Rate and equilibrium constants for phosphoryltransfer between active site histidines of Escherichia coli HPr and the signal transducing protein IIIGlc.

The bacterial phosphoenolpyruvate:glycose phosphotransferase system (PTS) plays a central role in catabolizing many sugars; regulation is effected by phosphorylation of PTS proteins. In Escherichia coli, the phosphoryltransfer sequence for glucose uptake is: PEP → Enzyme I(His191) → HPr(His15) → IIIGlc(His90) → IIGlc(Cys421) → glucose. A rapid quench method has now been developed for determining the rate and equilibrium constants of these reactions. The method was validated by control experiments, and gave the following results for phosphoryltransfer between the following protein pairs. For phospho-HPr/IIIGlc (and HPr/phospho-IIIGlc), k1 = 6.1 × 107 M−1 s−1, k−1 = 4.7 × 107; for the mutant H75QIIIGlc in place of IIIGlc, k1 = 2.8 × 105 M−1 s−1, k−1 = 2.3 × 105. The derived Keq values agreed with the Keq obtained without use of the rapid quench apparatus. Keq for both reactions is 1-1.5. The rate of phosphoryltransfer between HPr and wild type IIIGlc is close to a diffusion-controlled process, while the reactions involving the mutant H75QIIIGlc are 200-fold slower. These rate differences are explained by an hypothesis for the mechanism of phosphoryltransfer between HPr and IIIGlc based on the structures of mutant and wild type proteins (see Pelton et al. (Pelton, J. G., Torchia, D. A., Remington, S. J., Murphy, K. P., Meadow, N. D., and Roseman, S. (1996) J. Biol. Chem. 271, 33446-33456)).

The bacterial phosphoenolpyruvate:glycose phosphotransferase system (PTS) 1 comprises at least two dozen cytoplasmic and membrane proteins. Among the diverse functions governed by the PTS is the translocation of PTS sugars across the cell membrane concomitant with their phosphorylation, and regulation of the expression of several non-PTS sugar operons (for reviews see Refs. [1][2][3][4][5][6]. In Escherichia coli, the phosphoryltransfer sequence for transport via the glucose-specific system is as follows: PEP 3 Enzyme I(His 191 ) 3 HPr(His 15 ) 3 III Glc (His 90 ) 3 II Glc (Cys 421 ) 3 glucose.
While this system has been extensively studied since discov-ery of the PTS (7), many important questions remain to be answered. For example, the complete, balanced equations are written as second order reactions, assuming binary complexes as the transition state intermediates, i.e. phospho-A ϩ B ϭ [A•phospho•B] ϭ A ϩ phospho-B. It is possible, however, that transient ternary, or possibly even quaternary complexes are formed during the reactions. Furthermore, the mechanisms of phosphoryltransfer are unknown, as are the rate-limiting steps during the transfer from PEP to glucose, the rates in the reverse direction and the equilibrium constants for each step in the pathway. As a first approach to answering these questions, this paper describes a rapid quench method for determining the apparent rate and equilibrium constants of the phosphoryltransfer reactions. The protein pair HPr and III Glc was selected for initial studies for several reasons. First, phospho-HPr is a central branch point in phosphoryltransfer by the PTS, but it is very labile (8), and the technical problems encountered in working with this phosphoprotein had to be solved to collect meaningful data. Second, III Glc is a critical signal transducing protein in bacterial metabolism. It interacts with at least 10 other proteins, some by phosphoryltransfer reactions, and others by non-covalent binding (6); the latter are involved in regulating gene expression, which depends on the ratio of III Glc to phospho-III Glc . Third, important active site mutants of III Glc are available for comparative studies. Finally, in the only study on the phosphoryltransfer between HPr and III Glc (9), the technology available at the time gave only an estimate of the apparent K eq . E. coli III Glc , also designated IIA Glc , 2 is an 18.1-kDa protein containing two histidine residues, His 75 and His 90 , in the active site. His 90 accepts the phosphoryl group from phospho-HPr, but His 75 is conserved in many III or IIA type proteins (see Refs. 1-6 for reviews). The physiological significance of the His residues was tested by substituting glutamine for each His, giving the mutant proteins H75Q III Glc and H90Q III Glc , respectively (10). The mutants exhibited some unexpected physiological and biochemical properties. For example, H75Q III Glc accepted the phos-phoryl group from phospho-HPr, but was apparently not a phosphoryl donor to glucose (or methyl ␣-glucoside) via II Glc . It appeared possible that clarification of this apparent anomaly might be obtained by kinetic analysis of the phosphoryltransfer reactions and a detailed structural study of the proteins; the structures are presented in the accompanying paper (11).
We report here the apparent equilibrium constants (K eq ), the forward (k 1 ), and the reverse (k Ϫ1 ) rate constants for the transfer of the phosphoryl group between phospho-HPr and III Glc , and between phospho-HPr and the mutant H75Q III Glc .
These results, along with the structural information, suggest a mechanism for the phosphoryltransfer reaction (see accompanying paper; Ref. 11).

MATERIALS AND METHODS
Bacterial Strains-The mutant crr genes that encode H75Q III Glc and H90Q III Glc were constructed by site-directed mutagenesis as described (10), and transferred to the overproducing plasmid, pVEX-11 (12). The plasmids were used to transform E. coli BL21 (DE3) in which a kanamycin resistance cartridge was substituted for the coding region of the crr gene by Dr. Cing-Yuen Wong, to whom we are most grateful. In brief, the procedure was as follows. The plasmid pDS45 (13) was used as the source of the crr gene, which was precisely excised using the method of Kunkel et al. (14); after enlarging the size of the flanking region by ligating in a fragment of the gene for Enzyme I from plasmid pDS20 (13), the kanamycin resistance gene from pUC4-KIXX (Pharmacia Biotech Inc.) was ligated into the plasmid. The Km R gene was integrated by homologous recombination into the chromosome of E. coli V355 (recD 1014) (15) by transformation, and, finally, E. coli strain BL21 (DE3) was transduced to kanamycin resistance using phage P1, creating strain CYW 14. III Glc , the product of the crr gene, was not detected in extracts of CYW 14, using a sensitive, immunological rocket assay (9).
Purification of Proteins-Previously published methods were used to purify HPr (16) and wild type III Glc (12). H75Q III Glc and H90Q III Glc were purified by the same procedure used for wild type III Glc . Enzyme I from E. coli was purified from an overproducing strain (17) by a modification of the method used for III Glc . The cells were grown as described (17) in batches of 3 liters of LB broth. The treatment of the cell suspension after harvesting was as described, except that p-aminobenzamidine was replaced by 40 mM ⑀-aminocaproic acid (18). A KCl gradient of 0.05-0.50 M was used to elute the DEAE-Sepharose 6B CL (Pharmacia) column. The concentrated pool containing the Enzyme I was applied to a 500-ml bed volume (2.6 cm ϫ 93 cm) Sephacryl S300 HR (Pharmacia) column equilibrated with 50 mM potassium phosphate buffer, pH 6.5, 5 mM MgCl 2 , 1 mM EDTA, 0.2 mM dithiothreitol, and 40 mM ⑀-aminocaproic acid. This procedure yielded 200 mg of homogeneous Enzyme I as determined by densitometric scanning of SDS-polyacrylamide gels; the specific activity of the enzyme was the same as preparations made by the original method (19).
The experiments described below were conducted with a minimum of two independent preparations of each of the proteins. One sample of HPr was a generous gift from Dr. E. B. Waygood (University of Sas-katchewan, Saskatoon, Saskatchewan, Canada).
Protein Concentration-Three methods were used for determining the concentrations of the reactant proteins in the rapid quench experiments. (a) The colorimetric protein assay of Markwell et al. (20) was calibrated with protein standards whose concentrations were determined by Trudy Carr of this department using the C o fringe counting method in a Beckman model E analytical ultracentrifuge. (b) The lactate dehydrogenase-coupled assay (21) measures the quantity of pyruvate produced when a PTS protein is phosphorylated by PEP; since the reaction stops when the protein is fully phosphorylated, this method measures the amount of phosphorylatable protein in the assay. (c) In the very dilute solutions used for the rapid quench experiments, the concentration of the phosphoryl donor protein was determined from the specific activity of the [ 32 P]PEP used for its preparation, as was the quantity of [ 32 P]phosphoprotein product formed in the reaction.
Because the phosphoryltransfer reaction is so rapid, very dilute solutions of the proteins were used, and a serious possible source of error was the loss of protein during the quench experiment and on the HPLC column. A series of experiments was therefore undertaken to measure the recovery of 32 P-labeled proteins through the entire procedure. Adsorption was, in fact, a problem but was resolved by adding albumin (1 mg/ml, Sigma, crystalline) to the reaction mixtures, and by pretreating all containers and the entire quench apparatus with albumin-containing solutions.
Under these conditions, protein concentrations were determined within Ϯ10%.  Table I. Ç, time points from the rapid quench apparatus; q, hand-mixed time point.
[ 32 P]PEP contained approximately 0.8 mCi of radioactivity in 10 nmol of PEP.
The specific activity of the [␥-32 P]ATP used in the synthesis of [ 32 P]PEP was 1.1 ϫ 10 8 GBq/mol, and after rigorous purification, the product was diluted with unlabeled PEP to about 1.0 ϫ 10 5 GBq/mol for phosphorylating the proteins. PEP concentrations were determined by the pyruvate kinase assay (23), which were reproducible to 4%. Hydrolysis of the [ 32 P]PEP during storage at 4°C and pH 7.6 was measured by thin-layer chromatography on polyethyleneimine-cellulose plates (Baker-flex cellulose PEI-F) developed with 2 M sodium formate, pH 3.4, and autoradiographed. The rate of hydrolysis was 0.16%/day.
The errors of the methods therefore yield an estimated error of Ͻ5% for the specific activities of the [ 32 P]PEP.
Preparation of [ 32 P]HPr and [ 32 P]III Glc -Reaction mixtures contained (final volumes, 0.3 ml): 5 nmol of the protein to be phosphorylated, a 4 -7-fold excess of [ 32 P]PEP (adjusted to the desired specific activity), 5 mM MgCl 2 , 50 units of Enzyme I, 1 mg/ml albumin, 0.35 M triethylamine bicarbonate, pH 7.6. For phosphorylating III Glc , 0.2 nmol of HPr was added to serve as a catalyst, and the mixtures were incubated for 15 min at room temperature. An HPLC Pharmacia Superose 12HR 10/30 column was used to separate the proteins, giving about the same resolution as the Superdex column described below. The Superose column was equilibrated and eluted with a mixture of 17 mM KHCO 3 , 3 mM K 2 CO 3 , pH 9.5, and 1 mg/ml bovine serum albumin, at a flow rate of 0.5 ml/min. Peak fractions containing the phosphoprotein were pooled and stored at Ϫ70°C.
Rapid Quench Apparatus-An Update Instrument Co. (Madison, WI) syringe drive apparatus and two Wiskind mixers were used (24 -26). It was essential to maintain constant ram speed and displacement, and to know their precise values. In recent models of the instrument, the ram is computer-controlled. In our instrument, the original model 1501/ 1502 motor control circuitry was replaced with an Intel 486-based computer control designed and written in C source code by Dr. Charles Long (Department of Chemistry, The Johns Hopkins University, Baltimore, MD). The original model 1500 controllable power supply was retained. This modification provided a continuous profile of the ram velocity and a computation of average ram velocity immediately following each experiment.
A set of reaction hoses was prepared from PEEK plastic tube (Upchurch Scientific) and calibrated (27) by measuring the rate of p-nitrophenyl acetate hydrolysis (data not shown).
Rapid Quench Experiments-In these experiments, the phosphoryl donor was injected into the first Wiskind mixer simultaneously with the acceptor protein. The mixture was then passed through a calibrated reaction hose and entered the second mixer at the same time as the quench solution; the quenched reaction mixture was collected for analysis. Equal volumes of each solution were injected into the apparatus using 1-ml Hamilton syringes (model 1001, C style; Hamilton Corp., Reno, NV). The solutions all contained 1 mg/ml albumin, and were as follows. (a) The donor 32 P-labeled protein was diluted to the desired concentration with the bicarbonate, carbonate buffer used for its elution from the Superose 12 10/30 column; (b) the phosphoryl-acceptor protein was diluted with a solution containing potassium phosphate buffer (0.1 M, pH 6.5), 1 mM EDTA, and 5 mM MgCl 2 ; (c) the quench solution was 5 M urea, 3 M KOH.
The efficiency of the quenching fluid was determined by mixing each of the proteins or phosphoproteins with quench fluid followed by the relevant second proteins. These experiments showed that the quench solution stopped the phosphoryltransfer reaction within 5 ms. These prequench values, although small, were subtracted from the data before the simulations were performed.
Unless otherwise stated, the ram speed was 15 mm/s, so that equal volumes of the protein solutions were driven through the mixer at flow rates of 500 l/s in the first mixing chamber; the reaction mixture and quench solution were mixed at 750 l/s in the second chamber. To obtain reaction times longer than 0.6 s, a calibrated hose of 350 l was quantitatively filled with reactants at a flow rate of 500 l/s, the ram was then paused for the desired length of time, and the contents of the hose were then quantitatively expelled with a second push of the ram. Typically, the distance of the pushes ranged from 17 to 25 mm, and the syringes delivered 16.7 l/mm, sufficient to obtain about 600 l of quenched reaction mixture. Experiments were performed at ambient temperature, which ranged from 25 to 26.5°C during the course of this work. Quenched reaction mixtures were immediately frozen on dry ice and stored at Ϫ70°C.
Each frozen mixture was thawed immediately before injecting a 200-l aliquot onto an HPLC Pharmacia Superdex 75HR 10/30 column, equilibrated with 3 M urea, 35 mM Na 3 PO 4 , pH 12.1. A Waters model 590 pump was used to operate the column at flow rates of 0.5-1.0 ml/min of the urea, phosphate buffer. Fractions were counted in a Packard 2200CA liquid scintillation counter using Packard UltimaGold XR scintillation mixture. The resolution obtained by the column is shown in Fig. 1, and   from the proteins, and we could therefore determine whether hydrolysis occurred while the solutions were in the syringes or after they were mixed, and the extent of hydrolysis at each time point.
[ 32 P]Phospho-HPr spontaneously hydrolyzes at significant rates on the minute time scale at the pH used for these experiments, or even at pH 7.5 (8). Phosphoryltransfer is so rapid between wild type III Glc and HPr that the hydrolysis of phospho-HPr does not significantly affect the results. However, when the mutant H75Q III Glc is used, the rate is much slower, and the simulated kinetics included a step for the hydrolysis of phospho-HPr. The rate constant that gave the best fit for this hydrolysis was 3 ϫ 10 Ϫ4 M Ϫ1 s Ϫ1 , which agrees with the published value (8).
Rate constants for the forward and backward transfer reactions were estimated from the experimental data using the kinetic simulation program, KINSIM (28) as modified by Anderson et al. (29), which allows entry of experimental data collected at unequal intervals of time.
Determination of Equilibrium Constants-Apparent K eq constants were obtained in two ways. The ratios of the rate constants, determined independently in each direction, gave one value. A second value was obtained without using the rapid quench apparatus, i.e. by hand mixing samples.
In the hand-mixed experiments, solutions containing [ 32 P]HPr and either III Glc or H75Q III Glc were prepared as described for the rapid quench experiments. The solutions were preincubated for 5 min at 25°C, mixed, and incubated for 30 s (wild type) or for 5 min ( H75Q III Glc ), at which time a one-third volume of quench solution was added and the samples frozen until analyzed. The distribution of radioactivity between HPr and III Glc was determined by the HPLC method. It is important to emphasize that the hand mixed experiments utilized much higher concentrations of proteins than employed in the rapid quench studies.

Rate of Phosphoryltransfer from [ 32 P]Phospho-HPr to III Glc and from [ 32P]
Phospho-III Glc to HPr-A typical progress curve for the transfer of the phosphoryl group from phospho-HPr to wild type III Glc is shown in Fig. 2A. The reverse reaction is shown in Fig. 2B. The data in each direction fit a model of second order kinetics over the entire time course.
A summary of several such experiments is presented in Table I. It should be emphasized that there was as much as a 10-fold difference in initial concentrations of some of the pro-teins used in these experiments. Nevertheless, excellent agreement was obtained in the different experiments, with a maximum variation of 2 for the derived rate constants. Most importantly, there is excellent agreement between the rate constants obtained by starting the reaction with phospho-HPr and III Glc or with HPr and phospho-III Glc .
Rate of Phosphoryltransfer from [ 2 P]Phospho-HPr to H75Q III Glc and from [ 32 P]Phospho-H75Q III Glc to HPr-Progress curves for the phosphoryltransfer between HPr and the H75Q III Glc mutant are shown in Fig. 3. As with the wild type proteins, the reactions fit second order reaction kinetic models over the entire time course, and reactions measured from either direction yielded the same values for the rate constants (Table II).

Validity of Measured and Calculated Kinetic Constants-
Extensive preliminary experiments showed that the rapid quench experiments were subject to a number of errors, some of which, such as ram speed, protein concentrations, protein losses, etc., are discussed above. A number of additional parameters were investigated to determine the significance of the calculated rate constants.
(i) The constants should be independent of the initial concentrations of the reactants, and they are, as shown in Tables  I and II. (ii) An important source of error in rapid quench measurements is insufficient mixing of the reactants on a time scale relevant to the shortest time being used, i.e. mixing must be so efficient that the solution is homogeneous well before collecting the first time point. Fig. 4 shows that this goal was achieved. In this experiment, three flow rates were used, ranging from 270 to 670 l/s into the first mixing chamber, and the results show that the data are free of artifacts caused by incomplete mixing. In other experiments, flow rates ranging from 150 to 500 l/s into the first mixing chamber also had no effect on the estimated rate constants (data not shown). These experiments satisfy the conditions of the velocity probe (30). In addition, in the experiments using H75Q III Glc , excellent agreement was obtained between time points that were collected at 500 l/s from the rapid quench apparatus and data that were obtained by mixing the reactants by hand (Fig. 3).
(iii) Another consideration is the quality of the simulation with the KINSIM curve fitting program. One test was to substitute arbitrary values of k 1 and k Ϫ1 for those derived from the simulations, and to determine how these substitutions affected the curve with respect to the data points. In general, a Ϯ20% change in the rate constants gave a "poor fit." (iv) The K eq values determined directly, and from the ratios of the rate constants (see "Discussion") were in good agreement.
Determination of Equilibrium Constants-One important measure of the validity of the rate constants is whether they yield K eq values (k 1 /k Ϫ1 ) that agree with values obtained independently by hand mixing. The K eq values derived from the kinetic data are shown in Tables I and II

DISCUSSION
The following reactions were studied by the methods described above: Phospho-HPr ϩ III Glc % phospho-III Glc ϩ HPr REACTION I Phospho-HPr ϩ H75Q III Glc % phospho-H75Q III Glc ϩ HPr REACTION II Apparent rate constants were found to be: wild type III Glc , k 1 ϭ 6.1 ϫ 10 7 M Ϫ1 s Ϫ1 , k Ϫ1 ϭ 4.7 ϫ 10 7 ; H75Q III Glc , k 1 ϭ 2.8 ϫ 10 5 M Ϫ1 s Ϫ1 , k Ϫ1 ϭ 2.3 ϫ 10 5 . Rapid quench measurements and their interpretations are subject to many kinds of error, and a major effort was undertaken to validate the methods, and therefore the rate constants. We have established the following points. (a) The derived k values are independent of the rate of flow (or mixing) under the conditions used here. (b) The reactions were quenched in less than 5-6 ms. (c) Recoveries of protein and phosphorylprotein were excellent. (d) Good agreement of the rate constants was obtained in independent experiments using different initial protein concentrations. (e) Hand-mixed samples, where they could be used, gave excellent agreement with those mixed by the rapid quench method. (f) Good agreement in k 1 and k Ϫ1 values were obtained, independent of which starting protein pair was used, phospho-HPr and III, or phospho-III and HPr.
Finally, the rate constants were used to calculate the appar-ent equilibrium constants (ratios of k 1 to k Ϫ1 ) and compared to K eq measured directly from hand-mixed samples. With wild type III Glc , the results were: k 1 /k Ϫ1 ϭ K eq ϭ 1.4 Ϯ 0.5; handmixed K eq ϭ 1.1 Ϯ 0.1. With the mutant H75Q III Glc , they were: k 1 /k Ϫ1 ϭ K eq ϭ 1.2 Ϯ 0.4; hand-mixed K eq ϭ 1.5 Ϯ 0.3. Thus, there was an excellent correlation between the calculated and measured equilibrium constants, which represents another criterion for the validity of the rate constants. We have previously estimated K eq for Reaction I (wild type protein) at about 0.1 (9). 3 But the correct K eq values for both Reactions I and II are in the range 1-1.5, and the standard free energy changes, ⌬G o , are close to 0.
The experiments reported here were conducted at pH 6.5. However, a few experiments (not shown) indicated that the same K eq values were obtained at pH 7.5. This was expected since a H ϩ is not required to balance the reaction. (pH 6.5 was selected because it is optimal for Enzyme I, and rapid quench studies with this enzyme are now in progress.) Two other important points emerge from the data. The k 1 and k Ϫ1 of Reaction I (wild type III Glc ) are only 2-3-fold less than the maximum possible, or diffusion-controlled rate (24). When the mutant, H75Q III Glc , is substituted for the wild type protein, the rate constants decrease by more than 200-fold, and both rate constants are equally affected.
The accompanying paper (11) compares the structures of III Glc and H75Q III Glc . The structural analyses and the data presented here are the basis of a relatively simple hypothesis that explains the 200-fold differences in rate constants and delineates a mechanism for phosphate transfer between HPr and III Glc .