Transient State Kinetics of Enzyme IICBGlc, a Glucose Transporter of the Phosphoenolpyruvate Phosphotransferase System of Escherichia coli

During translocation across the cytoplasmic membrane of Escherichia coli, glucose is phosphorylated by phospho-IIAGlc and Enzyme IICBGlc, the last two proteins in the phosphotransfer sequence of the phosphoenolpyruvate:glucose phosphotransferase system. Transient state (rapid quench) methods were used to determine the second order rate constants that describe the phosphotransfer reactions (phospho-IIAGlc to IICBGlc to Glc) and also the second order rate constants for the transfer from phospho-IIAGlc to molecularly cloned IIBGlc, the soluble, cytoplasmic domain of IICBGlc. The rate constants for the forward and reverse phosphotransfer reactions between IIAGlc and IICBGlc were 3.9 × 106 and 0.31 × 106 m–1 s–1, respectively, and the rate constant for the physiologically irreversible reaction between [P]IICBGlc and Glc was 3.2 × 106 m–1 s–1. From the rate constants, the equilibrium constants for the transfer of the phospho-group from His90 of [P]IIAGlc to the phosphorylation site Cys of IIBGlc or IICBGlc were found to be 3.5 and 12, respectively. These equilibrium constants signify that the thiophospho-group in these proteins has a high phosphotransfer potential, similar to that of the phosphohistidinyl phosphotransferase system proteins. In these studies, preparations of IICBGlc were invariably found to contain endogenous, firmly bound Glc (estimated K′D ∼10–7 m). The bound Glc was kinetically competent and was rapidly phosphorylated, indicating that IICBGlc has a random order, Bi Bi, substituted enzyme mechanism. The equilibrium constant for the binding of Glc was deduced from differences in the statistical goodness of fit of the phosphotransfer data to the kinetic model.

(110 TBq/m mol) (PB10168; Amersham Biosciences); and D-[6-3 H]glucose (1.9 TBq/mmol) (NET 100C; PerkinElmer Life Sciences) were purchased from the indicated sources. All buffer salts and other reagents were of a purity typical for research reagents from standard commercial sources. The pH of all buffers is reported at the temperature and concentration at which they were used.
Assays for Glc and for the Binding of Glc to Escherichia coli Membranes-Supplemental data describe the four methods used to characterize the Glc found "contaminating" both highly purified IICB Glc and membrane suspensions and for measuring the binding of Glc to these membranes. These are described in detail in supplemental data. For the routine assay of Glc in membrane suspensions being prepared for rapid quench experiments, two sources of data were used. The first was the hexokinase assay using adenosine 5Ј-[␥-32 P]triphosphate described in supplemental data. The second was the actual experimental results of the rapid quench assay when conducted with a stoichiometric excess of the phosphodonor, [ 32 P]IIA Glc . 4 The quantity of Glc measured by the two methods was similar.
Bacterial Strains, Plasmids, and Growth Media-All strains were grown on Luria-Bertani broth containing the required antibiotics and inducers. E. coli strain BL21(DE3) (F Ϫ ompT hsdS B (r B Ϫ m B Ϫ ) gal dcm (DE3)) (Novagen) was used as the host for plasmid pJBH, which encodes the IIB Glc -His 6 gene fragment (a generous gift of Prof. B. Erni, University of Basel) and was grown as described (7). E. coli strain ZSC112⌬G (⌬ptsG::cat manZ glk) from which the chromosomal gene for IICB Glc was deleted (7) was used as the host for plasmid pTGH11 (encoding IICB Glc -His 6 ) (both also gifts from B. Erni) for the preparation of membranes and for the purification of IICB Glc -His 6 . E. coli strain ZSC112⌬G was also used as the host for plasmid pCB30 (encoding wild type IICB Glc ) (9) for the preparation of membranes. Preparation of Washed Membranes-Cultures of 3 liters, at an A 600 of 0.6 -1.0, were harvested by centrifugation, washed twice with 50 mM Tris/Cl Ϫ buffer (pH 7.5) containing 150 mM KCl, and finally resuspended in this solution in a volume equal to 1% of that of the original culture. To discharge phospho-groups from the PTS proteins, 10 mM methyl ␣-glucoside and 10 mM KF were added to the final cell suspension, which was incubated at room temperature for 15 min (10) and then frozen at Ϫ80°C. After thawing, the cells were homogenized by two passages through a French pressure cell (Spectronic Instruments) at 110 megapascals, the homogenate was centrifuged at 5,600 ϫ g for 15 min, and the supernatant was centrifuged at 370,000 ϫ g for 2 h. The particulate fraction was resuspended in 10 mM Tris/glycine buffer (pH 8.9), 1 mM dithiothreitol (11) to the original volume of the homogenate and centrifuged again; the high speed centrifugation was repeated a third time unless otherwise indicated. The membranes were resuspended in 1 ml of the same buffer per g of original wet weight of cells and frozen in aliquots at Ϫ80°C.
The final membrane preparations contained variable quantities of Glc, and its concentration increased slowly upon storage or incubation and during the 1-3 h required to complete a rapid quench experiment (supplemental data). Whereas the source of Glc was not identified, a procedure was developed that eliminated the increase in Glc concentration but did not significantly affect the activity of the enzyme, reducing it by less than 20% as determined by PTS sugar phosphorylation assays. The method was to incubate the preparation in a dialysis cassette (Pierce Slide-A-Lyzer) versus Tris/glycine buffer, pH 8.9, 1 mM dithiothreitol or 5 mM ␤-mercaptoethanol, and 0.05% sodium azide at 37°C for 15 h and continued for several hours at 4°C.

Kinetic Properties of Endogenous Glc in Membrane Preparations-
The concentration of endogenous Glc after treating the membrane preparations as described above was variable but was always in the same range as the concentration of IICB Glc . Modeling the kinetics of Reactions V, VI, and VII (Fig. 2, Scheme I) required an understanding of the kinetic properties of this pool of endogenous Glc as well as decisions about how to model the kinetics of Reactions V(t), VI(t), and VII(t) when [ 3 H]Glc was added to the syringe containing the solution of [ 32 P]IIA Glc . These methods are described in supplemental data on kinetics.
General Methods-Assays for the PTS proteins by measuring the rate of sugar phosphorylation were performed as described (9,12). The method of Bradford (13) was used for soluble proteins; the reagent was from Bio-Rad. The modification of the method of Lowry by Markwell et al. (14), calibrated as previously described (6), was used for IIA Glc and for membrane proteins.
The concentration of HPr or IIA Glc was measured by using the lactate dehydrogenase coupled assay (12) (using homogenous auxiliary proteins), which measures the quantity of protein that can accept a phospho-group from PEP. The concentrations of HPr or IIA Glc estimated from the specific activity of the [ 32 P]PEP agreed with the results of the lactate dehydrogenase assay within 5%. IIB Glc was quantified by three methods: (a) by solutions of the protein, purified to apparent homogeneity, were thoroughly dialyzed and analyzed for nitrogen by the method of Jaenicke (15); (b) quantitative phosphorylation of the protein using an excess of [ 32 P]PEP (of accurately known specific activity) and catalytic quantities of Enzyme I, HPr, and IIA Glc ; (c) by the lactate dehydrogenase assay (12). When all three methods were applied to the same sample, the results agreed to within 10%. IICB Glc , both purified and in membranes, was quantified by two methods. (a) The sample was assayed for its activity in PEP driven sugar phosphorylation, using a range of concentrations of IIA Glc . These data were used to calculate the V max , which was converted to the concentration of the IICB Glc protein by using the specific activity of the homogenous enzyme (97 mol of sugar phosphate/min/mg of IICB Glc ) (9). (b) IICB Glc was also quantified by quantitatively labeling the protein in membrane suspensions with [ 32 P]PEP of accurately known specific activity (1-3 TBq/mol) (6) as follows. A mixture of 50 mM potassium phosphate buffer (pH 7.5), 5 mM MgCl 2 , 25 nmol of [ 32 P]PEP, 10 pmol of enzyme I, 7 pmol of HPr, 15 pmol of IIA Glc , and ϳ150 pmol of IICB Glc in a volume of 100 l was incubated at room temperature for 15 min. It was then quenched with 50 l of 0.6 M KOH and analyzed by gel filtration chromatography by the same methods used for rapid quench samples (see below). When applied to three membrane preparations, the two methods agreed to within 15%. Membranes prepared from ZSC112⌬G exhibited insignificant activity in the PEP-driven sugar phosphorylation assay as well as insignificant labeling with [ 32 P]PEP.
Purification of Proteins-Enzyme I, HPr, and IIA Glc were separately overproduced in cells carrying the relevant plasmids. The proteins were purified by the methods used previously (6). IIB Glc -His 6 was purified by the method of Buhr et al. (7), except that a Superose 12 HR 10/30 column (Amersham Biosciences) was substituted for Sephadex G75. The final preparations were apparently homogeneous as judged by SDS-PAGE. IICB Glc -His 6 was purified using modifications of the method of Waeber et al. (11); a Superose 12 HR 10/30 column was used, but neither Glc nor methyl ␣-D-glucopyranoside was added to solutions. Before being employed in either rapid quench experiments or in the PTS sugar phosphorylation assay, the IICB Glc was activated, except as noted, by mixing with an equal volume of a solution of lipid/detergent mixed micelles (5 mg/ml dioleoylphosphatidyl glycerol, 1 mg/ml sodium lauroyl sarcosinate), as described by Bouma et al. (9).
Synthesis of [ 32 P]PEP-The enzymatic synthesis (16) was performed with the modifications described previously (6). The purification by anion exchange chromatography was further modified by the substitution of KCl for triethylamine/H 2 CO 3 as the eluant. We suspect that triethylamine or a contaminant in it occasionally interferes with the phosphotransfer reactions (data not shown). To stop the enzymatic reaction, 25 l of 20% (v/v) Norite A suspension was added to the reaction mixture. The Bio-Rad AG1-x8 column was equilibrated with 10 mM BisTris/Cl, pH 6.0, which was also a component of all of the eluant solutions. The reaction mixture (including the Norite A) was placed onto the column, which was then washed with 5 ml of the buffer, and the P i was eluted with 5 ml of 0. The columns used to fractionate the phosphorylation mixtures were equilibrated with 20 mM carbonate/bicarbonate (pH 9.5) buffer containing 1 mg/ml bovine serum albumin. The specific activity of all four phosphoproteins ranged from 10 to 40 TBq/mol, with emphasis on the accuracy of the specific activity of the [ 32 P]PEP (6).

Stability of [ 32 P]IIB Glc and [ 32 P]IICB Glc under Quench
Conditions-[ 32 P]IIB Glc and [ 32 P]IICB Glc were isolated as described and stored at Ϫ80°C in 20 mM carbonate/bicarbonate buffer (pH 9.5). Tests of the effect of pH on the rate of hydrolysis of the phospho-group were made by diluting 10 l of 0.5 M [ 32 P]IIB Glc solution into 3.5 ml of buffer or diluting 100 l of 0.33 M [ 32 P]IICB Glc into 4.0 ml of buffer. All equipment and vessels were pretreated with bovine serum albumin to minimize adsorption of protein. The buffers were as follows: pH 2, 0.1 M HCl/KCl; pH 3.8, 50 mM citric acid/sodium citrate; pH 6.0 and pH 8.1, 50 mM KH 2 PO 4 /K 2 HPO 4 ; pH 10.1, 50 mM Na 2 CO 3 /NaHCO 3 ; pH 12, 25 mM Na 3 PO 4 ; pH 13, 0.1 M NaOH; pH 14, 1 M NaOH; and pH 14.3, 2 M NaOH (the last three solutions were prepared from fresh, commercial 2 M NaOH standard solution). The mixtures were incubated at 23°C for 5 min to 4 h and filtered through 23-mm diameter polyvinylidene difluoride transfer membranes (Millipore Corp.) in a vacuum apparatus that allowed collection of the filtrate; both the filter and the filtrate were counted to ensure quantitative recovery of the radioactivity. Tests of the membrane with [ 32 P]P i showed that the background was negligible and that washing of the filter was not required. Other controls showed that protein adsorption to the membranes was quantitative.
The high rate of hydrolysis above pH 13 (see "Results") made use of a quench solution containing 1 M KOH unsuitable for the phosphotransfer measurements involving IIB Glc , especially since heating of the quenched reaction is required to fully denature [ 32 P]IIA Glc (6). The conditions for quenching that were developed for maintaining the phospho-S-Cys bond intact were as follows: 0.1 M KOH, 3 M urea, and heat-ing for 5 min at 55°C. These conditions yield a level of hydrolysis sufficiently low (less than 1% per min) to allow preparation (with careful timing) of the quenched samples for separation by gel filtration (where the rate of hydrolysis is negligible).
We unexpectedly found that IICB Glc is rapidly fragmented when heated under the conditions developed for the chromatography of [ 32 P]IIB Glc . When heated to 55°C for 5 min in 0.1 M KOH, 3 M urea quench solution, as much as 65% of the radioactivity in [ 32 P]IICB Glc or [ 32 P]IICB Glc -His 6 appears in fractions containing 10 -20-kDa molecules. These fractions also contain the six histidine residues from IICB-Glc -His 6 , as shown by using dot blots treated with anti-His antibodies (data not shown); corresponding fractions from control membranes do not bind the anti-His antibodies. Urea (3 M) enhances the rate of fragmentation by about 30%. These results suggest that a peptide bond somewhere in the linker region between the B and C domains is very labile at high pH. Optimal conditions for attaining rapid quenching while minimizing protein cleavage and hydrolysis of the phospho-group were found to be 0.2 M KOH (final concentration in the quenched reaction) with no heating before injection onto the gel filtration column. Careful timing between thawing the quenched samples and injection produced a reproducible 13 Ϯ 3% fragmentation, with acceptable speed of quenching of the reaction. The raw data for the concentration of the phosphoproteins in quenched reactions was therefore corrected by 13%.
Rapid Quench Assays-The present study employed the rapid quench apparatus used previously, and all of the details for its set-up were the same (6). Stock solutions of 32 P-labeled proteins were diluted with the same solution used to fractionate the phosphorylation mixture at the time of its preparation (see above). Stock solutions of IIB Glc or membrane suspensions were diluted with 100 mM phosphate buffer (pH 7.5), 0.5 mM EDTA, 0.5 mM dithiothreitol, and 1 mg/ml bovine serum albumin. The phosphate buffer was pH 7.5 (rather than pH 6.5 (6)) to correlate with work on the kinetics of Enzymes II published by the time the present work was started (e.g. see Refs. 17 and 18). The rate of phosphotransfer between HPr and IIA Glc is not significantly affected by a change in pH from 6.5 to 7.5 (6). 5 Another significant modification (described above) was of the conditions used for quenching the reactions. Preparation of the solutions for rapid quench experiments required large dilutions from stock solutions and a change from the frozen state to ambient temperature (ϳ23°C), at which all experiments were performed. The diluted solutions were therefore preincubated for 1 h at ambient temperature before the experiment was started.
When the phosphotransfer between IIA Glc and IIB Glc was studied, a Superdex 75 HR 10/30 column (6) was used to separate the proteins in the quenched reactions. When the phosphotransfer reactions between IIA Glc and IICB Glc were studied, the column was a Superose 12 HR 10/30 (Amersham Biosciences). This column cannot resolve Glc-6-P from inorganic phosphate, which is always present because of hydrolysis of the phosphodonor protein during storage following its preparation. For this purpose, a separate aliquot of each quenched reaction mixture was chromatographed on a Superdex Peptide HR 10/30 column (Amersham Biosciences) that was equilibrated with 35 mM Na 3 PO 4 , 0.1 M Na 2 SO 4 .
When [ 3 H]Glc was used in rapid quench experiments, the [ 3 H]Glc-6-P was isolated by anion exchange chromatography using a modification of the method used for PTS sugar phosphorylation assays (12). Aliquots (100 l) of the quenched reactions were diluted with 900 l of water, and the pH was reduced to between 9.5 and 10 by the addition of 10 l of 0.5 M acetic acid. Inorganic phosphate and Glc-6-P (2 M each) were added as carriers. These samples were applied to 0.2-ml bed volume columns of Bio-Rad AG-1 X8 (200 -400 mesh) in the acetate form and washed with water, and the [ 3 H, 32 P]Glc-6-P was eluted with 1 M NaCl and counted by liquid scintillation counting using a double isotope quench correction program.
Methods Used to Model Experimental Data on the Rate of Phosphogroup Transfer-The goal of these experiments was to determine the rate constants (k XXX ) for each of the first and second order chemical reactions shown in Fig. 2. The mathematical model for each reaction is the differential equation defined by the chemical equation. The numerical integration program Kinsim (19), as modified by Anderson et al. (20), was used manually to fit the mathematical models to the experimental data. When experimental data met the criteria for nonlinear least squares fitting (21), the Fitsim module of Kinsim was used. These curve fittings gave the desired rate constants (k XXX ).
The convention used for numbering the reactions in Scheme I ( Fig. 2) is adopted from Rohwer et al. (22), in which the autophosphorylation of Enzyme I from PEP is called Reaction I. By this convention, the phosphotransfer reaction between HPr and IIA Glc (6) is Reaction III (see Fig. 1).

RESULTS
Introduction-In what follows, reactions are identified by the Roman numerals assigned in Scheme I (Fig. 2). Representative progress curves are shown in Figs. 3 and 5-7. It is important to emphasize that in these figures, each panel represents one experiment. The rate constants of the reactions were estimated from the experimental progress curves by numerical integration (see "Experimental Procedures"). The data from studying the phosphotransfer reaction between IIA Glc and IIB Glc (with experiments using either [ 32 P]IIA Glc or [ 32 P]IIB Glc ) were fitted to Reaction IVa. The data from the phosphotransfer reactions from [P]IIA Glc to Glc via IICB Glc were fitted to Reactions IV, V, VI, and VII. When [ 3 H]Glc was added to an experiment, Reactions Vt, VIt, and VIIt were included in the model. Rates of Phosphotransfer between IIA Glc and IIB Glc -His 6 -In the E. coli Glc-specific PTS, the last protein-protein phosphotransfer step in the upper pathway ( Fig. 2) is from His 90 in IIA Glc to Cys 421 in IICB Glc (Reaction IV in Figs. 1 and 2). The subsequent and final reaction (V) is the phosphotransfer to Glc. As described below, kinetic measurements with both purified and membrane-bound IICB Glc were complicated by the presence of endogenous Glc, a problem that could be avoided by using IIB Glc as the phosphoacceptor. IIB Glc is the cytoplasmic domain of the integral membrane protein; the cloned fragment (10,739 Da) comprises residues 1-4 of the amino terminus of IICB Glc , followed by residues 391-476, and is terminated by a His 6 cartridge (7). Molecularly cloned IIB Glc -His 6 is a soluble and readily purified protein containing the phosphorylation site (Cys 421 in IICB Glc ) but not the Glc binding site In modeling with the simulator, these constants were held equal to the corresponding constants for unlabeled Glc; therefore, they are not given in the tables or figures. Rate constants that are omitted were assigned values of 0 in the simulator because of their low thermodynamic reversibility. In this work, Reactions IV and V are referred to as the "upper pathway," and Reactions VI and VII are referred to as the "lower pathway." SCHEME 1 FIGURE 1. A diagram of the Glc-specific PTS from E. coli. The phosphorylated amino acid in each of the four proteins is indicated. There are five phosphotransfer reactions, each designated by the Roman numeral used throughout this work. The glucose permease, IICB Glc , is shown separated into its two domains, the phosphorylation domain IIB Glc , which extends into the cytoplasm, and the sugar recognition and binding domain IIC Glc , which is an integral membrane domain. The reactions of IICB Glc are drawn as conventionally represented and do not illustrate the random order mechanism, presented under "Results," in which Glc binds either to unphosphorylated or to phosphorylated IICB Glc . (7). Its phosphotransfer reaction is designated Reaction IVa in Scheme I (Fig. 2).
A typical progress curve and the estimated rate constants for the reversible transfer of a phospho-group from [ 32 P]IIA Glc to IIB Glc -His 6 are shown in Fig. 3. The rate constants obtained from a global analysis of the data from four experiments (three using [ 32 P]IIA Glc and one using [ 32 P]IIB Glc -His 6 ) are given in TABLE ONE, row 1. There was good agreement between the constants obtained by starting the reaction from either direction. This implies that there are no significant concentrations of intermediate complexes between the two reacting proteins prior to the last step: transfer of the phosphoryl group to the acceptor and separation of the proteins to yield the products. These rate constants yield an equilibrium constant of 3.5 for Reaction IVa, indicating that the thiophosphate linkage has a very high phosphate transfer potential, close to that of phospho-IIA Glc .
Stability of [ 32 P]IIB Glc and [ 32 P]IICB Glc under Quench Conditions-The thiophosphoesters [ 32 P]IIB Glc and [ 32 P]IICB Glc showed unexpected instability of the phospho-group at pH 14, the pH of the quench solution developed for the phospho-His proteins (6). The stability of both phosphoproteins was therefore studied as a function of pH; the results, from pH 2 to 14, are shown in Fig. 4. Between pH 2 and 12, the rate constants for the hydrolysis of the phospho-group are similar in magnitude to those published for the hydrolysis of butylthiophosphate (23), cysteamine S-phosphoric acid (24), and the thiophosphopeptides derived from IICB Glc (25) and from II Mtl (26). Although the rate constants for hydrolysis of butylthiophosphate and cysteamine S-phosphoric acid exhibit bell-shaped curves in the pH range 1-6, this was not observed with the thiophosphoesters of any of the PTS proteins.
There is, however, a more important difference in the properties of the thiophosphoproteins above pH 12. Butylthiophosphate is very stable in the pH range 10 -14, whereas the thiophospho-PTS proteins are not. Above pH 12, the behavior of the two thiophospho-PTS proteins

Rate constants of the phosphotransfer reactions from [ 32 P]IIA Glc to IIB Glc -His 6 or through IICB Glc to glucose
The constants were estimated either by manual fitting of the data from individual experiments using K insim (19,20), or by nonlinear least squares fitting of the data from groups of experiments using Fitsim (21). The analyses were performed by first choosing a KЈ D for the sugar binding reaction; the table shows the results obtained for K D ϭ 10 Ϫ6 , 10 Ϫ7 , or 10 Ϫ8 M. The KЈ D was used to calculate, from the total concentration of Glc and IICB Glc before mixing, the concentrations of free Glc, free IICB Glc , and IICB Glc ⅐Glc present in the syringe. For each value of the KЈ D , at least seven pairs of values for k VI and k ϪVI were chosen (the results from only three or four of these pairs are shown in the table). Finally, the simulation was performed keeping k VI and k ϪVI fixed while fitting the rate constants for the phosphor transfer reactions.

Fixed constants a,b
Fitted constants b S.D. c ؋ 10 9 Row Global, nonlinear least squares analysis of four experiments using IIB Glc -His 6 (116 data points) 8 a Constants associated with glucose binding. b Constants involving unlabeled glucose and tritiated glucose were forced to be equal, so only one is given here. c S.D. of all of the data points from the theoretical values. d The significance of the S.E. of the individual rate constants is limited to whether ir not it is less than one-fourth the magnitude of the constant itself (21,37), and in the fits with a K D ϭ 10 Ϫ7 M, the S.E. values range from about one-half to about one-tenth the magnitude of the rate constant with which they are associated. e In these experiments, ͓ 3 H͔Glc was added to the ͓ 32 P͔IIA Glc solution. Two additional time courses were obtained, one that had no Glc added and the other that had Glc added to the IICB Glc solution. The rate constants derived from the additional eight data sets agreed well with those presented in the table. f Varying the KЈ D for Glc binding to IICB Glc from 10 Ϫ6 to 10 Ϫ8 M had essentially the same effect as shown for IICB Glc -His 6 . The best fit was obtained when the KЈ D was set at 10 Ϫ7 M. ( Fig. 4) resembles the behavior of the mixed anhydride, ␤-aspartyl phosphate (27). Perhaps the increase in the rate of hydrolysis of the phosphogroup above pH 13 results from phospho-group migration from Cys 421 to the nearby Asp 419 when the protein is denatured in strong alkali. In the previous studies of phosphopeptides from Enzymes II, the highest pH tested was 12 (25) or 13 (26). As a result of these findings and also the observation that IICB Glc is rapidly fragmented under highly alkaline conditions, we developed the conditions for quenching given under "Experimental Procedures." Kinetic Competence of Glc Bound to IICB Glc : the Relevance of Reaction VII-We show in supplemental data on Glc that all of our preparations of IICB Glc were "contaminated" with Glc that binds to the enzyme. The binding appears to be rather tight, and the free and bound glucose are in equilibrium. For our analyses and simulations of the kinetics of phosphotransfer, it was essential to determine whether or not the Glc bound to the IICB Glc is kinetically competent.
The rapid quench experiment shown in Fig. 5 was designed to determine this. The experiment measured the rate of the phosphotransfer reactions from [ 32 P]IIA Glc to Glc via IICB Glc . A preparation of wild type membranes was used that was washed only once and neither incubated nor dialyzed, so that the molar ratio of endogenous Glc to IICB Glc was higher (22:1) than that in the other experiments reported here (2:1 to 4:1) The figure shows only the data on the production of [ 32 P]IICB Glc and Glc-6-[ 32 P], the utilization of [ 32 P]IIA Glc is not shown.
For the analysis shown in Fig. 5A it was assumed that the Glc in IICB Glc ⅐Glc was not kinetically competent (i.e. the rate constant, k VII , was forced to 0). The result was a poor fit between the theoretical curve and the data points, but this was the best fit that could we could obtain. If the bound Glc is not kinetically competent, then [ 32 P]IICB Glc should accumulate before any sugar phosphate is formed. It is clear, however, that Glc-6-[ 32 P] appeared more rapidly than [ 32 P]IICB Glc . Thus, as seen in Fig. 5B, when Reaction VII is assumed to be active and is assigned a non-zero value in the simulation, very good agreement is obtained between the theoretical curves and the data points. In all of our experiments, substantially better theoretical fits to the data were obtained when kinetically active IICB Glc ⅐Glc was included in the model.

Kinetics of Phosphorylation of Endogenous and Exogenous
Glc-At the instant of mixing of IICB Glc with exogenous Glc added to the [ 32 P]IIA Glc , there are three pools of the sugar: exogenous Glc, pool 3; free endogenous Glc, pool 2; and bound endogenous Glc (IICB Glc ⅐Glc), pool 1. The foregoing assumes that the endogenous Glc is all accessible to the IICB Glc and that it participates in a binding equilibrium with the enzyme. This is the case as shown in supplemental data on Glc. Further, as shown above, the endogenous Glc is kinetically competent, but what is its rate of phosphorylation relative to the exogenous Glc? In other words, how rapidly do the exogenous and endogenous Glc pools equilibrate relative to the phosphotransfer reactions starting with phospho-IIA Glc ?
The experiment shown in Fig. 6 clearly shows that the bound endogenous Glc is phosphorylated more rapidly (Reaction VII) than it equilibrates with the exogenous pool of Glc (Reaction VI). In this experiment, the rate of phosphotransfer from [ 32 P]IIA Glc to Glc via IICB Glc was measured, but only the data on the production of [ 3 H]Glc-6-[ 32 P] and total Glc-6-[ 32 P] are shown. The experiment was conducted in two parts. In the first part, [ 3 H]Glc was added to the syringe containing the IICB Glc and endogenous Glc. In other words, the exogenous labeled pool was permitted to mix and equilibrate for more than 30 min with the endogenous Glc before the measurements were begun. The data points and the fitted curve for total Glc-6-[ 32 P] and 3 H-labeled Glc-6-[ 32 P] were coincident, showing complete equilibration. In the second part of the experiment, the [ 3 H]Glc was added to the syringe containing the [ 32 P]IIA Glc and came into contact with the endogenous unlabeled Glc and IICB Glc only when mixed. There was a clear difference between the rates of phosphorylation of the endogenous Glc and the exogenous [ 3 H]Glc for about the first 10 s of the progress curve (Fig. 6 shows only the first 1.5 s). Complete equilibration of the two pools took about 10 s under the conditions used for the experiment shown in Fig. 6, whereas measurable phosphorylation of Glc from IICB Glc ⅐Glc is seen at the first time point (25 ms).
Phosphorylation of IICB Glc : Kinetics of the Complete System-The results described above establish Reactions VI and VII, the lower pathway in Fig. 2, as an active pathway for phosphorylating Glc. The transient state kinetics of the upper pathway in Fig. 2 (Reactions IV and V), the pathway most often used to describe the PTS enzymes II, will now be characterized. The rate constants of all of the reactions involving  [P]IIA Glc , IICB Glc , and Glc are summarized in Each row shows the effects of varying the KЈ D and/or the rate constants for the Glc binding reaction, and the interpretation of these effects is given below.
TABLE ONE shows the data from only one of three parts that were performed during each experiment. In the other two parts there was either no addition of exogenous Glc, or [ 3 H]Glc was added to the membrane suspension, where it had at least 30 min to equilibrate with the endogenous pools. The rate constants obtained from these additional eight time courses (data not shown) were in good agreement with those in TABLE ONE. These results suggest that exogenous Glc has no effect on the kinetic properties of [ 32 P]IIA Glc .   Two important tests of the validity of our rate constants are independence from the concentration of Glc and IICB Glc and evidence that the His tag did not affect the kinetic properties of the enzyme.
The effects of varying the concentration IICB Glc and Glc are seen in the two panels of Fig. 7 (the concentration of [ 32 P]IIA Glc was similar in both experiments). These experiments used either IICB Glc -His 6 ( Fig.  7A) or IICB Glc (Fig. 7B); in both, [ 3 H]Glc was added to the [ 32 P]IIA Glc . In Fig. 7A, the total concentration of Glc was 107 nM, and the total concentration of IICB Glc -His 6 was 40 nM, whereas in Fig. 7B, the total Glc concentration was 5 M, and the total concentration of IICB Glc was 132 nM. The concentration of [ 32 P]IICB Glc that appears depends on its rate of formation from [ 32 P]IIA Glc versus the rate of decay by transfer of the phospho-group to Glc. The very different concentrations of Glc and IICB Glc in the two experiments would be expected to affect the concentration of [ 32 P]IICB Glc during the time course, and indeed they do. When the total Glc and IICB Glc concentrations were low (Fig. 7A), about half of the total enzyme was detected as the phosphoenzyme, whereas at the high Glc and IICB Glc concentrations (Fig. 7B), the phosphoenzyme was barely detectable. We emphasize, however, that the rate constants that produced the best fit to the data for the phosphorylation of IICB Glc were the same in both experiments and therefore independent of the concentrations of Glc or IICB Glc .
The second important question was whether the His 6 tag attached to IICB Glc affected the kinetic behavior of the proteins. Fig. 7 shows that IICB Glc -His 6 is as catalytically efficient as the wild type protein, as does the more comprehensive summary in TABLE ONE (cf. rows 5-8, IICB-Glc -His 6 , with rows 12-14, IICB Glc ).

KЈ eq and Rate Constants for the Binding of Glc to IICB Glc and Their Effects on Determination of the Rate Constants of the Phosphotransfer
Reactions-It is evident that the kinetic characteristics of the sugar binding reaction (Reaction VI) will affect the analysis of the phosphotransfer reactions. The binding reaction determines the relative concentrations of free and bound reactants present at the initiation of the reaction as well as their behavior as phosphorylation proceeds. The rate constants of the sugar binding reaction cannot be determined by any known method. Moreover, even the apparent binding constant (KЈ eq ) could not be determined by flow dialysis for reasons presented in supplementary data on Glc. Semiquantitative values for KЈ D ranging from 1.8 ϫ 10 Ϫ7 to 9 ϫ 10 Ϫ8 were obtained from the centrifugation experiments (supplemental data on Glc). We were, however, able to deduce likely values for KЈ D from the statistics of fitting the phosphotransfer data. Analysis of four data sets by the nonlinear least squares method (TABLE ONE) showed the following. (a) The values chosen for KЈ D had a strong effect on the magnitude of the rate constants of the phosphotransfer steps and, importantly, on the statistical goodness of the fit. As shown in TABLE ONE, the smallest S.E. value of the rate constants of the four phosphotransfer reactions was obtained when a KЈ D of 10 Ϫ7 M was used. There was a very high degree of uncertainty in the phosphotransfer rate constants when the KЈ D was set at 10 Ϫ6 or 10 Ϫ8 M; the S.E. values were often larger than the constants themselves. (b) In sharp contrast, the rate constants for binding of Glc to IICB Glc and dissociation of the complex (k VI and k ϪVI ) could be varied as much as 6 orders of magnitude without a large effect on the rate constants for the phosphotransfer reactions. This small effect is consistent with the progress curves in Fig. 7, which show that the bulk of the reaction was completed in about 100 s, whereas the experiments from the gel filtration columns (supplemental data on Glc) suggest that the t1 ⁄ 2 of the binding reaction is about 12 min.
The experiment shown in Fig. 7B permitted independent estimates of the rate constants associated with Reactions VI and VII. In this experiment, a large proportion of the IICB Glc was complexed even when KЈ D was designated at 10 Ϫ6 M, and both solutions contained 5 mM Glc, so that the concentration of Glc did not change on mixing. The fit of the model to the early data points was, as expected, determined almost entirely by the rate constant of Reaction VII, phosphotransfer from [ 32 P]IIA Glc to IICB Glc ⅐Glc, which was estimated by manual fitting as 2.5 ϫ 10 6 M Ϫ1 s Ϫ1 (TABLE ONE, row 14), in agreement with the other estimates in rows 5-8. The rate constants for Reactions VI and VII were also estimated by the nonlinear least squares method (see supplemental data on kinetics) and corroborate those shown in TABLE ONE.

DISCUSSION
The transient state kinetic experiments reported here were intended to determine the rate constants for the last two steps in the phosphorylation and uptake of Glc by E. coli cells, namely the phosphotransfer reactions from phospho-IIA Glc to IICB Glc to Glc (Reactions IV and V in Figs. 1 and 2). Initially, we conducted these studies with highly purified preparations of IICB Glc in lipid/detergent mixtures, but the results were variable, whereas natural membranes containing active IICB Glc gave reproducible results (TABLE ONE).
Confirmation of the results obtained with membranes was obtained with IIB Glc , the soluble, homogeneous domain of the intact protein. IIB Glc contains the phosphorylation site Cys of IICB Glc . The cloned IIB Glc domain has kinetic properties that are very similar to those of the whole protein. Both the forward and backward rate constants of phosphotransfer between IIA Glc and IIB Glc are somewhat larger than those involving the intact membrane protein, IICB Glc , perhaps expected from the smaller mass of IIB Glc and the complexity of the membrane preparations.
Steady-state measurements of IICB Glc activity (9,22,28,29) also corroborate the rate constants reported here for Reactions IV and V. The rate constants k iv and k v are equivalent to the two respective specificity constants of IICB Glc for [P]IIA Glc and Glc (i.e. k iv ϭ k cat /K m([P]IIA Glc ) and k v ϭ k cat /K m(Glc) , assuming that the mechanism of the enzyme is Ping Pong (30). The agreement between our results and the calculated specificity constants 6 is good. The latter cluster around 4 ϫ 10 6 M Ϫ1 s Ϫ1 for k cat /K m([P]IIA Glc ) , compared with 3.5 ϫ 10 6 M Ϫ1 s Ϫ1 for k iv , and around 3.2 ϫ 10 6 M Ϫ1 s Ϫ1 for k cat /K m(Glc) , compared with 2.5 ϫ 10 6 M Ϫ1 s Ϫ1 for k v . The advantage of the rate over the specificity constants is that the rate constants are affected by fewer experimental errors.
A computer model has been developed that can predict the kinetic behavior of the Glc PTS under a variety of conditions, both in vivo and in vitro (22). The model was based, in part, on preliminary results from our kinetic experiments. What we consider to be the definitive experimental rate constants are presented here. The effects of the new constants on the predictions of the model will be presented in a separate report.
From the rate constants, we can calculate the corresponding equilibrium constants for the reactions, phospho-IIA Glc to IIB Glc or IICB Glc (3.5 and 12, respectively). These equilibrium constants appear to be the first data that permit comparison of the standard free energies of hydrolysis of two phosphocysteinyl PTS proteins with those of the phosphohistidinyl PTS proteins. Briefly, the phosphotransfer potential of [P]IICB Glc is somewhat less than that of [P]IIA Glc , but it is, like the other phosphoproteins of the PTS, a "high energy" phosphocompound. The implications of this observation will be elaborated in a future publication on the kinetics and thermodynamics of the complete pathway of the Glc-specific PTS in E. coli. Whether these phosphotransfer potentials are important for the catalytic action of another class of phospho-S-Cys proteins, the protein-tyrosine phosphatases of eukaryotic cells (8) remain to be determined. One could speculate, however, that these enzymes may transfer the phospho-group to substances in addition to water (i.e. they may act as phosphotransferases as well as phosphatases).
At the outset of this work, both the highly purified enzyme and the membranes containing IICB Glc were unexpectedly found to contain a "contaminant" that was phosphorylated by the enzyme when it was supplemented with [ 32 P]IIA Glc . The "contaminant" was identified (supplemental data) as Glc that is in equilibrium with IICB Glc with an estimated K D of 10 Ϫ7 M; the Glc is kinetically competent. Our data suggest that the sources were very low levels of contamination of laboratory water and reagents and a cellular source, possibly glycogen.
Erni and co-workers (31) purified IICB Glc to apparent homogeneity from Salmonella typhimuriun and E. coli and were the first to characterize this transporter, finding, for instance, that it contained a phos- 6 In order to calculate values for the specificity constants from data in the older literature, we estimated the concentration of IICB Glc from the amount of protein or dry weight used in the assays by applying the purification factors and specific activity of the pure protein that were found in later work. Since the present measurements were made at room temperature we also applied a correction of a factor of 0.4 to compensate for the effect of temperature between 37°C at which the steady-state measurements were made and 25°C.   DECEMBER 23, 2005 • VOLUME 280 • NUMBER 51 phorylation site Cys in the B domain similar to that found in II Mtl (26). They found that isolated [ 32 P]IICB Glc could transfer the phospho-group to Glc, but the rate of the reaction was exceedingly slow relative to the rate constants reported here (32). There are several possible explanations for this difference (e.g. the enzyme was perhaps partially detergent denatured during its isolation (32), or perhaps there are differences between the physical state of the purified enzyme in the lipid/detergent mixtures compared with its state in the natural membranes). Garcia-Alles et al. (18,33) reported that IICB Glc from E. coli exhibits steady-state kinetics that are biphasic when a large range of sugar concentrations (50 M to 5 mM) is tested. The authors attribute this to the presence of at least three (and perhaps four) catalytic sites that fall into two classes, one with higher affinity for Glc (K S ϳ 10 M) but lower phosphorylation activity and the other with low affinity for Glc (K S ϳ300 M) but about 6 times the phosphorylation activity of the high affinity class. II Mtl also has high and low affinity sites that are delimited at 5 M Mtl, and the low affinity site has the higher capacity (17). Our measurements were made at Glc concentrations between 0.08 and 0.2 M (with one instance of 5 M), which are all well within the high affinity region. We have no information about the kinetics of IICB Glc in the low affinity region. The presence of multiple reactive sites and their kinetic properties will bear on interpreting the physiological significance of the lower branch of the mechanism of IICB Glc (Fig. 2).

Kinetics of IICB Glc from E. coli by Transient State Methods
The unphosphorylated forms of several Enzymes II bind their sugar substrates (34); bound Mtl is phosphorylated (35), and the enzyme was postulated to have a random order of addition mechanism by analysis of steady-state kinetic data (17,36). We find that Glc bound to unphosphorylated IICB Glc is kinetically competent; therefore, IICB Glc also has a random order of addition mechanism. It is obvious that the relative flux through the two branches will be very dependent on the rate of binding of Glc to IICB Glc , but k VI is one of the least certain of the rate constants presented here. The lower branch of the pathway may be of physiological significance under conditions that deplete IICB Glc of phosphogroups (i.e. low cellular concentrations of PEP and/or the presence of other PTS sugar substrates) in the presence of Glc.
In summary, we have analyzed an Enzyme II of the PTS with transient-state kinetic methods and have found that IICB Glc has a random order of addition, Bi Bi, substituted enzyme mechanism with the following properties. (a) The lower branch has a small effect on the flux through the enzyme under the conditions used in our experiments. Since the magnitude of the effect is dependent on the magnitude of k VI (the rate constant for Glc binding to IICB Glc ) and the sugar concentration, under other conditions, the lower branch of the kinetic mechanism could become physiologically significant. (b) We have been able to estimate the rate constants for the binding of Glc to IICB Glc although they are not directly measurable. (c) Although IICB Glc is the fourth protein in the PTS pathway to which the phospho-group from PEP is transferred, the phosphoenzyme retains a phosphotransfer potential much higher than that of ATP. An overview of the kinetics and thermodynamics of the glucose-specific PTS will be presented elsewhere. (d) Finally, our results confirm the data used to build a kinetic model that showed that control of flux through the Glc-specific PTS of E. coli is exerted at the last steps of the pathway, the phosphotransfer reactions of IICB Glc , in cells grown on glucose to midexponential phase (22). The model successfully replicated the flux both in vivo and in vitro, which suggests that its extension to other sugar-specific Enzymes II will enhance our ability to predict cellular responses to a variety of physiological conditions.