Quantitative Structure-Activity Relationship Studies on Matrix Metalloproteinase Inhibitors: Piperazine, Piperidine and Diazepine Hydroxamic Acid Analogs
A quantitative structure-activity relationship study has been made on four different series of piperazine, piperidine and diazepine hydroxamic acid analogs acting as matrix metalloproteinase (MMP) inhibitors. The results suggest that in most of the cases the hydrophobic property of the molecules plays a major role in the inhibition of the enzymes MMP-1, MMP-9, MMP-13 and TACE. In many cases, MMP-9 and MMP-13 are shown to behave in a similar fashion with the different group of inhibitors.
In the recent years, the study of the inhibition of matrix metalloproteinases (MMPs) has become of great interest, resulting into development of broad spectrum MMP inhibitors, like marimastat, batimastat and a few others. It is because the hyperactivity of MMPs results in tissue degradation and a wide array of disease processes, such as osteoarthritis (Cawston, 1996; Blaser et al., 1996), rheumatoid arthritis (OByrne et al.,1995; Doughty et al., 1997; Brewster et al., 1998), tumor metastasis (Wojtowicz-Praga et al., 1997; Bramhall, 1997; Brown, 1997), multiple sclerosis (Yong et al., 1998; Matyszak and Perry, 1996), congestive heart failure (Coker et al., 1998; Spinale et al., 1999; Tyagi, 1998), chronic obstructive pulmonary disease (COPD) ( Burnett et al., 1988; Finlay et al., 1997; Ohno et al., 1997; Palmgren et al., 1992) and a host of others. Otherwise, it is well known that MMPs are a family of zinc-containing endopeptidases that collectively are able to cleave most of the structural components of extracellular matrix (ECM) like membrane collagen, fibronectin, laminin, versican, elastin, aggrecan, perlecan, tenascin, fibrinogen and proteoglycans (Murphy et al., 2002; Leung et al., 2000; Babine and Bender, 1997). The cleavages of these structural components are essential during the normal physiological and physiopathological events such as embryonic development, blastocyst implantation, nerve growth, ovulation, morphogenesis, angiogenesis, tissue resorption, wound healing, bone remodeling, apoptosis, cancer invasion and metastasis, arthritis, atherosclerosis, aneurysm, skin ulceration, corneal ulceration, gastric ulcer and liver fibrosis (Whittaker et al.,1999; Nagase, 1997; Nagase and Woessner, 1999; Bottomley et al., 1998; Dioszegi et al., 1995; Johnson et al., 1998). About 28 types of MMPs have been so far discovered and some of the recent development in the inhibitors of these MMPs has been recently reviewed by Supuran and Scozzafava (2002).
However, the clinical experiences of the inhibitors developed so far show intolerable
side effects of musculoskeletal syndrome (MSS), which is due to the undesirable
inhibition of some family members of MMP, e.g., MMP-1 (Rudek et al.,
2002). Therefore, recently the efforts have been made to selectively inhibit
the MMPs to develop molecules for specific diseases. The selective inhibition
of MMP-13 (Mitchel et al., 1996) and aggrecanase (Lohmander et al.,
1993) over MMP-1 may have therapeutic benefit in osteoarthritis without causing
MSS side effects. Similarly, the inhibition of MMP-9 may be valuable for preventing
tumor metastasis (Yip et al., 1999; Nelson et al., 2000).
In the design and development of drugs, quantitative structure-activity relationship
(QSAR) study has been of great value. Therefore, the present study reports a
QSAR study on some novel series of piperazine (1), piperidine (2 and 3) and
diazepine (4) hydroxamic acid analogs, so as to investigate the physicochemical
properties of these molecules which can make them selective for given enzyme
and also to explore the mechanism of drug-receptor interactions, which could
give a rationale to develop more specific and selective inhibitors.
These compounds have also been studied for the inhibition of TNF-α (tumor necrosis factor-α), which is also a zinc-containing endopeptidase that has gained equal importance. Its catalytic site is quite similar to that of MMPs (Maskos et al., 1998) and is involved in catalysis of a crucial physiological reaction, i.e., processing of membrane-bound form of protumor necrosis factor α (TNF-α), a 26 kDa propeptide on cell surface, to 17 kDa soluble form of mature TNF-α (Black and White, 1998; Moss et al., 2001). The release of this mature form of TNF-α from cell surface is responsible for causing several inflammatory events in the body leading to several diseases including rheumatoid arthritis (RA) (Feldmann and Maini, 2001), Crohns disease (Van Assche and Rutgeerts, 2000) and psoriasis (Kristensen et al., 1993). It has been therefore postulated that the inhibition of TACE, reducing levels of soluble TNF-α, might offer an effective treatment of RA (Nelson and Zask, 1999; Lowe, 1998; Newton and Decicco, 1999; Konttinen et al.,1999). Since a variety of MMPs have been found to be over-expressed in RA synovial tissue and have been implicated in the destruction of cartilage in RA joints, the optimal MMP/TACE selectivity profile for a drug to treat rheumatoid arthritis is still to be resolved. Therefore, the study of the inhibition of TACE is also of great importance.
Materials and Methods
The series of MMP inhibitors taken for QSAR study have been reported by the
different research groups: 1 and 2 by Letavic et al. (2002, 2003), 3
by Venkatesan et al. ( 2003) and 4 by Levin et al. (1998). The
derivatives of all 1-4 are listed in Tables 1-4,
respectively, along with their relevant physiochemical properties that were
found to be correlated with the MMP inhibition potencies. Tables
5-8 display the inhibition potencies of compounds of Tables
1-4, respectively, with their observed as well as calculated
values obtained from the correlations. In these tables, IC50 refers
to the molar concentration of the compounds leading to 50% inhibition of the
enzyme. The physicochemical parameters found to be useful in this QSAR study
are the calculated hydrophobicity parameter (ClogP) and polarizability (Pol)
of the whole molecules and the hydrophobic constant π of the substituents.
The hydrophobicity parameter ClogP was calculated using www.daylight.com
domain and polarizability was calculated from www.acdlabs.com
domain. The π values of substituents are taken from the literature (Hansch
and Leo, 1970). Some indicator variables were also used to account for the effects
of some specific structural features in the compounds. These variables are defined
in the text as and when they appear.
Results and Discussion
For the series of piperazine hydroxamic acid analogs 1 (Table 1), the QSARs obtained were as follows:
In these equations, n is the number of data points, r is the correlation coefficient, r2cv is the square of cross-validated correlation coefficient obtained by leave-one-out (LOO) jackknife procedure, s is the standard deviation and F is the F-ratio between the variances of calculated and observed activities (within parenthesis the figures refer to the F-valves at 99% level). The data with ± sign within the parentheses refer to 95% confidence intervals for the coefficients of the variables as well as for the intercept.
Equations 1 and 2 represent very significant
correlations and suggest that the MMP-1 inhibition by this series of compounds
will largely depend upon the hydrophobicity of the molecules. But since dependence
of the potency of the compounds on the hydrophobic parameters ClogP is parabolic,
the potency is optimized with an optimum value of ClogP equal to 2.79. For TACE
inhibition, however, the potency of the compounds is shown to have a negative
relation with the hydrophobicity of the molecules (Eq. 2).
For MMP-1 inhibition, a negative effect is shown by R1 = H, as described
by I1,H parameter in Eq. 1. It means that a replacement
of this hydrogen by any comparatively bulky group will be conducive to the activity,
which may be because of some hydrophobic interaction of the group with any specific
hydrophobic pocket of the receptor.
For the series of piperidine hydroxamic acid analogs 2 (Table 2), the QSARs obtained were as follows:
|| A series of piperazine hydroxamic acid analogs (1) and related
For this group of compounds, the MMP-1 inhibition is shown to be primarily governed by only the hydrophobic property of the X-substituents present in the R-moiety of OCH2R group of the aryl ring (Eq. 3). These substituents therefore seem to have specific hydrophobic interactions with the receptors. The additional factor to be favorable to the MMP-1 inhibition is the substitution of an OH group at the 5-position of piperidine ring (R1 = 5-OH). The same at the 4-position would be less effective. This comparative effect of OH is described in Eq. 3 by the indicator variable IR1 with a value of 1 for R1 = 5-OH and zero for R1 = 4-OH.
R1 = 5-OH is shown to be favorable to the TACE inhibition also (Eq. 4). The hydrophobic property of X-substituents in R is also shown to be conducive to TACE inhibition, however till only πX,R attains an optimum value of 0.67. Two additional parameters, IR,Ph and Io, describe the advantageous role of two discrete features of the molecules. IR,Ph stands with a value of 1 for R = C6H5 (i. e. unsubstituted phenyl moiety) and Io stands with a value of 1 for 2-X (i.e., 2-position substituents at phenyl ring). Thus, de facto, an unsubstituted or a 2-substituted phenyl is indicated to be of additional advantage, but it is hard to explain as to how they would produce additional effects as compared to a 3-or 4-substituted phenyl.
|| A series of piperidine hydroxamic acid analogs (2) and related
For the series of another piperidine hydroxamic acid analogs 3 (Table 3), the QSARs obtained were as follows:
|| A series of piperidine hydroxamic acid analogs (3) and related
|| A series of diazepine hydroxamic acid analogs (4) and related
||Observed and calculated MMP and TACE inhibition potencies
of compounds of Table 1. Observed activities have been
taken from Letavic et al. (2003).
|aNot included in the derivation of Eq.
1, bNot included in the derivation of Eq. 2
||Observed and calculated MMP and TACE inhibition potencies
of compounds of Table 2. Observed activities have been
taken from Letavic et al. (2002)
|aNot included in the derivation of Eq.
3, bNot included in the derivation of Eq. 4
It is to be noted that as for piperidine hydroxamic acids 2, for piperidine
hydroxamic acids 3 also MMP-1 and TACE inhibitions are controlled by the hydrophobic
property of the molecules (Eq. 5 and 6).
In this case, however, there exists a better similarity between the QSARs of
MMP-1 and TACE. For both, there exists a parabolic dependence of the inhibition
potency of the compounds on ClogP and for both the optimum value of ClogP (ClogPo)
is almost same. However, for the TACE inhibition, the polarizability of the
molecules is also found to play a role and, as obvious from Eq.
6, it is producing an adverse effect. It is of course in line with the fact
that polarizability will always play an opposite role to that of hydrophobicity.
For the series of 3, the hydrophobicity of the molecules is shown to govern
also the activity of the compounds studied against two other MMPs, MMP-9 and
MMP-13 (Eq. 7 and 8). The parabolic dependence
of the activity on ClogP in these two cases also leads to suggest that in the
inhibition of all the four MMPs here, the hydrophobicity of the molecules plays
almost an identical role. However, in all the cases, there are some indicator
variables describing the positive or negative effect of some typical substituents.
In the case of MMP-1 and MMP-13 (Eq. 5 and 8),
the variable I1,OMe describes the effect of a methoxy group substituted
at the aryl ring (R1 = OMe). It has a value of 1 for R1
= OMe and zero for R1 being any other substitutent. Now while a positive
coefficient of I1,OMe in Eq. 5 indicates a favorable
role of an OMe group at R1-position in MMP-1 inhibition, for MMP-13
inhibition a negative coefficient of it in Eq. 8 indicates
a detrimental effect of OMe. The one possible reason of this difference may
be the size of this substitutent. The methoxy substitutent is the smallest one
among all R1-substituents. A favorable role of it, as compared to
other substituents, in MMP-1 may be due to its optimum steric fit with the receptor
site in this enzyme and its comparative unfavorable role in MMP-13 may be due
to its insufficiently small size to have any interaction with the receptor site
in this enzyme.
||Observed and calculated MMP and TACE inhibition potencies
of compounds of Table 3. Observed activities have been
taken from Venkatesan et al. (2003)
|aNot included in the derivation of Eq.
5, bNot included in the derivation of Eq. 6,
cNot included in the derivation of Eq. 7, dNot
included in the derivation of Eq. 8
In Eq. 7, I1,PhCl stands with a value of unity for R1 = OC6H4-4-Cl. A positive coefficient of it exhibits a favorable role of this substituent for MMP-9 inhibition. Here the chlorine may be expected to have some electronic interaction with the receptor. Similarly, in Eq. 6 I4,benz describes a conducive role of a substituted or unsubstituted benzyl present at the piperidine nitrogen (R4-substituent). This variable has a value of 1 for R4 = CH2C6H4-X and zero for any other R4-substituent.
For the series of diazepine hydroxamic acid analogs 4 (Table
4), the QSARs obtained were as follows:
||Observed and calculated MMP inhibition potencies of compounds
of Table 4. Observed activities have been taken from Levin
et al. (1998)
|aNot included in the derivation of Eq.
9, bNot included in the derivation of Eq.
For most of the cases, the correlation obtained for MMP-9 and MMP-13 have been
found to be parallel. We observe the same for the series of 4, too (Eq.
9 and 10). Equation 9 and 10
clearly exhibit that for both these MMPs, the hydrophobicity of the molecules
of this series of compounds will be a dominant factor and that a benzoyl group
at the diazepine nitrogen (R1 = C(O)C6H5) would
be an additional advantage as described by the indicator variable I1,COPh.
The hydrophobicity of the molecules will obviously lead to a hydrophobic interaction
of the molecules with the enzymes and the benzoyl group at the nitrogen may
have some optimum polar interaction with some sites of the receptor.
Equations 1-10 exhibit very significant
correlations, devoid of any mutual correlation among the parameters used in
any equation, and have very good predictive value as judged from their r2cv
values. However, in deriving these equations, some compounds as indicated in
the foot-notes of the Tables 5-8 were not
included since they exhibited aberrant behaviors. Since in different equations
different compounds were excluded, it was hard to explain in each case the aberrant
behaviour of each compound. In such situations, the only reason that can be
assigned is the experimental error, or the conformational behavior of the enzymes.
This study suggests that for piperazine, piperidine and diazepine hydroxamic acid analogs, the hydrophobic property of the molecules plays a major role in the inhibition of the enzymes studied: MMP-1, MMP-9, MMP-13 and TACE. Therefore, one can assume that the nature of enzyme-ligand interaction is predominantly hydrophobic. In most of the cases, the QSARs for MMP-9 and MMP-13 have been found to be quite similar, hence in those cases the compounds are supposed to interact with these enzymes in a similar fashion.
One of the authors, S. Kumaran, is thankful to CSIR, New Delhi, for providing
him SRF, during this study.
Black, R.A and J.M. White, 1998.
Adams focus on the protease domain. Curr. Opin. Cell Biol., 10: 654-659.PubMed |
Bottomley, K.M., W.H. Johnson and D.S. Walter, 1998.
Matrix metalloproteinase inhibitors in arthritis. J. Enzyme Inhib., 13: 79-101.PubMed |
Blaser, J., S. Triebel, U. Maajosthusmann, J. Rimisch and U. Krahlmateblowski et al
Determination of metalloproteinases, plasminogen-activators and their inhibitors in the synovial fluids of patients with rheumatoid arthritis during chemical synoviorthesis. Clin. Chim. Acta., 244: 17-33.PubMed |
Bramhall, S.R., 1997.
The matrix metalloproteinases and their inhibitors in pancreatic cancer. Intl. J. Pancreatol., 21: 1-12.CrossRef |
Brown, P.D., 1997.
Matrix metalloproteinase inhibitors in the treatment of cancer. Med. Oncol., 14: 1-10.PubMed |
Burnett, D., S.C. Afford, E.J. Campbell, R.A. Rios-Mollineda, D.J. Buttle and R.A. Stockley, 1988.
Evidence for lipid-associated serine proteases and metalloproteases in human bronchoalveolar lavage fluid. Clin. Sci., 75: 601-607.PubMed |
Cawston, T.E., 1996.
Metalloproteinase inhibitors and the prevention of connective tissue breakdown. Pharmacol. Ther., 70: 163-182.CrossRef |
Coker, M.L., C.V. Thomas, M.J. Clair, J.W. Hendrick, S.R. Krombach, Z.S. Galis and F.G. Spinale, 1998.
Myocardial matrix metalloproteinase activity and abundance with congestive heart failure. Am. J. Physiol., 274: 516-523.PubMed |
Dioszegi, M., P. Cannon and H.E. Van Wart, 1995.
Vertebrate collagenases. Methods Enzymol., 248: 413-431.PubMed |
Doughty, J.R., E. O'Byrne, S. Spirito, V. Blancuzzi, H.N. Singh and R.L. Goldberg, 1997.
The effect of CGS 27023A on the level of 3B3 (-) epitope in a rabbit meniscectomy model. Inflamm. Res., 46: 139-140.CrossRef |
Feldmann, M. and R.N. Maini, 2001.
Anti-tnf alpha therapy of rheumatoid arthritis what have we learned. Annu. Rev. Immuunol., 19: 163-196.PubMed |
Finlay, G.A., K.J. Russell, K.J. McMahon, E.M. DArcy, J.B. Masterson, M.X. Fitzgerald and C.M. Oconnor, 1997.
Elevated levels of matrix metalloproteinases in bronchoalveolar lavage fluid of emphysematous patients. Thorax, 52: 502-506.PubMed |
Hansch, C. and A. Leo, 1970.
Substituent Constant for Correlation Analysis in Chemistry and Biology, John Wiley, New York
Johnson, L.L., R. Dyer and D.J. Hupe, 1998.
Matrix metalloproteinases. Curr. Opin. Chem. Biol., 2: 466-471.
Konttinen, Y.T., M. Ainola, H. Valleala, J. Ma, H. Ida and M. Takagi et al
Analysis of 16 different matrix metalloproteinases (MMP 1 to MMP 20) in the synovial membrane different profiles in trauma and rheumatoid arthritis. Ann. Rheum. Dis., 58: 691-697.PubMed | Direct Link |
Kristensen, M., C.Q. Chu, D.J. Eedy, M. Feldmann, F.M. Brennan and S.M. Breathnach, 1993.
Localization of tumour necrosis factor-alpha (tnf-alpha) and its receptors in normal and psoriatic skin epidermal cells express the 55-kd but not the 75-kd tnf receptor. Clin. Exp. Immunol., 94: 354-362.PubMed |
Letavic, M.A., M.Z. Axt, J.T. Barberia, T.J. Carty and D.E. Danley et al
Synthesis and biological activity of selective pipecolic acid-based tnf-alpha converting enzyme tace inhibitors. Bioorganic Med. Chem. Lett., 12: 1387-1390.CrossRef | PubMed |
Letavic, M.A., J.T. Barberia, T.J. Carty, J.R. Hardink and J. Liras et al
Synthesis and biological activity of piperazine-based dual MMP-13 and TNF-alpha converting enzyme inhibitors. Bioorg. Med. Chem. Lett., 13: 3243-3246.PubMed |
Leung, D., G. Abbenante and D.P Fairlie, 2000.
Protease inhibitors current status and future prospects. J. Med. Chem., 43: 305-341.PubMed |
Levin, J.I., J.F. DiJoseph, L.M. Killar, A. Sung and T. Walter et al
The synthesis and biological activity of a novel series of diazepine mmp inhibitors. Bioorg. Med. Chem. Lett., 8: 2657-2662.CrossRef |
Lohmander, L.S., P.J. Neame and J.D. Sandy, 1993.
The structure of aggrecan fragments in human synovial fluid evidence that aggrecanase mediates cartilage degradation in inflammatory joint disease joint injury and osteoarthritis. Arthritis Rheum., 36: 1214-1222.PubMed |
Lowe, C., 1998.
Tumour necrosis factor-α antagonists and their therapeutic applications. Exp. Opin. Ther. Patents, 8: 1309-1322.CrossRef | Direct Link |
Maskos, K., C. Fernandez-Catalan, R. Huber, G.P. Bourenkov and H. Bartunik et al
Crystal structure of the catalytic domain of human tumor necrosis factor-alpha-converting enzyme. Proc. Natl. Acad. Sci. U.S.A., 95: 3408-3412.PubMed |
Matyszak, M.K. and V.H. Perry, 1996.
Delayed-type hypersensivity lesions in the central nervous system are prevented by inhibitors of matrix-metalloproteinases. J. Neuroimmunol., 69: 141-149.PubMed |
Mitchell, P.G., H.A. Magna, L.M. Reeves, L.L. Lopresti-Morow and S.A. Yocum et al
Cloning, expression and type II collagenolytic activity of matrix metalloproteinase-13 from human osteoarthritic cartilage. J. Clin. Invest., 97: 761-768.CrossRef | PubMed |
Moss, M.L., J.M. White, M.H. Lambert and R.C. Andrews, 2001.
Tace and other adam proteases as targets for drug discovery. Drug Discov. Today, 6: 417-426.PubMed |
Murphy, G., V. Knauper, S. Atkinson, G. Butler and W. English et al
Matrix metalloproteinases in arthritic disease. Arthritis Res., 4: 39-49.PubMed |
Nagase, H., 1997.
Activation mechanisms of matrix metalloproteinases. Biol. Chem., 378: 151-160.PubMed |
Nagase, H. and J.F.J. Woessner, 1999.
Matrix metalloproteinases. J. Biol. Chem., 274: 21491-21494.PubMed |
Nelson, A.R., B. Fingleton, M.L. Rothenberg and L.M. Matrisian, 2000.
Matrix metalloproteinases biologic activity and clinical implications. J. Clin. Oncol., 18: 1135-1149.PubMed |
Nelson, F.C. and A. Zask, 1999.
The therapeutic potential of small molecule TACE inhibitors. Exp. Opin. Invest. Drugs, 8: 383-392.CrossRef | PubMed |
Newton, R.C. and C.P. Decicco, 1999.
Therapeutipotential and strategies for inhibiting tumor necrosis factor-α. J. Med. Chem., 42: 2295-2314.PubMed |
O'Byrne, E.M., D.T. Parker, E.D. Roberts, R.L. Goldberg and L.J. MacPherson et al
. Oral administration of a matrix metalloproteinase inhibitor cgs 27023a protects the cartilage proteoglycan matrix in a partial meniscectomy model of osteoarthritis in rabbits Inflamm. Res., 44: S117-S118.CrossRef |
Ohno, I., H. Ohtani, Y. Nitta, J. Suzuki and H. Hoshi et al
Eosinophils as a source of matrix metalloproteinase-9 in asthmatic airway inflammation. Am. J. Resp. Cell Mol. Biol., 16: 212-219.PubMed |
Palmgren, M.S, R.D. de Shazo and R.M. Carter, 1992.
Mechanisms of neutrophil damage to human alveolar extracellular matrix: the role of serine and metalloproteases. J. Allergy Clin. Immunol., 4: 905-915.PubMed |
Rudek, M.A., J. Venitz and W.D. Figg, 2002.
Matrix metalloproteinase inhibitors do they have a place in anticancer therapy. Pharmacotherapy, 22: 705-720.PubMed |
Spinale, F.G., M.L. Coker, S.R. Krombach, R. Mukherjee and H. Hallak et al
Matrix metalloproteinase inhibition during the development of congestive heart failure effects on left ventricular dimensions and function. Circ. Res., 85: 364-376.PubMed |
Supuran, C.T. and A. Scozzafaca, 2002.
Matrix Metalloproteinases. In: Proteinase and Peptidase Inhibition Recent Potential Targets for Drug Development. Smith, H.J. and C. Simons (Eds.). Taylor and Francis, London and New York, pp: 35-61
Tyagi, S.C., 1998.
Dynamic role of extracellular matrix metalloproteinases in heart failure. Cardiovasc. Pathol., 7: 153-159.CrossRef |
Van Assche, G. and P. Rutgeerts, 2000.
Anti-tnf agents in crohn's disease. Expert Opin. Invest. Drugs, 9: 103-111.PubMed |
Venkatesan, A.M., J.M. Davis, G.T. Grosu, J.L. Baker and J. Ellingboe et al
Synthesis and structure-activity relationship of N-substituted 4-arylsulfonylpiperidine-4-hydroxamic acids as novel, orally active matrix metalloproteinase inhibitors for the treatment of osteoarthritis. J. Med.Chem., 46: 2376-2396.PubMed |
Whittaker, M., C.D. Floyd, P. Brown and A.J.H. Gearing, 1999.
Design and therapeutic application of matrix metalloproteinase inhibitors. Chem. Rev., 99: 2735-2776.CrossRef | Direct Link |
Wojtowicz-Praga, S.M., R.B. Dickson and M. Hawkins, 1997.
Matrix metalloproteinase inhibitors. Invest. New Drugs, 15: 61-75.PubMed |
Yip, D., A. Ahmad, C.S. Karapetis, C.A. Hawkins and P.G. Harper, 1999.
Matrix metalloproteinase inhibitors applications in oncology. Invest. New Drugs, 17: 387-399.PubMed |
Yong, V.W., C.A. Krekoski, P.A. Forsyth, R. Bell and D.R. Edwards, 1998.
Matrix metalloproteinases and diseases of the cns. Trends Neurosci., 21: 75-80.PubMed |
Babine, R.E. and S.L. Bender, 1997.
Molecular recognition of protein ligand complexes applications to drug design. Chem. Rev., 97: 1359-1472.CrossRef | PubMed | Direct Link |