11648
J. Phys. Chem. 1994, 98, 11648-11656
Energy Flow from Solute to Solvent Probed by Femtosecond IR Spectroscopy: Malachite Green and Heme Protein Solutions Tianquan Lian,? Bruce Locke, Yuriy Kholodenko, and Robin M. Hochstrasser* Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 191 04 Received: January 11, 1994; In Final Form: June 20, 1994@
Femtosecond IR spectroscopy has been used to study the energy transfer from solute to solvent in various solutions by monitoring the change of solvent vibrational spectrum. A model system consisting of malachite green and D20 is used to study the heating of D20. An increase in transmission in the 1800 cm-' region of the D20 spectrum after photoexcitation of the solute at 580 nm is explained by the heating of surrounding water which shifts the water infrared absorption bands. The response time for the water spectrum shift to the temperature change was measured to be 4 f 3 ps. The rise times of the heating signal in deoxyhemoglobin (Hb) and deoxymyoglobin (Mb) solutions are studied in detail to investigate the energy transport mechanisms in heme proteins. The kinetics of this increase of transmission is fitted to a model that consists of a fast and a slow component. The fast component is best fitted by a Gaussian rise function with time constants of 7.5 f 1.5 and 8.5 f 1.5 ps for Mb solution and Hb solutions, respectively. The slow component (ca. 20 ps), with 40% of the total amplitude, is attributed to energy transfer from heme to water through the protein via a classical diffusion process based on agreement between the measured time and that calculated with classical diffusion theory. The fast component, almost identical for both Hb and Mb, could not be described by classical diffusion theory and is suggested to proceed through collective motions of the protein.
Introduction The photodissociation of carboxyhemoglobin (HbCO) into Hb and CO occurs in less than 100 f ~ . ' - ~As a result of severing the Fe-CO bond, there occurs an immediate relaxation of the heme pocket structure that inhibits the rebinding of CO. The excess energy is released into low-frequency modes of the protein by means of translational and rotational cooling of the photogenerated CO and vibrational cooling of the heme product of reaction. The released energy ultimately warms not only the protein but also the surrounding solvent. This picture of the effects of photodissociation was used to explain results obtained using subpicosecond infrared spectroscopy.',2 The vibrational spectra of reactants and products of the HbCO dissociation evidence changes in structure that are not necessarily accompanied by significant changes in the optical spectrum. Furthermore, unlike electronic spectra, these changes can be directly associated with particular chemical bonds and hence are more readily interpreted in terms of chemical structure. Thus, an important goal of such IR studies is the assignment of each observed spectral change to a portion of the molecular structure. This step is least straightforward at the shortest times when the vibrational states are changing on a time scale shorter than the vibrational depha~ing.~ In this regime the vibrational spectra are dynamically broadened, and their interpretation will usually not be so clear. For this reason it was obvious that a more detailed study of the effects of optical excitation on the IR spectra of Hb was needed in order to better understand the results observed for HbCO and the ongoing study of HbNO. The excitation of deoxyHb generates vibrationally excited ground states extremely rapidly, so that this system may serve as a model for the process occurring in the early stages of the HbCO photodissociation in which vibrationally excited ground state deoxyHb is also involved. t Present address: Department of Chemistry, University of California, Berkeley, CA 94720. * To whom correspondence should be addressed. Abstract published in Advance ACS Abstracts, August 15, 1994. @
0022-365419412098-11648$04.50/0
Recently, we carried out a detailed study of two of the early events noted in transient IR studies of hemoglobin.'q2 A very short, close to pulse limited, transient absorption was noted in the region between 1950 and 2015 cm-': it is shown here that this signal is a result of two-photon absorption by Hb. The previous study also noted an increase of IR transmission in the same region over a period of ca. 30 ps after optical excitation: it is shown here, through much more detailed experiments, that this effect is caused by the energy flow from the heme into the protein and the aqueous environment, in agreement with the previous suggestion. In this paper the heating of water is considered in expanded detail. In order to understand the energy transfer mechanism in heme proteins, we have to understand the effect of rapid heating of water on its IR spectrum. A model system for studying the heating of water should contain only water and a well-studied heat source. The system we decided to use as a model is malachite green in D20. Malachite green was chosen because its excited state dynamics and vibrational relaxation in the ground state are well-~tudied.~-'~ All our previous experiments's2 were carried out in D20 because it has better transmittance than H20 in the 1800 cm-' region. Detailed kinetics of the water heating in deoxyHb and deoxyMb solutions were studied. A classical diffusion calculation was carried out to predict the rate of water heating with a diffusional model for energy transfer in the protein. Comparisons of the measured rate and calculated rate for water heating suggest possible mechanisms for the energy flow in heme proteins.
Experimental Section An improved femtosecond IR spectrometer has been used to study the ultrafast energy transfer in deoxy heme protein in D20 solution following visible excitation. The details of the femtosecond R spectrometer have been published elsewhere.1q11.12 Briefly, a sample is pumped with a visible pulse and probed with continuous-wave (CW) IR from a CO laser operating from 1800 to 1890 cm-'. Gated detection of the CW IR beam 0 1994 American Chemical Society
J. Phys. Chem., Vol. 98, No. 45, 1994 11649
Energy Flow from Solute to Solvent is achieved with femtosecond time resolution by frequency summing the transmitted IR with a femtosecond visible pulse in a nonlinear crystal. The upconverted signal is proportional to the transmitted IR intensity over the slice of time defined by the gating pulse. The signal recorded is the change of IR absorbance (AA) of the sample induced by the pump pulses. Time-resolved IR spectra are obtained by measuring AA as a function of the probe IR frequency with a fixed optical delay between the pump and gating pulses. The kinetics at one IR frequency is obtained by measuring AA at different optical delays. The instrument response function of this technique is the cross-correlation of the pump and gating pulses. Since both the pump and the gating pulses are derived from the same optical pulse, the time resolution is limited by the autocorrelation width of the optical pulse. The spectral resolution is determined by the spectral bandwidth of the probe light. Hence, this approach permits a two-color pump-probe spectroscopic study with ultrafast time resolution but without sacrificing any spectral resolution. The optical pulses (580 nm) originate in a cavity-dumped rhodamine 6G dye laser that is synchronously pumped with the frequency-doubled output of CW mode-locked Nd:YAG laser. These pulses are shortened to 300 fs in an optical fiber-grating compressor and amplified to 5 pJ at 1 kHz in a multipass rhodamine B dye amplifier which is pumped by the frequencydoubled output of a CW Q-switched Nd:YAG laser. The amplified output is used to obtain both pump and probe pulses. The 1 kHz pump pulses are alternately blocked by a synchronous chopper at 500 Hz. The pump beam and the probe CW IR beam are focused collinearly in the sample with a spot size of 100 and 50 pm, respectively. The transmitted IR is frequency summed with the gating pulse (1 kHz) in a LiIO3 crystal. The upconverted signal is detected with a PMT and demodulated in two lock-in amplifiers, from which the change of absorbance is derived. The CW IR probe originates from a CO laser (Laser Photonics). The CO laser is line tunable from 1800 to 1890 cm-' with rovibrational transitions appearing at 4 cm-l intervals. The typical output power is about 300 mW. The CW output of this CO laser is synchronously modulated at 1 kHz by an acoustic optical modulator to allow the CW IR probe to interact with the sample for about 5 ps, which prevents the possible heating of the sample caused by the high average power probe beam. The noise level of the system can be limited by shot noise when the CW probe becomes less than ca. 10 mW. The improved beam quality of the CO probe compared with a CW diode laser makes it possible to focus the probe beam to a smaller size at the sample so that a higher signal can be obtained. As a result of using a CO laser instead of a diode laser, the signal-to-noise ratio of the system is greatly improved. For example, to obtain the same standard deviation of the data, the acquisition time is reduced by a factor of ca. 10 compared with ref 1. The hemoglobin samples were prepared by dissolving human hemoglobin (Sigma) in D20 containing 0.1 M potassium phosphate buffer at pH 7. The samples were reduced with a 3-fold stoichiometric excess of sodium dithionite in a sealed cell under N2 pressure to obtain deoxyhemoglobin samples. The myoglobin samples were prepared with the same procedure from sperm whale myoglobin (Sigma). Both the hemoglobin and myoglobin samples were made with about 15 mM heme concentration. Malachite green samples were prepared by dissolving malachite green (from Exciton) in D20 or benzonitrile. The concentration of the sample was about 3 mM. The solution was flowed through a 1 0 0 pm path length, CaFz
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Figure 1. Transient absorption spectrum of malachite green in D2O measured 100 ps after the pump pulse. The pump beam is at 580 nm, and the probe frequency is from 1800 to 1880 cm-'. The full circles are the measured data, and the dotted line is the static IR spectrum of D20 in the sample scaled by a factor of 340. This signal is attributed to the change of the water spectrum due to heating. 0.006 0.004
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Figure 2. Kinetics measured in malachite green in D20 solution at 1843 cm-l. The full circles are measured data. The dotted lines are the best fit to the data. The spike at r = 0, which is instrument response function limit, is attributed to the two-photon absorption of an IR and optical photon. The rise of the bleach signal is fitted to exponential rise function [l - exp(-th)] with a time constant t of 7 f 3 ps. The signal is measured at magic angle.
sample cell during the experiment. The integrity of the samples were frequently checked by absorption spectra.
Results Shown in Figure 1 is a difference absorption spectrum of malachite green in DzO at 100 ps after the sample is pumped with an optical pulse at 580 nm. An increase of IR transmittance (Le., negative absorption) is observed in the region from 1800 to 1880 cm-'. Also shown in Figure 1 is the static absorption spectrum of D2O in the sample scaled by a factor of 340. The time dependence of the transmission change at 1843 cm-' is shown in Figure 2. These kinetics are the same for probe wavelengths in the spectral region from 1800 to 1880 cm-'. The best fit to the data is a single-exponential rise with a time constant of 7 & 3 ps. The error bar corresponds to an increase of 0.5 in the x2 value of the fit. The spike around t = 0 is best fitted with an instantaneous rise and decay. Figure 3 shows the transient absorption spectrum of malachite green in benzonitrile taken at 100 ps after the sample is pumped by a 580 nm photon. Figure 3 also shows the static IR absorption of benzonitrile. An increase in the IR transmission is also observed for heme proteins in DzO solution from 1 ps to 1 ns after the sample is
11650 J. Phys. Chem., Vol. 98, No. 45, 1994
Lian et al.
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Figure 3. Transient absorption spectrum of malachite green in benzonitrile measured 100 ps after the sample is pumped at 580 nm. The full circles are the measured data, and the broken line is the static IR spectrum of benzonitrile scaled by a factor of 250. 0.002
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Figure 5. Kinetics of the signal observed for deoxyHb in D20 probed at 1843 cm-l. The full circles are the measured data. The spike at t = 0 is fitted to the instrument response function as shown by the broken curve. The kinetics of the bleach signal after the spike are discussed in detail in Figures 6 and 7. The kinetics are the same within our signal to noise for different probe wavelengths in the 1800 cm-' region. 0.001
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Figure 4. Transient absorption spectrum of deoxyHb in D2O measured 100 ps after the pump pulse. The pump beam is at 580 nm, and the
probe frequency ranges from 1800 to 1880 cm-I . The full circles are the measured data, and the dotted line is the static IR spectrum of D20 in the sample scaled by a factor of 340. This signal is attributed to a change of the water spectrum due to heating. pumped with an optical pulse at 580 nm. The frequency dependence of this signal for deoxyHb at t = 100 ps is depicted in Figure 4. The observed absorbance change in the region 1820-1890 cm-' decreases as the IR frequency increases. The D20 absorbance of the sample in the same frequency region scaled by a factor of 340 is also shown in Figure 4, and the same bleach signal can be seen in all the heme protein water (D20) solutions we studied including deoxyHb, deoxyMb, MbCO, HbNO, and HbCO. Detailed kinetics of the bleach signal from deoxyHb are shown in Figure 5 . The positive spike around t = 0 shown in the kinetics has the time profile of the instrument response function and can be best fit to an instantaneous rise and decay. This spike, present in all the heme protein solutions, is assigned to a two-photon absorption signal as discussed below. This twophoton absorption signal is subtracted from the kinetics to better demonstrate the long time bleaching signal as shown in Figures 6 and 7. The subtracted kinetics for deoxyMb solution is shown in Figure 8. Also shown in Figure 6 are the calculated water heating signals using a classical heat diffusion model, the details of which will be discussed later. It is clearly shown here that the observed kinetics cannot be described by the classical diffusion model. These kinetics cannot be fitted satisfactorily by a single Gaussian or exponential rise function. Although a single stretched exponential fits the kinetics well, a good fit is also obtained with a model that consists of a fast and a slower
-0.004 -10
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Figure 6. Kinetics of the bleach signal in deoxyHb in D2O. The instrument response function limited spike at t = 0 has been substracted
from the kinetics to better demonstrate the function form of the bleach kinetics. The measured kinetics are represented by the full circles. Also shown in the figure are the calculated heating signals from D2O for deoxyHb in DzO using eq 5-9 and parameters given in the text based on a classical diffusion theory. The broken curves represent the calculated results for three heme cooling times at 3, 5 , and 10 ps with the slower heme cooling time corresponding to the slower curves in the figure. This comparison clearly illustrates that these measured kinetics cannot be described by the classical diffusion model. components. The fast component, representing about 60% of the total bleaching signal, can be best fitted by Gaussian rise functions A[l - exp[-(t/~)~]]with time constants in the range of 8 ps. Due to the small signal amplitude, the slow component can be fitted satisfactorily by either Gaussian or exponential rise functions with time constants of approximately 20 ps. Since this slow component is in the time range predicted by the classical diffusion model, it is fitted to the functional form predicted by that model. The best fits to the data with a Gaussian rise function and the predicted slow functional form are shown in Figures 7 and 8. The amplitudes and time constants for the fast components are 60%, 7.5 f 1.5 ps and 63%, 8.5 f.1.5 ps for Mb solution and Hb solution, respectively. The error bars correspond to an increase of 0.5 in the x2 values of the fits. These time constants are independent of the probe frequency from 1809 to 1890 cm-'. The bleach spectrum is constant from 100 ps to 2 ns. Using the same pump laser energy, the maximum values of the bleach signals are the same for both deoxyHb and deoxyMb solutions that have the same heme concentrations. The signals at 100 ps shown here are
J. Phys. Chem., Vol. 98, No. 45, 1994 11651
Energy How from Solute to Solvent O.OO'
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Figure 7. Kinetics of the heating signal observed for deoxyHb in DzO probed at 1843 cm-'. The instrument response function limited spike at t = 0 has been substracted from the kinetics. The full circles are the measured data, and the broken curve is the fit to the data to the model discussed below. The fast component of the rise of the bleach signal is best fitted with a Gaussian rise functions, A[l - exp(-(f/ 2)*)], with amplitude and time constant of 60% and 7.5 f 2.0 ps, and the slow component is satisfactorily fitted by a functional form calculated from a classical diffusion theory, as discussed in the text. The kinetics are same within our signal to noise for different probe wavelengths in the 1800 cm-' region. 0.001
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Figure 8. Kinetics of the heating signal observed for deoxyMb in DzO probed at 1843 cm-'. The instrument response function limited spike at f = 0 has been subtracted from the kinetics. The full circles are the measured data, and the broken curve is the fit to the data to the model discussed below. The fast component of the rise of the bleach signal is best fitted with a Gaussian rise function, A[1 - exp(-(t/~)~)],with amplitude and time constant of 63% and 8.5 & 1.5 ps, and the slow component is satisfactorily fitted by a function form calculated from a classical diffusion theory, as discussed in the text. The kinetics are same within our signal to noise for different probe wavelengths in the 1800 cm-' region.
larger than that of Figure 4,because of the tighter focusing in these measurements. The amplitude of the bleaching signal in deoxyHb and deoxyMb was measured as a function of pulse width of the pump pulse from about 500 fs to 1 ps while the total energy of the pump pulse was kept unchanged. Our results show that the bleach signal at 100 ps does not change with the pulse width. The signal increases linearly with the total energy in the pump laser pulse. This clearly demonstrates that the magnitude of the bleach signal does not depend on the peak power. This signal was also shown to be isotropic with an anisotropy of -0.01 f 0.01. The spikes around t = 0 in Figures 2 and 5 have no spectral dependence within the measured probe frequency range. In
malachite green and D2O solution, there is no ground state IR absorption of the solute molecule in this region, so no pumpinduced IR absorption of the solute molecule is expected. Furthermore, molecular vibrational transitions normally have typical bandwidths of ca. 10 cm-'. This signal is present in all the different dye solutions we have investigated, but it does not exist in neat, transparent solvents. Although the probe field is tuned away from resonance with the vibrational transitions of the solute molecule, the combination of the IR photon and the visible photon can still be in resonance with the broad electronic transition in the visible. Therefore, the signal is attributed to the two-photon absorption resulting from the simultaneous absorption of a visible pump photon and a probe IR photon. A signal from this two-photon absorption should decay with the electronic dephasing time of the optical transition, which is on the 10 s of femtosecond scale for dye molecule^.'^ Our measured instantaneous rise and decay of this signal is thus consistent with this explanation. This two-photon absorption of an IR and optical photon should depend linearly on the pump power which is what is observed. The two-photon absorption cross section estimated from our measured signal for Hb and Mb is about 2 x cm4 s, which is in the range of cross sections measured for symmetry-allowed two-photon transit i o n ~ and ' ~ agrees ~ ~ ~ with the value calculated from the known properties of I-Ib and Mb electronic states. The anisotropies of the two photon absorption signals in the heme proteins were measured to be 0.1 f 0.01, which is expected if the transitions involved are polarized on the heme plane and the final state has B symmetry in the C4" point group. These results support the assignment of the fast spike at t = 0 to two-photon absorption, and the details will be given elsewhere.I6 The rise times of thermal grating signals in heme protein water solutions have been measured to be about 20 ps." It was concluded from these results that the energy transfer from the heme to the surrounding water is faster than 20 ps, which we will show is certainly the case. However, the bleaching signal observed here is not caused by a thermal grating which diffracts the IR probe beam. Since there is only one pump beam in our experiment and the back-reflection from the window of the sample cell is weak due to the large absorption of the sample (optical density about 1 at the pump wavelength), a thermal grating cannot be formed by the pump beam. However, the heated solvent molecules do form a thermal lens which can be probed at the up-conversion crystal.16 We have observed this lens and used it to confirm the explanation that the solvent molecules are indeed heated. The experiments reported here, however, are performed at a configuration where the thermal lens effect is minimal and negligible.
Discussion 1. Model System: Malachite Green in D20. After absorbing a 580 nm photon, malachite green molecules are excited to their S I excited states, which then undergo rapid internal conversion to create ground state molecules in highly excited vibrational state^.^-^ The time constant for the internal conversion depends strongly on the viscosity of the s o l ~ e n t , ~ ~ ~ ~ ~ J ~ ranging from subpicosecond in solvents with low viscosity to hundreds of picoseconds in solvents with high viscosity. In water, the internal conversion was found to be faster than 0.6 PS.~,' The cooling of the vibrationally excited ground state malachite green molecules in water was measured to be ca. 3 P S . ~ , The ~ cooling involves collisions of the dye with the solvent molecules which, as a result, acquire energy. Thus, a few picoseconds after absorbing the pump photon, most of the photon energy is deposited into solvent modes. The spectrum of water, an associated liquid, is very sensitive to temperature,'*-**
11652 J. Phys. Chem., Vol. 98, No. 45, 1994
and the spectral changes can be used to sense the dissipation of the solute vibrational energy into the solvent. However, the rate of change of the water spectrum reflects not only the rate of the cooling of the solute molecule but also the rate at which the water structure can adjust to changes in temperature. The IR absorption bands of liquid water are very broad because of the inhomogeneous distribution of hydrogen-bonded structures. When the water temperature increases, its IR absorption bands shift due to changes in the H-bond equilibria. The absorbance at a certain frequency may increase or decrease when the temperature increases, depending on how the particular IR absorption band shifts. The temperature dependencies of most of the water vibrational bands have been well studied.18-22 In the present experiment, the increase in transmission is observed in malachite green and D20 solutions from 1800 to 1890 cm-' as shown in Figure 1. This frequency range is in the region of so-called association band of D20 centered around 1500 cm-'. This association band is known to be a combination band of the bending mode and the hindered rotation, which is a property ascribed to associated water molecules. As the temperature increases, the hindered rotation equilibrium is altered by a barrier crossing process causing the association band to shift to lower frequency. Thus, the absorbance of D20 in the 1850 cm-' region at the high-frequency side of the association band will decrease as the water temperature increases. This is consistent with our observation of an increase in transmission. Pump pulses at 580 nm with ca. 1 pJ energy were used to pump the deoxy heme protein. The spot sizes of the probe CO laser beam and the pump beam in a 100 pm thick sample are 50 and 100 pm, respectively. The heat capacity of the solution is approximately the same as water at the concentration of protein we use in the experiment, namely, 1 c d ( g K).23 At 100 ps delay, when the dye and water molecules are in quasi-equilibrium in the sample volume, as shown in Figure 2, and the deposited energy in the sample does not diffuse significantly out in the probe region, the predicted increase of water temperature is about 0.36 "C. The change of absorption as a function of temperature has been measured for the H20 association b a ~ ~ d . ' ~At, ' around ~ 2470 cm-' in H20 corresponding to about 1800 cm-' in D20, the change of absorbance per degree centigrade per unit OD was found to be about -0.01.18J9 This quantity was found to be approximately the same for temperatures from 10 to 80 "C and for IR frequencies from 2300 to 2500 cm-* in HzO (corresponding to 1700 to 1890 cm-' in D20). Assuming that D20 and H20 have similar temperature dependencies in this band, the absorbance change in our sample after absorbing the pump photons can be estimated. At 1800 cm-', the D20 absorbance is 0.42; thus, the OD change is estimated to be -0.0014. At 1850 cm-' where the absorbance of D20 is 0.34, the pump-induced change can be estimated to be -0.0012. The experimentally measured OD change of about -0.001 in this region, as shown in Figure 1, agrees very well with these values. The bleaching signal due to the heating of water, depending linearly on the absorbance of DzO, follows the expected change in static IR spectrum as shown in Figure 1. The contribution of malachite green IR transitions to the observed absorption change is negligible. To further confirm that the observed signal is indeed from the solvent, other solvents were studied with the rationale that the IR absorption changes arising from the solute dye molecule should be similar for different solvents. Benzonitrile has a vibrational band peaked at ca. 1820 cm-', a combination band of CH bending modes (Y13 ~ 1 4 ) : ~and heating is expected to shfit this mode to lower frequency. The transient difference signal shown in Figure 3
+
Lian et al. is consistent with that resulting from a shift of the benzonitrile IR spectrum due to heating. For the present purpose it is only important to note that the observed signal is due to the heating of the solvent and that this supports the interpretation that the signal in malachite green in D2O is due to the temperature shift of D20 spectrum. The details of the change in the IR spectrum with temperature for benzonitrile will be discussed in another publication. The rise time of the signal in malachite green in D20 solution reflects both the cooling time of the solute and the response time of the solvent spectrum to the temperature change. The observed optical density changes of the solvent will not track the temperature change unless there is an immediate alteration of the hydrogen bond equilibrium. Assuming an exponential rise function for the response of the water structure to the temperature change, the time constant of this response can be calculated using the measured 7 iz 3 ps rise time of the bleaching signal shown in Figure 2 and the 3 ps cooling time of the solute.6 Deconvolution of the measured rise time with the exponential cooling yields a solvent response time of 4 iz 3 ps. The time scale for breaking hydrogen bonds has been extensively studied. For example, it was found that the dissociation of hydrogen bonds is a primary channel for vibrational relaxation of the OH stretch vibration of hydrogenbonded OH groups.25 In ethanol oligomers, the measured 5 ps vibrational relaxation time (TI) for the OH stretch (Y = 1) of the intemal OH group was considered to be the same as the time for breaking those H bonds.25 The population relaxation time for the OH stretch (Y = 1) for bulk H20 was estimated to be less than 3 ps,26,27which suggests an even shorter H-bond breaking time in bulk water. Recently, the 2'1 time of the OH stretch of HDO in D20 was measured to be 8 ps.28 The response time measured in our experiment is consistent with the times measured for breaking hydrogen bonds in many
solution^.^^-^^ After the initial change, the optical density is constant from 100 ps to 2 ns, indicating that the average water temperature is constant during this period. It is known that the spectral shift of H20 is linear with the temperature in the range of 300 K.18J9 Thus, a nonuniform temperature distribution in the sample will yield the same signal as a uniform distribution with the same overall energy deposition. This will be discussed in more detail below. The temperature is expected to decrease only when the heat diffuses out of the probe region. The probe beam size in the experiment was 50 pm. For a heat diffusion constant x of 15 A2/ps, the time t at which the mean diffusion length, 2@)'12, reaches 50 p m is about 4 ms, so the constant signal on the subnanosecond time scale is fully expected. In summary, the bleaching signal observed for malachite green in D2O is ascribed to the heating of the surrounding water. The magnitude of the signal, which is proportional to the average temperature change, agrees well with the value estimated from equilibrium properties of water. The spectrum of this signal is dependent on the static spectrum of the solvent and its change with temperature. The observed transient spectrum for D20 in this spectral region is consistent with that predicted from its static IR absorption spectrum. The response time of the D20 spectrum change to the deposition of energy is estimated to be 4 f 3 ps, which is within the range of times attributed to the breaking of hydrogen bond^.^^-^* The instrument response limited spike at t = 0 is attributed to the simultaneous absorption of an IR and optical photon. 2. Deoxy Heme Proteins in D20. After absorbing a visible photon, a deoxy heme is excited to an excited electronic state (Q band of the metalloporphyrin) which then relaxes to the
J. Phys. Chem., Vol. 98, No. 45, 1994 11653
Energy Flow from Solute to Solvent
ground electronic state within 300 fsS3sz9During this relaxation process, the energy of the absorbed photon is converted into vibrational energy of the heme. The intemal conversion process, at least for the low-frequency modes, is expected to involve a where r is the distance from the origin and Q , the strength of large enough number of modes that the vibrational energy the heat source, is defined as E/$ with E being the total energy distribution would be difficult to distinguish from a Boltzman distribution and therefore can be defined by tem~erature.~O-~~ deposited, the density of the medium, and C the heat capacity. The volume of the heme, the heat source, is much smaller The vibrationally hot heme will then cool via collisions with than that of a protein. One approach is to approximate the heme the surrounding protein. There are approximately 100 van der as a sphere with the volume of the heme. This spherical heat Waals contacts between the protein and the heme,32 which is source is then embedded in a protein sphere which is considered substantial thermal contact. The cooling of the heme will cause to be surrounded by a continuous medium with the thermal the temperature of the protein to rise. The heated protein properties of water. The thermal diffusivity for heme proteins meanwhile will be transferring its excess energy to the suris not known to the best of our knowledge. However, the rounding water which is at a lower temperature. In summary, thermal diffusivity for most protein and water mixtures t t room the energy of the absorbed photon heats the heme and is temperature is found to be in the range 10-15 A * / ~ s . ~ ~ eventually transferred through the protein to the surrounding Therefore, the thermal diffusivity of water, i.e., 15 A2/ps, was water until the whole system, defined by the active volume used for both water and protein, so that the calculated rate for excited by the pump pulse, reaches a new thermal equilibrium water heating probably represents an upper limit for a diffusive at a higher temperature. The bleaching signal we have observed process. This approach is valid for the case that the heme is attributed to the spectral shift of D2O arising from this proteins are far enough from one another that the region reached temperature increase. The kinetics of this signal should indicate through diffusion process from one heme does not overlap with the rate of energy flow from heme through protein to the that of the neighboring heme. At the concentration of heme surrounding water. protein used in the experiment, the mean separation between The observed signal in deoxyHb solution shown in Figure 4 two excited hemes is about 90 A. According to eq 2, it takes has a similar magnitude to that observed in malachite green in 140 ps to reach a temperature distribution with a width of 90 DzO using the same pump energy and sample volume, c o n f i i A, a radius at which the temperature is l/e of that of the origin. ing that at 100 ps the signal is determined by the solvent shift. Thus, it is not unreasonable to treat the solution as an infinite Though the temperature increase due to heme cooling can also medium on time scales shorter than this. Accordingly, the whole cause a shift of the protein or heme vibrational spectra, the system can be treated as a single infinite medium with a absorbance change due to such effects is much smaller than spherical heat source at the origin. Although the heme is better the absorbance change due to water: about 80% of the IR described as a disk than a sphere, the spherical model, which absorption of the sample is due to D20 at 1850 cm-l. Although simplifies the calculation greatly, should be adequate for we cannot exclude a small contribution from the protein and calculating the average water temperature. At a large distance heme, the good agreement between the observed signal size and from the heat source, the temperature distributions are similar the estimated signal due to the heating of water suggests that for different heat sources as long as the dimension of the heat most of the signal is indeed from the shift of water spectrum. source is much smaller than the distance. In Hb and Mb In earlier work,’ the 2000 cm-’ region for HbCO and solution, the heme dimension is much smaller than the size of deoxyHb in D20 solution was probed after photoexcitation. In the protein and less than the average distance from water to that experiment, the low-frequency side of the OD stretching heme center; thus, the average water temperature can be band centered at 2500 cm-’ is involved. The OD stretching calculated by treating the heme as a spherical heat source. This frequency decreases when the OD groups form hydrogen bonds. is confirmed by the virtually identical water heating kinetics Thus, when the temperature increases, there is less hydrogen obtained by using a spherical and a point heat source. Since bonding, causing a decrease of absorbance in the 2100 cm-’ we are only interested in the average water temperature, an region, as observed. average spherical protein is used instead of the real irregular 2.1. Classical Dzfision Picture. The rate of change of the shape of the protein. water spectrum depends on the rate of heme cooling, but also The process of cooling the heme represents a bottleneck in on the rate of energy transfer within protein, and the rate by the energy transfer from the heme to the surrounding water. which the water equilibria can be altered as discussed above. This part of the problem cannot be described by classical heat In this section, classical heat transport theory is used to describe diffusion theory. The cooling of the photoexcited heme was the energy transfer. The rate of temperature change of the studied by a variety of experiments and computer simulations. surrounding water is calculated, and by comparing the result Henry et aL3*have studied the vibrational cooling process of with the experimental measurements, possible mechanisms for heme proteins after laser excitation using a classical molecular energy transfer in heme proteins are proposed. dynamics simulation. They predicted that the vibrational In an infinite isotropic medium, the temperature distribution cooling of photoexcited deoxymyoglobin and cytochrome c in at any time t is described by33334 vacuo can be best described by two exponential of approximately equal amplitude: the fast component has time constant of 1-4 ps and the slow one has a time constant of 20-40 ps. Single-exponential fits to the cooling process gave (x - x’)2 01 - y ’ y ( z - 2’y time constants in the range 8-13 ps. The vibrational relaxation of several porphyrins in Hb and Mb after photo4Xt excitation has been measured by resonant Raman spectroscopy, yielding a range of decay times of 2-5,38,39ca. and e 3 0 where To(x’,y’,z’) is the initial temperature distribution and x is The vibrational cooling time for various porphyrin the thermal diffusivity of the medium. If the initial temperature molecules are measured to be about 10 ps by time-resolved distribution is a 6 function, Qd(x’) db’)d(z’), at the origin, then absorption and emission spectroscopy.@ These measured coolT is given by
+
+
11654 J. Phys. Chem., Vol. 98, No. 45, 1994
Lian et al.
ing rates are consistent with the knowledge of cooling of other large molecules in l i q ~ i d s . ~ ~ , ~ ~ The heme cooling was thus modeled by placing a timedependent heat source at the origin. The origin is located inside a sphere of radius rp (the proteins) at r, - rd from the center of the sphere in order to model the off-center positioning of the heme in the protein. So the initial temperature distribution is
To({$) = Qd(r’-ro) F(t’)
(3)
where ro is the radius of the spherical heat source, Q is the strength of the heat source as defined in eq 2, and F ( / ) is the function describing the rate at which energy is released from it. If heme cooling is modeled as a single-exponential decay, then ~ ( t=) (l/z)e-‘/r
(4)
For a sufficiently rapid heme cooling time, the temperature distribution in the sample can be described approximately by34
where r is the distance from the heme. The average temperature of water at any time, Tw(t), calculated by averaging T(r,t)in eq 5 over the volume occupied by water is given by 1 T J t ) = - s M T ( r , t ) P(r)4nr2dr vw O
where Vw is the volume of the surrounding water and P(r) is the fraction of the surface area of the sphere with radius r that is in the aqueous phase. This fraction is readily seen to be given by
P(r) = 0.5
- Rd) + r2 - Rd(2R, 4r(Rp
for R,
r
2Rp - Rd
Rd)
P(r) = 0 P(r) = 1
(7)
for r < Rd for r > 2Rp - Rd
where Rd is the smallest distance from heme center to the protein surface and R, is the radius for the average protein sphere. The average temperature of the protein sphere can be described by 1
T’(t)= -J’T(r,t)[l VP
- P(r)]4nr2dr
O
where V, is the volume of the protein. The absorbance change due to heating can be calculated from
where C is the absorbance change per unit temperature change and t~ is the response time for the water spectral shift, which was determined in our experiment on malachite green in D2O to be 4 f 3 ps. In calculating the average absorbance change from the average temperature, it is assumed that the absorbance change is linear with temperature change. In the 1800 cm-I region, D20 absorption decreases linearly with the temperature in the
temperature range from 10 to 80 “C according to steady state meas~rements.~*J~ The temperature distribution, given by eq 5, is a Gaussian function of the distance from the heme with the width of the Gaussian function broadening with time. The initial temperature at the heme could be on the order of 500 K just following absorption of a 580 nm photon.43 Under this initial condition and classical diffusion, the temperature at 5 8, from the heat source never rises more than 20 K. Thus, in our experiment, the change of optical density of water should be linearly proportional to the temperature change, and eq 9 is valid. Furthermore, because the spectral shift is linear with the temperature, the same average signal is obtained for any temperature spatial distribution that might exist with the same average temperature. The average radius for the protein, R,, is defined so that the volume of the sphere is the same as the volume of the real nonspherical protein, which is known from the X-ray ~tructure.4~ For hemoglobin R, = 35 8, and for myoglobin R, = 23 8,. Rd is taken as the nearest distance from the center of the heme to the protein surface, which is 10 8, for both Hb and Mb. The radius of the average sphere for the heme is taken to be 3.3 A, so that it occupies same volumes as the real planar heme.44The heme cooling is modeled by an exponential decay with a time constant t of 3-10 ps. The average absorbance change in water as a function of time is calculated for heme cooling times from 3 to 10 ps using eqs 5-9 and the parameters discussed above for Hb and Mb solution. The calculated results for deoxyHb with heme cooling times of 3,5, and 10 ps are shown in Figure 6. These kinetics curves can be very well described by double-Gaussian rise functions [ 1 - A exp( -tlzl)’ - (1 - A) exp( - t / t 2 ) ’ ] . With a 5 ps heme cooling time, the parameters for the Gaussian rise functions are A = 80%, t 1 = 16 ps, and t 2 = 38 ps in Mb and A = 63%, t 1 = 17 ps, and z2 = 44 ps in Hb. Although these rise times are much too slow compared with the rise time of ca. 8 ps for the fast component observed in our signal as is clearly demonstrated in Figure 6, they are in the range of the rise times for the slower component. These calculated functional forms are then used to fit the slow components in the measured data, giving a very satisfactory agreement between the measured data and the classical diffusion calculation with a 5 ps heme cooling time, as shown in Figures 7 and 8. The measured signals are thus explained to consist of predominantly two different energy transfer processes with the slow component corresponding to diffusion in the protein and the fast component corresponding to some nondiffusive processes. In fitting the slow components of the measured data to the calculated functional form, only the magnitude of the function is varied to obtain the best fit. The slow components can also be fitted to other models, where more fitting parameters are needed. Although the fit to the slow component is not unique, the classical diffusion model is the simplest model with the least adjustable parameters. At present, the data do not justify fitting to a model with more than two components where there would be more fitting parameters, but such a picture should not be excluded. Folded proteins are nearly close-packed and nonperiodic, so that they may have some quasi-liquid-like or glass-like physical properties.44 A recent molecular dynamics (MD) simulation45 of protein thermalization in reaction centers for photosynthetic bacteria gave results that agree with classical heat diffusion theory. In that classical molecular dynamics simulation, the excess energy in the protein is classical; Le., a MaxwellBoltzman distribution of velocities is present all the time. This may not be true in our heme protein experiments where the
Energy Flow from Solute to Solvent energy comes from the rapid cooling of vibrational modes of the heme. One may expect, however, that this energy will be redistributed over many local modes of the protein atoms near the heme very quickly and that the subsequent cooling will be classical. It is thus quite reasonable to assume that one possible way for energy transfer in the protein is through classical diffusion. Two possible ways for the fast release of the energy from the heme to the solvent are now discussed to account for the faster than diffusion component observed. The fist mechanism involves a collective motion of the protein which facilitates energy transfer to the solvent. The second mechanism involves the transfer of energy from heme to the solvent directly through the side chains of the heme that are exposed to the solvent. The time constant for the rapid excitation of the vibrational modes of the heme through its intemal conversion is estimated to be around 300 fs,3.29giving rise to a heme temperature of about 500 K.32 The possibility that the rapid heating and cooling of the heme may excite some low-frequency modes of the protein that involve the collective motion of large number of atom needs to be considered. These collective motions could be heavily damped by the surrounding water, thereby causing water molecules to heat faster than in a diffusional process. The time scales for the energy propagation from the heme to the protein surface through these collective motions are determined by the group velocities of these motions in the protein. These velocities have not been well measured to our knowledge. However, they are expected to be similar to a sound wave velocity, which falls in the range from 10 to 15 k p s in typical liquids and 12 to 100 k p s in typical solids.46 Using these parameters, the time scales for the energy propagation from the heme to the protein surface can be estimated to be in the range from 0.35 to 3.5 ps in Hb and 0.23 to 2.3 ps in Mb. The rate of water heating also depends on the rate at which these lowfrequency modes are damped by the surrounding water. Collision-induced ultrafast intermolecular energy dissipation for polyatomic molecules in solution has been observed to be faster than 5 If the damping of these modes is not the ratelimiting step, by combining a heme cooling time of ca. 5 ps, a water spectral response time of ca. 4 ps, and the times for energy transfer from heme to protein surface of less than 3.5 ps in Hb and 2.5 ps in Mb, the time scales for the water heating signal can then be estimated to be faster than ca. 12 and 11 ps in Hb and Mb. Taking into account the uncertainty in heme cooling time, 2-5 ps,38,39spectral response time, 4 k 3 ps, and energy transfer times in Hb and Mb, these estimated times agree with the measured times of 8.5 ps in Hb and 7.5 ps in Mb. Collective low-frequency modes of heme proteins have been calculated by conformational normal mode analysis4*and MD simulation49and observed experimentally by low-temperature hole-buming studies of phonon sidebands,50Raman ~cattering,~' and neutron ~ c a t t e r i n g ? ~Recently, .~~ the phase grating dynamics in MbCO and HbC053 was interpreted in terms of a collective motion triggered by the dissociation of CO. The photoexcitation of Hb and Mb studied in the present work is not understood to initiate any tertiary structure change, but the rapid excitation of the vibrational modes of the heme could excite some collective motions of the protein. Another possible mechanism, corresponding to rather a specific collective motion, is the direct energy transfer from the heme to the solvent through the side chains of the heme. Although the heme is almost completely protected by the globin in both Mb and Hb, the two propionic acid side chains are exposed to the solvent. Is it possible that the vibrational energy of the heme could be transferred directly to the surrounding
J. Phys. Chem., Vol. 98, No. 45, 1994 11655 water by the solvent-induced damping of these stimulated side chain motions? The ca. 8 ps time constant of the fast component in our measured data in Hb and Mb solution would then arise from the consecutive processes of exponential cooling, involving energy transfer to the side chain in ca. 5 ps and the water response of 4 ps. There is no precedent for such highly directed energy funneling in molecular relaxation processes. However, the cooling may be quite anisotropic. The part of the heme edge nearest the outside of the protein, which is surrounded by the protein atoms associated with the CD and FG comer of the helixes, may be facilitating the anisotropic release of energy into the water through the collective motion of those protein atoms. The collective motion picture is supported by the MD simulation32of the cooling of Mb and cytochrome c molecules following absorptoin of a photon at 532 nm. It was discovered in that work that the rate and magnitude of the temperature rise for the protein atoms close to the heme are very similar to those for the more distant protein atoms. These results suggested that there is a nondiffusive energy transfer occuring which was interpreted as involving a collective motion of a large number of atoms. These simulations gave no evidence of strong anisotropic heating of protein modes, thus providing no evidence for direct coupling through heme side chains. It is interesting to notice that this simulation revealed that the heme cooling could be best described by two exponential decays with approximately same magnitudes and time constants of 1-4 and 20-40 ps. Although this slow cooling component has not been observed in previous experimental measurements on the vibrational relaxation of a few heme these two heme cooling times give rise to two water heating times comparable with the two components observed in our experiment, assuming a collective motion model for the energy transfer in the protein. In summary, femtosecond IR spectroscopy was used to study the energy transfer process in malachite green and heme protein solutions by directly monitoring the change of the solvent IR spectrum. Malachite green in D20 was employed as a model system free from protein. The observed bleaching signal in the 1800 cm-' region was attributed to the shift of the water IR spectrum as a result of heating, and the response time of this spectral shfit to heating was found to be 4 & 3 ps. A similar bleach signal was observed for heme protein and D20 solutions and attributed to the heating of surrounding water. The signal in Hb and Mb was fitted to a model that consisted of a fast and a slow component leading to the explanation that the heat transfer from heme to the surrounding water in heme proteins proceeds through at least two different processes or possibly a range of processes. The slow component, about 40% of the total signal, was attributed to the diffusion of the heat through the protein. There was a good agreement between the measured kinetics and the kinetics calculated using a classical heat diffusion theory with a 5 ps heme cooling time. The fast component in the observed signal, with nearly identical amplitudes and time constants of 60%, 7.5 f 2.0 ps and 63%, 8.5 & 1.5 ps for Mb and Hb, is faster than the time scale for a thermal diffusion process. It is proposed here that the energy transfer from the heme to the surrounding water in heme protein solutions proceeds through both a diffusive process in the protein and nondiffusive processes that involve the collective, perhaps anisotropic, motions of the protein. Our experiments constitute a direct observation of the rate and magnitude of the temperature rise of the water surrounding a protein.
Acknowledgment. This research was supported by NIH and NSF. B. Locke thanks NIH for a Post Doctoral Fellowship.
11656 J. Phys. Chem., Vol. 98, No. 45, 1994 The authors also thank Dr. Nick hgliano for his comments on the manuscript.
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