Capturing the free energy of transition state stabilization: insights from the inhibition of mandelate racemase

Mandelate racemase (MR) catalyses the Mg2+-dependent interconversion of (R)- and (S)-mandelate. To effect catalysis, MR stabilizes the altered substrate in the transition state (TS) by approximately 26 kcal mol–1 (–ΔGtx), such that the upper limit of the virtual dissociation constant of the enzyme-TS complex is 2 × 10–19 M. Designing TS analogue inhibitors that capture a significant amount of ΔGtx for binding presents a challenge since there are a limited number of protein binding determinants that interact with the substrate and the structural simplicity of mandelate constrains the number of possible isostructural variations. Indeed, current intermediate/TS analogue inhibitors of MR capture less than or equal to 30% of ΔGtx because they fail to fully capitalize on electrostatic interactions with the metal ion, and the strength and number of all available electrostatic and H-bond interactions with binding determinants present at the TS. Surprisingly, phenylboronic acid (PBA), 2-formyl-PBA, and para-chloro-PBA capture 31–38% of ΔGtx. The boronic acid group interacts with the Mg2+ ion and multiple binding determinants that effect TS stabilization. Inhibitors capable of forming multiple interactions can exploit the cooperative interactions that contribute to optimum binding of the TS. Hence, maximizing interactions with multiple binding determinants is integral to effective TS analogue inhibitor design. This article is part of the theme issue ‘Reactivity and mechanism in chemical and synthetic biology’.

SLB, 0000-0003-4433-6174 Mandelate racemase (MR) catalyses the Mg 2+ -dependent interconversion of (R)-and (S)-mandelate. To effect catalysis, MR stabilizes the altered substrate in the transition state (TS) by approximately 26 kcal mol -1 (-ΔG tx ), such that the upper limit of the virtual dissociation constant of the enzyme-TS complex is 2 × 10 -19 M. Designing TS analogue inhibitors that capture a significant amount of ΔG tx for binding presents a challenge since there are a limited number of protein binding determinants that interact with the substrate and the structural simplicity of mandelate constrains the number of possible isostructural variations. Indeed, current intermediate/TS analogue inhibitors of MR capture less than or equal to 30% of ΔG tx because they fail to fully capitalize on electrostatic interactions with the metal ion, and the strength and number of all available electrostatic and H-bond interactions with binding determinants present at the TS. Surprisingly, phenylboronic acid (PBA), 2-formyl-PBA, and para-chloro-PBA capture 31-38% of ΔG tx . The boronic acid group interacts with the Mg 2+ ion and multiple binding determinants that effect TS stabilization. Inhibitors capable of forming multiple interactions can exploit the cooperative interactions that contribute to optimum binding of the TS. Hence, maximizing interactions with multiple binding determinants is integral to effective TS analogue inhibitor design.
This article is part of the theme issue 'Reactivity and mechanism in chemical and synthetic biology'.

Introduction: benchmarks for transition state analogue design
It has been almost three-quarters of a century since Linus Pauling pointed out that 'enzymes are molecules that are complementary in structure to the activated complexes of the reactions that they catalyze, that is, to the molecular configuration that is intermediate between the reacting substances and the products of reaction for these catalyzed processes' [1,2] [3, p. 709]. Pauling's prescient remarks were placed on a more quantitative footing by Wolfenden [4,5] and Lienhard [6] using transition state (TS) theory and a thermodynamic cycle (figure 1) to relate an enzyme's catalytic efficiency (k cat /K m ) to its ability to bind the altered substrate in the TS; i.e. K tx = k non /(k cat /K m ), where k non is the rate constant for the corresponding uncatalysed reaction [7]. Recognition that the lower limit for the binding affinity of the altered substrate in the TS, as estimated by the virtual dissociation constant K tx , was inversely proportional to the rate enhancement (k cat /k non ) afforded by an enzyme led to the notion that analogues of the TS, or high-energy intermediates of similar structure [8], should be bound tightly by an enzyme [4,9]. Because most biological reactions proceed extremely slowly in the absence of an enzyme [10], remarkably huge rate enhancements on the order of 10 6 -to 10 18 -fold have been reported for enzyme-catalysed reactions such that affinities of 10 nM to 10 -3 yM are estimated for formation of complexes between enzymes and their altered substrates in the TS [11,12]. This suggests that TS analogue inhibitors could be bound with similar affinities to the extent that a stable analogue of the TS can mimic the geometric and electronic features of the enzymatic TS and effectively capture the available binding energy. Indeed, over the past 50 years, numerous TS analogue inhibitors have been developed targeting enzymes from all five major enzyme classes [13][14][15][16][17], with some providing the basis for the development of drugs [18][19][20][21][22][23].
To establish benchmarks for judging the catalytic power of enzymes, Wolfenden and co-workers measured the nonenzymatic rate constants for a variety of model reactions corresponding to enzyme-catalysed reactions [10,24,25]. These studies revealed that while enzymes have evolved with catalytic efficiencies that typically fall within a narrow range of 2-3 orders of magnitude with the second-order rate constant for encounter of the enzyme and substrate in solution (approx. 10 9 M -1 s -1 ) as an upper limit [26], the rate constants for the corresponding uncatalysed reactions can vary over at least 16 orders of magnitude. Consequently, the variability of the catalytic proficiency (1/K tx ) among enzymes arises primarily owing to differences in their uncatalysed rates [27]. As such, it is the value of k non that furnishes the benchmark for judging the catalytic power (i.e. proficiency) of a given enzyme and its potential susceptibility to inhibition by TS analogue inhibitors. With K tx values approaching 10 -27 M for some enzymes [12], the anticipated binding of TS analogue inhibitors could indeed be dramatic relative to the substrate. This raises the question: how much of the available free energy of TS stabilization (ΔG Tx = RTlnK tx ) do known TS analogue inhibitors capture upon binding their respective enzymes and how does this compare to the change in free energy accompanying substrate binding (ΔG S )? Figure 2 illustrates the proportion of binding free energy captured upon binding of the most potent intermediate/TS analogue inhibitors with a selection of enzymes for which the k non values are known and for which the assay conditions used to determine the catalytic efficiency (k cat /K m ) and competitive inhibition constant (K i ) are closely matched, if not identical. Not unexpectedly, the free energy changes accompanying substrate binding fall within a limited range of approximately -3 to -8 kcal mol -1 ; however, the free energy changes accompanying binding of the altered substrate in the TS (ΔG tx ) span a wide range from approximately -16 to -39 kcal mol -1 . For the enzymes listed, the most potent intermediate/TS analogue inhibitors identified capture between 18 and 85% of the available TS stabilization energy (average = 50 (±19)%). On the other hand, the substrates in the ground state capture only 12-42% of the available TS stabilization energy (average = 24 (±7)%). Clearly, there is room for improvement since much of the free energy of TS stabilization remains unused by the intermediate/TS analogue inhibitors presented in figure 2.
To inform the design of TS analogue inhibitors, kinetic isotope effects studies, combined with quantum mechanical modelling, have been employed to estimate the extent of bond breaking and formation at the TSs of enzyme-catalysed reactions [28][29][30]. Much of this work has been conducted by Schramm and co-workers and has led to the development of extremely potent TS analogue inhibitors directed primarily at enzymes involved in purine and pyrimidine metabolism [22]. While these studies furnished important insights into the design of TS analogues, the techniques are not easily applied in most laboratories and some enzyme-catalysed reactions are not readily amenable to such an approach. Most often, enzymologists resort to designing potential TS analogue inhibitors using only the surmised structure of the TS or intermediate of an enzyme-catalysed reaction as a guide. Herein, I review work from our laboratory that has focused on developing TS analogue inhibitors of mandelate racemase (MR) to address the question: for a mechanistically 'simple' enzyme acting on a small molecule, is there a limit to the extent that the free energy of TS stabilization can be captured by an intermediate/TS analogue to effect strong binding?
2. The burden borne by mandelate racemase MR (EC 5.1.2.2) from Pseudomonas putida catalyses the Mg 2+dependent interconversion of the enantiomers of mandelic acid [31,32]. The enzyme is part of the mandelate pathway that converts the enantiomeric pair of mandelic acids to benzoic acid, which is further catabolised to yield succinate and acetyl-CoA by the enzymes of the β-ketoadipate pathway [31,33,34]. Figure 1. Thermodynamic cycle relating the parameters from TS theory and the thermodynamic parameters for the enzyme-catalysed and the corresponding nonenzymatic (uncatalysed) reactions. K S and K tx are the dissociation and virtual dissociation constants for the enzyme complexed with substrate (i.e. K m ≈ K S ) and the altered substrate in the TS, respectively. k non is the rate constant for the uncatalysed reaction and k cat is the turnover number [4][5][6]. (Online version in colour.) royalsocietypublishing.org/journal/rstb Phil. Trans. R. Soc. B 378: 20220041 Isotope exchange, site-directed mutagenesis and X-ray crystallographic studies revealed that the enzyme uses a two-base mechanism to catalyse the 1,1-proton transfer reaction [35][36][37]. At the active site, Lys 166 and His 297 act as enantiospecific His 297  value of approximately 29 [40][41][42] has made MR a useful paradigm for understanding enzyme-catalysed proton abstraction from carbon acids [43][44][45]. This is especially important considering the abundance of such reactions in enzyme mechanisms and the extremely high pK a values typically ranging between 13 and 30 for carbon acid substrates in aqueous solution [46]. In the absence of an enzyme, the rate constant (k non ) for the non-enzymatic racemization of mandelate is 3 × 10 -13 s -1 , which corresponds to a free energy of activation equal to 35 kcal mol -1 [47]. To effect efficient deprotonation of mandelate, MR must reduce this activation barrier by overcoming two challenges. The most significant challenge is that the enol or enolate intermediate is unstable and poses a huge thermodynamic problem for the enzyme [46,[48][49][50]. Hence, MR must stabilize the intermediate/TS through electrostatic stabilization and H-bonding interactions [50,51], as well as by enhancing the basicity of the Brønsted base catalyst [52,53]. A less significant challenge is that the rate of non-enzymatic abstraction of the α-proton from a carbon acid is usually slower than the rate of abstraction of a proton from a heteroatom or normal acid of equal acidity because of the larger intrinsic barrier for proton abstraction from a carbon acid (approx. 12 kcal mol -1 ) relative to that of a normal acid (≤3 kcal mol -1 ) [54][55][56]. This poses a kinetic problem for the enzyme.
MR overcomes these challenges to afford a rate enhancement (k cat /k non ) exceeding 15 orders of magnitude, stabilizing the altered substrate in the TS by approximately 26 kcal mol -1 [47,57]. This remarkable proficiency corresponds to an upper limit for the virtual dissociation constant for the enzyme and the altered substrate in the TS (i.e. K tx ) equal to a value of 2 × 10 -19 M and, therefore, MR is expected to be extremely sensitive to inhibition by analogues of either the TS or the highenergy intermediate formed during catalysis. To design such analogues, knowledge of the electronic and geometric characteristics of the enolic/ate intermediate or TS is required. Gerlt and Gassman proposed that concerted general acidgeneral base catalysis promotes both the enolization of the mandelate anion and ketonization of the enolic/ate intermediate [42,[58][59][60], while Guthrie & Kluger [51] argued that the principal source of catalysis is electrostatic stabilization. Probably, the interaction of an H-bond donor with the enolate oxygen at an enzyme active site contributes very little to reduction of the intrinsic barrier [61]; while electrostatic interactions that stabilize the π-system of the enolate may make a more significant contribution [62,63]. Substrate and solvent deuterium isotope effect experiments conducted using the MR variants H297N [64], E317Q [65], and K166R [37] further suggest that the reaction is stepwise. Thus, although the precise structure of the TS for the enolization reaction catalysed by MR is not known; for TS analogue design purposes, it is reasonable to expect that the TS resembles either the putative aci-carboxylate intermediate ( figure 3) or one of its conjugate acids. (For the present discussion, the term 'aci-carboxylate' is not meant to imply the extent of proton transfer from the general acid catalyst Glu 317 at the active site to the oxygen atom of the intermediate [60].)

Ground state analogues
To obtain a better understanding of the protein-ligand interactions that contribute to stabilization of the altered substrate in the TS by MR, we explored the ability of carboxylate-and phosphonate-based analogues of the substrate, product and aci-carboxylate intermediate to inhibit MR (figure 3) [66]. MR binds phenylacetate (K i = 200 µM) and benzoylformate (K i = 650 µM) with affinities similar to that observed for the substrate (for MR, K m ≈ K S [67]). Interestingly, in the ground state, the α-OH group does not appear to make a significant contribution to binding; however, it is required for catalysis since MR does not catalyse exchange of the α-protons of phenylacetate with deuterated solvent [36]. While benzoylformate has an sp 2 centre at the α-carbon, the observed binding affinity suggests that MR recognizes this ligand as a ground state analogue rather than a structural mimic of the aci-carboxylate. Examining the binding of phosphonate analogues was of particular interest since such analogues could serve as structural and electronic mimics of the putative aci-carboxylate intermediate. Interestingly, the dianionic benzylphosphonate (K i = 3500 µM) was bound more weakly than the substrate, while benzoylphosphonate exhibited a binding affinity (K i = 300 µM) similar to that of the substrate. In accord with the observation that the α-OH group makes little contribution to ground state binding but is required for catalysis, (R,S)-α-hydroxybenzylphosphonate (α-HBP) was a potent inhibitor (K i = 8.7 µM), suggesting that α-HBP was recognized by MR as an intermediate/TS analogue (vide infra) [66].
In addition to the observations above indicating that the α-OH plays a significant role in stabilizing the altered substrate in the TS, elimination of the interaction between Asn 197 and the α-OH by substitution of Ala in place of Asn indicated that the interaction furnishes approximately 3.5 kcal mol -1 of TS stabilization free energy [66]. As such, we explored how variations of substituents at the α-carbon might affect binding by conducting a 'fluorinated phosphonate scan' [68] using a series of mono-and di-substituted α-fluorobenzylphosphonates (α-FBP) since fluorine is often employed as an isosteric replacement for OH groups [69]. (R,S)-α-FBP (K i = 810 µM), (R)-α-FBP (K i = 1110 µM), and (S)-α-FBP (K i = 530 µM), as well as α,α-diflurobenzylphosphonate (α,α-F 2 BP, K i = 1.2 × 10 4 µM) were all competitive inhibitors of MR, but were bound with affinities that were similar to or much weaker than the binding affinity of mandelate [70]. In part, this lower binding affinity arises from the slight reduction of the pK a of the phosphonate group as a result of fluorine substitution at the α-position [71,72]. Our observation that the binding affinities of α,α-F 2 BP and (S)-α-FBP increased 12-and 6-fold, respectively, upon reducing the pH of the assay solution from 7.5 to 6.3, indicating that MR exhibits a preference for the phosphonate monoanion. Interestingly, MR exhibited a 2-fold binding preference for (S)-α-FBP over (R)-α-FBP, unmasking a functional asymmetry at the active site of this pseudosymmetric enzyme (vide infra). These results are consistent with the loss of coordination of the Mg 2+ ion owing to the absence of the α-OH group, as well as possible loss of interaction with Asn 197 since the α-fluoro group can only act as an H-bond acceptor. Despite its C α -H bond being more polarized [73] than in mandelate, (R)-α-FBP was not a substrate for MR since no change in the ellipticity of (R)-α-FBP was observed upon incubating the compound with the enzyme.

Substrate-product analogues
The hydrophobic pocket that envelopes the phenyl ring of the substrate at the active site of MR is able to accommodate royalsocietypublishing.org/journal/rstb Phil. Trans. R. Soc. B 378: 20220041 a variety of aryl-and heteroaryl-substituted mandelate derivatives, which serve as substrates to varying degrees [39,57,[74][75][76][77][78]. Most surprisingly, the hydrophobic pocket was able to accommodate the two phenyl rings of benzilate (K i = 670 µM, figure 3) [79]. This striking observation suggested that as the Walden inversion was effected by MR, the phenyl ring could potentially move from an Rpocket to an S-pocket within the active site and vice versa, with the phenyl rings of benzilate simultaneously occupying the R-and S-pockets to inhibit the enzyme. Subsequent sitedirected mutagenesis experiments, wherein steric bulk was introduced into the putative S-pocket formed, in part, by the 50s residues (i.e. the F52W, Y54W and F52W/Y54W variants), revealed that the slightly higher affinity of the wildtype enzyme for (S)-mandelate ðK ðSÞÀman m ¼ 540 mMÞ over (R)-mandelate ðK ðRÞÀman m ¼ 700 mMÞ could be reversed to yield preferential binding of (R)-mandelate by the variants [79]. Interestingly, steric obstruction of the putative R-pocket, which is comprised of the 20s residues from the active-site flap, did not produce a pronounced corresponding preference for binding of (S)-mandelate probably owing to flap mobility compensating for the increased size of the hydrophobic side chains [80]. Our attempt to enhance binding by substituting the carboxylate of benzilate by a phosphonate group (i.e. 1,1-diphenyl-1-hydroxymethylphosphonate (1,1-diphenyl-1-HMP), K i = 1410 µM) to mimic a portion of the structure of the aci-caboxylate intermediate did not yield enhanced binding as it did for α-HBP (vide infra), suggesting that simultaneous binding of the two phenyl groups obviates mimicry of the aci-carboxylate group by the phosphonate group [81].
During our investigation of the ability of the hydrophobic pocket of MR to accommodate various hydrophobic groups on the substrate, we discovered that β,γ-unsaturation was not an absolute requirement for catalysis by MR (cf. ref. [78]) and that MR was capable of racemizing the enantiomers of trifluorolactate (TFL) [82]. Although the k cat values for this substrate in both reaction directions were reduced approximately 100-fold relative to those for mandelate, the K m values of 1700 µM and 1200 µM for (S)-and (R)-TFL, respectively, suggested that the active-site hydrophobic pocket bound the trifluoromethyl group as well as the phenyl ring of mandelate. Considering the inhibitory effect of benzilate, we rationalized that an inhibitor of MR might be generated by replacing the two phenyl rings of benzilate with trifluoromethyl groups. Indeed, the so-called substrate-product analogue of TFL, i.e. 3,3,3-trifluoro-2-hydroxy-(trifluoromethyl)propanoate (TFHTP), was a potent inhibitor of MR (K i = 27 µM) [83], on par with the intermediate/TS analogue inhibitors (vide infra)! The X-ray crystal structure of the MR·TFHTP complex solved to 1.68-Å resolution revealed that TFHTP assumed a novel binding mode at the active site with the two trifluoromethyl groups intimately packing against the 20s loop and with the carboxylate group forming a salt bridge between the two Brønsted acid-base catalysts Lys 166 and His 297 ( figure 4). Consequently, the carboxylate and α-OH groups do not chelate the Mg 2+ ion as observed in all previous structures with bound substrate [37], substrate analogues [36,65,84,85], and intermediate/TS analogues [86]. Hence, the high binding affinity exhibited by TFHTP arises primarily from dispersion forces between the two trifluoromethyl groups and the hydrophobic side chains emanating from residues of the active-site flap.  3). (R,S)-α-HBP was a potent competitive inhibitor of MR with a K i value of 4.7 µM and 3.9 µM when assayed in the R→S and S→R reaction directions, respectively, using the circular dichroism-based assay (or 8.7 µM when  royalsocietypublishing.org/journal/rstb Phil. Trans. R. Soc. B 378: 20220041 assayed in the R→S reaction direction using a high performance liquid chromatography-based assay) [66]. Inhibition assays conducted with the partially resolved (R)-α-HBP (76% ee) and (S)-α-HBP (82% ee) gave K i values of approximately 34 µM and 1.1 µM, respectively, in the R→S reaction direction, indicating that (S)-α-HBP was the more potent inhibitor. Such a strong binding preference for one enantiomer over the other is unexpected for a 'pseudosymmetric' enzyme such as MR (i.e. approximately equal k cat and K m values in both the R→S and S→R reaction directions) [32], although such enantioselective binding preferences were also noted for the competitive inhibitors (R)-and (S)-atrolactate, as well as the irreversible inhibitor (R)-phenylglycidate [36]. Interestingly, the pH dependence of the inhibition of MR by (R,S)-α-HBP revealed that more potent inhibition arose when the phosphonate was in its monoanionic form [66] as was also observed for the α-fluoro-substituted phosphonate analogues discussed above. This result was surprising since the phosphonate dianion was anticipated to more closely resemble the electronic character of the intermediate. However, unlike the carboxylate or aci-carboxylate groups in which the negative charge is rotationally symmetrical about the line which bisects the angle made by the carboxyl carbon and the two anionic oxygens, the phosphonate monoanion is not rotationally symmetric. Consequently, orientation of the monoanionic phosphonate function so that the vector of its negative charge aligns with that of the substrate or aci-carboxylate intermediate results in skewed binding of this analogue. Indeed, such an altered binding orientation may account for the enantioselective binding of the enantiomers of α-HBP and why the (R,S)-α-HBP monoanion is an inhibitor of MR and not a substrate as evidenced by the lack of MR-catalysed exchange of the α-H with solvent deuterium in buffered D 2 O [66].

(b) Benzohydroxamate
Recognizing the importance of the α-OH for binding and the need to mimic the planar structure of the aci-craboxylate, benzohydroxamate (BzH) was examined as an inhibitor wherein the hydroxamate function was substituted for the glycolate moiety of the substrate (figure 3). Like α-HBP, BzH was bound approximately 100-fold more tightly than the substrate with a K i value of 9.3 µM [66]. The pH dependence of the inhibition revealed that MR preferentially bound the deprotonated form of BzH. Beyond the greater binding of BzH relative to mandelate, additional evidence supporting the notion that MR recognizes BzH as a structural and electronic mimic of the TS was apparent from the linear free energy relationship [87,88] between the efficiency of variant MRs and their corresponding binding affinities with BzH. The values of log(k cat /K m ) for wild-type MR and 20 variants varied linearly with the corresponding values of log(1/K i ) with a slope of 1.01 ± 0.14 (r 2 = 0.74), while the linear dependence of values of log(1/K m ) with the corresponding values of log(1/K i ) only had a slope of 0.25 ± 0.14 with much weaker correlation (r 2 = 0.14) [86]. Hence, BzH is not a ground state analogue but exhibits mimicry of the altered substrate in the TS.
The X-ray crystal structure of the MR·BzH complex was determined to 2.20-Å resolution (Protein Data Bank (PDB) ID: 3UXK, figure 5a) [86]. As expected for the intermediate, BzH was bound in a planar conformation with the hydroxamate moiety chelating the Mg 2+ ion at the active site. Enhanced interaction of the aci-carboxylate with the Mg 2+ ion is an expected feature of TS stabilization since both the intermediate and TS bear additional negative charge relative to mandelate in the ground state. Indeed, the distances between the Mg 2+ and the chelating oxygen atoms of the carboxylate and α-OH groups of bound substrate analogue (S)-atrolactate are 2.2 and 2.3 Å, respectively, while the corresponding distances in the MR·BzH complex are 2.2 and 2.1 Å (PDB ID: 1MDR [36]), respectively, suggesting that the interactions of BzH with the Mg 2+ are slightly stronger than those in the ground state. The N ζ and N ε2 atoms of Lys 166 and His 297, respectively, were positioned equidistant from the α-carbon of BzH, consistent with the expectation that, for a pseudosymmertric enzyme, these two acid-base catalysts would be equally poised to protonate the α-carbon of the aci-carboxylate

(d) N-Hydroxyformanilide
Reverse or retro-hydroxamates are potent inhibitors of a variety of enzymes, including metalloenzymes [92]. N-Hydroxyformanilide (HFA) was a competitive inhibitor of MR (K i = 2.79 µM), binding with an affinity similar to BzH and CfN ( figure 3). Crystal structures of metalloenzymes with bound reverse hydroxamate inhibitors reveal that the reverse hydroxamate moiety often coordinates the metal ion in a bidentate manner with the N-hydroxyl group in its deprotonated form [93]. When the pH dependence of the inhibition of MR by HFA was examined, it was found that MR bound both the protonated form of HFA (K i = 9 µM) and its conjugate base (K i = 0.91 µM), with a 10-fold binding preference for the latter form [90]. Although an Xray crystal structure of MR with bound HFA is not currently available, it is likely that the reverse hydroxamate function coordinates the Mg 2+ ion as its Z-(syn) conformational rotomer in a manner similar to BzH and CfN despite the E-(anti) rotomer being favoured in aqueous media [94,95].
(e) Why do these intermediate/transition state analogues fall short of the mark?
Overall, as analogues of the aci-carboxylate intermediate, BzH, CfN and HFA all bind MR with similar K i values, ranging between 2 and 10 µM. The Z-forms of BzH, CfN and HFA mimic the structure and planarity of the aci-carboxylate intermediate and permit bidentate coordination of the Mg 2+ ion, but, as monoanions, they fail to mimic the negative charge that is delocalized over the dianionic aci-carboxylate intermediate. The additional oxygen and negative charge present in the aci-carboxylate intermediate, but absent in these inhibitors, would be anticipated to contribute substantially to the free energy of TS binding through simultaneous interactions with the Mg 2+ ion and the adjacent electrophilic catalyst Glu 317 [51,65]. Consequently, the binding of these inhibitors captures only approximately 30% of the approximately 26 kcal mol -1 used to bind the altered substrate in the TS.

Boronic acids: clasping the catalytic machinery
The use of boronic acid-based inhibitors as TS analogues targeting hydrolases has proved quite successful [96][97][98]. Since the boron atom acts as a Lewis acid, its vacant p orbital can readily accept electrons from donor atoms typically located on the side chains of Ser, Thr, His or Lys residues to form a coordinate (dative) bond (i.e. N-B interaction) with concomitant conversion of the boron atom from a neutral sp 2 centre to an anionic sp 3 centre (figure 6a). The latter species mimics the geometric and electronic features of the tetrahedral intermediate(s) and/or TSs formed during hydrolysis. Moreover, hydroxyl groups covalently linked to the boron atom serve as additional points of molecular recognition by accepting or donating H-bonds. For these reasons, and its low toxicity [98], interest in incorporating the boronic acid functionality into drug molecules has grown over the past decade [99][100][101].

(a) Phenylboronic acid
Considering the architecture of the active site of MR, we hypothesized that positioning a boron atom at the location normally occupied by the α-carbon of mandelate would potentially permit N-B interactions [102] with the two active-site Brønsted base catalysts (i.e. Lys 166 and His 297) (figure 6b). Gratifyingly, we found that derivatives of phenylboronic acid (PBA) were potent, reversible competitive inhibitors of MR, with binding affinities exceeding the binding affinity of acicarboxylate analogues by approximately 1-2-orders of magnitude (figure 3) [103]. For a series of para-substituted PBA derivatives, both larger electron-donating (i.e. OCH 3 and CH 3 ) and electron-withdrawing (i.e. CN, NO 2 , and CF 3 ) substituents decreased the binding affinity relative to PBA probably owing to adverse steric effects at the active site, while halogens were well tolerated at the para-position with p-Cl-PBA exhibiting the most potent inhibition (K i = 81 nM). Thus, the binding affinity of p-Cl-PBA exceeded that of the substrate by 1.23 × 10 4 -fold. Interestingly, methylboronic acid itself was a very weak inhibitor of MR (K i ≈ 0.13 M), indicating that the boronic acid moiety is not solely responsible for the potent inhibition but that the synergistic binding contribution from the phenyl ring is also essential [104]. 11 B nuclear magnetic resonance (NMR) spectroscopy revealed an upfield shift of the 11 B NMR signal from 28.2 ppm, corresponding to the sp 2 -hybridized boron atom of free PBA in solution at pH 7.5, to a value of 0.97 ppm, suggesting formation of an N-B interaction with the bound inhibitor existing either partially or fully in its anionic, sp 3hybridized state [103]. Interestingly, isothermal titration calorimetry experiments revealed that the binding affinity of PBA was reduced 2.8 × 10 3 -fold and 31-fold for the K166M, and H297N MR variants, respectively, relative to wild-type MR, indicating that Lys 166 contributed markedly to the binding affinity. Solution of the X-ray crystal structure of the MR·PBA complex to 2.00-Å resolution (PDB ID: 6VIM) revealed that the boron atom was located between the N ζ and N ε2 atoms of Lys 166 and His 297, respectively (figure 7a,b) [103]. Surprisingly, however, the side chain of Lys 166 formed an H-bond with the hydroxyl group of the boronic acid and did not participate in a N-B interaction. Instead, the electron density was consistent with the boron atom being sp 2 -hydridized (trigonal planar) in chains A, C, E, G and possibly H of the homooctameric structure, but in chains B, D and F, the boron could be modelled as both sp 2 -hydridized (trigonal) and as sp 3 -hydridized (tetrahedral), each at 50% occupancy, with the (b) 2-Formylphenylboronic acid o-Carbonyl arylboronic acids such as 2-formylphenylboronic acid (2-formyl-PBA) have been used to covalently modify the ε-NH 2 group of Lys residues in proteins [102,106,107], as well as the N-terminus [108,109]. Since the ε-NH 2 group of Lys 166 did not form an N-B interaction with the boron atom of PBA (vide supra), we anticipated that Lys 166 might form a Schiff base with the 2-formyl group that would subsequently be stabilized by direct coordination of the lone pair of electrons on the imine nitrogen to the boron atom to form an iminoboronate [107,110]. In accord with these expectations, we discovered that 2-formyl-PBA is a slow-onset inhibitor of MR, exhibiting K i and K i * values of 5.1 µM and 0.26 µM, respectively [105], making it one of the most potent inhibitors of MR identified to-date that does not have any additional substituents on the phenyl ring (K m /K i * ≈ 3000, figure 3). Furthermore, substitution of Lys 166 by Arg obviated inhibition, confirming that the ε-NH 2 group of Lys was essential for inhibition. In the absence of enzyme, 11 B NMR spectroscopy revealed two signals for 2-formyl-PBA: one at 29.8 ppm corresponding to the neutral trigonal R-B(OH) 2 group and the other at 8.5 ppm corresponding to the anionic tetrahedral R-B(OR)(OH) 2 group formed from the reversible cyclization to benzoxaborole [111]. Upon addition of MR, a new signal at 6.0 ppm was observed, which was the sole signal present when the enzyme was present in slight excess over the 2-formyl-PBA. Addition of a 12-fold excess of the competitive inhibitor BzH (5.0 mM), relative to the concentration of 2-formyl-PBA, displaced all the 2-formyl-PBA from the active site, regenerating the 11 B NMR signals associated with free 2-formyl-PBA. These observations were consistent with reversible binding of the 2-formyl-PBA at the active site of MR and the observed 11 B NMR chemical shift change suggested formation of a bound species possessing a negatively charged, tetrahedral boron atom. Counter to our expectations of iminoboronate formation and an interaction of the boronic acid moiety with MR that might resemble that of PBA, the X-ray crystal structure of MR with bound 2formyl-PBA, solved to 1.91-Å resolution (PDB ID: 7MQX [105]), revealed that the ε-NH 2 of Lys 166 formed a 1.5-Å N ζ -B dative bond with 2-formyl-PBA accompanied by cyclization to form a benzoxaborole adduct [111,112]  For both PBA and 2-formyl-PBA, van der Waals interactions with the phenyl ring ensure proper binding and orientation of these ligands at the active site so that the boronic acid moiety is positioned proximal to the enolization machinery of the active site. Potent inhibition then arises from the resulting boronic acid moieties clasping the adjacent key catalytic residues and the Mg 2+ ion, in addition to the weak N ε2 -B interaction between His 297 and PBA, or the N ζ -B bond formed between the ε-NH 2 group of Lys 166 and 2-formyl-PBA. Of the inhibitors developed for MR, ≤38% of the available ΔG tx is captured by these inhibitors for binding ( figure 8).
Recognizing that ΔG tx is a thermodynamic expression that encompasses all modes of catalysis [104], how can additional free energy of TS stabilization be captured to maximize inhibitor binding [113]? Development of high-affinity TS analogue inhibitors must capitalize on both the number and strength of the H-bonding, electrostatic interactions, and dispersion forces or van der Waals interactions, that accompany an enzyme's tightening grip on the altered substrate at the TS. For example, the failure of BzH, CfN and HFA to capture more than approximately 30% of the approximately 26 kcal mol -1 of the free energy of TS stabilization furnished by MR arises, in part, from the binding of these intermediate/ TS analogues in the Z-conformation so that proton transfer from Glu 317 or H-bond formation are not possible. Moreover, these analogues are not dianionic, which diminishes their interaction with the Mg 2+ ion relative to that expected for the aci-carboxylate intermediate. While the enhanced binding affinity of p-Cl-PBA appears to arise from the increased dispersion forces [11,113] between the p-Cl-phenyl moiety and the hydrophobic pocket, which occur at the TS, it is the ability of the boronic acid group in either PBA or the benzoxaborole adduct to engage in multiple interactions with critical active site residues and the Mg 2+ ion that help capture more of the TS stabilization free energy. Furthermore, since optimum binding of the TS arises from cooperative interactions between the TS and the binding determinants [7,19,104], inhibitors that exhibit multiple interactions with the enzyme should be able to exploit these synergistic interactions. Thus, beyond simply using the surmised structural and electronic features of the TS to guide inhibitor design, considerations of maximizing interactions with multiple catalytic binding determinants may be integral to the design of effective TS analogue inhibitors capable of capturing a greater proportion of the free energy of TS stabilization for binding [114]. As Wolfenden pointed out, 'The remaining difference may not be insurmountable … a few adjustments in structure might generate inhibitors of almost unlimited potency' [104, p. 243].
Data accessibility. The data are provided in the electronic supplementary material [115].