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OCR for page 14
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.
OCR for page 15
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
OCR for page 16
16
PART I. STRUCTURE OF HEMOGLOBIN
I1 1
to
— 1
pH 71 x/
19°C. 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.
OCR for page 17
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.
OCR for page 18
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Representative terms from entire chapter:
velocity constants
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 (M—1 S—1) 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 -
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
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 MllLl£CS.
(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
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
22
PART 1 STR[CTURE OF HE~OOLOBIX
12 .
8
4
L°glOV
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.
VELOCITY CONSTANTS—NINSWORTH, 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.21°C. ~
\~'
OF - Cm
x ~
~o~4
0~2 °/o Na2S204 Monoxide after
0108 m M H b Jmixturc
l
~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. 21°C.
FIG. 16. Effect of CO on oxy-
gen dissociation constants.
VELOCITY CONSTANTS—AINSWORTH, 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. 23.5°C.
l4
0.042
0.044
one uses oxygen or nitric oxide as the replacer. It is, eve think, a very crucial
;~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.
