This journal is c The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2013 New J. Chem., 2013, 37, 4061--4068 4061

Cite this: NewJ.Chem.,2013,37, 4061

Modeling the cysteamine catalyzed cysteineproteinases using DFT: mechanistic insights into thehydrolysis of acetyl-p-nitroanilide†

Athanassios C. Tsipis,*a Dimitrios N. Gkarmpounis,a Christos E. Kefalidis,b

Emmanouel M. Papamichaelc and Leonidas G. Theodorouc

The hydrolysis of the peptide bond of acetyl-p-nitroanilide catalyzed by cysteamine, mimicking the

catalysis of cysteine proteinases, has been studied by means of DFT electronic structure calculations

in the gas phase and in aqueous solution. Accordingly, four plausible reaction profiles were

considered as follows: (a) a general-acid/general-base (GA/GB), (b) a concerted, (c) a stepwise

nucleophilic and (d) a concerted nucleophilic mechanism. Among these four reaction mechanisms,

the concerted nucleophilic one followed by that of hydrolysis is predicted to be kinetically the more

feasible in the gas phase having the lower activation barrier in line with previous experimental as

well as theoretical studies. Solvation introduces substantial changes in the energetic profiles which

are accompanied by modifications of geometry parameters of the stationary points. From the

comparison of the energetic profiles of the explored reaction pathways in solution it is concluded

that the concerted GA/GB mechanism is the preferred one having the lowest activation barrier of

20.9 kcal mol�1.

Introduction

The peptide bond cleavage is a major process of protein decom-position and metabolism of living matter. Both enzymatic andnonenzymatic hydrolysis of peptide bonds is of biological andtechnological significance.1–4 The reaction mechanism of none-nzymatic peptide hydrolysis has been studied from many pointsof view5–19 and is still an object of theoretical investigationby modern calculation methods.10–17 At present four differentmechanisms of hydrolysis are discussed: the concerted mechanismwith and without the additional water molecule and the stepwisemechanism with and without the additional water molecule. Thenucleophilic attack on the carbon atom is the rate limiting stepof all reaction mechanisms. Car–Parrinello Molecular Dynamics(CPMD) calculations with a plane-wave basis found no

intermediate in the reaction dynamics and showed that theconcerted attack of carbon and nitrogen atoms by water mole-cules directly results in products.15

Hydrolytic reactions of peptide bonds in protein moleculeshave been investigated with respect to the proficiencies ofhydrolases and proteases.7,8 Proteases have been establishedas important and useful enzymes, and applied in many fields ofindustry and technology, during the last few decades.18–20

Consequently, and instead of using bacterial and/or othermicroorganism cultures, a controlled hydrolysis of the industriallyexploiting proteins, by proteases of known properties andmechanism of action, is certainly preferable.19,21 Likewise, themechanism of action of cysteine proteinases of the papain-C1family has been extensively elucidated relatively recently, whoseimportant characteristics are: (a) the development of an ion-pairwhich promotes the formation of an enzyme–substrate anionictetrahedral adduct, (b) the relation kcat/Km = k1 is valid, as theratio k2/k�1 was estimated to be large enough, and (c) theassociation of substrate onto enzyme proceeds through a step-wise mode, whereas both acylation and deacylation of theseproteinases follow concerted reaction pathways.21 However,mechanistic features are still elusive and require supplementaryexplanation.22,23 Hence, and by also considering previousapproaches,21–33 cysteamine, a weak cysteine proteinase mimic,has been used to simulate the catalysis of the aforementionedcysteine proteinases by hydrolyzing the amide synthetic substrate

a Laboratory of Inorganic and General Chemistry, Department of Chemistry,

University of Ioannina, 451 10 Ioannina, Greece. E-mail: attsipis@uoi.gr;

Fax: +30 26510 44831; Tel: +30 26510 8333b LPCNO, CNRS & INSA, Universite Paul Sabatier, 135 Avenue de Rangueil,

Toulouse 31077, France. E-mail: christos.kefalidis@gmail.comc Laboratory of Biochemistry, Department of Chemistry, University of Ioannina,

451 10 Ioannina, Greece. E-mail: epapamic@cc.uoi.gr

† Electronic supplementary information (ESI) available: Selected structural para-meters for all solvated stationary points in aqueous solution (Table S1). Cartesiancoordinates and energetic results (in hartrees) (Tables S2 and S3). See DOI:10.1039/c3nj00769c

Received (in Montpellier, France)11th July 2013,Accepted 11th September 2013

DOI: 10.1039/c3nj00769c

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acetyl-p-nitroanilide.21,24 In that case, and for a 1st order reaction,the relations v = d[P]/dt = kobs[S], kobs = (k2[Cysteamine]0)/(KS +[Cysteamine]0), and KS = (k�1 + k2)/k1, as well as the minimumthree-step reaction scheme:

were postulated; then the methodology of proton inventorieswas applied.21,24,27,31–33 Subsequently, it was found that cysteaminecatalyzes the hydrolysis of the acetyl-p-nitroanilide by formingan ion-pair analogous to that of cysteine proteinases, as can bededuced by the bowed-downward proton inventories and thecorresponding estimated fractionation factors. Moreover, andin contrast to the employed cysteine proteinases (papain,chymopapain, bromelain), it seems more likely that the ion-pair of cysteamine is much less stable and less active than thatdeveloped in the case of cysteine proteinases, as relativelysmall-inverse, and/or large-normal solvent isotope effects wereobserved for the parameters kcat/Km, and/or k2 and KS, respectively,whereas the ratio k2/k�1 was estimated to be small enoughsuggesting that the relation kcat/Km { k1 is valid (4).

The mechanistic features and energetics of apase-catalyzedpeptide hydrolysis have been investigated employing quantumchemical calculations on a model reaction system consisting offormamide and an acetate–acetic acid pair.34 Four reactionpathways have been considered namely: (a) a stepwise general-acid/general-base (GA/GB), (b) a concerted GA/GB, (c) a stepwisenucleophilic and (d) a concerted nucleophilic mechanism. It wasfound that for all reaction pathways considered the protonationof the peptidic nitrogen atom is an essential step in crossing theactivation of barrier for the rupture of a peptide substrate.34

Taking into account the experimental results in the case ofmimicking the catalysis of cysteine proteinases of the papain-C1family by the cysteamine molecule, we report herein the results of acomprehensive study of the mechanistic details of the cysteaminecatalyzed cysteine proteinases employing Density FunctionalTheory (DFT) electronic structure calculation methods in thegas phase and in aqueous solution. The concerted GA/GB,concerted stepwise nucleophilic and concerted nucleophilicmechanisms for the hydrolytic reactions of the acetyl-p-nitroanilidemodel peptide have been scrutinized in the gas phase and inaqueous solution.

Computational details

In view of the good performance of DFT, we were compelled toperform DFT calculations on all stationary points of thepotential energy surfaces (PES) that we studied employing theM06-2X35,36 global hybrid of the Truhlar’s Minnesota classes offunctionals. Our selection of the M06-2X functional was based onits good performance for the description of the conformationalpreferences of the alanine, Ac-Ala-NHMe and proline, Ac-Pro-NHMedipeptides in the gas phase and in water and the accurateprediction of the hydration free energies of the model compoundsfor backbones and side chains of peptides consistent with

experimental data available.22,37 The Pople’s split-valence6-311+G(d,p) basis set was used. Structural parameters andenergies for reactants, intermediates, transition states andproducts were computed using the Gaussian09 programsuite.38 The geometries of all stationary points were fullyoptimized in the gas phase and in aqueous solution employingthe solvation model of density (SMD)37 to take into account theeffects of bulk water and their nature (minima or transitionstates) was verified by the analysis of the normal vibrationfrequencies. The correlation between minima and transitionstates (first-order saddle points) was checked by performingintrinsic reaction coordinate (IRC) calculations. The entropiesof transition states and minima are evaluated by summingthe translational, rotational, and vibrational contributions(S = Strans + Srot + Svib), each of which is in turn obtained fromthe corresponding molecular partition function. In the calculationof the molecular partition functions, rigid-rotor and harmonic-oscillator approximations are used to factorize the contributionsfrom rotation and vibration. The single imaginary frequencymode of the transition state is excluded in the calculation ofthe vibrational partition function, while all normal modes areconsidered for the structures of energy minima.

Results and discussion

The hydrolysis of the peptide bond of acetyl-p-nitroanilide uponinteraction with cysteamine, mimicking the catalysis bycysteine proteinases; is represented by the following simplereaction:

Before proceeding to the theoretical analysis of themechanism of the above reaction, it should be stressed thatthe zwitterionic form of cysteamine is highly unlikely to existin the gas phase, since our calculations revealed that thedissociation energy of the S–H bond of the neutral form iscomputed to be as high as 347 kcal mol�1. However,the zwitterionic form corresponds to a local minimum inaqueous solution 4.8 kcal mol�1 higher in energy than theglobal minimum which corresponds to the neutral form ofcysteamine. The optimized geometry of cysteamine in avacuum and in aqueous solution starting either from theneutral or the zwitterionic form are the structures displayedin Fig. 1.

Accordingly, it is the neutral form of cysteamine mostlikely to react with the acetyl-p-nitroanilide. The hydrolysisof the peptide bond of the latter has also been studied bymeans of DFT calculations at the M06-2X/6-311+G(d,p) levelof theory in the gas phase and in aqueous solution followingfour plausible reaction pathways: (A) the concerted GA/GBmechanism, (B) the concerted mechanism, (C) The stepwisenucleophilic mechanism, and (D) the concerted nucleophilicmechanism.

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A. Concerted general-acid/general-base (GA/GB) mechanism

The enthalpic and geometric profiles for the concerted GA/GBmechanism, calculated at the M06-2X/6-311+G(d,p) level oftheory, are displayed in Fig. 2.

According to the concerted GA/GB mechanism (Fig. 2) awater molecule assists the formation of the first minimumenergy structure Im1_A, corresponding to an R1–R2–watercomplex stabilized by 17.4 kcal mol�1 through the formationof the hydrogen bonds Ow–H� � �Nc (with the H� � �Nc distance of1.838 Å; Nc is the N atom of cysteamine), Ow� � �H–S (with theOw� � �H distance of 2.278 Å), and Nc–H� � �Oa (with the H� � �Oa

distance of 2.138 Å; Oa is the O atom of the amidic group).Then, the reaction proceeds via the six-member transition stateTS1_A, in which the S–H bond is further elongated by almost0.5 Å compared to Im1_A and the Na� � �H is 1.160 Å. Themissing proton, resulting from the donation from the S atomto the amide, is equalized by accepting a proton from the watermolecule. The distance of the S� � �Hw is 1.986 Å, while the H–Ow

bond is weakened at the same time (1.022 vs. 0.960 Å). Theformation of TS1_A requires a relatively high activation barrierof 41.7 kcal mol�1. In the vibrational mode corresponding tothe imaginary frequency of TS1_A (�331 cm�1), the dominantmotions involve formation of a S� � �H–Ow hydrogen bond forcingthe transfer of one hydrogen atom of the cysteamine molecule toNa and leaving the nucleophilic OH� group to attack theelectrophilic Ca atom. It is noteworthy that during this processa synchronous bond formation and breaking could be observed,

i.e. hydrolysis of the peptide C–N bond, dissociation of the watermolecule by O–H bond breaking as well as formation of C–O andN–H bonds. Further advancement of Ow–Ca bond formation andC–N bond rupture in TS1_A leads to the end point minimum,Im2_A comprising three molecules, loosely associated, throughhydrogen bonding, i.e. zwitterionic form of cysteamine, aceticacid and p-nitroaniline. Finally, upon lifting all hydrogen bondsin Im2_A the reaction products P1, P2 and R2 are obtained.Interestingly, the optimization of the zwitterionic form of cysteamineafter the separation of the products leads to the most energeticallystable form of the cysteamine. Overall the concerted GA/GBmechanism of the amide bond hydrolysis corresponds to analmost thermoneutral process (�2.1 kcal mol�1).

B. Concerted mechanism

The enthalpic and geometric profiles of an alternative concertedmechanism, calculated at the M06-2X/6-311+G(d,p) level oftheory, are displayed in Fig. 3.

The reaction pathway starts with the formation of anR1� � �R2 complex, Im1_B, in which the Na atom is hydrogenbonded to the Nc atom of the amine group of cysteamineforming a Nc� � �H–Na hydrogen bond (with the Nc� � �H andH–Na distances of 2.004 and 1.024 Å, respectively). Im1_B isfurther stabilized by the formation of a weaker S–H� � �Na

hydrogen bond (with the S–H and H� � �Na distances of 1.342and 2.620 Å, respectively). The reaction proceeds from Im1_Bwith the gradual shift of the sulfydryl H atom to the Na atomthat are separated by 1.058 Å and the concomitant approachof the S atom to Ca of the peptide C–N bond at a distance of2.776 Å forming the transition state, TS1_B. The Nc� � �H–Na

hydrogen bond (with the Nc� � �H and H–Na distances of 1.752and 1.066 Å, respectively) also makes a contribution to thestabilization of TS1_B which is located at 42.8 kcal mol�1

higher energy with respect to Im1_B. In the vibrational modecorresponding to the imaginary frequency of TS1_B (�177 cm�1),the dominant motions involve formation of the S–C bond andrupture of the C–N peptide bond leading to intermediate Im2_B.This process is endothermic by 5.8 kcal mol�1, while it is slightlyexothermic with respect to the entrance channel (2.5 kcal mol�1).

Fig. 1 Optimized geometries along with selected structural parameters ofcysteamine calculated at the M06-2X/6-311+G(d,p) level of theory. (a) Structureof cysteamine in the gas phase. (b) and (c) neutral and zwitterionic structures ofcysteamine in aqueous solution respectively.

Fig. 2 Enthalpic and geometric profiles for the concerted GA/GB mechanism.

Fig. 3 Enthalpic and geometric profiles for the alternative concerted mechanism.

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Products P1 and P3 are obtained after their separation and P3 isfurther involved in a hydrolysis reaction, following the reactionpathways, given in Fig. 4. The enthalpy and geometric profilesof the hydrolysis of P3 are illustrated in Fig. 4, involving one(numbers in parentheses), and two water molecules.

Hydrolysis of acetyl-cysteamine (P3) involves the weak associationof two water molecules to acetyl-cysteamine yielding Im3a which isstabilized with respect to the reactant P3 and two water molecules by14.9 kcal mol�1 (Fig. 4). For the structure Im3a the reaction isinitiated by the approach of one out of two Ow to the amidic carbonatom, Ca (Ow� � �Ca distance of 2.848 Å), facilitated by formation ofOw–H� � �S hydrogen bond (with the H� � �S distance of 2.433 Å). Whenthe Ow–Ca distance is reduced to 1.568 Å the reaction systemreaches the transition state TS2a. The latter corresponds to a sixmember transition state. Passing through the TS2a, the reactionsystem falls into an intermediate minimum energy structure,Im4a, surmounting an activation barrier of 33.5 kcal mol�1 atthe M06-2X/6-311+G(d,p) level. In Im4a the acetic acid formedis associated with a water molecule through an Ow� � �Hacid

hydrogen bond (bond distance of 1.706 Å) and it is stabilizedby 24.3 kcal mol�1 with respect to the reactants. The watermolecule in turn, is associated with cysteamine through anOw–H� � �S hydrogen bond (bond distance of 2.342 Å). The nextreaction step involves the dissociation of Im4a to cysteamine, P2,and acetic acid with an energy demand of 15.8 kcal mol�1.We have also examined hydrolysis by considering onewater molecule, but due to the very high activation barrier(44.2 kcal mol�1) required to overcome TS2b (Fig. 4), wasexcluded from further discussion.

C. Stepwise nucleophilic mechanism

The enthalpic and geometric profiles for a stepwise nucleophilicmechanism, calculated at the M06-2X/6-311+G(d,p) level oftheory, are displayed in Fig. 5.

The stepwise nucleophilic mechanism involves formationof Im1_C corresponding to an R1� � �R2 complex stabilized by8.2 kcal mol�1 through the formation of the Nc–H� � �Oa hydro-gen bond (with the Nc–H and H� � �Oa distances of 1.016 and2.226 Å respectively). It should be noticed that in the stepwisenucleophilic mechanism the target of the electrophilic attack is

the amidic carbonyl oxygen atom. Next, Im1_C surmounting anactivation barrier of 41.8 kcal mol�1 forms the transition state,TS1_C. The single imaginary frequency of TS1_C (ni = �426 cm�1)is dominated by the S–H bond breaking and the Oa–H bondforming processes. TS1_C is stabilized by the formation ofS–H� � �Oa hydrogen bond (with the S� � �H and H–Oa distancesof 2.066 and 1.021 Å, respectively). Passing through the firsttransition state TS1_C, the reaction falls into two intermediateminimum energy structures, i.e. Im2_C and Im3_C correspondingto two different conformers of the O2NC6H4NHC(OH)SCH2CH2NH2

molecule. The second reaction step is then initiated by lengtheningof the amidic C–N bond (C–N bond distance 1.594 Å) accompaniedby a proton transfer from Oa atom to Na atom forming aOa� � �H� � �Na hydrogen bond (with the Oa� � �H and H� � �Na distancesof 1.348 and 1.217 Å, respectively) that stabilizes the transition stateTS2_C, surmounting an activation barrier of 32.6 kcal mol�1.TS2_C is further stabilized by the formation of an S–H� � �Oa

hydrogen bond (with the S� � �H and H–Oa distances of 2.735and 1.035 Å, respectively). The single imaginary frequency ofTS2_C (ni = �1536 cm�1) is dominated by the O–H bond breakingand the Na–H bond forming processes. From TS2_C, a furtherincrease in the amidic C� � �N distance leads to the final minimumenergy structure Im4_C, which is stabilized by 8.1 kcal mol�1 withrespect to the reactants through the formation of Nc� � �H–Na

hydrogen bond (with the Nc� � �H and H–Na distances of 2.046and 1.021 Å, respectively). Upon lifting the Nc� � �H–Na hydrogenbond the P1 and P3 products are formed with 14.5 kcal mol�1

energy demand. Overall the concerted stepwise nucleophilicmechanism of the amidic bond rupture corresponds to anendothermic process (DH = 6.4 kcal mol�1).

D. Concerted nucleophilic mechanism

The enthalpic and geometric profiles for the concerted nucleo-philic mechanism, calculated at the M06-2X/6-311+G(d,p) levelof theory, are displayed in Fig. 6.

A crucial factor that distinguishes the concerted from thestepwise nucleophilic mechanism is the target for the electro-philic attack which is the amidic nitrogen atom instead of theamidic carbonyl oxygen atom. The concerted nucleophilicmechanism involves formation of Im1_D corresponding to anR1� � �R2 complex stabilized by 9.6 kcal mol�1 through for-mation of an Nc� � �H–Na hydrogen bond (with the Nc� � �H andH–Na distances of 2.050 and 1.023 Å respectively).

Fig. 4 Enthalpy and geometric profiles of the hydrolysis of P3 (numbers inparentheses refer to the hydrolysis involving one water molecule).

Fig. 5 Enthalpy and geometric profiles for the stepwise nucleophilic mechanism.

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Next, the reaction proceeds from Im1_D with the approachof the sulfydryl H atom to the amidic carbonyl Oa atom formingthe transition state TS1_D. At the transition state TS1_D anS� � �H� � �Oa hydrogen bond (with the S� � �H and H� � �Oa distancesof 1.951 and 1.055 Å, respectively) is formed that assists theapproach of the S atom to the amidic carbon Ca atom at adistance of 2.736 Å. TS1_D is further stabilized by formation of aNc� � �H–Na hydrogen bond (with the Nc� � �H and H–Na distancesof 2.219 and 1.021 Å, respectively). The estimated activationbarrier was found to be 35.4 kcal mol�1. The single imaginaryfrequency of TS1_D (ni = �667 cm�1) is dominated by the S–Hbond breaking and the Oa–H and Ca–S bond forming processes.

Passing through the TS1_D, the reaction falls into twointermediate minimum energy structures, i.e. Im2_D and Im3_Dcorresponding to two different conformers of the O2NC6H4NHC-(OH)SCH2CH2NH2 molecule. In conformers Im2_D and Im3_D theS atom approaches the Ca atom at distances 1.916 and 1.861 Å,respectively. Im3_D is stabilized by 3.8 kcal mol�1 with respect toIm2_D via formation of an Nc� � �H–Na hydrogen bond (with theNc� � �H and H–Na distances of 2.035 and 1.020 Å, respectively).

The second reaction step is then initiated by lengthening ofthe amidic C–N bond (C–N bond distance 1.448 Å) accompanied bya proton transfer from Oa atom to Na atom forming a Oa–H� � �Na

hydrogen bond (with the Oa–H and H� � �Na distances of 0.963 and2.451 Å, respectively) that stabilizes the transition state TS2_D,surmounting an activation barrier of 36.4 kcal mol�1. The singleimaginary frequency of TS2_D (ni = �1518 cm�1) is dominated bythe O–H bond breaking and the Na–H bond forming processes.From TS2_D, a further increase in the amidic C� � �N distanceleads to the final minimum energy structure Im4_D which isstabilized by 8.7 kcal mol�1 with respect to the reactants throughthe formation of Oa� � �H–Na hydrogen bond (with the Oa� � �H andH–Na distances of 2.633 and 1.009 Å, respectively). Upon liftingthe Oa� � �H–Na hydrogen bond the P1 and P3 products areformed with 15.1 kcal mol�1 energy demand.

Solvation effects

The effect of solvation on the enthalpic and geometric profilesof the explored reaction pathways was accounted for by per-forming M06-2X/6-311+G(d,p) calculations in aqueous solutionemploying the SMD solvation model. The thermodynamicproperties at the M06-2X/6-311+G(d,p) level of all stationarypoints for the four reaction pathways under consideration in

aqueous solution at T = 298 K are compiled in Table 1, whileselected structural parameters of all stationary points are givenin the ESI† (Table S1).

Comparison of the energetic profiles of the explored reactionpathways in aqueous solution with those calculated in the gasphase reveals that solvation introduces substantial changes whichare accompanied by the modifications of geometry parameters ofthe stationary points.

First the reactants R1 and R2 and products P1, P2 and P3are stabilized in aqueous solutions by 11.7, 6.2, 10.3, 7.3 and8.6 kcal mol�1 respectively, as a result of the electrostaticsolvent effects.

In the water-assisted concerted GA/GB mechanism solvationdestabilizes Im1_A by 10.1 kcal mol�1 due to the weakeningof the Ow� � �H–S (with the Ow� � �H distance of 2.464 Å), andNc–H� � �Oa (with the H� � �Oa distance of 2.565 Å) hydrogenbonds. The six-member transition state TS1_A, is stronglystabilized in aqueous solution by 10.7 kcal mol�1. The formationof TS1_A in aqueous solution demands the lowest activationbarrier of 20.9 kcal mol�1. The energy and structure of the end

Fig. 6 Enthalpy and geometric profiles for the concerted nucleophilic mechanism.

Table 1 Thermodynamic properties (in kcal mol�1) calculated at the M06-2X/6-311+G(d,p) level for all stationary points of the four reaction mechanismsexplored in aqueous solution

Stationary point DH DG

Concerted GA/GB mechanismR1 + R2 0.0 0.0Im1_A �7.3 14.0TS1_A (ni = �699 cm�1) 13.6 37.6Im2_A �12.7 9.4P1 + P2 + R2 0.8 0.7

Concerted mechanismR1 + R2 0.0 0.0Im1_B �5.9 5.9TS1_B (ni = �132 cm�1) 28.3 41.2Im2_B �1.6 11.2P1 + P3 3.4 3.2

Hydrolysis reaction stepP3 + 2H2O 0.0 0.0Im3a �6.6 12.0TS2a (ni = �288 cm�1) 24.4 47.2Im4a �9.2 8.2P2 + R2 + H2O �2.6 �2.5

Stepwise nucleophilic mechanismR1 + R2 0.0 0.0Im1_C �6.2 5.7TS1_C (ni = �170 cm�1) 28.2 40.9Im2_C 3.0 18.1Im3_C 7.1 22.2TS2_C (ni = �1667 cm�1) 37.3 52.4Im4_C �4.2 7.4P1 + P3 3.4 3.2

Concerted nucleophilic mechanismR1 + R2 0.0 0.0Im1_D �6.7 5.2TS1_D (ni = �85 cm�1) 27.3 40.3Im2_D 7.6 21.9Im3_D 4.8 19.9TS2_D (ni = �1643 cm�1) 37.7 52.8Im4_D �4.7 8.2P1 + P3 3.4 3.2

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point minimum, Im2_A are not affected by solvation. Overallthe concerted GA/GB mechanism of the amide bond hydrolysisin aqueous solution corresponds to an almost thermoneutralprocess (0.8 kcal mol�1).

In the reaction pathway following the concerted mechanismsolvation slightly destabilizes Im1_B by 2.4 kcal mol�1 for theNc� � �H–Na and S–H� � �Na hydrogen bonds stabilizing the Im1_Bremain practically unchanged. On the other hand, solvationstabilizes the transition state TS1_B by 6.3 kcal mol�1. TS1_B isstabilized by formation of Oa–H� � �S (with H� � �S distance of2.737 Å) and Nc–H� � �Oa (with H� � �Oa distance of 2.571 Å)hydrogen bonds. The activation energy barrier for TS1_B(DHa = 34.2 kcal mol�1) is 8.7 kcal mol�1 lower than the gasphase activation barrier. In the vibrational mode correspondingto the imaginary frequency of TS1_B (�132 cm�1), the dominantmotions involve formation of the S–C bond and rupture of theC–N peptide bond leading to intermediate Im2_B which isslightly destabilized by 0.9 kcal mol�1 upon solvation. Overallthe concerted mechanism of the amide bond hydrolysis inaqueous solution corresponds to a slightly endothermic process(4.4 kcal mol�1).

The hydrolysis of product P3 in aqueous solution followsthe reaction profile shown in Fig. 4, involving one and twowater molecules. Solvation destabilizes intermediate Im3a by8.3 kcal mol�1 due to the weakening of the Ow–H� � �S (with theH� � �S distance of 2.742 Å) hydrogen bond. The six membertransition state TS2a is also destabilized upon solvation by5.8 kcal mol�1. The activation energy barrier for TS2a (DHa =31.0 kcal mol�1) is 2.5 kcal mol�1 lower than the gas phaseactivation barrier. Intermediate Im4a is strongly destabilized(by 15.1 kcal mol�1) upon solvation due to the weakening of allpossible hydrogen bonds that stabilize Im3a. Overall the hydro-lysis of P3 in aqueous solution corresponds to a slightlyexothermic process (�2.8 kcal mol�1). The hydrolysis by con-sidering one water molecule has also been investigated, but dueto the very high activation barrier (42.7 kcal mol�1) required toovercome TS2b (Fig. 4), it will not be discussed any more.

In the stepwise nucleophilic mechanism solvation slightlydestabilizes Im1_C by 2.2 kcal mol�1 for the Nc–H� � �Oa (withthe Nc–H and H� � �Oa distances of 1.018 and 2.248 Å respec-tively) hydrogen bond is slightly weakened. In contrast, TS1_Cis stabilized upon solvation by 5.4 kcal mol�1. TS1_C is stabi-lized by the formation of S� � �H–Oa hydrogen bond (with theS� � �H and H–Oa distances of 2.736 and 0.978 Å, respectively).

The activation energy barrier for TS1_C (DHa = 34.4 kcalmol�1) is 7.4 kcal mol�1 lower than the gas phase activationbarrier. The two intermediate minimum energy structures, i.e.Im2_C and Im3_C corresponding to two different conformersof the O2NC6H4NHC(OH)SCH2CH2NH2 molecule are destabilizedby 3.4 kcal mol�1 upon solvation. The transition state TS2_C, ismarginally destabilized by 1.0 kcal mol�1 surmounting anactivation barrier of 30.2 kcal mol�1, only 2.4 kcal mol�1 lowerthan the gas phase activation barrier. The single imaginaryfrequency of TS2_C (ni = –1667 cm�1) is dominated by the O–Hbond breaking and the Na–H bond forming processes. The nextminimum energy structure Im4_C is also destabilized in

aqueous solution by 3.9 kcal mol�1. Overall the concerted stepwisenucleophilic mechanism of the amidic bond rupture correspondsto a slightly endothermic process (DH = 3.4 kcal mol�1).

Finally, in the concerted nucleophilic mechanism solvationslightly destabilizes Im1_D by 2.8 kcal mol�1 due to the weakeningof the Na–H� � �Nc (with the Na–H and H� � �Nc distances of 1.019 and2.595 Å respectively) hydrogen bond. The first transition state TS1_Dbeing marginally destabilized in aqueous solution surmounts anactivation barrier of 34.0 kcal mol�1 only 1.4 kcal mol�1 lower thanthe gas phase activation barrier. The two intermediate minimumenergy structures, i.e. Im2_D and Im3_D corresponding to twodifferent conformers of the O2NC6H4NHC(OH)SCH2CH2NH2 mole-cule are also destabilized in solution by 2.7 and 3.7 kcal mol�1

respectively. The second transition state TS2_D, surmounting anactivation barrier of 32.9 kcal mol�1 (only 3.5 kcal mol�1 lower thanthe gas phase activation barrier) is not affected by solvation(marginal destabilization by 0.2 kcal mol�1). The final minimumenergy structure Im4_D is destabilized by 4.0 kcal mol�1 in aqueoussolution. Upon lifting the Oa� � �H–Na hydrogen bond the P1 and P3products are formed with 7.6 kcal mol�1 energy demand.

Comparing the energetic profiles of theexplored reaction mechanisms

Comparison of the energetic profiles of the explored reactionpathways given in Fig. 2–6 reveals that the concerted nucleo-philic mechanism followed by that of hydrolysis is kineticallythe more feasible having the lower activation barrier, DHa =35.4 kcal mol�1. Considering that the entropic effects arisingfrom the thermal nuclear motions are important in determiningthe reactivity of weakly bonded complexes;1 we also comparedthe estimated free energy of activation (DGa) for all reactionpathways explored herein. Based on the estimated DGa values of45.5, 46.4, 42.6, and 39.7 kcal mol�1 for the concerted GA/GB,concerted, stepwise nucleophilic and concerted nucleophilicmechanisms, respectively, it is concluded that the concertednucleophilic mechanism is the most feasible one again. This isconsistent with the catalytic mechanism of aspartic proteinasesstudied previously by Lee and co-workers34 performing ab initiocalculations at the MP2/6-31G(d,p)//RHF/6-31G(d,p) level. Theauthors showed that the concerted and stepwise pathways areequally favored in the GA/GB mechanism and the concertedreaction pathway would be preferred in the nucleophilicmechanism. It is noteworthy that the estimated DGa valuesare comparable to the estimated DGa values for the water-assistedhydrolysis of formamide calculated at the MP3/6-31G**//3-21Gab initio level for neutral and H3O+-promoted processes.10

Solvation affects both the enthalpic and geometric profilesof the explored reaction pathways. From the comparison of theenergetic profiles of the explored reaction pathways in solutionwe can conclude that all reaction pathways are competitivesince they are characterized by analogous activation barrierse.g. DHa = 20.9, 34.2, 34.4 and 34.0 kcal mol�1 for the GA/GB,concerted, stepwise nucleophilic and concerted nucleophilicmechanisms respectively. The estimated free energy of activation

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This journal is c The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2013 New J. Chem., 2013, 37, 4061--4068 4067

(DGa) in aqueous solution are predicted to be 23.6, 35.3, 35.7,and 35.1 kcal mol�1 for the concerted GA/GB, concerted, step-wise nucleophilic and concerted nucleophilic mechanisms,respectively also indicating that all reactions pathways exploredshould be competitive.

Conclusions

In summary, on the basis of extensive calculations employingthe M06-2X/6-311+G(d,p) computational protocol, both concertedand stepwise mechanisms for the hydrolysis reaction of thepeptide bond of acetyl-p-nitroanilide catalyzed by cysteamine havebeen explored.

It was found that the hydrolysis reaction of the peptide bondof acetyl-p-nitroanilide catalyzed by cysteamine in the gas phaseis most probable to occur via the concerted nucleophilic reactionmechanism, for it is kinetically the more feasible one exhibitingan activation enthalpy barrier, DHa of 35.4 kcal mol�1.

Solvation plays an important role in the enthalpic andgeometric profiles of the explored reaction pathways introducingsubstantial energy changes which are accompanied by modifica-tions of geometry parameters of the stationary points. All reactantsand products are stabilized in aqueous solutions while most ofintermediates and transition states are destabilized upon solvation.

In aqueous solutions the concerted GA/GB mechanism is thepreferred one for the formation of the transition state TS1_A,demanding the lowest activation barrier of 20.9 kcal mol�1. Theremaining three reaction pathways explored are predicted to becompetitive in aqueous solution demanding high activationbarriers (DHa B 34.0 kcal mol�1).

Predicted thermodynamic values show good agreement withavailable data for the water-assisted hydrolysis of formamideand the catalytic action of aspartic proteinases.

Notes and references

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