Applications of quantitative structure—property relationships to pharmaceutics

Chemometrics and intelligent laboratory systems

ELSEVIER

Chemometrics and Intelligent Laboratory Systems 24 (1994) 77-87

Review

Applications of quantitative structure-property relationships to pharmaceutics J.C. Dearden School of Pharmacy, Liverpool John Moons University, Byrom Street, Liverpool L3 3AF, UK

Received 2 August 1993; accepted 23 February 1994

Abstract Most correlation analysis studies of drugs are concerned with the correlation of in-vivo or in-vitro biological activity with physicochemical or structural molecular parameters. However, it is also important to be able to predict such properties as solubility, melting and boiling points, adsorption behaviour, stability to degradation, viscosity, surface tension and dissolution behaviour, particularly for formulation purposes. This paper reviews the published research in each of these areas, and makes recommendations for further work.

1. Introduction

Quantitative structure-activity relationships (QSARs) define mathematically the relationship between a given type of activity within a set of (usually) congeneric compounds and one or more physicochemical or structural parameters. Traditionally the ‘activity’ has been a biological activity, such as analgesia or bacteriostasis, but there is nonetheless a long history of the correlation of chemical or physical ‘activities’ (such as reaction rate constants) with molecular parameters. Such correlations were known as linear free energy relationships (LFE?Rs) [l], and more recently have been called quantitative structure-property relationships (QSPRs). Many of them fall into the realm of physical organic chemistry, and thus have at best indirect relevance to drugs and their

actions, whilst QSAR studies have concentrated to a very large extent on what happens once a drug is in solution in an organism. Fig. 1 shows the various stages leading up to pharmacological response to a drug entity. QSAR studies have concentrated on the effect of absorption and receptor-binding (and to a lesser extent metabolism) on pharmacological activity, whilst the important areas of synthesis, formulation and dissolution have been studied relatively little. Formulation, in particular, is a potentially fruitful source of study, for example with respect to the prediction of solubility, melting point, boiling point, surface tension and other properties of importance to the formulator. This paper will give a brief review of the prediction of properties of potential interest in the area of pharmaceutics, i.e. of formulation and

0169-7439/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0169-7439(94)00020-J

78

J.C. Dearden / Chemometrics

,. SYNTHESIS

and Intelligent Laboratory

Systems 24 (1994) 77-87

aromatic hydrocarbons rectly related:

J

[5], since the two are di-

ABSORPTION METABOLISM

J FORMULATION

lRECEPTOR

?z = 15,

BINDING J DISSOLUTION

log S,, = - 4.528 log k’ - 0.0084MP - 2.053 r = 0.986,

s = 0.234

(3)

Regosz et al. [6] rather unusually introduced Kier’s first-order ‘K shape factor K instead of log P, for a series of sulphonamides:

-1 PHARMACOLOGICAL RBSFONSE . ,

4) = -0.622’~

log S,,(pH

Fig. 1. The stages in drug development, formulation, administration and biological activity

It = 10,

r = 0.941,

- 0.0117MP + 1.099

s = 1.094

(4)

dissolution. The paper does not seek to be comprehensive, but will draw attention to many of the key publications in the field.

Blair et al. [7] similarly used a steric term, molecular weight (Mw), in a correlation of the mole fraction aqueous solubility of halogenated benzenes; in this instance, Mw might be expected to correlate well with log P and thus be a good surrogate parameter:

2. Aqueous solubility

log Xa4 = - 12.23 log MB’- 0.0093( MP - 25) + 13.84

Of all the properties required for formulation, aqueous solubility has been studied most often by far. To some extent this reflects the importance of solubility in other areas of study, e.g. in environmental toxicity. As long ago as 1968 Hansch et al. [2] showed that for liquid solutes, aqueous solubility (S,,) was inversely proportional to the octanol-water partition coefficient (P):

Warne et al. [8] used an electronic term, approximate sigma electron density USED), which, like K, cannot be said to model hydrophobicity; they nevertheless obtained a good correlation for 16 compounds of various classes:

log S,, = - 1.339 log P + 0.978

log S,, = -6.789ASED

n = 156,

r = 0.935,

s = 0.472

(1) Such relationships do not generally hold for solid solutes, because the crystal lattice has to be disrupted in order for dissolution to occur. Yalkowsky and Valvani [3] showed that, if one assumes a constant entropy of fusion, a melting point term in addition to log P allows the aqueous solubility of solids to be well correlated: log S,, = - 1.05 log P - 0.012MP + 0.87 n = 155,

r = 0.989,

s = 0.308

(2)

where MP = melting point (“0. Briiggemann and Altschuh [4] have recently developed a similar equation for 355 organic compounds. High-performance liquid chromatography (HPLC) capacity factors (k’) have been used instead of partition coefficients in a study of

n =42,

n = 16,

r = 0.993,

r = 0.975,

s = 0.194

(5)

- 0.004MP + 4.166 s not given

(6)

It would be interesting to know whether the correlations of Eqs. 4-6 would hold up if extended to more compounds of different classes; it is doubtful whether they would. Baker et al. [9] have used total surface area (TSA) in lieu of log P for the prediction of aqueous solubility of polycyclic aromatic hydrocarbons. Whilst T&l has been shown to be correlated with log P, it is nonetheless strictly a size term, and doubt must be expressed as to its general validity for the prediction of solubility. Pinal and Yalkowsky [lo] have utilised ideal solubility instead of melting point, and obtained a good correlation (r = 0.941, s = 0.16) for the aqueous solubility of barbiturates at various temperatures. The use of the ideal solubility term

79

J.C. Dearden /Chemometrics and InteiIigentLaboratorySystems24 (1994) 77-87

(log Xideal= AS&T, - T)/2.303R)

allows the prediction of solubilities at different temperatures, but otherwise performs the same role as a melting point (T,) term, on the assumption of constant entropy of fusion (AS,). In a similar fashion, Hafkenscheid and Tomlinson [ll] have used the term T,/T together with HPLC capacity factor to predict the aqueous solubilities of drugs. A completely different approach to the prediction of aqueous solubility has been taken by Kamlet et al. [12]. Using their so-called solvatochromic parameters, modelling size, polarity and hydrogen bond acceptor ability, respectively, they were able to correlate the ~lubilities of 105 organic nonelectrolytes of various classes: log S,, = - 3.321//100 + 0.46a* + 6.17p + 0.54

example, these authors correlated the aqueous solubilities of alcohols, ethers and esters as follows:

+ 9.240 n = 98,

r = 0.995,

s = 0.137

(7)

These authors have utilised the same approach for the prediction of solubilities in body tissues such as blood and brain tissue [13], with good results. Bodor and Huang [14] have recently published a correlation of aqueous solubility of a wide range of organic compounds with a total of 17 calculated parameters, including atomic charges. Although their correlation is good (n = 331, r = 0.982, s = 0.299), one has to question the usefulness of a predictive equation ~ntaining so many variables. A very different approach, but one that also used a large number of parameters, was adopted by Klopman et al. [15]. Using 23 group contributions, they were able to predict the aqueous solubilities of 200 compounds (r = 0.985); with 33 group contributions the solubilities of 483 compounds were well modelled (r = 0.974). The criticism made above of the Bodor and Huang approach does not apply here, since the contributions of each group in a molecule are simply summed to give the overall solubility. Molecular connectivities (~1 are topological indices derived from graph theory, and have been applied extensively by Kier and Hall [16]. For

r = 0.984,

s = 0.357

(8)

Superscript numerals indicate the order of each x term; v indicates a valence-corrected x term; d is an indicator variable for hydrogen bonding. Ni~al~andan and Speece f171 have used a combination of molecular connectivities and a modified polarisability term @ to predict the aqueous solubilities of environmentally relevant chemicals: log S,, = 1.653 ‘,y - 1.312 “xv + 1.OtP.D+ 2.209 n = 145,

n = 105,

‘x + 2.819 ‘xv - 0.382d

In S,, = -5.423

@= -0.963

r = 0.962,

s not given

(no. of Cl) - 0.361 (no. of H)

- 0.767 (no. of double bonds)

(9)

The same authors, in a review [18] of various methods of solubility prediction, recommended their own method as the most useful; whilst that was only to be expected, it is certainly true that theirs appears to be the simplest method, requiring no experimental dete~inations such as melting point. Other reviews of methods of predicting aqueous solubility have been published by Andren et al. [19], Yalkowsky and Banerjee [20] and Horvath [21].

3. Solubility in aqueous-organic organic solvents

mixtures and in

One way by which the pharmaceutical formulator can increase the solubili~ of a drug in aqueous solution is by adding an organic cosolvent such as an alcohol. Yalkowsky and Roseman 1221showed how solubility varied with concentration of a wide range of such cosolvents, and later Rubino and Yalkowsky E231showed that the slope of the solubilisation graph (cr> was a function of Hildebrand’s solubility parameter S (Eq. 10) and

J.C. Dearden / C~e~ome?~icsand ~ntel~~~~t LaboratorySystems24 (1994) 77-87

80

interfacial surface tension y (Eq. ll), exemplified by diaxepam: u = - 0.2666 + 6.238 it = 15, r = 0.933,

s = 0.029

(10)

Lr= - 0.0817 + 3.704 n=15,

r = 0.951,

s = 0.007

(11) Martin and Miralles [24] observed a parabolic relationship between adhesive energy density w (characterising the potential energy of solutesolvent interactions) and the solub~i~ parameter of binary solvent mixtures. The equation developed for tolbutamide was:

(12) A different approach was adopted by Griinbauer et al. [25l, who used the UNIQUAC local composition model using descriptors obtained from group contributions and the solubility of the drug in pure water. Qood agreement was achieved between calculated and observed solubilities for various drugs in various aqueousorganic solvent pairs. Little work has been done on the correlation and prediction of soiubiiity in non-aqueous solvents. For ideal solutions:

AWT,, - T>

W

2.303RT

Asstmring an approximately constant entropy of fusion (AS,), then log Xa Tm;that is, the solubility should be independent of the nature of the solvent, and dependent only on the melting point of the solute. Yalkowsky et al. [26] showed that this was indeed so for the solubili~ in octanoi of a range of drugs of widely differing statures: log x,,

= -0.012MP

f2 = 36,

r = 0.92,

+ 0.26

Dearden and O’Sullivan [29] correlated cyclohexane solubility of drugs with their melting points: log x,,

= - 0.0423MP + 1.45 r = 0.902,

s = 0.644

(171 The gradient of the correlation is, however, considerably greater than that of Eq. 14, suggesting less than ideal behaviour. Dearden and Roberts [303 measured the ~clohexane-water partition coefficients of the same drugs, and the correlation between cyclohexane solubili~ and ~ciohexane-water P values is rather poor: log X,, = 1.09 log

P - 2.33

n = 10, r = 0.77,

s = 0.988

(18) This is clearly an area that needs further investigation.

4. Melting point It is clearly of value to know whether a proposed compound is likely to be a liquid or a solid. In addition, as we have seen, melting point is an important predictor of solubility, and so it is of great interest to be able to calculate it. Melting point has both enthalpic and entropic ~om~nents:

(19)

s = 0.32

(141 Using the same data set, Dearden [27] showed that there was only a very poor correlation between solubility in octanol and octanol-water partition coefficient: log XW, = 0.293 log P - 1.925 n = 35, r = 0.465, s =z0.512

logs,= 1.48 log P - O.O9(log P)2- 0.08 n = 41, r = 0.91, s = 0.24 (16)

n = 10,

w = 4.3346 -I-0.314a2 + 32.906 n=13, r=O.999, s=O.127

log x=

This suggests that it is incorrect to use the terms “lipid solubility’ and ‘hydrophobici~’ synonymously. On the other hand Chessells et al. [28] have recently reported a good parabolic relationship between lipid solubility (S,) and log P:

(15)

Hence, as well as intermolecular interactions, mol~ular s~rnet~ and orientation affect melting point. The compounds shown in Table 1 illustrate this. There have been relatively few attempts to predict melting points from calculated parameters. An interesting approach is that of Joback

J.C. Dearden /Chemometrics and Intelligent Laboratory Systems 24 (1994) 77-87

proach to melting point prediction. In a test using 520 compounds, they compared their predictions with those of the Joback and Reid method 1311. Using their method, the standard error was 39.2”, whilst the Joback and Reid method gave a standard error of 83.4”. Dearden [351 carried out a QSAR study of the melting points of 42 substituted anilines, and included a term for conformational flexibility, although it proved not to be significant. The best equation was:

Table 1 Some examples of factors affecting melting point Compound

Melting point (“0

SnCl, (ionic) SnCl, (covalent) Ethylbenzene (non-polar) Anisole (polar) 3-Nitrophenol (H-bonded) 3-Nitroanisole (non H-bonded) 2-Nitrophenol (intramolecularly H-bonded) Naphthalene (two fused rings) Anthracene (three fused rings) 1,3-Dibromobenzene (unsymmetrical) 1,4-Dibromobenzene (symmetrical) 4-Methylaniline (rigid alkyl) 4-Ethylaniline (flexible alkyl)

246 -33 -95 -33 97 39 45 80 217 -7 87 44 -5

and Reid [31], who used group contributions assumed additivity: T, = 122.5 + CAT,

81

T, = 182a - 38.2~ + 8.91MR - 62.28, - 26.61, + 329 n = 42,

and (20)

Despite the fact that this approach ignores the entropic contribution to melting point, Joback and Reid found, in a study of 388 compounds, an average absolute error of 22.6”, and a standard deviation of 24.7”. Abramowitz and Yalkowsky 132,331 have devised two parameters to take account of entropy effects on melting point; an eccentricity term allows for the large entropy of expansion of nonspherical molecules upon melting, and a rotational symmetry term indicates the orientation requirements within the crystal lattice. For example, benzene has a symmetry number of twelve, whilst that of toluene is only two. For PCB congeners, these authors [33] obtained the following equation: MP = 14.9 Cl + 117.6 SIGMXL. + 6.0 INTRA + 410 EXPANL - 26.0 INTER + 200 n = 58, r = 0.91, s = 22.1 (21) where Cl = no. of Cl atoms in molecule, SZGM4L = logarithm of the symmetry number, INTRA = no. of functional groups ortho to another group, EXPANL = logarithm of the cube of eccentricity, and INTER = indicator variable for lack of ring coplanarity. Simamora and Yalkowsky [341 have also developed a group contribution plus symmetry ap-

r = 0.941,

s = 24.6

(22) where T, is in kelvin, (Y= solvatochromic parameter for hydrogen bond donor ability (cf.[12]), r = Hansch hydrophobic substituent constant, MR = molar refractivity, B, = Sterimol width parameter, Z3= indicator variable for 3-substitution. It is interesting to note that the cr (hydrogen bond donor) term alone accounted for 67% of the variation of melting point within the series. The r term, having a negative sign, probably reflects polarity, MR is a measure of molecular bulk, and B, and 1, are probably modelling asymmetry. Similar results have been found [36] for a series of 28 monosubstituted benzenes. The standard errors found in all the above studies are really too high, and more work needs to be done to develop a general predictive model of melting point with a standard error of < 10”. Horvath [21] has given a detailed review of methods of prediction of melting point, many of which require knowledge of another property such as boiling point, and so have been omitted from the present review. 5. Boiling point and Henry’s constant Many methods have been published for the prediction of properties related to vapour pressure, and these have been reviewed by Reid and Sherwood [37] and by Horvath [21]. Because volatility is not usually a key factor in formulation, only brief mention will be made here of the prediction of volatility-related properties.

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J.C. Dearden /Chemometrics

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Joback and Reid [31], using group contributions as they did for melting point prediction, estimated normal boiling points for 438 compounds, with an average absolute error of 12.9” and a standard deviation of 17.9”. Simamora and Yalkowsky [34], also using group contributions, claimed better success for a set of 520 aromatic compounds, with a standard error of 10.6” compared with one of 17.2” for the Joback and Reid method. Kier and Hall [16] report several studies of the prediction of boiling point, largely for homologous series of compounds. Since molecular connectivities reflect mostly size and branching of molecules, it is perhaps only to be expected that they will correlate well with boiling points in such cases. Eq. 23 relates to the boiling points of primary, secondary and tertiary amines: BP = 184.58 rx - 133.51 ‘xv - 18.876;; - 28.57 r=0.995, s=3.94 n =21, SV,= 5 - (no. of H atoms on nitrogen)

(23) Hansen and Jurs [38] have correlated the boiling points of branched alkanes with rx values, with n = 19, r = 0.994. They also observed a slightly poorer correlation with the Wiener index, another topological index (n = 19, r = 0.971). So far as is known, no study has been published of the prediction of boiling points of heterogeneous compounds using topological indices, and it is likely that such predictions would not be particularly good. Nirmalakhandan and Speece [391 have used polarisability (4) and molecular connectivity to predict the Henry’s law constant of 180 compounds of various classes: log H = l.OOS+ - 0.468 ‘xv - 1.2581+ 1.29 n = 180 r=0.99

s=O.26

(24) where I = indicator variable for compounds containing an electronegative element attached directly to a carbon holding a hydrogen atom. Here the 4 and I terms are clearly modelling electronic effects, in order to complement the largely steric contribution of the rxv term. Seybold et al. [403 have used both molecular connectivities and ad hoc descriptors to correlate the boiling points of halogenated hydrocarbons.

For 25 compounds they obtained r = 0.985 using three x terms. Ad hoc descriptors proved slightly better, as Eq. 25 shows: Tb = 29.7& + 36.0&, + 61.1&, - 10.5& + 20.012, + 178.3 II =25,

r = 0.992,

s = 7.2

(25) where IV, = no. of carbon or halogen atoms in molecule, and Qu = polar hydrogen factor. Joback and Reid [31] have used their group contribution method to predict the enthalpy of vaporisation of 368 compounds, with excellent results (average absolute error 1.27 kJ mol-‘, standard deviation 1.79 kJ mol-‘I. Jain et al. [411 have used molecular connectivity to correlate the enthalpy of vaporisation of alkylbenzenes: AH, = 6.857 Ox” + 5.837 n = 47, r = 0.997, s = 1.44 (26) Seybold et al. [40] used molecular connectivities and ad hoc descriptors in the correlation of enthalpy of vaporisation of halogenated hydrocarbons; in this instance x values proved the more effective: AH, = 14.2 ‘xv + 6.07 lx - 2.90 “xv + 3.50 n = 17,

r = 0.995,

s = 0.93

(27)

6. Adsorption and wettability The adsorption of drugs onto excipients or other interfaces can affect bioavailability: little work has, however, been done on the prediction of adsorption. Kiihne et al. [421 showed that the free energy of adsorption of a number of polar compounds onto the dropping mercury electrode was a direct function of hydrophobicity: = 1.138AG;a,,ition - 11.46 AG&orption n = 30, r = 0.940, s = 0.177 (28) Sokolowski and Burczyk [43] examined the adsorption of alkyl monoethers of polyoxyethylene glycols at the aqueous-air interface: = -0.842m - 1.0112 + 0.046rnz AGaodsorption

n =

23,

+ 1 .272rr”.’ - 0.079mrr0.5 + 0 112z,rr”.5 - 7.014 r = b.998, s not given

(29)

J.C. harden / Chemometrics and Intelligent Laboratory Systems 24 (1594) 77-87

where m = no. of methylene groups in aliphatic chain, z = no. of ethoxy groups, and w = surface tension decrease in presence of solute. Surprisingly, no QSPR studies appear to have been carried out on adsorption of drugs onto pharmaceutical excipients. Storey [44] observed good correlations between both enthalpy and entropy of aqueous immersion of imidazoles and their frontier electron densities and summed superdelocalisabilities of atoms involved in hydrogen bonding (YLW, thus enabling wettability to be predicted. A more recent study [45] found a direct correlation between the contact angle of wettability of powdered drugs and CU. There is clearly scope for much more work in this relatively unexplored area of property prediction.

7. Stability As indicated earlier, there has been much work on the correlation of reaction rates, under the heading of linear free energy relationships, and it is inappropriate to review such work here. A few examples will suffice to show the correlations that have been achieved. Dearden and George [46] found that the acid hydrolysis rate constants of a series of aspirin derivatives were related to the Hammett constants of the substituents, indicating, as expected, that the electron-directing effect of a substituent was controlling the order of the cleaved bond. However, when bulky substituents were adjacent to the -OCOCH, group, the hydrolysis rate constant was lower. This was quantified by the use of a Sterimol width parameter: log k/k,

= 1.6200, - 0.6308,(3)

n = 15,

r = 0.969,

+ 0.704

s = 0.207

(30)

where a, = Hammett substituent constant for substitution relative to -OCOCH,, and B,(3) = Sterimol width parameter for substituents in 3position only.

83

In a similar fashion, Drossman et al. 1471correlated base-catalysed hydrolysis of esters with electronic and steric parameters: log k = 1.22~ + 0.62E, + 0.033 n=21,

r = 0.994,

s not given

(31)

where Es = the Taft steric constant. Schug et al. [48] showed that the Taft steric constant Es could be correlated with molecular connectivity indices, which could thus replace Es in correlations such as Eq. 31: Es = -2.25A

n = 19,

6Xpc- 1.58A “Xpc+ 0.08 r = 0.937,

s = 0.53

(32)

AflXpc= &h-order path cluster molecular connectivity difference between substrate and transition state species. Dearden et al. [49] have also reported extensive correlations between molecular connectivities and steric and other parameters. An interesting stability study has been reported by Bragger et al. [50]. Azopolymer-coated capsules have been promoted as a means of achieving colon-specific drug delivery; release of drug from such devices relies on the cleavage of the azo crosslinkers in the polymer by microbial reduction. Correlations of half-wave potential were obtained with the charge on the azo nitrogen (n = 9, r = 0.973) and with the energy of the lowest unoccupied molecular orbital (n = 9, r = 0.960). Such studies should lead to more rational design of polymeric coatings for site-specific drug delivery.

8. Viscosity and surface tension Very little work has been done on the correlation of these properties with structural parameters. Joback and Reid [31], using their group contribution approach, found that the viscosity of 36 compounds was predicted with an average absolute error of 18%, which was similar to predictions using methods developed by other workers [51,52].

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J.C. Dearden /Chemometrics and Intelligent Laboratory Systems 24 (1994) 77-87

Seybold et al. [40] have correlated the surface tension of halogenated hydrocarbons with molecular connectivities and ad hoc descriptors: ST = 21.6 ix’ - 4.86 “xv + 2.99 s=3.69 n = 20, r=0.921, (33) ST= 4.42Nc, + 8.04N,, - 7.21Nr + 5.2OQu + 10.94 n = 20, r = 0.952,

s = 3.09

(34) The symbols have the same meaning as in Eq. 25. Eq. 34 suggests that surface tension is, at least to a first approximation, an additive property. Again, it must be commented that there is a need for much more QSPR investigation of this area.

El-Yazigi and Sawchuk [55] measured the dissolution rate and in-vivo uptake of theophylline from six commercial products. They found a direct relationship between the fraction of drug dissolved after 60 min and the dose-normalised peak serum level, thus demonstrating the importance of dissolution rate in controlling bioavailability. This fact is often overlooked in QSAR and similar studies of in-vivo activity, where it is generally assumed that partitioning is the controlling step in transport. Dearden et al. [56] correlated the thermodynamics of dissolution of a series of barbituric acids with molecular connectivities and steric parameters: AG“ = 13.4 ‘xp - 3.6OL - 31.1 n = 8,

9. Dissolution

AH0=12.4 Most drugs are administered as solids, and therefore dissolution in aqueous medium must occur before the drug can be absorbed. Collett and Koo [53] showed that, for a series of substituted benzoic acids, dissolution rate constant was a function of hydrophobicity: 3-substituted benzoic acids log k = -1.25~-5.36 n = 7,

r = 0.977,

s = 0.172

(35)

4-substituted benzoic acids log k = -1.79pn-7,

5.80

r=0.901,

s=O.497

(36) Inclusion of the Hammett substituent constant u slightly improved the correlation. Dearden and Pate1 [54] similarly observed a dependence of dissolution rate (D) of alkyl derivatives of acetaminophen (paracetamol) upon hydrophobicity: log D = -0.990 n = 6,

log P - 4.655

r = 0.994,

s = 0.106

(37) Dearden and Pate1 observed that the dissolution rate correlated better with hydrophobicity than with aqueous solubility (for which r = 0.964). They also noted that the dissolution rate constant (i.e. D/solubility) was almost independent of hydrophobicity.

n = 8, AS“ = -4.82 n = 8,

r = 0.953,

s = 1.921

(38)

3x,-3.48L-25.7 r = 0.949,

s = 1.866

(39)

2xv + 0.855B, + 17.3 r = 0.950,

s = 0.780

(40) where “x, = third-order path molecular connectivity, and L, B, = Sterimol length and width parameters respectively. They observed that the correlation of these thermodynamic properties with log P was poor. The results suggest that molecular shape is controlling the dissolution parameters, perhaps through an influence on solvent-accessible surface area. 10. Conclusions Correlation analysis studies of properties relevant to formulation and other physicochemical aspects of drugs and drug delivery are far less common than QSAR studies relating biological activity to physicochemical and structural properties. The area that has received most attention is the prediction of aqueous solubility, and reasonably accurate forecasts of solubility can now be made, although there is room for improvement. Melting points can be predicted, with a rather high standard error, and more work is needed in

J.C. Dearakn /Chemomettics and Intelligent Laboratory Systems 24 (1994) 77-87

order to develop a reasonably accurate general method of melting point prediction. Roiling points can be predicted quite well, and the methods currently available are probably satisfactory. Adsorption characteristics of drugs have not been investigated extensively by correlation analysis and it is suggested that much additional study is needed in order to place the prediction of adsorption and wettability on a sound basis. Stability, for example to hydrolysis, can in general readily be correlated with electronic and steric parameters. However, applications such as the degradation of polymer coatings of drugs should repay further investigation. The prediction of viscosity and surface tension has not been studied widely, and further work is needed, particularly perhaps concerning the viscosity and surface tension of mixtures and solutions. Finally, dissolution studies indicate that dissolution rate is primarily a function of hydrophobicity, although enthalpies and entropies of dissolution appear, from the limited work done, to be dependent more on steric factors. Overall, there is a need for more QSPR-type studies of properties of importance in formulation and related areas.

References 111P.R. Wells, Linear Free Energy Relationships, Academic Press, London, 1968.

121C. Hansch, J.E. Quinlan and G.L. Lawrence, The linear free-energy relationship between partition coefficients and the aqueous solubility of organic liquids, Journal of Organic Chemistry, 33 (1968) 347-350. 131 S.H. Yalkowsky and S.C. Valvani, Solubility and partitioning I: Solubility of non-electrolytes in water, Journal of Pharmaceutical Sciences, 69 (1980) 912-922. [41 R. Briiggemann and J.

151

85

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