The statistical-thermodynamic basis for computation of binding affinities: a critical review.

Although the statistical thermodynamics of noncovalent binding has been considered in a number of theoretical papers, few methods of computing binding affinities are derived explicitly from this underlying theory. This has contributed to uncertainty and controversy in certain areas. This article therefore reviews and extends the connections of some important computational methods with the underlying statistical thermodynamics. A derivation of the standard free energy of binding forms the basis of this review. This derivation should be useful in formulating novel computational methods for predicting binding affinities. It also permits several important points to be established. For example, it is found that the double-annihilation method of computing binding energy does not yield the standard free energy of binding, but can be modified to yield this quantity. The derivation also makes it possible to define clearly the changes in translational, rotational, configurational, and solvent entropy upon binding. It is argued that molecular mass has a negligible effect upon the standard free energy of binding for biomolecular systems, and that the cratic entropy defined by Gurney is not a useful concept. In addition, the use of continuum models of the solvent in binding calculations is reviewed, and a formalism is presented for incorporating a limited number of solvent molecules explicitly.

Extending the trend vector: the trend matrix and sample-based partial least squares.

Trend vector analysis [Carhart, R.E. et al., J. Chem. Inf. Comput. Sci., 25 (1985) 64], in combination with topological descriptors such as atom pairs, has proved useful in drug discovery for ranking large collections of chemical compounds in order of predicted biological activity. The compounds with the highest predicted activities, upon being tested, often show a several-fold increase in the fraction of active compounds relative to a randomly selected set. A trend vector is simply the one-dimensional array of correlations between the biological activity of interest and a set of properties or 'descriptors' of compounds in a training set. This paper examines two methods for generalizing the trend vector to improve the predicted rank order. The trend matrix method finds the correlations between the residuals and the simultaneous occurrence of descriptors, which are stored in a two-dimensional analog of the trend vector. The SAMPLS method derives a linear model by partial least squares (PLS), using the 'sample-based' formulation of PLS [Bush, B.L. and Nachbar, R.B., J. Comput.-Aided Mol. Design, 7 (1993) 587] for efficiency in treating the large number of descriptors. PLS accumulates a predictive model as a sum of linear components. Expressed as a vector of prediction coefficients on properties, the first PLS component is proportional to the trend vector. Subsequent components adjust the model toward full least squares. For both methods the residuals decrease, while the risk of overfitting the training set increases. We therefore also describe statistical checks to prevent overfitting. These methods are applied to two data sets, a small homologous series of disubstituted piperidines, tested on the dopamine receptor, and a large set of diverse chemical structures, some of which are active at the muscarinic receptor. Each data set is split into a training set and a test set, and the activities in the test set are predicted from a fit on the training set. Both the trend matrix and the SAMPLS approach improve the predictions over the simple trend vector. The SAMPLS approach is superior to the trend matrix in that it requires much less storage and CPU time. It also provides a useful set of axes for visualizing properties of the compounds. We describe a randomization method to determine the optimum number of PLS components that is very much faster for large training sets than leave-one-out cross-validation.

Human immunodeficiency virus type 1 protease inhibitors: evaluation of resistance engendered by amino acid substitutions in the enzyme's substrate binding site.

The human immunodeficiency virus type 1 (HIV-1) protease is a homodimeric aspartyl endopeptidase that is required for virus replication. A number of specific, active-site inhibitors for this enzyme have been described. Many of the inhibitors exhibit significant differences in activity against the HIV-1 and HIV type 2 (HIV-2) enzymes. An initial study was conducted to ascertain the HIV-1 protease's potential to lose sensitivity to several test inhibitors while retaining full enzymatic activity. The substrate binding sites of the HIV-1 and HIV-2 enzymes are almost fully conserved, except for four amino acid residues at positions 32, 47, 76, and 82. Accordingly, recombinant mutant type 1 proteases were constructed that contained the cognate type 2 residue at each of these four positions. The substitution at position 32 resulted in a significant adverse effect on inhibitor potency. However, this substitution also mediated a noted increase in the Km of the substrate. Individual substitutions at the remaining three positions, as well as a combination of all four substitutions, had very little effect on enzyme activity or inhibitor susceptibility. Hence, the four studied active site residues are insufficient to be responsible for differences in inhibitor sensitivity between the HIV-1 and HIV-2 proteases and are unlikely to contribute to the generation of inhibitor-resistant mutant HIV-1 protease.

The NMR structure of the inhibited catalytic domain of human stromelysin-1.

The three-dimensional structure of the catalytic domain of stromelysin-1 complexed with an N-carboxyl alkyl inhibitor has been determined by NMR methods. The global fold consists of three helices, a five stranded beta-sheet and a methionine located in a turn near the catalytic histidines, classifying stromelysin-1 as a metzincin. Stromelysin-1 is unique in having two independent zinc binding sites: a catalytic site and a structural site. The inhibitor binds in an extended conformation. The S1' subsite is a deep hydrophobic pocket, whereas S2' appears shallow and S3' open.

Sample-distance partial least squares: PLS optimized for many variables, with application to CoMFA.

Three-dimensional molecular modeling can provide an unlimited number m of structural properties. Comparative Molecular Field Analysis (CoMFA), for example, may calculate thousands of field values for each model structure. When m is large, partial least squares (PLS) is the statistical method of choice for fitting and predicting biological responses. Yet PLS is usually implemented in a property-based fashion which is optimal only for small m. We describe here a sample-based formulation of PLS which can be used to fit any single response (bioactivity). SAMPLS reduces all explanatory data to the pairwise 'distances' among n samples (molecules), or equivalently to an n-by-n covariance matrix C. This matrix, unmodified, can be used to fit all PLS components. Furthermore, SAMPLS will validate the model by modern resampling techniques, at a cost independent of m. We have implemented SAMPLS as a Fortran program and have reproduced conventional and cross-validated PLS analyses of data from two published studies. Full (leave-each-out) cross-validation of a typical CoMFA takes 0.2 CPU s. SAMPLS is thus ideally suited to structure-activity analysis based on CoMFA fields or bonded topology. The sample-distance formulation also relates PLS to methods like cluster analysis and nonlinear mapping, and shows how drastically PLS simplifies the information in CoMFA fields.

Recognition by HLA-A2-restricted cytotoxic T lymphocytes of endogenously generated and exogenously provided synthetic peptide analogues of the influenza A virus matrix protein.

Experiments were carried out to determine whether complexes between MHC class I molecules and synthetic peptides are representative of those formed under more physiologically relevant conditions, with peptides derived intracellularly from processed antigens. Lysis of cells sensitized with exogenously provided and endogenously generated peptide analogues of the optimal nonameric peptide 58-66 (GILGFVFTL; derived from the influenza virus matrix protein) was compared. Endogenous loading was accomplished by expressing minigene DNA coding for alanine-substituted analogues of peptide 58-66 in HLA-A2-positive cells. Susceptibility to lysis by HLA-A2-restricted, peptide-specific cytotoxic lymphocytes was compared with lysis of cells sensitized with the same synthetic peptides. Although results were quite comparable, differences were observed. The endogenously presented analogues 58-66L60A, G61A, T65A, and L66A were recognized more efficiently than the corresponding exogenously presented analogues. This difference in recognition was most striking for peptide 58-66G61A. These results indicate the need for caution in using synthetic peptides in defining peptide binding motifs. Additional experiments with endogenously expressed analogues of 58-66 with substitutions other than alanine were carried out to define the interaction between this peptide and HLA-A2. Results are compatible with the interpretation that residues 58, 59, and 60 interact with pockets A, B, and D, respectively, in the HLA-A2 binding groove and that these interactions contribute to peptide binding.

Optimal humanization of 1B4, an anti-CD18 murine monoclonal antibody, is achieved by correct choice of human V-region framework sequences.

The murine anti-CD18 mAb 1B4 has been humanized using CDR grafting. Three VH (Gal, Jon, and New) and two VL (Rei and Len) human frameworks, whose selection was based exclusively on their sequence identity with m1B4, were used to construct five human gamma 4/kappa recombinant antibodies: Gal/Rei, Gal/Len, Jon/Rei, and New/Rei, and a "hemichimeric" antibody pairing the VH of m1B4 with grafted Rei. Each of these h1B4 constructs completely inhibited the binding of m1B4 to activated human leukocytes with avidities (IC50) ranging from 1.5 to 8.0 nM, compared to 0.5 nM for m1B4. Replacement of three VH residues in the best VH framework, Gal, with the corresponding m1B4 "packing" (nonsolvent exposed) residues gave an h1B4 (mutant Gal/Rei) with the same avidity as m1B4. Avidity correlated with overall percent identity between the human and murine VH frameworks and, in particular, with conservation of "packing" residues. Rei and Len VL frameworks proved to be interchangeable. Further characterization showed that the Gal/Rei prototype was equipotent to m1B4 in blocking adhesion of polymorphonuclear leukocytes and monocytes to human vascular endothelium in vitro, and polymorphonuclear leukocyte extravasation into C5a-injected rabbit or monkey skin sites. Dual-label immunofluorescence microscopy of bone marrow cells with Gal/Rei h1B4 and m1B4 demonstrated that the fine specificity of the combining sites had not been altered by humanization. Reduced immunogenicity was demonstrated in rhesus monkeys that tolerated weekly treatment with h1B4 for 6 wk, whereas m1B4 induced profound anaphylaxis at 3 wk. Anti-1B4 titers in h1B4-treated rhesus were 50 to 66% lower and developed 1 wk later than in m1B4-treated monkeys. Crucially, the anti-h1B4 antibodies were anti-idiotypic while the anti-m1B4 antibodies were directed against constant and framework regions. We conclude that sequence identity searches are sufficient to identify suitable human frameworks for CDR-grafting of m1B4, yielding functionally equivalent humanized antibodies that are tolerated better in primates.

Synthesis and use of 3-amino-4-phenyl-2-piperidones and 4-amino-2-benzazepin-3-ones as conformationally restricted phenylalanine isosteres in renin inhibitors.

The design of P2-P3 conformational restrictions in renin inhibitors by the use of a renin computer graphic model led to the synthesis of inhibitors containing N-Boc, N-acetyl, and N-phthalyl derivatives of 3(S)-amino-4(R,S)-2-piperidones and 4(S)-amino-2-benzazepinones in place of phenylalanine in the control compound N-acetyl-L-phenylalanyl-N-[4(S)-[(butylamino)carbonyl]-1(S)- (cyclohexylmethyl)-2(S)-hydroxy-5-methylhexyl]-L-norleuci namide (32). The piperidone inhibitors were prepared by utilization of the Evans chiral auxilliary to introduce the amino group with enantioselectivity and also to act as a leaving group in an intramolecular cyclization to the piperidone. The most potent inhibitor, 3(S)-(acetylamino)-alpha(S)-butyl-N-[4(S)- [(butylamino)carbonyl]-1(S)-(cyclohexylmethyl)-2(S)-hydroxy-5- methylhexyl]-2-oxo-4(R)-phenyl-1-piperidineacetamide (18, IC50 = 21 nM), was 25-fold less potent than the acyclic control 32. Considerable dependence of potency with the size of the P4 derivative was observed as had been expected based on the presynthetic modeling studies. Attempts to rationalize the observed potencies on the basis of further molecular modeling studies suggested that the loss in inhibitor potency was due to the conformational restrictions distorting the 3S center from the geometry present in the putative extended conformation present when the inhibitor is bound within the renin active site.

Macromolecular shape and surface maps by solvent exclusion.

A quantitative function equivalent to the "molecular" surface proposed by F. M. Richards [(1977) Annu. Rev. Biophys. Bioeng. 6, 151--176] is defined by the closest approach of solvent spheres to a macromolecule. The function can be used to visualize surface topography, polarity, and charge either as a three-dimensional net or by mapping onto a plane; to calculate surface areas; and to demarcate complementary sites in contacts between subunits. Applications to shape-specific recognition in protein structure and aggregation are discussed.