Chemical Physics Letters 491 (2010) 230–236
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Optimal control design of laser pulses for mode specific vibrational excitation in an enzyme–substrate complex Qinghua Ren, Kara E. Ranaghan, Adrian J. Mulholland, Jeremy N. Harvey, Frederick R. Manby, Gabriel G. Balint-Kurti * Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, UK
a r t i c l e
i n f o
Article history: Received 2 February 2010 In final form 30 March 2010 Available online 2 April 2010
a b s t r a c t High level combined quantum mechanics/molecular mechanics (QM/MM) methods are used to calculate the potential energy and dipole moment surfaces for the motion of the labile proton in an intermediate in the catalytic cycle of aromatic amine dehydrogenase (AADH). Quantum tunnelling is important in transfer of this tryptamine proton. Optimal control theory is used here to design laser pulses to excite the labile proton from its lowest to selected vibrationally excited states. Such pulses leading to excitation of specific vibrational modes might in future be useful to promote reactivity by enhancing proton tunnelling; we discuss practical difficulties in carrying this out. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction A central goal in chemical physics is the control of chemical reactions using shaped laser pulses. Optimal control theory (OCT) provides an efficient approach to the theoretical design of such pulses. It was pioneered in this context by Rabitz and co-workers [1,2] and has been recently reviewed by one of the authors [3]. From an experimental standpoint the ‘closed loop’ concept [4,5] has led to many successful applications of laser control of chemical processes [6,7]. The application of optimal control theory, in a theoretical context, requires knowledge of the quantum mechanical behaviour of the system during its interaction with a laser pulse. This approach [8,9] has not previously been applied to an enzyme reaction. Experiments and simulations show that in many enzyme catalysed reactions, the transfer of hydrogen (as hydrogen atom, proton or hydride) is the rate-determining step and that quantum mechanical tunnelling often plays a vital role in the reaction mechanism [10–15]. The rate-determining proton transfer step in the oxidative deamination of tryptamine catalysed by the enzyme aromatic amine dehydrogenase (AADH) is an excellent example [16,17]. The reductive half reaction of AADH with tryptamine proceeds via several steps [16], involving a tryptophan tryptophyl quinone (TTQ) cofactor. The crucial step involves proton transfer from an iminoquinone (Schiff base) intermediate, to an aspartate side chain (Asp128b). The sequence of these reactions is shown in Fig. 2 of Ref. [16]. The pre-reaction complex of the oxidative deamination of tryptamine catalysed by AADH has been well * Corresponding author. E-mail address:
[email protected] (G.G. Balint-Kurti). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.03.089
characterized and is illustrated in Fig. 1. A tantalising prospect in biochemical research is the designed, quantum control of enzyme reactions, for example designed excitation of particular vibrational states to augment or hinder a particular reaction. Designed excitation of particular vibrational states could significantly influence tunnelling rates. We show here that such excitation may indeed in principle be possible, by using OCT to design shaped infrared (IR) laser pulses for the excitation of the AADH–tryptamine substrate complex to specified vibrational quantum states. The pre-reaction complex of the oxidative deamination of tryptamine catalysed by AADH has been well characterized in previous quantum mechanics/molecular mechanics (QM/MM) studies [16,17]. The labile hydrogen can transfer to either one of the two oxygen atoms of the carboxylate base (Asp128b) and these alternative reaction paths show significantly different tunnelling behaviour [17]. In the present work we take the view that because of the relatively light mass of the labile hydrogen atom it will move far faster than the heavier atoms between which it is being transferred. As a first approximation we may therefore hold the heavier atoms and the rest of the framework fixed while taking account only of the motion of the hydrogen atom in the rigid framework of the rest of the complex. The initial vibrational quantum state of the proton within the complex will undoubtedly have a large effect on the rate of the chemical reaction. We will study two types of vibrational motion, namely excitation of the C–H–O bending and stretching motions. Excitation of the bending motion is likely to affect the choice of the oxygen atom to which the transfer will be made, while excitation of the stretching motion may directly affect the rate of the reaction. For an enzyme reaction involving tunnelling, the initial vibrational quantum state of the proton within the complex will
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Fig. 1. The active site of the AADH–iminoquinone complex (denoted as III in Fig. 2 of Ref. [16]) optimized using B3LYP/6-31G(d)-CHARMM27 QM/MM techniques. The proton (H1) is transferred from C1 to either one of two carboxylate oxygen atoms (O1 or O2) of the catalytic base, Asp128b in the rate-determining step of the reaction. Some important hydrogen bonds present in the active site are indicated by dotted lines.
undoubtedly have a large effect on the rate of the chemical reaction and on the propensity of the proton to tunnel through the reaction barrier. Fig. 2 shows the initial and final wavefunctions of the labile proton within the reactive iminoquinone complex (III) for an excitation from its ground vibrational state to one possessing a single quantum of stretching vibration along the C1–H–O2 bond. In this present work we show that it is possible to design a shaped IR laser pulse to excite the labile proton to a preselected excited vibrational state. Section 2 describes the QM/MM and OCT methods used, Section 3 presents the results, while Section 4 contains a short summary and discussion of the work. 2. Theory 2.1. Quantum mechanics/molecular mechanics (QM/MM) method and calculation of potential energy and dipole moment surfaces QM/MM methods [18,19] permit the realistic atomistic modelling of chemical reactions occurring in a condensed environment where the reaction is influenced by the presence of many nearby atoms, e.g. in enzymes. The proton transfer in the reaction of tryptamine catalysed by AADH has been investigated in detail with QM/ MM methods [16,17], as have similar enzymes such as methylamine dehydrogenase [20,21]. The rate-determining step has been shown to be the transfer of a proton from a saturated carbon atom to a nearby (carboxylate) oxygen [16]. Previous modelling applied semi-empirical methods such as PM3 [22] for the quantum mechanical part of the calculations. In the present application we wish to model the motion of the reacting proton and its interaction with the laser field. For this purpose we perform QM/MM calculations to map out the potential energy and dipole moment surfaces governing this motion. The molecule interacts with the laser radiation via its electric dipole moment. The dipole moment is a vector quantity and depends on the molecular geometry. We evaluate its value at each of the geometries at which the energy of the system is computed. This provides
Fig. 2. Schematic illustration of excitation process showing initial v ¼ 0 and final v ¼ 3 vibrational wavefunctions for the motion of the labile proton in the C1–H1– O2 plane of the reactive AADH complex.
a vector field. In the present initial treatment we assume that the laser is linearly polarized with its electric field vector lying in the C1–H1–O plane. The central core of the complex, consisting of 48 atoms including 3 link atoms, was treated quantum mechanically using a density functional, B3LYP [23,24]/6-31G(d) [25], approach. The remaining 8134 atoms are treated within an MM framework using the JAGUAR [26] and TINKER [27] computer codes together with the CHARMM27 [28] force field. The QM and MM parts of the calculation were interfaced using the QOMMMA software [29–31]. Fig. 3 shows the partitioning between the QM (shaded) and MM parts of the system. The B3LYP method provides a good description of the proton transfer reaction, and yields potential energy and dipole moment surfaces of good quality [20,32]. As already discussed, the labile proton is relatively light and therefore moves much further and faster than the other atoms in the system. As a first approximation we therefore hold all the other atoms fixed in the equilibrium geometry of the QM/MM optimized reactant complex and treat only the motion of the proton moving in the framework of the other atoms. Justification for this initial approach is provided by the fact that kinetic isotope effects calculated (by VTST/SCT) with a fixed protein environment agree well with experiment [16]. It has also been shown that this reaction is not driven by long-range protein dynamics effects [16]. As shown previously [16,17], transfer to either of the two carboxylate oxygens of Asp128b is possible in AADH (designated O1
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Y (a)
ε H θ
C
X
(b)
5 4 3 2 1 0
−0.2 0.2 0.6
0.3
0.9
1.5 X /Å
2.1
1 2.7 1.4
Y/ Å
E /eV
O
Fig. 4. (a). Schematic illustration of the coordinate system for H1 moving in the C1– H1–O plane. (b) B3LYP (6-31G(d))/CHARMM27 QM/MM potential energy surface for the motion of the proton H1 in the C1–H1–O2 plane. The C1–O2 separation is fixed at 2.995 Å. Fig. 3. Schematic diagram of the active site of the tryptamine–AADH system showing the QM/MM partitioning used in the calculations. Atoms within the shaded region are treated using QM at the B3LYP/6-31G(d) level with the rest of the enzyme model included using the CHARMM27 force-field. Hydrogens in circles represent link atoms used to fill the valence of covalent bonds ‘broken’ by the partitioning into QM and MM regions.
and O2 here, as in Ref. [16], but designated OD1 and OD2 in more systematic nomenclature). In the case of transfer to O1, we use the vectors C1–H1 and O1–H1 to define a plane in three dimensional space and examine the motion of the H1 atom, or proton, restricted to this two-dimensional plane. Similarly the dipole moment is also projected onto the plane and only the two components of the dipole in this plane are considered. Fig. 4a shows schematically the coordinate system we use. Also shown in the figure is an electric field vector . We will consider the use of linearly polarized light with its polarization direction pointing in different selected directions in the C–H–O plane. The carbon atom is taken as the origin of the coordinate system. While we have considered the motion of the labile proton in both the C1– H1–O1 and the C1–H1–O2 planes, previous analysis [16,17] has shown that the reaction is most likely to take place by proton transfer to oxygen atom O2. We therefore concentrate our description on the motion in the C1–H1–O2 planes. Fig. 4b shows a depiction of the potential energy surface in this plane. The surface in the C1–H1–O1 plane has a qualitatively similar form. 2.2. Time-dependent propagation method in two spatial dimensions In the present work, the nuclear dynamics of the AADH reaction complex under the influence of the electric field is treated by solving the time-dependent Schrödinger equation (TDSE):
i
o @wðR; tÞ n b ¼ T m ðRÞ þ VðRÞ l ðtÞ wðR; tÞ: @t
ð1Þ
We solve this equation using the split operator method [33,34]. The nuclear wavefunction is represented on a two dimensional grid in X and Y coordinates. One hundred and twenty eight grid points are used in each direction. The parameters used in the solution of the TDSE are shown in Table 1. The action of the radial part
b m ðRÞ, on the wavefunction is comof the kinetic energy operator, T puted using the Fourier transform method advocated by Kosloff [35,36]. Eq. (1) is written in terms of atomic units and all calculations are performed in these units. 2.3. Optimal control theory and conjugate gradient maximization In order to design a laser pulse to drive a system from an initial state, wðt ¼ 0Þ, to a final target state U at a fixed time t = T, the laser field is optimized so as to transform the wavefunction as completely as possible from the initial state to the specified final state. The underlying theory is based on the work of Peirce et al. [1,2]. In the present work we follow the methods described in Refs. [37,38]. An objective functional J is first defined by:
JðÞ ¼ jhwðTÞjUij2 a0 2 Re
Z 0
Z
T
½ðtÞ4 dt
0
T
hvðtÞj
@ b ðtÞÞjwðtÞidt : þ i HðR; @t
ð2Þ
The first term is the overlap of the computed wavefunction at time T with the target state wavefunction. This is the most important term in the objective functional and must be maximized so as to achieve our objective as closely as possible. The second term is a penalty function designed to limit the total energy of the laser pulse. ðtÞ is the electric field strength as a function of time and
Table 1 Details of grid and other parameters used in the solution of the time-dependent Schrödinger equation. Parameter
O1
O2
Range of radial grid points in X direction (Å) Range of radial grid points in Y direction (Å) Number of radial grid points in X direction Number of radial grid points in Y direction Number of time steps h (degrees)
0.5–2.7 0.45 to 0.95 128 128 262 144 45
0.3–2.6 0.15 to 1.35 128 128 262 144 45
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the parameter a0 is a positive parameter which we set at 150 [37]. vðtÞ is an undetermined Lagrange multiplier which ensures that the system satisfies the time-dependent Schrödinger equation at all times. 3. Results 3.1. Potentials and dipole moments from QM/MM calculations The QM/MM calculated potential energy surface for the inplane motion of the labile H atom (proton) (holding all the remaining 8178 atoms fixed at the equilibrium geometry of the reactant species) is shown in Fig. 4b for the case of proton transfer to oxygen atom O2. The potential has a distinct minimum. Using twodimensional spline interpolation on our grid of calculated potential energy points, we find that the minimum energy is situated at X = 0.789 Å, Y = 0.760 Å, which is quite similar to the coordinates of the optimized geometry structure (X = 0.794 Å, Y = 0.763 Å). The potential also has an incipient secondary minimum at a C1– H1 separation of 1.9 Å corresponding to the products in which the proton has been transferred to the oxygen atom O2. The dipole moment in the X direction is shown in Fig. 5a and the dipole moment in the Y direction is shown in Fig. 5b. 3.2. Optimal control calculations Our objective in the current study is to excite the motion of the proton from its lowest vibrational state to higher lying states. The first step is to calculate the different vibrational states. This is accomplished using numerical variational methods we have developed previously [39]. The wavefunctions for two of these vibrational states are shown in Fig. 2. The calculations yield also the energies of the vibrational states. The energy differences are then useful in determining the frequency of the radiation which will be most effective in accomplishing the desired excitation process. Table 2 presents the results of the OCT calculations for designing laser pulses to excite the AADH reactant complex from its lowest to its first and third excited vibrational states. The first excited vibrational state corresponds to excitation of motion perpendicular
−1 −2 −3 −4 −5 −6 0.3
0.9
1.5 X /Å
2.1
1 2.7 1.4
Å
−0.2 0.2 0.6
0.3
0.9
1.5 X /Å
2.1
2.7
1 1.4
Å
−0.2 0.2 0.6
Y/
μY /a.u.
(b)
0 −1 −2 −3 −4
Fig. 5. B3LYP (6-31G(d))/CHARMM27 QM/MM calculated dipole moment surfaces for the motion of the proton H1 in the C1–H1–O2 plane. (a) X component of dipole moment. (b) Y component of dipole moment.
v ¼0!v ¼1
and
Results
O1
O2
For ðv ¼ 0Þ ! ðv ¼ 1Þ Total time (ps) Optimal yield (%) Max. field amplitude (a.u.) Iterations
1.935 93.95 0.001291 14
4.814 99.24 0.003571 5
For ðv ¼ 0Þ ! ðv ¼ 3Þ Total time (ps) Optimal yield (%) Max. field amplitude (a.u.) Iterations
1.935 99.77 0.0008445 3
2.020 98.52 0.0009635 3
to the C–O coordinate while the third excited vibrational state corresponds to excitation of motion along the C–O coordinate, i.e. along the direction which ultimately leads to proton transfer and reaction. In each calculation the electric field polarisation vector was fixed at a chosen value of h (see Fig. 4a). The results were sensitive to this chosen value and we present here only the results for the value of h found to give the highest yield or population of the target state at the end of the laser pulse. For all processes examined (i.e. the vibrational excitations from v ¼ 0 to v ¼ 1 or v ¼ 3 for both the C1–H1–O1 and the C1–H1–O2 planes) an angle of h ¼ 45 was found to give the best results. The results are also sensitive to the pulse duration and to the chosen initial laser field strength and the values shown in Table 2 have been obtain only after very many calculations, many of which did not yield good results. However, once a ‘good’ combination of the pulse duration and the initial field strength has been found the optimized results are stable with respect to small variations. (A 10% increase in the pulse duration led to a change of 0.1% in the optimal yield and a 10% change in the initial field strength led to no discernible change at all.) Transition probabilities of 93.95% and 99.77% are achieved, respectively, for the two processes for O1 and transition probabilities of 99.24% and 98.52% for O2. The qualitative details of the OCT calculations and of the final optimized laser pulses for the excitations in the C1–H1–O1 and C1–H1–O2 planes are similar. 3.2.1. AADHðv ¼ 0Þ ! AADHðv 0 ¼ 1Þ excitation for H1 in the C1–H1– O2 plane The initial trial field is set as:
ðtÞ ¼ 0:001cosðx0!1 tÞsðtÞ;
Y/
μX /a.u.
(a)
Table 2 Results of the OCT calculations for the vibrational excitations v ¼ 0 ! v ¼ 3 in the tryptamine–AADH reaction complex.
ð3Þ 13
where x0!1 ¼ 0:0052729 a:u: ð3:469 10 s1 or 1157 cm1 Þ and corresponds to the ðv ¼ 0Þ ! ðv ¼ 1Þ vibrational transition frequency in the complex. The pulse duration T is 4.814 ps divided into 2 Nt ¼ 262 144 time intervals. The envelope function sðtÞ ¼ sin ðpt=TÞ has a single maximum and is zero at the extremes of t ¼ 0 and t ¼ T. This structure is preserved during the optimization. The low and high cut-off frequencies of the filter, (see Eq. (11) in the Ref. [38]), are x‘ ¼ 1:0 1013 s1 and xh ¼ 4:5 1013 s1 , respectively. The angle of the electric field of the linearly polarized light with the X-axis is h ¼ 45 . The optimized laser pulse yields a probability of 99.24% for the excitation of the AADH reaction complex from its ground vibrational state ðv ¼ 0Þ to its first excited vibrational state ðv 0 ¼ 1Þ and the maximum value of the electric field in the optimized pulse is only 0.003571 a.u. (1:8363 109 V=m). Fig. 6a shows the converged optimized electric field as a function of time. Using the Fourier transform method to analyze its spectrum, it can be seen that the frequency spectrum is mainly centered at the frequency m ¼ m0 ! 1 ¼ 3:469 1013 s1 (see Fig. 6b) which corresponds to the m0!1 transition energy, and is the same as the initially guessed
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0.006
where x0!3 ¼ 0:012839 a:u: ð8:448 1013 s1 or 2818 cm1 Þ and corresponds to the ðv ¼ 0Þ ! ðv ¼ 3Þ vibrational transition frequency in the complex. The pulse duration T is 2.020 ps divided into Nt ¼ 262 144 time intervals. The optimized laser pulse yields a probability of 98.52% for the excitation of the AADH reaction complex from its ground vibrational state ðv ¼ 0Þ to its third vibrationally excited state ðv 0 ¼ 3Þ and the maximum value of the electric field in the optimized pulse is only 0:0009635 a:u: ð0:4955 109 V=mÞ. Fig. 7a shows the converged optimized electric field as a function of time. It can be seen that the frequency spectrum is centered at the frequency m ¼ m0!3 ¼ 8:448 1013 s1 which corresponds to the m0!3 transition energy, and is the same as the initially guessed value (see Fig. 7b). It suggests that the mechanisms for the excitation involve a one-photon dipole induced transition between the two vibrational levels. Fig. 7c shows the populations of the ground vibrational state (v ¼ 0) and the third excited states (v ¼ 3) as a function of time over the duration of the optimal laser pulse. It should be noted that despite the very simple form of the optimised laser pulse shown in Fig. 7a, only a very special combination of the length of the pulse, the variation of the frequency with time and the variation of the field strength with time will yield a good
(a)
ε(t) / a.u.
0.003 0 -0.003 -0.006 0
1
2
3
4
t / ps
|ε(ν)| / arbitrary unit
100
(b)
80 60 40 20 0 0
2e+13
4e+13
6e+13
8e+13
0.002
ν / Hz
(a) 0.001
v=0
v=1 (c)
0.8
Population
ε(t) / a.u.
1
0.6
0 -0.001
0.4 -0.002 0
0.2 0
0.5
1
1.5
2
t / ps 0
1
2
v=2 3
4
25
value. It suggests that the mechanism for the excitation involves a one-photon dipole induced transition between the adjacent vibrational levels. Fig. 6c shows the populations of three lowest vibrational states as a function of time during the laser pulse. It is found that some population goes into vibrational states other than the target state, such as (v ¼ 2), during the laser pulse. The population in this state increases in the center of the laser pulse but decreases to nearly zero by the end of the pulse. The designed laser pulses are found to be very highly selective. For instance if the laser pulse optimized for the vibrational excitation of v ¼ 0 ! v ¼ 1 of C1–H1–O1 is applied to the C1–H1–O2 system, it excites only 0.009% of the molecules, while conversely the pulse designed to excite the v ¼ 0 ! v ¼ 1 transition for C1– H1–O2 excites only 0.0001% of the C1–H1–O1 molecules. 3.2.2. AADHðv ¼ 0Þ ! AADHðv 0 ¼ 3Þ excitation for H1 in the C1–H1– O2 plane The initial trial field is set as:
ðtÞ ¼ 0:001 cos ðx0!3 tÞsðtÞ;
ð4Þ
(b)
20 15 10 5 0 0
5e+13
1e+14
ν / Hz
1.5e+14
2e+14
1
v=0
0.8
Population
Fig. 6. Characteristics of the optimized laser pulse for the tryptamine—AADHðv ¼ 0Þ ! ðv 0 ¼ 1Þ excitation in the C1–H1–O2 plane. (a) The optimized electric field as a function of time. (b) The spectrum of the optimized electric field. (c) The change in populations of the ground state and the target excited state as a function of time.
|ε(ν)| / arbitrary unit
t / ps
v=3
(c)
0.6 0.4 0.2 0 0
0.5
1
1.5
2
t / ps Fig. 7. Characteristics of the optimized laser pulse for the tryptamine—AADHðv ¼ 0Þ ! ðv 0 ¼ 3Þ excitation in the C1–H1–O2 plane. (a) The optimized electric field as a function of time. (b) The spectrum for the optimized electric field. (c) The change in populations of the ground state and the target excited state as a function of time.
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result for the transition probability. Thus a random combination of an initially guessed field strength and a pulse duration together with the frequency x0!3 will not normally yield a good transition probability. It is only through many failed trial calculations and through the use of the optimal control procedure that a laser pulse yielding a very high transition probability has been achieved.
4. Conclusions Using optimal control theory we have been able to design laser pulses to excite the labile proton of the reactant complex of aromatic amine dehydrogenase with tryptamine, as represented by a simplified model, from its ground vibrational state to its first and third excited states with close to 100% efficiency. It can be seen from the results that the frequency profiles of the optimized laser pulses are much simpler for the v ¼ 0 to v ¼ 3 vibrational state excitation processes, promoting motion along the C–O coordinate, than for the excitation of the bending motion to the v ¼ 1 states. The optimisation process also converges more readily for these v ¼ 0 to v ¼ 3 transitions. The illustrative calculations were performed on a simplified, but realistic, two dimensional model for the dynamics of the system. An excitation of this type in the real system is likely to affect the rate of reaction both on energetic grounds and by changing the tunnelling probability. The present calculations represent the first preliminary study of such a process. Further extended studies will be essential to determine the effect of the simplifying approximations made in the current model study. The first improvement we envisage is to compute the motion of the labile proton in three dimensions. This would remove the need to treat the motion in the C1–H1–O1 and C1–H1–O2 planes separately. After this the effect of the motion of other atoms, particularly those included in the active site region, needs to be taken into account. The most practical way of doing this would be to use a Multi-Configuration Time-Dependent Hartree approach [40]. A full treatment would also need to consider multiple conformations of the protein, to include the effects of conformational variability. The effects of protein (and solvent) motion, and intramolecular vibrational energy redistribution, on the picosecond timescale of the laser pulses should also be considered in a full analysis. A factor that may affect the accuracy of the calculations is the use of density functional theory methods for calculating potential energy and associated dipole moment surfaces; this could be tested by comparison to high level ab initio QM/MM calculations [31]. It may also be possible in the future to set more adventurous objectives, involving for instance the excitation of the system to states closer to the transition state geometry or to the product state wavefunction. It would then be interesting to examine what effect specific vibrational excitation could have on the rate of proton transfer, e.g. to quantify the effect on the probability of quantum tunnelling. This study is a first step towards defining what would be necessary to achieve designed specific vibrational excitation in an enzyme–substrate complex. Such experiments have been postulated previously. Here we begin to probe what would actually be required. We have outlined some of the necessary theoretical improvements above. Optimal control calculations might not be required: self-teaching experiments using a feedback mechanism could remove the need for accurate predictive calculations, as has been the case in other optimal control experiments [6,41]. The practical difficulties of achieving such an experiment are formidable. It would be necessary to prepare and characterize a reactive enzyme complex coherently. Excitation of a single vibrational mode within a large molecule will clearly be challenging in reality (see below). Single molecule experiments would be ideal. In terms of understanding biological function, it would be preferable to
235
study an enzyme in a condensed phase, but this presents significant challenges. In solution there are strong absorption bands at the infrared frequencies we have used in the calculations. A possible practical way of overcoming this problem and of conducting the proposed experiments would be to perform the experiments on an aligned crystal of the reactant complex under cryogenic conditions, and to use frequencies in the near UV at a wavelength of about 400 nm where aspartate shows a strong absorption [42] utilizing a two photon stimulated emission pumping procedure [43,44]. Alternatively, the TTQ cofactor may provide useful absorptions distinct from the protein. In the results section above the vibrational excitation of the labile proton was described in detail only in the C1–H1–O2 plane. This plane was chosen as the reaction has been found to proceed preferentially via proton transfer to the O2 oxygen [16]. The properties of the optimized laser pulses required to accomplish the same vibrational excitations in the C1–H1–O1 plane are qualitatively similar, but we note that pulses optimised for the excitations in the C1–H1–O1 plane yield very small transition probabilities when applied to the excitation of the motion of the proton in the C1–H1–O2 plane. Acknowledgments The authors thank EPSRC for support. We also thank Dr. D. Leys and Prof. N. Scrutton for crystal structures of AADH used to develop models of Refs. [16,17]. We thank Prof. A. Brown, Dr. C. Sanz-Sanz, Prof. H. Singh and Mr. S. Sharma for useful discussions and Dr. C. Woods for assistance in the preparation of some of the figures. References [1] [2] [3] [4] [5] [6] [7]
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