(DAHP) Oxime - ACS Publications - American Chemical Society

Article pubs.acs.org/biochemistry

Linear Free Energy Relationship Analysis of Transition State Mimicry by 3‑Deoxy‑D-arabino-heptulosonate-7-phosphate (DAHP) Oxime, a DAHP Synthase Inhibitor and Phosphate Mimic Naresh Balachandran,† Frederick To,† and Paul J. Berti*,†,‡ †

Department of Chemistry & Chemical Biology and ‡Department of Biochemistry & Biomedical Sciences, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M1, Canada S Supporting Information *

ABSTRACT: 3-Deoxy- D -arabino-heptulosonate-7-phosphate (DAHP) synthase catalyzes an aldol-like reaction of phosphoenolpyruvate (PEP) with erythrose 4-phosphate (E4P) to form DAHP in the first step of the shikimate biosynthetic pathway. DAHP oxime, in which an oxime replaces the ketone, is a potent inhibitor, with Ki = 1.5 μM. Linear free energy relationship (LFER) analysis of DAHP oxime inhibition using DAHP synthase mutants revealed an excellent correlation between transition state stabilization and inhibition. The equations of LFER analysis were rederived to formalize the possibility of proportional, rather than equal, changes in the free energies of transition state stabilization and inhibitor binding, in accord with the fact that the majority of LFER analyses in the literature demonstrate nonunity slopes. A slope of unity, m = 1, indicates that catalysis and inhibitor binding are equally sensitive to perturbations such as mutations or modified inhibitor/substrate structures. Slopes 1 indicate that inhibitor binding is less sensitive or more sensitive, respectively, to perturbations than is catalysis. LFER analysis using the tetramolecular specificity constant, that is, plotting log(KM,MnKM,PEPKM,E4P/kcat) versus log(Ki), revealed a slope, m, of 0.34, with r2 = 0.93. This provides evidence that DAHP oxime is mimicking the first irreversible transition state of the DAHP synthase reaction, presumably phosphate departure from the tetrahedral intermediate. This is evidence that the oxime group can act as a functional, as well as structural, mimic of phosphate groups. acterial α-carboxyketose synthases of the NeuB superfamily are essential for bacterial survival/pathogenicity and have been the subjects of antibiotic development campaigns.1−5 One member, 3-deoxy-D-arabino-heptulosonate-7-phosphate synthase (DAHPS), catalyzes the first step of the shikimate pathway. 6 It catalyzes an aldol-like reaction between phosphoenolpyruvate (PEP) and erythrose 4-phosphate (E4P) to produce DAHP (Scheme 1). The reaction passes through a tetrahedral intermediate (THI). We recently characterized DAHP oxime, in which DAHP’s ketone is replaced by an oxime, as a DAHPS inhibitor.7 The oxime functional group, combined with two crystallographic waters, structurally mimicked a phosphate group, binding in the same location as the phosphate groups of PEP and the THI. This raised the question whether the oxime group can mimic a phosphate functionally, as well as structurally. That is, can DAHP oxime mimic DAHPS’s transition state? Transition state (TS) mimicry is frequently the goal of inhibitor design because enzymes catalyze reactions by binding to and stabilizing their transition states more tightly than any other species, with dissociation constants for the E·S‡ complex down to 10−26 M.8 If a stable molecule can capture even a fraction of that binding energy, it will be a potent inhibitor.9,10

B

© XXXX American Chemical Society

However, tight binding, on its own, is not evidence of TS mimicry. Several criteria have been proposed to distinguish TS mimicry from adventitiously tight binding, including slowbinding inhibition,11 pH dependence,12 binding enthalpy,13,14 and linear free energy relationship (LFER) analysis.15,16 While the other criteria are based on how TS mimics should behave in general, LFER analysis directly probes the experimental relationship between catalysis and inhibition, that is, between the free energies of TS stabilization and inhibitor binding. In a single substrate/single step reaction, the specificity constant kcat/KM reflects the pseudoequilibrium between the free substrate and enzyme, and the enzymatic TS complex, that is, E + S ⇌ E·S‡. Ki reflects the equilibrium between the free inhibitor and enzyme, and the complex, i.e., E + I ⇌ E·I.17,18 If an inhibitor is truly a TS mimic, then any perturbation that affects catalysis, such as mutagenesis, should have an equal, or proportional, effect on inhibition. Observing a linear correlation between log(KM/kcat) and log(Ki) implies a relationship Received: November 30, 2016 Revised: December 31, 2016 Published: January 3, 2017 A

DOI: 10.1021/acs.biochem.6b01211 Biochemistry XXXX, XXX, XXX−XXX

Article

Biochemistry Scheme 1. DAHPS Reaction

ions. Steady-state kinetic parameters were determined by fixing two substrate concentrations and varying the third. The fixed substrate concentrations were typically 250 μM, but were increased for some mutants with very high KM values. Mn2+ is an essential activator rather than a substrate, but its treatment as a substrate was necessitated by the fact that DAHP oxime binding is competitive with Mn2+, meaning that [Mn2+] affected the apparent Ki value.7 Reactions were run in reaction buffer (50 mM K-HEPES, pH 7.0, 100 mM KCl, 0.1 mM TCEP) at 25 °C. Enzyme concentrations ranged from 10 nM for DAHPSH6 to 3 μM for the C61A and K186A mutants. Ki values were determined using 0 to 1 mM DAHP oxime, generally with fixed substrate concentrations of 100 μM PEP, 100 μM E4P, and 2 μM MnCl2 in reaction buffer, though higher concentrations were used with some mutants. Steady-State Kinetic Parameters. As DAHPSH6 follows a rapid equilibrium sequential ordered ter ter kinetic mechanism,7 eqs 1 and 1a were used. As described previously,7 because DAHP oxime binding is competitive with respect to the essential activator Mn2+, it is necessary to account for Mn2+ binding in the kinetic mechanism, treating it as a substrate. Equation 1 was used to fit kcat values.51

between the free energies of TS stabilization and inhibitor binding, that is, TS mimicry. This is important for demonstrating how an inhibitor interacts with its target, and whether rational refinement of the inhibitor is likely to be possible. LFER analysis has also demonstrated that several inhibitors previously thought to be TS mimics based on their potency and similarity to putative TS structures were not TS mimics, at least for some enzymes. This includes isofagomine,19 the herbicide Roundup,20 and the drug Relenza.21 The significance of the slope in LFER analyses has been a point of debate. In its original formulation there is an implicit assumption of a unity slope, meaning that changes in the free energy of TS stabilization cause an equal change in the free energy of inhibitor binding.15,16 It is sometimes argued that TS mimicry requires a slope of unity, often citing Bartlett.16,22 However, there is no theoretical requirement for unity slope, Bartlett did not require it, and nonunity slopes are common. In fact, in studies in which LFER analyses revealed linear relationships, two-thirds contained at least one nonunity slope.22−43 This prevalence of nonunity slopes suggests that the assumption of equal free energy changes may not be justified and that proportional changes are more common. The question of TS mimicry by DAHP oxime is especially relevant because it structurally mimics a phosphate functional group. Phosphate groups are problematic for inhibitor design, as they are hydrolytically labile in vivo and cell impermeant due to their negative charges.44−46 However, they are ubiquitous, and many phosphate-acting enzymes are the targets of inhibition. Some phosphate bioisosteres, like phosphonates and sulfonates, are stable but similarly cell impermeant, while others like thiazolidinone dioxide47 and isothiazolidinone,48 are more cell permeant, but their size raises the possibility of not fitting all proteins’ phosphate binding sites. Thus, new phosphate bioisosteres are needed. In order to test DAHP oxime for TS mimicry, we generated and characterized a series of DAHPS mutants. The linear relationship between the tetramolecular specificity constant log(KM,MnKM,PEPKM,E4P/kcat) and log(Ki) demonstrated that there was a relationship between inhibition and TS stabilization, supporting DAHP oxime’s identity as a TS mimic.

v0 = [E]0 1+

kcat[Mn][PEP][E4P] KM,MnKM,PEPKM,E4P [Mn] KM,Mn

+

[Mn][PEP] KM,MnKM,PEP

+

[Mn][PEP][E4P] KM,MnKM,PEPKM,E4P

(1)

Equation 1a was used to fit the specificity constant kcat/ (KM,MnKM,PEPKM,E4P) (fitted as a single parameter) and individual KM values.

(

)

k

cat [Mn][PEP][E4P] KM,MnKM,PEPKM,E4P v0 = [Mn] [Mn][PEP] [Mn][PEP][E4P] [E]0 1+ K + K K + K K K M,Mn

M,Mn M,PEP

(1a)

M,Mn M,PEP M,E4P

The D326A mutant displayed substrate inhibition by PEP and was fitted to eq 2. v0 = [E]0

■

kcat[Mn][PEP][E4P] KM,MnKM,PEPKM,E4P

MATERIALS AND METHODS General. DAHP oxime, substrates, and N-terminally His6tagged Escherichia coli DAHPS(Phe) (DAHPSH6) were produced as described previously.7 Mutant DAHPSH6’s were generated with the Stratagene QuikChange Site-Directed Mutagenesis kit using the manufacturer’s instructions and the primers in Table S1 (see Supporting Information). The mutants were expressed in E. coli K-12 ΔaroG (aroG deficient) cells,49 a gift from Prof. Eric Brown (McMaster University). They were purified and characterized as for DAHPSH6. Rate Assays. Initial velocities (v0) were measured by following Pi production with the Malachite Green/ammonium molybdate colorimetric assay.50 Buffers and substrates, except MnCl2, were treated with Chelex 100 to remove divalent metal

1+

[Mn] KM,Mn

+


(1 +

[PEP] K i,PEP

)+


(2)

Ki values were determined using eq 3. v0 = [E]0 1+

kcat[Mn][PEP][E4P] KM,MnKM,PEPKM,E4P [Mn] KM,Mn

+


+


+

[I] Ki

(3)

+ offset

where offset is the residual rate at infinite [I]. B


Article

Biochemistry Table 1. Steady-State Kinetic Parameters for DAHPSH6 and Mutantsa enzyme DAHPSH6b T100A D326Ac H268A C61A R99A K186A

kcat/(KM,MnKM,PEPKM,E4P) (M−3 s−1) (1.5 (8.4 (2.4 (3.6 (5.9 (1.7 (2.7

± ± ± ± ± ± ±

0.2) 0.8) 0.4) 0.3) 0.6) 0.2) 0.2)

× × × × × × ×

15

10 1013 1011 109 108 108 107

kcat (s−1)

KM,Mn (M)

± ± ± ± ± ± ±

(5.5 ± 0.7) × 10−6 (1.1 ± 0.1) × 10−5 (5 ± 1) × 10−4 (7.0 ± 0.8) × 10−3 (9 ± 1) × 10−5 (3.1 ± 0.5) × 10−4 (3 ± 2) × 10−4

16.4 8.7 1.5 7.9 0.19 2.6 0.16

0.6 0.9 0.1 0.5 0.06 0.2 0.01

KM,PEP (M) (1.4 (2.4 (3.6 (3.0 (5.9 (1.4 (1.0

± ± ± ± ± ± ±

0.2) 0.3) 0.9) 0.3) 0.8) 0.3) 0.3)

× × × × × × ×

10−4 10−5 10−5 10−3 10−4 10−3 10−1

KM,E4P (M)

Ki (M)

(1.5 ± 0.2) × 10−5 (3.6 ± 0.5) × 10−4 (4 ± 1) × 10−4 (1.0 ± 0.2) × 10−4 (6 ± 2) × 10−3 (3.5 ± 0.6) × 10−2 (1.8 ± 0.4) × 10−4

(1.5 ± 0.4) × 10−6 (6 ± 2) × 10−6 (1.8 ± 0.5) × 10−5 (3.6 ± 0.5) × 10−4 (3.8 ± 0.6) × 10−4 (6 ± 2) × 10−4 (3.1 ± 0.9) × 10−4

Initial velocity data were fitted to eqs 1 and 1a for steady-state kinetic parameters, and eq 3 for Ki. bValues from ref 7. cD326A exhibited substrate inhibition by PEP. The steady-state kinetic parameters for D326A were fitted to eq 2. The fitted value of Ki,PEP was (1.3 ± 0.5) × 10−3 M. a

Table 2. Catalytic Impairment by Mutationsa enzyme DAHPSH6 T100A D326A H268A C61A R99A K186A

relative kcat/(KM,MnKM,PEPKM,E4P) 1 17 6 4 2 9 5

× × × × ×

103 105 106 106 107

relative kcat

relative 1/KM,Mn

relative 1/KM,PEP

relative 1/KM,E4P

relative 1/Ki

1 2 11 2 88 6 100

1 2 88 1300 16 56 61

1 0.2 0.3 21 4 10 680

1 24 25 7 440 2400 12

1 3 11 210 220 380 180

a

The decrease in kcat or kcat/(KM,MnKM,PEPKM,E4P) or increase in Ki or KM values relative to wild-type enzyme. For example, relative kcat = kcat,wild type/ kcat,mutant, and relative Ki = Ki,mutant/Ki,wild type.

■

RESULTS DAHPSH6 Mutants. His6-tagged E. coli DAHPS, DAHPSH6, follows a rapid equilibrium ordered sequential ter ter mechanism.7 In the presence of substrates and DAHP oxime, DAHPSH6 revealed two kinetically distinct active sites. The first set of sites bound DAHP oxime competitively with respect to Mn2+, PEP, and E4P. As a result, it was necessary to treat Mn2+, an essential activator, as a substrate in eq 1 and 1a in order to correctly account its effects on DAHP oxime binding. The correctness of this treatment was demonstrated by the agreement between Ki, as determined using eq 3, and Kd determined by ITC titrations in the absence of substrates.7 In other words, Ki reflects the E + I ⇌ E·I equilibrium. There was residual activity at high DAHP oxime concentrations, a consequence mainly of KM,E4P’, the apparent KM,E4P value in the second set of active sites, decreasing at least 10-fold in the presence of inhibitor. Slow-binding inhibition was also observed, with IC50 = 9 μM, and a residence time, tR, of 83 min. The IC50 was presumed to reflect inhibitor binding at the second, lower affinity active sites. DAHPSH6 mutants at six sites were generated in order to examine the relationship between catalysis and DAHP oxime inhibition (Tables 1 and 2). Mutant selection was based, in part, on previous studies,52,53 and encompassed the whole active site, from the E4P phosphate group to the metal binding site (Figure 1). A putative LFER relationship should be equally valid for distant mutations as for those close to the sites of bond-making and -breaking. In addition, a range of effects from mild to severe was needed in order to demonstrate the linearity of any relationship found. LFER Analysis. There was a linear relationship between log(KM,MnKM,PEPKM,E4P/kcat) and log(Ki), with slope, m = 0.34, and r2 = 0.93. The relationship held over a 5 × 107-fold range of kcat/(KM,MnKM,PEPKM,E4P) values (Figure 2). The correlation was worse for the two substrate specificity constant, log(KM,PEPKM,E4P/kcat), with m = 0.40 and r2 = 0.79, supporting the use of the three substrate specificity constant. A correlation

Figure 1. DAHPSH6 mutants. Residues mutated in this study are shown along with their interactions (black dashed lines) with DAHP oxime or Mn2+. Atoms O4 and O6 of DAHP oxime are labeled. Also shown are the crystallographic waters that occupy the same sites as PEP’s nonbridging oxygens in structure PDBID:1N8F.54 Mn2+, which was not present in the DAHPS·DAHP oxime 2 structure (PDBID:5CKS),7 was taken from structure 1N8F.

with log(1/kcat) is not expected, but was observed (with two outliers), with m = 1.11 and r2 = 0.98. The correlation with individual log(KM) values was poor, with r2 values of 0.41 to 0.53 (see Supporting Information, Figure S1). Correlations between Ki and KM can be taken as evidence of substrate-like binding, assuming that KM = Ks.

■

DISCUSSION Effects of DAHPSH6 Mutations. The effects of mutations on the specificity constant kcat/(KM,MnKM,PEPKM,E4P) ranged from 17 to 5 × 107-fold (Table 1). The smallest effect was in T100A; T100 hydrogen bonds with the E4P phosphate group at the distal end of the active site. The largest effects were from mutating residues K186, the presumed general acid catalyst promoting phosphate departure during THI breakdown,1,54−56 C


Article

Biochemistry

studies that the rate-limiting step, kcat, is THI breakdown or product release.61 A pre-steady-state burst of DAHP formation was observed under most conditions in quenched-flow experiments. However, because nonenzymatic THI breakdown is expected to yield predominantly DAHP (by analogy to the similar THIs of the AroA and MurA reactions),62,63 the observed DAHP could have been produced by nonenzymatic THI breakdown after the reaction was quenched. Thus, the presteady-state burst indicates that THI formation is fast, and either THI breakdown or product release is rate-limiting under most conditions. Since DAHP follows a rapid equilibrium kinetic mechanism,7 the individual KM values reflect the equilibrium dissociation constants for each substrate’s binding. Some effects were intuitive, such as the R99A mutation. The R99 guanidinium group forms a bidentate ion pair with E4P’s phosphate group, and removing it caused a 2400-fold increase in KM,E4P. Similarly, mutating H268, which forms part of Mn2+’s coordination sphere, increased KM,Mn 1300-fold. Also as expected, mutating K186, whose ε-amino group can form a ion-neutral hydrogen bond with the bridging oxygen of PEP’s phosphate group, caused a 680-fold increase in KM,PEP. However, the same mutation also caused 61- and 12-fold increases in KM,Mn and KM,E4P, with which it does not make contact. Other changes were harder to rationalize, such as KM,E4P increasing 440-fold in the C61A mutant, which coordinates with Mn2+, or KM,PEP decreasing 5-fold in T100A, which hydrogen bonds to the E4P phosphate. This emphasizes the fact that substrate binding involves a complex set of interactions between residues throughout the active site, and not simply the residues in direct contact with each substrate. LFER Analysis. The traditional derivation of the LFER analysis equation (eq 4) explicitly assumes that KM is the substrate’s equilibrium dissociation constant, that is, that KM = Ks.15,16 This is seldom justified in the absence of experimental evidence. Figure 2. LFER analysis of DAHP oxime for TS mimicry. The correlation of catalytic constants for DAHPSH6 mutants versus log(Ki) is shown for (a) tetramolecular specificity constant log(KM,MnKM,PEPKM,E4P/kcat), (b) termolecular specificity constant log(KM,PEPKM,E4P/kcat), and (c) log(1/kcat). The outliers in the log(1/kcat) vs log(Ki) plot are labeled, and were not included in the fit.

log(K i) = log(KM /kcat) + δ

(4)

where δ = log(dkun), kun is the uncatalyzed rate constant, and d reflects the proportionality between Ki and KM(kun/kcat). log(dkun) is not generally analyzed. Equation 4 also implicitly assumes that changes in the free energy of TS stabilization cause equal, rather than proportional, changes in the free energy of inhibitor binding. The fact that the majority of LFER analyses of inhibitor binding which find linear relationships also find nonunity slopes suggests that this assumption is frequently not correct. Revised LFER Analysis Derivation. An alternative derivation of the LFER equation uses less restrictive assumptions (see Supporting Information). First, instead of assuming that KM = Ks, a more general relationship is used, namely, that kcat/KM reflects the pseudoequilibrium between the reactant and transition states for the first irreversible step; that is, E + S ⇌ E·S‡.17 The meaning of KM individually is not important. Second, changes in the free energy of TS stabilization are assumed to be proportional, rather than equal, to changes in the free energy of inhibitor binding. That is

and R99, which forms a bidentate ion pair with the E4P phosphate group. The effects on kcat were much smaller. The largest effect was a 100-fold reduction for K186A. It is unclear why mutating catalytic residues had such a small effect on the rate-limiting step; decreases in kcat of >104-fold are common when catalytic residues are mutated.17,57 One possibility is that DAHPS functions largely through catalysis by approximation,58 in which most of the catalytic energy is devoted to bringing the reactants together in the correct orientation. Once the correct orientation is achieved, the chemical steps are relatively facile. Since the entropic penalty for bringing two molecules together can be >10 kcal/mol,59,60 or >20 kcal/mol for three molecules, DAHPS could accelerate the reaction >1016-fold by doing nothing more than the rapid equilibrium binding of Mn2+, PEP, and E4P together in one active site. If catalysis by approximation is an important factor, there could be larger effects on the specificity constant, which includes contributions from substrate binding, than on kcat, even if they both reflect the same transition state. There is evidence from pre-steady-state

ΔΔGinhibition = mΔΔGspecificity

(5)

When an enzyme is mutagenized, the changes in Ki and KM/ kcat are17 D


Article

Biochemistry ΔΔGspecificity = −R T ln

(KM/kcat)mutant (KM /kcat)wild type

that is, if k3/k−2 is in the range of roughly 0.1 to 10, then both steps will contribute to kcat/KM, making LFER analysis problematic.64 Conversely, observing a linear relationship for a multistep reaction implies that the inhibitor is a TS mimic, but does not identify which transition state is being mimicked. For multisubstrate reactions, the appropriate treatment will depend on the kinetic mechanism and the mode of inhibition. In a rapid equilibrium sequential bi bi kinetic mechanism with an inhibitor that is competitive with respect to both substrates, the specificity constant that reflects the E + A + B ⇌ E·A·B‡ pseudoequilibrium will be used, that is, log(KM,AKM,B/kcat). The binding order is not important, as the E·A·B complex’s energy is the same regardless of whether A or B binds first. The mode of inhibition is also important. If inhibitor I is uncompetitive with respect to substrate A and competitive with respect to B, then the correct comparison would be between log(KM,AKi), which reflects the E + A + I ⇌ E·A·I equilibrium, and log(KM,AKM,B/kcat), which reflects E + A + B ⇌ E·A·B‡. LFER Analysis for Non-Rapid Equilibrium Kinetic Mechanisms. In rapid equilibrium kinetic mechanisms, KM values equal Ks, the equilibrium dissociation constants. However, when the rapid equilibrium assumption is not valid, the steadystate (King-Altman) kinetic parameters have different meanings. In a sequential ordered ter ter mechanism, the steady-state KM value for substrate A, KM,A(ss), is the apparent KM,A in the presence of infinite concentrations of the other two substrates. The steady-state kinetic parameters that correspond to Ks are Ki,A(ss), Ki,B(ss), and KM,C(ss). An LFER analysis could be performed by plotting log(Ki) versus log(Ki,A(ss)Ki,B(ss) KM,C(ss))/kcat). Potential Failures of LFER Analysis. It is possible for a true TS mimic inhibitor to fail LFER analysis if it does not mimic the first irreversible transition state. For example, if the first step in a two-step reaction is irreversible, but the inhibitor mimics the second, rate-limiting step, then there may be no correlation between log(Ki) vs log(KM/kcat). This could potentially explain the failure of compounds like isofagomine19 or Relenza21 to display LFERs in spite of their expected similarity to the enzymatic transition states. In both cases the second step, deglycosylation, is at least partly rate-limiting. In addition, if there are several partially irreversible steps, or if mutations change the identity of the first irreversible step, a linear relationship may not be observed. Non-Unity Slopes in LFER Analysis. The question of whether a TS mimic inhibitor must have a slope of unity in LFER analyses has been addressed previously, with varying conclusions.10,24,25,65,66 A survey of the literature finds that twice as many studies in which a linear relationship was observed had nonunity slopes compared to studies where only unity slopes were observed (Table 3). In other applications of LFER analyses, such as in Brønsted or Taft plots, nonunity slopes are the norm. If a log linear relationship exists between two quantities, e.g., pKa and reaction rate, then the slope is the proportionality of that relationship, indicating, for example, the extent of bond breakage at the transition state, or more generally, the similarity of the transition state to some reference state.66−77 Similarly, the linearity of a plot of log(KM/kcat) versus log(Ki) indicates whether a relationship exists between catalysis and inhibition. The slope indicates the proportionality of that relationship. Nonunity slopes may arise from any factor that causes differential effects between transition state and inhibitor binding. For example, LFER analyses of cationic glycosylase/

(6)

and ⎛ K ⎞ i,mutant ⎟⎟ ΔΔGinhibition = mΔΔGspecificity = −RT ln⎜⎜ ⎝ K i,wild type ⎠

(7)

These can be rearranged to eq 8: log K i,mutant = m log(KM /kcat)mutant + δ

(8)

where δ = log

K i,wild type (KM /kcat)mwild type

Since δ is a constant, eq 8 is functionally equivalent to eq 4, with the added term m, the proportionality of the free energy changes in KM/kcat and Ki. This is the slope of the plot of log(Ki,mutant) versus log(KM/kcat)mutant. LFER Analysis for Multi-Step/Multi-Substrate Reactions. Kinetic constants’ meanings can change in multistep and multisubstrate reactions, which may require changes in the kinetic parameters being compared. Consider, for example, a single substrate/two-step reaction passing through intermediate J (Figure 3). The degree of reversibility of J formation is

Figure 3. Free energy profiles for multistep/single substrate reactions. (top) The first irreversible step, formation of intermediate J, is different from the rate-limiting step, product dissociation; that is, k−2 ≪ k3 ≪ k2. (bottom) Intermediate formation is rate-limiting, but its breakdown is the first irreversible step; that is, k−2 ≫ k3 ≫ k2.

determined by the k3/k−2 ratio. If the first step is irreversible (k−2 ≪ k3), the second step is rate-limiting (k2 ≫ k3), and substrate binding is in rapid equilibrium, then kcat/KM equals k2/Ks and it reflects the first irreversible step, i.e., E + A ⇌ E·A‡ (Figure 3, blue line).64 LFER analysis can therefore be performed by plotting log(KM/kcat) versus log(Ki). However, if the inhibitor is a mimic of the second, rate-limiting transition state, LFER analysis becomes problematic because there is no direct experimental measure of the E + A ⇌ E·J ‡ pseudoequilibrium. On the other hand if intermediate formation is rate-limiting (k2 ≪ k3) and fully reversible (k−2 ≫ k 3 ), then k c a t /K M reflects the E + A ⇌ E·J ‡ pseudoequilibrium (Figure 3, green line). In this case LFER analysis can probe mimicry of the second transition state, but not the first. If intermediate formation is “partially irreversible”, E


Article

Biochemistry

cooperativity of ligand binding increased the binding strengths of the inhibitory residue’s interactions with the enzyme, as has been observed in other contexts.80−84 LFER Analysis for DAHPSH6. DAHPSH6’s rapid equilibrium sequential ter ter kinetic mechanism means that the relevant kinetic parameter for LFER analysis is the tetramolecular (three substrate) specificity constant kcat/(KM,AKM,BKM,C), which reflects the E + A + B + C ⇌ E·A·B·C‡ pseudoequilibrium (Figure 4). There was excellent linearity, r2 = 0.93, in the plot

Table 3. Literature LFER Studies of Transition State Mimic Inhibitors enzyme nonunity slopes (slope 1.1)

only unity slopes (0.9 > slope < 1.1)

slope

references

acetylcholine esterase

2.4−1.0

23

cyclodextrin glycosyltransferase glucoamylase cathepsin S (cysteine protease) cathepsin S (cysteine protease) α-glucan phosphorylase adenosine deaminase papain (cysteine protease) trehalose phosphorylase trehalose-6phosphate synthase β-, ε-collagenases elastase (serine protease) β-mannosidases chymotrypsin (serine protease) multiple glycosylases

2.2, 1.6

24

≈2 1.46

25 26

1.42, 0.89

27

1.35

28

1.3 1.2

29, 30 31

1.14

32

0.98, 0.63

33

0.84, 1.07 0.74

34 35

0.60−1.09 0.5

36 37

1.1

38

1.05

22

1.03, 1.05 1 0.99

39 40 41

0.97, 1.07 0.93

42 43

thermolysin (metalloprotease) carboxypeptidase A xylanase thermolysin (metalloprotease) O-GlcNAcase carboxypeptidase A

Figure 4. Free energy profiles for DAHPS catalysis. The free energies of each step up to the first irreversible transition state, E·TS‡, are shown for DAHPH6, along with T100A and K186A, the least and most detrimental mutations, respectively. ΔGspecificity reflects the E ⇌ E·TS‡ pseudoequilibrium and is determined by the specificity constant kcat/ (KM,MnKM,PEPKM,E4P). It was calculated as ΔGspecificity = ΔGMn + ΔGPEP + ΔGE4P + ΔG‡, where the free energies of substrate binding were ΔGX = −RT ln([X]/KM,X), and ΔG‡ = −RT[ln(kobs) − ln(kBT/h)]. The substrate concentrations used were typical intracellular values in E. coli: 5 μM Mn2+,85 1 mM PEP and 150 μM E4P.86

of log(KM,MnKM,PEPKM,E4P/kcat) versus log(Ki), with m = 0.34 (Figure 2a). Using the two substrate specificity constant also showed a linear relationship, but with a lower r2 value (Figure 2b). One explanation for the low slope is that the THI’s phosphate group, with its −2 charge, interacts more strongly with the three cationic side chains (R165, K186, R234) than the neutral {oxime + 2 waters}. In addition, the K186 Nε··· Noxime hydrogen bond would be expected to be weaker than the K186 Nε···Obridging hydrogen bond. A slope of m = 0.34 implies that 1 kcal/mol of increased TS stabilization results in 0.34 kcal/mol stronger inhibitor binding. Equivalently, a 10-fold increase in the specificity constant corresponds to a 2.2-fold decrease in Ki. Given phosphate groups’ binding energies of up to 17 kcal/mol,87 that represents up to 5.8 kcal/mol of binding energy for the oxime functional group, or a factor of almost 20 000-fold in binding affinity. Which Transition State Is Being Mimicked? Both THI formation and THI breakdown in the DAHPS reaction can proceed through concerted or stepwise mechanisms, meaning that DAHPS stabilizes two to four transition states (Figure 5). Mechanistic studies have tended to focus on THI formation,5,56,88 though it is not clear which is the first irreversible transition state. The identity of the first irreversible step is governed by THI partitioning, which is hard to predict. If THI partitions mostly forward to products, then THI formation is the first irreversible step. If it partitions mostly back to reactants, as the structurally similar THI in the AroA reaction does,89 then THI breakdown is the first irreversible step. In that case, THI breakdown will dominate the value of kcat/KM. DAHPS’s pre-steady-state burst is not informative in this context, as it only shows that THI formation is faster than THI

phosphorylase inhibitors show both m > 124,25,28,32 and m < 1.33,36 Assuming that each reaction proceeds through an oxacarbenium ion-like transition state (whether or not a discrete oxacarbenium ion intermediate is formed) there will be an accumulation of positive charge on the anomeric carbon atom. However, that charge will not exceed approximately +0.2.78,79 If a cationic inhibitor has a full +1 charge located in exactly the same position as the anomeric carbon atom, it would be possible for the inhibitor to form a stronger electrostatic interaction with the enzyme than the transition state. As a consequence, changes in that electrostatic interaction would have a larger effect on inhibitor binding than on TS stabilization, leading to m > 1. Conversely, a poorly positioned positive charge in the inhibitor could have a weaker electrostatic interaction with the enzyme than the transition state in spite of its larger overall charge, leading to m < 1. This effect of inhibitor positioning would be consistent with the observation that closely related inhibitors can have different slopes with the same enzyme.36 Another possible source of nonunity slopes would be differences in the cooperativity of ligand binding. LFER analysis of acarbose using mutant glycosylases yielded slopes of 1.6 and 2.2 when compared against two different substrates.24 The authors argued that because acarbose, a pseudotetrasaccharide, extended into the +1 to +3 subsites, which the substrates did not occupy, binding cooperativity between the extra residues and the inhibitory valienamine residue at the −1 subsite strengthened the latter’s interactions with the enzyme. That is, F


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Figure 5. DAHPS reaction mechanism. (a) THI formation involves attack by PEP’s C3 onto E4P’s carbonyl carbon, and water attack at C2. This step can occur through a concerted transition state, or as a stepwise reaction (shown), beginning with C3 attack on E4P (a “cationic mechanism”), or water attack on C2 (an “anionic mechanism”).56,61,90−96 THI breakdown, which requires bridging oxygen protonation, phosphate departure, and oxygen atom deprotonation, could also be concerted or stepwise (shown). The THI’s stereochemistry is not known. Several proton transfer steps are omitted for clarity. (b) Proposed mechanism of phosphate group departure from the THI, based on the crystal structures of DAHP oxime7 and PEP54 bound in the active site. Crystallographic waters found in both structures are shown in black; the two crystallographic waters in the DAHP oxime structure that occupy the same binding sites as PEP’s nonbridging oxygens are shown in teal.

of TS stabilization and inhibitor binding, supporting its identity as a TS mimic. This implies that further rational optimization is possible. The LFER analysis equations for TS mimicry were rederived under more general assumptions to formalize the treatment of proportional, rather than equal, changes in the free energies of TS stabilization and inhibitor binding. This agrees with the majority of LFER analysis studies in the literature. DAHP oxime’s slope of m = 0.34 in LFER analysis implies that every 1 kcal/mol of TS stabilization corresponds to 0.34 kcal/ mol of improved inhibitor binding. The low slope may reflect differences between how the neutral oxime group interacts with DAHPSH6’s positively charged active site and the anionic phosphate group it mimics. The oxime group, combined with crystallographic waters, structurally mimics a phosphate group, and appears to function as a phosphate bioisostere. Phosphate groups are difficult to mimic in small protein ligands because they are hydrolyzed in vivo and cell impermeant.44−46 The oxime functional group is uncharged, making it likely to be cell permeant, and a number of drugs contain oxime functional groups.98 It is smaller than phosphate, making it likely to be accepted by a variety of phosphate binding sites.

breakdown/product release, not whether it can revert back to substrates during the catalytic cycle.61 The transition state for which strong phosphate interactions are likely to be the most important is phosphate departure during THI breakdown. Phosphate departure via C−O bond cleavage can only be catalyzed by protonating the bridging oxygen,55 which implicates K186 Nε as a general acid catalyst.1,54,56 This is consistent with the 5 × 107-fold decrease in kcat/(KM,MnKM,PEPKM,E4P) in the K186A mutant (Table 1). Alternatively, DAHP oxime could mimic a different transition state, though it is less obvious how interactions at the phosphate group would have large effects on the other steps. The K186 Nε···Noxime hydrogen bond is important for inhibitor binding, with Ki increasing 180-fold in the K186A mutant, corresponding to a hydrogen bonding energy of −2.8 kcal/mol. Other factors that could contribute to the inhibitor’s high affinity include the planar geometry at C2,97 the two crystallographic waters that occupy the same space as PEP’s nonbridging phosphate oxygens, and inhibitor-induced protein dynamic changes.7 The correlation between log(Ki) and log(1/kcat) was not expected (Figure 2c). The fact there were two large outliers, H268A and R99A, suggests a change in rate-limiting step for those mutants. However, because they fit well in the correlation with the specificity constant, there is no evidence for a change in the first irreversible step. The significance of the correlation with kcat is unclear because (i) the identity of the rate-limiting step is not known, and (ii) the initial states are different. For Ki, the initial state is inhibitor and enzyme free in solution, E + I, whereas for kcat, it is an enzyme·substrate complex, E·S. Thus, the environments of the ligand are different for Ki and kcat, making direct comparisons difficult.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.biochem.6b01211. Derivation of eq 8, LFER analysis of KM values, primer sequences (PDF)

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AUTHOR INFORMATION

Corresponding Author

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*E-mail: [email protected]. Telephone: (905) 525-9140 ext. 23479.

CONCLUSIONS LFER analysis of DAHP oxime inhibition of DAHPSH6 demonstrated a linear relationship between the free energies

ORCID

Frederick To: 0000-0001-9487-6027 G


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Paul J. Berti: 0000-0003-3409-7907 Funding

This work was supported by Canadian Institutes of Health Research Operating Grant MOP-64422. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Eric Brown for providing us with the aroG deficient E. coli. ABBREVIATIONS DAHP, 3-deoxy- D -arabino-heptulosonate-7-phosphate; DAHPS, DAHP synthase; E4P, erythrose 4-phosphate; IPTG, isopropyl β-D-1-thiogalactopyranoside; PEP, phosphoenolpyruvate; Pi, inorganic phosphate; TCEP, tris(2-carboxyethyl)phosphine; THI, tetrahedral intermediate; v0, initial velocity

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