ANALYTICAL

BIOCHEMISTRY

(1381)

197,231-246

Use of Dual Wavelength Spectrophotometry and Continuous Enzymatic Depletion of Oxygen for Determination of the Oxygen Binding Constants of Hemoglobin’ Todd

M. Larsen,

Department

Received

April

Timothy

of Chemistry,

C. Mueser,

University

and Lawrence

of Nebraska,

Lincoln,

J. Parkhurst

Nebraska

68588

16, 1990

A small stopped-flow cuvette was built into a computer-controlled Cary 2 10 spectrophotometer. The enzymatic depletion of oxygen in solutions of hemoglobin and myoglobin was initiated by flowing the hemeproteins with the enzyme against a solution of the hemeproteins containing the appropriate substrate. The deoxygenation was homogeneous throughout the solution. Oxygen activity was calculated at each instant of time from the fractional saturation of Mb, determined from observations at the Hb/HbO, isosbestic wavelength. Fractional saturation of Hb was determined from absorbances at the Mb/MbO, isosbestic wavelength. The spectrophotometer cycled between these two wavelengths during the deoxygenation. The deoxygenation of HbO, was largely complete in 20-25 min, whereas the deoxygenation of MbOz was allowed to proceed for about 1 h. This procedure eliminates equilibration of Hb solutions with a gas phase and replaces oxygen electrode readings with spectrophotometric sensing by Mb, providing essentially instantaneous determinations of oxygen activity and hence 250400 or more independent data points per run. The Mb and Hb data vectors require several manipulations to correct for small relative displacements in time and for small nonisosbestic effects. Detailed consideration of the enzyme kinetics allowed oxygen activities to be determined in regions where Mb is a poor sensor. Studies of HbOz deoxygenation as a function of wavelength show that the determination of the four Adair constants requires in addition the determination of three spectroscopic parameters. Values of the apparent Adair constants, de’ Grant Support NIH DK36288, Grant-in-Aid, Nebraska Affiliate. ’ To whom correspondence should Department of Chemistry, University braska 68588-0304.

American

Heart

Association

be sent at 525 Hamilton of Nebraska, Lincoln,

0003-2697191 $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.

Hall, Ne-

termined without these spectroscopic parameters, pend strongly on the monitoring wavelength. Academic

Press,

deo 1ssl

Inc.

Since the end of the last century measurements of the binding of oxygen to blood and to hemoglobin have been important in physiology and biochemistry. Following the development of dual beam spectrophotometers, the tonometric methods ( 1) , the thin-layer methods ( 2,3), and the automated methods (4,5) were developed. The oxygen concentration (or activity) was determined by dilution factors, calibrated flow methods (4)) or by oxygen electrodes (5 ) . In these latter methods, the number of data points is constrained by the stability of the Hb3 sample and by the time required for the Hb solution to reach equilibrium after each incremental change in gas composition. Our initial aim was to develop an instrument that would allow reasonably rapid and continuous determinations of both fractional saturation and oxygen depletion by spectrophotometry. Either of two enzyme systems were used to slowly deplete the oxygen in the cuvette. These were: glucose oxidase, ,&D-glucose, catalase (a system we had used earlier in hemoglobin kinetic studies (6))) or protocatechuate 3,4dioxygenase, protocatechuic acid. Oxygen activity is determined from absorbance changes in myoglobin, measured at ’ Abbreviations used: standard abbreviations of Hb, HbO,, Mb, and MbOl denote deoxy and oxy forms of hemoglobin and myoglobin, but Hb and Mb are also used generically for hemoglobin and myoglobin. The distinction will be clear from the context. Met-Mb and -Mb+ both denote ferrimyoglobin. CMC, carboxymethylcellulose; DTT, dithiothreitol; DIP, digital interface port; DACA, data acquisition and control adapter; X, activity of oxygen in solution; TNS, 2-ptoluidinylnaphthalene 6-sulfonate; 5, activity of oxygen for half-saturation; n*, Hill number at X = X; RC, resistor capacitor; PMT, photomultiplier tube; BSA, bovine serum albumin. 231

232

LARSEN,

MUESER,

585.9 nm, the isosbestic point for oxy-deoxy-Hb, and HbO, deoxygenation is followed at 590.6 nm, the isosbestic point for oxy-deoxy-Mb. In this manner, response time limitations, drift, and noise inherent in the use of oxygen electrodes are eliminated. Because the depletion is homogeneous throughout the sample, there is no lag time from gas-liquid equilibration and thus a large number of data points can be easily collected. Furthermore, since the solutions are not stirred during the reaction, there are no losses from surface denaturation. The first stopped-flow cuvette held 0.16 ml of solution, with an optical path of 1 cm, but only about half of this volume was sensed by the light beam. That cell is shown in Fig. 1. Later cells were similar in performance, but differed in detail in that no metal parts made contact with the protein solution. Typically, 375 data pairs (590.6,585.9 nm) are collected over the 25-min duration of the hemoglobin deoxygenation. Data collection is continued for an additional 40 min until the myoglobin deoxygenation has reached completion and to assure that the hemoglobin has reached a stable endpoint. We show from the dependence of fractional saturation on wavelength that at our monitoring wavelengths, fractional saturation is not exactly proportional to the absorbance change. MATERIALS

AND

METHODS

Materials Hemoglobin from one of Preparation of hemoglobin. us (T.M.L.) was prepared according to the procedure of Geraci et al. (7). For studies in phosphate free buffer, phosphate was removed according to Berman et al. (8). Stock Hb3 (2 ml, 2 mM in heme) solution, at 4”C, was passed over a 20 x 2.2 cm diameter G-25 Sephadex (G25-150, Sigma, St. Louis, MO) column equilibrated with a 0.1 M Tris-HCl (T-3253, Sigma), 0.1 M NaCl, pH 7.4, buffer (total Cl- 200 mM) to remove the phosphate from the Hb solution. The pH was measured at room temperature. The flow rate was adjusted for a total elution time of 3 h to allow complete removal of phosphate. The concentration of Hb after elution was 770 pM. For the studies reported here, the hemoglobin was not fractionated further. Preparation of oxymyoglobin. Freeze-dried horse skeletal metmyoglobin, approximately 1 mM (Calbiothem, La Jolla CA; No. 47592) was converted to the oxy form by the following procedure. The enzyme system of Hayashi et al. (9) was used to reduce the met Mb to at least 95% MbO,. This MbO, (5 ml) was passed over a CMC column (2 X 2.2 cm diameter) at 4°C equilibrated with 0.01 M potassium phosphate at pH 6.8 to remove the residual met Mb, which binds to the column and is later removed with 0.1 M NaCl. All components of the enzyme system of Hayashi et al. were obtained from Sigma (St. Louis, MO). The following amounts are

AND

PARKHURST

used for 5 ml of 1 mM met-Mb: 0.75 unit ferredoxinNADPH reductase (F-0628), 42 units of glucose-6phosphate dehydrogenase (G-6378)) 0.6 pg NADPH (N-1630), 40 pg ferredoxin (F-5875)) 36 pmol of glucose 6-phosphate (G-7879)) and 1300 units of catalase (C100). From isoelectric focusing, we determined that the crude oxy-Mb consisted of 88% Mb1 and 12% Mb11 with traces of minor acidic components. For the final studies, pure oxy-Mb1 was used, prepared in the following manner. The stock commercial “met-Mb” (2 ml, 2 mM) was completely oxidized with a few crystals of ferricyanide or nitrite for 5 min at room temperature. The sample was passed over G-25 Sephadex (Sigma), equilibrated at pH 6.5, 0.01 M phosphate. Three milliliters of the sample was applied to the CMC column described above (but equilibrated at pH 6.5 with 0.01 M potassium phosphate buffer) and eluted with the stock phosphate buffer at 4°C. (All pHs were as measured at 21°C.) Mb11 and all traces of minor components elute with the solvent front. Met Mb1 was eluted with 0.1 M NaCl in about 2.5 ml. From this point, either of two procedures can be employed to obtain a pure oxy-MbI. In the first procedure, catalase (Sigma, C-40 from bovine liver), was added to the Mb1 solution to a final concentration of 2 pM, and then, over a period of 5 min, single crystals of sodium dithionite (Manox Brand, Holdman and Hardman, Miles Platting, Manchester, UK) were slowly added with very gentle stirring to generate deoxy Mb. The sample was then passed over a G-25 Sephadex column equilibrated with 0.01 M potassium phosphate, pH 6.8, and applied to the CMC column described previously, from which pure oxy-Mb1 was obtained by elution as described above for crude oxy Mb. In the second procedure, the protein was first passed over the G-25 Sephadex column equilibrated with 0.01 M potassium phosphate, pH 6.8, then treated with the enzyme system of Hayashi (described above) for a few hours, and the oxy-Mb1 separated from met-Mb1 on the CMC column as for the crude Mb. For experiments requiring concentrated oxy Mb, the sample was concentrated to 1 mM using ultrafiltration (Centricell Y18673-2, Polysciences Inc., Warrington, PA) prior to application on the CMC column, from which oxy Mb1 was eluted (approximately 400 PM). Purified oxy Mb was stored immediately as frozen droplets in liquid nitrogen. Immediately prior to use, the thawed sample was passed over a G-25 Sephadex column equilibrated with the desired buffer. Deoxygenation procedure. For the deoxygenation studies, both stopped-flow syringes typically contained MbO, (60 PM), HbO, ( 100 pM in heme), bovine serum albumin (Calbiochem, No. 126609) (1 mg/ml), and dithiothreitol (DTT) (Calbiochem, No. 233153) ( l-8 mM). Additional reagents were added just prior to the run. Syringe A contained 7.6 jiM ( 2000 units /ml) catalase (Sigma, C-40 from bovine liver) and 5.8 pM D-D-

HEMOGLOBIN

EQUILIBRIA

ANALYSIS

glucose (Sigma, G-5250) and syringe B contained 0.126 (3 units /ml) glucose oxidase (Sigma, G-7016). Alternatively, for the second enzyme system, additional reagents were: Syringe A, protocatechuic acid, 5400 I.IM (Sigma, P 5630) ; Syringe B, 0.12 PM (0.28 unit /ml; 4.4 pg /ml) protocatechuate 3,4dioxygenase (Sigma, P 8279). The stock enzyme solution was prepared by reconstitution of the lyophilized powder in buffer and stored on ice. The concentration of the enzyme was based on a molecular weight of 700,000 (10). At this concentration, any absorbance changes from the enzyme were entirely negligible (10). In these experiments equal diameter syringes were used and thus, after mixing, the concentrations of the reagents from each syringe were halved. For the experiments reported here (Sigma T-3253)) 0.1 M the buffer was 0.1 M Tris-HCl NaCl (200 mM total Cl-), pH 7.4. PM

Apparatus The stopped-flow mixer assembly is shown in Fig. 1. It was made from Allegheny SS304 stainless steel and built into a semimicrocuvette by sealing it with General Electric silicone sealant (Clear Household Glue & Seal, Waterford, NY) and capping it with Scotch-Weld 3M

FLOW IN

BY

SPECTROPHOTOMETRY

233

Epoxy Adhesive (3M Center, St. Paul, MN). The stopped-flow apparatus uses an air piston (Model 031% 1202-010, Aro Corp., Bryan, OH) with the O-ring removed to prevent rebound, to drive approximately 0.3 ml of solution in 80 ms. Flow is stopped by a reversed third syringe, the steel plunger of which strikes an adjustable micrometer, or by front stopping with the exit stream throttled by a 20 gauge needle. Air pressure is controlled by a solenoid valve (Model 5433 33.01, Aro Corp., Bryan, OH) electrically controlled to release the pressure a few milliseconds before cessation of flow. Tests of the mixer made by flowing alkaline phenolphthalein against strong acid showed no trace of red colored filaments in the optical path at these flow velocities. Tests made by flowing met-Mb vs varying concentrations of azide gave an apparent optical dead time ( 11) of 1 ms. The cuvette assembly is held in a clamping apparatus in the sample compartment of a Cary 210 spectrophotometer. Data collection is initiated simultaneously with cessation of flow. The program (Master Kinetics Storage Program, Varian Associates, Inc., Palo Alto, CA) was used in the initial studies with the following parameters: two wavelengths, a period of 0.5 s, and a 0.5-s data averaging time. In our most recent studies on all but the lowest affinity hemoglobins, we have found that the entire procedure can be carried out in a jacketed cuvette in the following simple manner. The cuvette is filled nearly to the top with the required protein solution, allowed to reach thermal equilibrium, and 50 ~1 of the required substrate are added with brisk stirring with a glass capillary. The cuvette is then either capped with a stopper that excludes air, or with a thin layer of mineral oil, and the data acquisition begun. The entire mixing procedure can be completed in 3 s. Data Acquisition

FIG. 1. Stopped-flow spectrophotometer.

cuvette

with

four-jet

mixer

used in the Gary

The Cary Model 210 uv /vis spectrophotometer (Varian Instruments Division, Palo Alto, CA) was originally equipped with a digital interface port (DIP) accessory controlled by an Apple II+ microcomputer. This port accessory was replaced with an IBM XT I AT based data acquisition and control adapter (DACA) (Mendelson Electric Co., Dayton, OH) interfaced to the digital interface port of the Cary 210 system interconnect panel (DIP 513). The analog scan drive motor was also replaced with a stepper motor and driver (Rapid Syn Model 34H-508 and a rewired Rapid Syn Driver Model M43020, Computer Devices, Santa Fe Springs, CA). We determined that the Cary analog drive motor did not reproducibly return to the two desired wavelengths but rather showed small periodic oscillations about these wavelengths. The control software was written in QuickBasic 4.0 (Microsoft Corp., Redmond, WA). A complete description of these modifications will be presented elsewhere. A brief description of the IBM-based

234

LARSEN,

MUESER,

device is presented here. The readout display of the Cary 210 requires 24 bits of information to be transferred via the DIP to the IBM DACA. The DACA 16bit binary input has been multiplexed using quad lof-2 data selectors (74HCT157). The 12-V dc Cary output signals are converted for each data line to 5-V dc TTL compatible signals using voltage dividers compatible with the Cary signal pullups. For each measurement of the port, the data lines are latched (using three 74HCT573 octal D-type data latches), the DACA inputs the four low digits (4bit decimal), and the data selectors are then switched to read the last remaining digit, the position of the decimal point, and the polarity. The stepper motor is controlled by 2 bits of the 16-bit binary output port of the DACA. The DACA outputs pulse the forward and reverse logic lines of the stepping motor driver. The signals are made compatible using a hex buffer/driver with open collector outputs ( 74LSO7). The stepper motor requires 20 steps to drive the Cary monochromator 1 nm (step angle 1.8”, 200 steps per revolution). The rate at which the stepper motor can change the wavelength is dependent on the speed of the computer. For our system, a step of 100 nm requires approximately 9.7 s. The DACA binary output port is also used to initiate an experiment. The stoppedflow air piston is driven by an external exhaust solenoid that is triggered by a logic bit pulse and delayed by a solid state timer (555 timer IC with adjustable RC time constant). The timer output closes an optocoupler relay (3041) controlling the power line to the solenoid. The data acquisition cycle used in these experiments is depicted in Fig. 2. The segments of the graph represent time spent at a given wavelength (W). The Cary acquisition begins at the first wavelength (Wl) . Point 1 indicates the trigger pulse for the solenoid. A delay (850 ms, segment A) is implemented to allow for flow, then

d t t=o

TIME

FIG. 2. Timing pattern for data acquisition. center of the first data acquisition period, W’s lengths. See text for details.

Time t = 0 is the denote the two wave-

AND

PARKHURST

the first data collection is initiated (segment B) . During segment B, 20 data points are collected (0.32 s for the current computer) and the internal computer timer output is recorded after the tenth data point. The stepper motor is then driven to the second wavelength (segment C, 0.44 s for 4.5 nm). A l-s delay (segment D) precedes the second wavelength data collection (segment E, 0.2 s) to accommodate the experimentally determined time constant for the Cary. The stepper motor then returns to the first wavelength (segment F, 0.44 s) and a cycle time delay is requested (segment G, typically 4-8 s) . During the cycle time delay the 20 data points for each wavelength are averaged, recorded, and displayed on the monitor. The end of the cycle delay, segment G, begins the second cycle (point 4 ) , with a repeat of point 2 occurring 0.16 s later. Initial MB Data Transformations The Mb and Hb data are collected at times that typically differ by about 1.76 s. It is necessary for the Mb data to be interpolated to the Hb times, and this is accomplished by a simple five-point shifting Lagrange interpolation. We tested that this procedure did not introduce distortions in the following manner. From a deoxygenation run on HbO, alone at a single wavelength containing data pairs of absorbance vs time, the even-numbered pairs of points were removed and stored in a separate file. The remaining odd-numbered absorbance-time data were then interpolated to the evennumbered times. The residuals of the even-numbered absorbances minus the interpolated absorbances were random with a standard deviation of 0.0003 in absorbance. To test for wavelength reproducibility, we placed a Holmium oxide filter in place of the cuvette and set one wavelength to 449 nm, a steep shoulder on an absorption peak of the filter, and the other wavelength to 446 nm, an absorption maximum. We then cycled 25 times between the two wavelengths, collecting 25 points for each set and found no significant differences between the standard deviations in absorbances for each of the two sets versus the standard deviations at each without cycling. We thus concluded that insignificant error arose from wavelength jitter. Keq for Mb. The use of Mb as an oxygen sensor requires that we know the equilibrium constant for the binding of oxygen to Mb. K,, was determined from kinetic measurements in the following manner. MbO, (component I) was photolyzed using a Phase-R dye laser (XBH 2000, New Durham, NH) with P540 (Exciton, Dayton, OH) as the lasing dye. The absorbance change data for the recombination reaction were collected by the use of a fast 1%bit A/D converter (ISC-16, RC Electronics, Santa Barbara, CA) and analyzed by nonlinear least-squares to obtain the best fitting pseudo-first-order rate constant, K’( 0,). The oxygen ac-

HEMOGLOBIN

EQUILIBRIA

ANALYSIS

tivity was calculated from solubility tables ( 12)) knowing the temperature, the barometric pressure and humidity. Five to 10 reactions were followed at five temperatures from 6 to 27°C and the errors in the rate constants at room temperature were calculated from replicate runs rather than from the variance matrix, which underestimates the error owing to correlation of data points separated by less than two RC constants. The relative error (std dev) in k’ at 21°C was 0.2%. For the nonlinear least-squares analysis routinely employed (13) only one kinetic component could be determined. The dissociation constant for MbO, was determined in a stopped-flow apparatus by flowing MbO, vs 1% dithionite in various buffers, observing at 462 nm, the metdeoxy isosbestic wavelength. This rate constant was also measured as a function of temperature (five temperatures from 8 to 25’C). Ten measurements were made at room temperature. It was impossible to determine two exponentials in any of the runs and the standard deviation of the fit for one exponential was not significantly different from the spectrophotometric noise. Furthermore, the number of runs of residuals, approx 60 for 200 slightly correlated data points, (the PMT RC time constant was set at 1.5 ms) was remarkable. From previous studies (14) we would expect kinetic heterogeneity to appear, if present, in the dissociation rate constant. The mean value for k was 14.84 s-l (21°C) and the standard error of the mean was kO.09 S -l. The equilibrium constant for Mb, calculated at 21°C for the pH 7.4 0.1 M Tris-HCl, 0.1 M NaCl buffer, was 1.140 PM-’ with a standard deviation of 0.5%, calculated from the errors in the rate constants. The value of AH ’ was -14.4 kcal /mol with relative error of 4%, for a standard state for oxygen of 1 M in solution. The values for Keq (PM-~) and AH” (kcal/mol) at 21°C in 0.1 M potassium phosphate buffers at the indicated pHs were, respectively: pH 6, 1.075 f 0.010, -15.4 + 0.4; pH 7, 1.135 f 0.009, -14.0 f 0.4; pH 8, 1.271 + 0.006, -14.0 -+ 0.5. For 0.2 M borate, pH 9, the respective values were 1.297 -t 0.007 and -14.6 + 0.5. At 21°C Keg for Mb11 in the pH 7.4 buffer was 1.295 f 0.0146 PM-‘. Knowing the relative amounts of Mb1 and Mb11 in a crude oxy-Mb preparation (88 and 12%, respectively) and the two equilibrium constants, one can calculate the oxygen activity from the overall fractional saturation. Oxygen Activity In all Beer’s law expressions below, the path length is set to 1. The activity of oxygen at the beginning of the run was calculated from solubility tables (12) using Henry’s law, correcting for the barometric pressure and the pressure of the water vapor, determined, respectively, from a calibrated barometer and wet-bulb drybulb thermometer using tables ( 15) of the vapor pressure of water. The activity of oxygen, X,, at any time can

BY

235

SPECTROPHOTOMETRY

be determined (Ym) from

from

the fractional

YMb xt=

l&,(1

- Ym)]

saturation

Lb, - A,) ;

yMb=

A

of Mb

,

[l]

where A denotes absorbance of the myoglobin in solution, A, is the absorbance of completely deoxygenated Mb, and A is the difference in absorbance of completely oxygenated and deoxygenated Mb. Since the initial activity of oxygen and Km are known, the initial fractional saturation of Mb is known, and that saturation must correspond to the zero time value of the Mb absorbance. All deoxygenation runs were continued until the Mb absorbance was constant to within a standard deviation of 0.0003 in absorbance for at least 2 min. We sought to determine the residual oxygen concentration in two ways. In the first experiment, a solution of soybean Leg Hb ( Keq = 50 nM ( 16) ) was deoxygenated in the apparatus and the steady-state absorption spectrum taken after 45 min. Analysis of the spectrum in terms of oxy and deoxy as well as ferric forms over the wavelength range 600 to 535 nm showed that fractional saturation was less than lo%, implying that residual oxygen concentration was less than 5 nM. These results were limited in precision because of the presence of small amounts of met Hb in the Leg Hb preparations and the requirement for a three component analysis. Vanderkooi and colleagues (17) have recently reported on the phosphorescence of the dye TNS (2-p-toluidinylnaphthalene 6-sulfonate) in oxygen depleted solutions, using the glucose-glucose oxidase system. We repeated their phosphorescence decay measurements using a different apparatus. We excited the oxygen depleted TNS solution with the 325nm line from a He-Cd laser (Model 4110, Liconix, Sunnyvale, CA) and detected the emission that passed a Corning 540-nm longpass filter (Filter 3-67, Corning Glass Company, Corning, NY). The exciting beam was interrupted with a fast mechanical shutter and the phosphorescence decay monitored and stored on a digital oscilloscope (Nicolet Explorer III, Nicolet Instrument Corp., Madison, WI) interfaced to an IBM XT computer. Nonlinear least-squares analysis gave a phosphorescence decay time (7) of 18 ms, compared to a reported value of 11.2 ms, determined under the same conditions of pH and temperature (17). Since Vanderkooi’s group had reported residual oxygen concentrations in the region of 1 nM in other studies using other indicators (18) we appear to be reaching even somewhat lower levels. We therefore conclude that the residual oxygen is probably much less than 1 nM in our stopped-flow cuvet at the time when we terminate data collection. For a total absorbance change of about 0.3 in absorbance for Mb, further depletion of oxygen below 1 nM would fall within the noise of the instru-

236

LARSEN,

MUESER,

at this point be A,. Let X,, be oxygen activity, myoglobin absorbance, and fraction saturation of Mb under ambient condition at zero time. The oxygen activity at any time t corresponding to an absorbance A, is ment. Let the absorbance

A,, and YA, respectively,

x, = y

YA(A, - A,) Km[AA

= *

- A, - Y,(A,

-A,,)]

’

&b(XA) 1 +&&(X,)

[21

*

The following procedure was needed to obtain AA, owing to somewhat noisy data following the initial mixing. AA was determined using absorbances (A,) where the noise from initial mixing was absent, the decay constant for oxygen depletion (R) , I&,,, A,,, YA, and the kinetic order of oxygen depletion (n) from the equation A

= A t

where

+

(AA

-

0 yA

Ao)

Km&

1 + J&x,

[31

’

X, is X, = (X2-j

- (1 - n)Rt)“(‘-n),

n # 1.

[41

The unknowns (A, and R) in Eqs. [ 31 and [ 41 were determined from nonlinear least-squares fitting of the A, vs t data using the simplex algorithm ( 19). The order found in other experiments under our conditions for glucose oxidase was 0.37. For protocatechuate 3,4dioxygenase the order was essentially zero. In the fitting for A, and R, typically eight data pairs ( t, A,) were used, beginning with t = 15 s. It is clear that the ideal oxygen sensor would be one with a uniform error as a function of oxygen activity, but that is not possible with our optical detection. The uncertainty in oxygen activity, from simple propagation of error (neglecting correlation) is

6X -= X

[(%d2 + WJ21 L&i, - A,)’ + [(%aJ2 + Wo121 (Am - Ao12

1 1’2,

[,-l

where A, is the absorbance of Mb when fully saturated with oxygen. The major problem with using Mb to sense oxygen activity for the Hb studies is that it is insensitive at high activities of oxygen (second term in Eq. [ 51) where, for low affinity hemoglobins, there are significant changes in absorbance. Our procedure to deal with this problem was one of kinetics. We knew the activity of oxygen at time zero (ca. 270 pM) from solubility data. At some point, -90 pM in oxygen, the activity was cal-

AND

PARKHURST

culable because there was a significant change in absorbance from the zero time value. The problem was then one of determining the shape of the oxygen depletion curve from 90 to 270 pM. (Even drawing a straight line from initial oxygen to that at around 90 PM results in intermediate errors of only a few percent.) We verified, using an oxygen electrode (YSI 4004 Clark oxygen probe, Yellow Springs Instrument Co., Yellow Springs, OH), that the steady-state enzyme equation of Gibson et al. (20) was functionally appropriate for the glucose oxidase system. The reaction of protocatechuate 3,4dioxygenase with protocatechuate (P) and oxygen is an ordered bi-bi enzymatic reaction with a KM for (P) of 30 FM ( 10) and a KM for oxygen of about 43 pM (10) with a negligible product inhibition. Under these circumstances the steady state kinetics follow simple Michaelis-Menten kinetics ( 21) . The protocatechuate 3,4dioxygenase enzyme kinetics for 0, depletion from 270 to 90 pM were established by the following method. A 5 ml solution of 10 pM MbO, with 0.035 unit of enzyme was prepared. This solution was photolyzed using a Phase-R dye laser as described above. After collecting the initial data, a solution of protocatechuate was added to the solution to begin deoxygenation. The concentration of substrate present in the solution was the same as that used in deoxygenation runs (2700 PM). A stop watch was started upon substrate addition. A photolysis measurement was made approximately every minute until an 0, activity of 60 PM was reached. 0, activity was calculated by normalizing all rates to the initial rate and multiplying by the ambient oxygen activity. Oxygen activity vs time data were very well fit by linear regression, showing that the kinetics, within error, were zero order. For zero order enzyme kinetics, provided the second term in the numerator of Eq. [ 81 is negligible, one merely has to fit for one parameter (V,,,) to match the oxygen activity (e.g., 90 PM) at the known too, knowing the ambient 0, activity at to. The activity of oxygen at time zero was known. The Mb absorbance was followed until there was a significant change in absorbance at which time both the absorbance and the time derivative of absorbance could be obtained, typically when X = 90 pM. Let S = total oxygen concentration, and u the velocity of the enzymatic depletion of oxygen, then dS

-“=dt-vy,

dX

= - dt

dY.

4021

--+CH,-$ dt

(

1

dY.

(

1 + ox C H’&

1

3

[61 [71

where y, is the activity coefficient for 0, in buffer, “i” denotes myoglobin or hemoglobin, and Hi is the total

HEMOGLOBIN

EQUILIBRIA

ANALYSIS

heme concentration for species i at some X (here, 90 and the corresponding time (e.g., tsO) where the Mb data (at Xi) are sufficiently precise that both X, and -dXldt are determinable. Then

pM)

Substituting for u the Michaelis-Menten expression for protocatechuate 3,4dioxygenase, one obtains

A value for KM of 48 pM was determined with an 0, electrode under our conditions by monitoring 0, depletion in the absence of heme proteins. The summation term was approximated or expressed in terms of the Adair constants for both Mb and Hb, as discussed later. The integration was carried out by Simpson’s method with a step size, AX, of 0.5 pM. The oxygen activity data vector was usually smoothed by 17-point quadratic/ cubic digital filtering (22) prior to the integration. The parameter V, is varied until tgo from the right side of Eq. [ 91 agrees with the measured value. One then obtains from the integration of Eq. [ 91 noise-free oxygen activities from 270 to 90 pM. These data are then easily interpolated to the corresponding Hb absorbance times. If KM is not determined for a system, then the rate of 0, depletion at t = 90 pM (-dXldt) is used to solve for KM in terms of V, to reduce the number of parameters to one,

YXVMXSO KM = (-dXldt)(l

+ yx C Hi(dYi/dX))

- xgoy ‘lo1

where the term H( d YIdX) for Hb is obtained from Eq. [ 201. An initial estimate for VM is simply (X, - X9, ) / tgo. The integration of this expression for glucose oxidase is explained in Appendix 1. The hemoglobins studied to date have all reached apparent end points for deoxygenation before Mb. Thus, the large errors expected from Eq. [ 51 for the extremes of oxygenation of Mb were not encountered in practice. Should it be necessary, as for very high affinity hemoglobins, one could again use kinetic analysis of the oxygen depletion to fit the oxygen concentration vs time curve in the low oxygen concentration regime. The Mb data, after correcting for “cross-talk” as described below, were further smoothed by 25-point quadratic /cubic digital filtering. The digital filtering markedly reduced the errors in oxygen below 90 pM because it is a convolution procedure and is considerably aided by the “noise-free” data at earlier times. From simulations of our procedure

BY

SPECTROPHOTOMETRY

237

using Gaussian distributed random noise with a standard deviation in absorbance of 0.0003, we found that the random errors in oxygen concentration appeared to be grouped in three regions. These regions were: (I) 9020 pM; (II) 20-l pM; (III) tl PM. For a single run, the simulations gave average errors of 1.1,0.4, and 0.17% in oxygen for the three regions, respectively. Merely averaging three runs reduced the errors to 0.7, 0.2, and 0.08%, respectively. Further

Data Refinements

Excellent values of the apparent Hill number and of the apparent half-saturation oxygen activity can be obtained for many hemoglobins without considering the Mb data above 90 pM, and without any further refinement of the data, merely using Eq. [ 2 ] and calculating Y for Hb from the apparent fractional absorbance change. For many purposes, this may well be sufficient. To obtain the four Adair constants, however, one must correct or consider several other distortions of the data. First, one must determine that the tracking error of the spectrophotometer is negligible with respect to the u noise in absorbance. This was done by determining the transfer function for the Cary spectrophotometer by setting the Cary to the transmittance mode and suddenly opening a fast mechanical shutter and following the response via the DACA. The response change was found to be exponential with a relaxation time of 0.2 s at a period setting on the front panel of 0.5 s. With the delay settings employed (Fig. 1) and the maximum absorbance changes followed at the alternate wavelengths, we determined that the tracking error was well within the CTnoise in absorbance and confirmed the calculation by deconvoluting the measured absorbance data by iterative backward deconvolution. One must correct for two other distortions of the data. First, the isosbestic conditions do not hold exactly for Hb throughout the deoxygenation curve, though isosbesty is maintained for purified Mb in the absence of met formation. That means that there is “cross-talk” between the nominal Hb and Mb data in that small corrections in the Mb data, and hence, the oxygen concentrations, must be made because of very small changes in absorbance with time for Hb at the nominal Mb wavelength. Furthermore, for diode array detection, one in general will not be at an isosbestic wavelength. The matrix below is thus not quite diagonal during the entire course of deoxygenation. The cross-talk expression is

where 0 = A Abs(Hb),,/A Abs(Hb),2, and \k = A Abs (Mb) hB/A Abs (Mb) x,, and A Abs is the change in absorbance referenced to infinite time. The subscripts 1

238

LARSEN,

MUESER,

and 2 above denote wavelengths. In our studies these wavelengths were: Xi, 585.9 nm; X,, 590.6 nm. These wavelengths were determined by caljbrating the Cary with a mercury arc using the 5460.74 A line. The corrections are made as follows. Immediately before the actual run, Hb is run alone at the two wavelengths and ,9( t) = A Absxl ( t) /A Abs,, ( t) is calculated. (At some point, the numerator of f?(t) is zero, and remains so, within the spectrophotometric noise, and 0 is set to zero for those times.) We can convert 0(t) into 13(“Y “), where “Y” denotes approximate apparent saturation of Hb from “Y” = A Abs,, ( t) /A Abs,, ( t,,) , where the denominator approximates the overall absorbance change for infinite X. The quantity \k is determined for a run with Mb alone in the same way (‘I’ for pure MbO, in the absence of met Mb formation is 0 when X, is exactly the isosbestic wavelength). Next an initial “Y” for Hb and Mb is determined from the run involving Hb and Mb by using (A Abs,, ( t) /A AbsA1 (to) for Mb, and the corresponding expression at X, for Hb. In practice, Lagrange interpolation is used to obtain 13’~~(“Y”) for the Hb-Mb run from 0( “Y”) determined from the Hb run alone. Pi=’ (“Y “) for the Hb-Mb run is interpolated from *I( “Y “) from the Mb run alone. The matrix in Eq. [ 111 is then inverted to yield an iterative expression

A Absm(

A Abs,,(

t):’ t);;’

=

=

a

- @(t)A 1-

A Abstt),,

Abs(t),

s’(t)@(t)

- ‘Pi( 1 - *‘(t)@(t)

Abs(t),l

AND

PARKHURST

Parameter

Estimations

We assume that dimers can be neglected, so the partition function can be represented by a simple binding polynomial, D = 1 + &X

+ &X2

+ &X3

pi = fi Ki,

+ p4X4,

i==l

P41 where the K’s are Adair constants,4 and X corresponds to ligand activity. The usual assumption that fractional absorbance change corresponds to fractional saturation, yields

A = A + (Am - Ao)N 0 (40)

iI51

’

where A, is used to denote the absorbance at zero oxygen activity (infinite time), A, is absorbance at infinite oxygen activity, A is the absorbance at oxygen activity X, D is the binding polynomial, and N = XdD ldX. For a tetramer, this is a six-parameter model, though in our studies A, corresponded to the final absorbance for Hb. At the extremes of the isotherm, limiting forms can be obtained as

WI A = A, + (A,

(low

v31

where A Abs ( t) hl is the observed absorbance change at wavelength 1 during the actual run with both Mb and Hb present. The superscript i denotes the iteration index. From the left hand sides of Eqs. [12] and [13], new “Y ” values are calculated ( “Y” if1) from which new B and q estimates are made by Lagrange interpolation and the procedure continued to convergence. Experience shows that convergence within 10h4 in absorbance is achieved by the fifth iteration. (If \k( t) = 0, convergence is obtained at i = 2.) If this correction is not made, large residuals will be found in the region of half-saturation of Hb, far in excess of those expected from the spectrophotometric noise, and the value of K4 will sometimes exceed the value estimated from kinetics by a factor of 3-10. The other distortion arises from met Mb formation during the deoxygenation and results in \k( t ) being nonzero. Mb+ formation is entirely negligible using protocatechuate 3,4dioxygenase and DTT (l-8 mM). The Mb+ corrections required for the glucose oxidase system and for systems where DTT must be avoided are given in Appendix 2.

- A,)K,X oxygen concentration)

[ 16 ]

1

--=A,:Ao(‘+&) A - A, (high oxygen concentration).

P71

Data in these regions were fit in some instances to obtain estimates of Adair constants to compare with results from more elaborate models described below. Finally, for ligation to a tetramer representable by a binding polynomial, it can easily be shown (23) that for any model in which there are different absorbance changes for each stage of ligation (resulting from different absorbance changes for the a and p hemes, or R and T states) the full model has nine parameters, and can be written as A = A

+ 0

(A,

- Ao)N’

40

’

4 Various association constants have been termed “Adair” constants in the literature. Our Ki constants are the same as 4 of Edsall and Wyman (55) and our & is the same as their LT.

HEMOGLOBIN

EQUILIBRIA

ANALYSIS

where

WI

N’ = C iEipiXi

with E, = 1. The case for such an extended model is presented below. Data were fit by these models in which the simplex algorithm (19) was used to minimize the variance. For the nine-parameter model, a good estimate of A, is the average value of the Hb absorbance at X, over the last 5 to 15 min. An estimate for A, is the first absorbance reading at &. RESULTS

AND

DISCUSSION

This procedure employs a kinetic process to remove oxygen and the validity of the method requires that the various relaxation processes involving hemoglobin be much faster than those for oxygen removal. For human Hb under our experimental conditions, the relaxation constants are on the order of four orders of magnitude greater than the instantaneous first-order rate constant for the removal of oxygen. We verified that the removal rate was not too rapid by running the reaction three times faster. The Adair constants were within error of those obtained at the slower rate. The glucose oxidase reactions involved in the continuous removal of oxygen from solution are (a)

2 (@-D-glucose)

+ 20, + 2H,O 2 (D-gluconic

(b) (net)

2H,O,

+ acid) + 2H,O,

--, 2H,O + 0,

2 (P-D-glucose

) + 0, + 2 (D-gluconic

acid)

in which the first reaction is catalyzed by glucose oxidase and the second by catalase. We employed these reactions over ten years ago in preparing oxygen-free solutions to follow ligand kinetics in valency hybrids and reported a portion of that work (6). Winslow et al. (24) added oxygen to a hemoglobin solution by generating hydrogen peroxide, which was subsequently decomposed by catalase. It is essential that the activity of catalase be sufficient so that oxidation of the hemoglobin and myoglobin by peroxide be negligible. We found that catalase alone was not sufficient for solutions of myoglobin and for some unstable hemoglobins, but that solutions supplemented by at least 1 mM DTT were adequate. The reaction involved in the removal of oxygen from solution by the protocatechuate 3,4dioxygenase system is protocatechuate

+ 0, + P-carboxymuconic

acid

BY

SPECTROPHOTOMETRY

239

in which the reaction is catalyzed by protocatechuate 3,4dioxygenase. In the course of the development of this procedure, over 1000 curves, 200-500 data pairs each, were examined. Much of the development time involved working out procedures to eliminate initial met Mb and to minimize the generation of met Mb during the deoxygenation. Trace contaminants in the distilled water, in part leached from glass syringes, often led to met Mb formation. Those effects have been reported elsewhere (25) and were nearly eliminated by adding BSA to the solutions. The purification procedure for MbO, is given above. In earlier studies using solutions of Mb alone (from Sigma), we failed to obtain an isosbestic point throughout the reaction and concluded that the sample was contaminated with a modified horse Hb that could be removed on G-100 Sephadex, but not on a mercurial resin, suggesting that the -SH groups had been oxidized. CO association kinetics on this material showed altered Hb kinetics and a deoxy-HbCO isosbestic point corresponding to hemoglobin, not myoglobin. We then switched to horse Mb from Calbiochem which lacks this contaminant. It is essential that no initial met-Mb be present, since this species can compete with catalase for peroxides and give an additional spectroscopically distinct form (26). MbO, samples are removed from liquid nitrogen and allowed to thaw at room temperature. Freshly thawed MbO, is used for each run so met-Mh is initially present. In several runs using glucose oxidase we found that no detectable met-Mb formed during the entire reaction, but generally, the Mb+ formation is 1% during the deoxygenation of HbO, (at 3 pM 0,) in 0.1 M potassium phosphate and increases to about 3% 1 h after the initiation of the experiment. This is less oxidation than that usually found in hemoglobin during deoxygenation procedures that employ equilibration with a gas phase. Using 1-8 mM DTT and the protocatechuate system, no Mb+ was detectable. With no DTT present at 21°C in the protocatechuate system, ~1% Mb+ formed during deoxygenation by 1 pM O,, 20 min after mixing. This percentage depends on water purity and temperature. The Mb + corrections are given in Appendix 2. We were unable to detect met Hb formation. The attempts were carried out in the following manner. The conversion of HbO, to Hb using the glucose oxidase enzyme system with 2 mM DTT was allowed to proceed essentially to completion. The Hb solution was then passed over a G-25 column to remove glucose and allow reoxygenation. A spectral scan (scan 2) from 650 to 500 nm was taken of the reoxygenated solution to compare with that (scan 1) of the initial solution before deoxygenation. A few crystals of KCN were added to the solution and the solution scanned again (scan 3). Derivative spectra were compared to eliminate errors from small baseline shifts. The derivatives of the absorbance

240

LARSEN,

MUESER,

curves were obtained by using a Savitzky-Golay (22) cubic-quartic seven-point derivative filter. The residuals for the difference of derivative spectra, scans 2 and 3, were random, as were the residuals obtained by scaling the derivative spectra for scans 1 and 2. We found that met, Hb formation in the glucose oxidase system was no more than 0.5%, the limit of reliable detectability. In several experiments, the reactions were stopped after 5,10, 15, and 20 min by passing the reaction mixtures over a G-25 Sephadex column. The reoxygenated eluates were analyzed for met Hb as described above, but no met Hb was detectable. These experiments were carried out to rule out the possibility that met Hb was being significantly generated during the deoxygenation, but reduced by DTT by the end of the oxygen equilibrium runs. Such a cyclic process might contribute to the spectroscopic effects discussed below, but that possibility can now be discounted. Kilmartin et al. (27) reported that the Adair constants obtained for the normal mixture of human Hbs were essentially the same as for HbA,. In these preliminary studies, we did not attempt to fractionate the Hb, and thus in that sense regard the Adair constants reported here as preliminary. Furthermore, the concentration of Hb (100 PM) was such that dimers are virtually negligible, but future studies will be extended using a modified cell having a l-mm optical path length to allow measurements on Hb 1 mM in heme. According to Imai (28) the differences between apparent Adair constants K2, KS, and K4 for 100 PM in heme Hb (phosphate free) and those extrapolated for the tetramer are less than experimental error. For Kl , from the plot 4.13 of Imai (28)) the apparent value we report may be as much as 19% larger than the value for the tetramer. This difference is less than the error in Kl reported by others for the tetramer (29,30). We therefore neglect the effect of dimers for 100 PM Hb. The following flowchart summarizes the steps used in collecting and processing the data to obtain oxygen activities, X,, and absorbance changes for the hemoglobin deoxygenation. AbsX,(t)

Eqs.

(2

-+ El[ll]-[13]

+

2

X,( 1) (Y)

AND PARKHURST

should be close to that for Mb when both Mb and Hb are run together. Computer simulations of just myoglobin absorbance changes, using noise-free data above 60 PM, showed that the Savitzky-Golay polynomial filtering introduced small ripples in the oxygen vector X,( 3) in the region X = 6-20 PM. These were most evident in plots of - d( In [ 0,] ) ldt, which corresponds to a point-to-point first-order rate constant for the depletion of free oxygen. These small effects were eliminated by using exponential splines. Figure 3 shows the time course of oxygen activity X, (3) vs time, and Fig. 4 shows the actual data for the hemoglobin absorbance changes, scaled to give fractional saturation. The 250 data points are merely connected by straight line segments. Characters are not used to represent the data points since, were their sizes to represent standard deviations, they would not be visible on this scale. In practice, the integration in Eq. [9] (integration over 0, activity) was handled in the following manner. The summation term involved both Mb and Hb contributions. The Mb term was expressed analytically in terms of Km and X, and Mb heme. The Hb term was approximated by

%rb&4

x

A Abs(t

)

= O),, - A Abs(&& &-&Jo

* [201

The t’s were determined by spectroscopy and all other terms were determined from the data. Equation [ 9 ] was then integrated. The 0, vs Hb absorbance data were fit to obtain Adair constants. These Adair constants were then used in the analytical expression for the H(,,,d Y / dX in Eq. [ 91 to obtain new values for X. In practice, under our conditions, this refinement was not necessary. For 100 PM Hb, 60 I.IM MbO, in Tris-HCl buffer, pH 7.4, simulations show that the Adair constants were

X(Z) 4 (INT)

AbsX,(t)

Eq. [15]

or [18]

+ X,(3) (.%x6)

In this flowchart LI is Lagrange interpolation for matching the times, AA is the calculation of A, from Eqs. [ 31 and [ 41, INT is the integration of 0, from 270 to 90 PM (Eq. [9]), and SG17 and SG25 are, respectively, 17- and 25-point quadratic /cubic Savitzky-Golay (22) digital filters. If the Mb+ correction is needed, X,( 1) is determined from the equations in Appendix 2 after Eq. [3] is applied. Note that in this work the Hb absorbance data vector has not been digitally filtered. If the Mb+ correction is needed, then the time course for the run with Mb alone for the cross-talk correction

FIG. with

3. both

Log of the free oxygen activity vs myoglobin and hemoglobin present.

time for an experiment

HEMOGLOBIN

,_r

-0.4

0.4 1.2 LOG OXYGEN

EQUILIBRIA

ANALYSIS

2 @M)

FIG. 4. Apparent fractional saturation of hemoglobin free oxygen activity. The data set consists of 250 points, connected by straight lines. Concentrations of reactants the text. Experimental conditions: 0.1 M Tris-HCl, 0.1 mM total Cl-; pH 7.4; temperature, 21°C.

vs log of the shown here are given in M NaCl (200

changed by less than 0.03% when the summation term in Eq. [9] was eliminated. The activity coefficient for oxygen appears explicitly for X > 90 j&M. The importance of yx for parameter estimations depends on buffer and heme concentrations. The activity coefficient ( y ) in the buffer was calculated from the Setschenow equation (31) : log y = Kp, where k is the ratio of the solubility of oxygen in water to that of buffer and p is the ionic strength of the buffer. For 0.1 M Tris-HCl, 0.1 M NaCl at pH 7.4 the activity coefficient was calculated to be 1.11, assuming that y for 0, would be the same as for CO (32)) which was determined previously by one of us (33). From simulations with 100 ~.LM Hb and 60 PM Mb under our conditions we found the percentage change in the Adair constants to be less than 0.03% when y was changed from 1.11 to 1. Under our conditions, the 0, activity from 270 to 90 PM was very well fit by linear regression, showing zero-order kinetics. From simulations, the following percentage changes in the Adair constants were found when zero order kinetics (KM = 0) were used in Eq. [9] from 270 to 90 PM: K, 1.9%, K, 3.8%, KS 5.3%, K4 3.0%. In fitting data generated by this technique, there are several constraints that should obtain. First, if oxygen concentration is really below 1 IIM, then A, for Hb should be within the noise of the absorbances obtained at long times, giving an excellent estimate of one fitting parameter. Second, the data can be fit by referencing to ambient conditions, using X,, eliminating the need to obtain the absorbance corresponding to complete saturation. Third, K4 should be close to a value calculated from kinetic data. We estimate K4 from the kinetics in the following manner. In terms of a two state MWC model (34)) which need only be applicable for the last stepofligation,K,is(K,/4)[(1+Lc4)/(1+Lc3)].In general, this is not a simple ratio of measured rate constants, however, if Lc4 is ca. 0.0002, and if conformational relaxation at the tetraliganded state is rapid with

BY

241

SPECTROPHOTOMETRY

respect to ligand dissociation, the apparent k dissociation determined by replacing 0, with CO is given by: ( kR + &Lc4) /( 1 + Lc4), which, within experimental error, is just k, even if & is lo3 s-l. Let primed values represent association constants. At high oxygen concentration where the recombination process is much faster than the R + T transformation at triligation, &will be measured. If, as Imai suggests (35)) Lc3 is 0.05, K4 will be within about 5% of (k&/k,) 14, which is 0.7 PM-’ (36,37). The upper limit (95% confidence region) of the ratio of the observed k’ at low photolysis to the relaxation constant at zero [ (0,) /(CO) 1, divided by 4, is 0.75 - 0.85 PM (36,37), which must be an upper bound on K4, since any further contribution from “T,” corresponding to conformational equilibration, will only lower this value. Because K,, when calculated from Eq. [15] often exceeded 1 PM-‘, we were led to consider the possibility that at our monitoring wavelength (590.6 nm) the two hemes and /or two or more conformations might give different absorbance changes as ligation proceeded. This is not at all unreasonable. Gibson (38) long ago showed that the R and T states of deoxy-Hb had different molar absorptivities in the Soret, and Sugita (39) has assigned these differences to the alpha chain heme. Gibson et al. (40) first used the heme spectroscopic differences to follow ligation at the individual alpha and beta hemes. Adams and Schuster (41) reported a difference spectrum for HbO, and HbO, in the presence of IHP, the latter presumably partially in a T-state and remarked that apparent saturation should be wavelength dependent. The differences found in the present study would include such conformational differences along with those arising from alpha /beta heme spectroscopic and ligation differences. Figure 5 shows residuals

0.012, 0

I 1

0.2

-0.6

LOG

1.8

OXYGEN

‘@M)

FIG. 6. The difference in apparent fractional saturations calculated from absorbance changes at 556 and 540 nm vs log of the free oxygen activity. The experimental conditions were as for Fig. 4, except that Hb was run without Mb and the spectrophotometer was a HP 8452A diode array apparatus. The 200 raw data points are shown connected by straight line segments. Oxygen activities were obtained by solving Eq. [18] for X using data simultaneously collected at 590 nm and parameters from the nine-parameter fit of Table 1.

242

LARSEN,

MUESER,

for apparent fractional saturations ( “Y “) calculated at wavelengths 556 vs 540 nm from a Hewlett-Packard diode array spectrophotometer (Model 8452A, Hewlett-Packard Co., Palo Alto Ca.) for hemoglobin deoxygenation in the absence of myoglobin. “Y” was calculated for a given wavelength as (A, - A,,) /(A, - A,,). Were there no wavelength dependence to the fractional saturations, the residual pattern, A“Y “, would be just noise. We reported such wavelengths effects previously (42-44) and similar effects have also been reported recently by Ownby and Gill (45 ) . Nasuda-Kouyama et al. (46) have also reported spectroscopic differences such that fractional saturation is not exactly equal to the fractional change in absorbance. We have obtained essentially the same curves on the Cary spectrophotometer and on the diode array spectrophotometer; thus, the wavelength dependence of apparent fractional saturation cannot be due to slippage of the wavelength drive in the Cary. The spectrophotometric data reported here were not corrected for the slit width of the monochromator. Simulations of this effect were carried out in which the appropriate transformations between absorbances and transmittances were made and convolutions with the slit function were calculated. The slit-width effect is calculated to be no more than 2% of (Y - “Y “), when Y is calculated from Eq. [18], and to be of opposite sign at its maximum. With regard to Fig. 5, the slit-width effect is calculated to give a negative A“Y” for all values of X, the largest value being -3.4 X 10e4 at X = 10 PM. The equivalent slit width of the HP 8452A spectrophotometer was determined in the following manner. The transmittances at 586 nm of the diode array were read as a light beam from a THR 1500 1.5 monochromator (Instruments SA Jobin Yvon, Metuchen, NJ) stepped through a 2-nm wavelength range (586-584) with a step size of 0.1 nm and a bandwidth of 0.008 nm. From these absorbance measurements, the equivalent bandwidth was determined to be 1.5 nm. This compares with the l-nm equivalent bandwidth for the Cary. We conclude that bandwidth effects are negligible for either monochromator. Curves such as that shown in Fig. 5 provide the most telling argument for the use of Eq. [ 181 rather than Eq. [15], which lacks the E’s. As explained in detail elsewhere (23) the zeroes of the theoretical function with X as the independent variable are at x = 0, infinity, and at zero, one, or two intermediate values. Computer simulations based on the observed kinetics of Mb+ formation in the absence of DTT (assumed to be the same mechanism for Hb+ formation) and on the known difference spectra, showed that Hb+ formation cannot account for these A”Y” curves. If the fraction of met is directly proportional to the concentration of deoxy Hb, then Fig. 5, within the noise envelope, would be a flat line. If the final Hb+ were 1% of the total, a curve somewhat like Fig. 5 can be generated, which matches Fig. 5 at 8 PM in oxygen, but remains negative for all lower concentra-

AND

PARKHURST

tions of oxygen. Such best-fitting intermediate values for the concentration of Hb+ give a A“Y” curve for 600540 nm, however, that is the opposite in sign from what is observed. Although progressive met formation can clearly give rise to additional spectroscopic features and lead to altered values for Adair constants, such formation cannot account for our A““” curves. As emphasized above, however, we have no evidence for Hb+ formation during the deoxygenation process. Let Ei represent the molar absorptivity of the species HbXi. It is clear that Ei is merely an average of the molar absorptivities of the “j” microscopic species present (tij), each weighted according to its mole fraction (9ij):

[211 These microscopic species can represent different positional ligation isomers in the tetramer as well as different conformations for these isomers. Starting from the E’ quantities and using Beer’s law, it is straightforward to arrive at Eq. [IS] which adds three additional parameters to the fittting problem. In that equation, for example,E,=[E:-EA]/{(1/4)[Ei--EA]).Wefoundthat K4 obtained from Eq. [17] often agreed with the kinetic value, but that obtained by fitting the entire curve according to Eq. [ 15 ] did not. Table 1 gives the parameters and error estimates for 5 sets of data fitted by the two models. Estimates of the precision of Adair constants for a single run were obtained as follows. The value of the F statistic for the 68% confidence region was calculated from the appropriate complete and incomplete p functions (47). The variance contour expression (48) was used to find the extension of each parameter, which, when individually varied from its optimal value, increased the variance to the critical value corresponding TABLE Parameter K, Kz KS K,

(~0 (PM-') (PM-') (BM-')

E;

E9

-g x (/.M n*

CFit

1

Nine parameter 0.036 e 0.089 k 0.0618 + 0.64 k 1.76 + 1.45 + 1.15 + 10.40 + 3.03 + 0.00065

0.010 (0.025-0.052) 0.047 (0.027-0.155) 0.025 (0.036-0.105) 0.07 (0.55-0.72) 0.32 i1.32-2.14j 0.24 (1.2-1.94) 0.17 iO.S-1.3)' 0.21 (9.88-10.74) 0.09 (2.94-3.16)' (0.0005-0.00081)

Six parameter

0.086 0.032 0.063 6.61

f f f f

0.019 0.021 0.060 7.80

(0.058-0.125) (O.OOGO.072) (0.006-0.190) (0.7-22.2)

9.70 f 0.20 (9.26-9.89) 2.95 C 0.06 (2.85-3.04) 0.00074 (0.ooo55-0.00092)

Note. Parameter fits are for five data sets for 100 pM Hb in 0.1 M Tris-HCI, 0.1 M Cl-, pH 7.4, 21°C. Equations [18] and [15], respectively, were used for the nine- and six- parameter fits. The table lists the mean value for each parameter together with the standard error of the mean. The numbers in parentheses give the upper and lower values determined for the given parameter. For the six-parameter fitting, if one set that gave a value for Kd of 22.2 is excluded, the mean for K, is 2.97, the standard error of the mean is 3.30 and the range is 0.7-8.4.

HEMOGLOBIN

EQUILIBRIA

ANALYSIS

to the confidence limit. Such errors in the Adair constants were all about 1% and the errors in X and n* were respectively 0.02 pM and 0.002 for the nine-parameter fit. This procedure neglects correlations of the parameters. It is preferable to estimate parameter errors from replicate runs. In Table 1, the average parameters for five data sets are given f the standard error of the mean with the range of the parameters given in parentheses. Equation [18] was used for the nine-parameter model and Eq. [15] for the six-parameter model. In the variance minimizations, we assumed, as is customary, that the random errors in the Hb absorbances were more than those in the oxygen concentrations. Undoubtedly some of the variance derives from the errors in X and this can be estimated as follows. The error in the absorbance of Hb at some value of X from only errors in X can be estimated from simple error propagation theory as

IaAI= /(g)(s)($)W)I = 0.3X(Y)(l-

Y)

T I(

)I

1221

wheredAldYisjust(A, -A,) =0.3,dYldX= X(Y)(l - Y) /X, and X is the general Hill number (49) d In { Y / [ 1 - Y ] } ld In X, at the given values of Y and X. The fractional error 6X/X has been estimated above for three regions of the deoxygenation. We can estimate the contribution to 6A from error in X for those three regions, and estimate an overall error in A by combining the spectroscopic noise in A with that propagated through X (Eq. [ 22 ] ) using the usual summation principle (50). We find that the additional rms errors in A should be about 0.0003, 0.0005, and 0.00003, respectively, for regions I, II, and III referred to above. We have neglected this error in the work reported here by using a uniform weighting for fitting the data by Eqs. [15] and [18]. For five data sets, the average “a fit” (RMS variance in absorbance) for the nine-parameter model, 0.00065, is very nearly that expected from this small additional error, however, since the spectroscopic noise was 0.0004 in absorbance. Table 1 gives the Adair constants determined from the six- and nine-parameter fits. The parameter K,, for the six-parameter fit far exceeds (by a factor of nearly 10) the kinetic estimate, which should be an upper bound for this parameter. Within experimental error, KI for 0.1 M phosphate buffer, pH 7.4, is the same as that shown in Table 1 (nine parameter) and these numbers are in excellent agreement with KI (0.04 PM-‘) calculated from kinetic data (51) . The differences of KI and K4 for the six-parameter model from their respective kinetic estimates and the wavelength differences in Fig. 5 clearly shows the need to use Eq. [18] in the data fitting. It should be noted that when the E’s in Eq. [ 181 differ significantly from 1, values of apparent X may

BY

SPECTROPHOTOMETRY

243

differ considerably from the true values calculated from the Adair constants. For the particular five sets of data analyzed (Table 1) , the average apparent parameter values for X and n* were, respectively, 9.74 pM and 2.95, whereas the “true” values were 10.40 PM and 3.03. Our experimental conditions are similar to those of Chu et al. (29) and Gill et al. (30)) where the total Clwas 180 mM at 21.5”C. The total Cl- under our conditions was 200 mM at 21°C. Values of Xand n* for these studies were calculated from the reported Adair constants with conversion to units of micromolar for X. Corrections for differences in temperature and concentrations were made using appropriate data (52,53). The adjusted values of X and n* from Chu et al. at 21°C at 200 mM Cl- were 10.05 PM and 3.34, respectively. The error in X, (median oxygen activity) (29) was 0.2 PM, which was assumed to be the same error as the error in X. The adjusted values for X and n* for 2 mM Hb from Gill et al. (30) were 10.14 PM and 2.95, respectively with an error in X, of 0.1 PM. Within error, these values were in good agreement with our six-parameter values. Comparison of Adair constants is not useful since our data fitting equations are entirely different from those used in these studies. We did carry out some fittings using p’s rather than K’s, and found, as expected, the same values for K’s whether calculated directly or when derived from the p’s when E’s were used in the fitting equations. When only p’s were the fitting parameters, however, the minimization routine often converged on negative values for &, a problem noted by others (30,54). We have never obtained negative values for KS, however, and suggest that p3 is very sensitive to nonunitary spectroscopic parameters, E,, E,, and E, the effect of which will vary with the monitoring wavelength. Examination of the parameter ranges in Table 1 shows that the Adair parameters for the six-parameter fit are not well determined. Were the E’s not necessary, one should find instead large parameter errors for the nine-parameter fits. The large value for K4 for the sixparameter fit, resulting from neglect of spectrophotometric effects, may account for controversy regarding “quaternary enhancement” (36). APPENDIX

1

The integration procedure for determination of oxygen activity using the glucose oxidase system is given below. The enzyme velocity in the absence of HbO, and MbO, was simply - (dX/dt) ly,, which was obtained automatically from digital filtering (quadratic l7-point derivative filter ( 22 ) ) of the final deconvoluted oxygen electrode data. Our interest was in determining whether an even simpler form of the equation of Gibson et al. (20) involving only two parameters would fit - dXldt in the region from 270 PM oxygen (X,) down to 90 PM (X,,). The equation of Gibson et al. (20) can be

244

LARSEN,

MUESER,

rearranged to have but three parameters (Eq. [l] ) , but the cross term C(G) (X ) is usually very much smaller than the other two:

(G)(X) ’ = [A(G)

+ B(X)

+

C(G)(X)] (G)(X) = [A’(G) + B’(X)] ’ [‘I

where (G), the activity of glucose, is assumed to equal glucose concentration. We found that dX/dt could be fit very well with only two parameters (Eq. [l] ) , meaning that we could extract the parameters A’ and B’ from the spectrophotometric myoglobin data in the following manner. Substituting the velocity expression above at X,, into Eq. [ 71 from the text,

AND

PARKHURST

This reduces the number of parameters in Eq. [ 51 to one (A’). The integration is carried out by Simpson’s rule with a step size of 1 pM. One varies A’ until the calculated tw (right-hand side of Eq. [ 51) agrees with the measured tso. The integration generates a curve of 0, activity vs time that is used for interpolation to the corresponding Hb absorbance time points. The Mb term in the summation in the denominator can be expressed analytically, whereas the Hb term can be approximated by Eq. [ 201 of the text. An initial estimate for A’ can be obtained from Eq. [l] by using measured values of dX/dt at to and tsofrom Eq. [ 21, neglecting the terms in the summation and setting yx = 1:

A’ a

((G,IFz,) ((Go/X,)

where P = G,,/(-dxldt),,

(Go) L&o) -yx [A’(&,) + FL&,)1 =

g

- P) - m) ’ m = G,/X,

[71 and kI

= (-dXldt),=,. APPENDIX 1+r,CI&~,

In those caseswhen negligible Mb+ has formed by the completion of HbO, deoxygenation, it is feasible to drive the system to an end point by addition of a few microwhere G9,,, the concentration of glucose when oxygen liters of a concentrated dithionite solution. The followactivity is 96 PM, is ing discussion assumes that one follows the MbO, until only Mb and Mb+ are present. The Mb+ correction involves use of both spectroGso=Go-2[[xA;~xgo] , scopic and kinetic data. A scan of MbO, was taken from 650 to 500 nm. A crystal of sodium dithionite was then L31 added to the MbO, solution to obtain Mb and a second + &tyA yK,)M,, + &,tYA yK,)ff,, , J scan was taken. The exact isosbestic points for MbO, + where Gois the initial concentration of glucose. The Mb Mb were obtained from these scans. A third scan was term in Eq. [3] can be calculated exactly and the Hb taken of Mb+, generated from MbO, by addition of a coefficient can be approximated with negligible error as crystal of potassium ferricyanide, at the same concentration of protein as that for scans 1 and 2. A fourth scan of MbCN was taken after a few crystals of KCN were ( Abs, - Abs,, ) 141 added to the met Mb solution. The c values for MbO,, yA - ‘So = (Abs, - Abs,) ’ Mb, and Mb+ were calculated based on t5&cN = 11 mM-’ cm-‘. The MbO,-Mb isosbestic point for our experiwhere subscripts on Y correspond to oxygen activity, as ments was at 590.6 nm. Knowing this isosbestic, any above. Substituting for u in Eq. [8] from the text, the change in absorbance at 590.6 nm during the deoxygentwo parameter expression (Eq. [l] ) one obtains ation of MbO, (no HbO, present) could result only from Mb+ formation. From a deoxygenation run of MbO, without DTT the kinetics were unaltered by added BSA. Within the accuracy of our measurements, the ratio of (Mb+) /(Mb) was essentially constant. We thus When G at any X is calculated from an equation analo- assume that the small fraction of met formed for runs gous to Eq. [ 31, the rate of 0, depletion at Xso, ( -dXl with Mb alone is the same as when Hb is present, and dt),, is used to solve for B’ in Eq. [ 21 in terms of A’: that the percentage Mb+ is some function of the apparent saturation (“Y “) of the Mb. We assume, since the time for deoxygenation with and without Hb is nearly - YxGo the same, produced by adjusting total enzyme concenB’ = (dXldt),o[l + yx C Hi(dYildX)xx,] tration, that the same function relating (Mb+) and “Y” holds with and without Hb. The calculation of Mb+(t) -A+. [6] from data at 590.6 nm (X,) for Mb alone is so ( dt Hso

1

[21

2

HEMOGLOBIN

Mb+(t)

=

Abs(t

= 0) - Abs(t)

ANALYSIS

= A Abs’(t),, * 181 AC (Mt-hsb+)A~

t&,fb- E&.&#+

The change in absorbance erenced to infinite time, expression

EQUILIBRIA

BY

245

SPECTROPHOTOMETRY

where C=

~mJ[Mb+(t)l

- [Mb+(t = co)])

1

from production of Mb+, refcan be determined from the

tm(X,))

[15]

= 8.07 = 5.02 mM-’ cm-‘, Ed -’ cm-‘. Since [1Mb+( t = 0] is zero total heme (H) ErMb is calculated by dividing [ Mbd, ( t = 0) ] by YA, where YA is defined in Eq. [ 21 of the text. Deoxy-Mb is then

where AqmO,-~)A A Abs’(t

= ~0)~~ - A Abs’(t),, - Absm+(t

= Absm+(t)

= a)

= A Absm+(t),,

[9]

The absorbance change due to Mb+ at X, is determined by multiplying A Absfi+ ( t)hz by the ratio of a~(~-~+) at 585.9 to 590.6 nm,

[Mb(t)]

= H-

and oxygen activity A Abs,,+(t),,

- [Mb+(t)]

[16]

at any time can be obtained

WI

= A Absm+(t),,

[MbO,(t)]

from

[MbO,(t)l

v71

xt = [Mb(t)]&,. where the ratio in Eq. [lo] is 1.30. For a run with Hb present, the cross-talk is corrected as described in the text, and the ‘cY2VIb”i and q” from the last iteration are retained. Then A Absm+ ( t)x, is determined by multiplying 9” by A Absm( t) x1, and A Absm+ ( t)x, is determined as in Eq. [lo]. [Mb+(t)] at any time is determined from A Absm+ ( t)x, as shown:

[Mb+(t)]

=

A Absm+(t

= WA, - A Absm+(th, A

,111

where AE(~-~+)~~ = 3.75 InM-’ cm-‘. determined from Eq. [12] of the The A AbsMb(t)Al, text, written in terms of its constituent species is A Ah&h1

= Absm,,,(t)

- Abs,,(t

+ Abs,,(t)

= co) + [Absm+(t)

- Absm+(t

= co)],

WI where the term in brackets is A Absm+ ( t)x, and is determined as described above. Equation [ll] is then rearranged: A Abs,,WkI

- A Absm+&

= Absmo,(t)

+ Absm(t)

- Abs,,(t

= co)

[13]

To obtain [ MbO,] at the monitoring wavelength (i.e., 585.9 nm, “isosbestic” for Hb) in the presence of Hb, the following equation is used:

[Mb%(t)1 = A Absm(t),l

- A Absm+WA1 A,

-(MbO.+fb)X~

+ C,

,141

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