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INDIVIDUAL VELOCITY CONSTANTS IN THE CHAIN OF REACTIONS OF SHEEP HEMOGLOBIN WITH DISSOLVED GASES S. AINSWORTTI, Q. H. GIBSON AND lo. J. W. ROUGHTON* Dr. Edsall: you, sir, opened with what I think was a major contribution in spite of what you modestly said about our paper being the first major con- tribution. You began with a reference to the Barcroft Memorial Meeting ore Hemoglobin at Cambridge in 1948, a meeting which was greatly strength- ened by the team of visitors from this country. I am sure I express the feelings of the Cambridge folk, who are now here at the invitation of their Americans colleagues, in saying how grateful we are for this opportunity of a return trip. I look forward to this particular conference being just as memorable as the Barcroft Conference in 1948. There is one matter about that con- ference to which I might refer. You recall that a book1 was published des- cribing the proceedings. It is interesting to note that the publishers printed 2000 copies, and according to the most recent advices, 1970 copies have now been sold. It is not always the case, I am afraid, that experiment and calcu- lstion agree within one and a half per cent. That is, in matters concerned with hemoglobin. I will now get straight ahead with my main topic: the individual velocity constants in the chain of the four reactions of hemoglobin with oxygen, carbon rr~onoxide and nitric oxide. At Cambridge in 1948 wee only had very sparse k'~ Hb4 + X = Hb4X kl Karl l'l K1 _ Lo kl Hb4X + X=TIb4X, ~ - K. k Hb4~., + X = Hb4X3 ; K3 k: kt4 Hb4X3 + X = Hb4X4 k4 X = 0, or CO 11 l, Lo Zl3 L3 lo k'4 1~4 K4 _ L4 k4 1~ FIG. 1.Intermediate compound hypothesis of hemoglobin reactions. * This paper was presented by Dr. Roughton.

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VELOCITY CONSTANTS AINSWORTH, GIBSON AND ROUGHTON 15 knowledge as to the values of any of these individual constants. But since then we have learned quite a bit, largely resulting from the stimulus of that conference. We have reasonably good values for the four equilibrium constants of the reaction of oxygen with sheep hemoglobin through the work of Drs. Otis and Lyster and myself,-' and also of horse and human hemoglobin through the work of Dr. Lyster.3 It will be noted in figure ~ that in the case of the oxygen reaction we use K symbols, in the case of carbon monoxide L symbols, and in the case of nitric oxide, not shown in the figure we use ~ symbols. Over sixty years ago, Haldane and Lorrain Smith first observed that light dissociated CO from hemoglobin. Many others extended this work to CO home compounds in general. After the photo dissociation the CO recombined in the dark, and, as a matter of fact, this was the method by which Hartridge and Roughton over thirty years ago succeeded in measuring the kinetics of the first hemoglobin light reaction. But with the short intense lights obtained in flash photolysis, far more can be done, as Gibson4 has shown. The layout of his apparatus is quite simple. The solution to be examined is placed in a cell through which passes the observation light, rendered approx- imately monochromatic by a Alter, and then falls on the photocell and is recorded photographically by an oscillograph, after amplification. Then a brilliant flash for about two tenths of a millisecond is provided from the flash source, bringing about photodecomposition of the compound in the cell. f r Ll ~ ~ 1 Solution. Photocell. Oscillograph. FIG. 2. Block diagram of flash photolysis apparatus. Are there any photochemical after-effects of these flashes? Controls with myoglobin show-cd there were not; when CO myoglobin was photo-dissociated and the CO and myoglobin allowed to recombine the reaction followed a simple bimolecular course. The function plotted vertically in figure 3 against time gives a straight line, the slope of which is proportional to the velocity constant. If the same reaction is studied by one of the flow methods the same velocity constant is obtained. Furthermore, it does not matter whether all the carbon monoxide is dis- sociated from the myoglobin by the flash or only some. In each case a line of the same slope is obtained (see figure 4~. The velocity constant is independent of the amount of photo dissociation as would be expected in the case of a

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16 PART I. STRUCTURE OF HEMOGLOBIN I1 1 to 1 pH 71 x/ 19C. At FLOW x/ , / / a: FLASH ~ i: BIB = TOTAL Mgb = TOTAL CO ~ If = COMgbatt 0 2 4 6 8 10 12 14 16 18 20 22 24 TIME in MILLISECONDS FIG. 3. Recombination of CO with myoglobin. simple bimolecular reaction with one atom of iron per myoglobin molecule. Very different, however, is the state of affairs when different amounts of CO are initially split off from hemoglobin by the flash (see figure 5~. If the Rash is such as to split off the whole of the carbon monoxide, then there is only a relatively slow rate of recombination compared with that which occurs when a small fraction of the carbon monoxide is split offal The slope of the -0 1 1 30 >0 _ l .. . . . I. ~ em. o ~- 0 s 10 15 20 25 30 ; - TIME in MILLISECONDS FIG. 4. (left) Recombination of CO with myoglobin with 90 ;e rut z so O 70 60 te 50 40 0 20 0 TIME (MILLISECONDS) absence of interaction. FIG. 5. (right) Recombination of CO with hemoglobin, showing interaction.

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VELOCITY CONSTANTS AINSWORTH, GIBSON AND ROUGHTON 17 line in the latter case, i.e. the upper line, is of the order of 10 to 20 times greater than that of the louver line. This does supply an extraordinarily clear- cut and dramatic proof that it is indeed true in the case of sheep hemoglobin that the fourth reaction of combination of CO with hemoglobin goes vastly faster than the first one. 100 80 - c~ z 60 40 20 \Hb4 (CO)4 \ Mb4(C0)2 O ~ 100 80 60 40 20 0 % COHb otter LIGHT FrG. 6. Chart illustrating intermediate compound hypothesis. Concentration of in- termediate compounds as related to total reaction. Figure 6 shows the theoretical basis of the difference. According to the in termediate compound hypothesis, the dissociation will take in four steps forming successively compounds containing three, two, one and no molecules of combined CO. In calculating the quantity of each intermediate form when the amount of light applied is not enough to displace all the combined CO, it is assumed that the quantum yield is the same whichever intermediate compound is being irradiated. On that basis, the calculated amounts of the various intermediates at various total amounts of photolysis are as shown in figure 6. When only 10 to 157O of the CO is photolysed the main inter- mediate will be Hb4(CO)3. It is in that way that the value of 1~4 can be isolated. 1 - ~ _ Similarly, (especially if one starts not with fully saturated CO hemo- globin but with a mixture containing 10 per cent of CO hemoglobin and the rest reduced hemoglobin and one irradiates such a mixture), the compound present is almost exclusively Hb4, so that now the velocity constant 1'~ can be isolated. The correction for the later reactions can be reduced to 3 per cent or less. These applications of flash photolysis have thus provided very telling methods of dissecting out two of the individual velocity constants of the chain of the carbon monoxide reactions with hemoglobin. Figure 7 shows the effects of pH on these two velocity constants. The first curve, i.e. the full line, has a scale of values of about one eighth the scale of values of the last one. The scales are chosen so that the values of the two constants coincide at neutral pH. The discrepancy in the effects of pH on the two constants is very apparent. In the case of 1'~, the curare could be inter- preted in terms of the two heme-linked pK's, which Dr. Edsall discussed. In the case of 1~4, there is no obvious effect of pH on the acid side of neutrality.

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PART I. STRUCTURE OF HEMOGLOBIN 12. . 10 8 _ XIO{-IS 6 4 _ 2 0 , 4 5 ,'t4 ,' ~ ' \ 'Y A' 7 6 4 (4 xlo6 3 2 1 1 1 1 1 1 '0 6 7 8 9 10 11 pH FIG. 7. Effect of varying pH on values of l'1 and 1'4 (M1 S1) for sheep hemoglobin by flash photolysis. (Ainsworth and Gibson, 1957). :F~igure 7 thus provides a striking contradiction to the old creed that pH affects all the constants of the chain of reactions evenly. Later, another and sharper example of that type of contradiction will be shown. The next two figures demonstrate the effects of PCMB and the reversal of the PC~B effect by the addition of glutathione on the two velocity con- stants. The lower full curve in figure g is the same as that for 1', in the previous figure, but the upper curve is what is obtained when PCMB is added. The minimum is shifted to ~ rather different pH and there is a considerable increase in the actual value of lo of the order of 3-to-4-fold. The addition of glutathione, how-ever, restores the normal result. This parallels rather significantly some of the observations of Dr. Riggs on the effects of PCMB on the equilibrium of oxygen with hemoglobin. With 1~4 however, a different effect is observed (see figure 9~. PCMB, 40 36 32 28 10 - 5 I 1 16 12 8 4 to a\ bus olo Or t5 0 / ~ o} WITH PCMB WITH Path GSH In, o - OCR for page 14
VELOCITY CONSTANTS AINSWORTH, GIBSON AND ROUGHTON 19 9~ 81 7 1 0 - `;.1 ~ .L 3 2 rat ) WITH PUB WITH `~B+GSH /^ ~/ 1,0 11 FIG. 9. Effect of pH on 14 with additions of PCMB and of PCMB plus GSH. OH instead of increasing the velocity constant, now decreases it and the effect of pH almost disappears. The effect of PC~B is again reversible by glutathione. In a paper recently published in the B Series of the Royal Society of London,6 we have analysed the complete course of the kinetics of carbon monoxide and hemoglobin in terms of the four velocity constants, lit, lid, 1~3 and 1~4 in accordance with the equations: Hb4 + CO -~ Mb4CO, dt s q 1', U s I' qr I' qs HO ~ CO ~ + CO - ` Hb4 ~ CO ~ I, dt Hb4(CO), + CO -~ Hb4(CO)3, dt ~q Hi v q 1~4 W dv Hb4(CO):3 + CO ~ Hb4(CO)4, dt l Mu I ~qv Having two of the constants independently has made this possible. But even so we have had to resort to automatic electronic calculation on a large scale and to the assistance of Dr. Daniels and Nor. East of the Cambridge Statistical Laboratory. Fortunately, in this case the reverse constants of dissociation are so small that it is only over about the last five per cent of the reaction that they have any positive importance. By avoiding that range, we can effectively work with only the four combination velocity constants. Figure 10 shows how good is the agreement between calculation and experiment. Actually the agreement is within about 0.2 per cent between

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20 PART I. STRUCTURE OF HEMOGLOBIN 80 60 -6952,2-521-4, 13-3476 . 14 13904 :,,Hb4 X(CO) I 40 ~ ,, 0 ,, 20 o + 037a ~ ~3 - "~ olO`~ %~, --4--X- /Hb4X2 ,~b&~4 ' ~ ,,-- :~_ ;: -___ aft"" ;~~ 10 20 30 40 50 60 70 80 90 100 TIME IN MllLlCS. (CALC~D -art) f ~1 % XHb [Hb44 +2 [Hb4X23 + 3 [Hb4Xi ~ 4 [Hb4X4] K)O ~ [Hb4] + ~b4XJ +[Hb4X23 + ~b4X3] + [Hb4X43 ) FIG. 10. Comparisons of calculated and observed results. what one would expect on the basis of the four velocity constants and what one observed in regard to the total amount of CO hemoglobin formed at various times from the beginning of the reaction. The full line curve in the top panel displays the observed course of the combination. The dotted curves show the calculated course of the several intermediates. In the bottom panel, the discrepancy between observed results and calculated results are plotted against the extent of the reaction. The breadth of the panel is 0.3 per cent, so that the worst discrepancy is only about 0.2 per cent. Figure 11 shows the varying effects of pH on these various velocity con- stants. The speckled rectangles are for pH 7.1 and the clear rectangles for pH 9.~. When one passes from the first to the second constant, the speckled rectangle gets a little smaller, whereas the clear one gets quite a bit bigger. At the third constant, the speckled rectangle takes a leap up and the clear

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VELOCITY CONSTANTS AINSWORTH, GIBSON AND ROUGHTON 21 FIG. }1. Effect of pH on l 1' l ~' l 3 nd l' 7 1 ~3 9 1 7ln =1 1 Sty '2 9 l ~ _ . ~ ~4 one takes a leap down, and finally they are pretty close together on the last constant. Figure 11 thus demonstrates very clearly the differential effect of pH when the individual constants are dissected out and the effect of pH on each of them is studied. TABLE I Fitted ratios Experim ent - 1 1, lO 1'.3 3.5 1 1 C.V.'s (c, 0.3) 1 ., 1 3 Original 7/19 7/22 9/24 9/26 9/27 9/17 9/16 4 4 4 4 4 4 4 4 4.2 5.4 5.8 6.3 7.5 6.6 5.9 1.8 1.7 1.7 2.2 2.3 2.5 2.4 2.3 6.4 15.2 17.9 6.2 15.0 10.8 6.2 1 1.6 10.2 4.6 8.0 8.4 4.7 8.2 2.8 5.5 8.0 2.6 6.9 10.9 2.9 7.2 12.6 3.0 MEAN 4 : 5.6 : 2.1 6% 11.2C/o 7.3% Table I shows the values and standard errors of the first three constants for 8 different sheep samples, the first constant being taken as proportional to four. The standard errors are of the order of five to ten per cent, which is about as good as could be expected in this kind of work. Now, to turn a little to the other side of the story, the individual velocities of dissociation. Gibson and Roughton~ have shown (see figure 12) that the in dividual velocity constants of dissociation, as regards the first molecule

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22 PART 1 STR[CTURE OF HE~OOLOBIX 12 . 8 4 LglOV o 4 \ V ~ zz RT T ^~=~z_~ ' ~O) VT = vel const.ot no. =[li~s/~ ~ = Z 71SZ8 .. E = E~~y o' A~t~n R =~s ~"ont (~*colJ HzO+~C~4 \ H~+H~ \ O VT+IO / VT 0~ c~1~0 . . \ . IO~ 2~ 30,~0 4~0 ENE~ of ~TI~ION (colori's) FIG. 12.-Rel~tloD of actlvatloD ener~y to velocity constants. coming oR, do fall very nicely into line ~>h classic~1 kinetic theory, the logarithm of the velocIty const~nt bein~ linea[ly rel~ted to the ener~y ol activation. In accorJ~nce ~ith Dr. U auro~z's teaching' the d~sociatlon DETER~I\~IOX ~F ki ~XD ^~4 1/ r ~here At Constant p CO R~te of ~ispl~cement of C~ by CO 7 4(I + k4pO~ \ //4 P CO )4 [~2 Combincd ~ith H b] ~4 Nb4Oa = Nb4O6 I 02 k74 /4 Hb3CO)+ ~ Hh(CO)~ + CO //4 1 . ~ 4/k4 _ versus nC~ ~1VCS . ~ >- ~ ~ k 4// ~ FIG. I3.

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VELOCITY CONSTANTSNINSWORTH, GI:13SO>I AND ROUGHTON 23 reactions have been written in the form 8,0 + FIb4OS, etc. There is over a millionfold variation in rate between kit, the velocity constant for first oxygen coming off, and Jo, the velocity constant for first nitric oxide coming off. Nevertheless there is a good agreement with simple classical theory. We now turn to some of the improvements we have recently made in the determination of these dissociation velocities constants which it is hoped may be helpful when we come to the study of abnormal hemoglobins. Figure 13 illustrates the method used by Gibson and RoughtonS two years ago for obtaining k4. A solution of carbon monoxide was mixed with oxy- hemoglobin, which had been equilibrated with various pressures of oxygen ranging from a tenth of an atmosphere to a whole atmosphere, the carbon monoxide pressure being constant. The theory given in figure 13 then shows that if the inverse of the rate of displacement is plotted against the oxygen pressure, a straight line is obtained, of which the intercept on the vertical is equal to 4/k4. Figure 14 shows an application of the principle. The method, however, r 07 06 as 04 03 02 0-1 / } ~4 0-095 ream. Mb 0-5 1 norm. CO pH 91, 18 SAC. 0 0-1 02 03 04 05 06 07 08 m.rnol. O2 / LITRE. FIG. 1 5. EEect of CO on 0`, dis- . . SOCla~lOn. ~ < 100 80 6 O cat o o 40 o 20 O _ 0 20 40 60 80 100 TIME in MILLISEC5 r IG. 14. Displacement of GO from Hb by CO. \~ pH90,Temp.21C. ~ \~' OF - Cm x ~ ~o~4 0~2 /o Na2S204 Monoxide after 0108 m M H b Jmixturc l

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~4 PART I. STRUCTURE OF HEMOGLOBIN is laborious since it requires as many as six separate kinetic experiments. The determination of k4 has now been greatly shortened by the following device. solution of oxyhemoglobin is mixed with sodium dithionite (9670 pure trade name "Manox") saturated with carbon monoxide at one atmosphere. What happens ? The Hb4OS dissociates into O and Hb4Oe. The O is mopped up by the dithionite and the Hb~O6 by the carbon monoxide, these two reactions proceeding so fast that the overall rate of oxygen dissociation is conditioned throughout by the speed of the unimolecular reaction Hb4OS~ Hb4O6 + O.,, i.e. by kit. The upper curve in figure 15 is an example of such ar, experiment. The lower curve in figure 15 shows the result obtained when oxyhemo- globin is mixed with sodium dithionite without the carbon monoxide. Figure 16 gives the calculation of the unimolecular "constant" of oxyhemoglobin in the two cases. In the former, the value of the constant does not change as the reactions progress: the actual value of the constant in this particular case was equal to 11, in agreement with the value obtained by the more laborious extrapolation method previously used. In the latter case, however, the calcu- lated value of the "constant" rises progressively, since, in absence of CO, the reaction Hb~OS ~ Hb~O6 + O.,, is succeeded by the reaction Hb4Oc ~ ~ b~O4 + O., and further intermediate reactions of the same type. The velocity constants of some of these later reactions are greater than k4 and as their influence comes more and more into play the calculated value of the overall dissociation constant correspondingly increases. The determination of lo, the velocity constant of the first carbon monoxide ~1 z30 o 920 cr 0 1 0 ~1 I-) o I I I I 1 `_, O 20 40 60 80 100 PER CENT EXTENT OF REACT I ON I at _ ~07~ ~ ~ (O2Hb+Na252O4+co~i-~44/4 DH 9 0. 21C. FIG. 16. Effect of CO on oxy- gen dissociation constants.

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VELOCITY CONSTANTSAINSWORTH, GIBSON AND ROUGHTON 25 coming off, was first made over 20 years ago,9 by mixing very dilute CO hemoglobin with buffer containing various amounts of dissolved oxygen, following the rate of replacement and using a similar extrapolation procedure as in the first method of determining k4. Instead of using dissolved oxygen as a replacer, we now use dissolved nitric oxide. Nitric oxide has about 1500 times the affinity for hemoglobin that carbon monoxide has.~ 300 200 s 100 o 4 (1' [; [CO]N - (4 ~ oL4 [N]; 0 100 300 500 700 CO PRESSURE in mm. Hg (offer mixing) FIG. 17. Determination of 1'4 by use of the high affinity of NO for hemo- globin. Figure 17 shows a plot similar to figure 14 for a series of experiments in which CO hemoglobin in equilibrium with various pressures of CO was mixed with a buiEer containing some dissolved nitric oxide. Again a straight line is obtained but there is, in this case, an experimentally observed point on the vertical axis itself.l1 Such a point is obtained when a 100~7O CO hemo- globin solution in equilibrium with five millimeters of carbon monoxide is mixed with nitric oxide in solution. Since this point coincides with that gotten by the extrapolation of other points, the determination of l4 can be made in 3 single experiment. Table II shows how well the values of 14 agree whether TABLE II x 0~ NO 14 Hb4(CO)4 =~_ Hb4(C0)3 + CO Hb4(CO), + X ~ Hb4(CO)3X etc. Sheep Hb: pH 9.1, Temp. 23.5C. l4 0.042 0.044 one uses oxygen or nitric oxide as the replacer. It is, eve think, a very crucial

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;~6 PART I. STRUCTURE OF HEMOGLOBIN test of the whole theory upon which these types of measurements and the deductions from them are based. The determination of j4, the velocity constant for the rate of dissociation of the first nitric oxide from hemoglobin, can be carried out by simple classical methods. The reaction is so slow that if a dilute solution of NO hemoglobin is rotated in a tonometer containing carbon monoxide at one atmosphere pressure and rotated for several hours, the time course of reaction and the value of the unimolecular constant can be arrived at from spectroscopic determinations at 3-hourly intervals. The whole procedure is very simple. 9 1 8 o 17 o 16 15 20, ' \ j4,ooooos2 \ pH 91,16 SAC. \D ~. l O 2 4 6 8 TIME in HOURS. We are now applying constants to the different them to abnormal types fractions. It is, however, a rather striking fact that, although these different hemoglobins show much different electrophoretic and solubility patterns, yet the reactions with the small ligand molecules so far have not revealed anything like such great differences. In the case of human sickle cell hemo- globin, for example, both the oxygen equilibrium curve and the kinetics of dissociation of oxyhemoglobin are more or less the same. It will be very interesting to see whether this extends to various other types of human hemo- globin. Finally, a word as to the major kinetic problems in front of us at the moment. We are now trying to make a complete kinetic analysis of the reaction of oxygen with hemoglobin, involving eight velocity constants 100 90 80 70 60 OZ FIG. 18. Determination of j4, the O velocity constant for rate of dissocia- 50 ~ tion of first NO from Hb. Note reaction time is in hours. 40 these various methods for the individual velocity types of sheep blood and hope later on to extend of human hemoglobin and to various hemoglobin ~ ~ . ~ 1_ 1 _ _ _ ~ _ 1~ ~ _ ~ _ _ ~ ~ ~ ~ ~ _ _ _ tour combination, tour reversible ones. l o nave any chance or success in this problem, we must know independently at least six of the eight velocity constants. We have four of them at the moment, and I am pretty well sure that we may have five and possibly six. Then it will be a matter of going on to the electronic calculator. But what troubles will be in store for us, who can say? All I can do in closing is to ask for your prayers.