A Transition State Analog for Lysozyme*

Abstract The δ-lactone derived from tetra-N-acetylchitotetraose (TACL) has been prepared by oxidation of tetra-N-acetyl-chitotetraose with iodine. The binding of TACL to lysozyme has been investigated by its inhibition of the lysozymecatalyzed lysis of Micrococcus lysodeikticus cells and by its perturbation of the tryptophyl fluorescence spectrum of lysozyme. At pH 6.2 the concentration of TACL that is required for 50% inhibition of the rate of lysis is 0.7 µm, which is 1/110 of the concentration of the unmodified tetrasaccharide that is required for such inhibition. The association constants for the binding of TACL to lysozyme over the pH range from 2 to 8 were obtained by fluorescence measurements. Their pH dependence shows that TACL binds most strongly to the species of lysozyme in which the carboxyl group of glutamate 35 is dissociated. In agreement with this result, the fluorescence-pH profile of the TACL-lysozyme complex indicates that the pK of glutamate 35 is about 4.7 in the complex, whereas the pK of glutamate 35 in the enzyme alone is about 6.0. The value of the association constant for the binding of TACL at pH 5.0 and 25° is 3.3 x 106 m-1, which is 32 times larger than that for the binding of the unmodified tetrasaccharide under the same conditions. On the basis of these results and of the similarity between the known conformation of the lactone ring and the proposed conformation of the transition state for lysozyme-catalyzed reactions (both half-chair ones), we conclude that TACL is a transition state analog for lysozyme. Furthermore, with these results we can estimate that the affinity of Subsite D of lysozyme for the half-chair conformation of the pyranose ring of N-acetylglucosamine is greater by a factor of 6 x 103 than its affinity for the chair conformation and thus contributes this factor to catalysis.


SUMMARY
The d-lactone derived from tetra-N-acetylchitotetraose (TACL) has been prepared by oxidation of tetra-N-acetylchitotetraose with iodine. The binding of TACL to lysozyme has been investigated by its inhibition of the lysozymecatalyzed lysis of Micrococcus lysodeikticus cells and by its perturbation of the tryptophyl fluorescence spectrum of lysozyme.
At pH 6.2 the concentration of TACL that is required for 50% inhibition of the rate of lysis is 0.7 pM, which is l/110 of the concentration of the unmodified tetrasaccharide that is required for such inhibition.
The association constants for the binding of TACL to lysozyme over the pH range from 2 to 8 were obtained by fluorescence measurements.
Their pH dependence shows that TACL binds most strongly to the species of lysozyme in which the carboxyl group of glutamate 35 is dissociated.
In agreement with this result, the fluorescence-pH profile of the TACL-lysozyme complex indicates that the pK of glutamate 35 is about 4.7 in the complex, whereas the pK of glutamate 35 in the enzyme alone is about 6.0. The value of the association constant for the binding of TACL at pH 5.0 and 25" is 3.3 X lo6 M-l, which is 32 times larger than that for the binding of the unmodified tetrasaccharide under the same conditions. On the basis of these results and of the similarity between the known conformation of the lactone ring and the proposed conformation of the transition state for lysozyme-catalyzed reactions (both half-chair ones), we conclude that TACL is a transition state analog for lysozyme. Furthermore, with these results we can estimate that the affinity of Subsite D of lysozyme for the half-chair conformation of the pyranose ring of N-acetylglucosamine is greater by a factor of 6 x lo3 than its affinity for the chair conformation and thus contributes this factor to catalysis. Enzymatic catalysis has generally been described and accounted for in terms of proximity and orientation, general acid and general base catalysis, covalent cat.alysis, strain, and various microscopic environment.al effects (2, 3). The extension of the transition state theory of reaction rates to enzymatic catalysis allows an approach of different emphasis for the ullderstanding of enzymatic csatalysis. In terms of transition st,ate theory, catalysis is due to t,he fact that the enzyme binds the transition state for the corresponding nonenzymatic reartion much more tightly t,h:m it binds the substrate.
Consequently, the specific binding intera&ons that occur between the enzyme and the substrate in the enzyme-substrate complex and in the transition state of the enzymatic reaction can explain catalysis. In the case of the transition st.ate these binding interactions ca.11 be deduced by the use of transition st,ate analogs. A transition state analog for an enzyme is a compound whose stable complex with the enzyme resembles in structure the transition state of the enzymatic reaction (4-6).
This paper describes the preparation of such an analog for lysozyme and the studies of the binding of this analog to lysozyme.
There is considerable evidence that the glycosyl transfer reactions that are catalyzed by lysozyme proceed via a transition state in which the substrate portion resembles an alkoxycarbonium ion (7-10). _ *\\ Such an ion is expected t,o have a half-chair conformation in which carbon atoms I, 2, and 5 of the riug and the ring oxygen atom lie in the same plane, since carbon atom 1 a.nd the ring oxygen atom are probably sp%ybridized (II). The transition state analog that we have prepared is the Slactone derived from tetra-lVacetylchitotetraose (TACV).

CH3
Since the conformation of crystalline n-gluconic acid &lactone is known to be a slightly distorted half-chair (12)) TACL should be an analog of the transition state conformation. The lactone was prepared from the t,etrasaccharide in order to satisfy the spec-i6eit.y of lysozyme, which has three binding subsites referred to as A, B, and C, that, bind three p-(1 4 4)linked N-acetylglucosamine residues. These subsites are contiguous with t,he Subsite T>, at which t'he N-acetylglucosamine or N-acetylmuramic acid residue that contains the glycosidic linkage to be cleaved binds (7).
The perturbation of the tryptophyl fluorescence of lysozyme was used to determine the binding constants for T,lCL because of the fluorescence changes observed with GlcNhc inhibitors (13,14) and the sensitivity of the technique at the low enzyme concentrations required. This technique has, in addition, yielded informat.ion regarding some inter&ions between the analog and the enzyme. It is our hope that the binding interactions in the crystal will ultimately be determined by x-ray studies of the complex.2 While this work was in progress, Uactones related t,o the corresponding substrates were reported to be potent inhibitors of a number of other glycosyl-transferring enzymes and surmised to be transition state analogs (15-18).

Materials
Preparation and Chemical Properties of Ta4CL--A typica preparation was carried out in the following way.
One hundred milliliters of tetra-N-acetylchitotetraose (0.005 M) were oxidized to the corresponding acid (TACA) with iodine (0.01 M) in KI (0.05 M)-K&03 (0.045 M) at 4' in the dark (19). After 32 hours, when titration of an acidified aliquot with sodium thiosulfate (19) showed that 1 mole of iodine per mole of sugar had been reduced, the reaction mixture was adjusted to pH 2 with 5 N HzS04 and the excess iodine was extracted with benzene. The extracted aqueous solution was adjusted to pH 7 with 1 N KOH, concentrated to 15 ml on a rotary evaporator, and 'chromatographed on a column (135 x 5.7 cmz) of Bio-Gel P-2, 200 to 400 mesh, with water as the eluant (20). This chromatography separated the potassium salt of TACA from the inorganic ions. The 25-ml fractions from the Bio-Gel column were monitored for TACA by measuring the absorbance at 215 nm, which is due to the amide function, and also by boiling ZO+l aliquots with 1 ml of 12 N HCl for 2 hours and testing the neutralized mido-2-deoxy-o-n-glucopyranosyl-(1 + 4)-2-acetamido-2-deoxyn-gluconic acid; TACL, the &lactone of TACA; MurNAc, 2acetamido-3-0-(l-carboxyethyl)-2-deoxy-D-glucose.
2 D. C. Phillips and his collaborators are studying the crystal structure of the TACL-lysozyme complex.
hydrolysate for reducing sugar (21). The TACA eluted between 400 and 500 ml, whereas the inorganic ions, which were locat.ed by the formation of precipitates with aqueous silver nitrate, eluted after 600 ml. The potassium salt of TACA was isolated through removal of the water by rotary evaporation and was dried by storage in a desiccator over PzO~. Calorimetric tests for reducing sugar (21) with GlcNAc as a standard and for amine (22) with n-glucosamine and n-glucosaminic acid as standards showed that the potassium TACA contained 2 mole 07; unreacted sugar and 5 mole 7; monodeacylated product. The potassium salt of TACA was converted to a mixture of TACA and TACL by passing it through a cation exchange resin (Rio-Rad, AG50W-X-8, H+ form), removing the water on the rotary evaporator, and drying the solid in an evacuated desiccator over 1'tOo5 for a day. The yield on t,he basis of t,he amount of tetra-N-acetylchitotetraose was 807;. Calorimetric tests for reducing sugar (21) and amine (22) showed that the mixture contained 1.5 mole (7; reducing sugar and 1.0 mole To monodeacet)ylated product.
The lactone content and equivalent weight were determined by rapid titration of a freshly prepared solution to p11 5.5 (z moles of NaOH consumed in neutralizing TACA), at which pH the half-time for hydrolysis of TACL is greater than 60 mm, followed by titrat,ion from pH 5.5 to 9 (y moles of NaOTI consumed in hydrolyzing TACL), at which pH the half-t,ime for hydrolysis of TACL is less than 1 miu. The mixture contained 23 mole '5; TACL (100 x/x + y) and had an equivalent weight of 830 (weight of mixt.ure/(z + y), theoretical value 840). Acid t,itration of the sodium salt of TACA, which was prepared from the mixture of TBCL and TACA by neutralization with NaOH, gave an acid dissociation constant of 3.5 for TACA.
Thin layer chromatography of the potassium TACA and of the TACA-TACL mixture after hydrolysis of the lactone in carbonate buffer showed a single spot in each case (see below for details).
The concentration of TACL was routinely measured with the neutral hydroxylamine-ferric chloride test, with N , S-diacetylcysteamine as the standard (23,24). The solution of lactone was added to an equal volume of a 1: 1 mixture of 4 M hydroxylamine hydrochloride and 3.5 N sodium hydroxide. After 5 min 4 volumes of 0.46 M ferric chloride in 0.48 n; HCI were added and the absorbance at 540 nm was read. The test was standardized by use of a solution of the TACA-TACL mixture which had had its la&one content determined by titration.
The color yield of TACL is 1.05 times that of N, S-diacetylcysteamine.
The equilibrium between TACL and TACA was established by allowing solutions of potassium TACA and of the mixture of solid TACA and TACL, adjust,ed to pH 2.1 to 2.3 with HCl, to equilibrate at 23-25". The equilibration process, which required about 20 hours, was followed by assaying for lactone with the hydrosylamine-ferric chloride test. Tests for reducing sugar and amine (21,22) showed that during this period there was no hydrolysis of the glycosidic or amide linkages. At equilibrium there is 14 f 1 mole yc TACL. The results of an investigation of the kinetics of the hydrolysis of the la&one function of TACL are summarized in Table I. In the presence of an equimolar amount of lysozyme, under which conditions TACL is entirely in complex with lysozyme at these concentrations (see "Results"), the rate of equilibration between the lactone and acid is accelerated approximately 20.fold. Other Materials-The p-(1 ---f 4).linked oligosaccharides of GlcNAc were prepared from chitin by the method of Rupley  (25) and were further purified by the procedure of Raftery et al. (20). A mixture of Z-acetamido-2-deoxy-D-gluconic acid and its y-and &la&ones was prepared from n-glucosaminic acid by acetylation with acetic anhydride according to the method of C~OSS.~ The mixture contained about 60 mole y0 lactone on the basis of titration (see above), and paper chromatography showed that both the y-and s-la&ones were present (24). Other materials were purchased from the following sources: twice crystallized, salt-free, hen egg white lysozyme from Worthington Biochemical Corp.; four times crystallized, salt-free, hen egg white lysozyme from Miles Chemical Co.; dried Microc~~cus lysodeikticus cells from Sigma Chemical Co.; GlcNAc from Aldrich Chemical Co.; n-glucosaminic acid from Mann Research Laboratories.

Methods
Rates of Cell Lysis (.%'6)-About 2.9 ml of a suspension of M. lysodeikticus cells in buffer were prepared in a 3-ml cuvette from stock solutions of cells and buffer at 30". A small volume of the inhibitor solution was then added, followed within 15 s by the addition of a small volume of a solution of Worthington lysozyme. The final volume was 3.0 ml; and the final concentrations of lysozyme and cells were 0.11 PM and 53 pg per ml, respectively. The decrease in absorbance at 450 nm with time due to lysis was followed using either a Zeiss PM& II spectrophotometer or Gilford 240 spectrophotometer with recorder, both with cell compartments thermostatted at 30". The change in absorbance with time was linear for at least the period between t and 13 min after initiation, and the rate of lysis was arbitrarily taken to be the slope of the plot of absorbance versus time for this period.
Fluorescence &i'easurements-Stock solutions of the Miles lysozyme in buffer were prepared, and the concentration of lysozyme was determined from the absorbance at 280 nm by use of the molar absorption coefficient of 3.8 X 104 M-l cm-1 (27). These solutions were diluted with the same buffer and passed through 0.45 pm MF-Millipore filters in order to remove any light-scattering particles.
The first 25 ml of filtrate were discarded because it contained some fluorescing substance from the filter.
The stock solutions of the TACL-TACA mixture for the fluorescence measurements were prepared in 0.005 N HCl and left at room temperature for 20 hours in order to allow equilibration of the acid and la&one forms. The concentration of TACL in the equilibrated mixture was determined with the hydroxylamine-ferric chloride test. The stock solutions of TACA were prepared by hydrolyzing the TACA-TACL mixture with dilute NaOH and adjusting the hydrolysate to pH 7 with HCl.
The following procedure was used in making t'he fluorescence measurements for determining the association constants. About 1.9 ml of lysozyme in buffer was temperature equilibrated in a 3-m& l-cm cuvette at 25.0 =t 0.1". When necessary, sufficient NaOH or HCl was added to the lysozyme-buffer solution SO that the subsequent addition of the TACL-TACA mixture or of TACA would bring the pH back to that of the lysozyme in buffer alone. A small aliquot (0.10 ml or less) of a stock solution of TACL-TACA or of TACA was added to the lysozyme solution, and the fluorescence intensity was measured within 15 s. The recording fluorometer employs two Jarrell-Ash +meter monochromators, an EM1 9601B photomultiplier, and an Osram 150 watt high pressure Xenon lamp. The excitation and emission band widths were 7 nm. The exciting wave length was 280 nm, at which the absorbance of the solutions of lysozyme used varied between 0.005 and 0.024. The wave length at which the fluorescence intensity was recorded was chosen so that the intensity of the free enzyme fluorescence and the enzyme-inhibitor fluorescence differed markedly. This wave length varied with pH. The change in fluorescence was complete by the time of the iirst measurement, and the fluorescence was constant for at least 1 min (40 s at pH 7.84 due to la&one hydrolysis) thereafter. Before and after each such measurement the fluorescence of a standard solution of lysozyme was recorded.
The small variations in the fluorescence which occurred during a series of measurements as the result of fluctuations in the intensity of the light source were minimized by normalizing all the intensities to a value for the lysozyme standard.
The procedure for obtaining the fluorescence spectrum of lysozyme and of its complexes was the same as that just described, with the exception that 1 to 2 min were required for recording the spectrum over the range between 290 and 400 nm. A small contribution of the buffer to the spectrum was subtracted from the spectrum.
The inhibitors themselves exhibited no significant fluorescence.
Normalization of the spectra against the fluorescence of a standard solution of lysozyme, whose fluorescence was monitored at intervals during the measure-ment of each series of spectra, corrected for small changes in the lamp intensity. A control experiment was carried out to test for any hydrolysis of the glycosidic linkage of TACL or TACA under the conditions of the fluorescence measurements, Aliquots of a reaction mixture at 30" that contained 0.54 mM TACL, 3.0 rn~ TACA, and 0.11 mM lysozyme in 0.01 M sodium citrate buffer, pH 5.8, at 0.2 RI ionic strength with NaCl were analyzed for reducing sugar (21). The increase in the concentration of reducing sugar was less than 0.01 xnM aft,er 20 min, 0.10 InM after 50 min, and 0.45 mM after 80 min. Thus, the extent of hydrolysis was negligible during the fluorescence measurements.
The rates of hydrolysis of the lactone function in the presence and absence of lysozyme {Table I) show that during the fluorescence measurements the extent of this reaction was also negligible.
The compounds were detected with a calorimetric test for the amide function as follows: spray with 0.25";, NaOCl; dry; spray with 95cJ ethanol; dry; spray with 0.2(x, starch in 0.1 M KI.4 The limit of detection by this procedure is about 0.2 pg of di-N-acetylchitobiose.
This chromatographic procedure was used to search for lysozyme-catalyzed transglycosylation (28) under the conditions of the fluorescence measurements.
In the experiment with TACA, aliquots of a reaction mixture that contained 7.7 mM TACA and 0.53 mM lysozyme in 0.01 M sodium citrate buffer, pH 5.3, at 0.2 M ionic strength with NaCl were removed at time intervals and put into NanCOs buffer, pH 10.1, in order to stop the enzymatic reaction.
One microliter ( The samples that were taken at 1 and 3 min of reaction showed only a very large spot at the origin (lysozyme) and a spot at RF 0.2 (TACA). lysozyme catalyzes glycosyl transfer reactions of TACA and TACL, these reactions are sufficiently slow so that they do not interfere with t,he fluorescence and cell lysis measurements.

Effect of TACL upon Rates of Cell Lysis by Lysozyme-The inhibition
of lysozyme-catalyzed cell lysis in the presence of the TACL-TACA mixture, of TACA alone, and of tetra-N-acetylchitotetraose are shown in Fig. 1. It can be seen that although it required 700 PM TACA and 80 pM tetra-N-acetylchitotetraose for 50% inhibition, only 0.7 j&M TACL (3.6 ).bM in the TACL-TACA mixture) was required.
Similar values were obtained for the TACL-TACA mixture and the tetrasaccharide when the rates were measured in weaker buffer (0.01 M sodium phosphate, pH 6.2, at ionic strength 0.1 M with NaCl).
A mixture of 2-acetamido-2-deoxy-n-gluconate and its y-and &lactones that contained 2.3 mM total lactone did not inhibit the rate of lysis in 0.07 M sodium phosphate buffer, pH 6.2, at ionic strength 0.11 M with NaCl.
Association Constants for Binding of TACA and TACL to Lysozyme-The formation of complexes between lysozyme and TACA or TACL is accompanied by substantial changes in the fluorescence spectrum of lysozyme (Fig. 2). The fluorescence intensity changes, at a constant wave length and concentration of lysozyme, produced by changes in the concentration of the inhibitor were used to obtain the association constants (13, 14). Equations 1 and 2, which apply to the cases in which the fraction of inhibitor bound is small and large, respectively, were used to analyze the results with TACA and TACL, respectively. In Equation 1, FE, F are the same, with the exception that the subscript L applies to TACL and C,$ is the total lysozyme concentration.
In the case of TACA, the plots of l/(F-Fs) aga,inst l/[TACA]o were linear, as expected from Equation 1; and the ratios of intercept to slope yielded the values of K, given in Table II.
The determination of the association constants for the binding of TACL to lysozyme was complicated somewhat by the fact that TACL was added to the enzyme as part of an equilibrium mixture of TACL (14 mole T) with TACA (86 mole (x). Preliminary experiments revealed that at pH values above 4.5 the concentrations of TACA alone that were required to cause fluorescence intensity changes similar to those observed with the TACL-TACA mixture were 30 times or more greater than-the concen-  Fig. 3.
The values of KL that were obtained from the intercepts of such plots are presented in Table II. Below pH 4.5 the binding of TACA to lysozyme is comparable to the binding of TACL, and significant amounts of bot*h complexes form in the solutions of lysozyme, TACA, and TACL. By use of the following relationships (Equations 3 to 6), it was In the derivation of Equation 6, the concentrations of uncomplexed TACL and TACA are taken t,o he equal to the total concentrations of these species. Sufficiently low lysozyme concentrations mere used below pH 4.5 to allow this approximation (see Table II).
The plots of l/(2;" -FR) against l/C10 were linear and yielded values of K,s,.
Values of RL (see Table II) were calculated from the values of K,,,, by use of Equation 5 and the values of KA that were determined separately under the same conditions.
A comparison of the 111-I dependence of the association constants of TACL, TACA, and tri-N-acetylchitotriose is presented in Fig. 4.
Flourescence Xpecbu-Fluorescence spectra of lysozyme and of lysozyme in the presence of saturating concentrations of the TACL-TACA mixture, of TACA, and of tri-N-acetylchitotriose at pH values over the range from 2 to 7.9 were obtained. The wave lengths of maximum fluorescence intensity do not change markedly with pH: for lysozyme alone X,,, falls between 335 and 338 nm, and for all the lysozyme-inhibitor complexes X,,, is 325 to 328 nm. In order to separate the contribution of the fluorescence intensity of the TACL-lysozyme complex, the observed fluorescence intensities in the presence of the TACL-TAG4 mixtures were corrected for the contribution due to the  Table II, sodium citrate between p1-I 6.2 and 6.5), NaCl to ionic strength 0.2 M, and, where present, either 1 mM tri-N-acetylchitotriose, 0.4 mM (pH 2.1 and 4.9) or 0.8 mM (pH 34.5) TACA, or 0.077 mM (pH 4.4 to 7.9), O.lG mM (pII 3.9), or 0.3G mM (pH 2.1 to 3.1) TACT,-TACA mixture. Temperature, 25". The concentrations of the inhibitors are enough to convert 90% or more of lysozyme to the corresponding complex (Table II and  At p1-I 3.05 the fraction of lysozyme complexed w&h TACA and the fraction of Fs due to this complex are maximal and have values of 0.38 and 0.41, respectively. The pH dependence of the peak fluorescence intensities are presented in Fig. 5. The data for lysozyme and the tri-Nacetylchitotriose-lysozyme complex are in good agreement with earlier studies (13, 29). Although the pH dependence of the fluorescence of the TACA complex is very similar to that of the trisaceharide complex, the fluorescence-pH profile of the TACL complex is shifted in the acid direction by about 1.7 pH units. Thus, the ionizable group that quenches the tryptophyl fluorescence in lysozyme-inhibitor complexes has a considerably lower pK, in the TACL complex.

Mode of Binding of TACL to Lysozyme-If
TACL is a transition state analog for lysozyme, its four rings must bind in Subsites A through D in the cleft. The tryptophyl fluorescence changes reported here suggest this mode of binding.
It has been shown that tri-A-acetylchitotriose, in the crysbal (30) and in solution (31), binds predominantly in Subsites A through C and interacts with tryptophans 62,63, and 108 through hydrogen and hydrophobic bonds. The relative values of the association constants for a number of oligosaccharides (14) and limited nuclear magnetic resonance information (31) suggest that this binding register is also the predominant one for tetra-N-acetylchitotetraose.
Previous fluorescence studies have indicated that the blue shift in the fluorescence spectrum that is produced by binding of the GlcNAc trisaccharide is due to a change in the average tryptophyl environment to a less aqueous one (13, 32). From the pH dependence of the peak fluorescence of the lysozyme-trisaccharide complex, it was suggested (13, 29) and verified (32) that a carboxyl group with a pK, of about 6.3 in the complex (probably glutamate 35) interacts with tryptophan 108 to quench its fluorescence.
The present fluorescence results with the TACL-lysozyme complex show that the fluorescence intensity and the spectrum of the TACL and tri-N-acetylchitotriose complexes are very similar at pH 2.0 to 3.0 and at' pH 7.5 to 8.0 (same state of ionization of lysozyme), indicating similar interactions for both inhibitors at Subsites A through C. On the other hand, the different fluorescence pH dependence of the TACL-lysozyme complex compared to that of the trisaccharide-lysozyme complex, which is presumably due to the altered pK, of glutamate 35 (see Fig. 5 and below), is most easily explained by the additional binding of the lactone ring in Subsite D, which is adjacent to glutamate 35 (30).
The relative values of the association constants for the binding of TACL and tetra-N-acetylchitotetraose to lysozyme provide further evidence that TACL binds in the A through D mode. In agreement with the prediction that a transition state analog should bind much more tightly than the corresponding substrate (4-6), the association constant for TACL is 32 times greater than that for the unmodified tetrasaccharide at pH 5 (Table III).
This relative strength of binding is also shown by the fact that TACL is 110 times more potent than the tetrasaccharide as an inhibitor of lysozyme-catalyzed cell lysis. Although definitive proof of the binding mode for TACL may have to await the results of crystallography, we tentatively conclude that TACL binds in Subsites A through D.
pH Dependence of Fluorescence and, Association Constants-The increase in the association constant for TACL over the pH range from 2 to 6.2 and its constancy between pH 6.5 and 8 (Fig. 4) show that TACL binds more strongly to the species of the enzyme in which glutamate 35 (pK, 5.9 in the free enzyme, see below) is ionized than to the species in which it is protonated.
Conversely, the pK, of glutamate 35 must be lower in the complex than in the free enzyme.
In fact, this lowered pK, is evident in the pH dependence of the fluorescence intensity of the complex (Fig. 5), which suggests a p& of about 4.7 for glutamate35 in the complex. In contrast, tri-N-acetylchitotriose binds less tightly to the form of the enzyme in which glutamate 35 is ionized and the pK, of glutamate 35 in the complex is greater (Figs. 4 and 5). It is not possible to decide with confidence from the pH profile for KL whether the state of ionization of aspartate 52 (pK, 4.5 in the free enzyme, see below) also affects KL.
We have attempted to analyze quantitatively the pH dependence of the fluorescence intensity of the TACL-lysozyme complex (Fig. 5) and the pH dependence of the association constant for its formation (Fig. 4) by adapting the equations that describe the effect of the ionization of a single acid group of the enzyme (33,34) to these data. In such an analysis the pH dependence of the fluorescence yields values of the acid dissociation constant for the complex, and the pH dependence of the association const.ant yields values of the ionization constant of the acid group for both the complex and the free enzyme.
We have found that in both cases the values of the acid ionization constants that were so obtained are not constant, but decrease by a factor of 3 to 4 as the pH increases. Consequently, the ionization of a single group of the enzyme does not adequately account for the pH dependencies.
This conclusion is not surprising, since crystallography has shown that there are four dissociable groups in the region of Subsites A through D. These groups are aspartates 101 and 103, which may interact with the inhibitor at Subsites A and B, and glutamate 35 and aspartate 52, which may interact with the inhibitor at Subsite D (30). Parsons and Raftery have determined that the macroscopic pK, values for glutamate 35 and aspartate 52 in the free enzyme are 5.9 and 4.5, respectively, at 25" and 0.15 M KC1 (35); the pK, by guest on March 23, 2020 http://www.jbc.org/ Downloaded from values of aspartates 101 and 103 have not been determined.
A better fit of the pH dependencies of the fluorescence intensity and association constant can be made if one assumes the involvement of two ionizable groups. However, the data are not sufficiently extensive to warrant the inclusion of this analysis here.
It is interesting to note that in the transition state of lysozymecatalyzed glycosyl transfer the carboxyl group of glutamate 35 is probably largely ionized due to almost complete proton transfer to the RO moiety that is leaving or attacking the glycosidic carbon atom (see the introduction).
Thus, glutamate 35 is ionized in both the proposed transition state and in the tightest complex with TACL, although TACL lacks the positive charge that the alkoxycarbonium ion possesses. Crystallography of the TACL-lysozyme complex may reveal whether the effect of the ionization of glutamate 35 upon KL is due to a direct interaction between the carboxylate anion and the lactone function or due to the strengthening of other interactions between TACL and the protein, perhaps as the result of a change in conformation of the protein.

Role of Tight Binding of Half-Ch,air Conformation in Igsozyme
Catalysis-The binding of a pyranose ring in Subsite D appears to be accompanied by distortion of the pyranose ring from its normal chair conformation (36) toward the half-chair conformation which is expected for the transition state (14,30). The distortion occurs to prevent an unfavorable steric interaction between the 6 CH20H group of the pyranose ring and the enzyme without destroying the other favorable interactions between enzyme and substrate (30). Our results with TACL, which does not need to be distorted to bind in Subsite D, can be used to estimate how the tighter binding of the half-chair conformation contributes to catalysis.
We will assume that the most favorable conformations of the lactone ring of TACL and of the pyranose ring in the transition state are identical and that the strong binding of TBCL to lysozyme is largely due to the half-chair conformation of the lactone ring rather than to a specific strong interaction between the lactone function itself and the protein.
If these assumptions are correct, then the ratio of the binding constant for TACL to that for tetra-N-acetylchitotetraose bound in the A through D mode is an estimate of the factor by which the half-chair conformation of the transition state allows more favorable interactions with the enzyme than does the chair conformation of the substrate. This factor is equivalent to a factor in catalysis, since it represents a stabilization of the transition state relative to the substrate that does not occur in the corresponding nonenzymatic reaction. Although tetra-N-acetylchitotetraose does not bind predominantly in Subsites A through D, an estimate of this ratio can be obtained from other data. It is known that the interaction of an MurNAc residue or its methyl ester with Subsite D at pH 5.5 reduces the binding constant for association of the tetrasaccharide GlcNAc-MurNAc-GlcNAc-MurNAc with lysozyme by a factor of 130, relative to that for formation of the complex with the trisaccharide, GlcNAc-MurNAc-GlcNAc (Table III). Since the hexasaccharides of GlcNAc and of GlcNAc-MurNAc, which bind 50% or more in the A through F mode, have approximately the same association constants and are cleaved at the same rate in the complex (7,28,37,38), it seems likely that the lactyl side chain of an MurNAc residue bound in Subsite D does not interact strongly with the enzyme. In the crystal structure that has been proposed for the complex with the GlcNAc-MurNAc hexasaccharide, the lactyl side chain in Subsite D is directed away from the enzyme (30). Consequently, it seems probable that the introduction of a GlcNAc residue into Subsite D is also destabilizing by a factor of about 100, and thus we estimate on the basis of the association constant for tri-N-acetylchitotetraose at pH 5.5 (Table III) that the association constant for the tetra-N-acetylchitotetraose bound in the A through D mode is 2 x lo3 M-l.
This association constant is smaller than the maximal value of the association constant for the binding of TACL (Table  III) by a factor of 6 X 103. We take this factor to be an estimate of the contribution to catalysis that can be assigned to tighter binding of the transition state due to its half-chair conformation.