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In some of those enzymes that break stable C–H bonds the reaction proceeds purely by quantum tunneling, without the need to partially ascend the barrier.. Earlier reviews on enzyme catal

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M I N I R E V I E W

A new conceptual framework for enzyme catalysis

Hydrogen tunneling coupled to enzyme dynamics in flavoprotein and quinoprotein enzymes

Michael J Sutcliffe1,2and Nigel S Scrutton1

Departments of 1 Biochemistry and 2 Chemistry, University of Leicester, UK

Recent years have witnessed high levels of activity in

iden-tifying enzyme systems that catalyse H-transfer by quantum

tunneling Rather than being restricted to a small number of

specific enzymes as perceived initially, it has now become an

accepted mechanism for H-transfer in a growing number of

enzymes Furthermore, H-tunneling is driven by the

thermally induced dynamics of the enzyme In some of those

enzymes that break stable C–H bonds the reaction proceeds

purely by quantum tunneling, without the need to partially

ascend the barrier Enzymes studied that fall into this

cate-gory include the flavoprotein and quinoprotein amine

dehydrogenases, which have proved to be excellent model

systems These enzymes have enabled us to study the

rela-tionship between barrier shape and reaction kinetics This has involved studies with slow and fast substrates and enzymes impaired by mutagenesis A number of key ques-tions now remain, including the nature of the coupling between protein dynamics and quantum tunneling The wide-ranging implications of quantum tunneling introduce a paradigm shift in the conceptual framework for enzyme catalysis, inhibition and design

Keywords: H-tunneling; transition state theory; protein dynamics; flavoprotein; quinoprotein; kinetic isotope effect; computational simulation; quantum mechanics; stopped-flow kinetics; molecular mechanics

I N T R O D U C T I O N

The text-book description of catalysis states that enzymes

reduce the energy required to surmount the barrier between

reactants and products, which leads to enhanced rates This

classical over-the-barrier treatment, known as transition

state theory (TST), has been used to depict

enzyme-catalysed reactions over the last 50 years [3] Indications

that TST cannot be applied indiscriminately came in the late 1980s and the 1990s In these instances [4–11], however, the experimental observations could be modelled satisfactorily

by using a modified form of TST which incorporates an additional component, a quantum tunneling correction factor [1]; this permits tunneling below the saddle-point of the potential energy surface (i.e in these instances, the saddle point of the potential energy surface is never reached) The first indication that TST (with tunneling correction) may not model faithfully all enzyme catalysed systems came in 1996 [12]; these data show large deviations from classical TST behaviour The acid test of the generic applicability of TST to enzyme catalysed reactions came in

1999 from experimental studies on enzymes catalysing C–H bond breakage Our own studies with methylamine dehy-drogenase [13], and almost simultaneously that of Klinman and coworkers independently with thermophilic alcohol dehydrogenase [14], identified that, rather than ascending the classical energy barrier prior to tunneling, the reaction proceeds solely by quantum tunneling Furthermore, this work illustrated that quantum tunneling is driven by thermal vibrations of the enzyme-substrate complex, which serve to increase the tunneling probability (by reducing the width and/or height of the barrier) sufficiently for tunneling

to occur (Fig 1) Thus, at the dawn of the 21st century some enzymes were shown to gain their catalytic power from quantum mechanics—arguably the key scientific develop-ment of the 20th century; indeed the first suggestion that quantum mechanical tunneling may be a significant factor

in chemical reactions involving the transfer of hydrogen was made by Hund some 70 years ago [15]

Although to some individuals biological systems and quantum mechanics seem poles apart, with hindsight the

Correspondence to M J Sutcliffe or N S Scrutton,

Department of Biochemistry, University of Leicester,

University Road, Leicester LE1 7RH, UK.

Fax: + 44 116252 3369, Tel.: + 44 116223 1337,

E-mail: sjm@le.ac.uk or nss4@le.ac.uk

Abbreviations: TST, transition state theory; TTQ, tryptophan

trypto-phylquinone; MADH, methylamine dehydrogenase; AADH,

aroma-tic amine dehydrogenase; TMADH, trimethylamine dehydrogenase;

TSOX, heterotetrameric sarcosine dehydrogenase; KIE, kinetic

iso-tope effect; QM/MM, quantum mechanical/molecular mechanical.

Definitions: Strictly, the term semiclassical [1] rather than classical is

used to indicate the difference in zero point vibrational energies of C–H

and C–D bonds in studies using the kinetic isotope effect as a probe of

quantum tunneling In this review, we have used the term classical to

indicate over-the-barrier transfer to avoid confusion on the part of a

reader less familiar with the concepts of quantised vibrational energy

states Quantum tunneling allows the hydrogen to travel through the

barrier This is made possible by wave–particle duality A particle

cannot pass through – it must pass over-the-barrier However, wave–

particle duality also gives the hydrogen wave-like properties, and this

allows it to pass through a region (i.e the barrier) from which a particle

would be excluded See reference [2] for a more detailed description of

quantum tunneling.

(Received 7 March 2002, revised 21 May 2002, accepted 6 June 2002)

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only major surprise is perhaps that the key role of quantum

tunneling in enzyme catalysed H-transfer reactions is only

now being realized After all, quantum tunneling is an

attractive means of transferring hydrogen from reactant to

product for those enzyme-catalysed reactions with large

activation barriers, where it is difficult to understand how

the reaction can occur over-the-barrier Additionally, all

regions of the enzyme (not just the active site) likely

contribute to the vibrations that drive quantum tunneling,

thus providing a possible reason for why enzymes are much

larger than the active site alone Also, vibrationally assisted

quantum tunneling is, for example, well established as a

means of H-transfer in metals [16] and for enzyme-mediated

electron transfer [17,18] (a proton is much heavier than an

electron, reducing the probability for a proton to tunnel; this

is one reason why enzymatic H-tunneling was not

consid-ered a plausible mechanism until experimental results

proved otherwise) H-transfer in nonbiological systems is

also known to occur by quantum tunneling, but at low

temperatures (cf enzymatic H-tunneling, which occurs at

room temperature); for example, along hydrogen bonds in

benzoic acid dimers [19] and in the cyclic network of four

hydrogen bonds in calix[4]arene [20]

Earlier reviews on enzyme catalysed tunneling have

focussed on the inadequacies of TST for some enzyme

reactions and the first descriptions of H-tunneling aided by

protein motion along the reaction coordinate [2,21–23]

This review article summarizes our more recent kinetic

work on H-transfer by tunneling in quinoprotein and

flavoprotein enzymes that catalyse the oxidation of a

number of amine substrates, and computational studies of

enzymic H-tunneling in these enzymes

Q U I N O P R O T E I N A N D F L A V O P R O T E I N

A M I N E D E H Y D R O G E N A S E S

The quinoprotein and flavoprotein amine dehydrogenases are ideally suited to studies of H-transfer The reactions catalysed are conveniently divided into reductive and oxidative half-reactions Enzyme reduction occurs by breakage of a substrate C–H bond, the kinetics of which are conveniently followed by absorbance spectrophotome-try owing to reduction of the redox centre (and concomitant change in absorbance spectrum) in the enzyme active site The oxidative half-reaction usually involves long-range electron transfer to acceptor proteins (e.g cytochromes, copper proteins or other flavoproteins) The ability to interrogate each half-reaction by stopped-flow methods simplifies substantially the kinetic analysis Studies of steady-state reactions are often compromised by the inab-ility to focus on a single chemical step, owing to the existence of multiple barriers for binding, product release and a number of chemical steps, each of which may contribute to the overall catalytic rate Using the stopped-flow method, the chemical step can often be isolated and the true kinetics of C–H bond breakage determined without complications arising from other events in the catalytic sequence This feature of redox catalysis by the flavoprotein and quinoprotein enzymes makes them attractive targets for studies of H-transfer during substrate oxidation For this reason, our work has focused on the tryptophan tryptophyl-quinone (TTQ)-dependent amine oxidases methylamine dehydrogenase (MADH) and aromatic amine dehydroge-nase (AADH), and also the flavoenzymes trimethylamine dehydrogenase (TMADH) and heterotetrameric sarcosine

Fig 1 Schematic representation of the three

key steps involved in enzyme catalysed

H-tun-neling The TTQ-substrate iminoquinone

adduct and the active site aspartate (Asp428)

are represented as sticks Protein dynamics

(step 1) facilitate transfer of a proton from the

TTQ-substrate iminoquinone adduct to

Asp428 by quantum tunneling (step 2) In step

3, the proton is trapped on the aspartate

carboxyl group by subsequent protein

vibrations.

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dehydrogenase (TSOX) High resolution crystallographic

structures are available for MADH and TMADH, which has

also opened up complementary computational chemistry

studies of H-transfer in these enzymes

T T Q - D E P E N D E N T M E T H Y L A M I N E

D E H Y D R O G E N A S E A N D H E T E R O T E R A

-M E R I C S A R C O S I N E O X I D A S E

Our initial studies were focused on TTQ-dependent

MADH TTQ reduction is concerted with C–H bond

cleavage from an iminoquinone intermediate that forms

rapidly in the reductive half-reaction (Fig 2) The rate of

reduction of the TTQ cofactor has a large kinetic isotope

effect (KIE¼ 16.8 ± 0.5 at 298 K), larger than the upper

value expected for reactions described by transition state

theory, and is suggestive of tunneling Tunneling reactions

are associated with KIE values greater than unity, owing to

the higher probability of proton over deuterium tunneling

The inflated KIE for MADH prompted us to study the

temperature dependence of this reaction Reactions that

proceed purely by quantum tunneling are independent of

temperature, and thus the KIE should likewise be

inde-pendent of temperature Our studies of TTQ reduction in

MADH indicated that the value of the KIE was

tempera-ture independent, but significantly the reaction rate was

strongly dependent on temperature! Our explanation of this

anomalous finding was to couple protein dynamics to the

reaction coordinate (Fig 1); in other words, temperature

dependent fluctuations of the enzyme-substrate complex are

required to distort the active site into a geometry that is

compatible with a pure tunneling reaction These (isotope

independent) fluctuations required to drive the tunneling

reaction give rise to the temperature dependence of the

reaction The inferences drawn from our experimental data

are congruent with theoretical models of H-tunneling in

enzymes that invoke motion in the protein and/or substrate

as part of the tunneling reaction [24–26] An earlier study [27]

had observed temperature-independent KIE values ( 2–3)

in steady-state reactions catalysed by serine proteases

performed in deuterated solvent, and these were suggested

to indicate tunneling Note, however, that the effect of D2O

on the reaction dynamics is potentially complicated owing to

the exchange of protons throughout the protein scaffold

The data were modelled on earlier theoretical treatments of

H-tunneling propounded by Dogonadzhe and coworkers

[27] in which thermal vibrations bring the solvent into a

configuration favourable to tunneling

The observation of pure tunneling coupled to protein dynamics represents a major departure from the more traditional static barrier, quantum correction depictions

of TST that have been used to rationalize H-tunneling effects in enzymes Pure tunneling is an attractive means of promoting a reaction that has a high potential energy barrier However, H-tunneling occurs over relatively short distances (e.g  0.5 A˚) A key feature of the dynamic barrier model is the role of protein motion in transiently compressing the width of the potential energy barrier, which promotes the tunneling reaction Dynamic fluctuations in protein structure also prevent transfer from the product to reactant side of the potential energy surface Following tunneling from donor to acceptor atoms, distortion of the active site geometry away from the optimal configuration effectively traps the H nucleus on the product side of the barrier Pure tunneling (i.e tunneling without first ascending the barrier) facilitated by protein dynamics is a radically different view of enzyme catalysis compared with the alternative over-the-barrier depictions, but how general is this phenomenon? Soon after our own findings with MADH, Klinman and colleagues demonstrated extreme tunneling coupled to protein motion in a thermophilic alcohol dehydrogenase [14] They also made the interesting finding that the tunneling contribution was less at mesophi-lic temperatures where the low frequency vibrational modes

of the protein are less excited Our own work has been extended in the direction of H-tunneling with other amine oxidases to demonstrate the general importance of pure tunneling coupled to enzyme dynamics We have demon-strated that the C–H/C–D bond breakage catalysed by TSOX gives rise to a temperature independent KIE and that reaction rate is strongly dependent on temperature, consis-tent with a pure tunneling reaction driven by motion of the enzyme-substrate complex [28] TSOX is a flavoprotein, and our work with this enzyme, together with that of Klinman’s work with thermophilic alcohol dehydrogenase, was an early indication that pure tunneling reactions may occur in different enzyme families More recent reports have also made the connection between enzyme dynamics and tunneling [29] and in at least one case tunneling has been invoked in the reappraisal of the catalytic mechanism of the aspartate proteinase family of enzymes [30] Our own work, and that of others, on the link between dynamics and tunneling is inferred from the results of kinetic studies The findings are of potential fundamental importance, thus an independent method of assessing the role of tunneling in enzymes was sought Our approach here has been to use

Fig 2 Reproductive half-reaction of MADH (A) A reaction mechanism for the oxidation of methylamine by MADH The boxed reaction step is the step studied computationally The base in this reaction corresponds to an aspar-tate residue (Asp428) in MADH (B) The active site of MADH; the QM region is shown unshaded with link atoms circled.

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computational chemistry methods, which are described in

the following section

C O M P U T A T I O N A L S T U D I E S

O F H - T U N N E L I N G I N M E T H Y L A M I N E

D E H Y D R O G E N A S E

How can we gain a detailed picture of enzymic H-tunneling

reactions at the atomic level? Computational modelling

methods provide an answer in the form of combined

quantum mechanical/molecular mechanical (QM/MM)

methods These can simulate the contribution of quantum

tunneling to enzyme-catalysed reactions In the QM/MM

approach, a small region at the active site is treated

quan-tum mechanically, and is coupled to a simpler molecular

mechanics description of the surrounding protein and

solvent (Fig 2) This allows the reaction catalysed by the

enzyme to be modelled whilst including the effects of the

protein environment

H-Tunneling in the oxidative demethylation of

methyl-amine by MADH is a system well suited to study using the

QM/MM approach; a crystal structure of MADH has been

determined, and we have a large body of experimental data,

and the H-tunneling step is rate-limiting The H-tunneling

step, the step we have studied computationally, involves the

abstraction by the active site base (Asp428) of a proton

(C–H bond breakage) from the iminoquinone (Fig 2) Our

approach [31] was to determine the potential energy surface

over which the reaction proceeds, and then to calculate the

extent of tunneling by following the reaction over this

surface Details of the approach are as follows First, the

structure of the iminoquinone was produced by adding

methylamine to the TTQ in the crystal structure of

Methylophilus methylotrophusMADH (Fig 2B) The

par-tial charges of the iminoquinone were calculated using

SPARTAN(Wavefunction Inc., Irvine, CA, USA); the entire

protein (including iminoquinone) was then protonated and

solvated, and energy minimized Next the QM region was

defined as comprising the sidechain of the active site base

and the sidechain of the catalytically active modified

tryptophan of the TTQ that forms an adduct with

methylamine (Fig 2B) QM/MM calculations were then

performed to determine the reactant, product and transition

state structures, keeping the link atoms and MM atoms

fixed [32] and usingGAUSSIAN94 [33] andAMBER4.1 [34] A

reaction path profile was then generated, usingPOLYRATE

[35] and the transmission coefficient (extent of tunneling)

calculated

This computational study suggested that approximately

96% of the reaction proceeds by tunneling through the

barrier, whereas only 4% of the reaction occurs via the

classical over-the-barrier route Similar results were found in

an independent study [36], where 99% of the reaction was

calculated to proceed by tunneling through the barrier and

1% over-the-barrier This degree of tunneling with MADH

is significantly larger than that observed in other protein

systems; the next largest is approximately 60% of the

reaction proceeding via tunneling in liver alcohol

dehydrog-enase [37] Also, a significant tunneling correction is needed

to get closer to the experimental KIE value at 298 K; no

tunneling correction yields a KIE of 6.1, the largest

tunneling correction yields 11.1 and the experimental value

is 16.8 ± 0.5 [13] Interestingly, in the independent study

mentioned [36], the calculated KIE with tunneling correc-tion was 18.3, falling to 5.9 when tunneling was omitted

A R O M A T I C A M I N E D E H Y D R O G E N A S E :

S L O W E R S U B S T R A T E S C O M P R O M I S E

R E A C T I O N R A T E S B Y D I F F E R E N T

M E A N S

Aromatic amine dehydrogenase (AADH), like MADH, is a TTQ-dependent amine oxidase AADH transfers electrons, derived from the deamination of primary amines (aromatic amines are generally preferred over simple aliphatic amines),

to azurin [38] As with MADH, the rate-limiting step in the reductive half-reaction is abstraction by an active site base

of a proton (C–H bond breakage) from an iminoquinone intermediate (Fig 2) We used stopped-flow kinetics to study C–H bond breakage in three different substrates by Alcaligenes faecalisAADH [39], the fast substrates dopam-ine and tryptamdopam-ine, and the slow substrate benzylamdopam-ine Again,aswithMADHandTSOX,anindicationasto whether H-transfer occurs classically or by quantum tunneling was gained by investigating the temperature dependence of the rates of C–H and C–D bond breakage, and analysing this using an Eyring plot This indicated that, whilst the rates of both C–H and C–D bond breakage are temperature dependent for all three substrates, the KIEs are temperature independent Also, for dopamine and benzylamine (a) there was no significant difference between the apparent activa-tion energy (or to be more precise the enthalpy of activation) for C–H and C–D bond breakage (C–H bond breakage in tryptamine was too rapid to observe above

277 K), and (b) the ratio of the Arrhenius-like pre-exponential factors [13] was comparable with the KIE This illustrates that protium and deuterium do not ascend the potential energy barrier and that vibrationally assisted quantum tunneling is the mechanism for H- and D-transfer for all three substrates Additionally, the enthalpy of activation for benzylamine (67.1 ± 0.9 kJÆmol)1) is

 15 kJÆmol)1 higher than both that for trypta-mine (53.5 ± 1.2 kJÆmol)1) and that for dopamine (51.9 ± 1.1 kJÆmol)1), suggesting that more energy is required to deform the enzyme-substrate iminoquinone intermediate with tryptamine

How does barrier shape change with substrate? The relative rates of C–H and C–D bond breakage in dopamine, tryptamine and benzylamine, and the relative KIEs, give important insight into the shape of the potential energy barrier separating reactants from products Although a fluctuating potential energy barrier is consistent with our experimental observations, the tunneling event can be visualized as a two-step process (see, for example, [2,13,21]) (Fig 1) The first step is dynamic, and is required to activate the enzyme–substrate complex by thermal vibration In essence, this leads to a crossing over of the potential energy surfaces of the enzyme-substrate and enzyme–product complexes Once this crossing point is populated, the second step (H-transfer by quantum tunneling) can occur Thus, although the enzyme is dynamic, the barrier can be considered rigid for the lifetime of the tunneling event Our conceptual framework therefore uses a rigid barrier depic-tion of H-tunneling

To understand the effect of barrier shape on tunneling rates, the factors that enhance tunneling need to be

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considered These are (a) a small particle mass and (b) a

small area under the potential energy barrier The barrier

also needs to be sufficiently high to favour tunneling rather

than classical over-the-barrier reactions; high, narrow

barriers are particularly favoured for efficient tunneling

Based on these criteria, we investigated the compatibility of

different barrier shapes with our experimental rates and

KIEs [39] These data are inconsistent with both a

rectangular energy barrier and a truncated parabolic energy

barrier (Fig 3), two commonly used, idealized barrier

shapes However, the data are consistent with more complex

barrier shapes (Fig 3), the true nature of which remain to be

established

C O M P R O M I S I N G M U T A T I O N S

A N D E N Z Y M A T I C H - T U N N E L I N G

Over the years, the transition state theory has been the

foundation for our quantitative understanding of the effects

of compromising mutations on enzyme catalysis Altered

enzymic rates have often been modelled as changes in the

stabilities of transition states and ground states But how do

we rationalize the effects of compromising mutations in

those enzymes known to catalyse C–H bond breakage by

pure tunneling? Is reduced catalytic rate solely attributable

to changes in barrier width and height? Clearly, increases in

width and height will lead to lower tunneling probability

Mutations within the active site will also likely affect the

thermal fluctuations coupled to the reaction coordinate, and

may lead to differences in (a) the energetics of barrier

compression (as seen for benzylamine and AADH; [39])

and/or (b) extent of barrier compression (i.e is the active site

more relaxed in a mutant enzyme compared with the native

enzyme?) In the latter scenario, the equilibrium distance

between donor and acceptor atoms is larger and thus a

greater degree of thermal motion is required to form a geometry consistent with quantum tunneling This has been discussed recently in reactions catalysed by lipoxygenase and mutants thereof [40] We have attempted to gain an early insight into the effects of compromising mutations on catalysis by studying C–H and C–D bond breakage in TMADH In the wild-type enzyme, C–H bond cleavage is fast (> 1200 s)1[41]), and a number of transient kinetic, computational and mutagenesis studies [42–45] have indi-cated that the mechanism of flavin reduction in TMADH involves nucleophilic attack of the substrate lone pair on the C4a atom of the flavin followed by C–H bond breakage (Fig 4) Evidence now favours the transfer of hydrogen from the substrate methyl to the flavin N5 The rate of C–H bond breakage is lowered > 100-fold in a H172Q mutant TMADH [44], and by an additional factor of 4 in a Y169F mutant TMADH [43] Both His172 and Tyr169 are located near the substrate-binding site and the flavin isoalloxazine ring as part of a His-Tyr-Asp triad [42], and their mutation will likely lead to altered dynamics within the active site A KIE accompanies flavin reduction in the wild-type and mutant enzymes [44,46] The very fast flavin reduction rates

of wild-type TMADH with protiated substrate has preven-ted us from performing detailed temperature-dependence studies of this reaction However, we have shown with H172Q TMADH that the KIE is independent of tempera-ture over the experimental range (277–297 K) and that reaction rates are strongly dependent on temperature [46] This suggests, as with MADH [13] and TSOX [28], that the reaction proceeds by pure tunneling driven by protein motion Comparable studies with Y169F TMADH revealed a small temperature dependence on the KIE The data cannot be understood in terms of the TST We have previously suggested this might be due to partial thermal excitation of substrate (i.e partial ascent of the barrier)

Fig 3 Schematic illustrating how changing barrier width affects tunneling through a variety

of potential energy barriers Arrows indicate the paths of H and D nuclei; solid lines denote the classically allowed regions and dashed lines the classically disallowed (quantum tun-neling) regions The top two barriers (the rectangular barrier and truncated parabolic barrier) are commonly used idealized barrier shapes; these do not agree with the experi-mentally observed trends in rates and KIEs [39] The bottom barrier is a possible barrier shape that is consistent with the experiment-ally observed trends in both rates and KIEs [39] In this barrier, it is the narrowest part of the barrier, rather than the whole barrier, that becomes progressively wider, with the concave shoulder becoming progressively less pro-nounced For a full discussion of the effects of barrier shape on tunneling rate and KIE val-ues see reference [39].

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prior to H-tunneling by a vibrationally assisted

mechan-ism, although a Boltzman analysis suggests a very small

population in anything other than the vibrational ground

state An alternative explanation might be found in

invoking a more relaxed active site with larger degree of

vibrational motion required to reach a geometry

consis-tent with tunneling Our observations with Y169F

TMADH also find parallels with our recent data for the

reaction of MADH with the slow substrate ethanolamine

[39]

F U T U R E P E R S P E C T I V E S

Recent studies have established the importance of

H-tunneling in enzyme catalysis In the last three years, pure

tunneling (i.e without partial barrier ascent) driven by

protein motion has become established as a mechanism for

the enzymic breakage of C–H bonds; this may be a general

strategy for these energetically difficult reactions Our

current understanding of how protein motion is coupled

to the reaction coordinate is lacking, and unravelling this

represents a major challenge for the future As this

understanding is gained, H-tunneling can then be used as

a tool for (a) increasing the catalytic efficiency of enzymes in

the biotechnology industry (by enhancing the coupling of

dynamics to the reaction coordinate), and (b) producing

more effective enzyme inhibitors in the pharmaceutical

industry (by dampening those vibrations coupled to the

reaction coordinate) Such advances have broader

implica-tions, as they will also give insight into the role of dynamics

in driving classical over-the-barrier reactions—these issues

also impact on the tuning of enzyme performance under

extreme conditions (e.g high/low temperature) Thus, the

key challenge for the future is elucidating the inseparable

relationship between protein dynamics and

classical/quan-tum enzyme mechanisms

A C K N O W L E D G E M E N T S

The work described in this article was funded by the UK Biotechnology and Biological Sciences Research Council, the Wellcome Trust and the Lister Institute of Preventive Medicine N S S is a Lister Institute Research Professor.

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Fig 4 Our proposed mechanism for the oxidation of trimethylamine by

TMADH, which is based on mechanistic studies [45,46] and by analogy

with the work of Edmondson on monoamine oxidase [47] It is important

to note that steps 1 and 2 of this scheme are likely to be concerted; the

second species shown is therefore not intended to represent a true

enzyme intermediate Enz, enzyme.

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