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F. Spectral Diffusion of Vibrational Probes in Enzyme-Binding Pockets

F. Spectral Diffusion of Vibrational Probes in Enzyme-Binding Pockets

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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

Copyright © 2001 by Taylor & Francis Group, LLC

Proteins and Peptides


structure is stabilized by the hydrogen bond to E7, resulting in an increase

in the vibrational frequency.

These complexes (CA–N3 , Hb–N3 , and Hb–CO) therefore seem

to be ideal candidates for investigating local structural fluctuation of enzyme

reactive sites. The corresponding photon echo signals are shown in Fig. 9

together with global fits, which were obtained in the same way as described

in the previous paragraph for azide dissolved in water. The corresponding

first moment data M1 T and the initial decay of the transition frequency

fluctuation correlation function hυω10 υω10 0 i obtained from global fits

are shown in Fig. 10 and Fig. 11, respectively. The vibrational energy relaxation rate of carbon monoxide in hemoglobin (Hb–CO) (67) is considerably

longer than that of azide, so that a time window in excess of 40 ps is opened

for studies of spectral diffusion processes (note the different scale of the

time axis in Fig. 10c).

Nevertheless, the responses of the test molecules embedded to the

proteins differ significantly from that in solution (see Fig. 11). The fluctuation correlation function amplitude is considerably larger in solution

for small times, but it decays much more quickly, so that only a very

small quasi-static inhomogeneity 0.1 ps 2 remains within the observation

window available in this experiment (6 ps). A much larger inhomogeneity

remains for even longer times in the case of a protein environment. This

result is consistent with the interpretation of optical photon echoes in protein

environment (22–25,27), where a quasi-static contribution of the energy

gap correlation function has been observed up to 100 ps.

The time dependence of the inhomogeneous distribution has a special

significance in the case of proteins, since it measures the changes in the

structure of those parts of the protein that influence the probe vibrational

spectrum. As outlined before, the potential energy surface of the probe

molecule is changing as a result of the interaction with the protein. The

potential will be sensitive to forces that can influence the charge distribution in the probe. Therefore, this method is a probe of the local structure.

Long-range interactions can also cause frequency changes by shifting of

vibrational transition in response to the fields from the fluctuating charges

of the medium. However, the dipole needed to couple to those fields vary

only slightly with the quantum number of vibrational states because of the

small anharmonicity of the oscillators, so these perturbations will be small.

However, an important effect of longer-range interactions on the spectral

diffusion would be to cause energy and nuclear position fluctuations of

those parts of the protein that are involved in direct coupling to the probe

Copyright © 2001 by Taylor & Francis Group, LLC


Hamm and Hochstrasser

Figure 9 Stimulated photon echoes from various test molecules in different

enzymes: CaN3 (azide bound to carbonic anhydrase), Hb–N3 (azide bound to

hemoglobin), and Hb–CO (carbon monoxide bound to hemoglobin). The signal is

plotted against delay time for selected delay times T together with global fits

(solid lines). The oscillatory part in the experimental data, which is not reproduced

by these fits, reflects the anharmonicity of the transition and is due to interference

between fifth and third order nonlinear polarization term (52). (From Ref. 31.)

Copyright © 2001 by Taylor & Francis Group, LLC

Proteins and Peptides


Figure 10 The normalized first moments of the photon echo signal of

(a) CA–N3 , (b) Hb–N3 , and (c) Hb–CO as a function of delay time T. Note

the extended time axis of the Hb–CO data. The inhomogeneity decays with time

T due to conformational fluctuations of the proteins.

atoms. By this mechanism the local interactions can sense the bulk fluctuations of the protein. The local forces can be changed either by fluctuations

in the local structure or by the local structure responding to changes in other

parts of the protein. This picture suggests a plausible interpretation of the

time sequence of events in the evolution of the inhomogeneous distribution

around a local region.

Because of the small size of the utilized test molecules and the

fact that the molecules remain in their electronic ground states, accurate

calculations of the transition frequency fluctuation correlation function of

these systems fluctuations would seem to be achievable with state-of-the-art

quantum dynamics calculations.

Copyright © 2001 by Taylor & Francis Group, LLC


Hamm and Hochstrasser

Figure 11 The initial decay of the transition frequency fluctuation correlation

function hυω10 υω10 0 i obtained from global fits of the stimulated photon echo

data of azide dissolved in D2 O (solid line, same data as in Fig. 6), CA–N3 (dashed

line) Hb–N3 (dashed-dotted line), and Hb–CO (dashed-double-dotted line).

It is evident from these data that the transition frequency fluctuation

correlation function of samples that have the same probe molecule (azide)

embedded into two different proteins (hemoglobin and carbonic anhydrase),

or of the sample with different probe molecules (azide, carbon monoxide)

embedded to one protein (hemoglobin), all differ considerably. This, we

believe, is a consequence of sensitivity of this spectroscopic technique to

the local structure, which is different in each case. This result must be

contrasted with electronic dephasing, where it was found that the energy

gap fluctuation correlation function reflects the response of the bulk solvent

and is essentially independent of the chromophore used as a probe (81).

G. Spectral Resolution of the Echo

The properties of the various Feynman diagrams that contribute to the vibrational echo can often be measured separately by means of time resolution of

the spectrally resolved echo. The time t3 can be experimentally controlled

by a variety of methods. One way is to time gate the echo field, which

Copyright © 2001 by Taylor & Francis Group, LLC

Proteins and Peptides


has been done for electronic transitions and poses no major experimental

difficulties in the infrared. Another approach would be to examine the echo

by spectral interferometry. Finally, in systems where there is inhomogeneous broadening the inhomogeneous averaging naturally creates a time

gate that restricts t3 to a range around t1 [see Equation (13)]. The larger

the inhomogeneous width, the smaller is this range. In all cases the field

from R3 dominates the dispersed signal at ω10 - while that from R1 and

R2 dominates the signal at ω10 . Equation (13) assumes that the dephasing

rates for the 0-1 and 1-2 transitions are both 1/T2 . The dephasing time for

the 1-2 transition can be replaced by 1/T02 D C 1/T2 , where can be

regarded as the contribution to the damping from the fluctuations in the

anharmonicity. The dispersed gated signal is then the absolute square of

the Fourier transform of the response in Equation (13). It is easy to see that

the decay of the signal along the t1 axis (or t3 axis in an experiment with a

gating pulse) at the 0-1 frequency depends only on T2 , while that at the 1-2

frequency depends on both T2 and T02 . In the limit that the inhomogeneity is

larger than 1/T2 but smaller than , both decays are exponential, as is also

the case when the signals are time gated by an additional field. Of course

in a system undergoing spectral diffusion the situation is more complex,

but still the dephasing patterns for the 1-0 and 1-2 coherences contribute

to different extents to a given spectral component of the generated field.

An example of a frequency resolved echo (117) is shown in Fig. 12. The

0-1 and 1-2 coherences are clearly separated in frequency space. In this

example the two relaxation times are similar.



Vibrational spectroscopy has been used in the past as an indicator of

protein structural motifs. Most of the work utilized IR spectroscopy

(see, for example, Refs. 118–128), but Raman spectroscopy has also

been demonstrated to be extremely useful (129,130). Amide modes

are vibrational eigenmodes localized on the peptide backbone, whose

frequencies and intensities are related to the structure of the protein.

The protein secondary structures must be the main factors determining

the force fields and hence the spectra of the amide bands. In particular

the amide I band 1600–1700 cm 1 , which mainly involves the C Ostretching motion of the peptide backbone, is ideal for infrared spectroscopy

since it has an large transition dipole moment and is spectrally isolated

Copyright © 2001 by Taylor & Francis Group, LLC

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