news & views the large number of catalytically active sites per fibril makes the catalytic performance of these structures, relative to their total protein mass, comparable to that of the natural carbonic anhydrase. The strategy by which Korendovych and co-workers engineered a self-assembling biocatalyst is astonishingly simple, because it relies on small peptide units that can be readily synthesized and modified by chemical methods. Peptide synthesis is not limited to proteinogenic amino acids, suggesting possibilities to use this methodology to generate chemical functionalities that are absent in natural proteins. As impressive as this work is, there are still some considerable challenges remaining: (i) to prove that the design principle can be used to engineer catalysts for other — and perhaps more complex — chemical reactions; (ii) to increase the catalytic efficiency; and (iii) to rationally design specificity for certain substrate molecules. The latter property has obviously been a crucial factor in the evolution of biological enzymes. In an enzyme’s active
site, specificity depends on the formation of a complex network of chemical interactions between the enzyme and substrate, often with one or both partners adopting a favourable conformation (known as an induced fit). Yet amyloid fibrils are comparatively rigid structures that possess rather smooth surfaces at their spines and lack deep cavities. This rigidity may be an additional burden when attempting to improve on catalytic efficiency, if the latter requires dynamically folded protein structures8. Finally, it is tempting to speculate as to whether amyloid toxicity in human diseases arises, at least in part, from the ability of amyloid structures to bind to metal ions that then allow new, highly detrimental, catalytic activities. A related mechanism has previously been suggested for Aβ peptide, the amyloid-forming peptide in Alzheimer’s disease, which was shown to bind Zn2+, Cu2+ or other metal ions by a histidine-rich motif and to exhibit catalytic activity. In that example, however, the fibril promotes redox reactions and the formation of
harmful reactive oxygen species9. A better demonstration of the full pathophysiological relevance of these catalytic processes, within the context of the numerous toxicity mechanisms that have been suggested for amyloidogenic peptides, will remain an important goal of future research. ❐ Tobias Aumüller and Marcus Fändrich are at the Institute for Pharmaceutical Biotechnology, Ulm University, Helmholtzstrasse 8/1, 89081 Ulm, Germany. e-mail: [email protected]; [email protected] References 1. Chiti, F. & Dobson, C. M. Annu. Rev. Biochem. 75, 333–366 (2006). 2. Knowles, T. P. J. & Buehler, M. J. Nature Nanotech. 6, 469–479 (2011). 3. Cherny, I. & Gazit, E. Angew. Chem. Int. Ed. 47, 4062–4069 (2008). 4. Sackewitz, M. et al. Protein Sci. 17, 1044–1054 (2008). 5. Pilkington, S. M., Roberts, S. J., Meade, S. J. & Gerrard, J. A. Biotechnol. Prog. 26, 93–100 (2010). 6. Rufo, C. R. et al. Nature Chem. 6, 303–309 (2014). 7. Verpoorte, J. A., Mehta, S. & Edsall, J. T. J. Biol. Chem. 242, 4221–4229 (1967). 8. Eisenmesser, E. Z. et al. Nature 438, 117–121 (2005). 9. Cassagnes, L-E. et al. Angew. Chem. Int. Ed. 52, 11110–11113 (2013).
REACTION KINETICS
Isotope effects feel the cold
Kinetic isotope effects are widely used to elucidate reaction mechanisms and are generally interpreted in terms of simple kinetic models. Measurements of this effect for the Penning ionization reaction between helium and dihydrogen highlight the need for a quantum description of chemical reaction rates when sub-kelvin temperatures are approached.
Mark Brouard
W
hen interpreting kinetic isotope effects for gas-phase chemical reactions one often resorts to simple models of reaction rates, such as transition state theory 1. These approximate theories are really only appropriate for reactions studied under relatively hightemperature conditions, at which quantum effects such as tunnelling or resonances are less important. Figure 1a illustrates the origin of the kinetic isotope effect for a direct reaction possessing a potential energy barrier of height ΔE. On the basis of transition state theory 1, the rate of a chemical reaction can be written as being proportional to e–ΔE/RT. Changes in barrier height therefore lead to exponential changes in the rate of chemical reaction. Within this model of thermal rate coefficients other factors may also play a role, such as the vibrational and rotational energy level structure, which would be accounted for by the partition functions 274
of the reactants and transition state. But differences in barrier heights associated with the zero-point vibrational energies of the species involved usually dominate the kinetic isotope effect. Within this simple treatment, reactions involving D2 as a reactant are typically slower than reactions involving H2, because D2 reactions tend to have lower zero-point energies and thus higher reaction barriers (Fig. 1a). However, this simple theoretical picture provides only an approximate description of chemical reaction rates and it is put under severe scrutiny when applied to reactions at very low temperatures. It is well known, for example, that as the temperature is lowered, quantum mechanical effects, such as tunnelling, play a more important role, and can lead to reaction rates that differ by many orders of magnitude from the values expected on the basis of the simple ideas outlined above. Now, writing in Nature Chemistry, Narevicius and colleagues
describe such unanticipated reaction rates for the Penning ionization process He* + H2 → He + H2+ + e– at milli-kelvin temperatures. Interestingly, they also see a kinetic isotope effect; however, its origins differ greatly from the standard kinetic isotope effect described above. To understand the phenomenon observed by Narevicius and colleagues, one must first understand what happens when reactants collide. Figure 1b illustrates the classical encounter between two reactants A and B, represented as structureless spheres2. The particles approach with a well-defined impact parameter, b, which determines whether the collision is head-on or glancing in nature. More formally, the impact parameter defines the magnitude of classical orbital angular momentum, |ℓ|, associated with the collision |ℓ| = μvb, where μ is the reduced mass of the reactant pair and v is their relative velocity. As the temperature of the
NATURE CHEMISTRY | VOL 6 | APRIL 2014 | www.nature.com/naturechemistry
© 2014 Macmillan Publishers Limited. All rights reserved
news & views
a
b
Transition state [X-H2]# [X-D2]#
c
ΔE A
ZPE(X + H2) ZPE(X + D2)
V(R)
|ℓ| > 0
b
Reactants
R
B |ℓ| = 0 Products
Figure 1 | Kinetic isotope effects at low temperature. a, The transition state (labelled #) for a simple direct reaction possessing a potential energy barrier. The kinetic isotope effect for a reaction X + H2 can be largely explained by the different zero-point energies (ZPEs) and thus barrier heights, ΔE, associated with different isotopic species, which alter the rates of the isotopic reactions. b, A classical encounter between reactants A and B at some well-defined value of the impact parameter, b, which determines whether the collision is glancing, b >> 0, or head-on, b = 0. c, An illustration of the role of the centrifugal barrier as the reactants approach (that is, as their separation R decreases). At particular energies (as illustrated by the dashed line in the figure), quasi-bound states can be supported by the barrier, leading to what are known as orbiting resonances, and collisions that take place at energies close to these states can result in a dramatic enhancement of the reaction rate. The black line shows the potential energy curve, V(R), when the orbital angular momentum, |ℓ|, is zero. The blue line shows V(R) when |ℓ| is greater than zero.
system is reduced, the relative velocity of the colliding partners becomes smaller, and it is more appropriate to replace the above classical equation for the orbital angular momentum by the corresponding quantum mechanical expression |ℓ| = ħ l(l + 1) , where l is the orbital angular momentum quantum number of the collision pair. Different orbital angular momenta correspond to different ‘partial waves’, with l = 0,1,2,… corresponding to s, p, d,… partial waves, respectively. Classically, the reaction rate is given by an integral over all possible impact parameters, b, whereas quantum mechanically, the rate is determined as a sum over all partial waves, indexed by the quantum number l. As the temperature is reduced, fewer and fewer orbital angular momentum ‘states’ contribute to the reaction, and eventually, as the temperature tends towards zero, only ‘s-wave’ scattering is observed, for which l = 0. In the classical case, this would correspond to a headon, zero-impact-parameter collision, although this picture should be treated with caution in the quantum mechanical, low-temperature regime. Collisions that occur with finite orbital angular momenta possess centrifugal rotational energy, Ecent = |ℓ|2/(2μR2), which can lead to a centrifugal barrier as the reactants approach (see Fig. 1c). This centrifugal barrier can result in short-lived quasi-bound states, leading to what are known as orbiting (or shape) resonances, and collisions that occur at energies close to such features often display a dramatic enhancement in the reaction rate,
mediated by resonant tunnelling through the centrifugal barrier. At temperatures close to ambient, quantum effects such as those described are hard to observe, because many l values contribute to the reaction, and the influence from individual resonances become obscured. Narevicius and coworkers, in beautiful merged-beam experiments3, measure4 the reaction rate for the aforementioned Penning ionization process He* + H2 → He + H2+ + e– and its isotopologues at low temperatures, for which only a few partial waves (l values) contribute to the reaction rate. This means that the effects of resonances can be clearly observed. At energies close to the orbiting resonances, reactants can tunnel through the centrifugal barrier. Once in close proximity, they have a far higher probability of undergoing autoionization, and a dramatic rise in reaction rate is observed. Furthermore, the energies of the resonances are shown to be exquisitely sensitive to isotopic substitution4. Replacing H2 by HD or D2 changes the reduced mass of the collision pair, μ, and hence significantly alters the centrifugal energy. This changes the temperatures at which resonance enhancement of the reaction rate is observed. Indeed, at certain temperatures the rate of reaction with D2 can be orders of magnitude faster than for the corresponding reactions with HD or H2, in contrast to the predictions of simple rate theory described above. Supporting state-of-the-art ab initio and quantum mechanical scattering calculations4, obtained using methods discussed by Siska5, confirm the quantum
NATURE CHEMISTRY | VOL 6 | APRIL 2014 | www.nature.com/naturechemistry
© 2014 Macmillan Publishers Limited. All rights reserved
mechanical interpretation of the observed kinetic isotope effect. Analogous to optical spectroscopy — in which a potential energy surface is adjusted through knowledge of spectroscopic transitions — collision spectroscopy can be used to refine the potential energy surface of a reaction through measurement of resonances observed in the reaction rate. Narevicius and colleagues were therefore also able to use the temperature and isotope dependence of the resonance structures to refine the potential energy surface used in their theoretical calculations, thereby obtaining excellent agreement between experiment and theory 4. Narevicius and co-workers’ experiments open the door to future studies of chemical reaction rates in the low-temperature regime, where quantum mechanical behaviour dominates. Such measurements will not only provide a detailed test of the quality of reaction rate calculations, but will also help shed new light on phenomena such as tunnelling and resonances. ❐ Mark Brouard is in the Department of Chemistry, University of Oxford, The Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, UK. e-mail: [email protected] References 1. Pilling, M. J. & Seakings, P. W. Reaction Kinetics (Oxford Univ. Press, 1995). 2. Brouard, M. & Vallance, C. Tutorials in Molecular Reaction Dynamics (Royal Society of Chemistry, 2010) 3. Henson, A. B., Gersten, S., Shagam, Y., Narevicius, J. & Narevicius, E. Science 338, 234–238 (2012). 4. Lavert-Ofir, E. et al. Nature Chem. 6, 332–335 (2014). 5. Siska, P. E. Rev. Mod. Phys. 65, 337 (1993).
275
site, specificity depends on the formation of a complex network of chemical interactions between the enzyme and substrate, often with one or both partners adopting a favourable conformation (known as an induced fit). Yet amyloid fibrils are comparatively rigid structures that possess rather smooth surfaces at their spines and lack deep cavities. This rigidity may be an additional burden when attempting to improve on catalytic efficiency, if the latter requires dynamically folded protein structures8. Finally, it is tempting to speculate as to whether amyloid toxicity in human diseases arises, at least in part, from the ability of amyloid structures to bind to metal ions that then allow new, highly detrimental, catalytic activities. A related mechanism has previously been suggested for Aβ peptide, the amyloid-forming peptide in Alzheimer’s disease, which was shown to bind Zn2+, Cu2+ or other metal ions by a histidine-rich motif and to exhibit catalytic activity. In that example, however, the fibril promotes redox reactions and the formation of
harmful reactive oxygen species9. A better demonstration of the full pathophysiological relevance of these catalytic processes, within the context of the numerous toxicity mechanisms that have been suggested for amyloidogenic peptides, will remain an important goal of future research. ❐ Tobias Aumüller and Marcus Fändrich are at the Institute for Pharmaceutical Biotechnology, Ulm University, Helmholtzstrasse 8/1, 89081 Ulm, Germany. e-mail: [email protected]; [email protected] References 1. Chiti, F. & Dobson, C. M. Annu. Rev. Biochem. 75, 333–366 (2006). 2. Knowles, T. P. J. & Buehler, M. J. Nature Nanotech. 6, 469–479 (2011). 3. Cherny, I. & Gazit, E. Angew. Chem. Int. Ed. 47, 4062–4069 (2008). 4. Sackewitz, M. et al. Protein Sci. 17, 1044–1054 (2008). 5. Pilkington, S. M., Roberts, S. J., Meade, S. J. & Gerrard, J. A. Biotechnol. Prog. 26, 93–100 (2010). 6. Rufo, C. R. et al. Nature Chem. 6, 303–309 (2014). 7. Verpoorte, J. A., Mehta, S. & Edsall, J. T. J. Biol. Chem. 242, 4221–4229 (1967). 8. Eisenmesser, E. Z. et al. Nature 438, 117–121 (2005). 9. Cassagnes, L-E. et al. Angew. Chem. Int. Ed. 52, 11110–11113 (2013).
REACTION KINETICS
Isotope effects feel the cold
Kinetic isotope effects are widely used to elucidate reaction mechanisms and are generally interpreted in terms of simple kinetic models. Measurements of this effect for the Penning ionization reaction between helium and dihydrogen highlight the need for a quantum description of chemical reaction rates when sub-kelvin temperatures are approached.
Mark Brouard
W
hen interpreting kinetic isotope effects for gas-phase chemical reactions one often resorts to simple models of reaction rates, such as transition state theory 1. These approximate theories are really only appropriate for reactions studied under relatively hightemperature conditions, at which quantum effects such as tunnelling or resonances are less important. Figure 1a illustrates the origin of the kinetic isotope effect for a direct reaction possessing a potential energy barrier of height ΔE. On the basis of transition state theory 1, the rate of a chemical reaction can be written as being proportional to e–ΔE/RT. Changes in barrier height therefore lead to exponential changes in the rate of chemical reaction. Within this model of thermal rate coefficients other factors may also play a role, such as the vibrational and rotational energy level structure, which would be accounted for by the partition functions 274
of the reactants and transition state. But differences in barrier heights associated with the zero-point vibrational energies of the species involved usually dominate the kinetic isotope effect. Within this simple treatment, reactions involving D2 as a reactant are typically slower than reactions involving H2, because D2 reactions tend to have lower zero-point energies and thus higher reaction barriers (Fig. 1a). However, this simple theoretical picture provides only an approximate description of chemical reaction rates and it is put under severe scrutiny when applied to reactions at very low temperatures. It is well known, for example, that as the temperature is lowered, quantum mechanical effects, such as tunnelling, play a more important role, and can lead to reaction rates that differ by many orders of magnitude from the values expected on the basis of the simple ideas outlined above. Now, writing in Nature Chemistry, Narevicius and colleagues
describe such unanticipated reaction rates for the Penning ionization process He* + H2 → He + H2+ + e– at milli-kelvin temperatures. Interestingly, they also see a kinetic isotope effect; however, its origins differ greatly from the standard kinetic isotope effect described above. To understand the phenomenon observed by Narevicius and colleagues, one must first understand what happens when reactants collide. Figure 1b illustrates the classical encounter between two reactants A and B, represented as structureless spheres2. The particles approach with a well-defined impact parameter, b, which determines whether the collision is head-on or glancing in nature. More formally, the impact parameter defines the magnitude of classical orbital angular momentum, |ℓ|, associated with the collision |ℓ| = μvb, where μ is the reduced mass of the reactant pair and v is their relative velocity. As the temperature of the
NATURE CHEMISTRY | VOL 6 | APRIL 2014 | www.nature.com/naturechemistry
© 2014 Macmillan Publishers Limited. All rights reserved
news & views
a
b
Transition state [X-H2]# [X-D2]#
c
ΔE A
ZPE(X + H2) ZPE(X + D2)
V(R)
|ℓ| > 0
b
Reactants
R
B |ℓ| = 0 Products
Figure 1 | Kinetic isotope effects at low temperature. a, The transition state (labelled #) for a simple direct reaction possessing a potential energy barrier. The kinetic isotope effect for a reaction X + H2 can be largely explained by the different zero-point energies (ZPEs) and thus barrier heights, ΔE, associated with different isotopic species, which alter the rates of the isotopic reactions. b, A classical encounter between reactants A and B at some well-defined value of the impact parameter, b, which determines whether the collision is glancing, b >> 0, or head-on, b = 0. c, An illustration of the role of the centrifugal barrier as the reactants approach (that is, as their separation R decreases). At particular energies (as illustrated by the dashed line in the figure), quasi-bound states can be supported by the barrier, leading to what are known as orbiting resonances, and collisions that take place at energies close to these states can result in a dramatic enhancement of the reaction rate. The black line shows the potential energy curve, V(R), when the orbital angular momentum, |ℓ|, is zero. The blue line shows V(R) when |ℓ| is greater than zero.
system is reduced, the relative velocity of the colliding partners becomes smaller, and it is more appropriate to replace the above classical equation for the orbital angular momentum by the corresponding quantum mechanical expression |ℓ| = ħ l(l + 1) , where l is the orbital angular momentum quantum number of the collision pair. Different orbital angular momenta correspond to different ‘partial waves’, with l = 0,1,2,… corresponding to s, p, d,… partial waves, respectively. Classically, the reaction rate is given by an integral over all possible impact parameters, b, whereas quantum mechanically, the rate is determined as a sum over all partial waves, indexed by the quantum number l. As the temperature is reduced, fewer and fewer orbital angular momentum ‘states’ contribute to the reaction, and eventually, as the temperature tends towards zero, only ‘s-wave’ scattering is observed, for which l = 0. In the classical case, this would correspond to a headon, zero-impact-parameter collision, although this picture should be treated with caution in the quantum mechanical, low-temperature regime. Collisions that occur with finite orbital angular momenta possess centrifugal rotational energy, Ecent = |ℓ|2/(2μR2), which can lead to a centrifugal barrier as the reactants approach (see Fig. 1c). This centrifugal barrier can result in short-lived quasi-bound states, leading to what are known as orbiting (or shape) resonances, and collisions that occur at energies close to such features often display a dramatic enhancement in the reaction rate,
mediated by resonant tunnelling through the centrifugal barrier. At temperatures close to ambient, quantum effects such as those described are hard to observe, because many l values contribute to the reaction, and the influence from individual resonances become obscured. Narevicius and coworkers, in beautiful merged-beam experiments3, measure4 the reaction rate for the aforementioned Penning ionization process He* + H2 → He + H2+ + e– and its isotopologues at low temperatures, for which only a few partial waves (l values) contribute to the reaction rate. This means that the effects of resonances can be clearly observed. At energies close to the orbiting resonances, reactants can tunnel through the centrifugal barrier. Once in close proximity, they have a far higher probability of undergoing autoionization, and a dramatic rise in reaction rate is observed. Furthermore, the energies of the resonances are shown to be exquisitely sensitive to isotopic substitution4. Replacing H2 by HD or D2 changes the reduced mass of the collision pair, μ, and hence significantly alters the centrifugal energy. This changes the temperatures at which resonance enhancement of the reaction rate is observed. Indeed, at certain temperatures the rate of reaction with D2 can be orders of magnitude faster than for the corresponding reactions with HD or H2, in contrast to the predictions of simple rate theory described above. Supporting state-of-the-art ab initio and quantum mechanical scattering calculations4, obtained using methods discussed by Siska5, confirm the quantum
NATURE CHEMISTRY | VOL 6 | APRIL 2014 | www.nature.com/naturechemistry
© 2014 Macmillan Publishers Limited. All rights reserved
mechanical interpretation of the observed kinetic isotope effect. Analogous to optical spectroscopy — in which a potential energy surface is adjusted through knowledge of spectroscopic transitions — collision spectroscopy can be used to refine the potential energy surface of a reaction through measurement of resonances observed in the reaction rate. Narevicius and colleagues were therefore also able to use the temperature and isotope dependence of the resonance structures to refine the potential energy surface used in their theoretical calculations, thereby obtaining excellent agreement between experiment and theory 4. Narevicius and co-workers’ experiments open the door to future studies of chemical reaction rates in the low-temperature regime, where quantum mechanical behaviour dominates. Such measurements will not only provide a detailed test of the quality of reaction rate calculations, but will also help shed new light on phenomena such as tunnelling and resonances. ❐ Mark Brouard is in the Department of Chemistry, University of Oxford, The Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, UK. e-mail: [email protected] References 1. Pilling, M. J. & Seakings, P. W. Reaction Kinetics (Oxford Univ. Press, 1995). 2. Brouard, M. & Vallance, C. Tutorials in Molecular Reaction Dynamics (Royal Society of Chemistry, 2010) 3. Henson, A. B., Gersten, S., Shagam, Y., Narevicius, J. & Narevicius, E. Science 338, 234–238 (2012). 4. Lavert-Ofir, E. et al. Nature Chem. 6, 332–335 (2014). 5. Siska, P. E. Rev. Mod. Phys. 65, 337 (1993).
275
