Theoretically nanoscale study on ionization of muscimol nano drug in aqueous solution

In the present work, acid dissociation constant (pKa) values of muscimol derivatives were calculated using the Density Functional Theory (DFT) method. In this regard, free energy values of neutral, protonated and deprotonated species of muscimol were calculated in water at the B3LYP/6-31G(d) basis sets. The hydrogen bond formation of all species had been analyzed using the Tomasi’s method. It was revealed that the theoretically calculated pKa values were in a good agreement with the existing experimental pKa values, which were determined from capillary electrophoresis, potentiometric titration and UV-visible spectrophotometric measurements.

The tendency of a molecule to lose hydarogen atom as an acidic proton is quantified as pK a .It is well-known that pK a values are important for the development of new compounds with biological activity.It can be due to the relationships between the pK a values and those structures, which may help studies in drugs design and also explain the biopharmaceutical properties of substances (Duran, Aydemir, 2012; Barbosa et al., 2001).There are several experimental methods for determining the acidity constants in aqueous solutions for example, conductometry, spectrophotometric, capillary electrophoresis, calorimetric adsorption, potentiometric titration, HPLC, solubility, partition and distribution (Reijenga et al., 2013;Heinze, 1984;Thurlkill et al., 2005;Santos et al., 2010).
In addition to experimental methods, theoretical prediction of the pKa values has received considerable attention and many studies have been carried out on this topic in recent years (Kelly, Cramer, Truhlar, 2006;Ho, Coote, 2010).
The DFT methods provide reliable pK a values, which help us to better understanding of different effective factors on solvent-solute interactions.This understanding can be essential for interpretation of experimental values in various systems (Topol et al., 2000;Ho, Coote, 2010).
As the pK a equals to ∆G/2.303RT (where ∆G is a free energy change of the dissociation reaction either in a gas or solution) acidity of a compound can be determined by its ∆G value (Tosso et al., 2009).
In summary, the aim of this study was to calculate pK a values of muscimol using the DFT method and the results were compared with those of existed experimental values.At first, all structures were optimized using the B3LYP/6-31G(d) level of theory.The solvent effect was simulated using integral equation formalism of the polarizable continuum model (IEF-PCM).Also explicit solvent were used in our calculation to study hydrogen bond formation.Table II shows that there is a good agreement between experimental and calculated pK a values by considering their RD.

COMPUTATIONAL METHODS
All calculations about properties of muscimol molecule (Figure 1) were carried out, on a Pentium 4 computer, using the Gaussian_09 version (Frisch et al., 2009).The DFT-B3LYP/6-31G(d)/SMD method were applied on all structures.
To evaluate the conformational behaviour of these systems in solvent-solution phase, calculations were performed using the solvation model density (SMD) a method of implicit solvation model (Marenich, Cramer, Truhlar, 2009).The SMD uses the integral equation formalism of the polarizable continuum model (IEF-PCM) (Scalmani, Frisch, 2010;Cossi et al., 1998;Mennucci, Cances, Tomasi, 1997;Ribeiro et al., 2010) with a parameterized set of atomic radii, to calculate the bulk electrostatic energy contribution.
The model calculates short-range interaction energies between solvent and solute using a modified solvent-accessible surface area which incorporates parameters for atomic and molecular surface tensions and hydrogen-bond acidity and basicity, which has been proven to be an effective tool to investigate on a variety of solution phase physicochemical properties.Solvation of selected species was finally considered in terms of the intermolecular hydrogen bonds (IHBs) (see Table I and  Figure 2) (Remko, 2010).

RESULTS AND DISCUSSION
Muscimol naturally have both keto and enol forms (Oster, Harris, 1983).Fully protonated muscimol can lose two acidic hydrogens.The first proton can be lost from OH group and the second one from NH 2 group (Figure 2).In this study, several models of muscimol were investigated by the DFT-B3LYP/6-31G(d)/SMD method.Different reactions including cationic, neutral, and anionic species were tested and some of them were finally chosen for the studied system.Table II shows the selected reactions  and calculated pK a values of muscimol together with the relative deviations (RD) for pK a which can be obtained from the following equation: The very low values of RD (for pK a ) (see Table II) show that there is a good agreement between experimental and calculated values of pK a for muscimol .

First Ionization Constant of Muscimol
It was selected that in alkaline solutions muscimol suffers a total neutralization as follows: In the above reaction, H 2 L + (H 2 O) is the cluster of a cationic muscimol with one molecule of water, and HL(H 2 O) 2 represents a cluster of neutral muscimol with two water molecules.The above reaction was used to determine value of the first ionization constant of muscimol in water.Table II

Second Ionization Constant of Muscimol
It is selected that the neutral HL suffers a reaction of partial neutralization as follows: In the above reaction, HL and L -(H 2 O) 2 represent the neutral and anionic cluster forms of muscimol, respectively.The above reaction was used to determine value of the second ionization constant of muscimol in water.Table II shows  The pK a determination method was previously described, and its values for muscimol were used in this work (Krogsgaard-Larsen et al., 1980;Brehm et al., 1997).These values are listed in Table II together with the calculated values using the solvation model density (SMD) method at the B3LYP/6-31G(d) level of theory.The total energies of single and solvated muscimol species (cationic, neutral, and anionic) were calculated in water.Table I summarizes the variations of the free energy (G 0 sol , kcal.mol -1 ) per water molecule as a function of the total number of solvation water molecules for muscimol species.Figure 3 and Table I show the marked decrease of the total energies of ions when the number of solvation molecules increases.
The data of Table III shows that water, exerting its hydrogen bond donor (HBD) capability, forms intermolecular hydrogen bonds (IHBs) with the muscimol molecule.These hydrogen bonds can be classified as strong, moderate, and weak, according to their lengths, angles, and energies (Cilli et al., 1996;Corradi et al., 2000).According to ref (Blanco, Almandoz, Ferretti, 2005), the properties of the moderate hydrogen bonds have the following classification: bond lengths of H•B is between (1.5 and 2.2) Å and the bond angle is 130° to 180°.For weak hydrogen bonds, the bond length and angle are (2.2 to 3.2) Å and 90° to 150°, respectively, and for strong hydrogen bonds are (1.2 to 1.5) Å and 175° to 180°, respectively.
Molecular surface and volumes of muscimol's cluster were calculated using solvation model density (SMD) method and are summarized in Table IV.
The volume of clusters may be affected by two main factors.The first factor is the number and volume of atoms or molecules (solute and solvent) which form a cluster.The second factor is the interaction between positive or negative charge of ions (solute) and electrons of solvent molecules.The second factor can be more used in cases that clusters have (approximately) the same number and type of atoms or molecules.
The volume values (V) for the species of muscimol's cluster fall in the order of: As seen in the above order (and Table IV), HL has the minimum volume among four species of muscimol.The first factor is more effective in this case.HL has only one hydrogen atom but other species have hydrogen atom (or atoms) and water molecule (or molecules).The volume of hydrogen atom is less than water molecule.As an example, the calculated surface of HL(H 2 O) 2 is shown in Figure 4.It is reasonable to observe that molecular volume of the drugs solvated with two water molecules is approximately the sum of the molecular volumes of the species that form it (Figure 4).

CONCLUSION
The pK a values of muscimol (in water) have been predicted using the density functional theory calculation.
In summary, free energies and other molecular parameters were calculated for muscimol molecule, using the B3LYP/6-31G(d)/SMD method for shown species in Tables I, II and III.As shown in Table II, the theoretically calculated pK a values are very close to the experimentally calculated pK a values.So we can conclude that cluster continuum model, which uses implicit and explicit solvation model, is probably a good way of calculating pK a values for biochemical systems.

ACKNOWLEDGMENT
Thanks are gratefully extended to the Faculty of Chemistry, University of Islamic Azad University, Ayatollah Amoli Branch, for its valuable help with this work.

FIGURE 2 -
FIGURE 2 -Optimized molecular structure for muscimol clusters in presence of water molecules using the solvation model density (SMD) method.The most important hydrogen bond distances are shown in figures (green lines) and its distance are in angstrom (red number).The figures were generated using the Spartan 08 program a .The carbon atoms are represented by gray circles, oxygen, red; nitrogen, purple and hydrogen atoms, yellow sticks.a:Young, 2001; Spartan, 2008.
the calculated pK a and the difference of free energy between [L -(H 2 O) 2 , 2H 2 O] and [HL, OH - (H 2 O) 3 ] according to Equation 3 obtained at the B3LYP/6-31G(d) level of theory with solvation model density (SMD) method in water.
on water molecules Theoretically nanoscale study on ionization of muscimol nano drug in aqueous solution 217

FIGURE 4 -
FIGURE 4 -Calculated molecular surface (wireframe) of HL(H 2 O) 2 using the SMD method at the B3LYP/6-31G(d) level of theory.The carbon atoms are represented by gray circles, oxygen, red; nitrogen, purple and hydrogen atoms, white balls.

TABLE I -
Calculated shows the calculated pK a values and the difference of free energy between [HL(H 2 O) 2, 3H 2 O] and [H 2 L + (H 2 O), OH -(H 2 O) 3 ] according to Equation 2 obtained at the B3LYP/6-31G(d)/SMD level of theory.