THE JOURNAL OF Bro~oarca~ CHEMISTRY Vol. 239, No. 4, April 1964

Printed in U.S.A.

A Kinetic Study of the Phosphoglucomutase Pathway*

WILLIAM J. RAY, JR., AND GERTRUDE A. ROSCELLI

From the Department of Biological Sciences, Purdue University, Lafayette, Indiana

(Received for publication, August 26, 1963)

Phosphoglucomutase catalyzes the reversible transfer of a phosphate group between the l- and 6positions of glucose.’ According to Najjar and Pullman (l), the over-all reaction requires two steps,

and

EP + glucose-l-P + E + glucose-1,6-di-P (1)

E + glucose-1,6-di-P ti EP + glucose-6-P (2)

where EP and E are the phosphorylated and dephosphorylated forms of the enzyme, respectively. Indicative but not con- clusive evidence for this ping-pong type of pathway2 was pro- vided by the isolation of the reaction intermediates, dephoepho- enzyme and glucose 1,6-diphosphate (1). (Kaj jar and Pullman point out, however, that the phospho-enzyme of Step 1 is not necessarily identical with the phospho-enzyme of Step 2 with respect to phosphate attachment, and that in such a case a third step would be required for their interconversion.) On the other hand, Cleland (2) recently suggested a one-step se- quential pathway for phosphoglucomutase action based on Bodansky’s substrate-velocity measurements (3). In Cleland’s scheme,

E + glucose-l-P + glucose-l ,6-di-P =

E + glucose-l ,6-di-P+ glucose-6-P (3)

the dephospho-enzyme facilitates a direct transfer of phosphate between glucose 1 ,6-diphosphate and either glucose l-phosphate or glucose 6-phosphate, and is the most important catalytic form of the enzyme. Equations 1 and 2, involving the phospho- enzyme, would then represent slow side reactions rather than the main enzymic pathway.

The present work was undertaken to decide between Cleland’s sequential pathway and Najjar’s ping-pong pathway by re- examining substrate-velocity relationships. In addition, a study of substrate inhibition and of the role of glucose 1,6-diphosphate in the enzymic pathway was carried out to clear up numerous conflicting statements in the literature.

*This investigation was supported in part by Grant G.M- 08963-02 from the Division of General ,Medical Sciences, K’ational Institutes of Health, and in part by the National Science Founda- tion.

1 Unless expressedly stated, glucose-l-P and glucose-1,6-di-P will refer to the 01 isomers.

* Cleland (2) has designated pathways as “ping-pang” if “. . . one or more products are released before all substrates have added to the enzyme . . . ” since in such cases “. . . The enzyme will exist in two or more stable forms between which it oscillates during react)ion ”

EXPERIMENTAL PROCEDURE

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Phosphoglucomutase was isolated and chromatographed as described previously (4). The activity of the enzyme was 80 to 105 units per mg in the standard assay (below), based on Najjar’s definition of units (5). h molecular weight of 65,000 (6) and an absorbance of 7.7 for a 170 solution at 278 rnN (5) were used in all calculations involving enzyme concentration.

Glucose l-phosphate (California Corporation for Biochemical Research) was chromatographed, 1 mmole at a time, on a Dowea 1-formate column, 1.8 x 20 cm, 8yn cross-linked 200 to 400 mesh, by applying a linear, pH 3 pyridine-formic acid gradient, 0 to 0.75 M in formic acid in a total of 2 liters, with a flow rate of about 60 ml per hour. Two equivalents of potassium hydroxide per mole of acid-labile phosphate were added to the column ef- fluent, and the solution was taken to a viscous syrup under vacuum. After addition of water, the pH was adjusted to 8 with potassium hydroxide, and the product was crystallized according to McCready and Hassid (7). An aqueous solution of the product was adjusted to pH 7.4 before use. Unless otherwise indicated, all enzyme assays were run with purified glucose-l-P.

a-Glucose 1 ,6-diphosphate was prepared by the method of Posternak (8) by the silver-diphenyl phosphate route. How- ever, Posternak’s procedure of removing the inorganic phos- phate with magnesia, subsequent to the hydrogenolysis step, and resolving the (Y and p isomers of glucose-l ,6-di-I’ by frac- tional crystallization of their brucine salts, was not followed. Instead, the concentrated aqueous solution of products (from 1.5 g of cr-(2,3,4-triacetyl-6-diphenylphosphoryl)glucosyl bro- mide) was neutralized, diluted to 500 ml with water, and ab- sorbed on a column of Dowex 1-formate, 1.8 X 20 cm, 8% cross- linked 200 to 400 mesh. A linear pyridine-formic acid gradient, pH 3, 0.75 to 2.25 M in formic acid in a total of 4 liters, was applied at a flow rate of about 50 ml per hour. After addition of 4 equivalents of sodium hydroxide per mole of acid-labile phosphate in the column effluent, the product was isolated by solvent evaporation under vacuum. Several portions of water were successively added and evaporated to free the material from as much of the buffer as possible. The enzymically active peak was subsequently rechromatographcd twice in the same manner. After vacuum drying (over phosphorous pentoxide), aqueous solutions of the product were adjusted to pH 7.4 and stored at -15” until used.

Enzymic Assays

Standard dssay-A misture of 0.1 ml of enzyme (approxi- mately 0.02 unit of activity) and 0.2 ml of pH 7.4 buffer con-

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taining 0.08 M histidine-0.025 M Tris-chloride and 3 mM mag- nesium sulfate was used. After this mixture was incubated for 10 minutes at 30”, the reaction was initiated by addition of 0.2 ml of purified glucose-l-P (0.01 41) containing 0.1 mM glucose- 1,6-di-P. The assay was terminated with an equal volume of 2 N sulfuric acid after an additional interval of 10 minutes. Acid- labile phosphate was determined, and activity was calculated according to Najjar (5). Initial enzyme dilutions were made in a solution containing 8 mM histidine-2.5 mM Tris-chloride, pH 7.4, with 0.1 mg of serum albumin per ml, and were kept in ice. In some cases, just before use, a final dilution of at least 1: 100 was made in the above buffer, containing gelatin (30 pg per ml) instead of albumin. (The enzyme is more stable but somewhat less active in albumin; albumin interfered with the phosphate determination at low substrate concentrations; see below.) ,4n activity of 105 units per mg was obtained with our best enzyme preparations. All data obtained with less active enzyme were spot checked with our best enzyme preparations.

Modified Assay A (High Substrate Concentration)-The stand- ard assay was modified in the following manner. For activity measurements at 0.32 mM glucose-l-P, approximately 1.5 X 1O-3 unit of activity was used in an assay procedure similar to the standard assay. However, after the reaction was terminated with 0.5 ml of 2 N sulfuric acid, the resulting mixture was treated with 5.9 ml of N sulfuric acid, 0.25% in ammonium molybdate, and 0.3 ml of Fiske-SubbaRow reagent (9); color was developed concurrently with glucose-l-P hydrolysis by heating for 10 minutes at 100” (10).

For activity measurements at higher concentrations of glucose- l-P, both enzyme concentration and the fraction of the termi- nated assay mixture used for color development were varied in such a way that equal specific enzymic activities produced colors of equal intensity. For example, at lo-fold higher glucose-l-P concentration, a IO-fold more concentrated solution of enzyme was used and a O.l-ml aliquot of the (1 .O-ml) terminated reaction mixture was taken for color development. The assay interval was also varied from assay to assay in such a way that approxi- mately equal conversions of substrate to product (30 to 40%) were obtained, except where enzymic activity was quite de- pendent on glucose-l-P concentration. ,411 assays were run in duplicate or triplicate, and activity corrections were made for the various factors cited.

Modified Assay B (Low Substrate Concentrations)-Activity measurements in the range of 6.4 to 80 /AM glucose-l-P were carried out in new Pyrex test tubes washed in deionized water with a detergent of low phosphate content and rinsed exhaus- tively with doubly deionized water. The composition of the assay mixture was as above except for substrate and enzyme concentrations. The amount of substrate in each assay was 0.037 pmole (except for the assay at the lowest glucose-l-P concentration, in which 0.0235 Fmole was used). The amount of enzyme (about 1.7 x lop3 unit) was also the same in each assay; only the assay volumes were varied, i.e. from 0.5 to 4.0 ml. In each case the ‘assay was terminated with 0.4 ml of 11 N

sulfuric acid, 2% in ammonium molybdate, and diluted (if re- quired) to 4.40 ml with water. After addition of 0.20 ml of Fiske-SubbaRow reagent (9), the tubes were sealed with an oxygen torch (to prevent a change in volume during heating) and color was developed as above. After cooling to within hO.5” of room temperature, the contents of the tubes were mixed be- fore opening for color measurement. In this procedure also,

equal specific activities produced equal color density. The standard error for a single color determination with 0.040 pmole of glucose-l-P (optical density of 0.237) was ~0.27,. The assay interval was varied by trial and error so that 16.5 f l.OyO (s.d.) conversion to product was obtained in each assay. The difference in color before and after the enzymic reaction was therefore determined with a standard error of about &2% for a single assay. All assays were run in triplicate and the results were averaged.

Coupled &say-To facilitate the measurement of enzymic activity at high glucose-l ,6-di-P to glucose-l-P ratios, glucose- 6-P production was followed by means of a coupled enzymic re- action similar to that described previously (3, 11)) which utilized glucose B-phosphate dehydrogenase and TPN. A mixture of 0.7 ml of pH 7.4 histidine-Tris buffer (see “Standard Assay”), 0.1 ml of serum albumin (0.4 mg per ml), 1.0 ml of glucose-l ,6- di-P solution (0.11 to 3.3 m&r), and 0.1 ml of phosphoglucomutase (about 1.5 x low3 unit) was placed in a cuvette with a l-cm light path. After 7 minutes at 30” for temperature equilibra- tion and activation of the mutase, 0.1 ml of TPN (6.6 mg of the free acid per ml, adjusted to pH 7.4) and 0.1 ml of glucose 6-phos- phate dehydrogenase (0.2 mg per ml of a Boehringer and Sons preparation) were added. After 3 additional minutes, 0.1 ml of glucose-l-P was added and the change in absorbance was fol- lowed at 340 nm. After 20 to 30 seconds, the change was linear with time and was followed for 5 minutes. The change during this time ranged from 0.050 to 0.150 absorbance unit, depending on the concentration of glucose-l ,6-di-P used.

32P-Tracer Experiments

32P-Labeled phosphoglucomutase was prepared as described previously (12). To 0.2 ml of 0.03% gelatin containing 1.3 pg of labeled enzyme per ml was added 0.4 ml of histidine-Tris assay buffer, pH 7.4 (see “Standard Assay”). After 10 minutes at 30”, 0.4 ml of 10 mM glucose-l-P, 7.5 mM in glucose-l ,6-di-P, was rapidly added. After an interval of 15 to 45 seconds, the reaction was terminated with 0.2 ml of N sodium hydroxide. The glucose mono- and diphosphates were separated on a col- umn of Dowex 1 resin, 0.6 X 15 cm, by a procedure similar to that described above for the chromatography of glucose-l ,6-di-P. Specific radioactivity was determined for both phosphate-con- taining fractions. (Glucose-l-P and glucose-6-P were not sepa- rated by the column.) The amount of 32P-phosphate liberated after a lo-minute hydrolysis at 100” in N sulfuric acid was also determined for both fractions by the isobutyl alcohol-benzene extraction procedure (13).

RESULTS

Chromatography of Glucose-l ,6-di-P

Seven phosphate-containing peaks (besides inorganic phos- phate and glucose monophosphate) were obtained on chroma- tography of the products from the last step of the chemical synthesis of glucose-l ,6-di-P (Fig. 1). In runs involving smaller amounts of material, these peaks were sufficiently separated to verify a total phosphate to acid-labile phosphate ratio (PT:PlO) of 2.0 f 0.2 for each peak. However, only material in the first peak in the figure was active in the phosphoglucomutase assay. Rechromatography of both the first and second peaks gave prod- ucts for which the PT : PRO ratios were 2.00 i 0.04. Material from the first peak: the concentration producing half-maximal enzyme

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Phosphoglucomutase Pathway Vol. 239, x0. 4

I.5 20 25 3.0 EFFLUENT.1

4 FIG. 1. Chromatographic separation of products from glucose-

1,6-di-P synthesis on a Dowex I-formate column, 1.8 X 20 cm, with linear pyridine-formic acid gradient, pH 3, 0.75 to 2.25 M in 4 liters.

activity in Assay A was 0.5 pM (glucose-l-P, 6.0 m;ll) ; reported for a-glucose-l ,6-di-P at 6 mM glucose-l-P (under somewhat differ- ent assay conditions), 0.5 PM (8); [a]z5 +164 f 4” (0.5 g per 100 ml);3 reported for cY-glucose-l, 6-di-P, +83 f 4” (0.23 g per 100 ml) (8). Material from the second peak: [ali -18 & 2” (1.1 g per 100 ml); reported for &glucose-l ,6-di-P, -19 & 2” (0.37 g per 100 ml) (8). The material from this peak not only was inac- tive in the phosphoglucomutase assay but inhibited the enzyme when added to an assay mixture containing glucose-l-P and Lu-glucose-1,6-d&P. This inhibition was abolished by increasing the cr-glucose-l ,6-di-P in the assay.

Heating any of the remaining peaks (Fig. 1) at 100” in 0.1 N sodium hydroxide for 1 hour was later found to produce good yields of the a and fi isomers of glucose-l, 6-di-P in varying rela- tive amounts at the expense of the treated peak. Small amounts of inorganic phosphate and glucose monophosphate were also produced. A hydrolysis step such as this should presumably be carried out prior to the original chromatography for maximal yields; also a more gentle hydrolysis might well suffice. The nature of the material in these peaks was not further investigat.ed; however, the close to theoretical uptake of hydrogen during hydrogenolysis (90 to 97 %), the ret,ention vohmle on chromatog- raphy, and the hydrolysis to cy- and P-glucose-l ,6-di-P suggest that pyrophosphate esters were formed during the hydrogenolysis reaction.

Effect of Glucose-I-P Purification on Enzymic Activity

With 2.0 mM solutions of commercial glucose-l-P (California Corporation for Biochemical Research), but in the absence of added glucose-l ,6-di-P, phosphoglucomutase activity was 85 to 95% of the maximal activity that could be obtained with this concentration of commercial glucose-l-P and added glucose-l ,6- di-P (5). Chromatographic purification of t,he glucose-l-P re- duced the observed activity in the absence of added diphosphate by over 50-fold but did not completely eliminate it; maximal en-

3 Posternak (personal communication) has pointed out that an [o(]~ value of +164” for the a isomer is larger than that predicted by Hudson’s isorotation rules (14) and may be the result of an impurity with a high positive rotation in the chromatographed material, since no attempt was made to isolate an analytical sample.

zymic activity in the presence of added glucose-1,6-di-I’ was unaffected, however. Experiments relating to the small residual activity with purified substrate, which was ignored elsewhere, will be described in the section dealing with enzyme activity in t,he absence of added glucose-l ,6-di-P. Only purified glu- cose-1-P was used in the following experiments.

Substrate-Velocity Relationships

The effect of substrate concentration on enzyme activity was determined over a range of 6.4 X I Op6 to 1 .O X 10e2 M glucose-l -I’ and 5.0 X lo-* to 3.2 X lop3 M glucose-l ,6-di-P. Since sub- strate inhibition was observed for both substrates at concentra- tions above lo-3 M, substrate-velocity relationships in the lower concentration range, viz. in the range of the K,, values4 for both substrates, will be described first.

The left-hand side of Fig. 2 shows plots of 1 /VO versus 1 /[glucosr- 1 ,6-di-P] at four concentrations of glucose-l-P, where zlo repre- sents initial velocity; the righ,t-hand side of the figure shows the same data plotted as l/v0 versus l/[glucose-l-P] at four concen- trations of glucose-l ,6-di-1’. The glucose-l-P concentrations plotted are equal to (1 - [P]/Z[&]) [SO], where [SO] and [P] represent, respectively, initial substrate concentration and prod- uct formed during the a,csay. Since each assay was determined at [P]/[&] = 0.165 f 0.01 (s.d.), the plotted values are in each case equal to 0.92 [So]. Since the equilibrium constant for the forward rraction is about 17 (15), and since the K?n(Clurose-~.P): Km(glueose-6-P) ratio is apparently small,5 the measured A[P]/& values should be within a few per cent of the values of dP/dt at initial substrate concentrations equal to 0.92 [So], as estimated from the integrated rate equation (17).

Extrapolation of the plots on both sides of Fig. 2 to 1 /[glucose- 1,6-di-P] = 0 or l/[glucose-l-P] = 0 gives the reciprocals of the maximal velocities obtainable with each of the four concentra- tions of glucose-l-P or glucose-l ,6&P, resJ)ectivelg. Double reciprocal plots based on both of these sets of maximal velocities and the corresponding concentrations are shown, resJ)ectively, b> the solid squares and dashed lines on the oJ)posite sides of the figure. Values for Km(glueose-l-P), 8.5 X IO+ RI, and Km(ylucoso-1,6-di-P)t 6.2 x 10-a M, may thus be estimated. The data in all of these plots may be described by the following equa- tions for the apparent Michaelis constants.4

R~~$uoosp.l.P) = 8.5 X 1Om6 [glucose-l,6-di-P]/(6.2 + 10e8

+ [glucose-l,G-di-PI) (4)

K~~!$uoaae.1,6.di~~j = 6.2 X lo-* [glucose-1-P]/(8.5 X 1O-6

+ [glucose-l-P]) (5)

The over-all substrate velocity equation which holds in the region of dilute substrate concentration is therefore

vo = ~‘rn,x (6.2 X lOW/ [glucose-l ,6-di-P]

+ 8.5 X lOP/ [glucose-l-P] + 1)-l (6)

This equation, with a value of V,,, = 1.0 m/.mioles per minute

4 K5& is the measured Michaelis constant of substrate S under specific conditions, e.g. concentration of fixed substrate or inhibi- tor concentration; K,,(s, is the measured Michaelis constant of substrate S at saturating concentrations of the fixed substrate and in the absence of inhibition.

6 K7n (glucuee-1-P). .K,,, (glueose+~) is presumably less than 1, since the conversion of glucose-l-P to glucose-6-P at high substrate concentration is linear to about 65r0 completion (16).

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and with a minor correction for slight inhibition by the higher concentrations of glucose-l-P (see below), describes the data in Fig. 2 with a standard error only slightly larger than 1%.

Rate equations of the general form of Equation 6 and the related equations for the apparent Michaelis constants for both substrates, viz. Equations 4 and 5, are characteristic of two-sub- strate ping-pong pathways (2). Sis different reaction schemes representing all feasible pathways of this type for phosphogluco- mutase are presented as half-reactions in Equations 7 to 11, Scheme 1. The six over-all reactions are obtained by rombining Equations 7 or 8 with Equations 9 to 11. EP and EP’ represent enzymes iaomeric by virtue of phosphate attachment, ‘while E .glucose-1,6-di-P and E’.glucose-1,6-di-P represent different modes of dephoapho-enzyme to glucose-l ,6-di-P binding. The differences among these pathways will be considered under the section describing the phosphoglucomutase reaction pathway.

Fig. 3 shows plots of l/v,, versus l/[glucose-1,6-di-P] at four concentrations of glucose-l-P where [glucose-l-P] > 30 Km(plueose- I-pj. The variation of KZ~~lucos.+1,6-diW~~ with glucose-l-P in this concentration range indicates that inhibition by glucose-l-P is competitive with glucose-l ,6-di-P, and from the plot of Kapp m(gluoose-1,6-di-p) against [glucose-l-P] in Fig. 5 a value of Kiwurose-I-P) (the inhibition constant for glucose-l-P) approsi- mately equal to 1 mM is obtained. Since in the pathways in Scheme 1 glucose-l ,6-di-P is associated only with dephospho- enzyme, the inhibition noted here must be the result of a weak affinity of dephospho-enzyme for glucose-l-P, in addition to its normal affinity for glucose-l ,6-di-P. The intercept of the plot in Fig. 5 at [glucose-l-P] = 0 is the value for KkJt)lucose-1,6-di-p) at saturating concentrations of glucose-l-P, extrapolated to zero substrate inhibition. This value, 8 X lo-* M, is acceptably close to the value for the same constant (6.2 X 10V8 M) determined by extrapolation to glucose-l-P saturation of KkY$lucos,+1,6-di-p) ob- tained at low concentrations of glucose-l-P, where substrate inhibition was relatively unimportant.

Fig. 4 shows a similar plot of l/v0 versus l/[glucose-l-P] in which the concentration of glucose-l, 6-di-P is much greater than

FIG. 2. Lineweaver-Burk plots of phosphoglucomutase activity oer.sILs gIucose-1-P (G-1-P) and glucose-l,G-di-P (G-f ,6-P*) con- centration in the range of the respective Michaelis constants for both substrates; opposite sides of figure represent alternate plots of same data. The solid lines were calculated from Equation 6; extrapolated y-intercepts from right-hand plot shown on the left (m) and vice versa. The dashed lines show the extrapolation used to determine VmsX, Km (glucoae-1.+di-P), and Km(g~uoose-~-~). Assay B was used to measure the decrease in glucose-l-P at 30” produced by 1.9 mpg of enzyme, pH 7.4, in the presence of 34 mM histidine- 10 InM Tris-chloride, 1.2 mM MgSOa, and G Mg of gelatin per ml.

kl(glucose-1-P)

pr-- EP

II ks I

L5(glucose-G-P)

EP

k, (glucose-l -P)

k-1

ks k-6

kg EP’

k...5(glucose-G-P)

EP.glucose-1-P 1 k-2(glucose-l ,G-di-P)

(7)

(8)

EP.glucose-6-P < E (9)

kz

k-*(glucose-1 ,G-di-P)

k-r 11 kr E (10)

_c (11) ka(glucose-1,6-di-P)

SCHEME 1. Possible ping-pong pathways for phosphogluco- mutase action. For explanation of symbols, see the text.

Kn(glucose-I,&di-p) and exceeds the concentration of glucose-l-P by as much as 30-fold. The data, limited as they are, indicate that the variation in Kapp mCglucose-l-P) in this concentration range is the result of inhibition which is competitive with glucose-l-P.

Ki(gIucose-1,6-di-p) the inhibition constant for glucose-l, 6-di-P, may be roughly estimated as 0.7 rnnl by plotting K~~~~ueose-l~p~ against [glucose-l, 6-di-P] as in Fig. 5. Since in Scheme 1 glu- cose-1-P is associated only with the phospho form of the enzyme, inhibition by glucose-l ,6-di-P would represent a weak affinity of phospho-enzyme for glucose-l ,8di-P, in addition to its normal affinity for glucose-l-P. However, the inhibition observed here might actually be the result of impurities in the glucose-l, 6-di-P preparation (see Footnote 3), although inhibition was unaltered by rechromatography of the diphosphate.

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1232 Phosphoglucomutase Pathway Vol. 239, No. 4

O.Q4 -

0.03 -

0.01 0 I 2 3 4 5

FIG. 3. Lineweaver-Burk plots of phosphoglucomutase activity versus glucose-1,6-di-P at concentrations of glucose-l-P greater than 30 K, (g~uoose+~), showing competitive inhibition by glucose- 1-P. Assay A was used to measure decrease in glucose-l-P at 30” and pH 7.4 with 34 mM histidine-10 rnM Tris-chloride, 1.2 mM MgSO+ and 20 fig of albumin per ml.

G-I. 6-P,

3oL I 0 2 4

d3,[G-P-P] , M -?

IO 12

FIG. 4. Lineweaver-Burk plots of phosphoglucomutase activity versus glucose-l-P at concentrations of glucose-1,6-di-P greater

than 800 Km (glucose-l.&di-P), showing competitive inhibition by glucose-1,6-di-P. The coupled glucose-6-P dehydrogenase reac- tion was used to measure production of glucose-6-P at 30” and pH 7.4 with about 7 X 10V4 unit of phosphoglucomutase per ml, 26 mM histidine-8 mxx Tris-chloride, 1 mM MgSOd, 18 rg of albumin per ml, 0.4 mM TPN, and 9 fig of dehydrogenase per ml.

Enzymic Activity in Absence of Added Glucose-l ,6-di-P

It was briefly noted in the section describing the effect of glu- cose-1-P purification on enzyme activity that a residual enzymic activity was always observed in the absence of added glucose-l ,6- di-P, even with highly purified glucose-l-P. The following ex- periments relating to this activity were therefore carried out.

In assay mixtures 1 mM in purified glucose-l-P, specific enzymic activity in the absence of added glucose-l ,6-di-P increased

markedly with enzyme concentration above 10mg M ( l , Fig. 6). (In this figure, enzyme concentration was calculated on the basis of 75% purity since the activity of the enzyme used was 80 units

per mg as compared with 105 units per mg for our best enzyme.) That this increase in activity with enzyme concentration was not the result of glucose-l ,6-di-P added to the assay mixture as a contaminant of the enzyme was demonstrated by the following experiment. When the neutralized supernatant from the tri- chloroacetic acid precipitation of 1.5 x lo-lo mole of enzyme was added to a phosphoglucomutase assay mixture (glucose-l-P concentration, 1 mM), no detectable acceleration of the phospho- glucomutase reaction was observed. Similarly, no acceleration was detected when an equal aliquot from a neutralized solution of enzyme previously treated with 0.1 N sodium hydroxide for 15 minutes at room temperature was added. If the purified en- zyme preparation contained 1 mole of glucose-l ,6-di-P per mole of enzyme, releasable by treatment either with trichloroacetic acid or sodium hydroxide, the concentration of glucose-l ,6-di-P from 1.5 X lo-lo mole of enzyme (i.e. 3 X lo-’ M in the enzymic assay) would have been sufficient to produce approximately 60%

lO4[G-1,6-P,] ( M

0 4 8 12 16 20

0 1

2 4 6 8 IO"

103[G-I-P] , M

FIG. 5. KL?nPr;gIuoose-1.o-di-P) versus [glucose-l-P] (0) and K~p’&~ueo3B.~-~~ versus [glucose-1,6-di-P] (fJ), showing evaluation of Ki (E~ucose-~-~) and Ki (glucose-1,6-di-P). Data were taken from Figs. 3 and 4.

- LOG [ENZYME, M]

FIG. 6. Specific phosphoglucomutase activity in the absence of added glucose-1,6-di-P versus enzyme concentration at 1.0 mM glucose-l-P (a), showing division into concentration-dependent activity (m) and concentration-independent activity (- - -). The solid line, representing the theoretical concentration-depend- ent activity, was calculated from Equation 14. Assay A was used to measure the decrease in glucose-l-P under the conditions de- scribed in Fig. 3.

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April 1964 IV. J. Ray, Jr., and G. A. Roscelli 1233

of maximal activity in the phosphoglucomutasc assay as calcu- lated from the appropriate plot in Fig. 3, correction being made for the observed recovery of glucose-l, 6-di-P under identical conditions (85%). Hence the enzyme preparation could not contain more than 5 mole ryO glucose-l ,6-di-1’ that might be re- leased under the above conditions, an amount far from suficient to explain the dependence of specific enzymic activity on the enzyme concentration shown in Fig. 6.

A concentration-dependent enzymic activity in the absence of added glucose-l ,6-di-P is expected for phosphoglucomutase (see below), since phosphoglucomutase is able to generate glucose- 1,6-di-1’ via reaction with glucose-l-P (1) and since the concen- tration of glucose-l, 6-di-P generated depends on enzyme concen- tration. Such activity should approach zero as the concentration of enzyme in the assay approaches zero. However, a small and essentially constant specific activity was actually found in all cases at enzyme concentrations below 10hg Y, i.e. between 1.2 and 5 x lo-lo Y ( l , Fig. 6). This activity represented between 0.7 and 2r/;, of the maximal specific activity that could be obtained with added glucose-l, 6-di-P, depending on the enzyme prepnra- tion, and was unaltered when the glucose-l-P substrate was sub- jected to additional chromatography. Since the mono- and diphosphates of glucose were well separated by the chromato- graphic procedure, this residual activity cannot be explained as contamination of the substrate by glucose-l ,6-di-P. Neither can it be explained in terms of contamination of any other com- ponent of the assay mixture by glucose-l ,6-di-P as evidenced by the constancy of this activity as each assay component was separately varied by 4-fold. In the following discussion, the residual speciific enzyme activity at very low enzyme concentra- tion (less than 1O-g M) will be referred to as “concentration- independent” activity, (vo/E~)~, where E. denotes total enzyme “Concentration-dependent” specific activity, (oo/E~)~, will then refer to activity in excess of this small residual concentration- i&pen&nt specific activity. The difference between these activities is illustrated in Fig. 6 ((~o/Eo)~, ---; (vO/E~)~. n ), and they are discussed separately below.

Concentratim-dependent E,nzymic Activity-In the absence of added glucose-l, 6-di-P, each molecule of free glucose-l ,6-di-P generated by phosphoglucomutase (via Equation 1) decreases enzymic activity by increasing the fraction of enzyme in the free dephospho form. (Maximal activity in the presence of a large excess of added glucose-l ,6-di-P requires that the fraction of enzyme in the free dephospho form approach zero, contrary to the reasoning of PTajjar and McCoy (II).) For all pathways in Scheme 1, it can be shown that (z)o/E~)~, at saturating concentra- tions of glucose-l-P, is related via Equation 12 to the amount of free glucose-l ,6-di-1’ produced.

Cvo/Eo)o = (1/,,,/E0)(1 - [glucose-l,G-di-P]/[Eol) (12)

The concentration of free glucose-l ,6-di-P produced under these conditions may be related to the initial enzyme concentration by

[Glucose-l, N-PI = 3 Kkyilucose-1.6.di-P)

(dl + 4[E101K~~~luooss-l.B-di-P) - ‘) (13)

on the assumption that the enzyme is entirely in the phospho form. (Kk&,coso l,Gdi-P) isusedhereinsteadof Km(glucose-1,6-di-p) to correct for the dead end combination of dephospho-enzyme with glucose-l-P.) Combining Equations 12 and 13 gives (v~/E~)~ as a function of Eo.

bolEo)u = (v,F%,/&)

The solid line in Fig. 6 is a plot of Equation 14 with the measured values of (V,,, /Eo), 80 units per mg, and KZcElucose-1,Gdi-P), 1.24 x lop7 M. Except for the point at the highest enzyme con- centration (which was mcitsured under somewhat adverse condi- tions, viz. with an assay time of only 20 seconds), the plot of Equation 14 represents the conrcntration-dependent activity (m) quite well, and this activity can thus be adequately explained within the framework of the ping-gong pathway.

Concen,tration-independent ActizGty-k noted above? specific enzymic activity in the absence of added glucose-l ,6-di-P should approach zero as the concentration of enzyme in the assay ap- proaches zero. That this was not the case (minimal specific activity thus far obtained = 0.75, Tr,,,/Eo) was also pointed out. The following points relate to the residual concentration- independent activity measured at 2 X lo-lo .M enzyme concen- tration. (a) The value of (z’o/Eo)r was the same when assayed by disappearance of glucose-l-P or by appearance of glucose-6-P. (b) The value of (vo/Eo)r was constant with time, within experi- mental error, after 10cyO of a total reaction time of 6 hours had elapsed, i.e. after about 2’7; conversion of substrate. (c) When different values of (vo/l:‘,,)I were found with diffcrcnt enzyme preparations (accounting for 0.7 to 2.0~~ of the masimum attain- able activity), t.he effect was to raise or lower the entire plot ( 0) in Fig. 6.

Several esplanations for (vo/Eo), were esamined and discarded on the basis of the above results, including the possibility of a contaminating glucose transphosphorylase that could produce glucose-l ,6-di-P from glucose-l-P (18). The most likely explana- tion involves a contaminating mutate that can operate in the essential absence of glucose-l ,6&-I’; however, this is not a very satisfying explanation sinre no additional evidence is available for such an rnzyme.6 Fortunately, values of (u~/E~)~ were always small relative to L’,,, /I& and were ignored elsewhere.

*LP-Tracer Kcperiments

Table I shows the results of treating 32P-labeled phosphogluco- mutase with a large excess of a mixture of glucose-l-P and glu- COW1,6-di-P under assay conditions. The reaction time (15 seconds) was short enough that no appreciable amount of sub- strate turnover was realized (less than 1 T0 by actual assay), and the presence of a large excess of glucose-l, 6-di-P guaranteed that a,ny free V-glucose-l ,6&I’ produced (by reaction of the enzyme with the monophosphates) would have a negligible chance of reacting further (to give 32P-glucose-6-P). In all cases, about 95% of the 3?P label NW found in the monophosphate fraction and most of the label was in the 6-position of the glucose ring, i.e. as acid-stable phosphate, as predicted for initial label transfer to glucose-l-P. These results indicate that free glucose-l ,6-di-P is neither an obligatory nor an important reaction intermediate in the phosphoglucomutase pathway.

Phosphoglucomutase Reaction Pathway

The sis possible ping-pong pathways for phosphoglucomutase action consistent with the observed substrate-velocity relation-

6 The existence of two phosphoglycerate mutases which act via basically different pathways, one depending on, the other inde- pendent of, 2,3-diphosphoglycerate (19), lends credibility to this suggestion.

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Phosphoglucomutase Pathway Vol. 239, so. 4

TABLE I Reaction products of “2P-labeled phosphoglucomutase and

glucose l-phosphate, showing lack of label in glucose

1,6-diphosphate

Reaction conditions : to 0.26 rg of 3Wlabeled phosphoglucomu- tase in 32 rnnl histidine-10 mM Tris-chloride, pH 7.4, 1.2 mM in MgSO+ was added 4 mM glucose-l-P, 3 mnr in glucose-1,6-di-P. Reaction time: 15 seconds at 30”. The data given below were obtained after separation of the glucose mono- and diphosphates via column chromatography (see “Experimental Procedure”). Recovery of mono- and diphosphates and of the 3*P label ranged from 90 to 100%. The results of only single runs are shown; however, two additional runs under each condit.ion yielded comparable results.

Total =P Acid-labile a*P

Monophosphate Diphosphate Monophosphate

s?; + ;i ~ Ii j

Diphosphate

1 2*

3t

i

* Reaction time was 45 seconds. t A Vortex junior mixer was used to insure rapid mixing during

addition of the glucose phosphates.

ships (Scheme 1) may now be reduced by two, since the possibili- ties represented by Equations 7 + 11 and 8 + 11 require free glucose-1,6-di-P as a reaction intermediate. In addition, a re- striction is placed on pathways involving Equation 10, in which nonidentical dephospho-enzyme .glucose-1,6-di-P complexes (dif- fering in manner of glucose-l ,6-di-P binding) are produced ; such complexes must be interconvertible without dissociation of the diphosphate, i.e. via a relatively minor reorientation, which must occur at a rate at least 20 times faster tha.n dissociation of the diphosphate (see Table I). m7ith this restriction, Equation 10 becomes very nearly equivalent to Equation 9 (see “Discussion”).

Pathways involving Equations 7 and 8 may be distinguished by product inhibition patterns (2). Thus, at constant glucose- 1,6-di-P concentration, product inhibition by glucose-6-P in- volving combination with the phospho-enzyme would be com- petitive in normal pathways, e.g. Equation 7, but noncompetitive in “iso pathways,” e.g. Equation 8, which involves isomerization of stable enzyme forms (2). Although product inhibition has not been studied directly, three different observations provide tentative evidence with which to make distinction between the pathways in question: (a) the competitive nature of the glucose- 1,6-di-P inhibition, (5) the lack of noncompetitive inhibition at high levels of glucose-l-P, and (c) the linearity of product versus time plots at high glucose-l-P concentration. Thus glucose- 1,6-di-P inhibits competitively with glucose-l-P by combination with phospho-enzyme (Fig. 4). I f the iso pathway were opera- tive, noncompetitive inhibition by glucose-l ,6-di-P might be expected, i.e. combination with both EP and EP’. Moreover, dead end combination of glucose-l-P with EP’ (in addition to its normal combination with EP) might also be expected for the iso pathway at high levels of glucose-l-P, especially since glucose- 1,6-di-P combines with phospho-enzyme. This also would result in noncompetitive substrate inhibition. However, only inhibition competitive with glucose-l ,6-di-P was observed at concentrations of glucose-l-P up to 1O-2 Y. In addition, product versus time plots were linear within experimental error to at least

40% substrate conversion at 10-Z M glucose-l-P, indicating the lack of noncompetitive inhibition by the relatively high concen- trations of glucose-6-P thus generated. The iso pathway of Equation 8 may thus be tentatively ruled out, and the pathway represented by Equations 7 + 9 is therefore the simplest descrip tion of phosphoglucomutase action consistent with the present data.

DISCUSSION

Some of the inconsistencies in reported substrate-velocit) relationships for the phosphoglucomutase system may be attrib- uted to differences in the glucose-l ,6-di-P used in various studies, since it now appears that glucose-l ,6-di-P isolated from natural sources may contain impurities that inhibit the enzyme and that are difficult to eliminate. Thus samples of glucose-1,6-di-I’ isolated in this laboratory from both yeast (20) and whole blocd (21) inhibit phosphoglucomutase at concentrations of about, 10h5 M in the standard assay, i.e. at 4.0 mM glucose-l-P, despite their close to theoretical ratios of acid-labile to acid-stable pho+ phate. Inhibition by low concentrations of glucose-l ,6-di-1’ also obtained from natural sources has been reported by Bartlett, (21) and by Najjar and McCoy (11). That this inhibition doe:: not represent substrate inhibition but results from impurities in the diphosphate preparation is shown by the data of Bodansky (3) and by the present data. Both sets of data indicate that rhemi- tally prepared glucose-l ,6-di-P does not measurably inhibit in the standard assay at concentrations up to 10-3 M. (However, weak inhibition, competitive with glucose-l-P, was observed at higher concentrations of glucose-l ,6-di-P and lower concentra- tions of glucose-l-P; see Fig. 4.) These observations, coupled with the ease of effecting isomer separation of chemically prepared glucose-l ,6-di-P by the chromatographic technique described herein, should substantially increase the attractiveness of the chemical route to the diphosphate (8).

Although an impurity in the cliphosphate preparation used 1)~ Najjar and McCoy (11) is probably the source of the inconsist ency between their results and those reported here, another es- planation must be sought for the disparity between the present results and those of Bodansky (3). The uncompetitive inhibi- tion that Bodansky observed at high glucose-l-l’ concentration (present results indicate an inhibition strictly competitive with glucose-l ,6-di-P; see Fig. 3) can be explained by the presence of an inhibitor in the glucose-l-P preparation used by him. How- ever, a simple explanation for the disparity at low substrate con- centration is not apparent. Thus, at concentrations of glu- cose-1-P and glucose-l ,6-di-P in the range of their respective Michaelis constants, Bodansky reported that K%&ose-l n) and KkTiiurose-i,&di-P) were independent of glucose-l ,6-di-P and glucose-l-P concentration, respectively. Our results in this con- centration range (Fig. 2) indicate the opposite, viz. that K~$!&,se+P) and KZTiiuoosc-r,+di-n) are quite dependent on glucose-l ,6-di-P and glucose-l-P concentration, respectively, the precise relationships being described by Equations 4 and 5. Since the results of initial experiments differed from those of Bodansky, extensive precautions were taken to insure the accu- racy of the present data (see “Experimental Procedure”), and we would like to point out (a) that our assay system was somewhat more sensitive than Bodansky’s (about a g-fold larger change in measured optical density per mole of substrate converted), (b) that our enzyme preparation was apparently about 3-fold more active (although not necessarily a-fold purer (15)), and (c), per-

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April 1961 W. J. Ray, JY., and G. A. Roscelli 1233

haps more significantly, that our assay did not depend on a coupled enzyme system as did Bodansky’s. In addition, we offer in support of our data the fact that the standard deviation of the points in Fig. 2 from the set of parallel lines generated by Equation 6 of the relevant concentrations of fised substrate is only slightly greater than 1%. (Bodansky’s results would re- quire the lines in Fig. 2 to intersect on the abscissa.)

Cleland (2), noting that Bodansky’s data were not consistent with the ping-pong type of pathway originally suggested by Najjar and Pullman (l), recently proposed, as a substitute, a sequential pathway consistent with Bodansky’s results. With the present data, however, we have no alternative but to disre- gard Cleland’s otherwise very timely suggestion and to assign a ping-pong-like pathway to the phosphoglucomutase reaction.

In view of the present results, it seems inappropriate to refer to glucose-l, 6-di-P as either a substrate or a coenzyme for the phosphoglucomutase reaction (5); since its role in the enzymic pathway possesses unique features as demonstrated by experi- ments with 32P-labeled enzyme. These experiments (Table I) indicate that free gluco.se-1,6-di-P is not a necessary reaction intermediate and is not frequently formed during conversion of glucose-l-P to glucose-6-P (on the average of perhaps once in 20 turnovers). Hence added glucose-l ,6-di-P serves only to insure that the effect of the infrequent production of glucose-1,6-di-P is noncumulative, i.e. that the (phospho-) enzyme does not become even temporarily depleted in phosphate via production of free glucose-l ,6-di-P. The same conclusion has been reached independently by Horton and Koshland on the basis of more extensive rxperiments with labeled substrates and enzyme.7 This unusual role of glucose-l ,6-di-I’ in the enzymic process is further illustrated by experiments in which substantial enzymic activity (23(% of maximum) was induced in the absence of added glucose-l ,6-di-P by carrying out the cnzymic assay at relatively high concentrations of enzyme (6.7 X 1 O-8 nl). Under these con- ditions, part of the enzyme was used to generate a sufficientl? high concentration of free glucose-l ,6-di-P to insure that the remainder of the enzyme did not become depleted in phosphate through further production of free diphosphate (see below). In view of these considerations, glucose-l ,6-d-P might well be re- ferred to as an abortive product rather than a substrate or a coenzyme.

Scheme 1 includes all feasible ping-pang-type pathways for phosphoglucomutase action that are consistent with the present substrate-velocity data. Since substrate-velocity data cannot. provide values for rate constants in ping-pong pathways (2), some steps showing interconversion of central complexes were omitted and no attempt was made to differentiate between path- ways differing only in the composition of the central complex or complexes. Thus it is conceivable that the actual phosphogluco- mutaee pathway involves conversion of EP.glucose-1-P to EP.glucosc-6-P in a single step. In such a pathway, both the E . glucose-l, 6-di-P complex (or complexes) and the free dephos- pho-enzyme would represent abortive products. However, the synchronous, one-step transfer of two phosphates required by such a pathway seems unlikely on chemical grounds, since it would involve a g-membered cyclic transition state, and displace- ment reactions involving cyclic transition states leading to g-membered rings (via a single displacement) are notoriously slow (22). It is therefore assumed that all pathways in Scheme

7 H. R. Horton and D. E. Koshland. Jr., personal connnunica- tion.

1 involve one or more E ‘glucose-1,6-di-1’ complexes as obligator! intermediates.

32P-tracer experiments were used to eliminate two reaction pathways (Equations 7 + 11 and 8 + 11). Of the remaining possibilities, Equation 7 rather than Equation 8 probably reprc- sents one portion of the enzymic pathway because of substrate inhibition patterns, although a final decision on this point must await product inhibition studies. An experimental distinction between the two possibilities for the complementary portion of the pathway (Equations 9 and 10) may br very difficult, although the following descriptive distinction can readily be made: Equa- tion 9 represents a branched pathway in which one branch (pro- duction of free dephospho-enzyme) is a dead end; Equation 10 represents a branched pathway in which both branches are opern- tive although the branch involving free dephospho-enzyme is onI>, used infrequently. Demonstration of different binding sites for glucose-l-P and glucose-6-l’ would substantiate the latter possi- hility, although failure to find different binding sites would not necessarily rule out this pathway, since different but partially overlapping sites might bc involved.

SUMMARY

Substrate-velocity relationships for the phosphoglucomutasr system were investigated over wide concentration rangra of both glucose l-phosphate (6.4 X 10-G to 1 X 1OW 1~) and glucose I ,6-diphosphate (5.0 X 1O-8 to 3.2 X IO-3 nr). At low substrate concentrations, the apparent Michaelis constants for glucose l-phosphate and glucose 1 ,6-diphosphate were related, resper- tively, to the concentration of glucose 1,6-diphosphate and gln- case l-phosphate in such a \vay as to indicate the involvement of both phosphorylated and del~hosl~horylattd forms of the enzyme in a ping-pang-like pathway similar to that previously suggested by Najjar and Pullman (1). -it high substrate concentration+, inhibition by glucose I -1)hosphate (competitive with glucose 1 ,6-diphosphate) and by glucose 1 1 6-diphosphate (competitive with glucose l-phosphate) was observed. Six possible ping-pong- like pathways for phosphoglucomutase action were considered. Esperiments in which 3Wlabeled phosphoglucomutase was treated with excess amounts of glucose l-phosphate and glucose 1 ,6-diphosphate indicated that free glucose 1,6-diphosphate was neither an obligatory nor an important reaction intermediate. Substrate inhibition patterns tentatively eliminated two nddi- tional pathways. The remaining two pathways differ as to \?-hether one or tsvo binding sites for glucose 1,6-diphosphate are present on the dephospho-enzymr, and cannot be distingui.?hed with the present data.

Phosphoglucomutase activity in the absence of added glucose 1 ,6-diphosphate was also studied. Specific activity under these conditions increased markedly with enzyme concentration, and the increase could be quantitatively related to the amount of free glucose 1,6-diphosphate generated by the enzyme.

The following kinetic constants were evaluated: Kn(giurorc-~-pl. 8.5 X low6 M; Rm(~lueose-1.6-di-P), 6.2 X 1OP M; K~(gluroee-I-P), 1 X 10e3 M; ~i(Rlurose-1,6-di-p), 7 X 1O-4 hf.

.S chromatographic procedure for separation of the cy and /3 isomers of glucose 1,6-diphosphate is given.

Acknowledgments-We are pleased to acknowledge helpful discussions with Drs. W. \V. Cleland and D. E. Koshland, Jr. The communication, prior to publication, of data on thr moleru- lar weight of phosphoglucomutase and on 3ZP-tracer experiment.<

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1236 Phosphoglucomutase Pathway Vol. 239, No. 4

by Drs. D. L. Filmer, H. R. Horton, and D. E. Koshland, Jr., is 11. NAJJAR, V. A., AND MCCOY, E. E., Federation Proc., 17, 1141

gratefully acknowledged (1958). 12. RAY, W. J., JR., ASD KOSIILAXD, D. E., JR., J. Am. Chem.

1. 2.

3. 4.

5.

6.

7.

8.

9.

10.

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William J. Ray, Jr. and Gertrude A. RoscelliA Kinetic Study of the Phosphoglucomutase Pathway

1964, 239:1228-1236.J. Biol. Chem. 

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