520
J. Phys. Chem. 1981, 85, 526-531
Flash Photolysis Reactions of Myoglobin and Hemoglobin with Carbon Monoxide and Oxygen at Low Temperatures. Evidence for a Transient Diffusion-Controlled Reaction In Supercooled Solvents Brian B. Haslnoff Department of Chemistry and the Faculty of Medlclne, Memorlal Unlversw of Newfoundland, St. John’s, Newfoundland A 18 3x7, Canada (Received: December 18, 1979; In Flnal Form: October 20, 1980)
The fast reaction kinetics of ligand binding to myoglobin (Mb),hemoglobin (Hb),horseradish peroxidase (HRP), and microperoxidase-11(MP-11)were studied down to -90 OC in supercooled mixed solvents by both dye laser and flash lamp photolysis. The recombination kinetics of photodissociated MbCO, MbOz,HbCO, HRP-CO, and MP-1140 were followed in several solvent mixtures. The time dependence of this reaction is characteristic of a caged geminate transient diffusion-controlledreaction. At higher temperatures a fraction of the photodissociated ligand can escape into the bulk solvent. This slower recombination reaction is partly steady-state diffusion controlled and partly chemical activation controlled. The transient process within the protein cage and the nontransient process from the bulk solvent occur simultaneously. The effect of temperature on the time-dependenttransient diffusion rate constant is slight. The kinetics do, however, show a pronounced effect on varying the flash lamp pulse width but not on the power of the laser pulse. Transient effects were less pronounced in lower-viscosityethylene glycol-water and glycerol-water mixtures and were not observable in methanol-water. Neither HRP nor MP-11 exhibited transient recombination kinetics.
Introduction In a preliminary communication1 the flash photolysis initiated recombination kinetics of CO with the heme protein myoglobin (Mb) in supercooled glycerol-water at -78 “C were described. Upon photodissociation in this very high-viscosity solvent (e.g., lo8 P in 83 w t 9% glycerolwater) recombination had characteristics of diffusioncontrolled transient kinetics. The photodissociated CO is not exchanged with the bulk solvent CO and returns by diffusion to its original binding site. This is the “fast” low-temperature [CO] independent reaction. At higher temperatures and lower viscosities some of the CO escapes from the protein cage before recombining. This is the “slow” [CO] dependent reaction. The present study was undertaken to extend the temperature range and to examine other heme proteins, other solvent mixtures, and another ligand, 0% Kinetics at temperatures where both fast and slow reactions contribute are of interest so that both transient and nontransient diffusion contributions can be examined?B Assumptions in diffusion theory have been critically reviewed by Noyes4 and developed and tested by others.6-12 Transient diffusion-controlled kinetics with its characteristic time dependence have been observed in the reaction of solvated electrons in frozen aqueous glasses,lO the decay of free radicals in an irradiated polymer,” in the quenching of fluorescence,4 in the annealing of radiation-damaged g e r m a n i ~ m ,in~ ?the ~ pico(1)Hasinoff, B. B. J. Phys. Chem. 1978,82,2630. (2) Waite, T. R. Phys. Rev. 1957,107,463. ( 3 ) Waite, T.R. Phys. Rev. 1957,107,471. (4)Noyes, R. M. Prog. React. Kinet. 1961,1,129. (5)Peak, D.; Corbett, J. W. Phys. Rev. B 1972,5,1226. (6) Abell, G. C.; Mozumder, A. J. Chem. Phys. 1972,56,4079. Mozumder, A. Zbid. 1978,69,1384. (7)Chuang, T. J.; Hoffman, G. W.; Eisenthal, K. B. Chem. Phys. Lett. 1974,25,201. (8)Chuang, T.J.; Eisenthal, K. B. J. Chem. Phys. 1975, 62,2213. (9)Northrup, S.H.; Hynes, J. T. J. Chem. Phys. 1979, 71,871,884. (10)Buxton, G. V.; Cattell, R. F. C. R.; Dainton, F. S. J. Chem. SOC., Faraday Trans. 1 1975,71,115. (11)Dole, M.; Salik, J. J. Am. Chem. SOC.1977,99,6454. (12)Evans, G. T.;Fixman, M. J. Phys. Chem. 1976,80,1544. 0022-3654/81/2085-0526$01.25/0
second geminate recombination of iodine atoms in carbon tetrachloride and in hexadecane,7112and in the picosecond charge-transfer interaction between excited anthracene and N,N-diethylaniline.8 Recent ligand recombination kinetic studies13-16 after nanosecond laser photolysis of carboxyhemoglobin (HbCO) in aqueous solutions have been interpreted in terms of an initial ultrafast caged recombination, though a full kinetic analysis has not yet been given. The low-temperature nonexponential recombination kinetics of ligand binding to Mb,17-21isolated Hb and ferroprotoporphyrin IXZ3have been interpreted with various models. These include transient diffusion,’ multiple conformation,’g2o and multiple barrier models.” However, it has now been c ~ n c l u d e at d ~the ~ ~higher ~ ~ temperatures (-73 to 77 “C) in high-viscosity glycerol-water solvents the recombination of CO and O2 with Mb, Hb, and CO with ferroproto(13)Duddell, D. A.; Morris, R. J.; Richards, J. T. J. Chem. SOC.,Chem. Commun. 1979,75;Biochim. Biophys. Acta 1980,621,l; Duddel, D. A.; Morris, R. J.; Muttucumaru, N. J.; Richards, J. T. Photochem. Photobiol. 1980,31,479. (14)Alpert, B.; El Mohsni, S.; Lindqvist, L.; Tfibel, F. Chem. Phys. Lett. 1979,64,11. (15)Coppey, K.; Tourbez, H.; Valat, P.; Alpert, B. Nature (London) 1980,284,568. (16)Friedman, J. M.; Lyons, K. B. Nature (London) 1980,284,570. (17)Beece, D.; Eisenstein, L.; Frauenfelder, H.; Good, D.; Marden, M. C.; Reinisch, L.; Reynolds, A. H.; Sorensen, L. B.; Yue, K. T. Biochemistry 1978,18,3422. (18)Fesenko, E.E.; Kulakov, V. N.; Lyubarskii,A. L.; Vol’kenshtein, M.V. Dokl. Akad. Nauk SSSR 1972,205,485. (19)Kulakov, V. N.; Lyubarskii, A. L.; Fesenko, E. E.; Vol’kenshtein, M. V. Mol. Biol. 1973,9,246. (20) Iizuka, T.; Yamamoto, H.: Kotani, M.: Yonetani, T. Biochim. Biophys. Acta 1974,371,126. (21)Austin, R. H.; Beeson, K. W.; Eisenstein, L.; Frauenfelder, H.; Gunsalus, I. C. Biochemistry 1975,14,5355. (22) Alberding, N.; Chan, S. S.;Eisenstein, L.; Frauenfelder, H.; Good, D.; Gunsalus, I. C.; Nordlund, T. M.; Perutz, M. F.; Reynolds, A. H.; Sorensen, L. B. Biochemistry 1978,17,43. (23)Alberding, N.; Austin, R. H.; Chan, S. S.;Eisenstein, L.; Frauenfelder, H.; Gunsalus, I. C.; Nordlund, T. M. J. Chem. Phys. 1976,65,4701. (24)Marden, M.C.; Beece, D.; Eisenstein, L.; Frauenfelder,H, Good, D.; Reinisch, L.; Reynolds, A. H.; Sorensen, L. B.; Yue, K. T. Bull. Am. Phys. SOC.1979,24,318. (25)Austin, R. H.; Chan, S. S. Biophys. J . 1978,24,175.
0 1981 American Chemical Society
The Journal of Physical Chemlstry, Vol. 85, No. 5, 1981 527
Transient Diffusion Reactions of Mb and Hb
porphyrin IX the rates are in good agreement with a diffusion model. Also a Mossbauer spectroscopic study26 of the recombination of photodissociated MbCO at 5-65 K yielded frequency factors in disagreement with optical recombination dataS2lr2’
MbrCO a t -86’in 86 I wt. % Glycerol-Water
IIR
Experimental Section
The experimental procedures and the basic photolysis apparatus with its spectrophotometric detection and computer-linked data acquisition systems have been de~cribed~+~O but for the following. The temperature in the 1-cm path length jacketed reaction cell was maintained (*0.5 “C) with a Varian V-6040 variable temperature controller with cooled N2 gas. The temperature was measured with a thermocouple inserted directly in the reaction cell. The side of the cell was frosted glass to remove spatial inhomogeneities in the photolyzing light. Results at short times (>ZOO ns) were obtained with a Phase-R Model 2100-B dye laser (3 J output at 18 kV at 578 nm with Rhodamine 590 dye in absolute methanol) with a pulse width of 300 ns. Even with the 300-11s pulse only the last half of the reaction could be followed. Results were also obtained with a miniature flash lamp but with a pulse width that could be varied from 50 to lo00 ps. Residual flash light limited results in these experiments to a minimum of 300 p s after the flash. Depending on the pulse width used, the last 5% or more of the reaction was followed. The 256 or more voltage-time digitized data points were computer fitted to various equations by weighted linear least-squares analyses. Since the absorbance change at t = 0 is obscured by the photolyzing light and that at t = m may be only very slowly attained (in the order of seconds), the end of the fast reaction was sometimes obscured by the slow reaction complicating the analysis. The infinity absorbance value for the fast reaction was determined as circumstances warranted by systematically varying the infinity absorbance value in order to minimize the sum of the squares of the residuals or by using the averaged absorbance just prior to the flash. Examples of the reaction record are given in Figure 1. Myoglobin (sperm whale, Sigma), hemoglobin (human, Sigma), horseradish peroxidase (HRP, ICN), and microperoxidase-11 (Sigma) were determined spectrophotometrically as the reduced CO complexes. The molar absorptivity changes (in M-l cm-l) used in converting absorbance changes (AA) into concentration changes were determined to be the following: MbCO-Mb at 422.5 nm, -8.9 X lo4; MbCO-Mb at 440 nm, 6.4 X lo4; Mb02-Mb at 440 am, 5.8 X lo4;and HbCO-Hb at 436 nm, 6.4 X lo4. Typically the changes in molar absorptivities are 5O-100%. The sodium dithionite reduced stock heme protein solutions had unbound CO removed by flowing a stream of Nz above the stirred solution for -1 h in the dark. The efficiency of this procedure was checked by comparing the room-temperature kinetics with those obtained at higher [CO].28i29Thus the slow ligand concentration dependent reaction could be slowed to its minimum rate so that the fast process could be followed over the widest time scale. The buffer (KH2P04-NaOH) concentration in the reaction cell was 0.1 M with an aqueous pH of 7.1.
-
(26)Marcolin, H.;Reschke, R.; Trautwein, A. Eur. J.Biochem. 1979, 96,119. (27)Austin, R. H.;Beeson, K. W.; Eisenstein, L.; Frauenfelder, H.; Gunsalus, I. C.;Marshall, V. P. Phys. Reu. Lett. 1974,32,403. (28) Hasinoff, B. B. Arch. Biochem. Biophys. 1978,191,110. (29)Hasinoff, B.B. Arch. Biochem. Biophys. 1977,183,176. (30)Hasinoff, B. B. Can. J. Chem. 1977,55, 3955.
AT
-4f ‘ t I/
(“4I / i -I0
-151
-9
A
L:
5
0
15
IO ths)
I
3
HbtCO at -46. in
88.3 u t . K Glyaml- w o t u
‘?ah liphl
X * 436nm [HbCO] *17pM(honw)
.f
/ B
0
3
2
I t (ms)
LO.,
~
S
80.8 u t . n ~ r o r - w o h r A * 440 nm [MbCO] a I S p M
8
0
-‘I I
-2
.
k
b
:“i[ -70
1
J
1
0
20
40
60
80
t (ps) Flgure 1. Change In percent llght transmlsslon ( A T )vs. time for the recombination of flash-photolyzed CO with Mb and Hb at low tern perature. Traces are chart-recorder records of the digital-to-analog conversion of data stored in the translent recorder. A and B were obtained from flash lamp photolysis and C from laser photolysis.
528
The Journal of Physical Chemistry, Vol. 85, No. 5, 1981
Hasinoff
IO'
AA
I
2
I tt(rns4)
I 0"
Io-'
IO-^
lo-'
1
IO
t (SI Figure 2. Change in absorbance (AA) vs. time on a log-log scale after flash lamp photolysis of 21 pM MbCO in 86.1 wt % glycerol-water at 440 nm. The AA is measured from the base line just before the flash. The two straight lines on the left are drawn with slopes of -I/*. The -34 'C (corrected) data were obtained from the -34 'C data directly above by using the indicated infinity value. The pulse width of the flash was 50 ps for the 34 "C data and 90 ps for the -34 and -95 "C data. Some representatlve fl SD error limits are shown.
Results and Discussion The recombination of photodissociated ligand from heme proteins in mixed solvents displays normal secondorder kinetics at room temperature^.^^^ However, as the temperature is lowered, a fast reaction, independent of concentration, appears and gradually increases in amplitude with a concomitant decrease in amplitude of the slow reaction (Figure 2). This transition depends upon the solvent mixture, the heme protein, and the ligand. For reaction of Mb and CO in the highest-viscosity glycerolwater solvents, the fast reaction is first observed at --25 "C. In the low-viscosity methanol-water mixtures it could not be observed even at -60 'C. The results are consistent with the reaction scheme heme
+
L
( s l o w higher-temperature reaction)
heme-L ( 3 x v r h e m e
+
Llcage (fast low -temperature reaction)
where a fraction of the ligand L bound to the heme is photodissociated in process 1into a protein cage and the remainder in process 2 goes into the bulk solvent where it is free to exchange with other ligand molecules. At the highest temperatures dissociation into bulk solvent essentially predominates. In very high-viscosity solvents at the lowest temperatures of this study, dissociation can occur only into the cage. Reaction 4 is ligand recombination from bulk solvent and in high-viscosity solvents is controlled partly by chemical activation and partly by diffusion. The latter predominates as the temperature is lowered.2s30 Reaction 3 is geminate recombination from the cage and follows diffusion-controlled transient kinetics.' A mechanism in which ligand from the bulk solvent forms a cage and subsequently undergoes fast reaction would be kinetically indistinguishable from the mechanism above. As shown in Figures 2-4 at low temperatures and very high viscosities the kinetics follow eq I,' where a t t = 0, l/[heme] = kt1I2+ 1/[hemeIo (1) [hemelo= [L], and k is the second-ordertransient diffusion rate constant having units of M-' s-'/~. Toward the end
Flgure 3. Reciprocal change in absorbance vs. square root of time for the recomblnatlon of CO and O2 with Mb and Hb after flash lamp photolysis. The flash lamp pulse width was 90 ps. Mb 01
+ CO in Gbcerol-
Water 80 8 %
-87'
30! 70
fT
I
ITT
005
1
I f
Ti 1
1
.
8
i
010
015
t+(ms+) Flgure 4. Reciprocal change in absorbance vs. square root of tlme after laser photolysls of MbCO. The straight lines are weighted linear least squares calculated from 256 data polnts, only a fraction of which are plotted. From eq I the slopes yield k . Voltages refer to laser charge voltage.
of the reaction, eq I predicts that a plot of log [heme] vs. log t should approach a slope of -lI2 (Figure 2). At higher temperatures where there is also recombination from bulk solvent the slow reaction can be subtracted from the fast. As an example data at -34 "C, after being corrected as shown in Figure 2, approach a slope of -lI2, indicating the reaction still follows eq I. At -34 and 34 "C at long times the slopes approach -1 as expected for a normal secondorder reaction with equal initial reactant concentrations. Diffusion-controlled reactions that show time-dependent reactivity due to the importance of transient terms characteristically display a t'I2 time dependence. The theory has been developed from the basis of several standpoints. The development4 based on concentration gradients around reactive molecules gives eq 11, where k'is the rate k ' = 4arD/(1 + 47rrD/k,) (11) constant for molecules in which a steady state has been obtained; k, is the rate constant for reaction when a equilibrium molecular distribution has been maintained (chemicalactivation control); r is the radius of the reaction cage, and D the sum of the diffusion coefficients of the reactive species. Equation I1 has been tested extensively for the reactions of MbF8 HbF9 and ferroprotoporphyrin IX,3O and in high-viscosity glycerol-water mixtures both diffmion and chemical activation contribute to the kinetics. Equation I1 yields the familar Smoluchowski equation k ' = 4arD when k , >> 4arD. This limit is nearly achieved at --30 "C for the reaction of Mb, Hb, and ferroprotoporphyrin IX with ligands from the bulk solvent. Equation I1 is but
The Journal of Physical Chemistty, Vol. 85, No. 5, 1981 529
Transient Diffuslon Reactions of Mb and Hb
a steady-state approximation, and the diffusion reaction rate constant k , is really time dependent4
[
kc k , = k' 1 + -exa 4arD
erfc x
where x = [(Dt)1/2/r][(l
1
M b t C O in GlyceralWater 80.8% at -82'
a i 2ps
0.2
I c\ I
0.11
+ kc/(4arD)l
For normal liquids and molectlar sizes and for a fast reaction, a series expansion of ex erfc x said4 to be valid at times longer than lO-''s gives
k, = k'(1 + k ' / [ 4 ( ~ D ) ~ / ~ t ' / ~ ] ) For the reactions at hand the disappearance of unreacted heme i s -d[heme]/dt = k,[heme][L]
(111)
and with [hemelo = [L], at t = 0 the integrated expression2i3is l/[heme] = 4arD[1 + 2 r / ( ~ D t ) ' / ~ ]+t l/[hemeIo (IV)
At t > 4r2/(rD) eq IV reverts to the familar Smoluchowski equation k = 4wD. A far more general development4based on the behavior of molecular pairs gives for the time-dependent rate constant k, = kc[l - /3' + 2 ~ / t ' / ~ ] where a is a parameter describing molecular reactivity and ,8' is the probability that two molecules separating will ever react again. Since it is an experimental observation that all photodissociated ligands recombine, putting 0' N 1 gives
k, = 2 k , ~ / t ' / ~ In terms of the concentration gradient development
k, = 4 ( ~ D ) l / ~ r ~ / t ' / ~ which with eq I11 yields eq V directly. The assumptions and the final forms of the molecular pairs and the concentration gradient models have been compared?p8 An assumption in the concentration gradient development is that the photodissociated pairs have a uniform (random) initial di~tribution.~?~ Also at small separations of reactants the relative molecular motions may be correlated and not describable by a random that is, D may vary depending on how close it is to the binding site. This might also arise because the protein cage is not a continuous and isotropic medium.8 As well, it has been recognized that the boundary conditions may not be It has been shown that, depending upon strictly the relative magnitudes of D, t, r, and kc,2theuse of only the first term in the series expansion of ex erfc x may not always be strictly valid.8 For the picosecond chargetransfer interaction between excited anthracene and N,Ndiethylaniline, the effect of the second term in the expansion was reduced to 10% only after 30 ps and 1% after 300 pa. Transient kinetics were observed in the picosecond
I
*I
\
I
-0,3t \/
I
-0.4
U
-0 5 400
410
420 430 440
450
X (nm) Figure 5. Transient spectra obtained after laser photolysis of MbCO at low temperature. The soild line is the difference spectrum of Mb and MbCO obtained at room temperature in aqueous solution.
geminate recombination of I atoms produced by laser photodissociation of I2 in carbon tetrachloride and hexadecane.I A standard Fick's law model with reflecting sphere boundary conditions was in good agreement12with these I atom recombination data.' Attempts to fit the kinetic data at intermediate temperatures (data at -34 "C of Figure 2 for example) to both linear and polynomial forms of eq IV were not successful. Thus at the intermediate temperatures where there is a significant fraction of slow reaction the kinetic behavior indicates that there are but two simultaneous reactions contributing to the kinetics: the reaction from bulk solvent and the transient diffusion reaction in the protein cage. At the lowest temperatures only the t1/2term was significant. For the 2 r / ( ~ D t ) ' /term ~ of eq IV to be 10 (a detectable limit) at 10 ms, to make the kinetics solely transiently diffusion-controlled with D = 2.3 X lo4 cm2 s-l requires r = 1.3 X lo5 A. This is much larger than the dimensions of the protein and is unreasonable if it is assumed that the photodissociated ligand cannot penetrate the very high-viscosity solvent. The kinetic behavior of the photodissociated ligand inside the protein cage and outside in the high-viscosity bulk solvent must be clearly distinguished. The values of r and D would not be expected to be the same in both. As found previously2e30eq I1 describes the bulk-solvent kinetics where nontransient terms predominate and both diffusion control and chemical activation contribute to the kinetics. Dye-Laser Results. Transient spectral changes at 0.2 and 1.2 ps after laser photolysis of MbCO are given in Figure 5 and are compared to the characteristic static absorption difference spectrum of Mb and MbCO. These results indicate that the transient photodissociated species has a spectrum close to that of unligated Mb. Thus there is no spectral evidence for any radically different transient Mb species. These results accord with static measurements20at 4.2 K of photodissociated MbCO though some spectral differences with the unligated form were noted in the near-infrared. Even 0.2 ps after the laser pulse full photolysis has not been achieved. It can be estimated from the plots of Figure 4 that the half-time of the reaction is (31) With the smallest k observed of 0.065 pM-'ms-'lz (Mb A d CO in ethylene glycol-water) eq VI yields D = 2.3 X lo4 cma e-' assuming r = 40 A, the diameter of Mb.
530
The Journal of Physical Chemistry, Vol. 85, No. 5, 1981
Hasinoff
TABLE I: Transient Diffusion Rate Constants at Varying Observation Wavelengths for the Laser-Initiated Reaction of Mb and CO in 80.8 wt % Glycerol-Water at -82 "C wavelength: k , b pM-I wavelength,n k , b pM-' nm ms-1/2 nm ms-l/z
420 9.2 435 11.7 422.5 8.6 440 10.8 425 9.4 445 7.4 a Bandwidth was generally 2 nm or less. b Laser pulse energy was at a charge voltage of 15 kV and was sufficient to yield 100% photodissociation. Changes in molar absorptivities at room temperature in aqueous solution were used to calculate these rate constants. TABLE 11: Transient Diffusion Rate Constants at Varying Dye Laser Energy Outputs for the Reaction of Mb and CO in 80.8 wt % Glycerol-Water at -87 "C k , b pM-l % MbCO laser charge voltage: kV ms-"* photodissociatedC
11.3 23 8 13.9 41 9 11 11.5 83 13 12.2 -100 15 9.6 -100 15 10.8d 100 a Laser output increases approximately as the square of the charge voltage, At 18 kV the laser output is 3 J. The percentage standard deviation is -8% for the determination of k at 100% photodissociation. Calculated from the intercepts of AA-I vs. tilZ plots at 440 nm and At -82 the spectrophotometrically determined [Mb],. C.
I
AA
-350 ns and hence the first half of the reaction is obscured by the laser pulse. Kinetic results obtained with the dye laser were qualitatively similar throughout all time regions to those obtained using the flash lamp. The dye laser, however, enabled the study of the kinetics to much shorter times. Plots of AA-' vs. t 1 / 2(Figure 4 ) are linear at times where [Mb] and [MbCO]are comparable. Hence the laser results provide for a rigorous test of eq I. The results of Table I indicate that there is but a single reacting species. There was no observable effect on k for the reaction of Mb and CO when the energy output of the dye laser was varied by a factor of 4 (Table 11) and the initial percent photodissociation varied from 23 to 100%. This result indicates that the kinetics are not a function of the laser power output. Further experiments are required to determine whether the kinetics depend upon the output wavelength of the laser and hence the excess kinetic energy that the photodissociated ligand has above that required for photodissociation. Pulse- Width Effects. The pulse width of the flash lamp has a large effect on the fast reaction kinetics (Figure 6, Table 111). The value of k at the fastest flash lamp pulse
I
1
,o-a
,0-35
10-2t
t(s)
Flgure 8. P A vs. ton a log-log scale after flash lamp photolysis of 12 pM MbCO in 88.3 wt % glycerol-water at -75 'C and 440 nm. The solid lines are calculated from weighted linear least-squares analyses. Pulse wldths are measured at onahalf height. Only 10% of the points are plotted with some representative *ISD error limb. T("C)
-
TABLE 111: Variation of Transient Diffusion Rate Constant, k , with Photolyzing Pulse Width for the Reaction of Mb and CO pulse width, k: p M k l teomp, photolyzing ms-'/z C source us -87 laser 0.3 11.7 -81 laser 0.3 10.8 -7 5 flash lamp 50 13.6 -7 5 flash lamp 90 3.1 -7 5 flash lamp 170 1.6 -75 flash lamp 320 1.3 -75 flash lamp 400 0.8 a Laser results obtained in 80.8 wt % glycerol-water, flash lamp results in 88.3 wt % glycerol-water.
I
-40
-60
,
-80
T-I x I O ~ ( K - I )
Flgure 7. Arrhenlus plots of the transient diffusion rate constants for ligand binding to Mb and Hb obtained from flash lamp photolysis. The straight lines are least-squares calculated. The flash lamp pulse wldth was 90 ps. The square is for Mb CO in 54.2 wt % glycerol-water. For clarity the Hb CO data is displaced upwards by one-half unit on the scale.
+
+
width (50 ps) is the same as is observed with the 300-ns laser pulse. The value of k for the reaction of h4b with CO increased 16-fold upon narrowing the flash lamp pulse width from 400 to 50 ps. Similar effects and trends were also observed for the other fast reactions studied. In terms of eq VI the increase in k with decreasing pulse width could be due to an increase in either r or D or both. This could come about because of either the changing spectral distribution of the lamp or the pulse duration causing different distributions of energies of photodissociated ligand. Since the recombination rate is initially very rapid, newly recombined ligand molecules may be photodissociated a second time with a new distribution of energies and hence be given the opportunity to diffuse back from a different part of the protein. While changes in k occur over times that are much shorter (- 1000-fold) than expected for the rotational relaxation time of Mb, they may be occurring over times that segments of the protein are relaxing and thus allowing photodissociated ligand to reach otherwise inaccessible parts of the protein. The rephotolysis explanation has been advanced for the changing kinetics of the reaction of Hb and CO.I4 This effect could be particularly noticable with the flash lamp where only the last part of the reaction is followed. %photolysis has also been invoked in the nanosecond photolysis of HbCO to explain the change in percentage of a fast recombination reaction with temperature.13 As well, the effect of pulse energy and
Transient Diffusion Reactions of
Mb and
Hb
TABLE IV: Apparent Activation Energies for Low-Temperature Transient Diffusion-Controlled Ligand Recombination Reactions apparent activation energy,a kcal mol-' reaction solvent Mb iCO 88.3 wt % glycerol-water -1.9 i 0.5 Mb i0, 88.1 wt % glycerol-water 1.9 i 0.5 Hb c CO 88.3 wt % glycerol-water -1.6 * 0.5 Mb c CO 70.2 wt % ethylene glycol-water -9.0 * 0.9 Obtained from kinetics with a flash lamp pulse width of 90 MS.
repetition rate on the recombination of CO and Hb after picosecond laser photolysis has also been noted.32 Temperature Effects. The effect of temperature on k is generally quite slight (Figure 7). The linear least squares calculated apparent activation energies and their standard deviations are listed in Table IV. The apparent activation energies may, in terms of eq VI, be due to temperature dependencies of either r or D. Since, in the temperature range of the study, glycerol-water solutions undergo very large increases in v i s ~ o s i t y land ~ ~ ~large changes in other physical properties,33the small apparent activation energies would indicate that the recombination of ligand is from within the protein cage and is relatively unaffected by the bulk-solvent properties. Flash Lamp Results with Other Heme Proteins and Other Solvents. In 54.2 wt % glycerol-water the fast reaction of Mb and CO was not seen until -50 "C with the slow reaction still significant. The solution froze at - 4 0 "C. At -53 "C k was only slightly larger than in 88.3 wt % glycerol, again indicating the absence of any gross bulk-solvent effects. In the 70.2 wt % ethylene glycol-water of lower viscosity (-1/1000 of 88.3 wt % glycerol-water), the fast reaction of Mb with CO first appeared at -60 "C with the slow reaction still significant. In low-viscosity60 vol % methanol no fast reaction could be observed down to -60 "C for the reaction of Mb and CO. Likewise in 44 vol % methanol no fast reaction could be seen down to -36 "C. In these low-viscosity solvents a much larger fraction of CO is able to escape from the protein. Thus the transient kinetics are not solely a lowtemperature effect. In 78.1 w t % glycerol-water saturated with CO (0.48 mM) no fast reaction was observed between ferro-HRP and CO down to -82 "C though the slow reaction could be followed down to -58 "C but with decreasing amplitude. At -20 "C the rate of the slow reaction is -1000-fold smallerBthan the reaction of Mb with CO.% It is, however, possible that the recombination is too fast to be observed. In 88.3 wt % glycerol-water no fast reaction was observed between microperoxidase-11 (the heme portion of cytochrome c with amino acids 11-21 still attached) and CO down to -87 "C though the slow reaction with decreasing amplitude could be observed down to -40 "C. Since in this case the binding site is likely exposed to the solvent, recombination too fast to observe may occur. (32) Noe, L. J.; Eisert, W. G.; Rentzepis, P. M. Biophys. J. 1978, 24, 379. (33) Segur, J. B. In "Glycerol"; Reinhold New York, 1953; Chapter 7.
The Journal of Physical Chemistry, Vol. 85, No. 5, 1981 531
The fast recombination of CO with Hb in 88.3 wt % glycerol-water at low temperatures occurred with lower amplitude than the reaction of Mb and CO. There was no evidence of mixed transient kinetics due to differences in a and /3 heme sites. Equations for two simultaneous transient reactions have been derived.34 Diffusion within the Cage. If one assumes reasonable values of r in eq VI, values of D , the diffusion coefficient of the ligand inside the protein cage, may be calculated. Assuming a maximum r = 40 A, the diameter of Mb, with observed values of k ranging from 0.065 to 12.1 pM-l r n d 2 one finds values of D ranging from 2.3 X lo4 to 7.8 X cm2 s-l. It should be noted that, since D is proportional to r4, its value is quite sensitive to variations in r. These values can be compared to D = 2 X cm28-l for O2 in water at 25 "C. Results from the quenching of tryptophan fluorescence of proteins indicated that the apparent O2 diffusion rate through the protein matrix is 2O-50% of that in water.% Likewise laser photolysis studies of oxygen quenching of the iron free triplet porphyrin-globin of Hb3' and MbZ5indicated that the diffusion-controlled rate is -15% of that of free porphyrin. The fact that the kinetics were strictly first order indicated that the four porphyrin sites are equally accessible to ligand, a result that accords with this study. Theoretical trajectory ~ a l c u l a t i o n sof~ ~ the motion of photodissociated CO and O2 from myoglobin have been made based on the X-ray crystal structure. The results indicated that the motion of the photodissociated ligand inside the protein had diffusional character. This conclusion is consistent with a transient diffusion kinetic model. Of 150 trajectories examined only 55 ever left the heme pocket even though the test particle had an effective diameter somewhat smaller than either CO or 02. Of the remaining 95 some 50 remained trapped in the principal heme pocket; 20 remained in a low-energy region between Leu B10 and Leu E4 and 25 in a region separated from the heme pocket by a barrier formed by side chains from Val E l l and Ile G8. It was also concluded that the escape of the ligand into such low potential energy spaces might compete with escape into bulk solvent and hence affect the time course of ligand rebinding. These conclusions would also support the hypothesis that there is an initial ultrafast caged re~ombination'~-'~ after flash photolysis that can compete with escape of ligand into bulk solvent. Note Added in Proof. A recent paper (Beece, D.; Eisenstein, L.; Frauenfelder, H.; Good, D.; Marden, M. C.; Reinisch, L.; Reynolds, A. H.; Sorensen, L. B.; Yue, K. T. Biochemistry 1980,19,5147) has presented a new evaluation of the higher temperature region ligand binding k i n e t i c ~ ~where l - ~ ~ the t1/2kinetics do not predominate. Viscosity is now selected as a "crucial variable" that determines the kinetics; however, a simple Smoluchowski diffusion model is considered only in passing. Acknowledgment. This work was supported in part by a Natural Sciences and Engineering Research Council Canada Grant, No. A9430.
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(34) Dole, M.; Hsu,C. S.; Patel, V. M.; Patel, G. N. J. Phys. Chem. 1975, 79, 2473. (35) Jordon, J.; Ackerman, E.; Berger, R. L. J. Am. Chem. Soc. 1956, 78, 2979. (36) Lakowicz, J. R.; Weber, G. Biochemistry 1973, 12, 4171. (37) Alpert, B.; Lindquist, L. Science 1975, 187, 836. (38) Case, D. A.; Karplus, M. J. Mol. Biol. 1979,132, 343.
