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A. Vibrational Echo Results and Dephasing Mechanisms

A. Vibrational Echo Results and Dephasing Mechanisms

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258



Rector and Fayer



(54). In all cases, the pure dephasing rates were calculated from these results

using Equation (2). Figure 12 shows the pure dephasing contribution to the

linewidth, 1/ TŁ2 , versus temperature on a log plot for MbCO in trehalose.

Trehalose is a sugar that is a glass over the entire temperature range of the

study. As can be seen in Fig. 12, between 11 and ¾200 K the functional

form of the data is a power law,

1

D aT1.3

TŁ2



(10)



where the prefactor a D 3.5 ð 107 š 0.1 ð 107 Hz/K1.3 . The error bar on

the power law exponent is š0.1. There is a change in the functional form

of the data at ¾200 K. The points above ¾200 K can be fit with

1

D 3.3 ð 1012 e

TŁ2



650

kB T Hz



(11)



where kB is Boltzmann’s constant, kB T has units of cm 1 , and the error bars

on the prefactor and activation energy are š0.2 ð 1012 Hz and š25 cm 1 ,

respectively. However, it is important to emphasize that the form of

Equation (1) is not unique given the small number of points. If this is

done, the value of the exponent changes, but the power law is identical. A

very good fit is obtained with a power law plus a Vogel-Tammann-Fulcher

(VTF)–type equation (88–90):

1

D aŁ exp

TŁ2



E

T T0



(12)



A VTF function often describes the temperature dependence of properties

of glass-forming liquids. T0 is referred to as the ideal glass transition

temperature and is typically a few tens of degrees below the laboratory

Tg . A fit to the data with Equation (10) plus Equation (12) yields a T0

of ¾180 K and an E corresponding to a temperature of ¾230 K. These

parameters can vary somewhat about the given values. However, the power

law is always identical, independent of the form used to fit the points above

¾200 K. If the exponential fit and the VTF fit are extended to higher

temperatures, they do not become distinguishable below 500 K. Therefore,

experiments at temperatures below the Mb denaturation temperature cannot

distinguish these two forms. Regardless of the form that is used to fit the

data, it is clear that there is a sudden change in the nature of the temperature

dependence of the pure dephasing.

The myoglobin dynamics near ¾200 K have been the subject of

considerable investigation. There have been many experiments show a



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Infrared Vibrational Echo Experiments



259



Figure 12 Log plot of the pure dephasing width, 1/ TŁ2 , versus temperature for

native MbCO in trehalose. Below ¾200 K the temperature dependence is dominated

by a power law, T1.3 , which appears linear on the log plot. Above 200 K the data

can be fit with an exponentially activated process or a VTF process.



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260



Rector and Fayer



break near 200 K (71,91–97). However, there have been other experiments

that do not see a change near 200 K (93,98–101).

Given the many other types of studies that have observed changes in

the Mb dynamics at ¾200 K and that have been interpreted as evidence of

a protein glass transition (16), it is reasonable to assume that the vibrational

echo data do, indeed, display a manifestation of a change in the basic nature

of the protein dynamics, i.e., they reflect the protein glass transition. The

protein glass transition is not a true glass transition but, rather, reflects a

change in the nature of protein dynamics that is akin to the liquid/glass transition. As discussed below, MbCO pure vibrational dephasing arises from

global fluctuations of the protein structure (16,20,102). The CO dephasing

is caused by electric field fluctuations produced by overall protein motions,

rather than very local protein dynamics near the CO. A change in the

nature of the protein dynamics, which influences the various observables

that have been studied previously, can also produce a change in temperature

dependence of the vibrational pure dephasing.

Figure 13 shows pure dephasing linewidths as a function of temperature for MbCO in three solvents. The circles are the trehalose data shown in

Fig. 9; the diamonds are data for MbCO in the solvent 95:5 glycerol:water,

(16,20) and the squares are data for MbCO in the solvent 50:50% ethylene

glycol:water (54). The line through the trehalose data is the fit from Fig. 12.

The lines through the other data are guides to facilitate discussion.

In all three solvents, at temperatures below their respective break

points, the data fall on the same T1.3 power law line. The fact that the

vibrational dephasing comes solely from protein fluctuations, and not from

the solvent, has been discussed in detail previously (16,20,102). The identical power law temperature dependences, which have the same dephasing

rates in three solvents, is a demonstration that the vibrational pure dephasing

is a measure of protein dynamics.

The T1.3 temperature dependence observed at lower temperatures for

the MbCO vibrational dephasing is reminiscent of the vibrational dephasing

and other experimental observables measured in true glasses. In the MbCO

vibrational dephasing, the T1.3 temperature dependence is observed to much

higher temperatures than in true glasses. Like the results in Rh(CO)2 acac,

one possible explanation of the power law temperature dependence is thermally assisted tunneling among slightly different protein configurations.

Small internal protein structural changes might be described in terms of

protein two-level systems (PTLS) (16,20). The PTLS are the equivalent

of the two-level systems discussed above, except the protein energy landscape would have to be such that tunneling is the dominant process at



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Infrared Vibrational Echo Experiments



261



Figure 13 Pure dephasing of MbCO in three solvents. The circles are the trehalose

data shown in Fig. 12. The diamonds are data taken in 95:5 glycerol:water (16). The

squares are data taken in 50:50 ethylene glycol:water. Below ¾150 K the dynamics

for all three solvents are fit with the identical T1.3 power law. Above ¾200 K the

trehalose data are fit with an exponentially activated process. The glycerol:water

and ethylene glycol:water data have both a temperature dependence and a viscosity

dependence at the higher temperatures.



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262



Rector and Fayer



temperatures up to 200 K. If this is the case, the same statistical mechanics

machinery used to describe the low-temperature (¾1 K) optical dephasing

of electronic transitions of chromophores in low-temperature glasses (7,103)

can be used to describe the PTLS induced vibrational dephasing of MbCO

at much higher temperatures (¾100 K).

In Fig. 13 it can be seen that the discontinuities in the dephasing

in the three solvents do not occur at the same temperature and that the

temperature dependences are not the same in the three solvents at higher

temperatures. At all temperatures studied in trehalose, the viscosity is effectively infinite since it is a glass. The observed temperature-dependent pure

dephasing comes from protein fluctuations in a solid medium in which

the topology of the protein/surface interface is fixed. In the two liquid

solvents, the situation is quite different. As the temperature is increased, the

viscosity of the solvents decrease. Recent vibrational echo studies on MbCO

conducted at room temperature as a function of solvent viscosity (data not

shown here) show that there is a strong viscosity dependence to the MbCO

pure dephasing (104). At constant temperature, as the viscosity of the

solvent is decreased, the MbCO vibrational pure dephasing rate increases.

Therefore, the temperature dependences observed in the glycerol:water and

ethylene glycol:water solvents are actually combinations of a pure temperature dependence and a viscosity dependence. For this reason, the data in

these solvents were not fit with the functions given in Equation (11) or

(12). The trehalose data characterize the protein dynamics responsible for

the pure dephasing with the protein/solvent boundary condition static.

The order from lowest temperature to highest temperature of the break

in the functional form of the temperature dependences displayed in Fig. 13

is ethylene glycol:water (¾150 K), glycerol:water (¾180 K), and trehalose

(¾200 K). This is also the order of the solvents’ glass transition temperatures. From Fig. 12 it is clear that the dynamical transition displayed in the

vibrational echo data does not depend on the solvent undergoing a glass

transition. However, the data show that if the solvent goes through its glass

transition at a temperature below the protein glass transition temperature,

TPg , then TPg is reduced. This is not a slaved protein glass transition, but,

rather, a protein/solvent boundary condition influence on TPg (19).

B. Coupling of Protein Fluctuations to the CO Ligand at the

Active Site



For vibrational dephasing of CO bound to the active site of Mb to occur,

the fast motions of the protein must be coupled to the vibrational states of

the CO in a manner that causes fluctuations in the CO vibrational transition



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Infrared Vibrational Echo Experiments



263



energy. Two models have been proposed to explain the dephasing in Mb

(20,102). One involves global electric field fluctuations and the other local

mechanical coupling.

In the global electric field model, motions of polar groups throughout

the protein produce a time-dependent electric field. The fluctuating electric

field causes modulation of the electron density of the heme’s delocalized

-electron cloud. Fluctuations of the heme

electron density modulate

the magnitude of the back bonding to the CO Ł orbital, causing timedependent shifts in CO , or pure dephasing. In essence, the protein acts as a

fluctuating electric field transmitter. The heme acts like an antenna, which

receives the signal of protein fluctuations and communicates it to the CO

ligand bound at the active site via the back bonding.

In the local mechanical fluctuation model, the local motions of the

amino acids on the proximal side of the heme are coupled to the heme

through the side group of the proximal histidine. The side chain of the

proximal histidine is covalently bonded to the Fe. This bond is the only

covalent bond of the heme to the rest of the protein. Thus, motions of

the ˛-helix that contains the proximal histidine are directly coupled the Fe.

These motions can push and pull the Fe out of the plane of the heme. Since

the CO is bound to the Fe, these motions may induce changes in the CO

vibrational transition frequency causing pure dephasing.

To test these models, we have performed a temperature-dependent

vibrational echo and pump-probe study on two myoglobin mutants, H64VCO and H93G(N-MeIm)-CO, and compared the results to those of the

wild-type protein. To test the global electric field model, we studied H64V,

a myoglobin mutant in which the polar distal histidine is replaced by a

nonpolar valine (105). If the global electric field model of the dephasing

is operative, then the decrease in the electric field in the mutant should

reduce the magnitude of the frequency fluctuations, producing slower pure

dephasing. To test the local mechanical model of pure dephasing, we studied

H93G(N-MeIm), a myoglobin mutant in which the proximal histidine is

replaced by a glycine (106). This mutation severs the only covalent bond

between the heme and the globin and leaves a large open pocket on the

proximal side of the heme. Inserted into this pocket and bound to the heme

at the Fe is an exogenous N -methylimidizole, which has similar chemical

and electrostatic properties as the side group of the histidine. Effectively,

the proximal bond has been severed without changing significantly the electrostatic properties of the protein. If dynamics of the f ˛-helix are causing

the pure dephasing by producing Fe motions via the proximal histidine, then

the dephasing of this mutant should be less than that of the native protein.



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