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E. Origin of the Barrier to CO Rebinding

E. Origin of the Barrier to CO Rebinding

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ascribed primarily to the steric constraints imposed by the docking site

in Mb.

The geminate-rebinding dynamics measured after photolysis of

MbCO and microperoxidase-CO are shown in Fig. 9. The survival fraction

denotes the fraction of photolyzed hemes that remain in the deoxy form

after CO dissociation. The population was determined by measuring the

time dependence of the vibrational absorbance of bound CO. According to

Fig. 9, CO rebinds to microperoxidase much more rapidly than to Mb.



Figure 9 Geminate recombination after photolysis of MbCO (ž) and microperoxidase-CO ( ). The survival fraction refers to the population that remains unbound

after photolysis. The population was determined by measuring the IR absorbance

at frequencies corresponding to the peak of the bound CO stretch. (Adapted from

Ref. 67.)



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Infrared Studies in Heme Proteins



223



The rebinding dynamics to microperoxidase are nonexponential due

to a solvent cage effect. To deduce the time constant for rebinding CO from

the solvent cage, the recombination kinetics were modeled according to

kBA



kBC



kCS



the scheme A

B k ! C k ! S where A represents the population of

CB

SC

bound CO, B represents the population of CO trapped within the solvent cage

surrounding the heme, C represents the population of CO trapped just outside

the first solvent shell, and S represents the population of CO that has escaped

beyond C. With this model, kBA D 110 ps 1 . Modeling the Mb dynamics

with a similar kinetic scheme leads to kBA Ä 3 µs 1 . Consequently, the

rate of CO binding to microperoxidase is more than 27,000 times faster than

the corresponding rate in Mb. In fact, the rate of geminate recombination in

microperoxidase is not much slower than the 27.6 ps 1 rate observed for

NO rebinding to Mb (28). It appears that the reason CO rebinds slowly to

Mb is not because of a large electronic barrier, but because the docking site

inhibits access to the transition state for CO binding.



V. CONCLUSIONS



Ultrafast time-resolved near- and mid-IR spectra of ligand-binding heme

proteins have unveiled numerous details that have contributed to our understanding of the relations between protein structure, dynamics, and function. These studies showed that carbon monoxide binds to Mb to form

nearly linear Fe–C–O. Upon dissociation from the heme iron, CO becomes

˚ from the heme-binding site. This

trapped in a docking site located Ä2 A

docking site constrains CO to lie nominally parallel to the plane of the

heme, an orientation approximately orthogonal to that of bound CO. Ligand

translocation proceeds along one of two pathways, with the faster, 0.2 ps

pathway leading to B1 and the slower, 0.5 ps pathway leading to B2 . Of

the two states, B1 is lower in energy and is assigned to a structure with the

O end of CO pointing toward the heme iron. The conformational response

of the protein to ligand translocation proceeds with a 1.6 ps time constant

and appears to tighten the orientational constraint imposed on the docked

CO. The photoexcited heme was found to relax electronically with a 3.4 ps

time constant and relax thermally with a 6.2 ps time constant. A modest

amount of “docked” CO appears vibrationally hot ¾4% but relaxes back

to its ground state with a 600 š 150 ps time constant. The sluggish geminate rebinding rate in Mb is approximately 27,000 times slower than the

geminate rebinding to a heme that lacks a docking site. Consequently, most



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Lim et al.



of the docked CO manages to escape from the docking site on the time

scale of a few hundred ns (>98% at 32° C).

The use of photolysis to explore ligand dynamics in ligandbinding heme proteins appears to be well justified, as the heme

quickly loses memory of the dissociation pathway. The orientational and

spatial constraints imposed on “docked” CO have the effect of slowing

dramatically the rate of CO rebinding and facilitate efficient expulsion

of this toxic ligand from the protein. Evidently, the highly conserved

residues circumscribing the heme pocket of Mb fashion a docking site

that orientationally constrains the dissociated ligand and thereby influences

the rates and pathways for ligand binding and escape. A docking site near

an active site may be a general property among proteins that must shuttle

ligands to and from an active site in an oriented fashion. To probe more

deeply the role of the residues that fashion the docking site will require

additional time-resolved IR studies involving mutants of Mb.



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6

Infrared Vibrational Echo Experiments

Kirk D. Rector∗ and M. D. Fayer

Stanford University, Stanford, California



I. INTRODUCTION



The advent of the nuclear magnetic resonance spin echo experiment in 1950

began a new era in spectroscopy (1). The spin echo was the first spectroscopic experiment to take advantage of coherent interactions of a radiation

field with the system to obtain information not available in a straight absorption measurement. The spin echo, which involves the application of two

radio frequency pulses, is the simplest of all pulsed magnetic resonance

experiments. Since 1950, a large number of complex pulse sequences have

been developed and applied to the study of magnetic spin systems (2). All

of these have direct lineage to the spin echo experiment.

In 1964, the spin echo experiment was extended to the optical regime

by the development of the photon echo experiment (3,4). The photon echo

began the application of coherent pulse techniques in the visible and ultraviolet portions of the electromagnetic spectrum. Since its development, the

photon echo and related pulse sequences have been applied to a wide variety

of problems including dynamics and intermolecular interactions in crystals,

glasses, proteins, and liquids (5–8). Like the spin echo, the photon echo

and other optical coherent pulse sequences provide information that is not

available from absorption or fluorescence spectroscopies.

Ł



Current affiliation: Los Alamos National Laboratory, Los Alamos, New Mexico



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Rector and Fayer



Today, radio frequency coherent pulse sequences are used extensively

in nuclear magnetic resonance and in electron spin resonance spectroscopies.

Visible light coherent pulse sequence techniques, while not as ubiquitous

as magnetic resonance, are widely used. In contrast, the use of coherent

pulse sequences in the infrared (IR) portion of the spectrum to study vibrational states of molecules, rather than spin states or electronic states, is

just beginning. The delay in applying coherent pulse sequences in the IR

has been mainly caused by technological difficulties. The first applications

of coherent IR pulse sequences to probe molecular vibrations occurred

in the early 1970s (9,10). Because of limitations imposed by electronic

switching of CW lasers to create pulses, experiments were restricted to small

molecules, long times scales, and low-pressure gases. These novel experiments did not find general applicability and were not useful in studying

condensed matter systems because of the lack of time resolution.

In 1993, the first ultrafast vibrational echo experiments on condensed

matter systems were performed using a free electron laser as the source of

temporally short, tunable infrared pulses (11). Recently, the development

of Ti:sapphire laser-based optical parametric amplifier (OPA) systems has

made it possible to produce the necessary pulses to perform vibrational

echoes using a tabletop experimental system (12,13). The development

and application of ultrafast, IR vibrational echoes and other IR coherent

pulse sequences are providing a new approach to the study of the mechanical states of molecules in complex molecular systems such as liquids,

glasses, and proteins (14–20). While the spin echo, the photon echo, and

the vibrational echo are, in many respects, the same type of experiment,

the term vibrational echo is used to distinguish IR experiments on vibrations from radio frequency experiments on spins or vis/UV experiments

on electronic states. In this chapter, recent vibrational echo experiments on

liquids, glasses, and proteins will be described.

The vibrational levels of a molecule in a condensed matter system are

influenced by the surrounding medium through intermolecular interactions.

The time-averaged forces exerted by the solvent on a molecular oscillator

cause a static shift in the vibrational absorption frequency. The frequency

shifts of the vibrational transitions of a molecule between the gas phase and

a condensed matter environment is an indicator of the effect of the solvent

on the internal mechanical degrees of freedom of a solute.

The fluctuating forces that a medium exerts on a solute molecule

produces fluctuations in the molecular structure, time-dependent vibrational

eigenstates, and, thus, time-dependent vibrational energy eigenvalues. Time

evolution of the vibrational energy eigenvalues produces fluctuations in the



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Infrared Vibrational Echo Experiments



229



vibrational transition energies. Fluctuating forces are involved in a wide

variety of chemical and physical phenomena, including thermally induced

chemical reactions, promotion of a molecule to a transition state, electron

transfer, and energy flow into and out of molecular vibrations. The extent

and time dependence of fluctuations of a solute’s vibrational energy levels

are sensitive to the nature of the dynamics of the condensed matter environment and the strength of intermolecular interactions.

In principle, information on dynamical intermolecular interactions

of an oscillator with its environment can be obtained from vibrational

absorption spectra. The forces experienced by the oscillator determine the

vibrational line shape and width. The line shape and width depend on

temperature and the nature of the solvent. However, a vibrational absorption

spectrum reflects the full range of broadening of the vibrational transition energies, both homogeneous and inhomogeneous. In glasses, liquids

and proteins, inhomogeneous broadening often exceeds the homogeneous

linewidth. Under these circumstances, measurement of the absorption spectrum does not provide information on vibrational dynamics.

The medium containing solute molecules of interest is referred to as

a bath. The bath includes bulk solvent degrees of freedom arising from the

solvent’s translational and orientational motions, the internal vibrational

degrees of freedom of the solvent, and the solute’s vibrational modes other

than the oscillator of interest. In a glass, bath fluctuations range from very

high frequency to essentially static. For a pair of energy levels, e.g., v D 0

and v D 1, coupling of the vibrational transition to the fast fluctuations

produces homogeneous pure dephasing, which, in the frequency domain,

is a source of homogeneous spectral broadening. Pure dephasing, which

results from the time evolution of the vibrational transition energy, is an

ensemble average property, which for an exponential decay of the off diagonal density matrix elements (Lorentzian homogeneous line shape) can

be characterized by an ensemble average pure dephasing time, TŁ2 . The

total homogeneous dephasing time, T2 , (total homogeneous linewidth) also

has contributions from the vibrational lifetime, T1 and, possibly, orientational relaxation (21). While the fast fluctuations give rise to the dynamical

homogeneous dephasing, the static structural disorder of a glass makes

one molecule’s environment, and, therefore, vibrational transition energy,

different from another. These static differences are the source of inhomogeneous broadening of an absorption spectrum.

Unlike a glass, a liquid does not have essentially static structures that

give rise to inhomogeneous broadening. Nonetheless, liquids can have fast

time scale fluctuations that give rise to homogeneous broadening and much



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slower time scale structural evolution. Evolution of the system on time scales

substantially slower than the homogeneous dephasing time, T2 , appears as

inhomogeneous broadening. Since the absorption spectrum measures the

transitions on all time scales, if the inhomogeneous broadening is significant compared to the homogeneous broadening, an absorption spectrum will

reflect the inhomogeneous linewidth, which does not provide information on

vibrational dynamics. Thus, vibrational echoes are useful in the studies of

liquids as well as more static structures like glasses and proteins.

In this chapter, the first detailed studies performed using ultrafast vibrational echo experiments are described. The experiments examine dynamics

in condensed matter systems as a function of temperature and other system

parameters. First, the vibrational echo method, including some details of the

experimental techniques, is described. Then vibrational echo experiments,

used to probe vibrational dynamics in liquids and glasses, are presented. In

addition, protein dynamics are studied using vibrational echo measurements

on the CO ligand bound to the active sites of the proteins myoglobin and

hemoglobin. In studies of liquids, glasses, and proteins, the vibrational echo

experiment is used as a time domain probe of dynamical intermolecular

interactions. A new two-dimensional spectroscopy, vibrational echo spectroscopy (VES), is also described. In VES experiments, vibrational echoes

are used to suppress unwanted background in a vibrational spectrum and

to enhance one peak over another in a manner akin to the methods used in

NMR. The combination of the experiments demonstrates that a new era of

IR ultrafast coherent vibrational spectroscopy has begun.

II. THE VIBRATIONAL ECHO METHOD AND EXPERIMENTAL

PROCEDURES

A. The Vibrational Echo Method



The vibrational echo experiment is a time domain, degenerate, four-wave

mixing experiment that extracts the homogeneous vibrational line shape

even from a massively inhomogeneously broadened line. Vibrational line

shapes contain the details of the dynamical interactions of a vibrational

mode with the motions of the environment (22–24). However, the vibrational line shape can also include low-frequency, structural perturbations

associated with the distribution of the vibrational oscillators’ local environmental configurations, i.e., inhomogeneous broadening. The presence of

inhomogeneous broadening in a wide variety of condensed matter systems

makes the vibrational echo a useful experimental tool.



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Infrared Vibrational Echo Experiments



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Vibrational echo experiments permit the use of optical coherence

methods to study the dynamics of the mechanical degrees of freedom

of condensed phase systems. Because vibrational transitions are relatively

narrow, it is possible to perform vibrational echo experiments on welldefined transitions and from very low temperature to room temperature

or higher. Further, vibrational echoes probe dynamics on the ground state

potential surface. Therefore, the excitation of the mode causes a minimal

perturbation of the solvent.

For experiments on vibrations, a source of ps IR pulses is tuned to

the transition of interest. The vibrational echo experiment involves a twopulse excitation sequence. The experiment is illustrated schematically in

Fig. 1A. Initially, all of the vibrations are in the ground state, j0i. This is

represented by an arrow pointing down in the first circle. The first pulse

excites each solute molecule’s vibration into a coherent superposition state

of the molecule’s ground vibrational state and the first excited vibration,

the j0i and j1i vibrational states. This is represented by an arrow in the

plane shown in the second circle. Each molecule in a superposition state

has associated with it a microscopic electric dipole, which oscillates at the

vibrational transition frequency. Immediately after the first pulse, all of the

microscopic dipoles in the sample oscillate in phase. Because there is a

distribution of vibrational transition frequencies, the dipoles will precess

with some distribution of frequencies. Thus, the initial phase relationship

is very rapidly lost. This is represented in the third circle by the arrows

fanning out. The molecules with lower transition frequencies fall behind

the average, and the molecules with higher frequencies get ahead of the

average. This effect is the free induction decay and occurs on a time scale

related to the inhomogeneous line width. After a time, , a second pulse,

traveling along a path making an angle, Â (see Fig. 1B), with that of the

first pulse, passes through the sample. This second pulse changes the phase

factors of each vibrational superposition state in a manner that initiates a

rephasing process. This is illustrated in the fourth circle. The fan of arrows

flips over so that the arrows that were moving apart are now moving toward

each other. At time 2 , the ensemble of superposition states is rephased.

This is shown in the fifth circle as the reformed single arrow. The phased

array of microscopic electric dipoles behaves as a macroscopic oscillating

electric dipole, which acts as a source term in Maxwell’s equations and

gives rise to an additional IR pulse of light, the vibrational echo. A free

induction decay again destroys the phase relationships, so only a short

pulse of light is generated. As shown in Fig. 1B, the vibrational echo pulse

propagates along a path that makes an angle, 2Â, with that of the first pulse.



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