一種計(jì)算水溶解度的經(jīng)驗(yàn)加合模型的適用范圍與局限

段寶根 李 嫣 李 婕 程鐵軍 王任小

(中國(guó)科學(xué)院上海有機(jī)化學(xué)研究所,生命有機(jī)化學(xué)國(guó)家重點(diǎn)實(shí)驗(yàn)室,上海200032)

1 Introduction

Aqueous solubility is perhaps the most important physicochemical property for orally available drugs since it affects absorption,distribution,metabolism,and elimination processes.1,2Poor solubility is often associated with poor druggability.Traditionally,solubility of a compound is measured experimentally through an equilibrium approach.However,this approach requires a fair amount of sample(1-2 mg)and is time-consuming(tens of hours to complete properly).3Besides,compound stability could be a serious issue in such measurement.Other approaches,such as nephelometry,4provide a kinetic solubility measurement with a low amount of sample,but they require a reliable dimethyl sulfoxide(DMSO)stock solution and multiple repeats to achieve accuracy.3

Since experimental measurement of solubility is often difficult to carry out,especially in a high-throughput scenario,theoretical methods serve as an alternative approach to predict solubility.Many methods have been proposed for this purpose.So far the most popular methods are empirical methods.Such methods can be classified roughly into two categories.(i) Quantitative structure-property relationships(QSPR)models. Aqueous solubility is either correlated with other experimental properties,5-7such as partition coefficient,melting point and so on,or molecular descriptors,8-12such as topological indices,solvent accessible surface area,and the numbers of donor and acceptor of hydrogen bonds and so on,through all sorts of data mining approaches.(ii)Atom/group additive models.13-16These models are based on the basic assumption that the physicochemical properties of a molecule can be described as a sum of the contributions from its parts,i.e.,chemical fragments.In other words,structural building blocks are directly used in such methods as descriptors to correlate with solubility or other properties.In addition,some“correction factors”are introduced to compensate any derivations from pure addition in order to improve accuracy further.

Empirical methods are convenient to use in practice.Nevertheless,a potential disadvantage of these methods is that their application may be limited by their training sets.If a query molecule is outside the training set of an empirical method, then the prediction made by this method is often less reasonable.Furthermore,these methods,especially QSPR models, cannot provide physical insights into the solvation process.A more fundamental approach to solubility computation is based on free energy calculations and thermodynamics relations.17There have been many studies in this field during the past 20 years.For example,Lindfors et al.18-21developed a model for estimating the amorphous solubility of drugs in water.They firstly computed the free energy of solvation in pure melt at 673.17 K using Monte Carlo simulations.Secondly,melting drug crystals and then rapidly cooled the melt to obtain the amorphous phase.The free energy associated with this process was computed.Then,the free energy change in bringing a drug molecule from the vapor into a pure drug amorphous phase was obtained,plus the hydration free energy allowed the solubility of amorphous drugs to be determined in water.Mitchell et al.22reported methods to predict the intrinsic solubility of crystalline organic molecules with two different thermodynamic cycles.They found that a mixed model of direct computations and informatics,which relied on the calculated thermodynamic properties and a few more key descriptors,yielded good results.On an external test set containing drug molecules,their model yielded R2=0.77 and RMSE=0.71 log units between experimental and calculated data.Here,R2is coefficient of determination,which reflects the goodness of curve fitting.The value closer to 1 means better fitting between the regression equation and the input data.RMSE is the abbreviation for rootmean-square-error,which is used to measure the deviations between the fitted value and the experimental data.The smaller RMSE indicates better fitting effect.Chebil and co-workers23used experimental data and all-atom molecular dynamics simulation to predict quercetin solubility in different solvents.If the experimental solubility of quercetin in one solvent is known, plus the hydration free energy computed from all-atom molecular dynamics simulation,its solubility in other solvent can be determined.

Compared to empirical models,methods based on thermodynamic energy computation can explain the solvation mechanics from a physical point of view.However,they are computationally much more expensive and thus not suitable for highthroughput tasks.Moreover,lattice energy,which needs to be compensated in the solvation of a solid compound,is still difficult to be computed accurately.These problems certainly limit the application of such methods in a wider range.Thus,empirical methods and first principles-based methods will co-exist in this field in the foreseeable future.

In this study,we aimed at improving the accuracy of additive model.Here,we describe a new model for logS computation,i.e.,XLOGS,by combining a knowledge-based approach with a conventional additive model.This approach is based on the assumption that compounds with similar chemical structures are associated with similar properties,a strategy that has been successfully applied in some research.24-27By this approach,the logS value of a given compound is computed based on the known logS value of an appropriate reference molecule.

2 Methods

2.1 Data set preparation

A set of organic molecules with experimental aqueous solubility data was necessary for calibrating our empirical model. This training set was selected from the PHYSPROP database (www.syrres.com/esc/physdemo.htm),which is probably the largest compilation of such data available to the public.Accepted molecules were selected with the following criteria.Firstly, only the molecules with experimental aqueous solubility data were considered since not every molecule included in the PHYSPROP database has this information.Secondly,only solubility data measured at room temperature,i.e.,20-25°C,were considered.Thirdly,each qualified molecule must not contain atoms other than hydrogen,carbon,oxygen,nitrogen,sulfur, phosphorus,and halogen atoms.As a result,a total of 4544 molecules were selected.The chemical structures of these molecules provided by the PHYSPROP database were then manually examined.Gas molecules,salts,or mixtures at room temperature were excluded.False molecular structures were corrected.Finally,a total of 4217 molecules were included in our training set.

An independent test set was also employed to verify the predictive power of our model.It was cited from the“solubility challenge”launched by Llinas et al.28,29recently.This set contains 132 drug-like compounds(Table 1),which are generally more complex than those in the training set.Molecular structural files of this set of molecules were downloaded directly from PubChem(http://pubchem.ncbi.nlm.nih.gov/).30Note that a total of 46 molecules in this test set overlapped with our training set described above.Thus,these molecules were removed from the training set,leaving the total number of molecules in our training set to be 4171.This final training set will be referred to as“Set I”throughout this article.

Set I was further classified according to the state information(liquid or solid)of each compound.State information is available in the PHYSPROP database for 3569 molecules in Set I.Among them,989 molecules that are liquid at room temperature were assembled as“Set II”.Among the compounds that are solid at room temperature,experimentally measured melting point data were available for 2357 of them.They will be referred to as“Set III”throughout this article.In our study, Set II and Set III were also employed for deriving additive models specifically applicable to liquid and solid compounds, respectively.Some basic features of the training sets and the test set used in this study are listed in Table 1.

2.2 The pure addictive model:XLOGS-AA

The additive model described in this study,i.e.XLOGS,is based essentially on the use of some atom types rather than chemical fragments.The advantage of an atom-based model is that a molecular structure can always be dissected into atoms without any ambiguity.Such a model is also much more straightforward to implement and is in principle free of the missing-fragment problem.

In XLOGS method,83 basic atom/group types are defined according to the rules set by the XLOGP3 method25for Sets I and III,and 73 atom/group types for Set II.Details of atom types are given in Table S1 in Supporting Information.In addition,three correction factors are introduced in XLOGS.The first correction factor(“HB”)accounts for intramolecular hydrogen bonds,which weaken the interactions between solute and water.The second correction factor(“AA”)is used on organic compounds with α-amino acid moieties.Such compounds usually exist in a zwitterionic form at the neutral pH condition,which is certainly very different from the corresponding neutral form in solvation.The third correction factor (“HDHA”)is the product of the number of hydrogen bond donors and the number of hydrogen bond acceptors on the solute molecule.It is an indication of the favorable polar interactions between solute and water.The additive model described above will be referred to as XLOGS-AA throughout the rest of the article for the convenience.

2.3 The knowledge-based model

The key idea of XLOGS is to calculate the logS value of a given compound from the known logS of a molecule with similar structure.Aconventional additive model computes logS as

Here,aiand Aiare the contribution and occurrence of the ith atom/group type in the given compound,respectively.cjand Cjare the contribution and the occurrence of the jth correction factor.M is the total number of defined atom/group types and N is the total number of defined correction factors.The XLOGS method is to compute the logS of a given compound from the known logS of a structural analog,i.e.,the reference molecule. logS of the reference molecule is computed by an additive model as;

By subtracting Eq.(2)from Eq.(1),one gets

Here,S0means the logS value of the reference molecule measured by experiment.A0and C0are calculated contributions oflogS for the reference molecule by atom/group types and correction factors,respectively.Then,the logS value of a given compound can be computed by Eq.(3)based on the known logS value of a reference molecule.This model is called XLOGS-full in our paper.This concept is illustrated in Fig.1 with an example.

Table 1 Some basic properties of the data sets considered in this study

Fig.1 Illustration of the basic computational procedure of XLOGS

In principle,the reference molecule should be found among a large set of organic compounds with known logS values.For the sake of convenience,in our study the training set used for calibrating XLOGS-AA was also employed as the knowledge set for finding the appropriate reference molecule.Obviously, the reference molecule should resemble the query compound as much as possible in terms of chemical structure.In our study,the structural similarity between any two molecules was computed with an algorithm based on topological torsion descriptors described previously.25,31For a given query molecule, a similarity threshold of 50%was applied to search the entire knowledge set.The molecule with the highest similarity score was selected to be the reference.If no molecule in the knowledge set met the similarity threshold of 50%,the pure additive model,i.e.,XLOGS-AA,was applied for instead to compute the logS value of the query.

2.4 Analysis of the relationship between solubility and partition coefficient

Partition coefficient(logP)is the ratio of concentrations of a compound between n-octanol and water phases.Conventional additive models work well for calculating logP.But this is not the case for solubility,where the effects like electron donating/ accepting contributions of substituents,and intramolecular hydrogen bonding can play an important role.Such complex effects cannot be properly described solely by fragment contributions.32If these complex effects on solubility are dominating, the prediction accuracy of an additive model may be poor.

Some studies have attempted to correlate logS with logP.5,33-36In these studies,the logP value came from either experiment or the computational methods.It was also found that the main factor in solubility was due to its lipophilicity for a particular scaffold of compounds.37In brief,the relationship between logS and logP can reflect the predictive power of an additive model of solubility to some extents.For example,a simple parameter called ΔSL was used to define the threshold of lipophilicity on solubility in Faller?s study:32

Here,log1/S is the reciprocal solubility value in molar terms. This parameter was introduced to separate lipophilicity from other contributions to solubility.If the ΔSL value is close to zero,it indicates that solubility is dominated by lipophilicity. Then,additive models have their advantages in solubility prediction.When the ΔSL value deviates from zero,it indicates that some nonlinear effects on solubility become more important,and thus additive models may not be appropriate in this case.

In addition,a variable(ΔRMSE)was defined in our study to measure the change in the accuracy of an additive model with the change in the contents of data set:

Here,RMSEoldand RMSEneware the RMSE values of a given additive model before and after some molecules with large ΔSL values are added to the data set,respectively;Noldand Nneware the size of the original data set and the new data set,respectively.

2.5 Other logS methods under evaluation

In order to make a comparison,three popular models for solubility calculation were applied to the same data sets for testing XLOGS,including the function in the molecular descriptor module in MOE software(version 2010),Qikprop in Schrodinger software(version 2011),and ALOGPS(version 2.1) available online at http://www.vcclab.org/lab/alogps/start.html.

3 Results and discussion

3.1 Regression results and model validation

Fig.2 Experimental logS values versus calculated values by XLOGS-AAon the entire training setN=4171,R2=0.82,SD=0.96 log units

A total of 86 descriptors were used in XLOGS-AA for Set I, including 83 basic atom/group types and three correction factors.Contributions of all descriptors were obtained by multivariate linear regression analysis on the 4171 compounds in Set I (Table S1(Supporting Information)).The R2between experimental and calculated values is 0.82,and the RMSE is 0.96 log units(Fig.2).A standard leave-one-out cross-validation was conducted to test the predictive power of this model,producing a Q2(cross validation coefficient,which indicates the prediction power of the model)value of 0.81,and a RMSE value of 0.98 log units.The results of leave-one-out cross-validation test are very close to the ones obtained from regression analysis,indicating that XLOGS-AAis not an over-fitted model.

Moreover,the XLOGS method(Eq.(3))was also applied to the entire Set I.A threshold of 50%was adopted in similarity comparison.Among all of the 4171 compounds in Set I,qualified reference molecules were found for 2386 compounds,accounting for 57.2%of the entire data set.Other compounds were still computed with the pure additive XLOGS-AA model. The final regression results of the XLOGS model are:R2=0.83, RMSE=0.94 log units.Compared to the results produced by XLOGS-AA,the improvement is rather limited.The reason is that many compounds in this data set cannot find the appropriate reference molecule,and thus the power of XLOGS is not fully verified.

To make a comparison,three logS models in popular commercial software,including MOE-logS,Qikprop,and ALOGPS, were also applied to Set I.The statistical results are summa-rized in Table 2.One can see that the performance of both XLOGS and XLOGS-AA are marginally better than the other three models.

Table 2 Results of different logS methods on three training sets

Fig.3 Experimental logS values versus calculated values by XLOGS on the test setN=121,R2=0.47,RMSE=1.08 log units

As described in the Methods section,the“solubility challenge”data set28,29were adopted as an independent test set to test XLOGS.Among the 132 compounds in this data set,eleven compounds were excluded in our study because their aqueous solubility values were not accurate.28,29The XLOGS model was applied to the remaining 121 compounds,producing a R2value between experimental and calculated values of 0.47,and a RMSE value of 1.08 log units(Fig.3).Correlations between the experimental values and the calculated values by MOE-logS,Qikprop,and ALOGPS are not high either(Table 3).Nevertheless,the statistical results produced by these three models are marginally better than XLOGS on this test set.This could be a coincidence since this test set is relatively small.It should be mentioned that XLOGS was actually applied to only 28 molecules in this test set while the remaining molecules were processed by XLOGS-AA due to lack of appropriate reference molecules in Set I.Thus,there is no significant difference between the statistical results produced by XLOGS and XLOGSAA.

3.2 Performance ofadditivemodelonSet IIandSet III

Dissolution of a compound in water is controlled by two types of interactions:3one is solute-solvent interaction,and the other is the internal interactions between solute molecules. Basically,solute-solvent interactions need to be strong enough to compensate solute-solute interactions in order to make a molecule soluble in water.As for liquid compounds,their solubility is mainly affected by the first type of interaction.As forsolid compounds,the entire solvation process can be dissected into two steps in a thermodynamic point of view:first,crystal melts into pure liquid phase,and then liquid phase is partitioned into water.The first step is dominated by solute-solute interactions whereas the second step is the same as solvation of liquid compounds.Therefore,the performance of additive models on liquid and solid compounds is different.

Table 3 Comparison of the performance of several logS models on the test set

In our study,both liquid and solid compounds were included in Set I.We attempted to treat compounds separately according to their states as follows.Set I was filtered further to extract liquid compounds(Set II)and solid compounds(Set III),respectively.

For understandable reasons,Set II consists of compounds with relatively simple structures.Thus,some atom types in our general atom typing scheme(Table S1)were absent or had very low occurrence on this data set.Such atom types were removed to obtain a valid regression model.Finally,73 atom/ group types and one correction factor,i.e.,intermolecular hydrogen bonds,were included in the regression model.The contribution of each descriptor was obtained through multivariate regression(Table S1).Regression results(R2=0.89,SD=0.65 log units)indicated that the fitted logS values have a good relationship with the experimental data(Fig.4).Results of leaveone-out cross-validation(Q2=0.87,RMSE=0.73 log units)indicate that this regression model is not over-fitted.As a comparison,three other logS methods were also applied to Set II.The results indicated that our XLOGS model was superior to others (Table 2).

Similarly,a regression model of 86 descriptors was obtained on Set III,i.e.,solid compounds with known logS values.Statistical results of regression were:R2=0.84,SD=0.94 log units (Fig.5).Statistical results of leave-one-out cross-validation were:Q2=0.83,RMSE=1.00 log units,which indicated that this regression model was also not over-fitted.Comparison of the performance of XLOGS and three other logS methods on Set III are summarized in Table 2.One can see that the performance of XLOGS is also better on this data set.Nevertheless, its performance on this data set is not as good as that on Set II. This difference was actually expected by us due to the more complicated solvation process of solid compounds.

Fig.4 Experimental logS values versus calculated values by XLOGS-AAon the liquid compounds in Set IIN=989,R2=0.89,SD=0.65 log units

One way to estimate the penalty of crystal energy to logS of solid compounds is to use melting points.Yalkowsky et al.33,38estimated solubility of solid non-electrolytes with an empirical equation including melting point and obtained reasonable results:

In the above equation,MP is the experimental value of melting point.In our study,we tested this method on Set III.In our calculation,logP values were all calculated using the XLOGP3 method25although the experimental logP values of many compounds in this data set are known.The statistical results are: R2=0.76,RMSE=1.17 log units.One can see that this method does not produce better results than our additive model XLOGS.Moreover,this method is not very practical since melting point and logP values are needed to carry out computation.Although computed melting points and logP values can be used for instead,it will introduce additional uncertainty into the final estimations of logS values by doing so.In particular, reliable estimation of melting points is as challenging as estimation of logS itself.

3.3 Relationship between ΔSL and accuracy of additive model

It has been demonstrated in the above discussion that an additive model like XLOGS is less successful in estimating logS values of solid compounds,primarily due to the inadequate consideration of crystal energy.The ΔSL parameter(Eq.(4))reflects the deviation between water solubility and octanol-water partition coefficient.The rationale is that partition of a solute between octanol phase and water phase does not involve crystal break and there is a“pure”process.It was used in our study to investigate the performance of additive model in logS computation.

Fig.5 Experimental logS values versus calculated values by XLOGS-AAon the solid compounds in Set IIIN=2357,R2=0.84,SD=0.94 log units

Fig.6 Scatter plot of log1/Sexpand logPcalvalues for(a)the liquid compounds in Set II(N=989), and(b)the solid compounds in Set III(N=2357)The diagonal line is colored in blue;while the linear fitting line is colored in red.

The relationships between log1/Sexpand logPcalfor liquid compounds(Fig.6(a))and solid compounds(Fig.6(b))were are firstly studied.Note that calculated logP values by XLOGP3 were used here because the experimental logP values of some compounds in our data are not available.One can see in Fig.6 that the correlation between log1/Sexpand logPcalfor liquid compounds is closer to unity than the corresponding scenario regarding solid compounds.Distribution of ΔSL values(Fig.7) also shows that ΔSL values have a larger fluctuation zone around zero for solid compounds.

Based on the above analysis,aqueous solubility of liquid compounds is more relevant to lipophilicity than other factors. In fact,the so-called general solubility equation(GSE)37developed for liquid compounds previously only correlates solubility with partition coefficient.But it is not the case for solid compounds.For solid compounds,some other factors other than lipophilicity,such as crystal energy,are not described adequately by additive models.But it also needs to be pointed out that solute-solute interactions are not completely ignored by additive models.Such interactions are also reflected in fragment contributions implicitly to some extents.That is why our XLOGS model still produced acceptable results on solid compounds.

Fig.7 Distributions of the ΔSLparameter for the liquid compounds in Set II(N=989)and the solid compounds in Set III(N=2357)

In our study,the ΔSL parameter was used as an indicator to judge whether an additive model is suitable for computing aqueous solubility.Although solid compounds have larger ΔSL distributions than liquid compounds in our data set,there are some solid compounds whose ΔSL values are close to zero.We further studied the performance of additive model on a data set consisting of molecules with smaller ΔSL values extracted from Set III.These molecules were selected in a stepwise procedure as follows.Firstly,the molecules with ΔSL values ranging from 0 to 1 were extracted from Set III to form an initial data set.Then,the molecules with ΔSL value lower than 2 in the remaining part of Set III were added into the current data set to form a new one.Then,some molecules with even larger ΔSL values were added to extend the range of ΔSL values.At each step,leave-one-out cross-validation was applied to analyze the predictive power of the additive model on the new data set.Statistical results obtained in different ΔSL spaces during this stepwise procedure are summarized in Table 4.As for the molecules with negative ΔSL values,the same strategy for data set compilation was employed.Leave-one-out cross-validation results on each version of data set are summarized in Table 5.

As one can see in Table 4 and Table 5,the performance of an additive model is less satisfactory on solid compounds with larger absolute values of ΔSL.Nevertheless,it still produces very acceptable results on solid compounds with ΔSL valuesclose to zero,e.g.,|ΔSL|≤2.0.Thus,whether an additive model is successful or not for predicting the aqueous solubility of a given compound is actually not decided by the condense state of the compound but rather its ΔSL value.If its ΔSL value is close to zero,its solubility is affected mainly by lipophilicity, and an additive model is well applicable.On the contrary,if some complex effects,such as hydrogen bonding,are dominating factors,one may want to seek options other than additive models for obtaining optimal results.

Table 4 Leave-one-out cross-validation results of XLOGS-AAon different subsets of solid compounds(ΔSL＞0)

Table 5 Leave-one-out cross-validation results of XLOGS-AAon different subsets of solid compounds(ΔSL＜0)

4 Conclusions

Wehavedevelopedanew empiricalmodel,namely XLOGS,for logS computation.The basis of this model is a conventional additive model.Nevertheless,a knowledge-based approach is introduced to improve accuracy.By this approach, the logS value of a query compound is computed by using the known logS value of a reference molecule as starting point. The difference between the query molecule and the reference molecule is then estimated by the additive model.Our results obtained on the training set indicate that this approach(XLOGS-full)indeed outperforms the pure additive model(XLOGSAA).Moreover,an obvious advantage of this knowledgebased approach is that it is able to utilize external experimental logS data in computation.This feature should be much welcome by users in pharmaceutical industry who have access to lots of in-house data.

XLOGS was compared to three popular logS models,including Qikprop,MOE-logS,and ALOGPS,on an independent test set containing 132 drug-like molecules.On this particular test set,the statistical results of XLOGS were marginally lower than those models.In fact,the difference between the average accuracy of XLOGS and the best player Qikprop,is smaller than 0.1 log units,which is not significant.

We also investigated the limitation of our model.As indicated by the results in Table 2,the performance of our model as well as several other models was apparently less satisfactory on solid compounds.This can be reasonably attributed to the more complex solvation process associated with solid compounds.The ΔSL parameter was used as an indicator in our investigation.It was found that our model still worked well on the solid compounds with this parameter close to zero.In such a scenario,solubility is determined mainly by lipophilicity. However,if the absolute value of ΔSL deviates from zero significantly,XLOGS is more likely to produce less accurate results.Although additive models are technically convenient to apply in practice,it certainly has some limitations.Our results provide useful guidance regarding application of additive models appropriately to the computation of aqueous solubility.

Program accessibility: The XLOGS program(version 1.0) is available by contacting the correspondent author.An on-line server of XLOGS is provided at http://www.sioc-ccbg.ac.cn/? p=42&software=xlogs for testing.

Supporting Information: The complete atom/group types and correction factors defined in XLOGS model have been included.This information is available free of charge via the internet at http://www.whxb.pku.edu.cn.

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