Properties of the T State of Human Oxyhemoglobin Studied by Laser Photolysis*

Using a dye laser with 1J output at 540 nm, points on the oxygen equilibrium curve in the range 0 to 0.2 saturation were determined by observing the absorbance excursion at 436 nm following photolysis. The results compare reasonably with those in the literature (Roughton, F. J. W., and Lyster, R. L. J. (1965) 48, 185-198). The saturation is obtained directly by this method rather than by subtraction, and contamination with CO is immediately observable as a slow relaxation.

and from studies of mutants (10,11). These have agreed in suggesting that the rate of dissociation of oxygen from the T state is many times larger than from the R state, and this has been confirmed experimentally by the so-called oxygen pulse experiments of Gibson (12). A rapid relaxation has also been observed in the careful T jump studies of Ilgenfritz and Schuster (131, although their results were not interpreted in terms of the two-state model. In this paper, we describe a new experimental approach which provides both kinetic and equilibrium data for the same solutions of hemoglobin. It is especially suited to the study of the properties of the T state, and so provides a more incisive approach to the application of the two-state model than has so far been possible.

EXPERIMENTAL PROCEDURES
Methods -The principle employed is to prepare a partially saturated solution of hemoglobin in equilibrium with a known concentration of free oxygen.
The bound oxygen is removed quantitatively by a laser pulse, so the amplitude of the absorbance excursion gives a measure of the saturation of the hemoglobin, and the recombination reaction after the flash reflects primarily the kinetics of the reaction of deoxyhemoglobin.
Hemoglobin was prepared from pooled hospital blood samples as previously described (14). For these experiments it is essential to remove CO as completely as possible. This should always be done when an equilibrium curve is to be determined. The average content of COHb was about 2%, and this was reduced to 0.1 to 0.2% by exposure of a thin film of a 5 rnM (heme) solution in a rotary evaporator at 0" to pure oxygen. The solution was illuminated for 30 min by a 300-watt floodlight placed 5 cm from the flask. Deoxyhemoglobin was prepared by rotation of a small volume (10 to 20 ml) of a 5 rnM solution in a 500-ml tonometer equipped with a serum stopper as well as the usual stopcocks. The tonometer was repeatedly flushed with purified N, delivered through a short length of butyl rubber tubing for 15 to 20 min.
Working solutions were prepared in two ways: (a) 0.05 M (pH 7.0) phosphate buffer was placed in a large syringe (30 ml) and deoxygenated by bubbling with purified N, for 10 min. The needle used for bubbling was then removed and the syringe closed with a small serum stopper which had its dead space filled by a stream of buffer as it was placed over the hub of the syringe, care being taken to avoid leaving a residual air bubble in the recess of the stopper. The required amount of hemoglobin stock solution was then injected into the large syringe using a suitable gas-tight microsyringe. A portion of the buffer solution was also equilibrated with oxygen by bubbling at a known temperature and pressure. The required amount of this solution, whose oxygen content was calculated from the standard tables (151, was then injected into the hemoglobin syringe using a microsyringe.
A cuvette of l-or 2-mm path was prepared by blowing nitrogen through needles passing through a serum stopper for 30 min. The inflow needle was then removed and the cuvette rinsed with a large excess of sample solution from the 30-ml syringe, removing bubbles as completely as possible. When this procedure was carried out without adding any oxygen, a 50 ELM solution of hemoglobin contained 0.1 to 0.2% of oxyhemoglobin.
The cuvettes were stored in ice until the experiment was to be performed (less than 40 min). Immediately before photolysis the cells were immersed in a water bath at 20". (b) The second method for preparing working solutions was to fill a tonometer of 105-ml capacity with N, by evacuation and refilling.
The vessel had a Z-mm path length cell fused to it, and also a Teflon stopcock at the other end. would be highly desirable, but the literature affords few suitable sets of experiments. The gasometric data of Roughton and Lyster (18) were obtained at the same pH but with much stronger hemoglobin solutions. Their points lie close to, but slightly to the right of ours, especially at low per cent saturation. Their buffer was 12 times stronger than ours, and the temperature 1" lower. In view of all these factors, the agreement is surprisingly good, perhaps because of a cancellation of effects due to dimerization and the temperature difference.
Data exactly comparable to ours by an automatic recording spectrophotometric method have been published by Imai and Yonetani (6) for similar buffers, temperature, and hemoglobin concentrations.
Their data were not presented as individual Study of T State of Human Oxyhemoglobin in the deoxy stock; these would have rather small effects on the position of the curve. The problem of MetHb formation during an experiment is more difficult to deal with but it appears to have been quite small since the residuals in the spectrophotometric procedure did not rise markedly nor was there evidence of an increase in absorbance at 405 nm as a tonometer experiment progressed.
There is a special problem in using flash photolysis for determining points on the equilibrium curve of oxyhemoglobin. This is the possibly different contribution of R and T species to the observed excursion following photolysis. The contributions of the deoxy forms are well known (19)(20)(21) and that difficulty may be avoided by working at 436 nm. At other wavelengths dimers and the R-T deoxy change must be expected to contribute, the R-T change becoming progressively more important as the per cent saturation is increased. For the present purpose this is mainly of importance because the excursion corresponding to 100% saturation has been determined experimentally by photolysis rather than from static optical measurements.
The effect is to decrease apparent saturations measured at 442 nm, for example, and to increase them at 430 nm.
A second, and less considered, problem will arise if the extinction changes associated with binding of oxygen to give T-liganded and R-liganded forms are different. In an attempt to investigate the point we have recorded the spectrum of oxy-deoxy hemoglobin mixtures over the range 400 to 460 nm and have scaled the difference spectra (mixture-deoxy) by multiplying by the reciprocal of the fractional saturation as defined by the amplitude of the difference spectra. The results presented in Fig. 3 show little difference between the spectra at 436 nm, although somewhat larger differences are observed near the oxyhemoglobin maximum. At 436 nm the effect is less than 5% of the observed saturation (i.e. less than 0.005 at 0.1 saturation) at the most. Had the spectra of Fig. 3 shown substantial differences, unambiguous determinations of fractional saturation by any spectrophotometric method would be impossible; as it is, the uncertainties are not signiflcant for our purpose, as R-liganded and T-liganded hemoglobins do not differ in their absorption at 437 nm.
It does seem, however, that there are significant changes in the spectrum near the oxyhemoglobin maximum with an isosbestic at about 410 nm and considerable variation in the difference spectrum at about 419 nm. An inset to Fig. 3 shows the amplitude of this difference as a function of fractional saturation. Although the precision with which the differences 2. Equilibrium data points for hemoglobin in pH 7 phosphate buffer between 10 and 60% saturation.
Experimental conditions and the calculated curves are as described in Fig. 1.
can be measured is low, there is a clear monotonic increase at low fractional saturation. The photolysis method is particularly suited for equilibrium points at low saturations since the deoxy standard is internal and its contamination with CO or extraneous oxygen cannot pass unnoticed. Further, the quantity to be measured is observed directly and not by comparison of different samples.
Kinetic Experiments-Families of curves obtained by following the return to equilibrium after photolysis are presented in Figs. 4 and 5. It is evident that the recombination reaction is markedly biphasic under all conditions examined. With both 40 PM and 500 PM hemoglobin the rate constant for the rapid component is virtually independent of initial saturation up to 0.2 or so, as shown in the semilogarithmic plots of Fig.  4. These results show that the two components of the recombination reaction are only slightly dependent upon the saturation at equilibrium in the range 1% to 20% saturation. In particular, the proportion of the rapid phase remains at about a half even when the reaction proceeds only as far as 1% saturation (although of course, as the excursion available for measurement was only 0.005 in absorbance, the noise contribution is appreciable). With differing hemoglobin concentration, the rate increases markedly at the highest concentrations which can be used without producing an excessive rise in temperature ( Fig. 5). At very low initial (preflash) saturations, the recombination reaction must be attributed to T state hemoglobin because, whatever the nature of the photoproducts, they are present in amounts too small to influence the observed reaction. For example, with 50 PM hemoglobin, 1% saturation corresponds to binding of oxygen to 0.5 PM heme, and total oxygen will be about 1.8 pM; then even if all of the photoproduct had R-like behavior and a rate constant of 50 x 10" the apparent rate of FIG (Fig. 6) and hence the observed reaction should represent the properties of the T state only. As shown in Fig. 4  The dashed curves were generated using the MWC model discussed in the text which neglects a,p chain differences.
The parameter values used are the same as those used in Fig. 1 largely independently of one another, but the distribution of the amplitudes of the fast and slow components continued to be systematically misrepresented, the model giving too large a fast phase for low oxygen saturation before the flash.
The third modification was to divide the T and R states between two distinct components, formally analogous to the (Y and p chains, i.e. present in equal amounts. The use of the two-state model was continued, but now with four different affinities and nine tetrameric species. The reactions assumed to occur are set out in Equations 3 to 11. R and T represent tetrameric R and T state hemoglobin. Dimers are represented by D. The distribution of bound oxygen is given in parentheses following each species. The subscripts on cxs and /Ss denote the number of oxygen molecules bound to these chains in the hemoglobin tetramer. The subscripts for the on rate constants for oxygen (h') and the dissociation rate constants (h) give the molecular species R, T, or D, and the chain (a or /3) which takes part in the reaction. In order to run the program, 11 different parameters must be specified. Of these, the four values for the R state were taken from the literature and from Appendix 1 (27) and, as before, the dissociation velocities for the dimeric species were set equal to those for the corresponding reactions of the R tetramer. The tetramer-dimer dissociation constant is not affected by the change in model and was set at 1 x lo-" M. The remaining five parameters were allowed to vary freely under control of the minimization program. Excellent representations of the kinetic data were now obtained, as illustrated in Figs. 9 and 10 fitting simultaneously the families of kinetic curves and the lower half of the oxygen equilibrium curve. As expected from the qualitative considerations already outlined, the kinetic properties of the two components are quite widely different, but with smaller differences in affinity than in rates. The data shown in the figures do not embrace a complete experiment: in the experiment of Fig. 10 several different initial saturations were examined in addition to that shown for 515 PM hemoglobin. The additional data were fitted as satisfactorily as those shown. The fixed and best fit parameters are presented in Table I.
It is clear that the model is sufficient: the question of how far the data serve to define the parameters is less easy. When parameters are fixed, as has been done in this case, the standard errors of those varied are calculated from the error matrix (see Ref. 28) as if the fixed parameters were precisely known, which is, of course, not the case. An attempt has been made to deal with the problem by assigning standard errors to the six fixed parameters from the literature or from experience. The minimization program was then run repeatedly using randomly chosen values for the six parameters and optimizing the remaining five. With sufficient (about 80) runs, an estimate of the variance in the five optimized parameters due to uncertainty in the six fixed ones could be obtained. This has been added to the conventional variance to give the estimates included in Table I [Ill their ratio remains relatively constant. Numerical experimentation suggests that this is due in part to the relatively much greater contribution of dimers in the runs with low hemoglobin concentration (Fig. 9). At the oxygen concentrations and concentrations of dimers present, the observed rates of oxygen binding to the slow component of the tetramer and to dimers are similar. A second difficulty results from the near-invariance in shape of kinetic curves obtained with varying oxygen   (Fig. 4). This means that there is little advantage in fitting a family of curves such as those in Fig. 9 over fitting a single curve. Both of these difficulties are reflected in differences in the rate constants obtained by fitting the low concentration data (legend to Fig. 9) and the values obtained by fitting data for a range of hemoglobin concentrations (legend to Fig. 10 sentation of the overall deoxygenation reaction. This figure is a simulation, and no optimization has been attempted. The large value of L of 1.4 x 10' which has been found indicates that the difference spectrum for R-liganded and Tliganded hemoglobins should be easily observed. In fact, in the Soret region, there is no large difference between the difference spectrum for 0 to 10% oxyhemoglobin and 0 to lOO%, although a small difference may readily be observed in the immediate region of the oxyhemoglobin maximum. The conclusion is that spectrophotometric determinations of saturation should be reliable to 0.5% saturation or so when made at any wavelength in this region reasonably removed from the isosbestic point, and, since the difference spectrum is isosbestic at about 410 nm, determinations made using several wavelengths may be expected to be closer still. The determinations made with the laser method agree well with the classic gasometric work of Roughton and Lyster (18) and have the advantage of showing clearly any contamination with CO. The importance of even small amounts of CO in shifting the curve significantly is illustrated in Fig. 1. In spite of these virtues, the laser method can scarcely be advocated as an everyday procedure, although provided that suitably thin films were prepared, concentrations up to 5 mM or so could be examined without producing a temperature rise sufficient to denature the hemoglobin. It seems that it is the inevitable association of a temperature jump with photochemical removal of oxygen which offers the main limitation to the use of the laser method for studying the kinetics and equilibria of the oxygen reaction. (See Appendix 2.) The differences betwen the components of deoxyhemoglobin (presumed to be the (Y and p chains) are the largest yet reported for a gaseous ligand and are of the same order as the differences reported earlier for the bulky ligand n-butyl isocyanide (31) and in the reaction of methemoglobin with dithionite (32). They are much too large to be neglected in analyses of hemoglobin kinetics, although in some circumstances a satisfactory approximation might be obtained by regarding the rates for the slower component to be zero. It is perhaps this effect which allowed Gibson (12) to describe his oxygen pulse experiments in terms of only two relaxations, the slower component simply did not contribute sufficiently to the observed kinetics to be detected in the presence of rapid T state and R state species.
The difference between the components derives from rate constants for combination (kfold difference) and dissociation (12-fold difference). These constants combine so as to produce only a 3-fold difference in affinity. There is no immediately obvious correlation with structure, but with differences as small as lo-fold this could scarcely be expected. In confirmation of earlier work (33) the rate of binding to R state tetramers was determined by partial flash photolysis of fully oxygenated (>200 PM free 0,) hemoglobin solutions. The rate constant obtained at 20" was 59 PM-I s-l. The rate for binding to dimers was obtained by full photolysis of dilute (<l PM heme) solutions of oxyhemoglobin.
These solutions show a biphasic reaction the greater part of which can be attributed to the dimer on the basis of the concentration dependence of the amplitude of the rapid phase. The rate constant obtained by subtracting out the slow phase was 30 /.LM-I S-' at 20". This is considerably less than the rate constants reported for isolated chains of 50 ? 20 pM-' s-l for a-SH and 71 ? 6 PM-' se * for @SH (34). The rate constants for the chains do not necessarily apply to the dimer, particularly for the /3 chain which is tetrameric in solution (35). No definite evidence of heterogeneity which might be attributed to chains was observed in these experiments. APPENDIX

Temperature
Rise on Photolysis of Oxyhemoglobin The low quantum yield for the photolysis of oxyhemoglobin (36) requires that large amounts of light be used to obtain essentially complete photodissociation.
Experiments and calculations performed earlier for 50 PM hemoglobin (16) suggested that 97 to 99% dissociation is associated with a temperature rise of about 0.3". In the present experiments it is important to use higher hemoglobin concentrations (up to 500 pM) in order to define the values of the kinetic parameters. The resultant temperature rise must be proportional to the hemoglobin concentration.
The temperature jump was determined using the rate of the R + T conformational change observed following photolysis of 500 PM carboxyhemoglobin in borate buffer at pH 9. This change has a large apparent activation energy (18 kcal/ mol, see Ref. 21). The rate of the conformational change was observed following photolysis using a laser pulse of the same energy used in photolysis of the oxyhemoglobin samples. The experiment was then repeated using a filter which reduced the energy incident on the sample by a factor of 15 yet still allowed essentially complete photolysis because of the high quantum yield of COHb. The rates of the R -+ T change followed at 425 nm and 30" for 500 PM COHb were 20,000 ss' for the full flash and 15,000 s-l for the attenuated flash corresponding to a temperature difference of about 3" in good agreement with the earlier work with oxyhemoglobin.
In order to determine rate constants for the reaction of deoxyhemoglobin with oxygen at 20" the cell holder was maintained at 17" before photolysis when 500 PM hemoglobin was used, and at 18.5" for 250 PM. For lower concentrations a temperature of 20" was employed. The change in temperature alters the oxygen equilibrium which is established before the flash. This was not taken into account in the calculations required to establish the initial concentration of dimers following the flash, but computation suggests that the effect of this neglect is unimportant at high hemoglobin concentration where a significant temperature jump occurs.