Solubility prediction COSMO

Fig. 11.1. Blind test for the COSMO-RS relative solubility prediction of commercial drugs from Merck Co., Inc. [119] All values are calibrated against the experimental solubility in ethanol. The 14 solvents are water, 1-propanol, 2-propanol, dimethylformamide, ethyl acetate, methanol, heptane, toluene, chlorobenzene, acetone, ethanol, acetonitrile, triethylamine, and 1-butanol.

The rms deviation of this COSMO-RS drug-solubility prediction is 0.66 log-units on the training set. Considering the fact that the available data sets for aqueous drug solubility typically have an intrinsic experimented error of about 0.5 log-units (rms), this... 

In the following paragraphs, some application examples will be presented, starting with a short introduction to COSMO-RS (Section 9.2), followed by solubility predictions in pure and mixed solvents (Section 9.3). A modification using several reference solubilities is shown in Section 9.4 whereas Section 9.5 is about quantitative structure-property relationship (QSPR) models of the melting point and the enthalpy of fusion. The final Sections 9.6 and 9.7 deal with COSMO-RS-based coformer selection for cocrystal screening and the related issue of solvent selection to avoid solvate formation. 

At a somewhat reduced accuracy it is also possible to circumvent the sometimes costly quantum chemical calculations and to generate o-profiles on-the-fly from fragments of precomputed COSMO files stored in a database. This approach is implemented in the software COSMOquick and is particularly useful for solubility prediction using one or several reference solvents (see also Section 9.4). 

Because the solubility prediction capabilities of COSMO-RS have been reviewed before [14, 23], here we summarize just shortly the theoretical foundations and then focus on some recent results. 

Table 9.1 compares the overall deviation of the predictions from the experiment. The overall prediction accuracy for the five drags amoimts to an RMSE=0.49 (root mean squared error of the decimal logarithm of the mole fraction solubility), which is about the typical error bar for COSMO-RS solubility predictions. Due to our experience this is already close to the usually achieved experimental accuracy. 

TABLE 9.1 Summary of COSMO-RS Solubility Predictions of Some Drugs, Computed at the TZVP Level of Theory... 

To overcome the limitations of the solubility parameters, chemists can use more advanced modelling methods that require no experimental data to predict solvent polarity and consequently solubility, particularly the COn-ductor-like Screening MOdel for Real Solvents approach (COSMO-RS). Firstly, the solute molecule is considered as embedded in a cavity that is surrounded by a virtual medium (COSMO). Secondly, the energies of interaction between molecules are quantified with statistical thermodynamics. These calculations allow for several representations of a molecule, in which it can be characterised as a substrate or as a solvent to provide solubility predictions. A medicinal chemist can use the COSMO-RS approach rather easily thanks to the user friendly COSMOtherm computer program developed by Klamt. ... 

As a result of Eq. (11) we are able to calculate the chemical potential of any molecule X in any liquid system S, relative to the chemical potential in a conductor, i.e. at the North Pole. Hence, COSMO-RS provides us with a vehicle that allows us to bring any molecule from its Uquid state island to the North Pole and from there to any other liquid state, e.g. to aqueous solution. Thus, given a liquid, or a reasonable estimate of AGjis of a soUd, COSMO-RS is able to predict the solubility of the compound in any solvent, not only in water. The accuracy of the predicted AG of transfer of molecules between different Uquid states is roughly 0.3 log units (RMSE) [19, 22] with the exception of amine systems, for which larger errors occur [16, 19]. Quantitative comparisons with other methods will be presented later in this article. 

Klamt, A., Eckert, F., Homig, M., Beck, M., Burger, T. Prediction of aqueous solubility of drugs and pesticides with COSMO-RSJ. Comp. Chem. 2002, 23, 275-281. 

Solubility modelling with activity coefficient methods is an under-utilized tool in the pharmaceutical sector. Within the last few years there have been several new developments that have increased the capabilities of these techniques. The NRTL-SAC model is a flexible new addition to the predictive armory and new software that facilitates local fitting of UNIFAC groups for Pharmaceutical molecules offers an interesting alternative. Quantum chemistry approaches like COSMO-RS [25] and COSMO-SAC [26] may allow realistic ab-initio calculations to be performed, although computational requirements are still restrictive in many corporate environments. Solubility modelling has an important role to play in the efficient development and fundamental understanding of pharmaceutical crystallization processes. The application of these methods to industrially relevant problems, and the development of new... 

Since most other modeling techniques for polymers are extremely demanding, the limited capabilities of COSMO-RS for efficient prediction of solubilities in polymers can be of great help in practical applications when suitable polymers with certain solubility requirements are desired. One application may be the selection of appropriate membrane polymers for certain separation processes. Predictions of drug solubility in polymers are sometimes of interest for pharmaceutical applications. Furthermore, it is most likely that COSMO-RS can also be used to investigate the mutual compatibility of polymers for blends. This aspect, and many other aspects of the potential of COSMO-RS for polymer modeling, still awaits systematic investigation. 

In this dilemma of contradicting interests, COSMO-RS can be a valuable tool for the computational characterization of the solubility behavior of the drug candidate as well as of its dissociation constants. Both are of crucial interest since the small and very expensive amount of compound has to be dissolved and embedded in different solvents and environments for the various steps of purification, crystallization, analysis, and formulation. At present, empirical solubility parameter approaches are often used in order to classify and predict the solubility behavior of the new drug, but despite their poor physical foundation, they have the additional disadvantage that the experimental measurement of the solubility parameters of the new drug consumes time and compound. In contrast, the required DFT/COSMO calculations can be started before the compounds come to the development laboratory, and a COSMO-RS solubility and dissociation screening can be completed—even at optimal computational level— when the work in the development department starts. Furthermore, none of the valuable substance is wasted in this step. 

In several tests on compound sets that are structurally very different from the training set, including a larger set of pesticide molecules, Eq. (10.3) proved to be very robust and transferable. Recently, the method was applied to polychlorinated dibenzo-/)-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) [137]. As shown in Fig. 11.3. it was found that the COSMO-RS predictions appear to be even more accurate than the experimental data, especially at the low-solubility end. While the experimental results for many compounds show a scatter of more than a... 

Fig. 11.3. Experimental solubilities of polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) from various sources vs. values predicted from COSMO-RS [137].

C22 A. Klamt, Prediction of the mutual solubilities of hydrocarbons and water with COSMO-RS, Fluid Phase Equilib., 206 (2003) 223-235. 

The previous considered methods usually depend on linear methods (MLR, PLS) to establish structure-solubility correlations for prediction of solubility of molecules. The work of Goller et al. [51] used a neural network ensemble to predict the apparent solubility of Bayer in-house organic compounds. The solubility was measured in buffer at pH 6.5, which mimics the medium in the human gastrointestinal tract. The authors used the calculated distribution coefficient log/1 (at several pH values), a number of 3D COSMO-derived parameters and some 2D descriptors. The final model was developed using 4806 compounds (RMSE = 0.72) and provided a similar accuracy (RMSE = 0.73) for the prediction of 7222 compounds that were not used to develop the model. The method, however, is quite slow, and it takes about 15 seconds to screen one molecule on an Intel Xeon 2.8 GHz CPU. 

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