (inside the circle on the right). It launches a wave front that propagates to the right, but cannot propagate to the left because of refractoriness. Only when the refractory tissue recovers excitability will the wave front begin to propagate leftward (curved arrow). Critical points (blue dots) are located where the line of critical refractoriness intersects the circle of critical stimulus. Two spiral waves—a type of cardiac arrhythmia where a wave front circles around a critical point, chasing its tail—rotate clockwise on the bottom and counterclockwise on the top.
The second paragraph of my communication begins with a question.
Is the S1 gradient of refractoriness essential for the induction of
reentry? In this communication, my goal is to show by counterexample
that the answer is no. In my numerical simulation, the transmembrane
potential is uniform in space before the S2 stimulus. Nevertheless, the
stimulus induces reentry.
The critical point hypothesis implies the answer is yes; without a refractory gradient there is no line of critical refractoriness, no critical point, no spiral wave, no reentry. Yet I claimed that the gradient of refractoriness is not essential. To explain why, we must consider what happens following the second stimulus.
Cathode break excitation.
The tissue is depolarized (D, yellow) under the cathode but is hyperpolarized (H, purple) in adjacent regions along the fiber direction on each side of the cathode, often called virtual anodes. Hyperpolarization lowers the membrane potential toward rest, shortening the refractory period (deexcitation) and carving out an excitable path. When S2 ends, the depolarization under the cathode diffuses into the newly excitable tissue (dashed arrows), launching a wave front that propagates initially in the fiber direction (solid arrows): break excitation. Only after the surrounding tissue recovers excitability does the wave front begin to rotate back, as if there were four critical points: quatrefoil reentry.
Problem 48. During stimulation of cardiac tissue through a
small anode, the tissue under the electrode and in the direction
perpendicular to the myocardial fibers is hyperpolarized,
and adjacent tissue on each side of the anode parallel to the
fiber direction is depolarized. Imagine that just before this
stimulus pulse is turned on the tissue is refractory. The hyperpolarization
during the stimulus causes the tissue to become
excitable. Following the end of the stimulus pulse, the depolarization
along the fiber direction interacts electrotonically
with the excitable tissue, initiating an action potential (break
excitation). (This type of break excitation is very different
than the break excitation analyzed on page 181.)
(a) Sketch pictures of the transmembrane potential distribution
during the stimulus. Be sure to indicate the fiber
direction, the location of the anode, the regions that are
depolarized and hyperpolarized by the stimulus, and the
direction of propagation of the resulting action potential.
(b) Repeat the analysis for break excitation caused by a
cathode instead of an anode. For a hint, see Wikswo and Roth (2009).
Now we come to the main point of the communication; the reason I wrote it. Look at the first snapshot in the illustration above, the one labeled S1 that occurs just before the S2 stimulus. The tissue is all red. It is uniformly refractory. The S1 action potential has no gradient of refractoriness, yet reentry occurs. This is the counterexample that proves the point: a gradient of refractoriness is not essential.
The communication contains one figure, showing the results of a calculation based on the bidomain model. The time in milliseconds after S1 is in the upper right corner of each panel. S1 was applied uniformly to the entire tissue, so at 70 ms the refractoriness is uniform. The 80 ms frame is during S2. Subsequent frames show break excitation the development of reentry.
An illustration based on Fig. 1 in “An S1 Gradient of Refractoriness is Not Essential for Reentry Induction by an S2 Stimulus” (IEEE TBME, 47:820–821, 2000). It is the same as the figure in the communication, except the color and quality are improved.
The communication concludes:
My results support the growing realization that virtual electrodes, hyperpolarization,
deexcitation, and break stimulation may be important
during reentry induction [8], [9], [14], [15], [21]–[24]. An S1 gradient
of refractoriness may underlie reentry induction in many cases [1]–[6],
but this communication provides a counterexample demonstrating that
an S1 gradient of refractoriness is not necessary in every case.
Does this calculation mean the critical point hypothesis is wrong? No. See my paper with Natalia Trayanova and her student Annette Lindblom (“The Role of Virtual Electrodes in Arrhythmogenesis: Pinwheel Experiment Revisited,” Journal of Cardiovascular Electrophysiology, Volume 11, Pages 274-285, 2000) to examine how this view of reentry can be reconciled with the critical point hypothesis.
One of the best things about this calculation is that you don’t need a fancy computer to demonstrate that the S1 gradient of refracoriness is not essential; A simple cellular automata will do. The figure below sums it up (look here if you don’t understand).
A cellular automata demonstrating that an S1 gradient of refractoriness is not essential for reentry induction by an S2 stimulus.
Here’s your first challenge: Go a week without writing
• Very
• Rather
• Really
• Quite
• In fact
And you can toss in—or, that is, toss out—“just” (not in the sense of “righteous” but in the sense of “merely”) and “so” (in the “extremely” sense, through as conjunctions go it’s pretty disposable too).
Oh yes: “pretty.” As in “pretty tedious.” Or “pretty pedantic.” Go ahead and kill that particular darling.
And “of course.” That’s right out. And “surely.” And “that said.”
And “actually”? Feel free to go the rest of your life without another “actually.”
If you can last a week without writing any of what I’ve come to think of as the Wan Intensifiers and Throat Clearers—I wouldn’t ask you to go a week without saying them; that would render most people, especially British people, mute—you will at the end of that week be a considerably better writer than your were at the beginning.
I tried to count how many times Russ and I use “very” in IPMB. I thought using the pdf file and search bar would make this simple. However, when I reached page 63 (a tenth of the way through the book) with 30 “very”s I quit counting, exhausted. Apparently “very” appears about 300 times.
Sometimes our use of “very” is unnecessary. For instance, “Biophysics is a very broad subject” would sound better as “Biophysics is a broad subject,” and “the use of a cane can be very effective” would be more succinct as “the use of a cane can be effective.” In some cases, we want to stress that something is extremely small, such as “the nuclei of atoms (Chap. 17) are very small, and their sizes are measured in femtometers (1 fm = 10−15 m).” If I were writing the book again, I would consider replacing “very small” by “tiny.” In other cases, a “very” seems justified to me, as in “the resting concentration of calcium ions, [Ca++], is about 1 mmol l−1 in the extracellular space but is very low (10−4 mmol l−1) inside muscle cells,” because inside the cell the calcium concentration is surprisingly low (maybe we should have replaced “very” by “surprisingly”). Finally, sometimes we use “very” in the sense of finding the limit of a function as a variable goes to zero or infinity, as in “for very long pulses there is a minimum current required to stimulate that is called rheobase.” To my ear, this is a legitimate “very” (if infinity isn’t very big, then nothing is). Nevertheless, I concede that we could delete most “very”s and the book would be improved.
Rather
I counted 33 “rather”s in IPMB. Usually Russ and I use “rather” in the sense of “instead” (“this rather than that”), as in “the discussion associated with Fig. 1.5 suggests that torque is taken about an axis, rather than a point.” I’m assuming Dreyer won’t object to this usage (but you know what happens when you assume...). Only occasionally do we use “rather” in its rather annoying sense: “the definition of a microstate of a system has so far been rather vague,” and “this gives a rather crude image, but we will see how to refine it.”
Really
Russ and I do really well, with only seven “really”s. Dreyer or no Dreyer, I’m not getting rid of the first one: “Finally, thanks to our long-suffering families. We never understood what these common words really mean, nor the depth of our indebtedness, until we wrote the book.”
Quite
I quit counting “quite” part way through IPMB. The first half contains 33, so we probably have sixty to seventy in the whole book. Usually we use “quite” in the sense of “very”: “in the next few sections we will develop some quite remarkable results from statistical mechanics,” or “there is, of course, something quite unreal about a sheet of charge extending to infinity.” These could be deleted with little loss. I would keep this one: “while no perfectly selective channel is known, most channels are quite selective,” because, in fact, I’m really quite amazed how so very selective these channels are. I would also keep “the lifetime in the trapped state can be quite long—up to hundreds of years,” because hundreds of years for a trapped state! Finally, I’m certain our students would object if we deleted the “quite” in “This chapter is quite mathematical.”
In Fact
I found only 24 “in fact”s, which isn’t too bad. One’s in a quote, so it’s not our fault. All the rest could go. The worst one is “This fact is not obvious, and in fact is true only if…”. Way too much “fact.”
Just
Russ and I use “just” a lot. I found 39 “just”s in the first half of the book, so we probably have close to eighty in all. Often we use “just” in a way that is neither “righteous” nor “merely,” but closer to “barely.” For instance, “the field just outside the cell is roughly the same as the field far away.” I don’t know what Dreyer would say, but this usage is just alright with me.
So
Searching the pdf for “so” was difficult; I found every “also,” “some,” “absorb,” “solute,” “solution,” “sodium,” “source,” and a dozen other words. I’m okay (and so is Dreyer) with “so” being used as a conjunction to mean “therefore,” as in “only a small number of pores are required to keep up with the rate of diffusion toward or away from the cell, so there is plenty of room on the cell surface for many different kinds of pores and receptor sites.” I also don’t mind the “so much…that” construction, such as “the distance 0.1 nm (100 pm) is used so much at atomic length scales that it has earned a nickname: the angstrom.” I doubt Russ and I ever use “so” in the sense of “dude, you are so cool,” but I got tired of searching so I’m not sure.
Pretty
Only one “pretty”: “It is
interesting to compare the spectral efficiency function with
the transmission of light through 2 cm of water (Fig. 14.36).
The eye’s response is pretty well centered in this absorption
window.” We did a pretty good job with this one.
Of Course
I didn’t expect to find many “of course”s in our book, but there are fourteen of them. For example, “both assumptions are wrong, of course, and later we will improve upon them.” I hope, of course, that readers are not offended by this. We could do without most or all of them.
Surely
None. Fussy Mr. Dreyer surely can’t complain.
That Said
None.
Actually
I thought Russ and I would do okay with “actually,” but no; we have 38 of them. Dreyer says that “actually…serves no purpose I can think of except to irritate.” I’m not so sure. We sometimes use it in the sense of “you expect this, but actually get that.” For example, “the total number of different
ways to arrange the particles is N! But if the particles
are identical, these states cannot be distinguished, and there
is actually only one microstate,” and “we will assume that
there is no buildup of concentration in the dialysis fluid…
(Actually, proteins cause some osmotic pressure difference,
which we will ignore.)”
Dreyer may not see its purpose, but I actually think this usage is justified. I admit, however, that it’s a close call, and most “actually”s could go.
Books I keep on my desk
(except for Dreyer’s English, which is a
library copy; I need to buy my own).
I was disappointed to find so many appearances of “very,” “rather,” “really,” “quite,” “in fact,” “just,” “so,” “pretty,” “of course,” “surely,” “that said,” and “actually” in Intermediate Physics for Medicine and Biology. We must do better.
For your own part, if you can abstain from these twelve terms for a week, and if you read not a single additional word of this book—if you don’t so much as peek at the next page—I’ll be content.
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
