A canonical manner to assess an allosteric behaviour of an enzyme is to ascertain the presence of a functional communication between its monomers. To this end, in the case of a homodimer enzymatic activity can be analysed at two homodimer:inhibitor stoichiometric ratios, whereby the inhibitor binds both active sites (1:2 ratio) or one only (1:1 ratio)³⁰.

The specific enzymatic activity of rFAAH was reduced almost completely (>95%) using the selective and irreversible FAAH inhibitor 3′-carbamoyl-[1,1′-biphenyl]-3-yl cyclohexylcarbamate (URB597)³¹ at a homodimer:inhibitor molar ratio of 1:2 (Fig. 1b). Interestingly, the same reduction of rFAAH specific activity was obtained also at a homodimer:URB597 ratio of 1:1 (Fig. 1b). Also other widely used FAAH inhibitors, like the irreversible blockers methoxyarachidonoyl fluorophosphonate (MAFP)¹⁴, N-phenyl-4-(quinolin-3-ylmethyl)piperidine-1-carboxamide (PF-750)¹⁵ and N-pyridin-3-yl-4-[[3-[5-(trifluoromethyl)pyridin-2-yl]oxyphenyl]methyl]piperidine-1-carboxamide (PF-3845)³², and the reversible blockers 7-phenyl-1-(5-pyridin-2-yl-1,3-oxazol-2-yl)heptan-1-one (OL-135)³³ and 1-biphenyl-4-ylethenyl piperidine-1-carboxylate (ST4070)³⁴ showed the same effects as URB597 at both molar ratios (Tables 1 and 2). Of note, similar inhibitions of hFAAH were observed with the same blockers at the same homodimer:inhibitor molar ratios used for rFAAH (Tables 1 and 2).

The amino acid F432 is in the active site of FAAH, where it is involved in activation of the AEA substrate with a pivotal role for substrate hydrolysis²⁷. Here, the F432A rFAAH mutant showed a markedly reduced (by half) specific activity compared to the wild-type enzyme (Fig. 1b). Much alike rFAAH, at a 1:1 homodimer:URB597 molar ratio F432A rFAAH mutant was fully inhibited, and so was at 1:2 ratio. These findings demonstrate that, in keeping with a position of F432 far from the monomer-monomer interface³⁵, this residue does not contribute to monomer-monomer functional communication.

A relevant rFAAH region proposed to mediate the inter-subunit functional interaction is the area around the evolutionarily conserved residue W445²⁹. The latter is indeed a protruding residue that makes the surrounding patch particularly rich in contacts between the two monomers. Thus, we analysed the specific activity of W445Y rFAAH mutant, alone or in the presence of URB597 at 1:2 or 1:1 homodimer:inhibitor stoichiometric ratios. Interestingly, W445Y mutation did not affect rFAAH specific activity per se, yet it led to ~50% reduction of enzyme activity at a homodimer:inhibitor ratio of 1:1, and to full inhibition at 1:2 ratio (Fig. 1b). These observations suggest that W445 is involved in the inter-subunit interaction, and that its substitution impairs monomer-monomer functional communication.

The same radiometric assay used to assess FAAH inhibition was used to perform kinetic analysis of the wild-type forms of human and rat FAAH (See Table 3 and Supplementary Fig. 1). The calculated Hill coefficient (n_Hill) values of both rFAAH and hFAAH are suggestive of a positive cooperativity of substrate hydrolysis (Table 3). The binding curve that better fits both rFAAH and hFAAH kinetics is a sigmoid obtained through nonlinear regression analysis using the Hill equation (with values of correlation coefficient R² and χ² of 0.9966 and 579, and of 0.9926 and 154, for rFAAH and hFAAH, respectively), with a K_0.5 of 12.3 ± 3.1 µM and 8.6 ± 2.7 µM and n_Hill of 1.6 ± 0.3 and 1.9 ± 0.3, for rFAAH and hFAAH, respectively (Table 3). Instead, analysis of the same kinetic data through Michaelis-Menten equation yielded a poorer fitting (with values of correlation coefficient R² and χ² of 0.9869 and 1045, and of 0.9521 and 1064, for rFAAH and hFAAH respectively) (Supplementary Fig. 1).

We further analyzed rFAAH and its two mutants by means of a fluorogenic assay that is widely used and accepted as a convenient alternative to the radiometric method. Such a fluorogenic assay yielded similar values of the kinetic parameters of the rFAAHs (see Table 3), and was used to perform all subsequent analyses.

Even by using the fluorogenic assay, we found that the isotherm that better described rFAAH kinetics had a sigmoidal shape (Fig. 2a), that could be fitted by Hill equation (with correlation coefficient R² and χ² values of 0.9952 and 412, respectively) with a K_0.5 of 15.7 ± 2.2 µM and a n_Hill of 1.6 ± 0.2 (Table 3). Instead, analysis of the same kinetic data through Michaelis-Menten equation yielded a poorer fitting (with values of correlation coefficient R² and χ² of 0.9869 and 1098, respectively) (Fig. 2b). The calculated n_Hill values of both rFAAH and hFAAH are suggestive of a positive cooperativity of substrate hydrolysis (Table 3).

At a homodimer:inhibitor ratio of 1.0:0.5, rFAAH showed a sigmoidal substrate dependence (Fig. 2c) with an increased K_0.5 value and the same n_Hill value of those of rFAAH alone (Table 3). These results demonstrate that at a 1.0:0.5 stoichiometry, the amount of inhibitor is not enough to saturate at least one of the two active sites; thus, under these experimental conditions, the higher value of K_0.5 compared to that calculated in the absence of inhibitor seems to reflect a reduced amount of inhibitor-free enzyme (Table 3).

In addition, kinetic analysis of F432A rFAAH showed a cooperative behaviour (Fig. 2d) with an increased value of K_0.5 and the same n_Hill values as wild-type rFAAH (see Table 2). Instead, kinetic analysis of W445Y rFAAH showed a loss of cooperativity (Fig. 2e), with a sigmoidal shape and R² and χ² values of 0.9721 and 1144, respectively. Of note, the kinetic data of the latter mutant were better fitted by Michaelis-Menten equation, with R² and χ² values of 0.9910 and 387, respectively (Fig. 2f), and n_Hill value ~1.0 (Table 3). These findings strongly indicate that W445Y substitution completely impairs rFAAH cooperativity.

In order to have indications on the possible molecular mechanism behind the allosteric behaviour of rFAAH, we performed high-throughput molecular dynamics (MD) simulations on two systems: URB597 bound to wild-type rFAAH (URB597/rFAAH complex) and to its W445Y mutant (URB597/W445Y-rFAAH complex). Inhibition of rFAAH by URB597 occurs through cleavage of the carbamate bond of the inhibitor³⁶, thus we modelled only the cyclohexane aminocarboxylic acid moiety of URB597 in the active site of one monomer (referred to as monomer A) of the enzyme (Fig. 3).

In the URB597/rFAAH complex we found a direct interaction between the two monomers that may explain the allosteric nature of the dimer. Indeed, in monomer A the loop comprising residues 266–275 contains an OH group (Oγ) of T274 that forms a hydrogen bond with side chain nitrogen of W445 in monomer B, and viceversa. The distance between these residues was often 2–3 Å over the entire trajectories (Fig. 3 upper panel a,b; lower panel, a-d). Instead, we failed to observe a similar interaction for URB597/W445Y-rFAAH, because distances between Y445 and T274 were >6 Å in all trajectories (Fig. 3 upper panel, d,f; lower panel, a-d).

All chemicals were of the purest analytical grade. AEA, arachidonic acid, ethanolamine, and Protease Inhibitor Cocktail were from Sigma Chemical Co. (St. Luis, MO USA). IPTG was purchased at Promega Corporation (Wisconsin, USA). The E. coli BL21(DE3)pLysS competent cells were purchased from Merck KGaA (Darmstadt, Germany). Threalose was from Cargill (Cargill Incorporated, Minneapolis, USA). [³H]-AEA was from Larodan (LARODAN Fine Chemicals AB, Malmö, Sweden). AAMCA was from BIOMOL (BIOMOL International, USA). The Talon resin was from Clontech (California, USA). All other chemicals were purchased from Sigma Chemical Co. (Milan, Italy), unless stated otherwise.

ΔTM rFAAH was purified as reported²⁰. In the F432A rFAAH mutant the protein codon TTT at position 1355 of cDNA was mutated into GCT resulting in the substitution of the phenylalanine in position 432 of the protein sequence with alanine. In the W445Y rFAAH mutant the codon TGG was mutated in position 1394 of the cDNA into TAC obtaining a consequent substitution of tryptophan in position 445 of the protein sequence with tyrosine. The catalytically active F432A and W445Y rFAAH mutants were expressed in Escherichia coli with a hexahistidine tag using the prokaryotic expression vector pTrcHisA, and were extracted from cell lysates according to the protocol of Patricelli et al.³⁵ x with modifications. Briefly, the proteins were expressed in the competent cells according to the manufacturer’s guidelines. To improve the protein recovery, cell pellets were subjected to mechanical rupture using the following lysis buffer: 0.5 M Tris/HCl, pH 7.5, 0.1 M NaCl, 0.5% (w/v) CHAPS, 10% (w/v) trehalose. Lysozyme at a final concentration of 1 mg/mL and a 10 μl/mL Protease Inhibitor Cocktail were added to the lysis buffer. The resulting lysate was then sonicated with a tip sonicator (Bandelin, Berlin Germany) with three 10 s pulses (50% power), and then centrifuged at 10,000 × g for 30 min at 4 °C. Subsequently, the proteins were purified by metal affinity chromatography with the Talon cobalt affinity resin (Clontech). The column was pre-equilibrated with 10 column volumes of 0.5 M Tris/HCl, pH 7.5, 0.1 M NaCl, 10% (w/v) trehalose (column buffer) containing 10 mM imidazole and washed twice with column buffer containing 15 mM and 20 mM imidazole, respectively, for the removal of unspecifically bound proteins. Each FAAH sample was completely eluted after the addition of 3 column volumes of elution buffer (column buffer containing 200 mM imidazole). The purified enzymes were dialyzed overnight with the column buffer to completely remove imidazole and stored at −20 °C until use.

Enzymatic activity of rFAAH, its mutants and hFAAH was assayed by measuring the release of [³H]-ethanolammine from [³H]-AEA (60 Ci/mmol) (Larodan Fine Chemicals AB, Malmo Sweden), using liquid scintillation counting according to the method of Gattinoni and coworkers⁴³. In substrate-dependence experiments, that were performed including several data points in the low substrate concentration range, enzymatic activity of rFAAH and its mutants was assayed by means of the fluorescent-based method by Ramarao and colleagues⁴⁴, by measuring the release of arachidonic acid and of the highly fluorescent 7-ammino-4-methyl coumarin (AMC) product from the non-fluorescent arachidonyl 7-ammino-4-methyl coumarin amide (AAMCA) substrate of FAAH. In preliminary experiments both methods (radiometric and fluorimetric) were found to yield the same catalytic constants, that were in keeping with literature data^15,34,45. Kinetic analysis were done both in the presence and in the absence of 1-palmitoyl-2-oleyl-sn-glycero-3-phosphocholine (POPC) large unilamellar vesicles prepared as described previously⁴⁶.

Protein concentration was determined spectrophotometrically, assuming a 0.1% extinction coefficient at 280 nm of ε = 1.11, as calculated from the primary structure using the ‘prot param’ tool in the expasy proteomic server (www.expasy.org). In all FAAH enzymatic assays carried out at a 1:1 homodimer:inhibitor stoichiometric ratio, 40 nm of the FAAH homodimer (i.e., with two active sites) and 40 nm of all the evaluated inhibitors were used. For the 1:2 homodimer:inhibitor stoichiometry 40 nm of FAAH and 80 nm of inhibitor concentration were used. All enzymatic assays were carried out at 37 °C using a pre-incubation time of 20 minutes of all the evaluated inhibitors with the different FAAHs before adding the substrate (final volume of 500 μL).

Kinetic parameters of the FAAH-catalyzed reaction were calculated from dose-dependence curves (0–100 μM substrate range) through nonlinear regression analysis using the software Kaleidagraph (Synergy Software). Allosteric behaviour was analysed by non-linear regression analysis of kinetic data using the Hill equation Y=1/{1+(K0.5/[S])n} and the MWC formalism^47,48.

As previously done²⁰, molecular dynamics studies were carried out in the presence of a POPC membrane. To better parallel these in silico data, we also evaluated the kinetic properties of FAAH in the presence and in the absence of POPC membranes. In agreement with previous data²⁰, no differences were found in enzyme activity under the two experimental conditions (data not shown). Two replicas for each rFAAH-membrane system were prepared for molecular dynamics simulations. Membrane position was taken from the OPM database using the HTMD software and run using ACEMD⁴⁹. Input coordinates of the systems were based on PDB code 1MT5, from where the inhibitor methyl arachidonoyl fluorophosphonate (MAFP), covalently bond to the catalytic nucleophile S241, was removed. The crystal structure of the FAAH-URB597 (PDB code 3LJ7) complex was used for superimposition in our URB597-bound models. The all-atom CHARMM36 force field was used for the protein, lipid and water atoms. With an identical setup also the W445Y mutation was prepared. For each complex, we performed two independent simulations of 1 μs, giving a final aggregate of 4 μs length. More details about the set-up of the inhibitor covalently bond to the protein are reported in the Supplementary Information.

Data reported in this paper are the mean (±S.D.) of at least three independent determinations, each performed in triplicate. Statistical analysis was performed by the non-parametric Mann-Whitney U test, analyzing experimental data by means of the Prism 5 program (GraphPAD Software for Science, San Diego, CA).