J. Phys. Chem. 1994, 98, 13791-13796
Picosecond Reaction of Picket Fence Heme with the Solvent Cage
0 2
13791
and CO: Geminate Recombination in
Tammy G. Grogan, Nilkamal Bag, Teddy G. Traylor, and Douglas Magde* Department of Chemistry, University of California, 9500 Gilman Drive, M o l l a , California 92093-0358 Received: August 15, 1994@
Hemes, types of iron prophyrins, have been developed over many years to model aspects of ligand binding in heme proteins. Recently, the heme-ligand system has proved useful for exploring the detailed kinetics of photodissociation-geminate recombination within a solvent cage. Oxygen is a key ligand for both purposes, but most hemes are unstable in its presence. Picket fence heme is an exception, it is reasonably stable with 0 2 . Cage recombination efficiency in toluene solvent after photolysis with 314 nm laser light is about 43% when methylimidazole is used as the trans base, reduced to about 20% when dimethylimidazole is used to introduce trans strain. Previously, geminate rebinding of CO was unmeasurable in any model heme system, but with picket fence heme and methylimidazole, recombination efficiency appears to approach lo%, again reduced significantly by dimethylimidazole. The lifetime of the caged geminate pair is longer in the picket fence system, about 30 ps in all cases. These observations fit well with expectations from prior studies but fill some crucial gaps in the emerging picture.
Introduction Understanding the kinetics of ligand binding to ferrous heme complexes is of interest partly because porphyrins are a large family of compounds with many applications but also because of two special considerations: First, model hemes are constructed to test hypotheses about the reactivity of hemoglobin and other heme proteins. Second, heme-ligand interactions show promise of being a good system for fast kinetic studies of the solvent cage effect. Model hemes were initially designed to mimic hemoglobin, which requires demonstrating reversibility in oxygen binding. Once reversibility was achieved, models were refined to show greater stability, to mimic closely the equilibrium ligand binding properties of a variety of different proteins, and ultimately to match even the kinetic properties of those proteins. Such classical issues have been reviewed When fast laser techniques were introduced, more detail about ligand reactivity inside proteins became accessible, because ligands dissociate under the influence of light and then recombine to some extent before they can escape from the protein. Such geminate recombination was observed both at low tem~erature~,~ and at ambient conditions6s7 following photolysis by nanosecond4s6or p i c o ~ e c o n d lasers. ~ . ~ We then asked the question whether model compounds that had been developed earlier with no regard for such behavior would show any analogous geminate recombination. It turned out that there are striking similarities over the first 20-40 ps; but at longer times the behavior diverges. Model hemes show fast recombination, in which a variable fraction of ligand recombines over a period of 20-40 P S . ~ - ' ~Some proteins, those in which the "ligand' is an amino acid side chain attached to the protein backbone, also show only this fast process, but with 100% re~ombinati0n.I~Transport proteins, such as myoglobin, in which the ligand photolyzed is free to move away from the iron, exhibit reduced amounts of the fast geminate recombination, but they also show an additional process that persists even at ambient temperature for hundreds of nanoseconds. The slow process may appear with some larger ligands as a single e x p ~ n e n t i a l , ~but ~ . ' with ~ other @
Abstract published in Advance ACS Abstracts, December 1, 1994.
0022-3654/94/2098-13791$04.50/0
large ligands it is m~ltiexponential,'~ and with the more common diatomic ligands it is now thought to be a complex process evolving continuously over Since 20-40 ps is a plausible duration (a few half-lives) for a contact pair in a solvent cage, we proposed that we were seeing a solvent-cage effect in the models and that there exists in the protein at early times something like a solvent-caged, contact pair that changes over 20-40 ps into a separated, but still protein-caged, pair that persists for hundreds of nanoseconds in an evolving environment. The variety of behavior observed in the model-heme-ligand systemsg-12became as interesting as an exploration of solventcage effects as from the pertinence to proteins. We had discovered a system in which direct, ultrafast laser methods could test the somewhat vague, pictorial models that had been introduced a quarter century earlier for understanding diffusioncontrolled chemical reactions in liquid solutions. Two aspects of geminate recombination in model heme systems remained unexplored during all those developments: the behavior of the all-important ligand dioxygen and the behavior of picket-fence model hemes. Although 0 2 is clearly
,,-o important, it is troublesome in model hemes, because irreversible oxidation occurs rapidly at room temperature; so it is often the last ligand studied. As for picket-fence heme and its relatives, they stand among the several families of model hemes, each of which is useful for testing some specific question, as perhaps the most successful overall, and the group for which an 0 2 solution is at least moderately stable. Picket-fence heme and
0 1994 American Chemical Society
13792 J. Phys. Chem., Vol. 98, No. 51, 1994 its derivatives were much studied by C ~ l l m a n as ~ ~well - ~ as ~ by In this report we show that oxygen behaves as we expected and is interesting in that it shows an intermediate amount of geminate recombination, more than CO but less than other ligands. Picket-fence heme is also interesting in that, while generally similar to other model hemes, it seems to show evidence for a small degree of ligand trapping by the picket fence structure, the first hint of such behavior in any model heme. Preparing a model heme complex requires specifying a base B, a heme Hm, and a ligand L to generate B-Hm-L. For B we used 1-methylimidazole MI and 1,Zdimethylimidazole DMI. For the heme we used iron(I1) meso-tetrakis(a,a,a,a-o-pivalamidophenyl)porphyrin, picket fence heme.lg For L, we were interested primarily in 0 2 but also characterized CO for comparison.
Grogan et al.
monitored, one wavelength at a time, at intervals between 370 and 450 nm. Different lamps and digitizers were used for fast and slow time ranges. Depending on signal strengths, from 10 to 200 laser shots were summed for each measurement. Geminate recombination was investigated using subpicosecond flash photolysis, with excitation at 314 nm. For each laser shot a spectral continuum probed the sample at a particular time delay, determined by an optical delay line, and then was dispersed in a spectrograph and detected by an intensified diode array. From transmitted intensities, measured with the pump pulse blocked or unblocked, absorbance values were calculated for 600 points over the wavelength interval from 380 to 480 nm. The optical delay line was scanned under computer control over a 200 ps (occasionally 750 ps) time range with spectra recorded at 1 ps intervals. Technical details of both laser systems were fully described recently.18 Also outlined there is our implementation of singular value decomposition SVD, which offers a systematic way of treating an array of 600 by 200 absorbance values when the number of kinetic components Experimental Section is unknown, spectra of intermediates are unknown, and data Materials. Toluene was distilled over calcium hydride. MI, may be contaminated by relatively large amounts of noise. from Aldrich, was dried over KOH and distilled under vacuum. Recently, a much-needed tutorial on SVD has been provided DMI, sodium dithionite, and 18-crown-6, all from Aldrich, were by the group that has made the most extensive application to used as received. CO, from Specialty Products & Equipment, nanosecond kinetic spectroscopy.28 We believe that SVD will Houston, and 0 2 , from G. S. Parsons, San Diego, were used as ultimately will ultimately be even more important in picosecond received. Picket fence [meso-tetrakis(a,a,a,a-o-pivalamido- studies, where it is less likely that one knows the spectroscopy phenyl)]po~phyri~n was synthesized and characterized according of intermediates and one cannot even assume that species are to literature procedures.20 in thermal equilibrium; however, we know of only one prior Solutions. Picket fence porphyrin was dissolved in toluene/ app1ication.l8 imidazole mixtures to achieve an absorbance at the Soret The solvent used here, toluene, exhibits a two-photon maximum of about 0.9 in a 1-cm cell, that is about (4-7) x absorption spectrum in the violet, overlapping the Soret region mol L-l, for preliminary studies and 5-8 times that of porphyrins. Because of temporal dispersion in the continuum concentration for picosecond studies, which are carried out in probe, it appears as a transient peak that shifts from the red to 2-mm path-length cells to minimize temporal dispersion. The the blue end of our spectral range over about 5 ps. Corrections concentration of MI was lop4M and that of DMI was M, for toluene absorption were made by subtracting scaled pure except when the effect of varying imidazole concentration was toluene spectra from the corresponding sample spectra. Since being investigated. The solution (5 mL) was transferred to a the two-photon absorption must be instantaneous at all wavetonometer with a total volume of 148.7 cm3, and residual air lengths, the toluene spectra also provide a reference that allows was removed by several freeze-pump-thaw cycles. Argon was correction for group velocity dispersion. After these corrections, added and the sample reduced from ferric to ferrous iron by SVD analysis was carried out using MATLAB software. the addition of either 2 p L of a saturated solution of sodium Components were deemed significant based on their singular dithionite/l8-crown-6/methanol or 60 mg of amalgamated zinc. values and the appearance of their kinetic traces. Kinetic traces The crowm ether complex was prepared by adding 190 mg (0.7 for both nanosecond-microsecond and picosecond data were "01) of 18-crown-6 and 58 mg (0.33 "01) of sodium fit to sums of exponentials (mainly a single exponential plus a dithionite to 5 mL of degassed methanol and the solution stirred constant offset) using a nonlinear least-squares fitting program under nitrogen for 30 min; a clear solution being obtained after written in house. centrifugation. For 0 2 samples, extra care was taken to use Results the minimum amount of reducing agent possible. After the iron was reduced, the tonometer was again degassed by freezeSpectroscopy. The wavelength of the Soret maximum was pump-thaw cycles. Pure CO or 0 2 gas was then added by measured for each solution: Initially prepared ferric MI-Hmneedle through a septum, either a measured amount in a syringe [Fe(III)] had A- = 415.5 nm and DMI-Hm[Fe(III)] had A, or sufficient to fill the tonometer to ambient pressure. The = 415 nm. After reduction to ferrous heme but before adding solubilities of COZ5and 0 z z 6 were taken to be 7.6 x and L, MI-Hm had Am = 428 nm, indicative of the bis(M1) adduct, 8.7 x mol L-' atm,-' respectively. The vapor pressure and DMI-Hm had A, = 437 nm, indicative of five-coordinate of toluenez7 was taken to be 26 mmHg. All data and results "deoxy" heme. After addition of L, at the concentrations of B are at 23 "C. and L used here, MI-Hm-CO had A, = 423 nm, MI-Hm-02 had ,A Spectrophotometry and Kinetics. UV-visible absorption = 422 nm, DMI-Hm-CO had A, = 423 nm, and spectra were measured using a Kontron Uvicon 810 spectroDMI-Hm-02 had A,= = 422 nm. Spectral shapes were as photometer. Spectra were acquired initially in order to deterexpected for the different instances, with the CO and bis(M1) mine the ligation state of the heme in solution under the complexes sharper than others. Wavelengths are the peak conditions used for the kinetic measurements. Spectra were maxima as quoted by the instrument software (or the average also measured routinely before and after each kinetic study in of replicates differing by 1 nm). An uncertainty of about 2 nm order to verify that sample degradation was minimal. Bimois plausible; features are generally similar to those listed by lecular association kinetics were determined using flash phoCollman et a1.20329 tolysis and kinetic photometry. A nanosecond pulsed laser Bimolecular Association Kinetics. Over a limited range of provided excitation pulses at 540 nm. Transient absorption was concentrations around those specified above, rates for a process
Picket Fence Heme
J. Phys. Chem., Vol. 98, No. 51, 1994 13793
that appears to be bimolecular association are linear in [L] and independent of [B] and yield second-order rate constants for ligand binding of khlf0 = 2.8 x lo7 M-’ s-’, kmo2 = 3.6 x lo8 M-’s-’, k~m“ = 1.4 x lo6 M-’ s - ~ ,and ~ D M I ’ ~= 1.1 x lo8 M-’ s-’. These are close to previous results, both early22 and more recent,23 and c o n f i i that we are working with the same system. There is not much doubt that these values are close to correct. We are, however, not as confident as previous workers that the assumed simple mechanism is fully justified, even at optimal concentrations of B and L. At least for CO, we find that measuring at several wavelengths with today’s improved signal averaging reveals an additional faster component (observed rate, (2-3) x lo5 s-’) as well as a whole range of slower components. One major concern is that B is expected to dissociate fairly rapidly from five-coordinate B-Hm, which opens a variety of reaction pathways. There is one detailed treatment of the equilibria and kinetics for all those processes in a “flat” heme, in which case the symmetry of the two sides of the porphyrin implies that “only” 12 rate constants are required.30 For the asymmetrical picket-fence heme, 24 rate constants are potentially involved. Loss of B and subsequent processes have no bearing on geminate recombination itself, which is finished at much earlier times. More important than the association rates themselves are the ratios among them, and these are likely to persist, approximately, for small modifications in the mechanism, given the observations listed in the first sentence of this paragraph and noted by earlier workers. Binding to 0 2 is always at least 10 times faster than binding to CO; and using DMI as B always reduces binding rates but much more for CO than for 0 2 . Geminate Recombination. For each of the four compounds, time resolved spectra were acquired over the time range from -20 to +180 ps at 1 ps intervals, for at least three different sample preparations. A few measurements were extended to +750 ps to verify that what appeared to be a plateau in transient absorbance reached by 200 ps was not changing significantly over the next 500 ps. The large matrix of “delta absorbance” values, AA(,?,t),was expressed as a sum of terms using SVD. Each term is the product of three factors: a difference spectrum, a weighting factor (which is the “singular value”), and a kinetic trace. Each term is a matrix, when its factors are multiplied. Altogether there are 200 (or 750) such matrix terms, but only the first few contain significant information; the rest express noise in the original data. Consequently, if the first few matrix terms are added together, their sum is a representation of the original data with random noise eliminated. This offers a mathematically robust means of smoothing a data set over both independent variables, A and t. Figure 1 compares a small part of a set of original data for MI-Hm-02 with its smoothed analogue. There is bleaching near 422 nm, where six-coordinate B-Hm-02 would absorb, that appears simultaneous with photolysis and decays over tens of picoseconds. There is transient absorption in the region where five-coordinate B-Hm would absorb; but it appears initially farther to the red and only later becomes centered near 437 nm. Consequently, the recovery of absorption near 422 nm is only partly due to oxygen recombination; some portion is attributed to the blue tail of the equilibrated B-Hm absorption “moving into view.” To estimate the latter contribution, one may consider the transient spectroscopy of B-Hm-CO, for which the evolution of the red edge is similar but recombination is very small.12 It is difficult to work even with the smoothed matrix, with its 600 wavelengths and 200 (or 750) time delays. (Figure 1 is simplified by showing only a few time delays.) Fortunately, some use can be made of the separate SVD components, basis
Original data, 0-50 ps in 4 ps steps I
-0.4
450 500 550 wavelength, nm Reconstructed data, 0-50 ps in 4 ps steps
400
350
-0.4‘
450 500 wavelength, nm
400
350
550
Figure 1. Time-resolved difference spectra following picosecond photolysis of MI-Hm-02 in toluene. The top panel shows fairly good
raw data; the botton is smoothed data, reconstructed from the first four SVD components. The smallest spectrum is from a time near the beginning of excitation. The remaining spectra come at 4 ps intervals, decreasing monotonically from the largest to the smallest. Positive values are transient absorption, negative are transient bleaching. 04
.o 2 ‘
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021
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0 051 IV
-O.0SL 350
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wavelength.nm
1 500
-4‘ 350
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I
I 500
wavelength,nm
Figure 2. The first four spectral components from an SVD analysis of the data in Figure 1. Note the changes in vertical scale.
spectra, and their associated kinetic traces. Figure 2 shows the fnst four spectral components and Figure 3 the associated kinetic traces for the data set of Figure 1. Each kinetic trace has been multiplied by its singular value, so that the actual AA values throughout the matrix for any term can be obtained by multiplying a point on the basis spectrum by a point on the associated kinetic trace. The contributions become rapidly smaller in successive terms. Unfortunately, each basis spectrum corresponds not to a single chemical species but to some superposition. If one knew independently the spectra associated with all transient species, one could unravel the superposition. For nanosecond or slower data, it is often possible to prepare intermediates and measure their spectra. For picosecond kinetics, however, one must expect that intermediates at early
13794 J. Phys. Chem., Vol. 98, No. 51, 1994
Grogan et al.
,-
diffuse apart:
0.1
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.O 05‘ 0
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5 0 . 0
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-
-001 0
50 100 150 wavelenglh,nm
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k-i
[B-Hm-L]
k,
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B-Hm -t L
(1)
Thermal bond breaking kl is not displayed in (1) in order to emphasize that it is too slow to be significant in picosecond kinetics; the caged pair [-] is formed here only by photolysis. The solvent-caged reactant pair is, however, postulated as an intermediate in liquid-phase association-dissociation reactions in order to rationalize a wide variety of empirical phenomena in both photo and thermal reactions. The experimental observables are kobs and 4. In terms of the kinetic rate constants in (l), they would be defined as
200
Figure 3. The f i s t four kinetic traces showing the contribution over
-
kobs = k-,
+ k,
time of each of the basis spectra displayed in Figure 2. Note the changes in vertical scale.
TABLE 1: Geminate Recombination for Picket Fence Heme in Toluene MI-Hm-02 DMI-Hm-02 MI-Hm-CO DMI-Hm-CO
0.40-0.46 0.15-0.25 0.08-0.1 1 0.01 -0.05
4 3 3 I
f l f 1 &1 f 3
36 11 2.8 0.14
times are not in thermal equilibrium and cannot be prepared in isolation. One must simply interpret the components as best one can by comparing different samples and various conditions. In the present study, we have four compounds to compare. They differ mainly in the appearance of the first kinetic component, more specifically, in the amplitude of the decaying portion. Therefore, the first kinetic trace for each compound was fit to a single-exponential decay plus constant offset. The fractional decay [A(O) - A(m)]/A(O) is an estimate of the amount of ligand recombination 4, and the rate of decay kobs sets a time scale for recombination. These are displayed in Table 1 but are shown with associated uncertainty ranges that also include the possibility that some recombination is mixed into higher components, as well as allowing for uncertainties in curve fitting and estimating reproducibility from one run to another. The second component is similar in spectrum and kinetics in all four compounds, which suggests that it is dominated by spectral relaxation among transient species. The third and especially the fourth components become progressively more noiselike but are discussed briefly below. They have some very fast features. Those can be distorted by the problems of correcting for two-photon absorption in toluene. Unfortunately, we must use toluene to make contact with prior work. (All aromatic solvents have the same problem, but we can and do use methylcyclohexane for other investigations, when we want to avoid the problem.)
Discussion As argued by Petrich et al.,I it seems clear that in both proteins and model hemes photolysis of B-Hm-L (with B = MI or similar) results in loss of L in much less than 1 ps with initial quantum yield close to loo%, although for most L other than CO, it is still possible that some small fraction, certainly less than 50%, either does not dissociate or recombines on a subpicosecond time scale. After photolysis, the dissociated partners, called the geminate pair, may be imagined to exist as a solvent-caged contact pair for whatever time transpires prior to full solvation; and during that time they may recombine or
However, kobs and 4 should be predictable by other models as well, and it may be best to emphasize observables, rather than presuppose the rate equations. One contact with traditional kinetics is by way of the rate constant for bimolecular association k~~ given by
(3) In this notation, the subscripted variable is understood to be coordinated to the iron throughout the reaction, while the superscripted variable is the ligand added. The formulation (1) has two implications, which should be distinguished. As written with microscope rate coefficients, (1) presupposes the “kinetic” model, or rate-equation treatment, in which rate constants can be defined and evaluated. It is possible to question whether the intermediate really has properties that would justify defining simple rate constants. Experimental evidence is sparse. Picosecond experiments have shown that, within rather limited precision, the caged pair (for our heme system) does disappear with single-exponential behavior over some range of time and amplitude. Such behavior is consistent with (I), but it could also be consistent with a variety of more elaborate models. The more basic implication in (1) is simply that some kind of intermediate exists and can be characterized in some fashion, with the rate coefficients not being seriously defended as anything more than (reciprocals of) characteristic time scales. On this qualitative level, the evidence is more compelling, but it does not lie primarily in spectroscopic or kinetic detail. Transient spectra are consistent with the existence of an intermediate, but there is no characteristic spectrum for the caged pair. Only the kinetic behavior distinguishes it from the separated, free species. Holten31 has pointed out that in this spectral region a whole variety of excited electronic states absorb (but with spectra poorly known) and might confuse assignments. Hence, the motivation for interpreting transient behavior in terms of a solvent-caged pair rather than seeking some altemative explanation is that for a broad range of B-Hm-L systems, picosecond kinetics for the transient have a “reasonable” time scale while matching in fractional recombination @ the predictions of the solvent-cage interpretation of conventional Whether in the long run a simple rate-equation treatment of the caged pair intermediate remains the best we have, or a more sophisticated analytical model evolves, or it develops that nothing less than full molecular dynamic simulation is adequate, it will likely be difficult to avoid qualitative reference to a solvent-caged intermediate.
Picket Fence Heme Since SVD is a novel method for data analysis, we displayed in full the first four spectral and kinetic components for MIHm-02. The SVD analysis makes explicit some assumptions that in previous picosecond studies have been hidden in subjective analyses of spectra or buried in a choice of the “correct” wavelengths at which to measure a few kinetic traces. Spectral component 1 is the unchanging spectrum that best matches the transient difference spectrum “on the average” at all times. It resembles very closely the “five- minus sixcoordinate difference spectrum” for thermally equilibrated ground-state heme, as can be measured in static experiments. The associated first kinetic trace reveals that whatever this difference spectrum may represent, it reaches a plateau in its amplitude well before 100 ps and persists at least to 200 ps (and we have verified that there are no changes out to 750 ps). Such a plateau can be noted qualitatively in raw data, as in Figure 1; but SVD permits a rigorous argument that after all higher kinetics components approach zero amplitude, the only features left in the data are the first spectral component and noise. Since there is a time interval after the higher components have decayed to near zero during which the first component is still decaying and approaching its plateau value, we argue that the decay of the difference spectrum at least during that time represents the loss of population of the solvent-caged intermediate. It is noteworthy that the time for geminate recombination is somewhat longer (and k&s smaller) than we have observed in other complexes. A reasonable inference is that the “solvent cage” in the present complexes is significantly affected by the picket fence structure and that the ligand remains near the iron a little longer because of the constraints of the picket fence upon its diffusion. This is also consistent with the observation that MI-Hm-CO seems to show a (barely) measurable amount of recombination, which is not seen in other models. Spectral component 2 is the single spectrum that best represents the difference between the first component and the actual transient spectra. It shows extra absorption on the red side and bleaching to the blue. If there were only two significant components in the SVD analysis, the zero crossing in the second component would imply an isosbestic point in the original data. The fact that additional components of the SVD have some significance shows that we do not have just two kinetic intermediates. There could be several intermediates; or, more likely, it could be that the transient absorption is shifting over time from longer to shorter wavelengths in a continuous fashion. Simple modeling of simulated data containing a continuous shift gave a set of SVD components rather like those shown. So we take the second spectral component to represent primarily vibrational relaxation in the geminate pair, along with any electronic relaxation there might be on that time scale. Interestingly, the time scale for decay of the second component (halflife of 6-9 ps) is longer in all four of the picket fence hemes than we have seen in any other species, either models or proteins. We infer that something about the picket fence structures slows relaxation to the equilibrated, five-coordinate B-Hm. Component 3 is smaller by an order of magnitude, and its spectrum has an additional node. The corresponding kinetic trace in Figure 3 appears to reflect two aspects of transient behavior: a very fast process immediately after excitation and a correction to the spectral changes occurring over the time scale of the second component. In other deconvolutions, these two features may be separated and one or the other may shift to the fourth component; but it is typical that there is a very fast process in one or both of these minor components. It is also
J. Phys. Chem., Vol. 98, No. 51, I994 13795 universal to find the low-amplitude, long-duration feature that we connect with a spectral shift continuous in time. Spectral component 4 is very noiselike in its kinetic behavior. Each of the higher components 5 and above is smaller yet and more random in time. One should not be impressed by the spectrum of any higher component. Any of them is balanced by some superposition of others, so that the total contribution is flat. Of major interest are differences among the four compounds. Striking differences between 0 2 and CO compounds were noted above and used to assign spectral features. In particular, 4 is much smaller for both CO complexes than for either 0 2 complex, although for the MI-Hm-CO complex, at least, we conclude that there is measurable recombination. CO is unique among common ligands in showing little or no geminate recombination to most hemes.12 In accord with this and (3), it also shows much smaller bimolecular association rates. There are less dramatic differences between MI and DMI for either L. The steric strain introduced by the extra methyl group in DMI interacting with the porphyrin plane is a standard means of reducing bimolecular association to mimic T-state hemoglobin, and it has been investigated with regard to picket fence heme from the earliest days.32 Picosecond studies of geminate recombination of an isocyanide with “flat” heme demonstrated that DMI reduced 4 by a factor close to 10 in parallel with a reduction of k~~ of 10-20. For 0 2 in picket fence heme, the drop in k~~ is about 3 and the decrease in 4 is 2-3. For CO in picket fence heme, DMI certainly reduces the measured 4, but for DMI-Hm-CO 4 is so small that no reliable ratio can be derived. We report a nonzero value, but we cannot really exclude zero. We infer, therefore, that DMI has qualtitatively the effect expected from the solvent-cagemodel in that it reduces both geminate recombination and bimolecular association. However, the two may not be reduced in strict ratio, as required by (3). If not, there are at least two explanations possible. First, it could be that 4 determined for photolysis is not quite the same as 4 appropriate for thermal reactions and that the discrepancy is somewhat different for MI and DMI. This is a general problem, not restricted to picket fence heme. Second, and specific to picket fence heme, it is possible that k-2 is slightly different for MI and DMI due to some influence of trans strain on the picket fence that affects the approach of ligands to the iron. Then part of the reduction of the overall association rate in (3) would be due to changes in the formation of the contact pair k-2. It was establishedg that steric blocking on the side of ligand approach can have very large effects on k-2, so it is not unreasonable to suspect that small changes in k-2 might be introduced by tension in the porphyrin system affecting the picket fence. The precision of neither the picosecond studies nor the conventional rate determinations really seems sufficient to support more quantitative analysis at this point. Unfortunately, even though the picket fence 0 2 complexes are much more stable than other 0 2 hemes, they are not really stable enough to allow the extensive signal acquisition that would be needed to substantially improve the kinetic data. We also tried, for comparison purposes, to measure 0 2 photolysis from “flat” heme, even resorting to “double flash” studies of B-Hm(CO+Oz) mixtures or rapid mixing of heme with 0 2 just prior to photolysis. We did not achieve useful results at the temperature needed for comparison with previous data. The fact that 4 for 0 2 turns out to be close to, but less than, 50% is consistent with the expectation from (3), since 0 2 has k~~ comparable to, or slightly less than, other ligands for which 4 is close to 50%.8,11,12 All of these ligands are said to associate with a “diffusion-controlled” rate, in contrast to CO, for which 4 and k~~ are both smaller. Association is diffusion controlled
13796 J. Phys. Chem., Vol. 98, No. 51, 1994 in that it reaches a limiting value for a variety of L and is viscosity dependent. The rate is not, however, that of hard spheres colliding; it is reduced by a steric factor involved in forming the “correct” caged pair, from which bond formation is possible. The effective caged-pair has L very close to the iron at the sixth coordination site. Nobody imagines a hollow solvent cavity in which L and B-Hm can rotate freely while L “searches for” the binding site on the iron. This steric factor is in addition to any steric factor, or transmission coefficient, involved in bond formation itself. The fact that q5 is smaller for 0 2 than for any other L except CO is consistent with its small size, which might facilitate “cageescape”. It is also consistent with predictions based on highpressure studies of bimolecular a~sociation,~~ which showed that increasing the solution viscosity by applying hydrostatic pressure actually increased the association rate, despite the fact that it must increase viscosity and slow diffusion. Although reactions far from the diffusion limit can either speed up or slow down under pressure, reactions that are really diffusion limited should only become slower. In the solvent-cage model, the increase in association rate for 0 2 under pressure is explained by proposing that q5 is being increased enough to overcome a reduced k-2 in (3). If q5 were already at a limiting value near unity and pressure were still able to increase bimolecular association rates, we would have a strong counter example to solvent-cage ideas (or at least to the claim that our transient spectra were measuring the cage population). The solvent-cage picture has been successful in at least a semiquantitative way for the B-Hm-L system now for all the common ligands and for a range of model hemes and heme proteins. At the same time, there are a number of places where small discrepancies occur. We believe that the next step is to explore the effects on geminate recombination of changing T and P. Work in that area is under way.
Acknowledgment. This work was supported in part by Grants NSF-CHE-9114613 to D.M. and by NSF-CHE-8721364 and NIH-PHSHL13581 to T.G.T. We thank Karen Bender for her assistance. References and Notes (1) Baldwin, J. E.; Perlmutter, P. Top. Curr. Chem. 1984,121, 181220. (2) Morgan, B.; Dolphin, D. Struct. Bonding (Berlin) 1987,64, 115203. (3) Jameson, G. B.; Ibers, J. A. In Bioinorganic Chemistry; Bertini, I., Gray, H. B., Valentine, J., Eds.; University Science Books: Mill Valley, CA, 1991. (4) Young, R. D.; Frauenfelder, H.; Johnson, J. B.; Lamb, D. C.; Nienhaus, G. U.; Philipp, R.; Scholl, R. Chem. Phys. 1991,158,315-327.
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