Kinetic characterization of hexokinase isoenzymes from glioma cells: Implications for FDG imaging of human brain tumors

Nuclear Medicine and Biology 28 (2001) 107–116

Kinetic characterization of hexokinase isoenzymes from glioma cells: Implications for FDG imaging of human brain tumors Mark Muzia,b,*, Scott D. Freemana, Robert C. Burrowsa,b, Robert W. Wisemana,c, Jeanne M. Linka, Kenneth A. Krohna, Michael M. Grahamd, Alexander M. Spenceb a

Imaging Research Laboratory, Department of Radiology, University of Washington School of Medicine, Seattle, Washington 98195, USA b Department of Neurology, University of Washington School of Medicine, Seattle, Washington 98195, USA c Department of Biochemistry, University of Washington, Seattle, Washington 98195, USA d Department of Radiology, Division of Nuclear Medicine, University of Iowa, Iowa City, Iowa 52242, USA

Abstract Quantitative imaging of glucose metabolism of human brain tumors with PET utilizes 2-[18F]-fluorodeoxy-D-glucose (FDG) and a conversion factor called the lumped constant (LC), which relates the metabolic rate of FDG to glucose. Since tumors have greater uptake of FDG than would be predicted by the metabolism of native glucose, the characteristic of tumors that governs the uptake of FDG must be part of the LC. The LC is chiefly determined by the phosphorylation ratio (PR), which is comprised of the kinetic parameters (Km and Vmax) of hexokinase (HK) for glucose as well as for FDG (LC ⬀ (Kmglc 䡠 VmaxFDG)/(KmFDG 䡠 Vmaxglc). The value of the LC has been estimated from imaging studies, but not validated in vitro from HK kinetic parameters. In this study we measured the kinetic constants of bovine and 36B-10 rat glioma HK I (predominant in normal brain) and 36B-10 glioma HK II (increased in brain tumors) for the hexose substrates glucose, 2-deoxy-D-glucose (2DG) and FDG. Our principal results show that the KmGlc ⬍ KmFDG ⬍⬍ Km2DG and that PR2DG ⬍ PRFDG. The FDG LC calculated from our kinetic parameters for normal brain, possessing predominantly HK I, would be higher than the normal brain LC predicted from animal studies using 2DG or human PET studies using FDG or 2DG. These results also suggest that a shift from HK I to HK II, which has been observed to increase in brain tumors, would have little effect on the value of the tumor LC. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Hexokinase; Glioma; Glucose; 2-Deoxyglucose; [18F]Fluorodeoxyglucose; Positron emission tomography; Lumped Constant

1. Introduction FDG with PET was originally developed to image regional brain metabolism. This procedure has been extended to widespread use in clinical oncology of many tumor types, for detection, staging, assessing therapy response, and distinguishing tumor necrosis from recurrence. Our understanding of the biology of FDG metabolism and what it tells us about glucose metabolism in tumors has not kept pace with advances in clinical applications, most of which are based on non- or semiquantitative assessments of FDG uptake. As a hexose substrate, FDG is transported into cells by facilitated transport and then subsequently metabolized in a reaction involving hexokinase (HK), which produces a phosphorylated hexose. In normal brain, the phosphoryla* Corresponding author. Tel. ⫹1-206-543-3517; fax: ⫹1-206-6858100. E-mail address: [email protected] (M. Muzi).

tion of FDG is the rate limiting step in the accumulation of the phosphorylated product, FDG-6-phosphate (FDG6P) [1,44], which undergoes very slow degradation in the time frame of PET imaging procedures [24,39,45]. In contrast, when glucose is the substrate for HK, the metabolism of glucose-6-phosphate (G6P) continues in complex metabolic pathways through intermediary metabolism. 2-Deoxyglucose (2DG) acts similarly to FDG in its limited metabolism (see Fig. 1). The metabolic rates of tracer levels of FDG and 2DG are dependent on the native glucose concentration because they are reported to be competitive inhibitors for hexokinase [3,6,7]. Since phosphorylation of FDG is the rate limiting step that regulates FDG accumulation in normal brain, determination of the HK reaction rate gives an estimate of the overall rate of glucose metabolism. The regional metabolic fate of native glucose is difficult to trace through glycolysis, the pentose shunt and the many other pathways that interconnect each other in intermediary metabolism. Imaging with FDG can be used to infer the rate of

0969-8051/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S 0 9 6 9 - 8 0 5 1 ( 0 0 ) 0 0 2 0 1 - 8

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Fig. 1. The biochemical degradation of glucose begins with hexokinase producing glucose-6-phosphate (G6P) which continues to be metabolized in many pathways. In brain, glycolysis (Emben-Myerhoff pathway) is predominant over limited metabolism via the pentose shunt or glycogen production. The deoxyhexoses 2DG and FDG are metabolized by hexokinase and the phosphorylated product is trapped inside cells. It undergoes relatively slow degradation by glucose-6-phosphatase [24] or via the aldose reductase pathway [39].

reaction of native glucose with HK, from which the metabolic rate of glucose (MRglc) can be calculated with the correction provided by the LC term. Since the HK reaction is rate-limiting, the variation in the isoenzyme pattern of HK within normal brain versus brain tumors may alter tissue glucose metabolism [65]. Hexokinase is expressed as four isotypes that possess distinctly different kinetic properties and tissue distributions [20,55, 65]. Of the four different types of HK, brain contains primarily type I (95%), and to a lesser extent type II (5%), with a trace amount of type III [27,61,64]. The increased proportion of HK II, which is used as a marker for brain tumors [4,5,12,22,25,42,43], could alter the rate and affinity of HK for FDG and other hexose substrates. HK II shows at least a 3 to 4-fold increase in the Km of glucose over type I [16,20,40]. The 2-deoxyhexoses, 2DG and FDG, routinely used to image the metabolism of glucose have been assumed to possess similar kinetic parameters. If these parameters were not identical, using 2DG kinetic parameters in place of FDG values would result in an incorrect estimate of glucose metabolism. 2-Deoxyglucose (2DG) has been reported to have a Km ranging from 0.11– 0.27 mM for HK I [20,35, 37]. For isolated HK II, the Km of 2DG has a wide variation, 0.86 mM to 0.124 mM [20,37]. However, there is only a single published report for the Km of FDG for HK I, 0.200 mM [36] and none for HK II. For such a widely used substrate for measurement of regional in vivo glucose metabolism in humans, there is little information regarding the characterization of FDG as a substrate for HK. In order to relate the uptake of FDG in quantitative human imaging studies to brain energy metabolism, a proportionality constant relating the metabolic rate of glucose (MRglc) to the metabolic rate of FDG (MRFDG) is applied. This proportionality factor was formally defined as the Lumped Constant (LC) and incorporates the Michaelis-

Menton kinetic parameters of hexokinase (HK) for FDG and glucose along with their distribution volumes [55]. This relationship is: LC ⫽

MR FDG ␭ ⫽ 䡠 PR, MR Glc ␾

(1)

K m 䡠 V *max , K *m 䡠 V max

(2)

where PR ⫽

lambda (␭) is the ratio of the initial transfer rates of FDG and glucose, and phi (␾) is a constant that reflects the proportion of glucose-6-phosphatase activity. ␾ is assumed to be 1 due to low levels of glucose-6-phosphatase in normal brain [54]. The phosphorylation ratio (PR) incorporates the Michaelis-Menton constants for HK using FDG (denoted *) and glucose as substrates. The present study is a part of our comparative analysis of the kinetics of glucose, 2DG and FDG for HK I and HK II, and was conducted in order to deepen our insights into the metabolism of tumor tissue, gliomas in particular, and normal brain.

2. Materials and methods 2.1. Chemicals 2.1a. Sugars. 2-Deoxy-D-glucose (2DG), and D-glucose were obtained from Sigma (St. Louis, MO); 2-fluoro2-deoxy-D-glucose (FDG) was obtained from RBI (Natick, MA). 2.1b. Enzymes. Bovine hexokinase I (EC 2.7.1.1, BHK), beef heart lactate dehydrogenase (EC 1.1.1.27, LDH), yeast

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glucose-6-phosphate dehydrogenase (EC1.1.1.49, G6PDH), and rabbit muscle pyruvate kinase (EC 2.7.1.40, PK) were obtained from Sigma (St. Louis, MO). 2.1c. Chemicals. ATP disodium salt (equine muscle), crystalline phosphoenolpyruvate trisodium salt (PEP), yeast NADP⫹, NADH disodium salt, EDTA, MgCl2, barbital buffer, HEPES, Triton X-100, phenylmethylsulfonyl fluoride (PMSF), and dithiothreitol (DTT) were also from Sigma (St. Louis, MO). All sugars, enzymes and chemicals were of the highest grade and purity. 2.1d. Radiochemicals. The production of 1-[11C]-D-glucose followed the method of Link [34] as modified from Shiue [53] with additional modifications introduced by Dence [10]. The production of 2-[18F]-fluoro-2-deoxy-D-glucose followed the method of Hamacher [21]. 2.1e. Cell Culture. Dulbecco’s modified Eagle’s medium (DMEM) and fetal bovine serum (FBS) were obtained from Life Technologies (Grand Island, NY). 2.2. Cell studies The origin of the ethylnitrosourea-induced 36B-10 astrocytic F-344 rat brain tumor cell line has been reported in detail elsewhere [56]. The malignant glioma cells were cultured in 100 mm plastic tissue culture plates in DMEM medium containing 10% FBS in an humidified incubator (5% CO2, 95% air) and passaged every 4 – 6 days. For isoenzyme isolation, cells were harvested at confluence. A minimum of 1 ⫻ 108 cells were homogenized on ice in 1 ml Buffer A (45 mM HEPES, 5 mM EDTA, 1 mM DTT, 75 ␮g/ml PMSF, 1% Triton X-100, pH 7.4) using a Dounce homogenizer with a tight-fitting pestle. During all the procedures that follow the cell extract was maintained at 0 – 4°C unless otherwise indicated. After centrifugation of the homogenate at 37,500 ⫻ g for 30 minutes the supernatant was collected and processed as indicated in the following procedures. 2.3. Preparative chromatography The cell extract (1 ml) containing approximately 4 –5 ⫻ 10⫺8 U/cell of HK enzyme from approximately 1 ⫻ 108 cells was applied to an LKB TSK-DEAE-5PW (21.5 mm ⫻ 15 cm) anion exchange column equilibrated with Buffer A. The sample was injected onto the column and washed for 15 minutes at 4 ml/min with Buffer A. Hexokinase isoenzymes were eluted using a linear gradient over 60 minutes beginning with 100% Buffer A and ending with 100% Buffer B (Buffer A ⫹ 0.4 M KCl). Fractions were collected each minute and each tube was assayed for hexokinase activity as previously described [26]. Individual isoenzymes, indicated by the NADPH absorbance profile, were pooled and concentrated (Millipore Ultrafree 50,000 MW, Millipore, Bed-

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ford, MA). Confirmation of isoenzyme identity was performed by electrophoresis. Kinetic assessment of each partially-purified isoenzyme was performed with glucose, 2DG and FDG as substrates. 2.4. Isoenzyme electrophoresis Electrophoresis using ice cold barbital buffer (50 mM sodium barbital, pH 8.6, 10 mM glucose, 5 mM EDTA) was performed using 2 ␮l sample aliquots on 0.4 mm agarose plates (Innovative Chemistry, Marshfield, MA) in a 4°C horizontal cell (Ephortec IEF cell, Haake-Buchler, Saddle Brook, NJ) applying a 248 volt (22.9 V/cm) potential for 45 minutes. Agarose plates were coated with 0.5 ml Authentizyme HK staining reagent (Innovative Chemistry, Marshfield, MA), and were allowed to develop for 30 minutes at 37°C. The gels were cleared in a circulating distilled water bath for 15 minutes, air-dried overnight, and scanned for image analysis. 2.5. Enzyme kinetic assays Different approaches to measuring the Michaelis-Menton kinetics for glucose and other deoxy analogs were required since the analogs cannot be effectively coupled to the reduction of NADP in the standard reaction with G6PDH. We have compared spectometric and radiometric assays for following the rate of HK reaction with glucose. Kinetic characterization was assessed at pH 7.4 at 25°C. The kinetic characterization of hexokinase was determined by coupling the phosphorylation of glucose to the reduction of NADP via G6PDH using HK reagent prepared as described above and recording the change in absorbance at 340 nm using various initial concentrations of glucose ranging from 0.016 to 4.0 mM. The kinetics of HK isoenzymes with 2DG, FDG or glucose as substrates was followed by coupling the HK reaction to the oxidation of NADH via PEP, pyruvate kinase, and lactate dehydrogenase (PK-LDH assay) and recording the change in absorbance at 340 nm as previously described. Validation that NADH oxidation was directly proportional to hexokinase activity has been reported previously by varying hexokinase and the coupling enzymes, while observing the change in the reaction rate using 2DG, glucose [26], and FDG [36]. There was no increase in rate for glucose, 2DG and FDG when the coupling enzymes varied from 1 to 10 units, however the reaction rate doubled using twice as much HK. In order to cross check the spectrometric assessment of the Michaelis-Menton rate constant (Km) using coupled enzyme assay systems, a radioactive-stopped reaction procedure was used [18]. In the radiometric assay non-radioactive hexose (either glucose or FDG) was spiked with a positron-labeled hexose (1-[11C]-D-glucose and 2-[18F]FDG, respectively) and serial dilutions were performed giving a range of concentrations bracketing the reported Km (0.016 to 2.0 mM). The isoenzyme sample to be tested was mixed

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to a final concentration of 50 mM HEPES, 5 mM MgCl2, 5 mM ATP and 1 mM DTT buffer and various concentrations of substrate to start the reaction. Aliquots were withdrawn periodically and combined with 1 M glucose to inhibit metabolism of the radioactive substrate. A 100 ␮l sample of this mixture was immediately placed on a 0.5 ml Dowex AG1-X8 minicolumn (Bio-Rad, Richmond, CA) and washed with 5 ml 10 mM HEPES buffer pH 7.4 which elutes the hexose and retains the phosphorylated product. Columns were counted in a gamma counter, after which initial velocities were measured and Km values were calculated. Initial velocities in U/min for the kinetic reactions were calculated by the method of linear least squares [47]. Michaelis-Menton constants, Km and Vmax, were determined by optimization of the non-linear model Vi ⫽ ([S]*Vmax)/(Km ⫹ [S]) using the method of Marquardt [46] without individual point weighting. Group values are reported as the mean ⫾ SEM. Comparisons between groups were assessed by either Student’s t-test or paired t-test for one or two samples, respectively.

3. Results Two peaks of HK activity were observed from samples of 36B-10 cell extract typically at a 60/40 ratio of HK I to HK II (Fig. 2). The resulting isoenzyme peaks from the HPLC separation (Fig. 2a) were identified by electrophoresis (Fig. 2b) by applying each isoenzyme alone and an aliquot of the original 36B-10 cell extract. Each isoenzyme co-migrated with its counterpart from the original sample. HK I typically eluted at 0.13 M KCl and HK II eluted at 0.23 M KCl. The Km estimates for the three sources of HK (BHK, HK I, HK II) from the two spectrometric methods (G6PDH, PK-LDH) were verified with several determinations using the radiometric assay described in the Methods using glucose and FDG as substrates. There were no statistical differences among all of the possible comparisons for the estimation of Km with the G6PDH assay, the PK/LDH assay, and the radiometric assay (G6PDH vs PK-LDH, G6PDH vs Rad, PK-LDH vs Rad) for either glucose or FDG as substrates using bovine HK (BHK). Multiple t-tests were performed for HK I and HK II with similar results of no statistical differences ( p ⬎ 0.5) between assay types for the same source enzyme and substrate. Representative progress curves demonstrating the quality of the data for the HK assays, from which initial velocity values were determined for various substrate concentrations, are shown in Fig. 3, while curve fits for a sample dataset appear in Fig. 4. Each isoenzyme was examined with glucose as substrate using the G6PDH assay and the PK/LDH assay. Since the 2-deoxyhexose analogs cannot be effectively coupled to the reaction with G6PDH, 2DG and

Fig. 2. a) DEAE ion-exchange HPLC chromatogram of 36B-10 cell extract applied to a semipreparative column (21.5 mm ⫻ 15 cm) and eluted using a gradient from 0 to 0.4 M KCl. The volume of each fraction was 4 ml. Each sample was assessed for glucose-phosphorylating activity by an assay observing NADPH at 340 nm described in the Methods. b) Electrophoresis of each HPLC peak (Fx 20 ⫽ fraction 20, Fx 35 ⫽ fraction 35) was performed by applying 2 ␮l to a 1% agarose gel wicked in barbital buffer. After electrophoresis HK activity was visualized by enzymatic staining (Authentikit, Innovative Chemistry, Marshfield MA).

FDG kinetics were determined spectrometrically only by the PK/LDH assay. The initial velocity for each substrate concentration was estimated from the progress curves by using a non-linear optimization method described above and typically fit the data with less than 2% residual error. For comparison of different substrates, double-reciprocal plots of BHK, HK I and HK II are presented in Fig. 5. The data in these plots were normalized such that the maximal velocity of glucose is 1.0 to facilitate data interpretation. Generally, the Km of glucose was lower than FDG or 2DG, with 2DG possessing the highest Km for any set of assays regardless of the enzyme source. In no assay was there more than one substrate for hexokinase. The 36B-10 isoenzyme Km values were lower for HK I

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Table 1 Three Assay systems were applied to the estimation of Km using glucose and FDG substrates for BHK, HK I, and HK II Source/Assay Bovine HK Bovine HK Bovine HK HK I HK I HK I HK II HK II HK II

FDG (mean ⫾ SEM)

Glucose (mean ⫾ SEM) Radioassay G6PDH PK-LDH Radioassay G6PDH PK-LDH Radioassay G6PDH PK-LDH

32 ⫾ 3 35 ⫾ 2 34 ⫾ 3 39 ⫾ 1 39 ⫾ 3 39 ⫾ 5 129 ⫾ 10 130 ⫾ 8 137 ⫾ 14

n⫽4 n ⫽ 10 n ⫽ 10 n⫽2 n ⫽ 13 n⫽7 n⫽2 n ⫽ 13 n⫽6

62 ⫾ 10

n⫽4 N/A

55 ⫾ 4 77 ⫾ 2

n⫽8 n⫽4 N/A

68 ⫾ 5 166 ⫾ 15

n ⫽ 12 n⫽3 N/A

174 ⫾ 14

n ⫽ 13

The values for Km (␮M) are presented as mean ⫾ SEM. The radioassay, which uses 1-[ C]glucose or 2-[ F]FDG, along with the two spectrometric assays involving G6PDH and PK-LDH are described in the Methods. Due to the complexity, cost and effort, the radioactive assay was used only as a validation for the more straightforward spectrometric assays. 11

than HK II for the three hexoses examined ( p ⬍ 0.001, paired t-test, n ⫽ 27). The Km of glucose for BHK, HK I, and HK II were all lower than the Km of FDG or the Km of 2DG (FDG vs glucose p ⬍ 0.002 n ⫽ 26, 2DG vs glucose p ⬍ 0.001 n ⫽ 27, both paired t-tests). Also the Km of FDG was lower than the Km of 2DG ( p ⬍ 0.001, paired t-test n ⫽ 27) for both isoenzymes (Table 2). Thus for both HK I and HK II the Km of glucose ⬍ Km of FDG ⬍⬍ Km of 2DG. The Vmax ratio of HK I for 2DG to glucose, which has been reported to be unity [20,55], was statistically greater than 1 for BHK (1.533 ⫾ 0.067, p ⬍ 0.003 n ⫽ 7), HK I (1.384 ⫾ 0.134, p ⬍ 0.02 n ⫽ 10), and HK II (1.261 ⫾ 0.082, p ⬍ 0.05 n ⫽ 10). However, the Vmax ratio for FDG to glucose was approximately unity for BHK (0.957 ⫾ 0.050) and HK I (0.923 ⫾ 0.051), but was significantly less than 1 for HK II (0.602 ⫾ 0.070, p ⬍ 0.001 n ⫽ 10). The PR values (Table 3) for 2DG determined by our laboratory for Bovine HK I (0.336 ⫾ 0.013) and glioma cell HK I (0.319 ⫾ 0.049) were both similar to the value of 0.3 reported by Sols [55] for rat brain HK I. The PR of 2DG for HK II (0.274 ⫾ 0.027) was statistically indistinguishable from the PR values for HK I or BHK. In contrast, the PR values for FDG were 0.617 ⫾ 0.039 for BHK, 0.593 ⫾ 0.089 for HK I, and 0.424 ⫾ 0.046 for HK II. These values have never before been reported by this method, and were greater than the PR values of 2DG ( p ⬍ 0.02 n ⫽ 27). The PR for HK I was not statistically different than the PR of HK II for either 2DG or FDG (paired t-test n ⫽ 16).

4. Discussion The gradient separation method for the 36B-10 cell extract via chromatography and electrophoresis resulted in isoenzyme profiles similar to other reports [65] and to our prior work on this cell line [26]. Since the spectrometric assessment of the Km and Vmax for FDG and 2DG could only be performed using the PK-LDH assay system, it was

18

necessary to validate the kinetic parameters by an independent assay. With glucose as substrate for HK, the two different spectrometric assays and the radiometric assay were statistically identical in their estimation of Km for a specific source of HK ( p ⬎ 0.5 for all comparisons). The validation of HK kinetic parameters with the PK-LDH assay using FDG and [18F]FDG in the radiometric assay showed more variability, but similar outcome for all HK groups ( p ⬎ 0.375). The increased variability may reflect an increased error in the estimation of Km for a substrate with lower affinity for HK than glucose. Thus, the Km for each substrate was independent of the assay system. Due to the complexity, cost and effort associated with short-lived radioisotopes, the radioactive assay was used only as a validation for the more straightforward spectrometric assays. The estimation of glucose Km for HK I with a range of 25 to 60 ␮M with a mean of 40 ␮M was consistent with other literature values [8,17,20,32,63]. A considerably different estimate of the glucose Km was reported by Sols [55]. Their value of 8 ␮M was probably due to the limited sensitivity of the available analytical methods. The reported values of the Km of glucose for HK II also varies widely between 28 and 330 ␮M [8,17,20,28,63], but our value of 131 ␮M is consistent with most of the values using various sources of HK II. The only reports on Km values of 2DG for HK II [20,37] bracketed our data range. These different values reflect assay conditions, purity of isoenzyme preparations, and modeling method for the estimation of the Michaelis-Menton constants. The observation that Km of Glucose is less than Km of 2DG for both HK I and HK II is similar to other reports [20,32,55,59]. With a mixture of yeast HK isoenzymes, Bessel [7] reported the Km of FDG was slightly greater than the Km of glucose as we would predict from our observations of the mammalian isoenzymes. The only account of Km for FDG using a similar source of enzyme (Bovine HK) and assay conditions [36] was 2-fold higher (200 ␮M) than any of our 28 assays (43 to 101 ␮M). It is difficult to explain this discrepancy, as their assay conditions were nearly iden-

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Fig. 3. a) A representative time-activity curve of a kinetic assay using G6PDH. The assay conditions were 50 mM HEPES, 5 mM MgCl2, 5 mM ATP, 1 mM NADP, 1 U G6PDH, 1 mM DTT at pH 7.4, 25°C with substrate concentrations ranging from 2.0 (■) to 0.016 (F) mM in a volume of 1 ml. b) A representative time-activity curve of a kinetic assay using PK and LDH. The final conditions were 50 mM HEPES, 5 mM MgCl2, 5 mM ATP, 0.4 mM NADH, 5 mM PEP, 10 IU PK, 10 IU LDH, 1 mM DTT at pH 7.4, 25°C with substrate concentrations ranging from 2.0 (■) to 0.016 (F) mM in a volume of 1 ml. c) A representative time-activity curve of a kinetic assay using [18F]FDG. The assay conditions were 50 mM HEPES, 5 mM MgCl2, 5 mM ATP, 1 mM DTT at pH 7.4, 25°C with substrate concentrations ranging from 1.0 (■) to 0.16 (F) mM in a volume of 1 ml. The three assay activity curves use glucose as a substrate with HK I.

tical to those reported here with the exception that their assays were performed in the presence of 0.1 M KCl. The variation of salt in the reaction buffer for hexokinase assays has been reported to be a major confounding variable that leads to a wide variation in estimations of kinetic parame-

Fig. 4. Representative BHK reaction progression curves for each substrate from a single dataset, using the PK-LDH assay. Reaction velocity values (F) were normalized to glucose maximal velocity. The curve fits (—) were determined by a model solution for the function Vi ⫽ ([S] 䡠 Vmax)/(Km ⫹ [S]) using the optimization method of Marquardt [46].

ters [14]. There are no other reported measurements of the Km for FDG using HK II with which to compare our present values. Glucose Km and FDG Km are much closer in value than they are to 2DG Km for all three enzyme preparations. These kinetics suggest that metabolism of 2DG is different from FDG and that FDG metabolism more closely approximates glucose metabolism than does 2DG metabolism. This may reflect the structures of the hexoses and their interaction in the HK catalytic binding pocket involving the hydrogen-bond at carbon-2 [7,32,65]. The Vmax ratio is important in the calculation of the PR, and has a direct influence on the value of the LC. The value

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Table 2 Kinetic results on the characterization of Bovine HK I, isolated HK I and HK II with respect to Glucose, 2DG and FDG as substrates are presented as a mean ⫾ SEM

Km Glc Km FDG Km 2DG VmR FDG VmR 2DG

Type I Bovine HK n⫽7 (mean ⫾ SEM)

Type I 36B-10 Cells n ⫽ 10 (mean ⫾ SEM)

Type II 36B-10 Cells n ⫽ 10 (mean ⫾ SEM)

33 ⫾ 1 51 ⫾ 2 152 ⫾ 9 0.957 ⫾ 0.052 1.533 ⫾ 0.067

40 ⫾ 4 68 ⫾ 6 180 ⫾ 18 0.923 ⫾ 0.051 1.384 ⫾ 0.134

131 ⫾ 9 174 ⫾ 15 613 ⫾ 38 0.602 ⫾ 0.070 1.261 ⫾ 0.082

Michaelis-Menton constants were determined from non-linear model optimization with units of ␮M for Km. The ratio of the Vmax for an alternate hexose to the Vmax of glucose (VmR) gives an estimation of the relative velocity of the 2-deoxyhexoses for the HKs.

Fig. 5. Double-reciprocal plots for Glucose (a), FDG (b) and 2DG (c) using Sigma bovine HK (F), HK I (Œ) and HK II (■). The curve fits for BHK (—), HK I (– –) and HK II (- - - .) were determined by a model solution for the function Vi ⫽ ([S] 䡠 Vmax)/(Km ⫹ [S]) using the optimization method of Marquardt [46] and plotted in double-reciprocal format. The values of initial velocity for each substrate concentration were determined by the method of linear least squares from the reaction activity profile and normalized to glucose Vmax. These plots represent the average Km and normalized Vmax for the 3 different hexokinases for three different hexose substrates all using the PK-LDH assay system described in the Methods.

of the Vmax ratio of FDG for HK I reported by Machado de Domenech [36], (Vmax ratio 0.9), was within the statistical bounds of our values. FDG Vmax was significantly different than glucose Vmax for HK II, which may indicate that the active site that binds hexose substrates on HK II is different than HK I [2]. The Vmax ratio for 2DG was relatively constant for BHK, HK I, and HK II, but was not unity, as has been assumed in simple Km ratio assessments of the PR in the past [26]. Ureta [61,62] reported values for the 2DG Vmax ratio of 1.4, nearly identical to our result.

The Vmax ratios were not the same for FDG and 2DG. The FDG Vmax ratio was approximately 1, but greater than 1 for 2DG. This probably reflects the different hydrogen bond interactions at the active site with the OH on glucose, the F of FDG or the H of 2DG at the carbon-2 position [20,32,65]. Equations 1 and 2 show the relationships of Km and Vmax for glucose and deoxyhexose comprising the PR. Although there are many conditions that are different between in vitro and in vivo experiments, it is worthwhile to compare the relative metabolism of glucose and deoxyhexoses through the PR and LC values. The PR is a critical component of the LC, which is necessary for calculating the MRglc using FDG or 2DG. The PR for FDG has been estimated by Crane [9] from in vivo rat experiments as 0.55 and agreed well with our determinations. Using our PR values and the values of ␭ that we previously reported for normal rat brain [26], the rat normal brain LC is 0.510 ⫾ 0.077 for 2DG similar to Sokoloff’s [54] in vivo value of 0.464 ⫾ 0.099. The normal rat brain LC for FDG would be 0.949 ⫾ 0.266 which is within the range of several other estimates of the normal brain FDG LC in humans [9,19,23, 31,57], but is much larger than the value typically applied [45]. The PR of FDG is statistically different from the PR of

Table 3 The phosphorylation ratio (PR) for 2DG and FDG are calculated from the Km and Vmax values as described in equation 2

Bovine HK I 36B-10 HK I 36B-10 HK II

PR 2DG n ⫽ 7 (mean ⫾ SEM)

PR FDG n ⫽ 7 (mean ⫾ SEM)

0.336 ⫾ 0.013 0.319 ⫾ 0.049 0.274 ⫾ 0.027

0.617 ⫾ 0.039 0.593 ⫾ 0.089 0.424 ⫾ 0.046

The PR is a critical component of the LC which is used as a correction factor for relating the metabolism of deoxyglucose analogs to native glucose metabolism. The PR of 2DG was similar for the three HK groups as was FDG. However, the PR of FDG was greater than the PR of 2DG for all groups ( p ⬍ 0.02 n ⫽ 27).

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2DG ( p ⬍ 0.01), suggesting that the use of 2DG parameters for calculating the LC used in the estimation of the MRglc for FDG PET studies is inappropriate. Our observations of an elevated FDG LC for contralateral brain in brain tumor patients, 0.86 ⫾ 0.14, [57] and normal brain, 0.85 ⫾ 0.12 [19], with respect to prior reports on human PET imaging studies, are consistent with our prediction of the LC based on the FDG kinetic constants reported in the present paper. The most widely applied methods for determining the MRglc from FDG imaging studies in humans is through fitting the observed kinetic data with a model of FDG metabolism and applying previously determined kinetic constants from dynamic FDG studies in humans and an indirect estimate of the LC as 0.42 [45]. This prevailing method results in essentially one-half of our estimate of the FDG LC and thus leads to an over estimation of the actual glucose metabolic rate in PET imaging analysis. Gjedde et al. [15] have correctly concluded that the in vivo affinities of hexokinase for FDG or 2DG and glucose are subject to competition in PET studies, and that their relative affinity must vary with glucose concentration. In an attempt to simplify the modeling of human dynamic PET data by constraining the FDG model within physiological limits, they used the rat 2DG PR of 0.3 to estimate the LC in human PET brain experiments with the other deoxyhexose, FDG [15,30]. It would be more rigorous to use an FDG PR to estimate the LC for FDG than the 2DG PR, which is of about half that of FDG. The outcome of these modeling efforts could vary by as much as 2-fold, had they applied the appropriate kinetic values for FDG. Reivich et al. [49] determined the in vivo LC in an equilibrium-based study for FDG and 2DG in human brain using PET. They predicted the LC based on the MRdeoxyhexose from the asymptotic rise in the brain extraction fraction for FDG or 2DG relative to historic measurements of MRglc from earlier reports. Their conclusion was that the FDG LC (0.52) was less than the 2DG LC (0.56). Their 2DG LC was within statistical error of the estimate presented here, but their FDG LC was about half the value predicted from our in vitro determinations. Of the many differences between in vitro measurements and human PET imaging, some of the variability between these estimates must lie with their assumptions that there was no dephosphylation of FDG, an equilibrium between blood and brain was achieved, and that a 20% impurity of [18F]fluorodeoxymanose had no effect on the determination of the LC. Lear and Ackermann [33] among many others [9,13,38, 48,52] determined the in vivo LC ratio of FDG to DG in normal rat brain by various techniques arriving at values that ranged from 1.25 to 1.63. Using PR values determined here coupled with rat distribution volumes for FDG and 2DG [33,54] the LC ratio of FDG to DG would be approximately 1.4. In human gliomas we have observed an elevation in the FDG lumped constant compared to contralateral brain [57].

It is reasonable to hypothesize that tumor tissue, which has a higher proportion of HK II, possesses a different lumped constant than normal tissue. For HK II, which may reach 20% in human gliomas [41], the Kms for glucose, 2DG, and FDG are all greater than with HK I ( p ⬍ 0.001). However, the Km ratio of 2DG (0.242 ⫾ 0.036 for HK I, 0.227 ⫾ 0.028 for HK II) and FDG (0.623 ⫾ 0.077 for HK I, 0.772 ⫾ 0.036 for HK II) and, concordantly, the PR ratio of 2DG to FDG (0.647 ⫾ 0.136 for HK I, 0.663 ⫾ 0.089 for HK II) are not significantly different between HK I and II ( p ⬍ 0.05 paired t-test n ⫽ 10). If the Michaelis-Menton constants for HK were the only determinant of the LC, a shift to HK II would maintain or lower the tumor LC, assuming that there was no change in ␭. Thus, it is unlikely that a change in isoenzymes alone accounts for the observation via FDG PET imaging of an increased LC in human gliomas. It has been reported that the compartmentation of HK between mitochondria and cytosol results in a change in HK Km for glucose and FDG [11,29,40,51,58]. The binding of HK to mitochondria changes the Km for Glucose and FDG in different ways. Russell [51] has shown that the Km for HK II of FDG increases 8 fold with binding to the mitochondria whereas the Km of glucose decreases slightly. The distribution of intracellular HK is governed by the metabolic state of the cell, where intracellular levels of metabolites (G6P, ATP, Pi) regulate mitochondrial binding of HK [50,60]. Oudard [41,42] has reported that in human brain tumors approximately 50% of HK is mitochondrially bound compared to 95% for normal brain [65]. The substrate specificity of HK for FDG, 2DG, and glucose coupled with the binding or unbinding of HK I and II on active mitochondria may account for the increase in the LC in brain tumors. Studies of this hypothesis are currently underway in our laboratory. In summary, our results show that (1) the hexose substrates, glucose, FDG and 2DG have distinctly different Km’s for both HK I and HK II, (2) the kinetic parameters of FDG are closer to those of glucose than 2DG, and (3) the LC of FDG predicted from our detailed enzyme kinetic studies would be 2-fold higher than the LC of the other deoxyhexose, 2DG, in either normal or neoplastic brain tissue. The elevated PR and thus LC is consistent with our prior work on PET imaging of normal brain [19]. The increased proportion of HK II in human gliomas does not explain an elevated FDG LC in these tumors. In this study we have only addressed the effects of substrate and soluble isoenzymes on the PR and LC. The application of this data to an in vivo situation, where many physiological parameters are quite different, may not result in the same LC due to some difference in the metabolism of the deoxyglucoses relative to glucose. It can be hypothesized that a shift in the tumor phenotype to more HK II may affect the LC by other mechanisms affecting hexokinase kinetics such as mitochondrial binding. Although our primary interest is in gli-

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omas, the insights we gain in these malignancies may well pertain to other types of cancer.

Acknowledgments This work was supported in by a grant from the National Institutes of Health to (Grant No: P01-CA42045-14). The authors would like to thank Dr. David Mankoff for his helpful suggestions and discussions.

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