THE JOURNAL OF B~LOGICAL Crm>rwm~ Vol.245, No. 10,Issueof May 25, pp. 2584-2572, 1970

Printed in I;.S.A.

Kinetic Mechanism of Rabbit Muscle Glycogen

Phosphorylase a* (Received for publication, November 12, 1969)

ALLEN M. GoLI),~ ROBERT M. JOHNSON,~ AND JOHN Ti. TSENG

Prom the Department qf Rioch,emistry, College qf Physicians and Surgeons, Columbia University, New York, New York iOO.%?

SUMMARY

Isotope-exchange rates at chemical equilibrium were de- termined for the glycogen-a-D-glucopyranose l-phosphate- Pi system in the presence of phosphorylase a. Exchange of 32P from a-n-glucopyranose l-phosphate (glucose-l-P) into Pi and exchange of 14C from glucose-l-P into glycogen were followed simultaneously by the use of glucose-l-P containing both isotopes. Concentrations of glucose-l-P and Pi were varied together in their equilibrium ratio at constant glycogen concentration, and the concentration of glycogen was varied at fixed concentrations of phosphates. Exchange rates for the two isotopes were equal under all conditions (with the possible exception of measurements at the highest concentrations of the phosphates) and gave linear reciprocal plots. One exception was noted in which the reciprocal plot was concave upward at low concentrations of substrate, probably because of allosteric effects. The re- sults support a rapid equilibrium mechanism.

Initial velocity of the reaction in the absence of product was determined by the use of an isotopic assay. The results were characteristic of a sequential mechanism.

Isotope-exchange rates were also determined under non- equilibrium conditions. Exchange of s2P from glucose-l-P into Pi was followed as a function of glycogen concentration at a fixed concentration of glucose-l-P and several fixed concentrations of P is The exchange was also followed as a function of glucose-l-P concentration at fixed glycogen con- centration and several fixed Pi concentrations. Similar experiments were done while following the exchange from Pi into glucose-l-P. These experiments are equivalent to conventional product inhibition experiments. The results indicate that the two phosphates are noncompetitive in- hibitors with respect to glycogen, but are competitive with respect to one another.

Our conclusion is that phosphorylase (I has a rapid equilib- rium Random Bi-Bi mechanism involving binary complexes of enzyme with glycogen, glucose-l-P, and Pi, and ternary

* A preliminary account of this work has been published (1). 3 Recipient of a Grant-in-Aid from the American Heart Associa-

tion, Research Grant GM-10513 from the National Institute of General Medical Sciences, and Research Career Development Award NB-K3-5423 from the National Institute of Neurological Diseases and Blindness.

5 Recipient of Fellowship GM-34504 from the National Insti- tutes of Health, United States Public Health Service.

complexes of enzyme with glycogen and glucose-l-P and with glycogen and Pi.

Numerous kinetic studies have been performed on glycogen phosphorylase of rabbit muscle (ol-1,4-glucan :orthophosphate glucosyltransferase EC 2.4.1.1) ; nevertheless, the kinetic mech- ‘anism of this enzyme remains unknown. This is partially attributable to the fact that the catalyzed reaction is difficult, to subject to ordinary kinetic analysis. Since polysaccharide is both substrate and product, it is impossible to vary its concen- tration in an initial velocity experiment without changing the concentration of product simultaneously. Product inhibition studies are subject to a similar ambiguity when polysaccharide is considered the product inhibitor; when Pi or Lu-n-glucopyra- nose l-phosphate’ is the product inhibitor a back reaction occurs which obscures the inhibitory effect. Another source of difficulty lies in the allosteric properties of both phosphorglase b (2, 3) and a (4) which further complicate the kinetic analysis.

The most comprehensive studies of the steady-state kinetics of rabbit muscle phosphorylase were carried out by Lowry, Schulz, and Passonneau (5, 6) who limited their work to initial velocity experiments. Their results with phosphorylase a are consistent with a sequential mechanism in which both polysac- charide and phosphate must bind to the enzyme before any products are liberated. This agrees with the findings of Cohn and Cori (7) and Illingworth et al. (8) who observed that phos- phorylase a will not catalyze 32P exchange between Pi and glu- cose-l-1’ in the absence of polysaccharide. The kinetics of phosphorylase b are complicated by nonlinear reciprocal plots characteristic of allosteric enzymes and no conclusions could be drawn about its mechanism. Lowry et al. and many others have assumed, for purposes of calculation and discussion, that muscle phosphorylase has a rapid equilibrium Random Bi-Bi mecha- nism (9), although an ordered mechanism in which polysaccha- ride is the first substrate to bind and last product to dissociate is equally consistent with the evidence.

Maddaiah and Madsen (10) have reported a careful study of the kinetics of rabbit liver phospholylase by means of initial velocity and dead-end inhibition experiments, while Chno, Johnson, and Graves (11) have carried out a thorough investiga-

1 This is referred to as glncose-1-P in t,he text.

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tion of the kinetic mechanism of the maltodextrin phosphorylase of Escherichia coli by means of initial velocity, dead end inhibition, and equilibirum isotope-exchange experiments. Both groups found strong evidence for rapid equilibrium Random Bi-1% mechanisms for their respective phosphorylases, although the isotope-exchange data of Chao et al. (11) was not com- pletely consistent with a rapid equilibrium mechanism.

In the present work we have attempted to Jucidate the kinetic mechanism of rabbit muscle phosphorylase a by means of equi- librium and nonequilibrium isotope-exchange rate measurements. The evidence clearly indicates a rapid equilibrium Random Bi-1% mechanism for this enzyme. Following completion of our studies a publication by Engers, Bridger, and Madsen (12) appeared reporting the results of their kinetic experiments on phosphorylase b. Engers et al. came to the conclusion that phosphorylase b also has a rapid equilibrium Random 1%Bi mechanism on the basis of equilibrium isotope-exchange studies and comparison of kinetic constants with enzyme-substrate dissociation constants determined in independent experiments.

EXPERIMENTAL PROCEDURE

Illaterials-Phosphorylase b was prepared from frozen rabbit skeletal muscle (Pel-Freez Biologicals, Inc., type I) by a modifi- cation (13) of the method of Fischer and Krebs (14). Phosphoryl- ase a was prepared from three times recrystallized phosphorylase b by the method of Krebs and Fischer (15) using a crude prepara- tion of phosphorylase b kinase (15). The procedure was modified by substituting gel filtration on Bio-Gel P-10 for dialysis of the ammonium sulfate precipitate of phosphorylase a. The phos- phorylase a was recrystallized at least three times in the presence of 0.019 M glycerophosphate, 0.012 M dithiothreitol, and 0.1 M NaF.

A?\/Ll’, ATP, glucose-l-P dipotassium salt, and shellfish glyco- gen were obtained from Sigma Chemical Company. The glyco- gen was freed of possible ionic contaminants, such as AMP, by passing a 4y0 solution through a column of AG 501-X8 mixed-bed resin (Bio-Rad, Richmond, California) and precipitating the glycogen with an equal volume of ethanol.

321’-Labeled phosphoric acid (carrier-free) was purchased from New England Nuclear Corporation and uniformly labeled [14C]glucose-l-1’ (specific activity cu. 200 mCi per mmole) was obtained from Amersham-Searle. [32P]Glucose-l-P was pre- pared enzymatically from carrier-free 32P-pllosphoric acid and sucrose using sucrose phosphorylase (I 6). The reaction mixture was spotted directly on a strip of Whatman No. 1 paper and developed in the descending mode with a solvent containing methanol, water, and concentrated ammonia in a ratio of 6:3 :l. Glucose-l-P migrates faster than Pi and can be separated easily. Product obtained in this way usually contained no more than 0.2 to 0.3% free Pi after elution from the paper.

Glucostat reagent, for the enzymatic determination of free glucose, was obtained from the Worthington Biochemical Corpo- ration.

dIethods-Concentration of phosphorylase a was determined spectrophotometrically at 279 nm using A:?,, 13.0. Glycogen concentration in kinetic runs is expressed as total concentration of glucosyl residues and is based upon dry weight of glycogen. All experiments were carried out at 30” and pH 6.8.

Initial velocity in the direction of glycogen synthesis was determined by estimating the release of 32P-phosphate from isotopic glucose-l-P. All rate measurements were done in 1 .O-ml

volumes containing final concentrations of 0.025 M potassium maleate, 0.10 mM EDTA, 7.0 mM cysteine, 0.10 m&f ;\>\IP, 1 pg per ml of phosphorylase a, and glucose-l-P and glycogen as indicated. Each solution contained 5 X 10” cpm of [32P]glu- case-1-P and sufficient potassium chloride to bring the ionic strength to 0.28 M (calculated using pK, 6.1 for glucose-l-l’, 6.6 for maleate, and 7.2 for Pi). All components except glycogen were combined in a volume of 0.90 ml and equilibrated for 5 to 10 min before adding 0.100 ml of glycogen to start the reaction. After incubating for a time sufficient to allow up to 3% conversion of isotopic substrate, the reaction was stopped by adding 1 drop of concentrated ammonia and cooling in ice. When all samples were collected, 1 pmole of Pi carrier was added and the Pi was extracted by the method of Berenblum and Chain (17). One milliliter of acid molybdate (5% ammonium molybdate in 1 M H$O.J was added and the solution was extracted with 5.00 ml of water-saturated benzene-isobutanol, 1: 1. One milliliter of the organic phase was taken for liquid scintillation counting.

Blanks were determined by omitting enzyme and treating the solution in the same manner. Total 32P was det,ermined by adding 0.100 ml of the reaction mixture to I ml of 0.1 M HBS04, heating at 80” for 30 min to hydrolyze the glucose-l-l’, and extracting the Pi as described.

Nonequilibrium isotope-exchange rates in the direction of glycogen synthesis were determined similarly to initial velocities, with t,he difference that the reaction mixtures contained varying concentrations of potassium phosphate in addition to the other components. Since the concentration of Pi exceeded that which could be extracted as described above, it was necessary to remove 0.200-ml aliquots of the quenched solutions for treatment. with 1 ml of acid molybdate and 3.00 ml of benzene-isobutanol. Because of the small aliquots taken, 4 times the concentration of isotopic glucose-l-l’ was used to get adequate levels of 321).

Initial velocity in the direction of glycogen breakdown was determined by estimating the synthesis of [32P]glucose-l-P from 32P-l~hosl)hate. The procedure was similar to that used for the synthetic reaction, except that potassium phosphate was substi- tuted for glucose-l-P and 6 X lo6 cpm of 321’-phosphoric acid was substituted for the isotopic glucose-l-P. Because of the high phosphate concentrations, 0.200.ml aliquots were t.aken for treatment with 1.00 ml of acid molybdate. The solutions were extracted twice with 4 ml of benzene-isobutanol, taking care to remove as much organic solvent as possible each time, and 0.200 ml of the aqueous phase was taken for liquid scintillation count- ing.

Nonequilibrium isotope-exchange rates in the direction of glycogen breakdown were determined similarly to the initial velocities with the difference that the reaction mixtures contained varying concentrations of nonisotopic glucose-l-P in addition to the other components. In all cases above, suitable blanks were run and total 321’ was determined.

Equilibrium isotope-exchange rates were determined by meas- uring the initial rates of 14C and 32P exchange. All reactions were carried out at final concentrations of 0.020 M potassium maleate, 15 mM cysteine, 1 to 3 pg per ml of phosphorglase a, and AhIP, glucose-l-l’, Pi, and glycogen as indicated. I’i and glucose-l-l’ were always present in the equilibrium ratio of 3.56 : 1, respec- tively. Sufficient potassium chloride was present to keep the ionic strength constant in a particular experiment, but esperi- ments were carried out at different, ionic strengths. All compo- nents except isotopes were combined in 2.00 ml and incubated at

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2566 Kinetic Mechanism of Phosphorylase a Vol. 245, No. 10

30” for ca. 5 min before adding 0.050 ml of a mixture of 14C- and 32P-labeled glucose-l-P. Four aliquots were taken at appro- priate time intervals (the first immediately) and quenched by addition to 2.0 ml of 0.1 N ammonia. The radioactivity of 32P- phosphate was determined with 1.00 ml of the quenched aliquot as described above. Specific activity of glycogen was deter- mined with the remaining solution. Phosphates were removed by passing the solution through a small column (0.6 X 5 cm) of AG l-X8 chloride (200 to 400 mesh) resin (Bio-Rad, Richmond, California) and washing with 1 to 2 ml of water. A portion of the combined eluate was used for liquid scintillation counting while the remainder was used to determine the concentration of glycogen. High concentrations were determined by means of optical rotation at 323 nm. Low concentrations were deter- mined in triplicate by making the solution 0.1 N in HCl and hydrolyzing in an autoclave at 125” for 45 min. Samples were contained in screwcapped test tubes with Teflon cap liners. After neutralizing the solutions with NaOH, the concentration of free glucose was determined with Glucostat reagent. In both methods, a stock solution of glycogen was used as a standard. The hydrolytic method yielded 92 $Z.. of the theoretical amount of glucose based on dry weight of glycogen.

Total radioactivity of l4C and 32P in the doubly labeled glucose- 1-P was determined by first hydrolyzing an aliquot of the glu- cose-1-P in the presence of an accurately known amount of carrier and then subjecting it to the procedures described above. The AG 1 eluate was analyzed directly with Glucostat reagent.

Radioassay was done with a Nuclear-Chicago 720 liquid scintillation counter. 32P was counted in a phosphor solution consisting of 10 ml of 0.5% 2,5-diphenyloxazole (PPO) and 0.03701,4-bis[2-(5-phenyloxazolyl)]benzene (POPOP) in toluene, 5 ml of absolute ethanol, 0.5 ml of Hyamine hydroxide (1 M in methanol), and 1 ml of benzene-isobutanol sample or 0.200 ml of aqueous sample. In the equilibrium isotope-exchange experi- ments the Hyamine was usually omitted. Quenching corrections were applied when needed. W-Glycogen was counted as an emulsion of 1 ml of sample in 10 ml of a mixture of 2 parts 2,5- diphenyloxazole - 1,4 - bis[2 - (5 - phenyloxazolyl)]benzene - toluene (PPO-POPOP) and 1 part Triton X-100.

Exchange rates were calculated by estimating the fraction of the total isotope transferred to product. The fraction trans- ferred was multiplied by the concentration of glucose-l-P and divided by the time of incubation and the total amount of enzyme present. In the equilibrium isotope-exchange experiments the rate of 14C exchange was sometimes found to decline with in- creasing time of incubation and in these cases the rate was extrap- olated to short times.

For the analysis of our results we have adopted the nomencla- ture and system of kinetic constants proposed by Cleland (9). Kinetic constants were obtained from initial velocity data by use of a computer program described by Cleland (18) for the sequen- tial mechanism rate equation. This program computes standard errors for the kinetic constants. The same program was used for calculation of constants in nonequilibrium isotope-exchange experiments since the equations are of the same form as the initial velocity equations if the reciprocal of the product concen- tration is used in place of the concentration of fixed substrate. In all of the reciprocal plots, other than those from equilibrium isotope-exchange experiments, the lines were drawn using the constants obtained from the computer solution; this eliminates the necessity of showing secondary plots of slopes and intercepts,

which were nearly linear in all cases. Kinetic constants obtained from replots of slopes and intercepts always agreed with the computer-derived constants. In the reciprocal plots from equi- librium isotope-exchange experiments the lines are drawn from constants obtained using another computer program described by Cleland (18) to fit a hyperbolic equation. Data from both isotope exchanges are pooled for the solution.

RESULTS

The simplest types of kinetic mechanism that might apply to a polysaccharide phosphorylase have been considered by Chao et al. (11) in their studies on the maltodextrin phosphorylase of E. co&. Four mechanisms they enumerated are rapid equilibrium Random Bi-Bi; Ordered Bi-Bi, with polysaccharide the first substrate to bind and last product to dissociate; Ordered Bi-Bi, with polysaccharide the last substrate to bind and first product to dissociate; and Bi-Bi Ping Pong. The last two of these mechanisms may be eliminated as possibilities for phosphorylase a on the basis of work presently in the literature. Initial velocity experiments reported by Lowry et al. (5) exclude the last two mechanisms since both give rise to nonlinear reciprocal plots when polysaccharide is the variable substrate. Furthermore, the last mechanism gives linear reciprocal plots when phosphate is the varied substrate but increasing the concentration of polysac- charide increases the slope of the plot, opposite to what has been observed. Isotope-exchange experiments of Cohn and Cori (7) and Illingworth et al. (8) exclude a Ping Pong mechanism. A distinction between the first two mechanisms can be made on the basis of isotope-exchange rates in the presence of all reactants.

Initial Tieloci&-Measurements of reaction rates in this work were generally done at high ionic strength (0.28 M) so t,hat the ionic strength could be kept constant while the glucose-l-P and Pi were varied up to high concentrations. In this way substrate or product inhibition could be detected without interference from changing ionic strength. Since the most reliable values for the kinetic constants of phosphorylase a were determined at low ionic strength (5) we repeated some of these initial velocity experi- ments under our experimental conditions, both to arrive at more applicable values for the kinetic constants and to test our iso- topic assay method. Results for the glycogen synthesis reaction in the presence of AMP are shown in Figs. 1 and 2, while data for the degradative reaction are shown in Figs. 3 and 4.

These results are qualitatively similar to those reported by Lowry et al. (5) although the values of the kinetic constants differ greatly in some cases. The pattern of lines intersecting at a point to the left of the vertical axis is characteristic of a sequential reaction mechansim and is representd by the initial velocity equation

VlAB ’ = Ki.Ka + KbA + K,B + AB

Equation 1 refers to the synthetic reaction in which A is poly- saccharide and B is glucose-l-P. A similar equation holds for the degradative reaction in which P, representing Pi, replaces B. Kinetic constants derived from the data are presented in Table I.

Duplicate experiments carried out at different times afforded kinetic constants which differed from one another by as much as a factor of 2, even though the standard errors were much smaller within each experiment. The basis of this variability may lie in the chemistry of the enzyme. It is known that phosphorylases

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800

t

600 I- A

- I I I I I I I I

12 3 4 5 6 UGLYCOGEN (mM-l)

FIG. 1. Phosphorylase a activity as a function of glycogen concentration at fixed concentrations of glucose-l-P. AMP is 0.10 mM. Concentration of glucose-l-P: 10 miw, 0; 4.0 mM, 0; 2.5 mM, 0; 1.4 mM, H; 1.0 mM, A; 0.60 m&i, A.

I I I I I I

’ A’1

/

I I I I I I I I 0.25 0.50 0.75 1.00 1.25 1.50 17

l/GLUCOSE-l-P (mM-1) FIG. 2. Phosphorylase a activity as a function of glucose-l-P

concentration at fixed concentrations of glycogen. AMP is 0.10 mM. Glycogen concentration: 24.7 mM, 0 ; 0.617 mM, 0 ; 0.420 mM, q ; 0.308 mM, n ; 0.185 mM, A. The data is the same as in Fig. 1.

a2 and b (13) contain two extraordinarily reactive sulfhydryl groups in each identical subunit and that substitution of these sulfhydryl groups in phosphorylase b leads to large changes in the kinetic constants. Furthermore, it has been our experience that phosphorylase b rarely contains the full complement of reactive sulfhydryl groups and that the reactive sulfhydryl content declines with the age of the enzyme despite all precautions to

2 A. M. Gold, unpublished observations.

VGLYCOGEN (mMi) FIG. 3. Phosphorylase a activity as a function of glycogen

concentration at fixed concentrations of Pi. AMP is 0.10 mM. Concentration of Pi: 10 mM, 0; 5.0 mM, 0 ; 3.0 mM, 0; 2.0 mM, n ; 1.0 rnM, a.

I I I I I I

I

n

il.- /yg,

/ ,::;,y-o- 0,. o/o-

’ I I I I 0.2 0.4

l/Pi% M-l) 0.8 1.0

FIG. 4. Phosphorylase a activity as a function of Pi concentra- tion at fixed concentrations of glycogen. AMP is 0.10 mM. Gly- cogen concentration: 12.4 mM, 0; 1.24 miw, 0 ; 0.617 mM, 0 ; 0.432 mM, n ; 0.308 mM, A. The data is the same as in Fig. 3.

maintain them in a reduced state. If these considerations are valid with respect to phosphorylase a they could explain the variability in the kinetic constants. No other investigators have reported similar variability; it may be that our conditions (high ionic strength or the absence of a protective protein such as bovine serum albumin) promote expression of the variability in some way.

If the data in Table I are applied to the Haldane relationship in Equation 5, the equilibrium constant is calculated to be 1.8, compared with a value of 3.56 from direct measurement. This is fair agreement in view of the observed variability of the kinetic constants. The other Haldane relationship in Equation 6 gives equivalent agreement since it is not independent. A more serious discrepancy exists with respect to the values of Ki, determined in the synthetic and degradative reactions. The

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2568 Kinetic Mechanism of Phosphorylase a Vol. 24ci, No. 10

TABLE 1 1 I I I

Kinetic constants for phosphorylase a from initial velocit?/

experiments

The conditions are pH 6.8, 30”, ionic strength 0.28 M, 0.10 mM AMP. The limits shown are standard error. The constants are derived from data in Figs. 1 through 4.

Glycogen synthesis K, = 0.15 f 0.03 mM

Ki, = 0.56 f 0.07 rnM

Kb = 2.7 f 0.2 mM K<p = 10.1 f 2.5 mM

VI = 0.026 f 0.001 M mine1 mg-l

Glycogen degradation K’, = 1.7 f 0.4 mM KC, = 2.0 f 0.6 mM

K, = 4.0 f 0.8 mM Ki,b = 4.7 f 2.0 mM

VQ = 0.021 f 0.002 M mine1 mg-1

a Calculated from Equation 3. 6 Calculated from Equation 4.

I I I , 0.50 l.00 $0 2.00

VGLYCOGEN (mW )

FIG. 6. Equilibrium isotope-exchange rates as a function of glycogen concentration at a fixed concentration of glucose-l-P and Pi. AMP concentration is 1.0 mM, glucose-l-P is 0.099 mM, Pi is 0.352 mM, and ionic strength is 0.23 M. W exchange (glu- cose-1-P into glycogen), 0; a2P exchange (glucose-l-P into Pi), 0.

I I I I I 1

1 2 3 4 5 l/GLUCOSE-l-P 3.56/Pi 4 (mM 1

FIG. 5. Equilibrium isotope-exchange rates as a function of glucose-l-P and Pi concentration at a fixed concentration of gly- cogen. AMP concentration is 1.0 mrvf, glycogen is 41.6 mM, ionic strength is 0.17 M except at the highest concentration point, where it is 0.31 M. 1% exchange (glucose-l-P into glycogen), 0 ; a2P exchange (glucose-l-P into Pi), l Glucose-l-P concentrations at the follr highest points are 30.8 mM, 8.82 mM, 6.86 InM, and 4.63 mM.

kinetic mechanism deduced in t,his work requires that Ki, be the same regardless of the direction in which the reaction is fol- lowed; in fact, the constant differs significantly when determined in the two types of experiment. It is tempting to attribute this difference to the variability in the constants, but the difference is relatively large and the ranges of values observed in several experiments of each type do not overlap. No satisfactory explanation can be offered at t.he present time.

Equilibrium Isotope Exchange-Considerable information about the kinet,ic mechanism of a reaction can be obtained by determining the rates of isotope exchange among the reactants when the reaction is at chemical equilibrium. The theory has been developed in detail by Uoyer (19) and Boyer and Silver- stein (20). In the case of muscle phosphorylase there are only two eschange reactions that can be followed, exchange of 32P

I I I I

0.50 1.00 1.50 2.00 l/GLYCOGEN (mM-1)

FIG. 7. Equilibrium isotope-exchange rates as a function of glycogen concentration at a fixed concentration of glucose-l-P and Pi. AMP concentration is 1.0 mM, glucose-l-P is 0.279 mM, Pi is 0.99 mM, and ionic strength is 0.17 M. 1% exchange (glucose- 1-P into glycogen), 0 ; azP exchange (glucose-l-P into Pi), 0.

between glucose-l-l’ and Pi and exchange of 14C between glu- cose-l-1’ and glycogen. Exchange of Y’ would be expected to follow a normal first-order approach to equilibrium but the 14C exchange should not follow simple kinetics because of the struc- tural heterogeneity of the terminal chains of glycogen and because the redistribution of glucose residues that t.akes place under the influence of phosphorylase should “bury ” labeled residues in the polyglucose chains where they are less readily available for exchange. Both predictions were verified experimentally; the 14C exchange rate falls off faster than the Y? exchang;e rate which follows the expected first-order course. This problem was cir- cumvented by measuring the initial rates of both exchange reactions and by limiting the extent of l*C exchange to no more than 50/, of the calculated concentration of terminal glucose residues.

The result of an experiment in which glucose-l-P and l’i were varied together at constant glycogen and AMP concentration is shown in Fig. 5, while Figs. 6 and 7 illustrate the results obtained when the glycogen concentration was varied at two fixed concen- trations of glucose-l-P and Pi in the presence of AMP. Similar experiments performed in the absence of AMP are shown in Figs. 8 to 10.

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of May 25, 1970 A. d/l. Gold, R. IV. Johnson, and J. K. Tseng 2569

l/GLUCOSE-l-P 356/Pi (mMbl)

FIG. 8. Equilibrium isotope-exchange rates as a function of glucose-l-l’ and Pi concentration at a fixed concentration of glycogen. AMP absent, glycogen 7.4 mM, ionic strength 0.17 M. 14C exchange (glucose-l-P into glycogen), 0; 32P exchange (glu- cose-1-P into Pi), l . Tinsel, five highest concentrations glucose-l-P plotted on an expanded scale.

of

15oc

I I 1 I I I I I I 0.10 0.20 0.30 0.40 0.50 0.60 0.70

l/GLUCOSE-l-P 3.56/Pi (ITIM-‘)

FIG. 9. Equilibrium isotope-exchange rates as a function glucose-l-P and Pi concentration at a fixed concentration

of of M. glycogen. AMP absent, glycogen 114 mM, ionic strength 0.13 :

l*C exchange (glucose-l-P into glycogen), 0; 32P exchange (glu- cose-1-P into Pi), 0.

A striking feature of the data is the similarity of the rates for T and 14C exchange in all cases, with the possible exception of those measured at the highest concentration of phosphates (Fig. 5). Another important feature is the linearity of all the reciprocal plots at high sub&rate concentrations. The curve in Fig. 8 is nonlinear at low substrate concentration, probably because of allosteric effects. There is no evidence for inhibit,ion of either of the exchange reactions at high concentrations of variable substrates.

These results strongly support a rapid equilibrium mechanism in which the rate-limiting step is interconversion of central com- plexes. Since all exchanges must go through the same rate- limiting step they will have the same rate under all conditions. An ordered mechanism in which polysaccharide is first substrate to bind and last product to dissociate requires that at. high con- centrations of phosphates the 14C eschange be inhibited while the

z 6000

2 “i 4000

-I

;fi-

e ‘A’

- 2000 */:

A 0.50 1.00 1.50

VGLYCOGEN (mM-l)

FIG. 10. Equilibrium isotope-exchange rates as a function of glycogen concentration at a fixed concentration of glucose-l-P and Pi. AMP absent; glucose-l-P, 0.102 mM; Pi, 0.363 mM; ionic strength, 0.17 M. W exchange (glucose-l-P into glycogen), 0 ; 32P exchange (glucose-l-P into Pi), l .

A B

Kia Kb

EA

E

EB

Kib Ka

B A A P

FIG. 11. Rapid equilibrium Random Bi-Bi mechanism. a

T exchange continues to rise to a maximum. The alternative ordered mechanism requires inhibition of both 14C and T’ ex- change at high polysaccharide concentration. In either ordered mechanism the two exchange rates would not be equal except at low substrate concentrations.

If the kinetic mechanism is accepted to be rapid equilibrium, then the form of the initial velocity equations requires the esist- ence of binary complexes of enzyme with glucose-l-P, Pi and polysaccharide and ternary complexes of enzyme with glucose-l-P and polysaccharide and with Pi and polysaccharide. The simplest random mechanism that can describe the phosphorylase reaction is shown in Fig. 11. This mechanism leads to the rate equation

VIAB - VlAP/K,,

’ = KiaKb + KaA + K,B + AB + (KLP + AP)VI/VzK,, (2)

where the Michaelis constants are dissociation constants of the designated ligand from a ternary complex and the inhibition constants are dissociation constants of the binary complexes. K, and K’, are Michaelis constants for polysaccharide in the synthet.ic and degradative reactions respectively; only one Ki, is required. Several relations between the constants are appar- ent.

KiaKb = KibK, (3)

Ki,Kp = K,,K: (4)

(5)

(f-5)

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In the rate equation for a rapid equilibrium mechanism the Nonequilibrium Isotope Exchange-Isotope-exchange rates in first numerator term over the denominator expresses the total this system are direct estimates of the total reaction flux in one reaction flux in the forward direction, while the second numerator direction or the other. Consequently, we may circumvent the term over the denominator expresses the flux in the reverse problem arising from back reactions in product inhibition studies direction. The rate equation for isotope-exchange in the direc- when glucose-l-P or Pi are the inhibitors. The rate equation tion of glycogen synthesis under any concentration conditions describing the initial velocity of 32P exchange from glucose-l-P can, therefore, be derived by simply dropping the second numer- into Pi may be derived by dropping the second numerator term ator term in Equation 2 (20, 21). For experiments at chemical in Equation 2. This equation may then be rearranged to express equilibrium P can be eliminated from the equation by substitu- the reciprocal exchange rate as a function of reciprocal glycogen tion of BK,,; an identical rate equation can be derived by the concentration at a fixed concentration of glucose-l-P and various method of Boyer and Silverstein (20). Rearranging the result- fixed concentrations of Pi ing equation for analysis of data obtained at constant phos- phates and varying polysaccharide concentration gives

1 (9) -= (7) V

+ ~(l+%)(l+~,~(i ,PH:K~) while the corresponding equation for constant polysaccharide concentration and varying phosphates is or to express the reciprocal exchange rate as a function of recip-

rocal glucose-l-P concentration at a fixed concentration of glycogen and various fixed concentrations of Pi.

These equat.ions qualitatively describe the equilibrium isotope- exchange data presented in this work. Since the equations are (10) quite complex it is not very rewarding to test them quantitatively PC1 + X/A)

against the experimental results without having kinetic constants * ’ + Kp(l + J-W-4 > of high reliability; however, it is possible to compare the ex- change rate at saturating substrate concentrations, vex&, with Inorganic phosphate is seen to be a competitive inhibitor of the value predicted on the basis of V1 and vzTz, which have much glucose-l-P and a noncompetitive inhibitor of polysaccharide. greater reliability than the other kinetic constants. Fromm, A completely analogous pair of equations can be derived for Silverstein, and Boyer (22) have pointed out the relationship, inhibition of the degradative reaction by glucose-l-P. This v eX& = VIVz/(V, + V,), which holds for a rapid equilibrium differs from the usual case of a rapid equilibrium Random Bi-Bi Random Bi-Bi mechanism and this equation may be verified for mechanism in which all product inhibition is competitive, in the the present case by inspection of Equations 7 and 8. Using the absence of “dead end” complexes. The difference is due to the constants in Table I, Vexch = 0.0117 M min-r mg-l. The equi- fact that glycogen is both a substrate and a product, thus an AP librium isotope-exchange experiment in Fig. 5 is the only one term appears in the rate equation for isotope-exchange in the from which FeXch can be evaluated since it is the only one done direction of glycogen synthesis and gives rise to an intercept at a high concentration of fixed substrate in the presence of AMP. effect in the reciprocal plot when glycogen is the varied substrate. The intercept gives Vex& = 0.0112 M min-1 mg+, in excellent Figs. 12 to 14 present data for three of the four types of agreement with the theoretical value. product inhibition experiments described, all in the presence of

AMP. It is notable that in certain cases the net reaction flux

2500 r-----l I I 1 I

2000 I

_ 5001 A

/ 1 5 1500- E

l/GLYCOGEN (mM-l) l/GLUCOSE-l-P (mW1l

FIG. 12. Nonequilibrium isotope-exchange rates as a function FIG. 13. Nonequilibrium isotope-exchange rates as a function

of glycogen concentration at fixed concentrations of glucose-l-P of glucose-l-P concentration at fixed concentrations of glycogen and Pi. 32P exchange from glucose-l-P into Pi. AMP is 0.10 mM and Pi. z2P exchange from glucose-l-P into Pi. AMP is 0.10 mM

and glucose-l-P is 0.50 mM. Concentration of Pi: no Pi, 0 ; lOmM, and glycogen is 24.7 mM. Concentration of Pi: no Pi, 0 ; 10 mM, -̂

0 ; 20 ^̂

rnM, 0 ; 30 rnM, a. l ;zomM, q ;30mM,H.

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Issue of May 25, 1970 A. M. Gold, R. M. Johnson, and J. K. Tseng 2571

FIG. 14. Nonequilibrium isotope-exchange rates as a function of glycogen concentration at fixed concentrations of Pi and glucose-l-P. 32P exchange from Pi into glucose-l-P. AMP is 0.10 mM and Pi is 1.0 mM. Concentration of glucose-l-P; no glucose- l-P, 0;5mM, l ;lomM, 0.

is opposite to the flux in the direction measured, sometimes by a large margin. These measurements confirm the prediction that the phosphates are competitive inhibitors with respect to one another, while both are noncompetitive with respect to poly- saccharide.

Since the competitive nature of the inhibition by Pi with respect to glucose-l-P is critical for the conclusions that will be drawn, it is necessary to have an objective criterion by which to judge whether the intersection point in the reciprocal plot is indeed on the vertical axis. This was done by determining the intercepts and slopes of the individual lines by means of a com- puter program described by Cleland (18) for a hyperbolic func- tion. Table II shows the results of three similar experiments carried out at different concentrations of polysaccharide. It appears reasonable to conclude that the lines in each experiment have a common intercept on the vertical axis, within the pre- cision of the experiments.

DISCUSSION

The foregoing experiments are consistent with a rapid equi- librium Random Bi-Bi mechanism and a rate equation of the form of Equation 2 for rabbit muscle phosphorylase a. One discrepancy is apparent in Fig. 5 where the 14C exchange is slightly slower than the 32P exchange at high concentrations of phosphates. It is possible that the difference is due to a sys- tematic error at the high concentrations of phosphates used here. However, greater differences have been observed with other enzymes (11, 22) that appear to have rapid equilibrium random mechanisms. In these cases the effect is interpreted to indicate that interconversion of central complexes is not completely rate-limiting. Cleland (23) has stated that theoretical studies in his laboratory show that most random mechanisms will resemble rapid equilibrium mechanisms in initial velocity and product inhibition experiments; only isotope-exchange rates can accurately distinguish a true rapid equilibrium mechanism. None of our other data show significant differences in the ex- change rates but none of these were collected at such high glu- cose-1-P and Pi concentrations.

TABLE II

Intercepts and slopes for reciprocal plots from nonequilibrium isotop’e-exchange experiments

Glucose-l-P is the variable substrate, glycogen is present at a fixed concentration, and AMP is present at a concentration of 0.10 mM. Conditions are the same as in Table I. Limits shown are standard error.

Experiment

1. 24.6 mM glycogen

2. 12.3 mM glycogen

3. 0.60 mM glycogen

Pi

0 3 6

10

Intercept

‘u-1 min mg min mg

30.7 f 2.8 0.058 f 0.011 20.4 f 1.7 0.141 f 0.011 19.4 f 0.4 0.191 f 0.003 19.9 f 2.6 0.277 f 0.020

72.9 f 5.4 68.6 f 5.4 76.9 f 7.8

35.2 f 2.6 36.3 f 4.8 38.5 f 3.5

43.0 f 1.1

0.115 f 0.020 0.225 zt 0.032 0.247 f 0.037

0.048 f 0.020 0.110 f 0.041 0.139 & 0.032 0.275 f 0.008

Slope

The apparent competitive relation between glucose-l-P and Pi in the nonequilibrium isotope-exchange experiments is evi- dence for the lack of ABP and BP terms in the denominator of the rate equation. The presence of a BP term is excluded by Experiment 3 in Table II, in which the competition is studied at low glycogen concentration. The presence of an ABP term is excluded by all the experiments in Table II, since it would pro- duce a noncompetitive effect regardless of the glycogen concen- tration. Similarly, an RBP term would give rise to substrate inhibition in the equilibrium isotope-exchange experiments when phosphates are the varied substrates. A term containing BP would have the same effect only at low glycogen concemrations, which were not studied. Absence of an ABP term, which represents a quaternary complex of enzyme, glucose-l-P, Pi, and glycogen, and a BP term, which represents a ternary complex of enzyme, glucose-l-P, and Pi, is a reasonable basis for conclud- ing that there is only one kinetically significant site in each en- zyme subunit capable of binding glucose-l-P or Pi at the con- centrations used in these experiments.

No evidence was found for substrate inhibition in any of our experiments, in agreement with the results of Lowry et al. (5). This excludes terms involving A2, B2, or P2 and provides sug- gestive evidence that there is only one site for binding glucose-l-P or Pi. I f separate sites for the two ligands existed it is likely that substrate inhibition would result from P; binding to the glucose-l-P site and possibly glucose-l-P binding to the Pi site.

Alternate kinetic mechanisms for the phosphorylase reaction are rapid equilibrium Ordered Bi-Bi with dead end complexes. For example, the upper branches in Fig. 11 with dead end en- zyme-glucose-1-P and enzyme-Pi complexes would give a rate equation identical with Equation 2. Similarly, the lower branches in Fig. 11 with a dead end enzyme-glycogen complex would give the same rate equation. These mechanisms cannot be distinguished from a rapid equilibrium Random Bi-Bi mech- anism by steady-state methods, as long as the rapid equilibrium condition holds.

Our kinetic model includes only one enzyme-glycogen com- plex although it seems logical to assume that two such com-

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2572 Kinetic Mechanism of Phosphoylase a Vol. 245, No. 10

plexes can exist. A complex of enzyme and glycogen in which the latter is bound as a glucosyl acceptor (EA.) should function in the synthetic reaction, whereas a complex with glycogen bound as a glucosyl donor (&Id) should function in the degradative reaction. A rat.e equation based on two such complexes is identical with Equation 2. However, Ki, now becomes a func- tion of two intrinsic dissociation constants so that it represents the macroscopic dissociation constant of the total enzyme- glycogen complex. If R1 and K, represent the intrinsic dissocia- tion constants of the two enzyme-glycogen complexes, then Ki, = K1K2/(K1 + Kz). Michaelis constants for glucose-l-P and I’i also become macroscopic dissociation constants. These two models cannot be distinguished by steady-state kinetic methods, by equilibrium binding studies, or by combinations of the two. Dead end complexes, such as EAdB or EA,P, will also have no effect on the rate equation, other than further complicating the interpretation of the kinetic constants in terms of intrinsic dissociation constants. In view of these observations we have used the simplest model which describes the data, the case involving only one enzyme-glycogen complex. It, must be clearly understood that the kinetic constants are macroscopic dissociation constants and are not meant to represent intrinsic dissociation constants.3

Phosphorylase a has been shown to have allosteric properties but a low allosteric constant (4). Therefore, all of our experi- ments carried out in the presence of AMP would be expected t,o show 110 allosteric effects and relate only to the active form of the enzyme. In the absence of AMP and at low substrate concentrations we would expect to see sigmoid substrate satura- tion curves. The only case in which this is observed is the equilibrium isotope-exchange experiment shown in Fig. 8. The points in the reciprocal plot are linear at high concentration of phosphates but form a distinct upward concave curve at lower concentration. Our conclusions are not affected by the allo- steric properties since they are based upon results obtained under conditions where the enzyme is completely in the active form.

3 Engcrs et al. (12) have presented a rate equation for phos- phorylase b that is similar to Equation 1 but differs by having a factor of 2 in the term that represents the Michaelis constant for Pi (or glucose-l-P) and a factor of $ in the term representing the inhibition constant for glycogen. The factors arise from their having assumed the presence of two different enzyme-glycogen complexes with equal intrinsic dissociation constants and using intrinsic constants in the rate equation. If the kinetic constants had been defined according to Cleland (9) they would represent macroscopic dissociation constants. Engers et al. erroneously used their calculated intrinsic constant for comparison with the enzyme-glycogen dissociation constant determined by direct measurement of binding; the latter constant is a macroscopic dissociation constant and should have been compared to t the intrinsic constant (within the framework of their assumptions).

It is interesting to note that the most widely discussed models for allosteric enzymes, those of Xonod, Wyman, and Changeux (24) and Koshland, Nemethy, and Filmer (25), assume rapid equilibrium mechanisms and thereby avoid some of the compli- cations that can arise in multisubstrate reactions.

Acknowledgments-We wish to thank J. Voet and R. I-1. Abeles for their generous gifts of sucrose phosphorylase, and W. W. Cleland for kindly providin, q us with copies of his computer programs.

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Allen M. Gold, Robert M. Johnson and John K. TsengaKinetic Mechanism of Rabbit Muscle Glycogen Phosphorylase

1970, 245:2564-2572.J. Biol. Chem. 

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