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E. Spectral Diffusion of Small Molecules in Water

E. Spectral Diffusion of Small Molecules in Water

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Proteins and Peptides



295



chosen as our first example of IR-stimulated echo spectroscopy. Our expectation was that N3 could be used as a probe of the dynamics of the solvent,

which in this case was water. Its energy relaxation rate (T1 D 2.3 ps), orientational diffusion constant D D 0.023 ps 1 , and anharmonicity /2 c D

25 cm 1 are known from pump-probe and anisotropy experiments (66).

Figure 5a shows the stimulated photon echo signal from azide ion in

the k1 C k2 C k3 and the Ck1 k2 C k3 directions, which were collected

by two independent IR detectors. The beam directions were arranged in

the so-called box configuration, (101) (see Fig. 3). The experiments show

clearly that neither the k1 C k2 C k3 nor the Ck1 k2 C k3 signals are

symmetrical with respect to D 0. Moreover, the asymmetry diminishes

with T and has mostly disappeared by T ³ 5 ps. These results show that

the vibrational coherence introduced by pulse 1 and the corresponding

phase information stored in the population created by pulse 2 continues

to be detectable after rephasing is induced by pulse 3, albeit in an everdecreasing manner, as T increases. The rephasing process that generates

the echo only occurs when there is some memory of the original inhomogeneous distribution of frequencies. In other words, the difference between

both signals is due to a delayed photon echo, which is formed only under

rephasing conditions ( > 0 for the k1 C k2 C k3 signal and < 0 for

the Ck1 k2 C k3 signal), so that these results clearly prove that a certain

amount of inhomogeneity is present for small T. The inhomogeneity is

diminished on the picosecond time scale by spectral diffusion processes.

Clearly, the asymmetrical stretching mode of the azide ion in water is not in

the motional narrowing limit, which is what is generally assumed for vibrational dephasing. The normalized first moment M1 T of the k1 C k2 C k3

signal (see Fig. 6) indicates that the inhomogeneity decays on at least two

time scales. Furthermore, the fact that M1 T is still finite at the longest

measured times implies the existence of a small inhomogeneous contribution, which is essentially static on the time scale of these experiments.

Consequently, the following model for the transition frequency correlation

function was used to fit the photon echo data (Fig. 5):

2



hυω10



υω10 0 i D



i 2 e



t/



i



C 0 2



(20)



iD1



A global fit was performed by applying the formalism outlined in

Section III. A [Equation (7)–(12), (14)–(17)], which connects the transition frequency fluctuation correlation function hυω10 υω10 0 i to the

three-pulse photon echo signal S T, and by varying the five parameters in the right-hand side of Equation (20). The fit and the resulting first



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Figure 5 (a) Stimulated photon echo signal of the azide ion N3 in D2 O at

2043 cm 1 as a function of and T for the k1 C k2 C k3 (gray surface) and the

Ck1 k2 C k3 (white surface) phase matching directions. (b) Representative traces

for four selected values of T. The solid lines represent a global fit of all the scans

to the model correlation function Equation (20). (From Ref. 41.)



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297



moment are compared with the corresponding experimental data in Fig. 5b

and Fig. 6, respectively. An excellent agreement is obtained. The derived

transition frequency fluctuation correlation function hυω10 t υω10 0 i is also

shown in Fig. 6 (insert). The initial fast decay gives rise to a dephasing

contribution, which is essentially in the motional narrowing limit 1 Ð 1 D

0.2 − 1 , corresponding to a pure dephasing time of (1 2 Ð 1 1 D 1.8 ps

and a homogeneous linewidth of 6 cm 1 , respectively. It is followed by a

slow tail, which decays on a 1 ps time scale. In order to verify the selfconsistency of the entire formalism, the linear absorption spectrum was

calculated from this transition frequency correlation function according to

Equation (4b) and

1



I ω D 2 Re



ei ω



hω10 i t



e



gt



t/2T10 2Dt



dt



(21)



0



As seen in Fig. 7, the calculated absorption spectrum agrees quite

well over three orders of magnitudes with a measured spectrum.

A classical molecular dynamics simulation of N3 dissolved in water

revealed that six to seven water molecules are hydrogen bonded to the negatively charged terminal nitrogen atoms, (102) with an estimated hydrogen



Figure 6 The first moment M1 T of the data measured in the k1 C k2 C k3

direction (dots) of N3 and CO2 . The solid line is the first moment M1 T as

obtained from global fits. The insert shows the correlation functions obtained from

global fits.



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Figure 7 Linear IR absorption spectrum of NaN3 in D2 O (dots). The solid line

shows the line shape as calculated with the parameters obtained from the global

fit of the photon echo signal. The small shoulder at the low frequency side of the

spectrum appears to be the absorption of 14 N15 N14 N . (From Ref. 41.)



bond lifetime of 1.3 ps. Similar conclusions were drawn from MD simulations of CN in water (103,104). Since the long-term tail in the fluctuation

correlation function decays on exactly that time scale, the spectral diffusion process is interpreted as the dynamics of the formation and breaking

of these hydrogen bonds. This interpretation is supported by the significant

influence of the solvent on the vibrational frequency of the asymmetrical

stretching mode of azide, as seen from the large blue shift from 1987 cm 1

in gas phase, (105) to 2043 cm 1 in solution. Consequently, intermittent Hbond interactions cause a fluctuating transition frequency, giving rise to the

observed spectral diffusion process. The vibrational frequency of carbon

dioxide, which is isoelectronic to the azide ion, is much less shifted by

the solvation process (2349 cm 1 in gas phase, 2345 cm 1 in water), even

though it also forms strong hydrogen bonds to water. As a consequence,

the amplitude of the slow tail of the fluctuation correlation function is

considerably smaller than in the case of the azide ion (see Fig. 6) (95),

although, interestingly, the total line width of CO2 in water 7 cm 1 is

essentially the same as the homogeneous contribution to the total linewidth

of N3 1 2 1 /c D 6 cm 1 .

The slow tail of the spectral diffusion process (1.3 ps) of azide in

water is not the same as the relaxation of bulk water (800 fs), which has

been measured with the help of optical dynamical Stokes shift experiments



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299



(106). We have argued that the correlation function obtained from the

vibrational photon echo experiment senses especially the hydrogen bonds

between azide ions and water molecules, in contrast to long-ranged

Coulomb interaction between the dipole moment of the optical chromophor

and the fluctuating charges of the solvent. In that sense, the vibrational

photon echo experiment is considered to be more sensitive to local structure

fluctuations.

F. Spectral Diffusion of Vibrational Probes in

Enzyme-Binding Pockets



It is this local character of vibrational dephasing that is utilized in the experiments described in this section. In these experiments, spectral diffusion of

test molecules bound to enzymes has been investigated in order to study the

fluctuations of the reactive sites. The local character of these interactions

can be pictured in great detail since in many cases high-resolution x-ray

structure of the complexes are available. One example we have studied,

shown in Fig. 8, is azide bound to carbonic anhydrase CA–N3 (107).

Carbonic anhydrase is a zinc enzyme that catalyzes the interconversion of



Figure 8 The structure of the binding pocket of azide bound to carbonic anhydrase CA–N3 (107). The atoms of the azide ion, which is bound to the active

site ZnC2 , is in close contact with Thr-199 (indicated by the dotted lines). (From

Ref. 31.)



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Hamm and Hochstrasser



CO2 and bicarbonate. The azide ion, which is a competitive inhibitor of

this reaction and isoelectronic with CO2 , binds at Zn2C without compromising the three-dimensional structure of the active site (107). The azide

nitrogen N 1 closest to the Zn2C ion and the central nitrogen N 2 have

˚ to the hydroxyl oxygen of Thr-199. In addition,

short contacts (3.3 A)

˚ and N 3 (at 3.5 A)

˚ must sense the amide nitrogen of ThrN 2 (at 3.7 A)

199. Therefore, it is natural to invoke the nearby Thr-199 as the group that

modifies the potential energy function and controls the charges of Zn-bound

azide. Recent calculations have shown that the charges on the azide nitrogen

atoms are changed considerably when the effect of the enzyme environment,

mainly the Thr-199, is taken into account (108). These simulations and

quantum chemical calculations suggest that the coupling to the protein environment increases the admixtures of the triple-bonded valence bond structure N NC1 –N 2 compared with the symmetrical form N 1 NC1 N 1

of the azide ion. Since each admixture corresponds to a different potential

energy function of the ground state, the vibrational frequency should be

structure sensitive. The presence of a small admixture of the triple-bonded

structure causes the averaged frequency to increase significantly, in agreement with the azide vibrational frequency in the enzyme being increased

by ca. 50 cm 1 compared with azide in water and by 110 cm 1 compared

with azide in the gas phase (105). In other words, azide is a very sensitive sensor to local charges. As a consequence, fluctuation of the contact

between Thr-199 and the azide ion appears to be a likely mechanism for

dephasing and spectral diffusion. Put another way, the three-pulse photon

echo exposes the dynamics of couplings between the azide ion and nearby

partially charged atoms in the protein.

High-resolution structural information is also available for the azide

ion bound to hemoglobin Hb–N3

and carbon monoxide bound to

hemoglobin (HbCO) and myoglobin (MbCO) from x-ray diffraction studies

(109,110) and transient IR spectroscopy (111–113) so that detailed pictures

of the interaction between the vibrational probe molecule and the binding

pocket of the enzyme can be derived. For example, it is known that the CO

vibrational frequency, and hence the potential energy for the CO-stretching

motion, is extremely sensitive to the presence and positioning of His-E7

in hemoglobin (114) and myoglobin (115,116). On the other hand, the CO

frequency is less sensitive to mutations of Val-E11, another heme pocket

residue. The frequency shifts from the variations in the relative positioning

of the polar His-E7 and the CO can be rationalized as resulting from the

mixing of the valence bond structures Fe C O and Fe–C O. The latter



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