Prediction of aqueous solubility of organic compounds by the general solubility equation (GSE)

The revised general solubility equation (GSE) is used along with four different methods including Huuskonen's artificial neural network (ANN) and three multiple linear regression (MLR) methods to estimate the aqueous solubility of a test set of the 21 pharmaceutically and environmentally interesting compounds. For the selected test sets, it is clear that the GSE and ANN predictions are more accurate than MLR methods. The GSE has the advantages of being simple and thermodynamically sound. The only two inputs used in the GSE are the Celsius melting point (MP) and the octanol water partition coefficient (K(ow)). No fitted parameters and no training data are used in the GSE, whereas other methods utilize a large number of parameters and require a training set. The GSE is also applied to a test set of 413 organic nonelectrolytes that were studied by Huuskonen. Although the GSE uses only two parameters and no training set, its average absolute errors is only 0.1 log units larger than that of the ANN, which requires many parameters and a large training set. The average absolute error AAE is 0.54 log units using the GSE and 0.43 log units using Huuskonen's ANN modeling. This study provides evidence for the GSE being a convenient and reliable method to predict aqueous solubilities of organic compounds.     

Prediction of drug solubility by the general solubility equation (GSE)

The revised general solubility equation (GSE) proposed by Jain and Yalkowsky is used to estimate the aqueous solubility of a set of organic nonelectrolytes studied by Jorgensen and Duffy. The only inputs used in the GSE are the Celsius melting point (MP) and the octanol water partition coefficient (K(ow)). These are generally known, easily measured, or easily calculated. The GSE does not utilize any fitted parameters. The average absolute error for the 150 compounds is 0.43 compared to 0.56 with Jorgensen and Duffy's computational method, which utilitizes five fitted parameters. Thus, the revised GSE is simpler and provides a more accurate estimation of aqueous solubility of the same set of organic compounds. It is also more accurate than the original version of the GSE.     

In silico prediction of drug solubility: 1. Free energy of hydration

As a first step in the computational prediction of drug solubility the free energy of hydration, DeltaG*(vw) in TIP4P water has been computed for a data set of 48 drug molecules using the free energy of perturbation method and the optimized potential for liquid simulations all-atom force field. The simulations were performed in two steps, where first the Coulomb and then the Lennard-Jones interactions between the solute and the water molecules were scaled down from full to zero strength to provide physical understanding and simpler predictive models. The results have been interpreted using a theory assuming DeltaG*(vw) = A(MS)gamma + E(LJ) + E(C)/2 where A(MS) is the molecular surface area, gamma is the water-vapor surface tension, and E(LJ) and E(C) are the solute-water Lennard-Jones and Coulomb interaction energies, respectively. It was found that by a proper definition of the molecular surface area our results as well as several results from the literature were found to be in quantitative agreement using the macroscopic surface tension of TIP4P water. This is in contrast to the surface tension for water around a spherical cavity that previously has been shown to be dependent on the size of the cavity up to a radius of approximately 1 nm. The step of scaling down the electrostatic interaction can be represented by linear response theory.     

Acidity,lipophilicity, solubility,absorption, and polar surface area of some ACE inhibitors

Computational chemical methods have been used to correlate the molecular properties of the 10 ACE inhibitors (captopril, enalapril, perindopril, lisinopril, ramipril, trandolapril, quinapril, fosinopril, benazepril, and cilazapril) and some of their active metabolites (enalaprilat, perindoprilat, ramiprilat, trandolaprilat, quinaprilat, fosinoprilat, benazeprilat, and cilazaprilat). The computed pK _a values correlate well with the available experimental values. In the dicarboxylic ACE inhibitors, the carboxyalkyl carboxylate group of the ACE inhibitors studied is more acidic than the C-terminal carboxylate. However, at physiological pH = 7.4 both carboxyl groups of ACE inhibitors are completely ionized and the dicarboxyl-containing ACE inhibitors behave as strong acids. The available experimental partition coefficients of these ACE inhibitors investigated are well reproduced by the neural network-based ALOGPs and the fragment-based KoWWiN methods. All parent drugs (and prodrugs), with the exception of fosinopril, are compounds with low lipophilicity. Calculated pK _a, lipophilicity, solubility, absorption, and polar surface area of the most effective ACE inhibitors for the prevention of myocardial infarction, perindopril and ramipril, were found similar. Therefore, it is probable that the experimentally observed differences in the survival benefits in the first year after acute myocardial infarction in patients 65 years of age or older correlate closely to the physicochemical and pharmacokinetic characteristics of the specific ACE inhibitor that is used.     

In silico prediction of drug solubility: 2. Free energy of solvation in pure melts

The solubility of drugs in water is investigated in a series of papers and in the current work. The free energy of solvation, DeltaG*(vl), of a drug molecule in its pure drug melt at 673.15 K (400 degrees C) has been obtained for 46 drug molecules using the free energy perturbation method. The simulations were performed in two steps where first the Coulomb and then the Lennard-Jones interactions were scaled down from full to no interaction. The results have been interpreted using a theory assuming that DeltaG*(vl) = DeltaG(cav) + E(LJ) + E(C)/2 where the free energy of cavity formation, DeltaG(cav), in these pure drug systems was obtained using hard body theories, and E(LJ) and E(C) are the Lennard-Jones and Coulomb interaction energies, respectively, of one molecule with the other ones. Since the main parameter in hard body theories is the volume fraction, an equation of state approach was used to estimate the molecular volume. Promising results were obtained using a theory for hard oblates, in which the oblate axial ratio was calculated from the molecular surface area and volume obtained from simulations. The Coulomb term, E(C)/2, is half of the Coulomb energy in accord with linear response, which showed good agreement with our simulation results. In comparison with our previous results on free energy of hydration, the Coulomb interactions in pure drug systems are weaker, and the van der Waals interactions play a more important role.     

In silico prediction of drug solubility. 3. Free energy of solvation in pure amorphous matter

The solubility of drugs in water is investigated in a series of papers. In this work, we address the process of bringing a drug molecule from the vapor into a pure drug amorphous phase. This step enables us to actually calculate the solubility of amorphous drugs in water. In our general approach, we, on one hand, perform rigorous free energy simulations using a combination of the free energy perturbation and thermodynamic integration methods. On the other hand, we develop an approximate theory containing parameters that are easily accessible from conventional Monte Carlo simulations, thereby reducing the computation time significantly. In the theory for solvation, we assume that DeltaG* = DeltaGcav + ELJ + EC/2, where the free energy of cavity formation, DeltaGcav, in pure drug systems is obtained using a theory for hard-oblate spheroids, and ELJ and EC are the Lennard-Jones and Coulomb interaction energies between the chosen molecule and the others in the fluid. The theoretical predictions for the free energy of solvation in pure amorphous matter are in good agreement with free energy simulation data for 46 different drug molecules. These results together with our previous studies support our theoretical approach. By using our previous data for the free energy of hydration, we compute the total free energy change of bringing a molecule from the amorphous phase into water. We obtain good agreement between the theory and simulations. It should be noted that to obtain accurate results for the total process, high precision data are needed for the individual subprocesses. Finally, for eight different substances, we compare the experimental amorphous and crystalline solubility in water with the results obtained by the proposed theory with reasonable success.     

Solubility of solids in liquids: one-parameter solubility equation

Buchowski, H. and Khiat, A., 1986. Solubility of solids in liquids: one-parameter solubility equation. Fluid Phase Equilibria, 25: 273–278.A new equation for solubility curves has been established based on the variation of vapour pressure over saturated solutions. Melting temperature and entropy of fusion of a pure solid as well as a single constant, depending on both solute and solvent, determine the solubility of the solid in the liquid. The agreement between experimental and calculated solubilities is very satisfactory. The shape of a solubility curve as well as the existence and position of an inflection point are correctly predicted.     

Scanning of the surface polar angle values in liquid crystal cells using the surface memory effect

An optical polarization method for indication of recorded oriented smectic C textures by the process of surface memorization and their accumulation and storage in the nematic temperature range is presented. The recorded accumulated data are identified with the surface conditions-the polar and azimuthal angles. Using strong boundary conditions the assumption is made that the interval for recorded and accumulated textures increases when the anchoring energy is weak.     

Scanning of the surface polar angle values in liquid crystal cells using the surface memory effect

An optical polarization method for indication of recorded oriented smectic C textures by the process of surface memorization and their accumulation and storage in the nematic temperature range is presented. The recorded accumulated data are identified with the surface conditions-the polar and azimuthal angles. Using strong boundary conditions the assumption is made that the interval for recorded and accumulated textures increases when the anchoring energy is weak.     

In silico prediction of blood-brain barrier permeation using the calculated molecular cross-sectional area as main parameter

The cross-sectional area, AD, of a compound oriented in an amphiphilic gradient such as the air-water or lipid-water interface has previously been shown to be crucial for membrane partitioning and permeation, respectively. Here, we developed an algorithm that determines the molecular axis of amphiphilicity and the cross-sectional area, ADcalc, perpendicular to this axis. Starting from the conformational ensemble of each molecule, the three-dimensional conformation selected as the membrane-binding conformation was the one with the smallest cross-sectional area, ADcalcM, and the strongest amphiphilicity. The calculated, ADcalcM, and the measured, AD, cross-sectional areas correlated linearly (n=55, slope, m=1.04, determination coefficient, r2=0.95). The calculated cross-sectional areas, ADcalcM, were then used together with the calculated octanol-water distribution coefficients, log D7.4, of the 55 compounds (with a known ability to permeate the blood-brain barrier) to establish a calibration diagram for the prediction of blood-brain barrier permeation. It yielded a limiting cross-sectional area (ADcalcM=70 A2) and an optimal range of octanol-water distribution coefficients (-1.4相似文献   

Evaluation the effect of cyclodextrin complexation on aqueous solubility of fluorometholone to achieve ophthalmic solution

In this study, the effect of different CDs including α-CD, β-CD, γ-CD, hydroxypropyl β-CD (HP β-CD), sulphobutylether β-CD (SBE β-CD) and HP γ-CD on aqueous solubility of fluorometholone (Flu) was investigated. Also the phase solubility studies were performed in the presence of eye drop excipients such as benzalkonium chloride, hydroxypropyl methylcellulose (HPMC) and buffers. The aqueous solubility of Flu was increased by 8, 15, 5, 100, 65 and 135 folds in the presence of 20% w/v α-CD, β-CD, γ-CD, HP β-CD, HP γ-CD and SBE β-CD, respectively. Aqueous solubility of Flu was 0.43 ± 0.08 and 1.16 ± 0.04 mg/mL in systems containing 5% w/v HP γ-CD and SBE β-CD, respectively. The aqueous solubility of Flu in the presence of HP γ-CD was not influenced by buffer type while the phosphate buffer caused a reduction in the aqueous solubility in the presence of SBE-β-CD. Also, investigations on the solubility of Flu in water in the presence of 5% HP γ-CD and SBE-β-CD and the additives such as benzalkonium chloride and HPMC indicated that these components had no remarkable effect on the aqueous solubility of Flu. In conclusion, CD complexation is able to improve the aqueous solubility of Flu and it would be possible to prepare ophthalmic solution of Flu by this method.     

Enhancement of the anthracene aqueous solubility by a synergistic effect of alcohols and β-cyclodextrin

The results presented in this paper show that the solubility of anthracene in water increases significantly when β-cyclodextrin and alkanols with carbon numbers from 1 to 4 are added to the solution. The concentrations of the anthracene chosen as a model hydrophobic pollutant were determined using UV–vis spectroscopy. It has been demonstrated that the solubility of anthracene in a 1.1 wt% β-cyclodextrin solution increases by the factor of 45 or 62 when 4 wt% of methanol or ethanol are added, respectively. Obviously, the increase of anthracene solubility is due both to the solvent effect of the alcohols and to the formation of anthracene–β-cyclodextrin (β-CD) “guest–host” complexes. We propose, to use the solubility enhancement based on the β-cyclodextrin/alcohol effect for improving the availability of hydrocarbon pollutants in the biodegradation processes.     

On the modeling of calcium sulfate solubility in aqueous solutions

The electrolyte–NRTL model used in a previous work (B. Messnaoui, T. Bounahmidi, Fluid Phase Equilibr. 237(1–2) (2005) 77–85), was extended for modeling of α-hemihydrate and gypsum solubilities in the complex system Ca²⁺–H⁺–SO₄²⁻–HSO₄⁻–H₂PO₄⁻–H₃PO₄–H₂O, at wide range of temperature and P₂O₅ concentration. The chemical equilibrium constant was evaluated as function of temperature according to the Gibbs–Helmholtz equation. The temperature dependence was taken into account in the expression of the standard state heat capacity of ionic, molecular and cristalline salts species. The standard-state heat capacity of Ca²⁺at 298.15 K is calculated to be 27.30 J mol⁻¹ K⁻¹. It is also shown that the experimental data agree with the predicted values of gypsum and anhydrite solubilities in water, at high temperature, by using only the values of parameters ${\tau }_{{\text{H}}_2\text{O}-(\text{C}{\text{a}}^{2+},\text{S}{{\text{O}}_4}^{2-})}$, ${\tau }_{(\text{C}{\text{a}}^{2+},\text{S}{{\text{O}}_4}^{2-})-{\text{H}}_2\text{O}}$ which were calculated, at 298.15 K from data of gypsum solubilities in phosphoric acid solutions.     

Studies of polar and nonpolar probes in the determination of infinite-dilution solubility parameters

Partial molar heats of mixing ΔH and Flory-Huggins χ parameters have been determined for a series of polar and nonpolar organic probes in the polymer systems polychloroprene, poly(butadiene-acrylonitrile) (34 wt. % acrylonitrile), poly(ethylene-vinylacetate) (40 wt. % vinylacetate) and cis-1,4-polybutadiene in the range 65–85°C. Using the Flory-Huggins χ parameters, infinite-dilution solubility parameters δ were calculated for the polymers at 75°C to be 8.8 ± 0.2 for polychloroprene 10.0 ± 0.3 for poly(butadiene-acrylonitrile), 8.3 ± 0.2 for poly(ethylene-vinylacetate) and 7.9 ± 0.1 for polybutadiene. These δ values are in good agreement with literature δ₂ values. δ values were also calculated using only polar or nonpolar probes. The change in δ as the set of probes changed was negligible, leading to the conclusion that Hanson's three-dimensional solubility parameter concept may not be applicable to the infinite-dilution case.     

Solubility of lysozyme in the presence of aqueous chloride salts: common-ion effect and its role on solubility and crystal thermodynamics

Understanding protein solubility is important for a rational design of the conditions of protein crystallization. We report measurements of lysozyme solubility in aqueous solutions as a function of NaCl, KCl, and NH4Cl concentrations at 25 degrees C and pH 4.5. Our solubility results are directly compared to preferential-interaction coefficients of these ternary solutions determined in the same experimental conditions by ternary diffusion. This comparison has provided new important insight on the dependence of protein solubility on salt concentration. We remark that the dependence of the preferential-interaction coefficient as a function of salt concentration is substantially shaped by the common-ion effect. This effect plays a crucial role also on the observed behavior of lysozyme solubility. We find that the dependence of solubility on salt type and concentration strongly correlates with the corresponding dependence of the preferential-interaction coefficient. Examination of both preferential-interaction coefficients and second virial coefficients has allowed us to demonstrate that the solubility dependence on salt concentration is substantially affected by the corresponding change of protein chemical potential in the crystalline phase. We propose a simple model for the crystalline phase based on salt partitioning between solution and the hydrated protein crystal. A novel solubility equation is reported that quantitatively explains the observed experimental dependence of protein solubility on salt concentration.     

Equation of solubility in triple water-salt systems. Communication 1. Theoretical derivation of the solubility equation

Summary The solubility equation in ternary water-salt systems was obtained and analyzed.The article is published on the basis of a resolution of the Conference of Editors-in-Chief of the Journals of the Academy of Sciences, USSR, of July 12, 1962, as the dissertation work of A. N. Kirgintsev.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 1591–1598, September, 1965