Effect of Alkylation on the Kinetic Stability of Arsenodiester and Organoarsenicals against Hydrolysis: A Theoretical Study 96 D O I: 1 0. 15 82 6/ ch im te ch .2 01 8. 5. 2. 01 Boota Singh, Rohan Ranjan Waliya, Sougata Santra, Zyryanov G. V., Kousik Giri Chimica Techno Acta. 2018. Vol. 5, No. 2. P. 96–103. ISSN 2409–5613 Boota Singh1, Rohan Ranjan Waliya1, Sougata Santra2, G. V. Zyryanov2,3, Kousik Giri1* 1Department of Computational Sciences, Central University of Punjab, Bathinda, Punjab, India 2Department of Organic and Biomolecular Chemistry, Chemical Engineering Institute, Ural Federal University, 19 Mira St., Ekaterinburg, 620002, Russian Federation 3I. Ya. Postovskiy Institute of Organic Synthesis, Ural Branch of the Russian Academy of Sciences, 22 S. Kovalevskoy St., Ekaterinburg, 620219, Russian Federation *E-mail: kousikgiri@gmail.com Effect of Alkylation on the Kinetic Stability of Arsenodiester and Organoarsenicals against Hydrolysis: A Theoretical Study Arsenic diesters have same structural and chemical properties as P i (phos- phate) diester. Beside this structural similarity, arsenate is not considered by cel- lular processes to replace phosphate. Quantum calculation reveals that this hap- pens due to very high hydrolysis rate of As i diester (As–O-bond-based compounds) as compared to P i , but how organoarsenicals (As–C-bond-based compounds) that are produced by alkylation of As i survive in highly aqueous tissues of marine organisms? We found that this alkylation results in lower hydrolysis rate of As i diester. Our work concluded that alkylating effort by our body on As i is to avoid structural ambiguity with phosphate and excrete out arsenic in the form of or- ganoarsenicals from body. Keywords: arsenic, arsenobetaine, arsenocholine, arsenosugar, DMA, MMA, arsenate or- ganoarsenicals, arsonic acid, hydrolysis Received: 14.06.2018. Accepted: 27.07.2018. Published: 30.07.2018. © Boota Singh, Rohan Ranjan Waliya, Sougata Santra, Zyryanov G. V., Kousik Giri, 2018 Introduction Arsenic (As) is one position be- low phosphorus (P) in  the same group of the periodic table, that is why it shares the fundamental chemical properties with phosphorus. In the environment arsenic exists in  four oxidation states:  –3, 0, 3, and 5, while the elemental arsenic occurs rarely [1]. Arsenite [As (III)] is the most toxic form of  inorganic arsenic, mainly found in anoxic environments, whereas less toxic arsenate [As (V)] occurs in aqueous, aerobic environments [1]. Due to  struc- tural similarities of arsenate and phosphate, phosphate transporters cannot easily dis- tinguish between Asi and Pi, which results in the substitution of Asi in many Pi-based metabolic pathways (Table 1) [2]. However, Asi-based compounds are hydrolysed much 97 faster than phosphate compounds [3], but the kinetics of hydrolysis decreases by in- creasing size of alkyl substituent on arse- nate due to steric effect [4]. Alkylation is al- so utilised by marine organisms to produce organoarsenical products from arsenate, like arsenobetaine (Me3As +CH2COO –), arsenocholine (Me3As +CH2CH2OH) and arsenosugar [1]. Even different pathways, proposed for arsenic metabolism in mam- mals, also lead to methylated end product of Asi [5]. A very high percentage (> 70 % of total arsenic) of these organoarsenicals is found in kidney and muscles of marine animals [1]. The quantum chemical calculations performed by Mlàdek et al. [11] reveals that neither steric hindrance nor polarity of the solvent is able to reduce the high hydrolysis rate of arsenate monoesters as compared to monoesters of phosphate. But Mlàdek et al. [11] performed the theoretical mo- delling on the kinetics of the arsenate-ester hydrolysis by using mono-alkyl-arsenates only, whereas arsenate in organisms occurs as diester forms. Chemically, diester has a very profound role in the kinetics of Asi hydrolysis because of steric hindrance and electronic effect as compared to mono es- ter, where Asi is enclosed by a single ester linkage. One interesting fact about pro- tecting hydrolysis of Asi is itself provided by organoarsenicals produced by marine organisms. These organic Asi compounds have a direct As–C bonding as compared to inorganic Asi which have As–O bond- ing. Because As–C bond is less polar as compared to As–O bond due to lesser electronegativity of C than O, this would leads to the decrease in the reactivity of nu- cleophilic water towards As–C-bond-based compounds. The process of converting As– O-bond-based compounds to  As–C was also proposed in  mammals, where liver cell first reducts Asi diester by using glu- tathione and then, after methyl transferases for methylation, finally produced various species of arsenic acid from Asi diester (see Fig. 1). In this regard, a  theoretical model based study is essential to  compare the hydrolysis rate of  alkylated Asi diester with diester of  Pi and to  understand the mechanism behind the alkylation of  Asi during metabolism in mammals that differ from alkylation in diester where arsenic is directly (and not through the oxygen atom) bonded to carbon atom. Table 1 Evidence of arsenate substitution for phosphate in biochemical processes Reaction or enzyme Arseno-analogue Phosphate compound Reference Adenylate deaminase 5’AMAs 5’AMP [6] Adenylate kinase 5’AM (CH2) As AMP [7] Chloroplastic electron transport ADP-As ATP [8] Glucose-6-phosphate dehydrogenase Glucose-6-arsenate Glucose-6-phosphate [9] Hexokinase ADP-As ATP [9] Human red blood cell sodium pump Asi Pi [2] Purine nucleoside phosphorylase Asi Pi [10] 98 Methods Hydrolysis pathways for Asi diester are well documented in the literature [4, 12]. The associative pathway was claimed to be dominated over dissociative pathway [4]. This pathway follows SN2 mechanism, where the attack of water nucleophile on es- ter results in a reaction intermediate having a pentacoordinated centre with trigonal bi- pyramidal geometry. Further internal pro- ton transfer leads to the breaking of As–O bond carrying the alkyl substituents. To see the effect of  alkyl substituent on  hydrolysis rate of  both As–O- and As–C-bond-based compounds, proto- types of  chemical species in  Fig.  3 were modelled. PBE1PBE functional from DFT (Den- sity Functional Theory) was used for the quantum chemical calculation in this work because it was recommend after bench- marking of  DFT functionals for  the hy- drolysis of  phosphodiester bonds [13]. 6-31G+ (d, p) basis set was selected for the calculation of  hydrolysis rate constant. Polar solvent (ε  = 78.4, water) was em- ployed with the Polarizable Continuum Model (PCM) using the integral equation formalism variant (IEFPCM) [14]. Since Fig. 1. A general outline depicting mechanism of arsenate metabolism in mammals: MMA – monomethyl arsonic acid, DMA – dimethyl arsenic acid Fig. 2. Reaction pathways for hydrolysis of arsenate ester (TS – Transition State) 99 we already described that the hydrolysis of Asi follows SN2 mechanism where rate determining step is the attack of nucleo- phile, we modelled structures for reactants and TS only (see Fig. 2) for the determi- nation of  rate constant of  hydrolysis re- action. Both optimization and frequency calculation of  reactants” structures were performed by  using PBE1PBE / 6-31G+ (d, p). Transition state structure was mo- delled first by using lower methods like hf (Hartree-Fock) with less computationally demanding gaussian basis set 3-21G with redundant internal coordinates geometry where we applied bond constrained on one proton of  water molecule, which tunnel between negatively charged oxygen atom of  ester and oxygen atom of  water. Hes- sian displays negative eigenvalues, which verify the nature of a transition state that has been optimized, and shows the correct vibration of  proton along a  bond vector where we applied constrained (see Fig. 4) further optimization of TS geometry, fol- lowed by frequency calculation by using ultrafine grid and PBE1PBE DFT method with 6-31G+ (d, p) basis set. Aside from display of  negative vi- brational frequency, it is also necessary to identify the minima connected through the transition state. This latter part is per- formed through the intrinsic reaction co- ordinate (IRC), defined as the minimum energy reaction pathway in mass-weighted cartesian coordinates between the transi- tion state of  a  reaction and its reactants and products [15]. IRC is basically a path that the molecule takes while moving down the product and reactant valleys with zero kinetic energy [15]. We calculate IRC with maximum 50 steps on both side with each step size of 0.0750 bohr (see Fig. 5). The key equation for calculating reac- tion rates is k H k T hc eB G RT o 298, . � � � � � We use c0 = 1 for the concentration. Be- cause of  the final geometry, cartesian force constants and electronic energy are independent of the masses of the atoms, and only the vibrational analysis is mass- dependent [16]. The first step in  calculating the rates of these reactions is to compute the free energy of activation, � � � G Ho of reaction at 298 K, which is calculated by using Eq. 1: � � � � � � �� � � �� �� � , G K E G E G o o corr products o corr reactants 298 (1) where � �� � � �� �E G E Go corr products o corr reactants, is sum of electronic and thermal free en- ergies for products and reactants, respec- tively.Fig. 3. As–C- and As–O-bond-based arsenic compounds 100 Fig. 4. Bond constrains, applied along bond vector A, B and C in transition state structure geometry optimization of dimethylarsenate Fig. 5. Intrinsic reaction coordinates pathway for the rate-determining step in hydrolysis of arsenate with 50 steps on each side and step size of 0.0750 bohr 101 Results and discussion Hydrolysis rate for both As–O- and As– C-bond-based compounds summarized in tables 2 and 3. We also calculated the hydrolysis rate of alkyl-O-phosphate diester. On average, it was found to be ~10–18 sec–1, whereas for alkyl-O-arsenate diester it was ~10–4 sec–1. It is clear that arsenate diester is less stable as compared to phosphate diester. This is because As have higher metallic charac- ter than P in diester and that is why it is a  stronger site for  a  nucleophilic attack as  compared to  P. In  Fig.  6 we provide ESP (Electrostatic potential) charges for arsenate and phosphate in  their respec- tive diester. We use ESP charges in place of conventional Mulliken charges because Fig. 6. ESP (Electrostatic Potential) charges on central atom of diester of Arsenic and Phosphorous. Arsenic atom is more positively charged in its diester as compared with P. Polarizable Continuum Model (PCM) using the integral equation formalism variant (IEFPCM) was used to mimic effect of solvent (ε = 78.4, water). Atomic charge is given in units of e Table 2 Hydrolysis Rate for As–O-bond-based compounds № Arsenic Compounds Rate of Hydrolysis (in sec – 1) 1 Dimethyl-O-Arsenate 2∙10–4 2 Diethyl-O-Arsenate 6∙10–4 3 Dipropyl-O-Arsenate 1∙10–2 Table 3 Hydrolysis Rate for As–C-bond-based compounds № Arsenic Compounds Rate of Hydrolysis (in sec–1) 1 Arsenate 8.0∙10–2 2 Monomethyl-Arsenate 4.49∙10–5 3 Dimethyl-Arsenate 1.18∙10–6 4 Trimethyl-Arsenate 6.0∙10–7 102 they are much less dependent on the choice of basis set [17]. About 10 to 100 times fall in hydroly- sis rate of As–C-bond-based compounds as  compared to  As–O-bond-based com- pounds was observed. This fall is due to the decrease in positive charge on central As atom (1.54e in case of dimethyl) because of the direct bonding of alkyl substituents to As, which are potent electron donating groups. Now, because As in As–C-bond- based compounds has lower positive charge as  compared with charge on  As in  As– O-bond-based compounds, attack of nu- cleophilic water is less favoured over As in  As–C compounds compared to  As–O compounds. Our findings directly support the proposed mechanisms for the metabo- lism of arsenate in mammals [5] because arsenate needs to be stabilized first, then, to support excretion of methylated arsenic products by highly aqueous excretory or- gans, some polar groups must be attached, like carboxylic acid, hydroxyl, etc. After that, arsenate is fully metabolized and ready to excrete in form of becomes organoarse- nicals (see A, B, and C in Fig. 3). Conclusions In our study we found that Asi diester is highly prone to hydrolysis under physi- ological conditions as  compared with Pi diester, whereas organoarsenicals products are formed to protect Asi from hydrolysis, otherwise it would be converted further to toxic AsIII (arsnite). Hence, methylation followed by  attachment of  a  polar group to arsenate is a way to excrete out Asi from body as  organoarsenicals like arsenosu- gar, arsenobetaine, arsenocholine etc. Our work could help to  understand the arse- nic metabolic pathway inside living orga- nisms. Same kind of  approach could be useful for studying the mechanism of ar- senite (AsIII) toxicity. It was reported that As in arsenite is a potent bonding partner for sulphur by breaking disulfide linkages in  proteins, which would results in  dys- function of  that protein. 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