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where the two sums run over the partial charges of the fragment. Equation 12 differs from Equation 11 due to the presence of the self-energy term^. ,Eiself. This term is not zero only in the case of intramolecular energies. Eiself is the self-energy of charge i and represents the interaction between the charge itself and the solvent. It is calculated as [13,34]:

where RvdW is the van der Waals radius of charge i.

The difference in the intramolecular fragment energy upon binding to an uncharged receptor in solution is:

where Edocked and Efree are the energies in solution of the fragment bound and unbound to the receptor, respectively. They are evaluated according to Equation 12. For the unbound fragment (Efree) the effective radii are calculated considering as solute the volume enclosed by the molecular surface of the fragment. For the bound fragment (Edocked) the solute is the volume enclosed by the molecular surface of the receptor-fragment complex. Efree is evaluated only once per fragment type, while Edocked is recalculated for every fragment position in the binding site.

Validation

The approximations inherent to our continuum electrostatic approach were validated by comparison with finite difference solutions of the Poisson equation [12]. For this purpose, the three electrostatic energy terms were calculated with SEED and UHBD [52,54] for a set of small molecules and ions distributed over the binding site of thrombin and at the dimerization interface of the HIV-1 aspartic protease monomer. The molecule set included acetate ion, benzoate ion, methylsulfonate ion, methylammonium ion, methyl-guanidinium ion, 2,5-diketopiperazine, and benzene. The total number of fragment-receptor complexes analyzed were 1025 for thrombin (Figure 3) and 1490 for the HIV-1 protease monomer. The agreement between the two

Figure 3. Correlations in the electrostatic energies calculated by finite difference solution ofthe Poisson equation (x-axis) and SEED (y-axis). Values are plotted for 1025 complexes of thrombin with small molecules. The total electrostatic energy is the sum of the protein desolvation, screened interaction, and ligand desolvation scaled by 0.78, 1.28, and 1.14, respectively. The finite difference calculations wereperformed with the program UHBD [52,54]. An interior dielectric of4, solvent dielectric of 78.5, and grid spacing of 0.5 A were used for both SEED and UHBD.

Figure 3. Correlations in the electrostatic energies calculated by finite difference solution ofthe Poisson equation (x-axis) and SEED (y-axis). Values are plotted for 1025 complexes of thrombin with small molecules. The total electrostatic energy is the sum of the protein desolvation, screened interaction, and ligand desolvation scaled by 0.78, 1.28, and 1.14, respectively. The finite difference calculations wereperformed with the program UHBD [52,54]. An interior dielectric of4, solvent dielectric of 78.5, and grid spacing of 0.5 A were used for both SEED and UHBD.

methods is very good, and better for a solute dielectric constant of 4.0 (Figure 3) than 1.0 (Figure 2 of Reference 12). In Table 2 of Reference 12 it was shown that systematic errors (slope ^ 1) are independent of the receptor and the solute dielectric constant and consequently can be corrected by the use of appropriate scaling factors for the different energy terms.

Application to thrombin

Apart from a relatively small rigid body motion of the Tyr60A-Trp60D loop, thrombin assumes the same conformation in complexes with different inhibitors [55,56]. Figure 4 shows the most relevant results of a SEED run (interior dielectric of 1.0) on the nonprime region of the thrombin active site while a more detailed description of the SEED functionality maps of thrombin is given in Reference 12. The hydrophobic fragments bind preferentially to the S3 and S2 pockets (Figure 4a). The +1 charged groups, e.g., benzamidine (Figure 4b), 5-amidine indole (Figure 4c) and methylguanidinium, are involved in optimal hydrogen bonds with the Asp189 side chain in the S1 pocket. The SEED results are in agreement with the large amount of structural data on thrombin/inhibitor complexes [10,39,40,55-61].

The fragments docked by SEED were then connected by the program CCLD [15] as a further test of the usefulness of SEED for ligand design. CCLD generated 390 candidate ligands in 33 min on a R10000 processor. Four interesting hits, which ranked as 2nd, 37th, 42nd and 90th, are shown in Figures 5c-f.

Hits 1 and 2 (Figures 5c and d) are similar to Argatroban (Figure 5b), which is a reversible inhibitor of thrombin with a Kt of 19 nM [40,62]. They have nonpolar groups in S3 and S2 and a guanidinium in S1. The sulfonamide NH of compounds 1,2, and Argatroban donates a hydrogen bond to the backbone CO of Gly216. Moreover, the carbonyl group in 2 and Argatroban accepts from the NH group of Gly216. Additional hydrogen bonds, with respect to Argatroban, are present in 1 and 2, namely between an SO2 oxygen and the NH group of Gly219, and between the guanidinium and the main chain CO of Gly219. Furthermore, the amide group close to the guanidinium in compound 1 donates to the carbonyl of Ser214. Argatroban has less polar interactions with thrombin than hits 1 and 2 but its double ring moiety fills the S3 pocket better than the cyclohexyl ring of compounds 1 and 2. Hits 3 and 4 (Figures 5e and f) have a benzamidine in the S1 pocket and a benzene in S2. The benzamidine moiety of compound 3 donates to the two oxygens of the Asp189 side chain and to the carbonyl group of Gly219. In the S3 pocket the hydroxyl substituent of cyclohexane donates to the main chain CO of Glu97A. Compound 4 is similar to 4-TAPAP (Figure 5a), a reversible inhibitor of thrombin [40,63] whose racemic mixture has a Kt of 640 nM. In 4-TAPAP and hit 4 the benzamidine is involved in a salt bridge with the Asp 189 side chain, the sulfonyl part accepts from the NH group of Gly219 and one NH donates to the carbonyl group of Gly216. The interaction with

Figure 4. (a) Relaxed-eyes stereoview of the SEED cluster representatives of benzene (thick lines) in the thrombin active site (thin lines). The NAPAP inhibitor is also shown (medium lines), though it was removed during the SEED procedure. The SEED cluster representatives are labeled according to their binding energy rank within representatives of the same type. (b) Same as in (a) for benzamidine. Hydrogen bonds between protein and ligands are shown with dashed lines. (c) Same as in (b) for 5-amidine indole. Reprinted with permission from [12].

Figure 4. (a) Relaxed-eyes stereoview of the SEED cluster representatives of benzene (thick lines) in the thrombin active site (thin lines). The NAPAP inhibitor is also shown (medium lines), though it was removed during the SEED procedure. The SEED cluster representatives are labeled according to their binding energy rank within representatives of the same type. (b) Same as in (a) for benzamidine. Hydrogen bonds between protein and ligands are shown with dashed lines. (c) Same as in (b) for 5-amidine indole. Reprinted with permission from [12].

I TrpSODl

| Asp 1891

5d. Hit 2

| Asp 1891

Sg314 [

Sg314 [

Figure 5. Schematic representations of the interactions between thrombin and (a) 4-TAPAP, (b) Argatroban, and (c-f) CCLD hits 1 to 4. Reprinted with permission from [12].

Table 1. SEED results for the p38 MAP kinase

Rank of cluster

Intermolecular

Electrostatic desolvation

AG b binding

Sitec

vdWaals

Elect

Receptor

Fragment

Benzene

1

-14.7

-0.6

3.4

0.3

-11.6

Phenyl

2

-10.1

0.0

2.0

0.3

-7.8

Pyridine

3

-11.3

0.3

3.1

0.3

-7.7

Phe169

4

-10.7

0.5

2.8

0.3

-7.2

Phe169

5

-11.0

0.1

3.6

0.3

-7.0

Phenyl

Pyridine

1

-9.1

-0.6

1.4

0.8

-7.4

Pyridine

2

-8.5

-2.0

4.1

0.8

-5.6

Lys53

3

-7.6

0.1

1.3

0.8

-5.4

Pyridine

4

-9.2

-1.6

4.9

0.8

-5.1

Lys53

5

-9.1

-2.2

6.1

0.8

-4.4

Lys53

■ Each cluster contains 10 fragment positions. Energy values (in kcal mol-1) are given for the cluster representative which has the most favorable binding energy among the 10 members of the cluster. Cluster 1 is shown in Figure 6.

b Sum of the values in the four preceding columns, i.e., intermolecular interactions and electrostatic desolvation energies.

c The site is defined by the substituent of the triarylimidazole inhibitor (in boldface) or the closest side chain of the p38 MAP kinase.

■ Each cluster contains 10 fragment positions. Energy values (in kcal mol-1) are given for the cluster representative which has the most favorable binding energy among the 10 members of the cluster. Cluster 1 is shown in Figure 6.

b Sum of the values in the four preceding columns, i.e., intermolecular interactions and electrostatic desolvation energies.

c The site is defined by the substituent of the triarylimidazole inhibitor (in boldface) or the closest side chain of the p38 MAP kinase.

NH of Gly216 is missing in 4 but there are two additional hydrogen bonds, with the CO groups of Ser214 and Gly219. This last hydrogen bond also occurs in the NAPAP thrombin complex. The naphthalene ring of 4 fills the S3 pocket as NAPAP [55]. These representative examples and visual analysis of other SEED-CCLD hits indicate that the present approach generates candidate ligands with interaction patterns similar to known thrombin inhibitors.

Application to the p38 MAP kinase

The SEED maps of benzene and pyridine were obtained with an interior dielectric of 4, solvent dielectric of 78.5, and grid spacing of 0.5 Á. A complete analysis ofthe results for a library of about 100 fragments and a comparison with the available structural data ofp38 MAP kinase/inhibitor complexes will be given elsewhere (Tenette-Souaille et al., manuscript in preparation).

Figure 6. Relaxed-eyes stereoview of the 10 best benzenes and pyridines docked by SEED into the p38 MAP kinase. The bound conformation of the SB203580 inhibitor [48] is displayed to show that the 10 best benzenes and pyridines match the corresponding groups of SB203580.

Benzene The first cluster of benzene occupies the hydrophobic pocket, which contains the phenyl group of the known triarylimidazole inhibitors. The orientation of the members of the first cluster is similar to that observed in the crystallographic structure (Figure 6). A remarkable gap of 3.8 kcal mol-1 in the binding energy is found between the representative of the first cluster and the other cluster representatives (Table 1). Furthermore, even the other nine members of the first cluster have a more favorable energy than the representative of the second cluster. This difference is mainly due to the very favorable van der Waals term in the first cluster. The representatives of clusters 2 to 5 display similar energy values. Most of the fragments containing a phenyl ring (e.g., naphthalene, tetraline, N-methyl indole, and dibenzocyclohexane) match the phenyl group of the known triarylimidazole inhibitors. Moreover, there is a large energy gap (from 2.5 to 4.0 kcal mol-1) between the first cluster and the other clusters.

Pyridine Pyridine, as well as other fragments containing an aromatic ring with a hydrogen bond acceptor, overlaps the pyridine substituent of the tri-arylimidazole inhibitors (Figure 6). The orientation of the members of the first cluster is very close to that of the known inhibitors and they are involved in a hydrogen bond with the backbone NH of Met109 as in the crystal structure [49]. The main chain NH of Met109 is indeed the privileged partner of fragments with a hydrogen bond acceptor. As in the case of benzene, there is a significant gap (1.8 kcal mol-1) between the first cluster representative of pyridine and the second cluster (Table 1).

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