estimation of pathwav contributions to glucose metabolism and of

THE Jou~ivar. OF RIOLOQ~CAL CHEMISTRY Vol. 239, No. 3, March 1984

Printed in U.S.A.

Estimation of Pathwav Contributions to Glucose Metabolism

and of

RERN~RD R. LANDAu,t

thL Rate of Isomerization of

Hexose &Phosphate*

GLENN E. BARTSCH, JOSEPH KATZ,t AND HARLAND G. WOOD

From the Departments qf Medicine and Biochemistry and the Division of Biometry, Western Reserve University, Cleveland 6, Ohio, and the Institute for Medical Research,

cedar.9 of Lebanon Hospital, Los Angeles 29, Cali;Tornia

(Received for publication, July 22, 1963)

Glucose is metabolized (Fig. 1) to CO% and triose phosphate via the pentose cycle and Embden-Meyerhof pathway.l Many investigators have attempted to estimate the contribution of these pathways to glucose metabolism in intact cells, usually by determining yields of 14C02 or 14C-labeled triose-P derivatives from glucose-l-14C and -6-14C (1). Katz and Wood (2-4) noted in these estimations the failure to consider recycling of fructose- 6-P to glucose-6-P and that for every molecule of glucose-6-P metabolized to CO2 and triose-P, 3 molecules of glucose-6-P enter the pentose cycle

1c 2c 2c 2c 3c 3c

3c 2c 3c 4c + 3 1coz + 4c + 4c + 4c 5c 5c 5c 5c (1)

GC GC GC 6C 3 Glu- + 3COn + 2 fruc- + t,riose-P

case-6-P tose-6-P

with distribution of their carbon atoms as indicated. Thus (Fig. l), when glucose-6-14C is substrate, the specific activity of fructose-6-P formed via the pentose cycle is the same as that of

* Supported by Grants A-4411 to B. R. L. and A-3682 to J. K. from the National Institute of Arthritis and Metabolic Diseases; by Grants to B. R. L. from the Cleveland Diabetes Association and American Heart Association; by Training Grant 2G-17 to G. E. B. from the National Institutes of Health; and by Contract AT-30-1- (1320) to H. G. W. from the Atomic Energy Commission.

t This work was done during the tenure of an Established In- vestigatorship of the American Heart Association.

1 The terms used in this paper are defined as follows. Pentose Cycle-Conversion of glucose 6-phosphate via 6-phos-

phogluconate to pentose phosphate and COB followed by conversion of the pentose phosphate to hexose 6-phosphate and triose phosphate.

Embden-Meyerhof Pathway-Conversion of glucose g-phosphate via fructose g-phosphate to fructose 1,6-diphosphate and then to triose phosphate via the aldolase reaction.

Nontriose Phosphate Pathways-Utilization of glucose B-phosphate by pathways not yieldingtriose phosphate. -

Total Metabolism of Glucose-The sum of the above three nath- ways: PC + EM + “NTP = 1, where PC, EM, and NTP dknote the fraction of total metabolism of glucose occurring by each of the three pathways.

Equilibration VabLe-The ratio of the quantity of fructose B-phosphate isomerized to glucose B-phosphate compared to the total quantity of hexose phosphorylated to hexose 6-phosphate. This ratio is denoted by E-F, in the equations of this paper.

the glucose-6-P entering the cycle. Therefore, fructose-6-P formed via the pentose cycle does not alter the specific activity of the hexose 6-phosphates from which COZ and triose-P are derived. Since carbon 1 is oxidized to 14C02 when glucose-l-*4C is substrate, the fructose-6-P formed via the pentose cycle is non- radioactive. Therefore, the specific activity of the hexose g-phosphates formed when glucose-l-% is substrate will b3 les than for glucose-6-14C, although both substrates have the same specific activity. Corrections for this are necessary in compar- ing yields of 14C02 and triose-P from glucose-l-14C and -6-14C. To make these corrections, Katz and Wood (2-4) assumed that fructose-6-P is in complete isotopic equilibration with glucose- 6-P; i.e. the rate of isotopic equilibration of fructose-6-P with glucose-6-P is very fast relative to the rates of their subsequent metabolism. This they referred to as “complete recycling.” Other inadequacies in estimations based upon triose yields and more particularly COZ yields were also discussed (2, 4). Re- cently (3), the application of specific yields of CO2 to the estimation of pathway contributions has been considered.

Katz and Wood (2, 4) introduced a procedure for estimating pentose cycle contribution dependent upon randomization of 14C of specifically labeled glucose during conversion to glucose-6-P. Thus, with glucose-2-14C as substrate, glucose-6-P-l ,3-14C is formed from fructose-6-P by recycling (Equation l), and the quantity formed is dependent upon the extent of glucose metabolism by the pentose cycle. The quantity of glucose-6-P-2-14C formed is dependent upon the amount of glucose utilized, i.e. phosphorylated to glucose-6-P. They derived expressions by which the percentage of glucose utilized via the pentose cycle could be estimated from the ratio of carbon 1 to carbon 2 or of carbon 3 to carbon 2 in glucose-6-P. In tissues thus far examined

(5, 6), recycling has proved to be extensive. Therefore, estimations based upon the model of metabolism assumed by Katz and Wood are probably good approximations, and those of investigators assuming no recycling are not. However, at least under some conditions, there is evidence that recycling is incomplete

(5, 6). In this paper, expressions are derived for the estimation of

pathway contributions to glucose metabolism by employing a model in which no assumption is made as to the extent of isotopic equilibration between glucose-6-P and fructose-6-P. Experi- mental data required for the solution of the system and various methods to test the validity of the model are presented. A by-

686

by guest on January 31, 2018http://w

ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

March 1964 B. R. Landau, G. E. Bartsch, J. Katz, and H. G. Wood 687

product of these theoretical considerations is the introduction of a method for quantitative estimation of the rate of the phosphohexose isomerase reaction in the intact cell. This, to our knowledge, represents the first method offered for estimating the rate of such a reaction without recourse to measurement of enzymatic activity in subcellular preparations.

DESCRIPTION OF MODEL

The pathways of glucose metabolism are depicted by the model presented in Fig. 2. Rates designated by V are expressed as atoms of carbon per unit of time. Fructose, as well as glucose, is presented as substrate to the system, since the use of fructose has advantages in the experimental solution of the model. I f g and f designate, respectively, the fractions contributed by glucose and fructose to the total hexose metabolized, then g + f = 1. The atoms of glucose carbon converted to glucose-6-P per unit of time are gVO, and of fructose converted to fructose-&P, fVO, where VO denotes the rate of phosphorylation of the hexoses to hexose g-phosphate. Isomerization of glucose-6-P to fructose- 6-P occurs at the rate Vh, and this reaction is reversible at the rate V-h. As indicated by Equation 1, one-third of the glucose- 6-P entering the pentose cycle is converted to COZ and triose-P, and two-thirds to fructose-6-P. If VI atoms of glucose-6-P carbon enter the cycle per unit of time, one-sixth this quantity, 1/6V1, is metabolized to CO* and one-sixth to triose-P, n hereas 2/3V1 is converted to fructose-6-P. The reactions of the pentose cycle are considered irreversible. The rate of entrance into the nontriose phosphate pathways, as in glycogen formation in which no triose-P is formed (2-4), is denoted by Vs, and the hexoses metabolized by the Embden-Meyerhof pathway leave the fructose-6-P pool to form triose-P at the rate V2.2 These reactions are also considered irreversible. Triose-P is further metabolized to COz and other products, such as glycerol and lactate. The rate of these conversions is not pertinent to present considerations. Steady state conditions are to operate, and therefore the number of atoms of carbon entering the glucose-6-P and fructose-6-P pools must equal the number of atoms leaving as represented mathematically by expressions a and b of Fig. 2. The sizes of these pools in atoms of carbon are designated by the terms M, and Mf.

DERIVATIONS

In this section, expressions are derived for the specific activity of the carbon atoms of glucose-6-P and fructose-6-P when specifically labeled glucose or fructose is presented to a system represented by the model. These expressions will be in terms of the rates of the reactions in the model, and these rates in turn will be expressed as a function of pathway contributions to hexose metabolism. In a subsequent section, experimental procedures for determining the specific activity of the carbon atoms of glucose-6-P and fructose-6-P will be considered which allom estimation of these contributions.

In the first derivations, Vs is assumed to be zero; i.e. no nontriose phosphate pathways are present. In the last part, of this section, they are introduced. The derivations are under conditions when both glucose and fructose are substrates and are then simplified by considering the circumstances when only glucose

2 In the presentation to follow, except where estimations employ yields in COZ and triose-P, the fate of fructose-6-P at the rate 112 is not relevant and may proceed by the pathways other than the Embden-Meyerhof; for example, the Entner-Doudoroff pathway.

glucose -

fructose-6-P

triose-P ___j CO2

FIG. 1. Scheme for the conversion of glucose to COZ and triose phosphate via the pentose cycle (PC) and Embden-Meyerhof pathway (EM).

v3 T

V2 EM

STEADY STATE EXPRESSIONS

0) C&t”-h=“,,tv, t v,

b) f”ot”ht2/3”,=V-htV,

1/6V, - co,

-cop and other products

FIG. 2. Model of metabolism. The fraction of hexose entering the system as glucose is g, and as fructose, f; Vo represents the rate of phosphorylation of hexoses to hexose B-phosphate. Pools of glucose-6-P carbon atoms and fructose-6-P carbon atoms are represented by the rectangles, and their quantities, as &l, and M,, respectively. The conversion of glucose-6-P to fructose&P pro- ceeds at the rate Vh, and in the reverse direction, at the rate Vvh. In met.abolism via the pentose cycle, glucose-6-P leaves at the rate VI, and two-thirds of this quantity is returned as fructose-6-P while one-third is converted to triose-P ($VI) and CO2 (iv,). Metabolism via the Embden-Meyerhof pathway is at the rate Vf to form triose-P. Met’abolism via nontriose phosphate-forming pathways is at the rate V%. Triose-P is further metabolized to CO2 and other products at undesignated rates. At steady state, the conditions recorded in the lower left comer of the figure must be fulfilled.

(g = 1; f = 0) or fructose (j = 1; g = 0) is the substrate. The specific activities of glucose-6-P and fructose-6-P are denoted by z and y, respectively, and the specific activities of the individual carbon atoms of these phosphates by subscripts, i.e. zl, x2, etc. In all derivations, the procedure is to determine the rate of change of 1% in the glucose-6-P and fructose 6-P pools, expressed mathematically as dM,x/dt and dJJ~y/dt, respectively. These rates

depend on the difference between the inflow and outflow of 14C from the pools as depicted in Fig. 2. At isotopic steady state, the quantities of 14C entering the pools will be equal to those leaving the pools.

Specijk Activities of Curbon Atoms of Hexose B-Phosphates when


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

688 Pathway Contributions to Glucose Metabolism Vol. 239, No. 3

l- and 6-W-Hexoses are Substrates-At steady state for total carbon transfer, if a tracer of glucose-l-l% and fructose-l-l% is presented to the model (Fig. 2), the rate of change of 14C in carbon 1 of glucose-6-P is equal to the rate at which 14C arrives in carbon 1 of the glucose-6-P pool minus the rate at which it leaves. That is, from Fig. 2,

dM,Xl - = gVoG, + V-a/l - (Vh + VI) x1

dt (2)

The equation representing the change in the quantity of 14C in carbon 1 of fructose-6-P is from Fig. 2.

d@5!e = fVoF1 + VhX1 - (VA + V&l dt (3)

The term representing the fructose-6-P formed in the pentose cycle (2/3Vlxl), does not appear in Equation 3, since x1 = 0; i.e. carbon 1 of glucose-6-P-l-14C is converted to l4cO2 in the pentose cycle (Equation 1).

Equations 2 and 3 are true at any instant of time after the addition of isotope. At the time t, when isotopic steady state conditions are attained, the quantities of isotope in the pools do not change and the derivatives are equal to zero. Then the specific activity in carbon 1 of glucose-6-P, by eliminating yl from the equations, is

x 1

= (VA + V&V&l + V-@O~I V2Wh + Vl) + v-hV1

(4)

The specific activity of carbon 1 of fructose-6-P is

V2(Vh + Vl) + v-hV1 (5)

These expressions for the specfic activities can be placed in terms of E-h, PC, G1, F1, g, and f by obtaining expressions for VI, Vh, V-h, and Vz in terms of these parameters (Equations 6 to 9).

At steady state, when V, = 0, inflow equals outflow and the relationship VO = 1/3V1 + Vz holds. This mathematically states that the quantity of hexose phosphorylated at steady state equals the sum of the hexose metabolized by the pentose cycle (1 /3V1) and Embden-Meyerhof pathway (V,). Hence, the fraction of total metabolism proceeding via the pentose cycle is PC = 1/3V1/V0 or, solving for VI,

Vl = 3PCVo (6)

The fraction via the Embden-Meyerhof pathway is EM = (1 - PC) = V2/V0 and, solving for VZ,

vz = (1 - PC)Vo (7)

An equilibration value, E--h, has been defined (see footnote I), which is mathematically

E-h = V-JVo (8)

This value serves as a measure of recycling, since it represents the quantity of fructose-6-P converted to glucose-6-P, V-h, as the fraction of the total quantity of hexose utilized, VO . Substitut- ing Equations 6 and 8 into condition a of Fig. 2 yields the expression

VA = (g + E-h - 3PC)Vo (9)

The expressions for the specific activity of carbon 1 of glucose-6-P

and fructose-6-P as recorded in Table I are obtained by substitution of Equations 6 through 9 in to Equations4 and 5. These are recorded when both fructose and glucose are presented to the system and glucose is labeled (Fl = 0) or fructose is labeled (GI = 0).

The corresponding differential equations employing glucose- 6J4C and fructose-6-l% as substrates are

dM,X, ~ = gV&‘s + V-Q/~ - (V, + V&A

dt (10)

and

dMry, = fVd’6 + (Va + 2/3Vh - W--h + V&/c clt

(11)

They yield the expressions for x6 and ys in Table I. From the results in Table I, the ratios x1/x, and yl/y~ are

obtained as given in Table II. These ratios represent, respectively, the specific activities to be found in glucose-6-P and fructose-6-P as a function of PC, E-h, g, and f, and the specific activities of the substrates G1, Gs, FI, and Fe. If the specific activities of the labeled substrates are prepared so that G1/Gs and F1/F6 are both equal to unity, certain consequences of the ratios recorded in Table II are apparent. (a) When both glucose and fructose are substrates, the ratio of specific activity in carbon 1 to that in carbon 6 of glucose-6-P will be the same irrespective of which of the two substrates bears the 14C. (b) When equilibration is complete (E-h = CO), all expressions for the ratios of activity of carbon 1 to 6, i.e. xl/xg and yl/y~, reduce to the expression derived by Katz and Wood (2-4), l/(1 + 2PC). This result is apparent when the numerators and denominators of the expressions are divided by E-h, e.g.

E-h + d1 - PC) 1 + g(1 - PC)/Ea

E-h + 2PC E-h + g(1 - PC) = 1 + 2PC + g(1 - PC)/E-h

As&h + ~0, the ratio approaches l/(1 + 2PC), since g(l - 2PC)/E-h approaches zero. (c) When labeled fructose is the only substrate (g = 0), xl/x6 = yJy6 = l/(1 + 2PC). Thus, with labeled fructose as sole substrate, the ratio observed will be that which would be observed if isomerization were complete regardless of the actual value of E-h.

Sp&ic Activities of Carbon Atoms of Hexose B-Phosphates when 6-%‘-Labeled Hexoses are Substrates-When glucose-2-14C or fructose-2.1% is substrate, 14C is introduced into the first 3 carbon atoms of glucose-6-P and fructose-6-P via the pentose cycle (Equation 1). The equations expressing the changes in the quantity of 1% at time tin each of the first 3 carbon atoms of glucose- 6-P are

dM,s ~ = V-Q/l - (Vh + VJX,

dt (12)

and

d&,x, - = gVoG + V-hyz - (Vh + Vlh

dt (13)

dM,xa - = V-i&Y3 - (Vh + Vlh

dt 04)

The derivation of the corresponding equations for the carbon atoms of fructose-6-P is more complex than for their counter- parts in glucose-6-P because of the rearrangement of the carbon


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

March 1964 B. R. Landau, G. E. Bartsch, J. Katz, and H. G. Wood

TABLE I

689

Expressions for specijic activities of hexose 6-phosphates for several substrate conditions

PC is the fraction of hexose utilized via the pentose cycle; E-h is the quantity of fructose-6-P isomerized to glucose-6-P relative to the quantity of hexose utilized; g and f are the fractions of the hexose represented by glucose and fructose, respectively; and G and F are the specific activities of the hexoses with subscript designating the position of label.

Substrate

Glucose-l-W with unlabeled fructose [E--h + (1 - PC)] gG1

xl = Eeh + g(l - PC) + %‘CE-h

Fructose-1-r4C! with unlabeled glucose E--hfFl

‘I = Ewh + g(l - PC) + 2PCE-h

Glucose-B-% with unlabeled fructose [E--h + (1 - PC)] 45 x6 = E-h + g(1 - PC)

Fructose-6-14C with unlabeled glucose EmhfFs

X6 = E-h + g(1 - PC)

Specific activity of glucose-6-P (2) Specific activity of fructose-6-P (y)

[E-I, + (1 - 3PC) - (1 - g)l gG, Yl =

E-h + g(l - PC) + Z-XL,

(g + E--h) fF1

” = E-h + g(l - PC) + 2PCE-h

ye = [E--h + (1 - PC) - (1 - g)l gGs

E-h + g(1 - PC)

(g + E--h) fF6

y6 = E-h + g(l - PC)

TABLE II

Relative speci$c activity of glucose-6-P and fructose-6-P when glucose-i-14C and -6-l% or fructose-i-l%’ and -6.146 are substrates

These equations are derived from the expressions given in Table I. S.A. denotes specific activity.

Substrates

Glucose-l-‘4C and -6.r4C with fructose present

Glucose-1.1% and -6-l% (g = 1, f = 0)

Fructose-l-W and -6-r% with glucose present

Fructose-1-*4C and -6-1% (f = 1, 9 = 0)

S.A. in C-l of glucose-h-P = s S.A. in C-6 of glucose-6-P X6

E-h + g(1 - PC) G1

E-h + g(l - PC) + =cE-h ’ G,

E-h + (1 - PC) G

E-h + (1 - PC) + 2PcE-h ’ G,

E-h + g(1 - PC) F1

Ewh + g(1 - PC) + 2PCE-h ’ F,

1 Fl ~.- 1 + 2PC FE

S.A. in C-l of fructose-6-P ye S.A. in C-6 of fructose-6-P = ii

[Eeh + (1 - 3PC) - (1 - g)l[E-h + g(1 - PC)] GI

F-h + g(1 - PC) + 2PcE-nl[E-h + (1 - PC) - (1 - g)] ’ G,

E-h + (1 - 3pC) G1

Eph + (1 - PC) + PPCE-I, ’ G,

E-h + g(1 - PC) F1 Eeh + g(l - PC) + 2PCE-h ’ F,

1 F1 ~ .- 1 + 2PC Fc

atoms of glucose-6-P as they traverse the pentose cycle (Equa- tion 1). The equations are

dMfY1 __ = dt

V~XI + 2/3Vlxz - (V-h + VdY, 05)

dMryz = fvo’oFz + VhxZ + 2/3Vlx3 - (V-h + v&/Z

dt (16)

and

dMrys ~ = vhX3 -+ 1/3v1(22 + xd - (V-h + v2)‘&

dt (17)

Only one term of each of these three equations is not apparent from Fig. 2. In Equation 15, the term 2/3V1x2 reflects the introduction into carbon 1 of fructose-6-P of two-thirds of the label in carbon 2 of the glucose-6-P entering the pentose cycle (see Equation 1). In Equation 16, the term 2/3Vlxs reflects the introduction into carbon 2 of fructose-6-P of two-thirds of the label in carbon 3 of the glucose-6-P entering the pentose cycle. In Equation 17, the term l/3V1(zz + x3) reflects the introduction int,o carbon 3 of fructose-6-P of one-third of the label in carbon 2 and carbon 3 of the glucose-6-P.

At isotopic steady state, the derivatives in Equations 12 to 17

are equal to zero, and, by eliminating y1 from Equations 12 and 15, the following relationship is obtained.

Xl z/31/‘-hTi, -=

X2 VdVh + VI) + v--Iv1

Similarly, by eliminating y3 from Equations 14 and 17,

X3 1/3v-hv1 -=

X2 vdvh + VI) + 2/3v-hv1

(18)

(19)

The ratios in Equations 18 and 19 are related by the equation

(20)

By dividing Equation 14 by Equation 12 after equating both to zero, the relationship y~/yr = x3/x1 follows. From this, the relationship between ya/yz and yr/y~ in fructose-6-P is

y3 (YllY2) (x3/22) -= (21) Y2 XliX2

Further, from Equations 12 and 13, the relationship

Xl Ti-hyl -= <y’ (22) X2 gVoGz + v-h@ yz


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


1

0.6

PC 0.5

In Fig. 3, PC is plotted as a function of the ratio of 14C activity to be found in carbon 1 to the activity in carbon 2 of glucose&P when glucose-2J4C is sole subst#rate (g = 1) and E-h varies from 0.1 to m. The ratio proves markedly dependent upon E-h, for a given PC, and a given ratio may indicate a wide range of pentose cycle contributions depending upon ILh. For example, a ratio of specific activity in carbon 1 to that, in carbon 2 of glucose-6-P of 0.2 may be consequent to a pentose cycle contribut’ion of 12 to 60%, depending upon the extent of recycling (E-h from m to 0.1). The values given by Katz and Wood (2), assuming complete recycling, are represented by the curve designated E-h = m. It is clear that measurement of the pentose cycle using glucose-2J4C and the ratio of 14C in carbon atoms 1 and 2 of a glucose-6-P derivative will be very dependent on the equilibration of fructose-6-P with glucose-6-P (E-h).

I f fructose-2-r4C is the only substrate (Gz = 0), yl/y2 = xl/x? (Equation 22) and is at a maximum (Equation 24). The pentose cycle contribution is then measured by the curve E-h = m in Fig. 3 irrespective of the actual value of E--h. Thus, from Fig. 3, if the xl/x2 ratio is 0.2 in glucose-6-P with fructose-2J4C as sole substrate, the pentose cycle contribution is 12%. If glucose- 2.r4C and fructose are substrates, the ratio yr/yt in terms of E-.-h and xl/xz is, from Equations 12, 16, 6 to 9, 20, and 23,

0 _I .2 .3 4 .5 .6 7

SA OF CARBON I OF GLUCOSE-6-P XI

S A OF CARBON 2 OF GLUCOSE-6-P x2 0

FIG. 3. Pentose cycle as a function of the ratio of 1% in carbon atoms 1 and 2 of glucose-6-P from glucose-2-14C and the effect of recycling. A family of curves is shown for different values of E--h. The ratio of specific activities in carbon 1 and 2 of glucose-6-P (x1/x2) to be expected with glucose-2-l% as substrate and a PC value of 0 to 1.0 is plotted as a function of the degree of recycling as measured by the equilibration value, E-n, from 0.1 to 00. The graphs are obtained by substitution of E-h and PC values in Equa- tion 23 of the text. Note that when E-h is 5, the ratios are quite similar to those when E-h = m . S.A., specific activity.

is obtained. Thus, if glucose-2-14C is substrate, and V-J, is finite, the ratio of the specific activity in carbon 1 to that in carbon 2 of glucose-6-P will be less than that of fructose-6-P. As 17-h approaches infinity, E-h + m and x1/x2 approaches y1/y2, since the effect of the term gVoGz upon the expression approaches zero. When fructose-2-r4C is substrate, whether or not nonlabeled glucose is present, the two ratios are equal, since Ge is zero.

Introducing Equations 6 through 9 into Equation 18,

Xl 21’ClLh -=

X2 I&, + g(1 - PC) + WCE-h (23)

For a fixed PC, the maximal value x1/x2 occurs if either g = 0 (only fructose-2-l% is substrate) or E-h + M, and is

(24)

Yl

Yz (271

[2E-h(l - x,/xp) + gxJxJxJx2 + (2 - 3x1/22)x1/x2 2E-h(l - xl/xp) + gxl/x? + (5x1/22 - 6) (xl/xz)/@ - x,/x*)

When glucose-2-r4C is the only substrate (g = I), Equation 27 simplifies and, when solved for E-h, yields the expression

E_

h

= [(2 - x1/x*) + 2Y1/Y*lXdX2

(ydy2 - x1/22) (2 - x1/22) cm

Setting g equal to 1 in Equation 25 and substituting Equation 28, the expression for PC in terms of the ratios of the specific activities of carbon atoms 1 and 2 of glucose-6-P and fructose-6-P is

(2 + ddYllY2

PC = (6 - 5x,/x?)y,/y2 + (2 - x~/xd (2 - 3%/a) (29)

Equation 24 is that given by Katz and Wood (2,4) for calculation of the randomization of glucose-2J4C into glucose-6-P for a given pentose cycle when isomerization is complete. Equation 23 is the general equation. It may be rearranged to yield the expression

PC = (E--h + gh/xz 2E-h(l - x1/x2) + gxl/xs

(25)

and

Xl/X6 = 1 - Xl/X2 (30)

Yields in Triose-P and CO2 from Hexose-l-14C and -6-r4C-In the model of Fig. 2, triose phosphates formed via the Embden- Meyerhof pathway and pentose cycle form a common pool. The yield of 14C in triose-P with glucose-1-r4C as substrate is equal to the quantity formed via the Embden-Meyerhof pathway, since E-h =

$70 - PC)x1/22 2PC - (1 + 2PC)x1/x2

(26) no IJC-triose-P is formed via the pentose cycle. Therefore, the

Relationship between Distribution of 14C in Glucose-6-P with Hexose-W4C Compared to Hexose-l-14C and -6-r4C-Algebraically the identity

E-h + ~(1 - PC) 2PCE-,,

E--h + g(1 - PC) + 2PCEL = ’ - E-h + g(1 - PC) + 2PCE-1

exists. The expression on the left is equal to x1/x6 as recorded in Table II, where the ratio of the substrate specific activities G1/G6 is adjusted to unity. The expression on the right is 1 minus the expression for xl/x2 (Equation 23). Therefore xr/xg is the complement of xl/x2 .


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

&larch 1964 B. R. Landau, G. E. Bartsch, J. Katz, and H. G. Wood 691

yield of 1%’ is the quantity of fructose-6-P going to triose-P multiplied by the specific activity of the fructose-6-P.

14C in kiose-P from glucose-lJ4C = ‘c’~y,

With glucose-6i4C as substrate, all the 14C utilized appears in triose-P.

1% in triose-P from glu~css-6-~~C = gVoG8

The ratio of yield in triose-P, designated T,, is from Equation 7.

14C from glucose-l-i% Tg = 14C from glucose-6-W

712 yl (1 - POY, _______- = v. g& = g(&

When the value for yl in Table I is substituted with G1/G6 adjusted to 1,

T = (1 - PC)[E-h + (1 - 3PC) - (1 - g)l - - B E-h + g(1 - PC) + 2pCE-h (31)

The corresponding ratio of i4C yield in triose-P from fructose-l- 14C and fructose-6J4C, designated Tf, is

(1 - PC) (g + E--h) Tf=----- -- E-h + g(1 - PC) + 2PCE-h

(32)

I f glucose is sole substrate, g in Equation 31 is 1. If fructose is sole substrate (g = 0), Equation 32 reduces to (1 - PC)/(l + 2PC) as for complete recycling (l-3). Equations 31 and 32 are useful for the measurement of PC and E-h. The solution of the two equations for PC is

I - T,(l - g) - gT, PC = - -

1 + 2Tj

The ratios, T, and T,, and g can be determined experimentally, and EMh can then be obtained by solution of Equations 31 and 32. Fig. 4 illustrates the effect of E--h on the ratio of 14C yields in triose-P from glucose-lJ4C and -6-14C, where g = 1, for pentose cycle contributions of 0 to 100%. The smaller the ratio observed, the more uncertain PC is unless E-h is established. Thus, when T, = 0.1, the pentose cycle is 3576 if E-h = 0.25 and 75% at E-h = m. A ratio of 0.7 would indicate a pentose cycle of 10 to 13T0 with E-h from 0 to M. For any value of T,, PC is little changed as E-h varies from 5 to 00. Thus, if equilibration of the hexose phosphates is rapid, the error of estimation is not great even if equilibration is assumed to be complete.

COz yields from glucose-1-14(’ can be expressed in a manner similar to that detailed for complete recycling (Table I of (3)). I f the fraction of carbon 3 of triose-P oxidized to CO2 is designated as X, the i4C yield in CO2 from glucose-l-i4C is equal to the 14c of the utilized hexose converted to CO2 via the pentose cycle and via triose-P.

1%” yield = r’013PC~i + (1 - PC)y,N]

The yield from glucose-6-i4C is equal to the 14C of the utilized hexose multiplied by X since all the 14C’ appears in triose-P.

1% yield = gVoG&’

Specific yields of 14C are obtained by dividing the actual yields of 14C02 by the 14C of the utilized hexose. Thus, the specific yield from glucose-6-i4C, G6coa, is simply N (2,3). Expressions based upon specific 14C yield, derived as for complete recycling (3), are then, for glucose-l-14C and -6J4C,

-0 0.1 02 0.3 0.4 05 0.6 0.7 08 0.9 1.0 Cl4 YIELD IN TRIOSE FaOM GLUCOSE-I-C’4

Cl4 YIELD IN TRIOSE FROM GLUCOSE-6-Cl4 (Tg 1

FIG. 4. Pentose cycle as a function of the yield of 14C in triose-P from glucose-l- and -6-14C and the effect of recycling. A family of curves is shown for different values of E-h, the degree of recycling. The ratios of 14C yields in triose-P from glucose-l-14C and -6-14C are plotted as a function of PC from 0.0 to 1.0 with E-h varying from 0 to m. Glucose is the sole substrate presented to the system (g = I). The graphs are obta.ined by substitution of the values of E.-h and PC in Equation 31 of the text.

C:lcot - C:6c02 3P<‘[E-h + (1 - PC)]

1 - G6c02 = IE h + g(l--t’c)~2PcE-h (31)

and correspondingly, for fructose-l-Y and -6-14C’,

Flco, - FGco, 3P(‘E-h ~ -- =- 1 - F6c0, E-h + g(1 - PC) + 21’CE-h (35)

If Equations 31 and 34 as well as 32 and 35 are added, the sum is 1, and thus these pairs of equations are complementary as when recycling is complete (3).

I f g and the specific yields in Equations 34 and 35 are known, PC and E-h can be est’imated. Designating the ratio in Equa- tion 34 by S, and in Equation 35 by SJ,

Sf + s(& - $1 p(y = --- - 3 - 235, (36)

Contribution of Xontriose Phosphate Pathways- In derivations thus far, V3 has been assumed to be zero, so that the fraction of hexose metabolism via nontriose phosphate pathvvays, V3/V0, is zero and PC = 1 - EM. The derivations of the steady state equations and their solutions in the presence of a nontriose phosphate pathway are in principle similar to those already given. They will therefore not be detailed. It is found that with hexose-I and -6J4C as substrates, the solutions are identical with those appearing in Tables I and II, if for the recurring term 1 - PC, the term 1 - PC - NTP is substituted and the term 1 - 3PC is replaced by 1 - 3PC - KTP. When fructose is labeled and is the sole substrate, the expression for x1/x6 and yl/yG in Table II (bottom line) contains neither of these terms. Therefore, with fructose as sole substrate, PC can be calculated from these ratios regardless of the extent of a nontriose phosphate pathway contribution. When glucose is labeled and is the sole substrate, the ratios are a function of NTP unless E-h = M . PC


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

692 Pathway Contributions to Glucose Metabolism Vol. 239, x0. 3

0.8

0.6

0.5

0.4

0.3

0.2

0.1

0 0 .I .2 .3 .4 .5 .6 .7

S.A. OF CARBON I OF GLUCOSE-6-P XI

S.A. OF CARBON 2 OF GLUCOSE-6-P 0 x2

FIG. 5. Pentose cycle as a function of 1% in carbon atoms 1 and 2 of glucose-6-P formed from glucose-2-W and the effect of the nontriose phosphate pathways, where E-h = 0.25. A family of curves is shown for different values of XTP. Glucose is sole substrate (g = 1) and labeled with glucose-2-r%. PC is varied from 0 to 1.0 and NTP from 0 to 0.9, while E-h is kept constant at 0.25. The graphs are obtained by substitution of these values in Equa- tion 37 of the text. S.A., specific activity.

P

i

1 -I

-J

the ratio for a given PC is less subject to change by alteration of NTP.

APPLICATIONS

To illustrate how the equations that have been derived with their modified forms when T\;TP is present might be used in practice to estimate pathway contributions, a few theoretical examples will be presented. Ideally glucose-6-P and fructose-6- P should be isolated and degraded, but this will not usually be practical. However, recourse can be made to the isolation and degradation of derivatives reflecting the distribution of label in these substrates. Thus, glucose isolated from glycogen may be assumed to reflect the distribution in glucose-6-P, and perhaps glycerol or lactate, the distribution in fructose-6-P. Typical calculations based upon assumed observations follow.

Example i- Tissue slices were incubated with glucose-W4C, and glycogen and glycerol were isolated and degraded. Setting the activity of carbon 2 to 100, the distributions of 14C were found to be

Glycogen Carbon A &Ji:y

I 24.0 2 100 3 13.6

hence, xl/x2 = 0.24; x3/x2 = 0.136

GlyCWOl Carbm A&dy

3 35.4 2 100 1 20.1

hence, &y~ = 0.354; y3/yz = 0.201

From Equation 28 we obtain

can then be estimated from the r4C in carbon atoms 1 and 6 of hexose B-phosphate when there is a significant nontriose phosphate pathway contribution, only if E-h approaches infinity.

Similar considerations apply to the introduction of nontriose phosphate pathway contributions into the expressions derived with hexose-2-r4C as labeled substrate. Equation 23 becomes

Xl 2PcEeh

= E-h + g(l - PC - NTP) + 2PCE-h (37)

X2

Thus, with glucose-2-**C as substrate, the ratio of r4C’ activity in carbon 1 to that in carbon 2 of glucose-6-P is a function of NTP unless E-h = 00, when the expression again simplifies to 2PC/ (1 + 2PC) (Equation 24). Although with glucose-2-14C as substrate, nontriose phosphate pathway contribution will affect the ratios x1/x2 and yr/yz, the changes are such that the expression for E.-h, Equation 28, remains independent of NTP. Expression 27 for yl/yZ, when both substrates are present and glucose-2J4C is the labeled substrate, becomes more complex in the presence of an NTP contribution. Equation 27 is modified by the multi- plication of the terms (2 - 3xi/x2)xr/x2 and (521/x2 - 6)x1/x2 by the quantity [g(l - NTP) + E-h]/(g + E-h - NTP).

In Fig. 5, PC is plotted as a function of x1/x2 when glucose-2- i4c is substrate, E-h = 0.25, and the NTP is varied from 0 to 0.9. Fig. 6 presents an identical plot except that E-h = 1.0. It can be seen that when the equilibration (E-h) increases to 1,

E_h = [(2 - 0.24) + 2(0.354)]0.24 -=3 (0.354 - 0.24)(2 - 0.24)

From Equation 25,

(3 + 1)0.24 PC = 2 X 3(1 - 0.24) + l(O.24)

= 0.2

Thus, 20 y0 of the glucose was utilized via the pentose cycle. PC may also be determined directly from Equation 29.

It was also found experimentally that 20 pmoles of glucose were utilized in the tissue per g per hour. Hence, the rate of glucose- 6-P oxidation to pentose-P and COZ (Equation 6) is 3 X 0.2 x

20 = 12 pmoles per g per hour. From Equation 9, the rate of isomerization of glucose-6-P to fructose-6-P is rh = [l + 3 - 3(0.2)]20 = 68 pmoles per g per hour. The rate of phosphofruc- tokinase, from Equation 7, is 16 pmoles per g per hour.

The experimental data assumed are also sufficient to test the adequacy of the model. The relationship between the ratio of activity in position 1 to that in position 2 of glucose and the ratio of activity in position 3 to that in position 2 is the same as predicted for the system from Equation 20, i.e. 0.136 = (0.24)/ (2 - 0.24). The relationship between the ratios in glycerol as given by Equation 21 also holds, i.e. 0.201 = (0.354) (0.136)/ (0.24).

In this and the following example, equations are used in which Vg is assumed to be zero. Although glycogen is used experi-


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

March 1964 B. R. Landau, G. E. Bartsch, J. Katz, and H. G. Wood 693

mentally, the pathway to glycogen must be negligible compared to Embden-Meyerhof pathway and pentose cycle contributions for the equations to be applicable.

Example g-Tissue was incubated in two parallel flasks, which differed only in that in one fructose-2J4C was substrate and in the other, glucose-2J4C. Glycogen was isolated and was found on degradation to have the distributions (specific activity of carbon 2 = 100).

Glycogen from Carbolz Glucose-2-W Fructose-2-w

1 24 27.5

2 100 100

3 13.6 16.1

PC is immediately obtained from the fructose data (Equation 24).

2PC 0.275 = ~ *

1+2Pc’ PC = 0.2

We may now use Equation 26 to solve for E-h with the data ob- tamed with glucose-2-14C.

I(1 - 0.2)(0.24) 0.192

E-h = 2(0.2) - 11 + 2(0.2)]0.24 =-----=3

0.064

The remaining calculations parallel those of Example 1. Example S-Glucose and fructose were present together in four

simultaneous experiments with replicates of the same tissue; glucose-l and -6J4c and fructose-l and -6-l% of the same specific activities were used. Utilizations and yields in glycerol (a

-J “0 .I .2 .3 .4 .5 .6 .?

S.A. OF CARBON I OF GLUCOSE-6-P XI

S.A. OF CARBON 2 OF GLUCOSE-6-P 0 x2

FIG. 6. Pentose cycle as a function of 1% in carbon atoms 1 and 2 of glucose-6-P formed from glucose-2J4C and the effect of the nontriose phosphate pathways, where E-h = 1.0. Graph as in Fig. 5 except that E-h = 1.0.

measure of triose-P yields) were

Yidd Labeled substrate w utilized GlyCWOl cot

c.p.m. x 10-a c.pm x 10-x

G* 80 18.7 51.9

G6 80 40.0 20.0

Fl 20 7.1 9.4

F6 20 10.0 5.0

From these data, g = 0.8;f = 0.2; T, = 18.7/40.0 = 0.47; T, = 7.1/10.0 = 0.71; Glcoz = 51.9/80 = 0.65; G600z = 20/80 = 0.25; Flcoz = 9.4/20 = 0.47; F6coz = 5/20 = 0.25.

The pentose cycle contribution using triose-P ratios is calculated from Equat’ion 33.

pc = ‘__: 0.721 - 0.8) - (0.8)(0.47)

1 + 2CO.71) = 0.2

When this value is substituted in Equation 31 or 32, E-h is found to be 1.

From the specific yields of CO2 (Equations 34 and 35), 8, = 0.53 and Xf = 0.29. By substituting in Equation 36, PC can also be determined.

0.29 + 0.8cO.53 - 0.29) pc = - --.--.-- - = 0.2 3 - 2CO.29)

E-h = 1 is then obtained from Equation 34 or 35. Example 4-A tissue was studied as in Example 2, except that

a significant nontriose phosphate pathway contribution was present and glycerol obtained on incubation with glucose-2-14C as substrate was also degraded. Distributions were as follows.

Glycogen.from Carbon Fructose-Z-W Glucose-2-K Glycerol

1 27.5 24 37.2 2 100 100 100 3 16.1 13.6 65.6

PC is again immediately obtained from the fructose data (Equa- tion 24), i.e. 0.275 = 2PC/(l + 2PC); PC = 0.2. From Equa- tion 28,

E_ A

= [(2 - 0.24) + 2(0.656)10.24 = l,. ~- (0.656 - 0.24)(2 - 0.24)

The nontriose phosphate pathways contribution may now be estimated from Equation 37.

2(0.2) (1) o’24 = 1 + l(1 - 0.2 - NTPj-+ 2(0.2)?ii

Solving, XTP = 0.53. Since EM = 1 - PC - XTP, 20% of the glucose utilized is metabolized via the pentose cycle, 53 y0 via nontriose phosphate pathways, and 27Y0 via the Embden- Meyerhof pathway.

DISCUSSION

Nethods previously proposed for evaluation of pathways of glucose metabolism in tissues are based upon models which assume that isomerization of fructose-6-P to glucose-6-P is either negligible or so rapid that the specific activities of the hexose g-phosphates are essentially equal (1). Experimental results in- consistent with these assumptions (5, 6) have necessitated the development of the present model, which contains no limitation


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


to the rate of isomerization. The experimental data required to measure pathways in such a system have been indicated and sample calculations presented. It remains to discuss the assumptions and limitations of the model, conditions under which incomplete isomerization must be considered, and restrictions in the selection of experimental conditions.

Validity of Model -The experimental procedures prove relatively simple (5). The model is more general than those previously used and is thus more likely to approach physiological reality. However, the assumptions present still are very re- strictive. In a given tissue, reactions considered irreversible or negligible may be reversible and extensive, and a more complex model may actually be required. Thus, the reversal of reaction V2 after formation of triose-P and its isomerization via triose-P i3omerase would interchange carbon atoms 1, 2, and 3 with carbon atoms 6, 5, and 4 of the hexose B-phosphates. The activity in carbon 1 relative to carbon 6 would then be distorted from that predicted by the model. This reaction would not affect the relative specific activities in carbon atoms 1, 2, and 3 of the hexose 6phosphates, so that estimations dependent upon the randomization of glucose-2-14C in hexose 6-phosphates remain suitable. Only if triose-P were randomized via the Krebs cycle before resynthesis to hexose phosphates, or if the transketolase as well as the transaldolase reactions were operative (4), would distortion of the relative specific activities occur in positions 1, 2, and 3.

The transaldolase reaction, a part of the pentose cycle (2), and the transaldolase exchange reaction (7) result in the incorporation of carbon atoms 1, 2, 3 into carbon atoms 6, 5,4 of fructose- 6-P. Although the transaldolase reaction must be present., it has not been expressed in the equations since it does not affect calculations based upon the use of glucose-2-14C nor estimations, unless nontriose-P pathways are present, based upon yields of 14C in triose-P or COz from glurose-1-X and -6-14C. It does modify to some extent the expressions for .r6 and y6 of the hexose 6-phosphates presented in Table I, the equations in Table II and Equation 30.3 The reversal of the pentose cycle via transketolase-transaldolase-catalyzed reactions would be evident from the failure to find the relationship represented by Equation 20.

Transient and Steady States-An intermediate, whose amount remains unchanged, is in isotopic steady state when the ratio of its specific activity to that of the labeled substrate, measured at the same time, becomes constant. This definition applies equally well to conditions under which the specific activity is constant as assumed in this paper, or is changing, as after a single isotope injection in viva. The establishment of isotopic steady state requires time and will be faster with a smaller intermediate pool and with fewer steps between it and the substrate. The differential equations that have been derived are valid for any time, but during the transient period are not equal to zero. The system during transient state has not been analyzed,4 and

3 J. Katz, B. R. Landau, and G. E. Bartsch, manuscript in preparation.

4 Equations of this paper, derived for substrate inflow of constant specific activity, can be generalized to conditions of changing activitv. The snecific activities G and 8’ then have to be expressed as a function of time. To obtain 14C yields in any product at time 1, it will also be necessary to integrat.e 14C inflow from glucose (or fructose) from zero to t and to consider the kinetics of excretion of the product from the circulation. The method is well illustrated by the experiments and analysis of Segal, Berman, and Blair (8), who measured 14C02 production from glucose-l- and -6.lnC in man and evaluated the contribution of the pentose cycle. Unfortu-

the period required for attainment for practical purposes of steady state is unknown. However, pool sizes of hexose B-phosphates are very small relative to hexose utilization, so that turnover rates are rapid. It therefore seems probable that 14C distribution patterns would be rapidly established in the hexose phosphates. The degradative procedures as applied to the phosphates and their immediate derivatives thus have an ad- vantage over procedures dependent upon products many steps distant and present in large quantity, such as COZ, in which transient state effects are likely to persist for longer periods. Since rates may depend upon substrate concentrations, the quantity of substrate present must be sufficient so that during the period of the experiment only a relatively small decrease in concentration occurs.

Selection of Substrate and Derivative- It is necessary to measure experimentally two independent quantities for complete solution, since E-h and PC determine the remaining parameters in the model. Where a derivative of fructose-6-P as well as glucose-6-P can be conveniently obtained, as in Example 1, a single incubation with glucose-2-14C is the simplest. By com- bining data obtained on parallel incubations with glucose-2-14C and fructose-2-r4C, a derivative of glucose-6-P suffices (Example 2). A single incubation with glucose-l, 6-14C cannot be employed unless fructose phosphate can be isolated and degra,ded. This is so since a fructose-6-P derivative, such as glycerol, will not permit differentiation between 14C from carbon atoms 1 and 6 of glucose. Further, a determination of the relative activities in carbon atoms 1 and 6 of the initial substrate is necessary. It is possible to use glucose-l-14C and -6-14C in parallel incubations, but this entails twice as much experimental work as with glucose-2-14C, and in- troduces variability between incubations. Glucose-l 6-i% does provide a confirmation of the validity of the model when used in parallel with glucose-2-14C as illustrated by Equation 30. When a nontriose phosphate pathway is present, three variables determine the solution of the model. Experimentally, two incubations appear indicated to obtain the necessary information as illustrated in Example 4. The use of glucose-3-14C has not been introduced, since this substrate is not generally available. Equations similar to those derived for glucose-2-14C are applicable.

When only the pentose cycle and Embden-Meyerhof pathways are significant pathways in a tissue, PC and hence EM, but not E-h, can be estimated by employing fructose-2-i4C as sole substrate and degrading glucose-6-P or a derivative of glucose-6-P (see Example 2). Although convenient, this approach requires the assumption that the relative proportion of metabolism via the two pathways is unchanged by the use of fructose instead of glucose. There are also possible disadvantages associated with the use of fructose. In many tissues the use of fructose may be impractical because of a low rate of metabolism. In liver, metabolism of fructose occurs via fructose-l-P as well as fructose-6-P (9). The methods dependent on triose ratios and COZ yields are then not applicable. Mannose-2-i4C may replace fructose-2-i4C with benefit in those tissues in which mannose is metabolized extensively and via fructose-6-P. The equations to be used for mannose are the same as those derived for fructose.

The selection of a suitable derivative of glucose-6-P will depend upon the tissue under study. In most mammalian tissues, glycogen is available. Trehalose may be employed in bacterial

nately, as indicated elsewhere (3), their analysis is based on the assumption of irreversible hexose B-phosphate isomerization.


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

March 1964 B. R. Landau, G. fi. Bartsch, J. Katz, and H. G. Wood 695

cells (10) or lactose in mammary gland (11). The selection of a derivative of fructose-6-P may be more difficult. In adipose tissue, glycerol has proved adequate (5). In most tissues, lactate is formed and can be readily isolated and degraded. However, the more distant metabolically a derivative is from glucose-6-P or fructose-6-P, the more likely its pattern is to have been distorted, With lactate and glycerol, it is necessary to demonstrate that distortion via the Krebs cycle has not occurred. Experi- mentally, if w;ith glucose-l and -6-l% as substrate, activity in the derivatives is found only in position 3, distortion probably has not occurred. Another possible check on the presence of a distortion is the failure of the relationship between y3/yZ and y1/y2 to hold as given by Equation 21 and illustrated in Example 1.

PC and E-h may be estimated in tissues with glucose-l and -6J4C and fructose-l and -6-14C as substrates by use of triose-P derivatives (Example 3). Again it is necessary to assume that the presence of fructose does not alter pathway contributions from those when glucose is sole substrate. Triose-P derivatives, such as lactate, fatty acid, and CO%, as previously noted, are subject to greater distortion of pattern than t’he hexose 6-phosphates or their close derivatives. When triose-P derivatives are employed, it is also necessary to assume, as depicted in the model, complete isotopic equilibration of dihydroxyacetone phosphate and glyceraldehyde phosphate. This is not the case in many tissues (la), but a model can be developed that encompasses nonequilibration via triose-P isomerase.3 The use of CO2 as a derivative requires that specific 14C yields be employed, and therefore the quantity of glucose utilized must be determined

(3). I f estimations are made on the assumption that equilibration

of fructose-6-P and glucose-6-P is complete, when it is not, the degradation of glucose-6-P or its derivatives from glucose-2J4C will cause an underestimation of the pentose cycle and the use of fructose-6-P or its derivatives, triose ratios, or CO% yields will cause an overestimation. This is illustrated in Fig. 7 for a tissue having an actual 20y0 pentose cycle and with E-h varying from oto m. When E-h = m, all methods yield a value of 20y0. However, when the specific activities in positions 1 and 2 of t’he glucose-6-P are determined with glucose-2-14C as substrate, the smaller the value of E-h, the more the apparent value is below 204”~ (Curce A). When specific activities in the carbon atoms of fructose-6-P (Curve B) or the triose-P ratio or specific yield of COZ from glucose-l and -6-14C are determined (Curve C), the apparent values are greater than 20$&

Necessity for Consideration of Nontriose Phosphate Pathways-- - When equilibration of hexose phosphates is incomplete, two types of nontriose phosphate pathways may have to be considered: (a) those originating from glucose-6-P and (b) those originating from fructose-6-P. In the model, the contribution represented by V3 has been considered to arise from glucose-B-P, as would be the cast in the formation of glycogen, trehalose, lactose, and pentose phosphates via the oxidative portion of the pentose cycle. Drainage from fructose-6-P, as during the synthesis of hexosamines and pentose phosphate formation via the nonoxida- tive portion of the pentose cycle, would result in an overestimation of the Embden-Meyerhof pathway contribution.

Unless NTP is large, a good approximation of the pentose cycle contribut,ion can be obtained by calculat’ing PC and not differ- entiating between EM and NTP. This is illustrat,ed by Figs. 5 and 6, where the effect of ?;TP on the randomization of label in position 2 is plotted. The ratios prove relatively insensitive

0.5

0 t 6 f ’ ’ I 0 I 2 3 4 5 IO W

EQUILIBRATION CONSTANT ( Emh)

FIG. 7. Apparent pentose cycle contributions on assumption of complete equilibration of hexose 6-phosphates. The apparent pentose cycle that would be calculated under an assumption of complete recycling (E h = m) when isotopic equilibration is ac tually incomplete is indicat.ed. Metabolism of the system is assumed to be actually 20th by the pent’ose cycle and 80°6 by the Embden-Meyerhof pathway. The apparent pentose cycle is calculat,ed from the equations of Kat,z and Wood (2 -4) wit.h t.hr “cx- perimental” data they have presented in examples in which complete recycling wasassumed. &rue A is obtained from determination of 14C in carbon atoms 1 and 2 of glucose-6-P (s,/sz) when glucose-2-W is substrate. Curve B is obtained from the W distribution in carbon atoms 1 and 2 of fructose-6-P (yJy2). Curve C is obtained from the ratio in W of triose-P or the ratio of specific C’OZ yields with glucose-l-W and -B-Cl4 as substrates.

to XTP. Even with a low value of E--h, 0.25 (Fig. 5), the effect of 30% nontriose phosphate pathway contribution on the ratios is smaller than the probable experimental errors of measurement. For example, from Fig. 5, if a tissue had a 20% pentose cycle and an XTP of 0.3, a ratio of 0. I2 would be expected in carbon atoms 1 and 2 of glucose-6-P with glucose-2-i4C as substrate. Were STP assumed to be zero, this ratio would be interpreted to indicate a pentose cycle contribution of 267;. The error becomes larger if the pentose cycle is greater than 20%. If isomerization is more extensive (E-h = 1 in Fig. 6), the ratios become more insensitive to changes in XTP. Thus, from Fig. 6, if PC = 0.2 and XTP = 0.4, the ratio observed in glucose-6-P would be 0.22. Were IjTP assumed to be zero, this ratio would give an apparent PC value of 0.24. PC and E-I, then can be determined even in the presence of large nontriose phosphate pathway contributions by procedures such as those illustrated in Examples 1 and 2, in which XTP is assumed to be absent. It is of course impossible then to distinguish between Embden-Meyerhof and nontriosc phosphate pathways contributions, and they would have to be lumped as “nonpentose cycle pathways.”

Sensitivity of kfethod for Determining Isomerization Rate-The procedures outlined offer a means of determining the rate of hexose 6-phosphate isomerieation in the intact cell. However, in many tissues, the enzymatic activity of phosphohexose isomerase has been shown to be high relative to most other enzymes (1, 13), so that in these tissues E-h may be expected to be large. As is apparent from Fig. 3, for a given PC, E-h at low values will markedly affect the distribution observed in a glucose-6-P derivative on incubation with glucose-2J4C. However, E-h may vary from 5 to infinity with only small and experimentally probably undetectable changes in distribution. Thus, from Fig. 3, when PC = 0.2 and E-h = 5, the ratio of carbon 1 to carbon 2


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


in glucose-6-P would be 0.27, and at E-h = m it would only in- crease to 0.29. Also, from the shape of the curves in Fig. 3, it is apparent that E-h has a lesser effect upon the randomization at small and large values of PC than at values near 0.5. Similar relationships exist between positions 1 and 6 of glucose-6-P with glucose-l ,6-W as substrate and E-h and PC. This is evident from Equation 30. Also triose-P ratios (Fig. 4) are insensitive to changes in E-h from 5 to infinity.

Experimentally, precise estimation of E-h may prove difficult even for values of E-h below 5. This is apparent from Equation 28 as applied to Example 1, where the term xl/x2 - yl/y~ in- volves the difference of two similar quantities and therefore produces an unstable or ill conditioned equation (3); i.e. small changes in one variable result in large changes in another. The effect of variation in xl/x2 for a fixed PC on the estimate of E-h can be seen from Fig. 3. For example, for PC = 0.30 and xdxz = 0.30, E-h is estimated at 1.75. For the same PC, a change in x1/x2 to 0.25 results in an E-h of 0.875 and a ratio x1/x2 of 0.35 corresponds to E-h = 6.125. The effect of variation in the triose-P ratios produces similar effects in the estimate of E-h as shown in Fig. 4. For PC = 0.30 and T, = 0.37, E-h is again equal to 1.75. If T, is changed to 0.32 and PC is held constant, E-h = 0.819, whereas if T, is changed to 0.42, E-h becomes 8.00.

SUMMARY

A general model for glucose metabolism is constructed encom- passing the pentose cycle, Embden-Meyerhof pathway, and nontriose phosphate pathways and allowing for incomplete equilibration of isotopically labeled glucose B-phosphate and fructose g-phosphate. Equations are derived for a specified model, and experimental data required for solution are indicated. By using specifically labeled hexoses, pathway contributions and the rate of hexose 6-phosphate isomerization can be estimated. This can be done when only the pentose cycle and Embden- Meyerhof pathway are present by adding glucose-2J4C or fructose-2-14C to the system and degrading glucose B-phosphate and fructose 6-phosphate or their derivatives. In the presence of a significant nontriose phosphate pathway contribution, information obtained with both substrates is employed for solution. Solution is also possible by measuring the incorporation of 14C of glucose-1-14C and -6J4C into triose phosphate derivatives or COZ. The assumptions and limitations in the procedures are presented. The model allows experimental tests by which its validity can be

determined. Nontriose phosphate pathway contributions, unless large, have little influence on the estimation of the pentose cycle.

Addendum-;A review has recently been published (14) de- scribing the various methods now available for estimations of pathway contributions. In the review, it is incorrectly stated that the transaldolase reactions will cause an error in calculations based on 14C yields in triose-P and COz. This is only true if there is metabolism via nontriose-P pathways. After the sub- mission of the review and the present paper it was recognized that carbon atoms 6, 5, 4 of a glucose-6-P derivative are indica- tors of the distribution in carbon atoms 1, 2, 3 of fructose-6-P. This is so, since carbon atoms 1, 2, 3 of fructose-6-P are introduced into carbon atoms 6, 5, 4 of glucose-6-P via the phospho- fructokinase, aldolase, triose-P isomerase, transaldolase, and phosphohexose isomerase reactions. Therefore, PC and E-h can be estimated solely from distributions in a glucose-6-P derivative. In support of this conclusion, if the ratios from carbon atoms 4, 5, 6 of the glucose unit of glycogen rather than those from the carbon atoms of glycerol are employed, the estimates in the accompanying paper (5) remain the same (unpublished results).

REFERENCES 1. KATZ, J., in H. RCHWEIGK AND F. T~RBA (Editors), Raclioac-

tive isotopes in physiology, diagnostics and therapy, Vol. I, Springer-Verlag, Berlin, 1961, pp. 705.-751.

2. KATZ, J.. AND WOOD, H. G., J. Viol. Chem., 236, 2165 (1960). 3. KATZ; J.; AND WOOD’, H. G.‘, J. Biol. Chek., 238, 517 (1963). 4. WOOD. H. G.. AND KATZ. J.. J. Biol. (‘hem.. 233. 1279 (1958). 5. LAND~F, B. fi., BND KATZ, i., J. Biol. Chek, 239, 697‘(196$. 6. MERLEVEDE, W., WEAVER, G., AND LANDAU, B. R., J. Clin.

Invest., 42, 1160 (1963). 7. LJFNGDAHL. L., WOOD, H. G.,RAcKER,E., AND COURI, D., J.

Biol. Chek., i36, 16i2 (196i). 8. SEGAL. S.. BERMAN. &f.. AND BLAIR, A.. J. Chin. Invest.. 40.

1263’(1961). ’ ’ I I I

9. HERS, H. (+., Le metabolisme du j”wctose, fiditions Arscia, Bruxelles, 1957.

10. QTJERNHOLM, R., AND WOOD, H. G., J. Biol. Chem., 236, 2757 (1960).

11. HANSEN, R. G., WOOD, H. Cr., PETERS, G. J., JACOBSON, B., B., AND WILKIN, J., J. Biol. Chem., 237,1034 (1962).

12. Ro&,I.A., KELLERMEYER, R., STJERNHOLM, R., AND WOOD, H. G.. J. Biol. Chem.. 237. 3325 (1962).

13. WEBER,‘(;., Proc. Sot. kzptl: Biol. ked.; 108,631 (1961). 14. WOOD, G. G., KATZ, J., AND LANDAU, B. R., Biochem. Z., 338,

809 (1963).


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

Bernard R. Landau, Glenn E. Bartsch, Joseph Katz and Harland G. WoodIsomerization of Hexose 6-Phosphate

Estimation of Pathway Contributions to Glucose Metabolism and of the Rate of

1964, 239:686-696.J. Biol. Chem.

http://www.jbc.org/content/239/3/686.citation

Access the most updated version of this article at

Alerts:

When a correction for this article is posted•

When this article is cited•

to choose from all of JBC's e-mail alertsClick here

http://www.jbc.org/content/239/3/686.citation.full.html#ref-list-1

This article cites 0 references, 0 of which can be accessed free at


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/content/239/3/686.citation

http://www.jbc.org/cgi/alerts?alertType=citedby&addAlert=cited_by&cited_by_criteria_resid=jbc;239/3/686&saveAlert=no&return-type=article&return_url=http://www.jbc.org/content/239/3/686.citation

http://www.jbc.org/cgi/alerts?alertType=correction&addAlert=correction&correction_criteria_value=239/3/686&saveAlert=no&return-type=article&return_url=http://www.jbc.org/content/239/3/686.citation

http://www.jbc.org/cgi/alerts/etoc

http://www.jbc.org/content/239/3/686.citation.full.html#ref-list-1

http://www.jbc.org/

estimation of pathwav contributions to glucose metabolism and of

Documents