Tunneling That ClicksBonus ⑤ / Do living things use tunneling?

Sorting "quantum biology" into three ── demonstrated, promising hypothesis, and walked back

Do living things use tunneling? The answer is yes. But somewhere other than where the headlines were.
The most certain case is the reaction you are breathing with right now.
The detection tool is Episode 5's isotope effect ── swap hydrogen for deuterium and see if orders change.

Tools you'll need: \(T_0\) from Episode 3, the isotope effect from Episode 5, the Arrhenius law The heart of this episode: k_H/k_D ≫ 7 means it is tunneling

The phrase "quantum biology" comes with equal parts expectation and wariness. When "quantum coherence" in photosynthesis appeared in Nature in 2007 it was reported as "plants use quantum computing," and it was substantially walked back afterwards. Meanwhile, there are quantum effects that are completely established and never make the news ── every time you breathe, electrons tunnel across 15 Å. This episode sorts the relationship between life and tunneling into three: ① firmly demonstrated ② promising but still hypothesis ③ walked back or refuted. The sorting tool is the same trick that pinned down the phonon mechanism of BCS in Episode 5 ── the isotope effect.

01The detection tool ── swap hydrogen for deuterium

Tunneling is ferociously sensitive to mass (exercise 4 of Episode 1, \(T_0\propto1/\sqrt m\) in Episode 3). So replacing hydrogen with deuterium and comparing the rates tells you whether tunneling is happening. The ratio \(k_H/k_D\) is called the kinetic isotope effect (KIE).

The classical upper limit is about 7

The KIE is not one even without tunneling. A C–H bond has zero-point motion, and deuterium lowers the frequency by \(1/\sqrt2\), lowering the zero-point energy and raising the energy needed to break the bond.

$$\Delta\mathrm{ZPE}=\tfrac12\hbar\omega\left(1-\tfrac{1}{\sqrt2}\right)\approx 0.054\ \mathrm{eV} \quad\Longrightarrow\quad \frac{k_H}{k_D}=e^{\Delta \mathrm{ZPE}/k_BT}\approx \mathbf{7\text{–}8}\ (298\ \mathrm{K})$$

That is the "classical upper limit." So ── if \(k_H/k_D\) at room temperature substantially exceeds 7, it is tunneling. Exactly the logic by which the isotope effect became evidence for the phonon mechanism in Episode 5.

02What do real enzymes do?

Systemk_H/k_D (298 K)Verdict
an ordinary organic reaction2–7within the classical range
aromatic amine dehydrogenaseabout 55tunneling
soybean lipoxygenase (SLO-1)about 80tunneling (the flagship case in the field)

SLO-1's value of 80 is more than ten times the classical limit. And there is a second clincher ── the rate has almost no temperature dependence. As Episode 3 showed, temperature-independent means tunneling.

In fact, room temperature is already on the tunneling side

Put a C–H stretching vibration (about 3000 cm⁻¹ = 0.37 eV) into Episode 3's \(T_0=\hbar\omega_b/2\pi k_B\):

$$T_0=\frac{\hbar\omega}{2\pi k_B}\approx \mathbf{690\ K}$$

Room temperature (298 K) is far below that divide. That is, hydrogen transfer inside living things is already in the tunneling regime from the outset. Nothing special is happening ── hydrogen is light, so at the temperatures of life it happens automatically.

03Try it ── judging by the isotope effect

The figure applies Episode 3's tools directly to hydrogen and deuterium. Above, Arrhenius plots for the two; below, their ratio \(k_H/k_D\). The classical limit (7) and SLO-1's measured value (80) are marked.

Raise the frequency (stiffen the bond) or the barrier and the KIE leaps. Confirm that the vertical line for body temperature already sits to the left of the divide.

Figure: above = Arrhenius plots for hydrogen (H) and deuterium (D), applying Episode 3's T₀ = ℏω_b/2πk_B to each via ω ∝ 1/√m. Below = the rate ratio k_H/k_D, with the classical limit of 7 and SLO-1's measured 80 marked
hydrogen (H) deuterium (D) rate ratio k_H/k_D classical limit (7)

04The most certain case ── your breathing

The most firmly established quantum effect in biology involves not hydrogen but electrons. And it never makes the news ── because it is too obvious.

Electron transfer in respiration and photosynthesis

In the mitochondrial respiratory chain, electrons hop from metal centre to metal centre inside proteins. The distances are 10–20 Å. In between is protein, which to an electron is a barrier. Classically it could never be crossed.

It is crossed because they tunnel. The rate falls cleanly and exponentially with distance (Dutton's ruler) ── about a factor of ten for every 1.7 Å. Exactly the same form as the scanning tunneling microscope in bonus ③.

Between the oxygen you inhale and the water it becomes, electrons tunnel many times. This is not a hypothesis; it is basic biochemistry, established by Marcus theory and a vast body of measurement. Photosynthesis moves its electrons the same way.

This fact is a good antidote to how the phrase "quantum biology" gets used ── of course living things use quantum effects; chemical bonds are a quantum effect. The question worth asking is not "are there quantum effects?" but "are there special quantum effects that ordinary chemistry cannot explain?"

05Promising but still hypothesis ── a bird's magnetic compass

Migratory birds sense the Earth's magnetic field. The leading candidate mechanism is the radical-pair mechanism.

The strong evidence: the compass is light-dependent (it needs blue light); it reads inclination rather than polarity (impossible for a magnetic compass); and weak radio waves at particular frequencies disrupt the birds' orientation ── which corresponds to spin resonance of a radical pair. In 2021 cryptochrome-4 from migratory birds was also shown to respond magnetically in vitro.

But the chain is not yet closed

Between in-vitro magnetic sensitivity and the behaviour of a living bird there is a chain that has not been established ── whether cryptochrome really plays that role in the retina, and how the signal reaches the nervous system. A promising hypothesis, not an established mechanism. Also, strictly speaking this is not tunneling but spin coherence.

06Walked back ── "quantum coherence" in photosynthesis

This is the part this episode most owes the reader honestly.

YearEvent
2007Engel and colleagues (Nature). Two-dimensional electronic spectroscopy of the light-harvesting protein (FMO) of green sulfur bacteria showed oscillations lasting 660 fs at 77 K, interpreted as long-lived electronic coherence enhancing energy transport
2007–2014Widely reported as "plants use quantum computers." The starting point of the "quantum biology" boom
late 2010sReanalysis proceeds. The long-lived oscillations were concluded to be largely not electronic coherence but mixing with molecular vibration (vibronic). Pure electronic coherence at physiological temperature lasts under 100 fs
presentCoherence exists but is short-lived, and there is no evidence that it plays an essential role in improving efficiency. The prevailing understanding is that photosynthesis's high efficiency is well explained by conventional (semiclassical) Förster/Redfield theory
This is not a failure of science The 2007 measurement itself was correct and an excellent experiment. What was wrong was the interpretation and the way it was reported. And over ten years the community corrected it itself.
Compare it with cold fusion in bonus ① ── there, the controversy continues without reproducibility; here, the result reproduced and the interpretation shrank. The latter is a far healthier course. The field of "quantum biology" itself became more serious after this correction.

07Refuted ── the vibrational theory of smell

One more example, this one leaning clearly toward refutation. Does the sense of smell read a molecule's shape, or its vibrational frequencies?

In 1996 Turin proposed that receptors work like inelastic tunneling spectroscopy, reading molecular vibration frequencies. An attractive hypothesis, and a testable one ── deuterate the molecule and the frequencies change, so the smell should change.

The tests came out negative. Humans cannot distinguish deuterated musks, and the human musk receptor has been shown not to discriminate isotopes. The vibrational theory is not currently supported. (Discrimination has been reported in fruit flies, but other explanations besides smell have been suggested.)

This is a good example ── a testable hypothesis was proposed, tested, and refuted. As science, one could not ask for a better course.

08The sorting table

Life and tunneling ── ordered by strength of evidence
PhenomenonTypeStrength of evidence
electron transfer in respiration and photosynthesiselectron tunnelingestablished (basic biochemistry)
hydrogen transfer in enzymes (SLO-1 and others)proton/hydrogen tunnelingestablished (KIE ≈ 80, no temperature dependence)
DNA base tautomerisation and mutationproton tunnelinga contribution exists, but its share of total mutation is undetermined
a bird's magnetic compass (radical pairs)spin coherencea promising hypothesis. Demonstrated in vitro; the in-vivo chain incomplete
long-lived electronic coherence in photosynthesiselectronic coherencewalked back. Mostly vibrational in origin; no demonstrated contribution to efficiency
the vibrational theory of smellinelastic tunnelingnegative

Conclusion: living things do use tunneling ── quietly, and openly. The pattern is that the more loudly something was reported, the more it shrank; and the thing that was never reported (breathing) is the most certain of all.

◇ ◇ ◇
The honest line

Established: that the semiclassical upper limit of the kinetic isotope effect at room temperature is about 7–8; that SLO-1 has a KIE of about 80 with weak temperature dependence and is the representative case of hydrogen tunneling; other large-KIE examples such as aromatic amine dehydrogenase; that the crossover temperature \(T_0\) estimated from the C–H stretch exceeds room temperature, so hydrogen transfer in living systems is inherently in the tunneling regime; that long-range electron transfer in proteins is tunneling (Marcus theory, the distance-dependent "Dutton's ruler"); the observation of oscillations in two-dimensional spectroscopy of the photosynthetic FMO complex (Engel et al. 2007) and the subsequent reanalysis concluding the long-lived component is mostly vibrational in origin; that migratory birds' compasses are light-dependent, inclination-based and disrupted by weak radio waves, and the in-vitro magnetic sensitivity of cryptochrome-4; and the negative human tests of the vibrational theory of smell.

Caveats and open questions: (1) The figure applies Episode 3's simple model (a parabolic barrier plus a zero-point-energy correction) to H and D; it is not a calculation reproducing real enzyme rates. Real theory treats these as proton-coupled electron transfer (PCET) coupled to environmental fluctuations. (2) Whether enzymes evolved to promote tunneling is debated. The claim that "enzymes exploit motions that shorten the donor–acceptor distance" coexists with the claim that "tunneling is just a property of light particles, not a special enzymatic trick." (3) The radical-pair mechanism is a promising hypothesis; the full in-vivo mechanism is not established. It is also spin coherence, not tunneling. (4) On photosynthesis the statement is not "coherence does not exist" but "it exists but is short-lived, and no functional contribution to efficiency has been shown." (5) The relation between proton tunneling in DNA and mutation is theoretically supported as a contribution, but its quantitative share of actual mutation rates is undetermined. (6) On the vibrational theory of smell, isotope discrimination has been reported in fruit flies, but non-olfactory routes have been suggested.

Exercises
  1. Why is \(k_H/k_D=80\) at room temperature evidence for tunneling?
    See the answer
    Because the semiclassical upper limit from the zero-point energy difference alone is about 7–8. Eighty is more than ten times that, explicable only by tunneling, which depends exponentially on mass. And the near absence of temperature dependence matches Episode 3's "tunneling does not depend on temperature."
  2. Why is "do living things use quantum effects?" not a very good question?
    See the answer
    Because chemical bonds are themselves quantum effects, so the answer is trivially yes. The good question is "are there special quantum effects that ordinary chemistry cannot explain?" Put that way you can sort: electron tunneling in respiration and hydrogen tunneling in enzymes, definitely yes; long-lived coherence in photosynthesis, (currently) no.
  3. "A factor of ten for every 1.7 Å" in protein electron transfer matches which other episode?
    See the answer
    Bonus ③'s scanning tunneling microscope (about an order per 0.1 nm = 1 Å) ── the same form. Both are \(I\) or \(k\propto e^{-2\kappa d}\); only the barrier height, and hence the coefficient, differs. Exactly the same physics of distance riding on the exponent.
  4. What is the difference between the photosynthesis "quantum coherence" story and cold fusion in bonus ①?
    See the answer
    In photosynthesis the measurement reproduced and the interpretation shrank. In cold fusion the reproducibility of the measurement itself is not established. The former is a normal case of science self-correcting; the latter has gone thirty years unresolved. "The story got smaller" and "it never got settled" are entirely different things.

Bonus ⑤ summaryThey do use it ── quietly, and openly

The tool for judging is the isotope effect, the same as in Episode 5. From zero-point energy alone the room-temperature limit on \(k_H/k_D\) is 7–8. Soybean lipoxygenase gives about 80, with almost no temperature dependence ── Episode 3's "tunneling does not depend on temperature," verbatim. In fact the C–H stretch gives \(T_0\approx690\) K, so the temperatures of life are already in the tunneling regime. Nothing special; just a consequence of hydrogen being light.

And the most certain example is somewhere that never makes the news ── electron transfer in respiration and photosynthesis. Electrons tunnel across 10–20 Å, with rates falling by a factor of ten per 1.7 Å (the same form as the STM in bonus ③). Every time you breathe, electrons tunnel.

Meanwhile the heavily publicised claims shrank. Photosynthesis's "long-lived electronic coherence" is mostly vibrational in origin, with no demonstrated contribution to efficiency. The vibrational theory of smell is negative. A bird's magnetic compass is a promising hypothesis (and spin coherence, not tunneling). The unreported case is the most certain and the reported ones shrank the most ── that pattern itself teaches you how to read this field.

This document is Bonus ⑤ of the "Tunneling That Clicks" series, a reading piece for physics-loving high-schoolers and undergraduates. The semiclassical upper limit on the kinetic isotope effect, the large KIE and weak temperature dependence of soybean lipoxygenase (SLO-1), that the crossover temperature estimated from the C–H stretch exceeds room temperature, that long-range electron transfer in proteins is tunneling (Marcus theory and the empirical distance rule), the two-dimensional spectroscopy of the photosynthetic FMO complex (Engel et al. 2007) and the subsequent reanalysis attributing the long-lived component mainly to vibration, the light dependence, inclination sensitivity and radio-wave disruption of migratory birds' compasses together with the in-vitro magnetic sensitivity of cryptochrome-4, and the negative human tests of the vibrational theory of smell are all published results. That the figure applies Episode 3's simple model rather than reproducing enzyme rates, that whether enzymes evolved to promote tunneling is debated, that the radical-pair mechanism is a hypothesis and involves spin coherence rather than tunneling, that on photosynthesis the statement is "coherence exists but its functional contribution is unshown," that the quantitative share of DNA proton tunneling in mutation rates is undetermined, and that fruit-fly reports on the vibrational theory admit other explanations ── all spelled out in the body's "honest line." ── To print, use your browser's "Print" and "Save as PDF" (in the print version the sliders and answers are frozen and hidden). Adjacent: Bonus ④, How many seconds does tunneling take? / Bonus ⑥, Thirty years of room-temperature superconductivity / Contents / sister series Learning That Clicks.

Print / make a PDF: ⌘+P (Ctrl+P on Windows). On screen, moving the barrier height and frequency shows how far k_H/k_D exceeds the classical limit of 7. "Match SLO-1" sets conditions near the measured value of 80. "See the answer" opens each solution.