Problems 1, 7, 17 and 19
Through the wall: how enzymes move hydrogen by quantum tunnelling
A hydrogen nucleus is light enough to behave like a wave. In many enzymes it does not climb over the reaction barrier; it passes through it.
The evidence comes from swapping hydrogen for deuterium and watching how much the reaction slows down.
Tunnelling beats hopping over the top at 300 K by 3.1×.
Rectangular barrier, WKB estimate P = exp(−2d√(2mU)/ħ) for a single attempt. Amplitudes inside the barrier are drawn on a compressed scale; the true decay is far steeper.
Why hydrogen, and not carbon
Every particle has a wavelength. For a proton at body temperature, the thermal de Broglie wavelength, λ = h / √(2πmkBT), is about 1 Å. That is as long as the distance a hydrogen moves when an enzyme transfers it from one atom to another. A carbon atom, twelve times heavier, has a wavelength under 0.3 Å and behaves almost classically. An electron, nearly two thousand times lighter, tunnels across 10–20 Å of protein routinely.
Tunnelling probability falls exponentially with the barrier's width and with the square root of the particle's mass. The panel above uses the simplest estimate, P = exp(−2d√(2mU)/ħ). Make the barrier a few tenths of an ångström wider and the probability drops by orders of magnitude. Replace hydrogen with deuterium and it drops much further.
- ~1 ÅProton wavelength
Comparable to the distance a hydrogen travels in a transfer reaction.
- ×2 massDeuterium
Same chemistry, same barrier, but a shorter wavelength and far less tunnelling.
- ~0.1 ÅDistance matters
Small changes in donor–acceptor distance change the tunnelling rate dramatically.
The isotope effect as a fingerprint
The kinetic isotope effect, KIE = k(H) / k(D), compares the rate with hydrogen to the rate with deuterium. Even without tunnelling it is larger than one: a C–H bond vibrates faster than a C–D bond, so it sits higher in its well by its zero-point energy, about 1.1 kcal/mol. That alone gives a KIE of about 7 at room temperature for breaking a C–H bond.
Tunnelling leaves three tell-tale signs:
- a KIE well above 7;
- an Arrhenius prefactor ratio A(H)/A(D) outside roughly 0.7–1.2;
- a KIE that changes little with temperature, even though it is large.
Soybean lipoxygenase-1 shows all three. Its KIE is about 80 at 30 °C, the ratio A(H)/A(D) is about 18, and the activation energies for H and D differ by under 1 kcal/mol.
Tunnelling signature: KIE above the semiclassical ceiling of about 7; A(H)/A(D) outside 0.7–1.2.
Measured by Knapp, Rickert and Klinman (2002): a KIE of about 80, almost independent of temperature.
What the protein does
The first clear evidence for hydrogen tunnelling in an enzyme came from yeast alcohol dehydrogenase in 1989. Since then it has been reported in dehydrogenases, oxidases, lipoxygenases and amine-oxidising enzymes. In aromatic amine dehydrogenase, combined experiments and simulations found that nearly all of the proton transfer happens by tunnelling.
The model most groups now use separates two things. The hydrogen tunnels in a single quantum step, and the protein's slower, classical motions decide how often donor and acceptor come close enough for that step to be likely. The temperature dependence of the reaction then reflects the protein's motions, not the hydrogen's.
Lipoxygenase gives the strongest support. Replacing leucines that pack against the substrate with smaller alanines keeps the KIE large but makes it strongly temperature dependent. Loosening the active site leaves the hydrogen further from its acceptor, and the protein has to work harder to bring them together.
For protein engineering, this means the active site's geometry and stiffness are design variables for the quantum step, not just for the chemistry around it.
What is still argued about
That hydrogen tunnels in enzymes is well established. How much it matters for catalysis is not. The same reactions also tunnel in solution, so tunnelling alone does not explain why an enzyme is millions of times faster. Arieh Warshel and others argue that the main source of catalysis is electrostatic preorganisation of the active site, and that protein dynamics do not drive the chemical step. Others, including Judith Klinman's group, argue that protein motions which shorten the tunnelling distance are part of how enzymes work.
Telling these views apart needs measurements that connect specific protein motions to the moment of transfer, on the right timescales. That is the kind of experiment our open problems ask for.
Where this leads on Quantum Proteins
Hydrogen tunnelling connects four of the open problems: tunnelling in enzyme catalysis, enzymatic hydrogen transfer, isotope effects in biological systems and nuclear quantum effects in hydrogen bonds. For the same physics in a light-driven protein, see channelrhodopsin.
Key papers
- Cha Y., Murray C. J., Klinman J. P. Hydrogen tunneling in enzyme reactions. Science 243 (1989).
- Knapp M. J., Rickert K., Klinman J. P. Temperature-dependent isotope effects in soybean lipoxygenase-1: correlating hydrogen tunneling with protein dynamics. J. Am. Chem. Soc. 124 (2002).
- Masgrau L. et al. Atomic description of an enzyme reaction dominated by proton tunneling. Science 312 (2006).
- Warshel A. et al. Electrostatic basis for enzyme catalysis. Chem. Rev. 106 (2006).
- Klinman J. P., Kohen A. Hydrogen tunneling links protein dynamics to enzyme catalysis. Annu. Rev. Biochem. 82 (2013).
- Bell R. P. The Tunnel Effect in Chemistry. Chapman and Hall (1980).
The panels are teaching models: a rectangular barrier with a single-attempt WKB estimate, and an Arrhenius model of the isotope effect. Real enzymes need thermally averaged, multidimensional treatments.