Activation modelling of β- and γ-class of carbonic anhydrase with amines and amino acids: Proton transfer process within the active site from thermodynamic point of view

Abstract Activation mechanisms of an inactive form of β-carbonic anhydrase (β-CA), [Zn+2(cys)2(his)(H2O)], and γ-carbonic anhydrase (γ-CA), [Co+2(his)3(H2O)], with amines and amino acids have been investigated extensively using quantum mechanical calculations. Two DFT methods including B3LYP/6-31G∗ and B3PW91/def2-SVP have been employed to calculate the details of electronic structure and electronic energy of different compounds and complexes through the reaction mechanism path. Conformational analysis of three activators of β-CA, including d -phenylalanine, l -tyrosine and histamine and three activators of γ-CA, including 2-pyridyl-methylamine, serotonin and l -phenylalanine, and a complex between different conformers of these activators and active center of β- and γ-carbonic anhydrase have been studied. In addition, thermodynamic functions for the total reaction and for the complexation between activators and β- and γ-CA are evaluated. The calculated results indicate that protonatable moiety of above mentioned activators participate in proton transfer from zinc (in β-CA) and cobalt (in γ-CA) bond water molecule and lead to the formation of the catalytically active species of CA enzyme, hydroxide coordinated to the zinc and cobalt ions. In all calculations, solvent effects have been considered in three solvents including water (e = 78.9), 1-bromooctane (e = 5) and 1, 2-ethanediol (e = 40) using PCM model. Further, the interaction between the most stable and more effective activators conformers with β- and γ-CA in presence of water solvent were studied by employing explicit solvent model.


Introduction
Carbonic anhydrases (CAs, EC 4.2.1.1) belong to biological metalloenzymes that facilitate the proton transport and present in all three domains of life (Eucarya, Bacteria and Archaea) which are encoded by five distinct, evolutionarily gene classes: a-CAs, b-CAs, c-CAs, d-CAs and f-CAs [1][2][3][4][5][6][7][8]. The a-, b-, and d-CAs use zinc ion (Zn(II)) at their active site [9][10][11][12], the c-CAs are mostly Fe (II) and Co(II) enzymes but they are active also when Zn 2+ ions bond, whereas the f-CAs use Cd 2+ or Zn 2+ to perform the physiologic reaction catalysis [9,[13][14][15]. Fig. 1 shows the active site of these five families of CAs. As depicted in Fig. 1 the metal ion ligands are three histidine (his) residues in a-, c-, and d-CAs or one his and two cysteines (cys) residues in b-and f-CAs. These superfamily of metalloenzymes efficiently catalyze very simple physiological reaction, the conversion of carbon dioxide to bicarbonate ion, and then bicarbonate replaced by a water molecule to generate catalytically inactive form of this enzyme, [EM 2+ (H 2 O)], that M refers to central atom in active center in the enzyme [9,[16][17][18][19][20], Scheme 1. In order to regenerate the catalytically active form of this enzyme, a proton shuttling processes between the metal ionbound water molecule (M 2+ ) in the enzyme active center and the environment [21,22] takes place which may be assisted either by active site residues (such as His 64 in a-CA) or by the buffers present in the medium, This leads to enhanced formation of the metal hydroxide, catalytically active species of the enzyme, Eq. (1).
CA activators do not have pharmacological applications is due to their difficult pharmacology at this moment. However, it has been reported that some CA activators (such as phenylalanine or imidazole) administered to experimental animals may produce an very important pharmacological enhancement of synaptic efficacy, spatial learning, and memory, proving that this class of relatively unexplored enzyme modulators could have essential applications in conditions in which learning and memory are impaired, such as Alzheimer's disease [28,29]. In addition, that it was reported that the levels of CA are significantly diminished in the brain of patients affected by Alzheimer's disease [30] and these facts strongly support the involvement of different brain CA isozymes in cognitive functions.
However, no clinical trials for the use of carbonic anhydrase activators for the management of these conditions were done at this moment.
According to results of previous studies on a-CA [31], it has been proved that in the presence of an activator, the enzyme/activator complex forms and the activator participates in proton transfer process which is the rate determining step in the catalytic cycle, Eq. (1) [32][33][34][35][36][37].
In order to understand the catalytic mechanism of CA enzyme belonging to b-and c-CA classes, it is importance to study these enzymes such as a-CAs that can be activated by compounds which can transfer protons between the active site and the environment.
Since no theoretical activation studies of these enzymes have been performed, here we have reported the first theoretical study of carbonic anhydrase activation belonging to the b-and c-classes.
We are hopeful that this study sheds light on the activation phenomena of b-and c-CAs, which have been spread especially in Bacteria, Archaea and in microscopic and macroscopic Eukarya such as fungi and plants.
The results of recent experimental studies indicate that Dphenylalanine (D-phe) and L-tyrosine (L-tyr), for the b-CA and 2pyridyl-methylamine (pyr) and serotonin (ser) for c-CA, act as efficient activators; Also histamine (hst) and L-phenylalanine (L-phe) acts as weak activators for b-and c-CAs respectively [2,9,[38][39][40][41][42], In the present research, the complexation of different activators to the active site of b-CA and c-CA enzyme from different positions have been studied thermodynamically and calculated results have been compared with experimental data to confirm the accuracy level of calculations. Despite the extensive use and study of different enzymes in the presence of some organic solvents, for some enzymes such as carbonic anhydrase, the effect of organic solvent is unknown. Since macromolecular targets may be affected by the presence of different solvents in such a way that conformational changes perturb their active center geometry accompanied by variations in activity when performing biochemical screenings. To address this issue, in this work we studied the effects of three different solvents including water (e = 78.9), 1, 2-Ethanediol (e = 40) and 1-Bromooctane (e = 5). In addition medium and biocatalyst engineering are novel techniques to improve the efficiency and stability of enzymes in different kind of solvents. Moreover, these kinds of solvent effect study illustrations of applications of such systems in different areas of chemistry such as organic synthesis, analysis and polymer chemistry. Interaction energies, electronic states and all thermodynamic functions such as standard enthalpy of complexation (DH°c om ) Scheme 1. Catalytic mechanism of carbonic anhydrase; a proton transfer reaction from the active site to the environment take place that is assisted by active site residues or by activators (B). and the standard Gibbs free energy of complexation (DG°c om ) for all CA/activator complexes have been determined according to reaction 1 in solution phase. Also, all thermodynamic functions, DH°r xn , DG°r xn and DS°r xn , for the total reaction are evaluated in different three solvents.
Determination of the energies and geometry of active site of CA and activators in CA-activator complex using QM calculations will contribute to advance our knowledge on the mechanism of activator actions. These results may bring novel insights to design new band c-CA activators.

Computational details
The geometries and energy of active and inactive form of b-and c-CAs active site, different conformers of activators and their protonated form (AcH + ), the complex between activators and b-and c-CAs from different positions were calculated with the density functional theory (DFT) [43] with no symmetry constrains. The hybrid of Beck's nonlocal three parameter exchange and corrected functional with Lee-Yang-Parr correlation functional (B3LYP) [44] for the close shell system and UB3LYP for open shell system have been used. The calculations were performed with standard 6-31G ⁄ basis set. Also, some calculations are repeated with B3PW91/def2-SVP method [45,46]. DFT methods, can be used for calculations involving metals. Hybrid methods, such as B3LYP, are often the method of choice for reaction calculations. The most significant advantage to DFT methods is a significant increase in computational accuracy without the additional increase in computing time.
The harmonic vibrational frequencies were computed to confirm that an optimized geometry correctly corresponds to a local minimum that has only real frequencies. In addition, the vibrational frequencies have been employed to obtain enthalpies and Gibbs free energies at 298.15 K and 1.0 atmosphere pressure. All reported enthalpies were zero-point (ZPE) corrected with unscaled frequencies. The solvent effects on the conformational equilibrium and contribution to the total enthalpies were investigated with using polarized continuum (overlapping spheres) model (PCM) of Tomasi and coworkers [47] at the B3LYP/6-31G ⁄ and B3PW91/ def2-SVP levels. The water is the main solvent in all physiological Comparison between X-ray and optimized structure of the b-CA active center enzyme in water solvent in active form (left) and inactive form (right) with some structural details using B3LYP/6-31G * and B3PW91/def2-SVP methods. Bond distances are according to Å.
liquids, but according to presence of different kinds of molecules and components in the medium the polarity of the solvent could be changed. Since the solvation calculations were carried out for three different dielectric constants including water (e = 78.9), 1, 2-Ethanediol (e = 40) and 1-Bromooctane (e = 5) with the geometries optimization for these solvents. Generally, the PCM method shows good accuracy, reliability, adaptability and more reduced computational effort to describe solvent effect [48][49][50].
Moreover, the interaction between the most stable and efficient activators conformers with b-and c-CA in presence of solvent (water) was studied by employing explicit as well as an implicit solvent model. Finally, some single point calculations were also carried out with B3LYP/6-311++G ⁄⁄ method to provide a check on the B3LYP/6-31G ⁄ method. Since in open shell system the accuracy of energy evaluation is sensitive to spin contamination, so spin contaminations of open shell systems were found in the 0.76-0.78 range. They dropped to correct value 0.75 after the annihilation of the first spin contaminant. Therefore spin contamination cannot bias found reaction enthalpies. All calculations were performed using the Gaussian 2003 [51] software. The structure of b-carbonic anhydrase active center in active (zinc-bond hydroxide) and inactive (zinc-bound water) forms were fully optimized at B3LYP/6-31G ⁄ and B3PW91/def2-SVP methods with no initial symmetry restrictions and assuming C 1 point group. The fully optimized geometries in gas phase re-optimized by considering the solvent effect using PCM method in different Table 1 Presentation of some chemical structural details of optimized geometry for the active and inactive forms of b-CA in water solvent using different methods and comparison with experimental data.

Connected atoms
Active  solvents including, water, 1-bromooctane and 1,2-ethanediol. The calculated results indicate that the active form of b-CA is stabilized by about 61.67 and 43.91 kcal/mol in titled three solvents at B3LYP/6-31G ⁄ and B3PW91/def2-SVP respectively; and inactive form of b-CA are stabilized by 28.3 and 12.64 kcal/mol in above mentioned three solvents at B3LYP/6-31G ⁄ and B3PW91/def2-SVP respectively. Fig. 3 shows the optimized structure of b-carbonic anhydrase in both forms at two levels of calculations in water solvent.
Some structural details are presented in Table 1. The primary goal of this study is to assess the ability of quantum chemistry calculations to predict the geometry of active center enzyme such as carbonic anhydrase via comparing with the available X-ray crystal structure. Comparison between theoretical and X-ray [52][53][54][55] data indicates that the standard deviation of bond distances and bond angles for the B3LYP/6-31G ⁄ and B3PW91/def2-SVP levels are very small and almost similar however the results of the B3PW91/def2-SVP method shows more conformity with experimental data. Thus B3PW91/def2-SVP method has been employed for the remaining calculations. As Table 1 indicates the average (N(his)-Zn-O(OH 2 ), S (cys)-Zn-O(OH 2 ) and N(his)-Zn-S(cys) bond angle in inactive and active forms are equal to 107.93°and 107.00°respectively, therefore both active and inactive forms of CA have tetrahedral geometry.
Calculation of vibrational frequencies has confirmed stationary point with no negative eigenvalue observed in the force constant matrix.

Optimization of c-carbonic anhydrase active center in active
form: [(OH) Co +2 (his) 3 ] and inactive form: The structure of c-carbonic anhydrase active center in active (cobalt-bound hydroxide) and inactive form (cobalt-bound water) was fully optimized using the UB3PW91/def2-SVP method with no initial symmetry restrictions and assuming C 1 point group. Two different spin states of cobalt, including high spin (S = 3/2) and low spin (S = 1/2) states, are possible. The fully optimized geometries at high spin state in gas phase re-optimized by considering the solvent effect using PCM method in water, 1-bromooctane and 1, 2 11.27 and 13.60 kcal/mol more stable than low spin state respectively in solution phase. As Fig. 4 indicates the average N(His)-Co-O(OH 2 ) and N(his)-Co-N(his) bond angles is equal to 107.44°and 107.69°in active and inactive form respectively, so both active and inactive forms of c-CA like b-CA have tetrahedral geometry.
Calculation of vibrational frequencies has confirmed stationary point with no negative eigenvalue observed in the force constant matrix.

Geometry optimization of CA activators
In order for the compounds acting as efficient CA activators, at least two conditions should be satisfied: (1) a steric factor to allow the activator to bind within the enzyme active center in a suitable orientation for shuttling protons between the active center and environment. (2) An electronic factor which is related to protonatable moiety present in the activator structure in order to release the proton from the central metal-bond water molecule (zinc or cobalt) toward the external active center [56][57][58][59][60]. To reply to the question that how do different activators interact with CA active center and why are different activators differ in their behavior as activators toward the active site, the CA activation mechanism must be considered with most stable conformer of activators. Therefore in the next step, the conformational analysis for all activators to find the most stable conformer especially in the solvent media has been done. Table 2 Some structural details of the lowest conformers of b-and c-CA activators.

Conformers
Dihedral angles b-CA activators -CA activators  6. Optimal geometries and relative energy of most stable conformers of 2-pyrdil-methylamine, serotonin and L-Phe in water solvent at B3PW91/def2-SVP method.
3.2.1. Optimization and conformational analysis of b-CA activators b-CA was activated by two amino acids including Dphenylalanine (D-phe) and L-tyrosine (L-tyr) and amines like histamine (hst). According to experimental results, D-phe and L-tyr act as efficient activators but hst weakly activated b-CA [9].
In the main part of amino acids skeleton, three internal degrees of freedom exist; rotation about the CAN, CAC and CAO bonds that gives several conformations.
The conformational search for D-phe and L-tyr and hst around different torsion angles according to Fig. 2, has been done. According to conformational search results several different conformers were found for D-phe and L-tyr which four of them are more stable than the other conformers. It is noticeable that the conformers with the energy difference between 0-10 kcal/mol has been considered and with this consideration one stable conformer for hst was found. Fig. 5 presents the optimized geometry of all conformers with relative stability energy in gas phase. The stability order of different conformers for L-tyr is I > II > III > IV by 1.50, 2.00 and 8.00 kcal/mol and for D-phe is I > II > III > IV by 1.20, 2.00 and 3.30 kcal/mol. To compare energies and some geometrical parameters of all more stable conformers of three activators, Table 2 as well as Fig. 5 summarizes the computed results. The most important factors for stabilization of different conformers, especially in amino acid stems from the number of internal hydrogen bonding as well as the sterical hindrance between side chain amino acids and atoms existing in the main part of amino acids skeleton. As Fig. 5 illustrates conformation I in D-phe and L-tyr has one intramolecular hydrogen bond between the hydrogen atom of the amino group and the carbonylic O atom. However in conformation II to IV, there is not any intramolecular hydrogen bond while ath the same time the sterical hindrance between phenyl ring, amino and the carbonyl group is increased. This order of stability for amino acids is in good agreement with the previous study on amino acids [61][62][63][64][65].
All other more stable conformers of activators re-optimized in water, 1-bromooctane and 1,2-ethanediol solvents to react with b-CA active site. The stability order and geometrical parameters of different conformers remained almost unchanged. The single point calculations were also carried out with B3LYP/6-311++G ⁄⁄ method on different conformers of two above mentioned activators. The same trends have been observed when comparing the total energy with each other; for example the stability order of different conformers for L-tyr is I > II > III > IV by 3.50, 7.00 and 12.00 kcal/mol and for D-phe is I > II > III > IV by 3.25, 5.20 and 7.30 kcal/mol.

Optimization and conformational analysis of c-CA activators
According to experimental results 2-pyrdil-methylamine (pyr) and serotonin (ser) acts as effective activators and Lphenylalanine (L-phe) act as a weak activator to activate the c-CA [9]. The conformational analysis of c-CA activators is carried out by following way. Three dihedral angles including u1 to u3 for pyr and ser was scan within the range from À180°to 180°. In each structure, all geometrical parameters were relaxed, except for the constrained torsion angles. The minima observed through the scan procedure were the subjected to fully optimization at the same level of calculations and followed by a second derivative analysis, frequency calculation, with no imaginary frequencies which proved all of them to be minima. According to conformational search results, we found three, two and one different conformers for L-Phe, pyr and ser respectively which are more stable than the other conformers. The stability order of different conformers for ser is I > II > II by 1.87 and 2.65 kcal/mol and for pyr I > II by 2.57 kcal/mol. To compare energies and some geometrical parameters of all stable conformers of three activators, Table 2 as well as Fig. 6 summarizes the computed results. All stable conformer of activators re-optimized in water, 1bromooctane and 1, 2-ethanediol solvents to react with the b-CA active site. The stability order and details of geometrical parameters of different conformers remained almost unchanged.
The single point calculations with B3LYP/6-311++G ⁄⁄ method on different conformers of two c-CA activators confirm the previous results and the same trends have been observed when comparing the total energy with each other; for example the stability order of different conformers for ser is I > II > II by 3.45 and 6.27 kcal/mol and for pyr I > II by 5.42 kcal/mol.

Interaction between activators and inactive form of band c-CA active site in gas and solvent phase
According to reaction 1 and obtained results from activators conformational analysis, the different conformers of different activators are bonded at the entrance of the active center cavity by hydrogen bond to water molecule, [EX 2+ -OH 2 Á Á ÁAc)]; X = Zn 2+ or Co 2+ . To analyze the interaction between different conformers of activators and b-and c-CA active site in the optimized geometries, the complexation energy (DE com ) are estimated using the equation 2 [66] from amine and imine nitrogen atoms which have protonatable potential.
The complexation energy has been calculated as the difference in energies of isolated different conformers of activators and CA active site, at their optimized geometry, from that of the complex. Calculated DE com and all thermodynamic data for the complexation, including enthalpies (DH com ), Gibbs free energies (DG com ) and entropies (DS com ) are calculated in the gas phase and different solvents for b-and c-CA and presented in Table 3 and Table 4 respectively. As the calculated results show the negative DE com value for both b-and c-CA active sites in all phases shows the tendency of different conformers of activators to interaction with both active sites. In order to obtain more reliable relative energies the single point calculations at B3LYP/6-311++G ⁄⁄ level on different complexes between different activators and both b-and c-CA active sites have been done and the same trends have been observed.
In general, the Gibbs free energy shows the criterion of the thermodynamically preferred process. According to our results the following two facts can be concluded from the analyses of the reported results in Tables 3 and 4 Tables 5 and 6 for different conformers of different activators from thermodynamic view point the more negative value of DG rxn , Na direction in Dphe and L-tyrosine and Np direction in histamine for b-CA; and N1 in ser and pyr and Na in L-phe for c-CA refers to more preference atom to form hydrogen bonding in catalytic mechanism. Therefore, amine nitrogen atom (Na and N1) in D-phe, L-tyr, Lphe, ser and pyr and imine nitrogen atom (Np) in histamine is the suitable atom to interact with the hydrogen atom in waterbonded molecule to zinc atom in enzyme active site. The single point calculation at the B3LYP/6311++G ⁄⁄ level have been done to obtain more reliable relative energies; Table 5 and 6. Figs. 7, S1 and S2 shows the optimized geometry through the reaction path from N a atom in D-phe, L-tyrosine and N k atom in histamine directions for the most stable conformers of these activators respectively.
Also Figs. 8, S3 and S3 demonstrate the optimized geometry through the complexation path from the amine nitrogen (N a and N1) for most stable conformers, of 2-pyridyl-methylamine, serotonin and L-Phe with inactive form of c-CA respectively. By taking a look at the geometrical parameters, Figs. 7 and 8, a decrease of H wat Á Á ÁN k , H wat Á Á ÁN a or H wat Á Á ÁN 1 distance ($1.66 Å) in all enzyme/activator complexes has shown intramolecular proton transfer, between b-CA (c-CA) and activators.

Effect of considering the second-shell of ligands in activation mechanism
To consider the role of second-shell of ligands in activation mechanism of b-and c-carbonic anhydrase some amino acids including asp34 and arg36 for b-CA [52] and Glu62 and gin75b for c-CA [18] has been considered around the active and inactive form of the enzyme and re-optimized in water solvent. Fig. 9 illustrates the structures as well as some geometrical parameters of [Zn +2 (cys) 2  In the next step the most stable conformer of L-tyr and pyr has been interacted with active form of b-and c-CA respectively. In continue the complexation energy (DE com ) and all thermodynamic functions for the complexation and total reaction are estimated, Table 7. Comparison between calculated results in Table 7 with Tables 3-6 indicate the same trend but with more negative relative energies and all other thermodynamic functions with considering the second shell ligands. Figs. 10 and 11 illustrate the optimized geometry through the complexation path for most stable conformers, of L-tyrosine and 2-pyridyl-methylamine with inactive form of b-and c-CA respectively.

The specific solvent effect
The results of our previous study on activation of a-human carbonic anhydrase (II) with L-histidine and histamine confirm the important role of water molecules and hydrogen bonding in the stabilization of carbonic anhydrase/activator complexes [31].
Therefore   [   which n = is 1 to 3 and refers to number of water molecule, have been optimized. The complexation energy and all thermodynamic parameters for all complexes formation and for the total reaction have been evaluated and presented in Tables 7, 8 and 9. Figs. 12 and 13 present the optimized geometry of these six above mentioned complexes as well as some geometrical parameters and relative energy. As the calculated results indicate by adding each water molecule the studied complexes are stabilized about 10 kcal/mol.
The results of our calculations indicate the more negative values for the complexation energy and other thermodynamic functions for the studied complexes in the presence of the water molecule as a solvent.
Moreover, the negative values of thermodynamic functions for the total reaction, Tables 7 and 8, show the activation of inactive form of b-and c-CA enzyme by L-tyrosine and 2-pyridylmethylamine activators is exothermic and occurs spontaneously. Thus, the enhanced complexation energy and thermodynamic functions values for all complexes confirm the role of water as a hydrogen bonding contributor and proton transferring to activate the inactive form the CA enzyme.

Conclusion
DFT calculations have been carried out to study the interaction between different important activators, including D-phenylalanine, L-tyrosine and histamine for the b-CA active center and 2-pyrdilmethylamine, serotonin and L-phenylalanine with active center of c-CAs. The results of our calculations indicate that the activator molecule participates in proton transfer in catalysis mechanism of carbonic anhydrase by forming the CA/Activator complex and leads to form active species of CA. Therefore, the results of this study could be useful for examination of long-range proton transfers and the role of hydrogen-bonded water networks. Also computationally, the nature of interactions between activators, and CA enzyme in presence of water has been studied by using implicit and explicit solvent models. We found that the complexation energy, relative Gibbs free energy and relative enthalpy slightly decrease to more negative values with adding the water molecules as an explicit solvent.
It is apparent from above calculated data that the activation mechanism of the three different classes, a-, b-and c-CAs are similar, involving the formation of enzyme/activator complex in which the proton shuttling is favored by the proton accepting moieties that is present in the activator molecule, that leads to catalytic turnover increase. Since no X-ray crystal structures for b-and c-CAs with activators are available up to now, and also homologies modelling with a-carbonic anhydrase activators are not useful due to the various structures of the different families of such enzymes, our result could bring novel information in the field of different isoforms of CA enzyme. Finally, the good agreement between our predicted results and experimental data confirm the accuracy of the level of our calcula-tions to predict the interaction site of newly designed activators to the CA active site.
We are hopeful that our results be helpful to design new activators with interesting pharmacological applications to synthesize new drugs to manage the Alzheimer's disease.