Synthesis, Structure–Activity, and Structure–Stability Relationships of 2‐Substituted‐N‐(4‐oxo‐3‐oxetanyl) N‐Acylethanolamine Acid Amidase (NAAA) Inhibitors

N‐Acylethanolamine acid amidase (NAAA) is a cysteine amidase that preferentially hydrolyzes saturated or monounsaturated fatty acid ethanolamides (FAEs), such as palmitoylethanolamide (PEA) and oleoylethanolamide (OEA), which are endogenous agonists of nuclear peroxisome proliferator‐activated receptor‐α (PPAR‐α). Compounds that feature an α‐amino‐β‐lactone ring have been identified as potent and selective NAAA inhibitors and have been shown to exert marked anti‐inflammatory effects that are mediated through FAE‐dependent activation of PPAR‐α. We synthesized and tested a series of racemic, diastereomerically pure β‐substituted α‐amino‐β‐lactones, as either carbamate or amide derivatives, investigating the structure–activity and structure–stability relationships (SAR and SSR) following changes in β‐substituent size, relative stereochemistry at the α‐ and β‐positions, and α‐amino functionality. Substituted carbamate derivatives emerged as more active and stable than amide analogues, with the cis configuration being generally preferred for stability. Increased steric bulk at the β‐position negatively affected NAAA inhibitory potency, while improving both chemical and plasma stability.


Introduction
Palmitoylethanolamide (PEA), the endogenous amide of palmitic acid and ethanolamine, belongs to the family of fatty acid ethanolamides (FAEs), a class of lipid-derived messengers that participate in the control of multiple physiological functions, including pain and inflammation. [1] PEA is produced by most mammalian cells, [2] and has been shown to inhibit peripheral inflammation and mast cell degranulation [3] and to exhibit antinociceptive properties in rat and mouse models of acute and chronic pain. [4] It has also been suggested that PEA might attenuate skin inflammation and neuropathic pain in humans. [5] These effects are mainly attributed to the ability of PEA to activate peroxisome proliferator-activated receptor-a (PPAR-a), a member of the steroid/nuclear receptor superfamily. [6] FAEs such as PEA and its monounsaturated analogue oleoylethanolamide (OEA) are produced on demand and their endogenous levels are regulated by enzymes responsible for their formation and degradation. [7] They are enzymatically biosynthesized from membrane glycerophospholipids via their corresponding N-acylphosphatidylethanolamines (NAPEs). [8] The major pathway for degradation of FAEs is the hydrolysis to free fatty acids and ethanolamine, which is carried out by two intracellular lipid amidases: fatty acid amide hydrolase (FAAH) and N-acylethanolamine acid amidase (NAAA). [9] Although NAAA and FAAH share the ability to cleave lipid amide bonds, they show major differences in primary structure, substrate selectivity, and cellular localization. NAAA is a cysteine amidase that belongs to the N-terminal nucleophile (Ntn) family of enzymes, [9c, 10] preferentially hydrolyzing saturated or monounsaturated FAEs that activate PPAR-a, such as PEA and OEA, over the polyunsaturated endocannabinoid anandamide. [9c, 11] NAAA has no sequence homology to FAAH, [9c] but is linked to the choloylglycine hydrolase family of enzymes, members of which are characterized by the ability to cleave carbon-nitrogen bonds in linear amides, with the exception of peptide bonds. [12] Like other Ntn enzymes, NAAA is produced as an inactive pro-enzyme and is activated at acidic pH by autocatalytic cleavage at a specific site of the peptide chain. [13] Site-directed mutagenesis experiments have univocally identified Cys131 (in mice) and Cys126 (in humans) as the catalytic residue responsible for both auto-proteolysis and FAE hydrolysis, [12,14] N-Acylethanolamine acid amidase (NAAA) is a cysteine amidase that preferentially hydrolyzes saturated or monounsaturated fatty acid ethanolamides (FAEs), such as palmitoylethanolamide (PEA) and oleoylethanolamide (OEA), which are endogenous agonists of nuclear peroxisome proliferator-activated receptora (PPAR-a). Compounds that feature an a-amino-b-lactone ring have been identified as potent and selective NAAA inhibitors and have been shown to exert marked anti-inflammatory effects that are mediated through FAE-dependent activation of PPAR-a. We synthesized and tested a series of racemic, diaste-reomerically pure b-substituted a-amino-b-lactones, as either carbamate or amide derivatives, investigating the structure-activity and structure-stability relationships (SAR and SSR) following changes in b-substituent size, relative stereochemistry at the aand b-positions, and a-amino functionality. Substituted carbamate derivatives emerged as more active and stable than amide analogues, with the cis configuration being generally preferred for stability. Increased steric bulk at the b-position negatively affected NAAA inhibitory potency, while improving both chemical and plasma stability. and have indicated Cys126, Arg142, and Asp154 as the residues that constitute the catalytic triad of human NAAA. [14a] Because NAAA has been shown to primarily deactivate PEA and OEA, [9c, 11] selective NAAA inhibitors could be envisaged to increase local levels of these FAEs, which may lead to anti-inflammatory and analgesic effects via PPAR-a signaling. This hypothesis was confirmed experimentally. [15] As the discovery and initial characterization of NAAA are quite recent, only a limited number of NAAA inhibitors have been reported. Among them, palmitic acid derivatives, [16] lipophilic amides [17] and amines [18] were reported to inhibit NAAA activity with medium-to-low micromolar potencies. Recently, compounds featuring an aamino-b-lactone ring as a reactive electrophilic warhead were identified as the first class of potent and selective NAAA inhibitors. [19] The b-lactone ring is present in many biologically active natural products such as lipstatin 1, [20] the clasto-lactacystin b-lactone (omuralide) 2, [21] salinosporamide A 3, [22] and obafluorin 4 [23] ( Figure 1) and represents a promising privileged structure that can react covalently with the active sites of certain enzymes, such as lipases, [20b] cysteine [24] and serine [25] proteases, and the proteasome. [22b, 23a, 26] Over the last 20 years naturally occurring b-lactone (oxetan-2-one) derivatives have been extensively studied as potential drug candidates for several human disease conditions, including hypercholesterolemia and cancer. [27] Among them, a-amino-b-lactone derivatives have been studied as proteasome inhibitors and have progressed to clinical studies as novel anticancer agents. [22a, 23a, 27d] Within this class of compounds, (S)-N-(2-oxo-3-oxetanyl)-3phenylpropionamide [(S)-OOPP, 5, Figure 1] was reported to be a relatively potent NAAA inhibitor [rat NAAA (rNAAA): IC 50 = 0.42 mm], and was shown to increase PEA and OEA levels in activated leukocytes and decrease responses induced by inflammatory stimuli both in vitro and in vivo. [19a,b] Further investiga-tions aiming at a structure-activity relationship (SAR) expansion of a-amino-b-lactone derivatives examined the effects of side chain modifications on NAAA inhibition and the stereochemical requirements for introduction of a methyl group in the b-position. These studies led to the identification of compounds that are highly potent at inhibiting both rNAAA and human NAAA (hNAAA), such as b-lactones 6 (rNAAA: IC 50 = 0.050 mm, hNAAA: IC 50 = 0.007 mm) [19c, 28] and 7 [28b] (r and hNAAA: IC 50 = 0.007 mm; Figure 1). The in vitro characterization of 6 proved that this compound inhibits rNAAA through a mechanism that is rapid, noncompetitive, and fully reversible after overnight dialysis. [29] Furthermore, topical administration of 6 was shown to elevate FAE levels in mouse skin and sciatic nerve tissues, and to attenuate nociception in mice and rats through a mechanism engaging PPAR-a activation. [29] The b-lactone moiety, which is crucial for NAAA inhibitory activity, displays low chemical and plasma stability, thus limiting the therapeutic applications of these compounds. [19c, 30] However, threonine-derived b-lactones, which bear a b-methyl substituent, are known to have enhanced stability in aqueous media relative to their serine-derived b-lactone counterparts, which are readily hydrolyzed to the corresponding b-hydroxy acids. [19c, 24b, 30] In the present work, we focused our attention on b-substituted a-amino-b-lactones, envisioning that the presence of a bulkier substituent at the b-position of the oxetan-2-one scaffold could improve the hydrolytic stability in aqueous media and provide new insight into substitution patterns that may lead to improved potency. To address the SARs as well as the structure-stability relationships (SSRs), we synthesized and tested a series of racemic, diastereomerically pure b-substituted a-amino-b-lactones as cis-and trans-carbamic acid esters and amide derivatives and examined both their potency and stability. In particular, we investigated the effect of the b-substituent size (Me, Et, iPr, tBu) and relative stereochemistry at positions 2 and 3 on NAAA inhibitory activity and chemical and plasma stability. Finally, quantum chemical calculations at the density functional theory (DFT) level were carried out to help explain the results of our experimental SSR studies.

Chemistry
The synthesis of b-substituted a-amino-b-lactones as carbamate 23 a-c-26 a-c and amide 27 a-c-30 a-c derivatives was undertaken following a racemic, diastereoselective synthetic pathway, which allowed the independent generation of cisand trans-stereoisomers (Scheme 1).
Racemic cis-b-substituted a-amino-b-lactones 23 a-c and 25 a-c were obtained by [benzotriazol-1-yloxy(dimethylamino)methylidene]dimethylazanium tetrafluoroborate (TBTU)-mediated cyclization from the corresponding erythro-a-substituted b-hydroxy acids 15 a-c-16 a-c, prepared following a previously reported protocol by Guanti et al. (Scheme 1). [31] Microwave irradiation of a mixture of dibenzylamine and ethyl chloroacetate gave dibenzylamino ethyl acetate (8), [32] which was acylat- ed with the desired acyl chloride (R 1 = Et, iPr, tBu) to give the corresponding b-keto esters 9 a-c. Acidic chemoselective reduction of the keto functionality with sodium borohydride in the presence of ammonium chloride [31] allowed complete stereoselective synthesis of racemic erythro-b-hydroxyamino esters 10 a-c. After deprotection of the amino functionality by hydrogenation, hydrolysis of the corresponding ester moiety of 14 a-c followed by carbamoylation of the free amino group with activated alcohols 41-44 [28b] (see Supporting Information) led to the desired carbamic acid ester intermediates 15 a-c-16 a-c.
Diastereomeric threo-b-substituted a-amino-b-hydroxy acids 17 a-c-18 a-c were obtained by a modification of the procedure described above. One-pot deprotection of dibenzylamino derivatives 9 a-c, followed by in situ Boc protection of the free amino group in the H-Cube, furnished b-keto esters 11 a-c in good yields (55-75 %). As previously reported, [33] sodium borohydride reduction of compounds 11 a-c led to threo/erythro mixtures of the corresponding b-hydroxy esters 13 a-c in ratios of 8:2 (R 1 = Et and iPr) to 9:1 (R 1 = tBu). After one-pot acidic N-Boc deprotection and hydrolysis of esters 13 a-c, [34] isomeric mixtures of compounds 17 a-c-18 a-c were obtained by N-carbamoylation with activated alcohols 41-44. Cyclization performed in the presence of TBTU led to the final b-substituted a-amino-b-lactones as a 8:2-9:1 mixtures of trans/cis isomers, which after chromatographic purification afforded the diaste-reomerically pure trans-b-lactone carbamates 24 a-c and 26 ac. Because the cyclization of N-acylated-b-hydroxyamino acids to b-lactones has been reported to mainly produce the corresponding five-membered ring azalactones, [35] an alternative route to racemic cis-and trans-b-substituted a-amino-b-lactone amide derivatives 27 a-c-30 a-c was envisaged, starting from intermediates 10 a-c and 13 a-c, respectively. Concerning cisamide derivatives, in situ one-pot hydrogenation/N-Boc protection of intermediates 10 a-c provided diastereochemically pure erythro-b-hydroxy esters 12 a-c, which, after basic hydrolysis and TBTU cyclization, gave N-Boc-a-amino-b-lactones 19 ac (Scheme 1). As already reported for similarly protected aamino-b-lactones, [19b, 24b] reaction of 19 a-c with p-toluenesulfonic acid in TFA gave the corresponding toluenesulfonate salts 21 a-c, which could be functionalized by coupling reaction with the desired carboxylic acid or acyl chloride in the presence of TBTU to give the final amides 27 a-c and 29 a-c. trans-Amide analogues 28 a-c and 30 a-c were prepared by following a similar procedure as for cis derivatives, starting from intermediates 13 a-c. Diastereomerically pure trans-b-lactone amides were isolated after chromatographic purification of the corresponding mixtures of trans/cis isomers.

Structure-activity relationship (SAR)
In our previous studies on serine-and threonine-derived aamino-b-lactones, we found that the introduction of a methyl group at the b-position of the oxetan-2-one moiety proved to be beneficial for potency on both rat and human NAAA. [19c, 28b] Furthermore, the type of functionalization of the amino group of the b-lactone, that is, amide versus carbamate, proved to be important in terms of activity and stability. [19b,c, 28b] Here, to investigate the possible influence of various alkyl groups at the b-position on potency, a series of b-substituted a-amino-b-lactone derivatives were designed and synthesized as carbamic acid esters (hereafter referred to as the "carbamate series") and amides (hereafter referred to as the "amide series"). The amino group was functionalized with different chains, selected among those previously disclosed in potent blactone NAAA inhibitors. In particular, we selected the 5-phenylpentyl [19c, 28b] and the 4-phenylphenylmethyl [28b] chains for the carbamate series (Table 1), and the 4-benzyloxyphenyl [19b,c] and 6-phenylhexyl [28a] chain for the amide analogues ( Table 2).
We first focused on the carbamate series, investigating the role of the alkyl groups-Et, iPr, and tBu-at position 2 of the b-lactone ring. Compound 23 a, the racemic cis-2-ethyl stereoisomer carrying a 5-phenylpentyl side chain, turned out to be a nanomolar inhibitor of hNAAA (IC 50 = 0.009 mm), showing similar potency to 6 (IC 50 = 0.014 mm), the (2S,3R)-2-methyl analogue (Table 1). Increasing the steric bulk at the b-position while maintaining a cis configuration led to compounds 23 b (R 1 = iPr, IC 50 = 0.063 mm) and 23 c (R 1 = tBu, IC 50 = 0.302 mm), which respectively showed 6-and 30-fold lower potency than 23 a. We then investigated the effect of stereochemistry on  NAAA inhibition, while keeping the same substituents on the a-amino group. Along with a generally slight increase in inhibitory activity, compounds with a trans configuration displayed an analogous pattern to that of the corresponding cis stereoisomers, showing a decrease in potency for more sterically hindered b-substituted compounds (IC 50 values from 0.004 mm for 24 a to 0.234 mm for 24 c).
Moving to compounds 25 a-c and 26 a-c, which carry a 4phenylphenylmethyl chain, we similarly observed a positive influence on NAAA inhibitory potency of a trans relationship between the substituents at positions a and b, with compounds 26 a-c (IC 50 = 0.006-0.507 mm) slightly more active than stereoisomers 25 a-c (IC 50 = 0.015-0.576 mm). The detrimental effect of bulky substituents at the b-position was also evident in this subset of compounds. Notably, increasing steric hindrance at the b-position (from methyl to tert-butyl) led to a progressive decrease in NAAA inhibition of this series of compounds, independently from the carbamate functionalization (5-phenylpentyl or 4-phenylphenylmethyl).
Replacement of the carbamate function with an amide, as in derivatives 27 a-c-30 a-c and 35 g, h, resulted in an evident decrease in potency ( Table 2). A > 40-fold drop in NAAA inhibitory activity was observed for the b-lactone amide 27 a (IC 50 = 0.408 mm) relative to the corresponding carbamate analogue 23 a (IC 50 = 0.009 mm). A more pronounced effect was observed for the enantiomerically pure threonine-derived compounds 6 (IC 50 = 0.014 mm) and 35 g (IC 50 = 1.56 mm), which showed a~100-fold difference in potency.
While the activity of b-ethyl (27 a) and b-isopropyl (27 b) analogues turned out to be quite similar (IC 50 values of 0.408 and 0.379 mm, respectively), a significant drop in potency was observed in the case of the tert-butyl group in b-position (27 c, IC 50 = 2.87 mm), confirming the trend observed in the carbamate series. Although the previously described l-serine-derived amide carrying a 4-benzyloxyphenyl chain had shown nanomolar potency against NAAA, [19b] all substituted cis-amides 29 a-c and 35 h disappointingly turned out to be poorly active (IC 50 > 100 mm). The data obtained for d-threonine analogue 35 h suggests that the low activity observed for this set of compounds relative to the l-serine-derived amide, could be ascribed to the opposite configuration at a-position (R vs. S configuration) and/or the substitution at the b-position (Me vs. H).
Moving to amides with the trans configuration, whereas analogues 28 a,b and 30 a could not be tested due to their low intrinsic chemical stability (see the following section), compounds 28 c and 30 b,c showed moderate NAAA inhibition (IC 50 values from 0.277 mm for 28 c to 1.98 mm for 30 c).
Chemical stability b-Lactones are known to exhibit limited stability in water due to ring-opening to the corresponding b-hydroxy acids, which relieves the strain of the four-membered ring. In a-amino-blactone derivatives, it has been reported that a methyl group at the b-position of the oxetanone ring, as in threonine-derived b-lactones, improves the hydrolytic stability of such compounds with respect to the corresponding unsubstituted serine-derived analogues. [19c, 24b] On the other hand, replacement of the substituted benzyl group in the naturally occurring obafluorin (4, Figure 1) with a less bulky methyl led to a decrease in the hydrolytic stability of the b-lactone ring. [30] These findings prompted us to expand previous studies on the role of the b-substituent on the hydrolytic stability of a-amino-b-lactones. [19c] We focused our attention on the effect of the size of the b-substituent and on the role of the relative stereochemistry at positions 2 and 3. The role of the amino group functionalization, as amides and carbamic acid esters, was also investigated with the aim to understand the contribution of this modification to the susceptibility of disubstituted a-amino-b-lactones to chemical hydrolysis. Chemical stability data for 2substituted N-(4-oxo-3-oxetanyl)carbamic acid esters 6, 7, 23 ac-26 a-c, 38 d,e and amides 27 a-c-30 a-c, 35 g, h are summarized in Tables 1 and 2, respectively. Compound stability was evaluated as the half-life (t 1/2 ), in minutes, in buffered solutions at pH 7.4 (physiological pH) and 5.0 (pH of the hNAAA assay), at 37 8C, by measuring the disappearance of each tested compound at various time points. Previous stability studies had shown (2S,3R)-2-methyl-4-oxo-3-oxetanylcarbamic acid ester derivative 6 to have an improved chemical stability profile relative to serine-derived blactone analogues. [19c] These results led us to consider 6 as the starting point for our SSR investigations.
The effect of the relative stereochemistry at positions 2 and 3 of the b-lactone ring, carrying respectively the alkyl substituent and the functionalized amino group, was initially investigated. Whereas for the carbamate series, derivatives with a cis configuration (23 a-c: t 1/2 = 223-611 min, 25 a-c: t 1/2 = 183-605 min) showed slightly higher hydrolytic stability at pH 7.4 than the corresponding trans counterparts (24 a-c: t 1/2 = 145-235 min, 26 a-c: t 1/2 = 151-181 min; Table 1), for the amide analogues the relative stereochemistry had a more pronounced impact on the stability depending on the b-substitution. In fact, although cis-amides (27 a-c: t 1/2 = 127-356 min, 29 a-c: t 1/2 = 54-98 min; Table 2) displayed an overall higher tendency toward hydrolysis than the carbamate analogues, a significant effect of the size of the b-substituent was observed with transsubstituted compounds. Replacement of the less sterically hindered ethyl group with the bulkier tert-butyl moiety resulted in a considerable increase in chemical stability (28 a, 30 a: t 1/2 < 10 min, 28 c, 30 c: t 1/2 = 152-156 min; Table 2). A rationalization of the lower stability of a-amino-b-lactone amides with respect to the corresponding carbamic acid ester derivatives has been previously provided for serine-and threonine-derived b-lactone amides (A, R 1 = H, Me; Scheme 3). This type of compound has been described to undergo two possible degradation pathways, leading to either N-acylhydroxy acids (B), resulting from the hydrolytic opening of the b-lactone ring, or the corresponding O-acyl isomers (D), as a product of an intramolecular rearrangement followed by acid-mediated hydrolysis of the oxazoline-carboxylic acid intermediate (C) (Scheme 3). [19c, 30, 37] To determine whether a similar degradation mechanism also occurred to b-substituted higher homologues, we selected the two diastereomeric amides 29 b and 30 b, and we carried out a time course UPLC-UV analysis, at pH 7.4 and 5.0, of their chemical degradation. Similar to what we observed with serine-and threonine-derived b-lactones, both b-isopropylamide stereoisomers 29 b and 30 b showed the formation of a consistent amount of degradation products deriving from an intramolecular nucleophilic attack of the amide carbonyl group to the b-position of the lactone ring (see Supporting Information, figures S1 and S2). [19c, 24b, 30] Whereas at pH 7.4 trans-isomer 30 b (t 1/2 = 20 min; Table 2) converted in a time dependent manner over 24 h, mainly (~70 % mol) into the corresponding 4,5-dihydro-2-(4-benzyloxyphenyl)-5-isopropyl-4-oxazolecarboxylic acid (C, R 1 = iPr; Scheme 3), the O-4-benzyloxybenzoyl-bhydroxyamino acid D (R 1 = iPr, Scheme 3) was the only species detected at pH 5.0 (Supporting Information, figure S1). [19c] Interestingly, unlike the trans stereoisomer, cis-b-lactone amide 29 b (t 1/2 = 62 min; Table 2 Considering that the functionalization of the amino group of a-amino-b-lactones as carbamate has been reported to positively affect the chemical stability of such derivatives, [19c] a similar study was also conducted on cis-and trans-carbamate stereoisomers 25 b and 26 b. At pH 7.4, both b-lactones (25 b: t 1/2 = 305 min, 26 b: t 1/2 = 191 min; Table 1) afforded exclusively the corresponding diastereomeric N-(4-phenylphenyl)methoxycarbonyl-b-hydroxyamino acids 16 b and 18 b. This indicates the hydrolytic opening of the b-lactone ring, leading to adduct B (Scheme 3), as the main degradation pathway for this kind of compound (Supporting Information, figures S3 and S4).
The peculiar behavior observed with a-amino-b-lactone amide derivatives could be reasonably explained by two possible competitive nucleophilic attacks occurring at different reaction rates, that is, intramolecular attack of the amide carbonyl moiety to the b-position of the b-lactone, versus attack of an external nucleophile (water) to the electrophilic endocyclic carbonyl moiety. The intramolecular pathway is expected to proceed more rapidly in trans isomers as a result of an antiperiplanar attack of the amide carbonyl group at the b-position relative to cis derivatives. [30,38] This degradation pathway, although possible also for the carbamate analogues, is expected to be more favored in amides due to the higher nucleophilicity of their carbonyl oxygen atom, as previously described. [19c] Therefore, the overall higher stability of b-lactone carbamate derivatives than amide analogues might be explained by the weak nucleophilic character of the carbamate carbonyl moiety, resulting in only one degradation pathway, that is, water attack with formation of the b-hydroxy acid. [39] Scheme 3. Substituted b-lactone amides (A) degradation products: N-acyl-bhydroxy acids (B), and O-acyl-a-amino acids (D).
The influence of the various b-alkyl substitutions on stability was examined on both the carbamate and amide series of aamino-b-lactones. A consistent trend was observed in the stability at pH 7.4 and 5.0 for carbamate and amide derivatives with the cis configuration. Increasing the steric demand of the alkyl group at the b-position led to an increase in the stability of such compounds. In fact, cis-amides 35 g, h, 27 a-c and 29 a-c bearing simple methyl to larger tert-butyl groups, displayed half-life (t 1/2 ) values ranging from 50 to 356 min at pH 7.4 and from 229 to more than 1440 min at pH 5.0 (Table 2). Interestingly, compounds 29 a-c and 35 h, featuring a benzamide side chain (R 2 = 4-benzyloxyphenyl) generally exhibited a lower half-life than the other substituted amides 27 a-c and 35 g having an aliphatic side chain (R 2 = 6-phenylhexyl).
The b-lactone carbamates with cis configuration-6, 7, 23 ac and 25 a-c-showed a similar trend concerning the effect of b-substitution (Table 1). Whereas methyl and ethyl substitution resulted in similar chemical stabilities (6, 23 a: t 1/2 :~220 min), increasing the size of the alkyl group at the b-position led to a significant improvement in hydrolytic stability (23 b: t 1/2 = 354 min and 23 c: t 1/2 = 611 min), particularly at pH 7.4. Unlike amide derivatives, for cis-carbamates no relevant differences in hydrolytic stability were observed among compounds with different chains linked to the carbamate function.
Interestingly, the effect of the alkyl substituent at the b-position was much less evident for the series of trans-carbamates. In fact, contrary to what previously observed for cis-analogues, in compounds 24 a-c, 26 a-c, and 38 d,e the evident impact of steric hindrance at the b-position on degradation was somehow lost at pH 7.4. All trans-stereoisomers, regardless of the alkyl group at the b-position, showed a similar t 1/2 (38 d, 24 ac: t 1/2 = 184-235 min), with this result being more evident for the 4-phenylphenylmethyl side chain (38 e, 26 a-c: t 1/2 = 159-181 min; Table 1). [40] To provide a rational explanation of the variation in stability of the carbamate series at pH 7.4, we carried out DFT-based calculations simulating lactone hydrolysis in water of the truncated form of compounds 6, 23 c, 24 c and 38 d, where the side chain of the carbamate function was replaced by a methyl group. In detail, we studied the nucleophilic attack of a water molecule at the carbonyl carbon of the b-lactone ring (Scheme 4). The hydrolysis was studied for both cis (6 and 23 c) and trans (24 c and 38 d) configurations, simulating the water nucleophilic attack from both sides of the ring (hereafter referred to as "syn" and "anti" attack with respect to the carbamate moiety; see Supporting Information). The reaction mechanism turned out to be quite similar for both the syn and anti attacks.
Starting from the noncovalent complex, the reactants (R), the oxygen atom of one of the two water molecules (O 3 , according to the numbering reported in Scheme 4) approached the carbonyl carbon of the lactone ring (C 1 ). The C 1 ÀO 2 bond length increased, while the distance between O 2 and H 4 (i.e., a hydrogen atom of the second water molecule) decreased. O 4 was thus able to accept a proton (H 2 ) from the water carrying the nucleophilic attack. The main geometrical features characterizing the reaction mechanism are reported in the Supporting Information (table S2). All eight reactions occurred through a concerted mechanism, that is, at the transition state (TS) the nucleophilic attack and the proton transfers occurred simultaneously, leading to hydrolysis of the lactone ring (Scheme 4).
In Table 3, we report the in vitro chemical stability, the 2D representation of the truncated forms of compounds of column 1 studied by means of computational studies, and the activation energy (E a ) barriers for both the syn and anti attacks. For compounds bearing a cis configuration (6 and 23 c), the difference between syn and anti attacks was higher than the same difference for compounds with a trans configuration (24 c and 38 d). This outcome could be explained by considering that for 6 and 23 c the cis substituents (methyl or tertbutyl) hindered the water molecule from approaching the carbonyl carbon of the lactone ring. This is particularly evident for 23 c, where the presence of the tert-butyl group led to an E a of 42.2 kcal mol À1 , almost 9 kcal mol À1 higher than the E a for the same nucleophilic attack occurring from the anti side. This means that compound 23 c has a lower probability of being Scheme 4. Representation of the hydrolysis mechanism of b-lactones. The nucleophilic attack and protonation steps are concerted (R = reactants, TS = transition State, P = products). hydrolyzed, as one of the two possible ways of attack is remarkably disfavored. The E a difference between the syn and anti attack was 4 kcal mol À1 also in the case of the cis derivative 6, carrying a methyl instead of a tert-butyl group, and was almost zero for the two trans derivatives (24 c and 38 d). In addition, although comparison among different compounds could be questionable, syn attack on compound 23 c showed the highest E a among all the reactions simulated here (Table 3). These DFT-based calculations help explain the half-life data obtained at pH 7.4 for these compounds (Table 1), pointing to 23 c as the compound with the highest stability in water among the whole series of lactones reported herein. The influence of the b-alkyl substitution on hydrolytic decomposition for trans-carbamate analogues again became evident when studies were conducted at pH 5.0. In fact, along with an expected higher stability of these b-lactones at acidic pH relative to pH 7.4, high amounts of parent compound were observed for derivatives displaying either the cis or trans configuration (Table 1). This pH-dependency of hydrolytic stability on b-substitution was also recognizable to some extent for cisamide derivatives 27 a-c, 29 a-c and 35 g, h ( Table 2).

Rat plasma stability
b-Substituted a-amino-b-lactone derivatives were also tested for their stability in rat plasma (80 % v/v; Tables 1 and 2). Most cis-and trans-carbamate analogues, regardless of b-substitution and side chain modification, showed low half-life values (t 1/2 < 5 min) due to extensive degradation of the parent compounds. As observed for chemical stability, a bulky substituent at the b-position also contributed to improve plasma stability, with compounds 24 c and 26 c having half-lives > 5 min (5.5 and 6.5 min, respectively). An analogous tert-butyl substitution effect was also highlighted for cis-amide 27 c, which showed a t 1/2 of 8.3 min, as a sole compound in this subset.
Although all the other cis-amides featuring a 6-phenylhexyl side chain were found to be quite unstable (t 1/2 < 5 min), cisbenzamide analogues 29 a,c and 35 h showed improved plasma stability with significant half-life values (t 1/2 = 6.3-10.3 min) for this class of compounds. The reason for this improvement in stability of compounds having a 4-benzyloxyphenyl chain is unclear at the moment and needs further investigation to be properly elucidated.

Conclusions
Herein we report on a novel series of b-lactone inhibitors of NAAA. NAAA is a promising target for the treatment of pain and inflammation, but few classes of inhibitors of this enzyme have been identified thus far. Among them, a-amino-b-lactones have emerged as potential candidates in this respect, as they can covalently and reversibly bind the catalytic cysteine residue of NAAA. In this study, we described SARs of two series of b-lactones: the carbamic acid ester and the amide series, which differed in the nature of the chain at the a-position and the aliphatic substituent at the b-position. We showed that derivatives of the carbamate series are generally more potent than analogues belonging to the amide series. In addition, we found that bulky substituents at the b-position of the b-lactone ring have a negative effect on NAAA inhibitory potency.
We next focused our attention on the hydrolytic stability of this class of compounds both under physiological (pH 7.4) and acidic (pH 5.0) conditions, and in plasma. Indeed, it is known that b-lactones have intrinsically low chemical stability due to their propensity toward hydrolysis into the corresponding bhydroxy acids. We measured half-life values of several of the present lactones, and laid down initial SSRs for these compounds. We first noticed that molecules of the amide series were generally less stable than carbamates. Second, in the carbamate series, the stability was related to the size of the alkyl substituent and relative stereochemistry at the b-position. This was particularly clear for compound 23 c, carrying a b-tertbutyl group in cis-configuration with respect to the chain at the a-position. Finally, DFT calculations showed that in the case of cis derivatives with a bulky substituent, one of the two possible pathways of attack by a water molecule was energetically disfavored, providing a possible explanation for the improved stability of 23 c over other derivatives. Most of the aamino-b-lactones were unstable in rat plasma. However, a few of them showed measurable half-life values on the order of a few minutes. This may be due to the mutual contribution of two effects, that is, increased b-substitution and amino group functionalization.
In summary, we have reported new SARs around a-amino-blactones as NAAA inhibitors, along with an investigation on the stability of these compounds in buffer and in plasma. This information may be valuable in the discovery of better NAAA inhibitors, which might help to validate NAAA as a therapeutic target and serve as starting points for the development of novel anti-inflammatory agents.

Experimental Section
Chemistry Materials and methods: All of the commercially available reagents and solvents were used as purchased from vendors without further purification. Dry solvents (THF, Et 2 O, CH 2 Cl 2 , DMF, DMSO, MeOH) were purchased from Sigma-Aldrich. Optical rotations were measured on a Rudolf Research Analytical Autopol II Automatic polarimeter using a sodium lamp (l 589 nm) as the light source; concentrations are expressed in g (100 mL) À1 using CHCl 3 as a solvent and a 1 dm cell. Melting points were determined on a Büchi M-560 melting point apparatus. Automated column chromatography purifications were done using a Teledyne ISCO apparatus (CombiFlash R f ) with pre-packed silica gel columns of various sizes (4-120 g). Mixtures of increasing polarity of cyclohexane and ethyl acetate (EtOAc) or cyclohexane and methyl tert-butyl ether (MTBE) were used as eluents. Hydrogenation reactions were performed using H-Cube continuous hydrogenation equipment (SS-reaction line version), employing disposable catalyst cartridges (CatCart) preloaded with the required heterogeneous catalyst. Microwave heating was performed using Explorer-48 positions instrument (CEM). NMR experiments were run on a Bruker Avance III 400 system (400.13 MHz for 1 H, and 100.62 MHz for 13 C), equipped with a BBI probe and Zgradients. Spectra were acquired at 300 K, using deuterated di-methyl sulfoxide ([D 6 ]DMSO) or deuterated chloroform (CDCl 3 ) as solvents. UPLC-MS analyses were run on a Waters Acquity UPLC-MS system consisting of a single quadrupole detector (SQD) mass spectrometer equipped with an electrospray ionization (ESI) interface and a photodiode array (PDA) detector. The PDA range was l 210-400 nm. Analyses were performed on an Acquity UPLC BEH C 18 column (100 2.1 mm ID, particle size: 1.7 mm) with a VanGuard BEH C 18 pre-column (5 2.1 mm ID, particle size: 1.7 mm). Mobile phase was 10 mm NH 4 OAc in H 2 O at pH 5 adjusted with CH 3 COOH (A) and 10 mm NH 4 OAc in CH 3 CN/H 2 O (95:5) at pH 5.0. ESI in positive and negative mode was applied. Accurate mass measurement (HRMS) was performed on a Synapt G2 Quadrupole-ToF Instrument (Waters, USA), equipped with an ESI ion source. All tested compounds (6, 7, 23 a-c-30 a-c, 35 g, h and 38 d,e) showed ! 95 % purity by NMR and UPLC-MS analysis. Compounds 6, [19c, 28b] 38 d, [28b] and activated alcohols 41-44 [28b] were synthesized by following published procedures; the synthesis of compounds 35 h and 38 e are described in the Supporting Information.
General procedure for the synthesis of cis-and trans-a-amino-blactone carbamic acid ester derivatives (23 a-c-26 a-c; Scheme 1).