When the substrate is in the shallow site [Fig. 5(a)], it is bound preproductively and is not in the catalytically correct juxtaposition to Glu461 and Glu537. The substrate has to move about 3 Å deeper into the active site (Ed•Gal-OR) for catalysis to begin. The roles of Glu461 and Glu537 as the acid catalyst and the nucleophile, respectively, have been well established by chemical modification,70, 71 site-directed mutagenesis,72–74 and structural studies.29 Deep-site binding is visualized by the binding of galactose to the free enzyme,29 in which the galactose stacks with Trp568 [Fig. 5(b)]. Galactose is a product of the reaction but is also a substrate in the reverse direction.26 The evidence that it binds like a substrate is that the loop, Arg599 and Phe601 are in the same position as when substrate is present. Specifically, when galactose is in the deep site, Phe601 does not rotate, Arg599 still interacts with Glu797, Ser796, and Gly794, and the loop does not close [Fig. 6(a)]. Galactose binds in the deep mode because it does not have a glucose or a hydrophobic aglycone to restrict it from readily leaving the shallow mode. Normally lactose or the synthetic substrates are constrained (presumably by Trp999) and would require energy to shift to the deep site. The Ki for galactose binding is high showing that binding to this site is not good (albeit galactose binds better to the deep site than it does to the shallow site as noted by the lack of any shallow mode electron density for a galactose).
Progression to the deep mode [Fig. 5(c)] involves a rotation about an axis connecting the galactosyl C4 and C6 hydroxyls, which maintain similar interactions in the two modes—the C4 hydroxyl interacts with Asp201 and an Mg2+ ligated water molecule while the C6 hydroxyl interacts with Na+, His540, and Asn604. The energies of these interactions in the two modes are, however, probably different. The other three hydroxyls undergo substantial changes in environment. The C3 hydroxyl displaces a water molecule to interact with His391 and two waters—one ligated to the active site Mg2+ and another ligated to His357 [Fig. 5(a–c)]. The C2 hydroxyl becomes close enough (<3.2 Å) to Asn460, Glu461, and Glu537 to form interactions. Of these three, the geometry is the most ideal for an H-bond to Asn460,67 although the geometry is also good for an H-bond to Glu537. The C1 hydroxyl now occupies the position of the shallow mode C2 hydroxyl, H-bonding with Glu461. As Glu461 is the acid catalyst and the C1 hydroxyl is in the β conformation and therefore is equivalent to the galactosidic oxygen of the substrate, this is expected.
It is of interest that early kinetic studies40, 75, 76 led to the conclusion that a protein conformation change occurs after substrate binds. It was postulated that the acid catalytic group must move into position before it can interact with the galactosidic oxygen. Such a conformation change does not occur. However, the step with substrate moving from the shallow nonproductive site (Es•Gal-OR) to the deep productive site (Ed•Gal-OR) so that the general acid (Glu461) contacts the galactosidic bond would be kinetically identical to a conformation change in which the acid group moves towards the substrate. Thus, the concept that there is a conformation change that moves the acid group into place was not too far off the mark.
Galactosylation (first transition state)
The activation energy needed for galactosylation (k2) may include the energy needed for the movement of the substrate from the shallow to the deep mode and that movement is included in the galactosylation step (k2) that is depicted in Figure 4. This movement has an unfavorable equilibrium as indicated by the lack of any electron density in the deep mode when E537Q β-galactosidase is incubated with substrates such as lactose, allolactose, or oNPG, or when native enzyme is incubated with substrate analogs such as IPTG. However, despite the unfavorable equilibrium, the shifting of substrate from the shallow to the deep position could be fast. The equilibrium may be unfavorable because movement back to the shallow mode is even faster. If the shifting is indeed rapid, the movement of the substrate from the shallow to the deep state would be kinetically irrelevant, and the rate would mainly depend on the activation energy needed to form the activated complex as the energy needed to transfer substrate from the shallow to the deep mode would be negligible in comparison. On the other hand, the shifting of substrate to the deep mode could be slow enough so that it does affect the reaction rate. The formation of the highly activated transition state would certainly still be a much more difficult process but the shifting of the substrate could be of significance. There is some experimental evidence consistent with movement to the deep mode being at least partially rate limiting. Isotopic substitution of the galactosidic oxygen of pNPG with O-18 affects catalysis, reducing kcat more than kcat/Km. One possible explanation for the smaller effect on kcat/Km is that the approach of the substrate to the Michaelis complex (the deep mode) is partially rate limiting.80 Similarly, solvent isotope effects on catalysis of pNPG suggest that proton transfer is part of the rate-limiting step for kcat but not for kcat/Km.81 Proton transfer from Glu461 is expected to be involved in the chemical step for galactosylation but not for movement to the deep mode. These isotope effects can be at least partially explained by a rate-determining bond cleavage for kcat, and rate-determining progression to the deep mode for kcat/Km.
The results of a theoretical study of the mechanism of β-galactosidase82 suggest that the galactose part of the substrate in the deep site is found in a “pretransition state” form with a 4H3 conformation. The report also suggests that the transition state is in a 4E conformation. The projections of bond lengths within the transition state are also of interest. It is predicted that the length of the galactosidic bond (from the anomeric carbon to the galactosidic oxygen) increases from 1.47 Å in the reactant to 2.25 Å in the first transition state. At the latter distance, the bond is almost broken. This is despite the fact that the study predicts that the proton of Glu461 is not totally transferred. The nucleophile (Glu537) also moves closer (from 3.01 Å in the enzyme substrate complex to 2.45 Å in the first transition state). The length of this bond is 1.53 Å in the covalent form.
If galactose binding in the deep site is indeed representative of the manner in which substrate binds in the deep mode, the lack of distortion noted for the galactose29 suggests that the transition state probably really only begins to form when Glu461 donates a proton to the galactosidic bond of the substrate in the deep site and that significant amounts of “pretransition state form” do not exist. As a result of the protonation, the oxygen of the scissile bond has a positive charge and attracts electrons from C1. This carbon with a partial positive charge and with partial sp2 hybridization in turn attracts electrons from the ring oxygen giving the galactosyl moiety oxo-carbenium ion characteristics. A partial double bond would then be present between the O5 and C1 atoms. This would impose an element of planarity on the pyranose ring, a likely feature of the transition state. For SN1 cleavage, stereoelectronic theories require that a ring oxygen lone pair be antiperiplanar to the bond that breaks,83 which necessitates some distortion away from a chair configuration. For SN2 cleavage, planarity is an inherent structural aspect of the mechanism. In either case, both galactonolactone and GTZ (transition state analogs) have planar properties because of partial double bonds between the O5 and C1 and between the N5 and C1, respectively. Their good binding as well as other transition state analog properties that they possess (see below) is evidence that the transition state has planar tendencies.
It is useful to provide evidence that D-galactonolactone [Fig. 6(b)] and GTZ are indeed legitimate transition state analog inhibitors and thus that their binding indicates the manner in which this enzyme stabilizes the transition state. The Ki of D-galactonolactone is ∼0.6 mM, much higher than expected of a transition state analog. The binding is, however, very strong when it is noted that δ-1,5-galactonolactone, the only structural isomer of D-galactonolactone that binds at the active site,29 is present in solution in such very small amounts that it is not detectable by NMR even in very concentrated D-galactonolactonesolutions.84 The γ-1,4-galactonolactone form overwhelmingly predominates. Thus, δ-1,5-galactonolactone must bind with very high affinity. GTZ binds very strongly to the enzyme when presented as a competitive inhibitor. Other evidence that these are good transition state analogs is that when β-galactosidases with substitutions for His357, His391, and Asn460 (residues that stabilize the transition state) were studied, the binding of these two transition state analogs was decreased more or less in parallel with the kcat/Km values of these substituted enzymes.67, 85–87 In addition, the C1 of these two transition state analogs have trigonal character as is expected of the transition state. To help neutralize the positive charge of the trigonal carbons in these transition state analogs, electrons are thought to move somewhat from the ring oxygen or nitrogen towards the C1 to form a partial double bond. Thus, these compounds have a partial planar structure. Again this is an expected property of an analog mimicking an oxocarbenium ion. In addition, the partial positive charge of the C1 of these two compounds is a property expected of the transition state, mimicking an oxocarbenium ion. Finally, they both bind well in the deep mode29 as expected for transition state analogs of this enzyme.10
If galactose binding is indicative of substrate binding in the deep mode while D-galactonolactone or GTZ are representative of the transition states, it is of interest that most of the H-bond interactions that stabilize the transition state are similar to those that hold galactose in the deep site [see Fig. 6(c) and the associated interactive image]. However, the Ki of galactose is about 25 mM while the binding of δ-1,5-galactonolactone and GTZ are orders of magnitude better. It has been suggested that active sites can be thought of as “designer solvents”88 that drive the development of the cognate transition state. One can think of the residues of the active site pocket as the solvent to partially explain the effects. The main differences in the positioning of galactose compared with galactonolactone and GTZ in the pocket [Fig. 6(c)] are in respect to Trp568, Tyr503, Phe601, and Na+. The C5 atoms of D-galactonolactone and GTZ are much closer (∼0.8 Å) to Trp568 than is the C5 atom of galactose while the O5 of D-galactonolactone is ∼1 Å closer to Tyr503 while the N5 of GTZ is about 0.5 Å closer. The O6 maintains its ligation to the Na+, but also shifts deeper into the active site as Ph601 swings closed to interact with Na+ and pack against the galactosyl C6 [Figs. 5(b) and 6(a,b)]. The transition state may form29 partly because the C5 atom is hydrophobically attracted to Trp568, because the O5 atom is attracted to Tyr503, because the C6 is attracted to Phe601 and because the O6 is better attracted to the Na+. Trp568, Tyr503, Phe601, and Na+ may be the components of the designer solvent that ‘dissolve’ the C5, O5, C6, and O6. C3 and C4 also edge 0.1–0.2 Å closer to Trp568. This occurs even though His391, His357, Asn460, Asp201, and the two waters attached to Mg2+ hold O2, O3, and O4 in place by roughly the same distances for both galactose and the transition state analogs. Asn460 seems to be especially important67 for interaction with the O2, although Glu537 probably also plays an important role. All the bonds with the transition state are obviously of importance. Possibly the bonds to the hydroxyls of C2, C3, and C4 are important to hold the rest of galactose in place while C5, O5, and C6 move. In addition to the above, the positive charge on the trigonal C1 group is close enough to interact with and be stabilized by the negative charge of Glu537. This interaction is at the same distance in galactose as in galactonolactone but the C1 would have very little charge in galactose compared with that in galactonolactone. As shall be seen below, the positive charge of the C1 is stabilized to such an extent that a covalent bond forms.
The Tyr503 interactions noted with galactonolactone and GTZ may be significant in relation to the transition states. The electrons of Tyr503 probably interact with the ring oxygen of the transition state and help “push” the ring oxygen electrons towards C1 and aid in the formation of a partial double bond between O5 and C1. This also implies that planarity is important. The electrostatic interaction with Tyr503 could be especially strong as it takes place after the substrate is in position with no water interactions. Electrostatic interactions are stronger in a less-polar environment. Furthermore, pucker in the sugar ring in both the deep mode galactose complex and the covalent intermediate seems to create suboptimal geometry for bonding between Tyr503 and the galactosyl ring oxygen. Planarity of the galactosyl group in the transition state would improve this geometry.
L-Ribose, a pentose, also binds in the deep mode. Although the furanose form of L-ribose is structurally similar to other deep mode inhibitors (e.g., D-galactonolactone) with hydroxyls in the same orientations and planarity in the sugar ring, it is the pyranose form of L-ribose that binds to the active site, in the 1C4 rather than the 4C1 chair configuration. L-Ribose does not bind as well as D-galactonolactone or D-galactotetrazole but relative to the binding of other pentapyranoses it has a very low Ki. In addition, its Ki value increases in proportion to the changes to kcat/Km when residues that are important for transition state stabilization are substituted.85, 87 L-Ribose binding puts hydroxyls within 0.4 Å of the positions of the lactone C6, C4, and C3 hydroxyls and within 1 Å of the lactone C2 hydroxyl, as well as stacking a hydrophobic surface of the sugar on Trp568. Thus, L-ribose is able to bind with hydroxyls in four of the five deep mode hexapyranose hydroxyl positions. Because L-ribose is a pentapyranose, the fifth deep mode hydroxyl position (the C1 hydroxyl, contacting Glu461) is unoccupied. Furthermore, L-ribose only uses a hydroxyl group to ligate the Na+ rather than a hydroxymethyl group. The combination of the 1C4 configuration with a rotation of the ring by ∼45° relative to the other deep mode inhibitors, puts the L-ribose ring oxygen in a perfect position to make 2.9 Å polar contacts to both Tyr503 and Glu537. Thus, of the inhibitor complexes whose structures have been determined, L-ribose is the only one whose ring oxygen makes two enzyme contacts, and it seems to take the greatest advantage of the H-bonding possibilities provided by Glu537.
As already implied, Glu537 is close to the C1 of the transition state and reacts to form a quasi-stable covalent bond. The physical presence of a covalent bond to Glu537 was first shown71 by reacting β-galactosidase with 2,4-dintrophenyl-2-F-β-D-galactopyranoside. 2,4-Dinitrophenol is a very good leaving group while the fluorine at the O2 position slows the degalactosylation reaction. 2-Fluoro-D-galactose is covalently bound to Glu537 as a normal chair in an α configuration.29 The enzyme is totally inactive upon substituting for Glu537.61 In general, the same interactions29 needed to stabilize the transition state also stabilize the covalent intermediate. The positions of the galactosyl hydroxyls and enzyme groups are very similar between the two complexes, with the exception of Glu537, which rotates slightly in response to forming the covalent bond. The interaction between Tyr503 and the galactosyl ring oxygen is less optimal than in the lactone complex, due to the pucker in the sugar.
D-Galactal also interacts with Glu537. D-Galactal was at first thought to bind as a competitive inhibitor because of its planar shape.89 However, it was shown that 2-deoxy-D-galactose forms when β-galactosidase is incubated with D-galactal90 and kinetic experiments28 also suggested that D-galactal reacts with the enzyme.
Before the studies mentioned here, kinetic findings20, 76, 91, 92 had also suggested that a covalent intermediate exists.
Transgalactosidic reactions (allolactose formation)
Almost all alcohols and sugars can act as acceptors of galactose.2, 95–98 They react in place of water. Bis-tris, a component of the buffer, binds nonproductively in the putative “acceptor” site when the enzyme has 2-deoxy-D-galactose covalently bound. Although it was not well defined, a glucose was also visualized in this enzyme form29 when a high concentration of glucose was added. These findings suggest that the acceptor comes into position to react when the enzyme is in the covalent form.
The intramolecular galactosyl transfer reaction of β-galactosidase with lactose2 that produces allolactose is of physiological importance because allolactose is the natural lac operon inducer.99, 100 In that reaction, the β-1-4 linkage of lactose is broken and the C6 hydroxyl of the glucose acceptor reacts with the C1 of the galactose to form allolactose. After the 1–4 bond is broken, glucose takes up a position so the O6 hydroxyl interacts with the anomeric carbon of galactose with Glu461 being the base catalyst. About 50% of the lactose molecules that react with β-galactosidase are initially hydrolyzed while 50% form allolactose intramolecularly. A physiological experiment demonstrated the role of β-galactosidase in the production of the inducer inside E. coli cells. A null mutant of lacZ β-galactosidase can still produce lacY permease when grown with IPTG but not when grown with lactose.100 Thus, the processing of lactose to allolactose (catalyzed by β-galactosidase) is needed to produce the inducer inside the cell. Allolactose is itself a substrate of the enzyme97 and when reaction with lactose has run its course, essentially only galactose and glucose are present. Thus, allolactose is a transient intermediate of the overall reaction with lactose. The intramolecular reaction occurs with glucoses that do not leave the active site after the β-1-4 galactosidic bond is broken but intermolecular allolactose production can also take place with glucose that has been hydrolyzed and subsequently rebinds and reacts as a transgalactosidic acceptor.2