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A. Vibrational Spectrum of Orientationally Constrained CO

A. Vibrational Spectrum of Orientationally Constrained CO

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Infrared Studies in Heme Proteins



197



dictated by Boltzmann statistics and degeneracy factors (Fig. 3A). As the

temperature is raised, the Boltzmann population distribution shifts to higher

J values and the overall envelope of the P and R branches becomes broader.

There are two relevant widths represented in the ro-vibrational spectrum:

the width of the individual transitions and the overall width of the envelope containing the P and R branches. According to the Fourier transform

relationship between spectra and dipole correlation functions, these two

widths in the spectral domain transform as two different time scales in

the time-dependent decay of the orientational correlation function. The

corresponding orientational correlation function for a Boltzmann-distributed

ensemble of quantum rotors is shown in Fig. 3B. The rapid initial decay of

the orientational correlation function arises from rotational motion, whose

Boltzmann-distributed angular velocities leads to rapid decorrelation of the

ensemble of quantum rotors and causes the orientational correlation function to decay toward zero. Because the decorrelation is incomplete at a



Figure 3 (A) Spectra of CO in a variety of environments and (B) corresponding

orientational correlation functions. In (A), the four curves correspond to (top to

bottom) CO in the gas phase, in cyclohexane, in water, and in an orientationally

constrained environment (theoretical spectrum with ˛ D 0.5; see text). In (B), the

corresponding ordering is bottom to top. Note the similarity of the fast, inertial

contribution to the orientational correlation function at early times.



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time corresponding to roughly one-half the average rotational period, the

orientational correlation function becomes negative before decaying to zero.

Clearly the decay dynamics are dictated by the average angular

p velocity of

the rotor, which is related to temperature according to ω ³ 2kT/I. For

CO at room temperature, the rapid inertial contribution to the decay of the

orientational correlation function transforms as a ¾90 cm 1 spectral width,

which is comparable to the overall width of the envelope containing the P

and R branches of the ro-vibrational absorption spectrum of CO. Consequently, the overall breadth expected for an absorption band can be rationalized in terms of a rotor’s temperature and its moment of inertia. How,

then, do we rationalize the narrow features observed in the ro-vibrational

spectrum of CO? Because the rotor is quantized, there are periodic recurrences of the orientational correlation function (see Fig. 3B), the amplitude

of which decays according to a phenomenological damping time . Therefore, the orientational correlation function can be considered biphasic, with

the faster inertial decay dictating how broad the overall absorption envelope must be and the slower damping time of the recurrences dictating

how narrow the widths of individual features can be. This minimum width

corresponds to the homogeneous width of the feature. Of course, environmental heterogeneity (inhomogeneous broadening) can broaden the feature

beyond its homogeneous width.

A diatomic dissolved in a solvent can be thought of as a hindered

rotor in a disordered environment with the diatomic rotating inertially

between angular momentum–changing collisions with the surrounding

solvent. Because the angular velocity of a diatomic is dependent on

temperature and its rotational inertia, the presence of the solvent need

not alter the velocity of its inertial rotation. Consequently, the inertial

contribution to the decay of the orientational correlation function and

the corresponding breadth of the absorption spectrum is expected to

be nominally independent of environment. The influence of the solvent

shows up at times corresponding roughly to the mean time between

angular momentum–changing collisions, whereupon the inertial motion is

interrupted and the orientation of the rotor can begin to evolve diffusively.

The orientational correlation function should, therefore, exhibit a transition

between inertial and diffusive motion. Where that transition occurs depends

on the average angular rotation between angular momentum–changing

collisions. Rotation by about 90 degrees between such collisions would

cause the orientational correlation function to decay to zero in a single

rapid phase. Rotation by about 180 degrees would cause the orientational

correlation function to become negative before decaying to zero. Rotation



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Infrared Studies in Heme Proteins



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by angles much less than 90 degrees would lead to a smaller amplitude

inertial decay followed by a larger amplitude diffusive decay. How narrow

a feature could appear in the spectral domain would be dictated by the

time scale for the slower diffusive decay of the orientational correlation

function. Moreover, the integrated absorbance contained within the narrow

feature would be dictated by the relative amplitudes of the diffusive

and inertial phases. Since angular momentum–changing collisions rapidly

destroy any coherence in the rotational motion, the orientational correlation

function would not exhibit periodic recurrences so the vibrational spectrum

would not exhibit rotational structure. Therefore, the spectrum of CO in a

disordered environment would exhibit a broad envelope with the possibility

of a single narrower feature centered on top of that envelope. The amplitude

of the narrower feature could be small or large, depending on the degree

of angular rotation between angular momentum–changing collisions. For

example, the IR spectrum of CO dissolved in cyclohexane, shown in

Fig. 3B, is approximately 90 cm 1 broad and nearly featureless, whereas

CO in water exhibits a ³20 cm 1 FWHM feature centered on top of a

broad pedestal with about one third of the integrated absorbance contained

within the narrower feature. These spectra suggest that the average rotation

of CO between collisions in cyclohexane is of the order of 90 degrees while

that for CO in water is significantly less than 90 degrees.

A diatomic localized within a protein can be thought of as a rotor in

an ordered environment. In this context, the distinction between ordered and

disordered environments is that an ordered environment can constrain the

rotor to point in a particular direction relative to the molecular frame. When

orientationally constrained, the rapid inertial contribution to the decay of

the orientational correlation function is reduced in amplitude and the decay

to zero becomes biphasic. As in the disordered case, the absorption spectrum is expected to have a narrower feature centered on top of a broader

pedestal with their relative integrated absorbances partitioned according to

the relative amplitudes of the slow and fast decay. In addition, the environment anisotropy can cause the vibrational frequency to be dependent

on orientation. If the rotational diffusion of the rotor is slow, the environment anisotropy will not be averaged out and the vibrational spectrum may

exhibit multiple features on top of a broad pedestal. How narrow those

features can become is limited by the time scale for interconversion among

the preferred orientations. Generally speaking, the greater the orientational

constraint, the greater the fraction of the oscillator strength appearing within

the narrower feature(s) and the narrower those features can become. Consequently, CO localized within a highly ordered protein might be expected to



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exhibit an absorption spectrum with more than one narrow feature approximately centered on top of a broad pedestal. Unless the pedestal contains the

majority of the integrated CO oscillator strength, it can easily “disappear”

into the background noise of a measured spectrum. A phenomenological

description for the decay of the orientational correlation function, based

on a sum of Gaussians with differing amplitudes and variances, has been

employed to illustrate how differing degrees of orientational constraints can

influence the vibrational spectrum of a rotor (11). The result obtained when

half of the decay is inertial ˛ D 0.5 is included in Fig. 3. Note that when

the amplitudes of the inertial and diffusive decays are the same, the broad

pedestal can be quite small in amplitude relative to the narrower feature.

B. Orientation of CO via Photoselection



When measuring absorption spectra, one records a signal that is related to

the wavelength-dependent probability of making a spectroscopic transition.

From the molecular point of view, this probability is proportional to the

dot product ˆ Ð pˆ where ˆ is the molecular transition moment and pˆ is

the photon polarization direction. When the orientational distribution of

the molecules is isotropic (not crystalline, liquid crystalline, or bound to

a surface), its absorption spectrum represents the orientationally averaged

probability of making a spectroscopic transition and the measured spectrum

is independent of polarization direction. When the orientational distribution

of the molecules is anisotropic, the probability of making a spectroscopic

transition depends on the polarization direction, and that dependence can

be exploited to deduce the direction of the transition moment relative to

the laboratory frame. Because transition moments are often trivially related

to the orientation of the molecule, structural information can be deduced

from polarized absorption measurements on anisotropic samples.

The pump pulse in time-resolved pump-probe absorption spectroscopy is often linearly polarized, so photoexcitation generally creates

an anisotropic distribution of excited molecules. In essence, the polarized light “photoselects” those molecules whose transition moments are

nominally aligned with respect to the pump polarization vector (12,13).

If the anisotropy generated by the pump pulse is probed on a time scale

that is fast compared to the rotational motion of the probed transition,

the measured anisotropy can be used to determine the angle between the

pumped and probed transitions. Therefore, time-resolved polarized absorption spectroscopy can be used to acquire information related to molecular

structure and structural dynamics.



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Infrared Studies in Heme Proteins



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The visible absorption spectrum of MbCO is dominated by the Q-band

of the heme. Over a broad range of wavelengths, the transition moments

along the x- and y-direction vectors of the heme (see lower panel of Fig. 1)

are nearly identical and the heme behaves as a circular absorber (14). In

contrast, near the red edge of the Q-band absorption, one of the two direction vectors has a stronger absorption probability and the heme becomes

an elliptical absorber. In either case, photolysis of MbCO with linearly

polarized visible light creates an anisotropic distribution of MbCO, Mb,

and CO molecules. Measurements of the generated anisotropy can unveil

the orientation of CO bound to and dissociated from Mb as well as the

rotational dynamics of CO as it translocates from the binding site to the

docking site.

First we focus on the CO orientation when bound to and after dissociation from a heme protein. When a solution containing a carbon monoxyheme protein is illuminated with linearly polarized visible light, hemes

whose planes are aligned with the polarization direction absorb light preferentially. The ligands bound to these “photoselected” hemes are dissociated

with high quantum efficiency, leading to a loss of bound CO and the

production of “free” CO. If the IR transition moment of CO is oriented

at a particular angle  relative to the heme plane normal, and if we assume

the heme is a circular absorber, the ratio of its perpendicular and parallel

polarized IR absorbance, A? /Ajj , becomes a simple analytic function

of  (15):

A?

4 sin2 Â

D

Ajj

2 C 2 sin2 Â



(2)



The measured polarization ratio can theoretically range from 2 (Â D

0 degrees) down to 0.75 (Â D 90 degrees). When polarized absorbance

measurements are made in a solution, rotational tumbling of the protein

randomizes the orientation of the photoselected hemes. Therefore, the

measurement must be made on a time scale that is short compared to

the rotational diffusion time, which is 8 ns for Mb in H2 O at 288 K

(16). When measurements are made in low-temperature glasses, where the

protein orientation is frozen and ligand rebinding is slow, the polarized

IR spectra can be measured with conventional IR spectrometers (17). In

either case, this equation is valid only in the small signal limit, i.e., the

fraction of molecules photolyzed must be small (the measured polarization

ratio asymptotically approaches unity as the fraction photolyzed becomes

large). Moreover, the angle calculated using this equation assumes that the

orientational distribution is a delta function in Â. Finally, what is determined



Copyright © 2001 by Taylor & Francis Group, LLC



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