Role of quantum effects
in proton transfer reactions
catalysed by enzymes
Ross McKenzie
condensedconcepts.blogspot.com
condensedconcepts.blogspot.com
condensedconcepts.blogspot.com
Theoretical chemical physics @UQ
Quantum many-body theory of complex
molecular materials
• Excited states of flourescent proteins and
methine dyes
• Organometallic complexes for LEDs and
solar cells
• Oxygen vacancies in cerium oxides
• Effective Hamiltonians for superconducting
and antiferromagnetic organic charge
transfer salts
condensedconcepts.blogspot.com
Outline
• Many believe quantum tunneling plays a key role in
hydrogen transfer reactions catalysed by enzymes
• However, there is only indirect evidence for quantum
tunneling from kinetic isotope studies
• A path integral approach shows tunneling can only
occur below a temperature T0 determined by the
curvature of the top of energy barrier.
• Quantum transition state theory describes temperature
dependence of kinetic isotope effects for 2 enzymes
claimed to exhibit tunneling
• Ref:J. Bothma, J. Gilmore, & RHM, arXiV.0910.1150
condensedconcepts.blogspot.com
condensedconcepts.blogspot.com
Key questions about proton
transfer reactions & enzymes
• Is quantum tunneling a necessary hypothesis to
explain the experimental results?
• To what extent is it necessary to go beyond
semi-classical transition state theory to explain
the observed kinetic isotope effects?
• If tunneling does occur, is it actually important for
the function of the enzyme?
• If so, have enzymes evolved in a manner that
enhances the contribution of tunneling?
condensedconcepts.blogspot.com
A clear case of proton tunneling in
a small molecule
Barrier is too high
for thermal activation.
Proton tunnels
but deuterium does
not.
Schreiner et al.,
Nature 453, 906
(2008)
condensedconcepts.blogspot.com
Klinman & Kohen's hypothesis
“The optimization of enzyme catalysis may
entail the evolutionary implementation of
chemical strategies that increase the
probability of tunneling and thereby
accelerate the reaction rate”
Acc. Chem. Res. 31, 397 (1998)
condensedconcepts.blogspot.com
Refuting the hypothesis
Doll, Bender, & Finke,
JACS 125, 10877 (2003)
synthetic catalyst
analogues of
Methylmalonyl-CoA
mutase had same
reaction rates and
isotope effects
condensedconcepts.blogspot.com
Temperature dependence of kinetic isotope effect
is same for non-enzymatic catalysts
Methylmalonyl-CoA mutase
• Actually we have shown that one does not
even need tunneling to describe this data!
condensedconcepts.blogspot.com
Evidence for tunneling?
Magnitude and temperature dependence of
kinetic isotope effects
Soybean lipoxygenase
Knapp et al., JACS
124, 3865 (2002)
condensedconcepts.blogspot.com
Evidence for tunneling
• Arrenhius form for reaction rate
L=H,D,T
• Semi-classical transition state theory
corrects for zero-point motion
condensedconcepts.blogspot.com
Quantum Kramers theory
Hanggi et al., Rev. Mod. Phys. 62, 251 (1990)
condensedconcepts.blogspot.com
Path integral approach
• Allows treatment of quantum effects, nonzero temperature and environment (protein +
water)
• Evaluate integral in semi-classical limit
• Imaginary time periodic solutions to classical
equations of motion describe tunneling
(called instantons or bounce solution)
• Only exist for T<
condensedconcepts.blogspot.com
Instantons describe tunneling
Miller (1975), Coleman,
Leggett, Weiss, …
condensedconcepts.blogspot.com
Quantum transition state theory
For T>T0 rate determined by quantum
fluctuations about the transition state
(tunneling just below the barrier and
reflection just above the barrier)
condensedconcepts.blogspot.com
Quantum transition state theory
• Kinetic isotope effect
ωb
ω0
condensedconcepts.blogspot.com
Quantum TST describes data
Methylmalonyl-CoA mutase
& synthetic analogues
Doll et al., 2003
• Fit gives T0 = 250 K, i.e., no tunneling
condensedconcepts.blogspot.com
Quantum TST describes data
• bovine
Monoamine oxidase
Jonnson et al.,
Biochemistry 1994
condensedconcepts.blogspot.com
Effect of the environment
• Enzyme and solvent are environment of
active site
• Modelled by a bath of harmonic oscillators
& Caldeira-Leggett Hamiltonian
• Produces frequency-dependent friction on
the reaction co-ordinate
condensedconcepts.blogspot.com
Frequency-dependent friction
• Quantum correction factor to semi-classical
reaction rate (Wolynes, 1982)
• Only high-frequency modes z > 1000 cm-1
affect the reaction rate
condensedconcepts.blogspot.com
Conclusions
• Claims that proton tunneling plays a key role in
enzymes need to be evaluated more critically
• A path integral approach shows tunneling can
only occur below a temperature T0 determined
by the curvature of the top of energy barrier.
• Quantum transition state theory describes temp
dependence of kinetic isotope effects for 2
enzymes claimed to exhibit tunneling
J. Bothma, J. Gilmore, & RHM, arXiV.0910.1150
condensedconcepts.blogspot.com