Docking a fragment library with SEED

Methods

The different types of fragments are docked by SEED in the order specified by the user. After each fragment placement the binding energy is estimated. The binding energy is the sum of the van der Waals interaction and electrostatic energy with continuum solvation. The successive fragment type is docked, after all placement-energy evaluations ofthe preceding fragment type have been made. The fragment docking procedure and energy evaluation are outlined in this section. Further details of the method, e.g., the clustering procedure, are given in the original paper [12]. For the docking of a library of 100 fragments into a binding site of about 25 residues, the latest version of SEED requires about 5 h of CPU time on a single processor (195 MHz R10000 or Pentiumlll 550 MHz). For more than one processor the speed-up is linear so that the docking of a library of 1000 fragments would require about 6 h of an 8-processor server or cluster.

Fragment docking

The binding site of the receptor is defined by a list of residues, which are selected by the user. Fragments are considered polar if they have at least one H-bond donor or acceptor. Due to this definition some 'polar' fragments can have considerable hydrophobic character (e.g., diphenylether). Therefore they can also be docked by the procedure for nonpolar fragments if specified by the user.

Docking of polar fragments These are docked so that one or more hydrogen bonds with the receptor are formed. The fragment is then rotated around the H-bond axis to increase sampling. Figure 2a shows the sampling of docked positions for pyrrole and acetone around a tyrosine side chain. Ideal and close-to-ideal hydrogen bond geometries are sampled in a discrete but exhaustive way.

Docking of nonpolar fragments The hydrophobicity maps are used to dock nonpolar fragments. The points on the receptor SAS are ranked according to the sum of van der Waals interaction and receptor desolvation (Equation 1), and the best n points (where n is an input parameter) are selected for docking. As an illustrative example, Figure lb shows the 70 most hydrophobic points on the ATP binding site ofthe p38 MAP kinase.

For both the fragment and the receptor, vectors are defined byjoining each point on the SAS with the corresponding atom. Finally, nonpolar fragments are docked by matching a vector of the fragment with a vector of the receptor

Figure 2. Relaxed-eyes stereoview of the fragments docked by SEED around a tyrosine side chain. (a) Acetone and pyrrole, (b) benzene. Carbon atoms are black, oxygen and nitrogen atoms dark gray, and hydrogen atoms light gray. Hydrogen bonds are drawn with dashed lines.

at the optimal van der Waals distance. To improve sampling, additional rotations of the fragment are performed around the axis joining the receptor atom and fragment atom (Figure 2b).

To increase efficiency, nonpolar fragments are discarded without calculation of the electrostatic energy, if the van der Waals interaction is less favorable than a threshold value.

For both polar and nonpolar fragments, the docking is exhaustive on a discrete space. The discretization originates from the limited number of preferred directions and rotations around them. Fragment symmetries are checked only once for every fragment type and are exploited to increase the efficiency in docking.

Electrostatic energy with continuum solvation

The main assumption underlying the evaluation of the electrostatic energy of a fragment-receptor complex is the description of the solvent effects by continuum electrostatics [13,14,30-35,50-52]. The system is partitioned into solvent and solute regions and different values of the dielectric constant are assigned to each region. In this approximation only the intra-solute electrostatic interactions need to be evaluated. This strongly reduces the number of interactions with respect to an explicit treatment of the solvent. Moreover, it makes feasible the inclusion of solvent effects in docking studies where the equilibration of explicit water molecules would be a major difficulty. The electrostatic effects of the solvent are relevant and it has been shown that the continuum dielectric model provides an accurate description of molecules in solution [14,53]. The difference in electrostatic energy in solution upon binding of a fragment to a receptor can be calculated as the sum of the following three terms [15,50]:

• Desolvation of the receptor: Electrostatic energy difference upon binding the uncharged (all partial charges switched off) fragment to the charged receptor in solution.

• Screened fragment-receptor interaction: Electrostatic interaction energy between the fragment and the receptor in solution.

• Desolvation of the fragment: Electrostatic energy difference upon binding the charged fragment to the uncharged (all partial charges switched off) receptor in solution.

The definition of the solute volume, i.e., the low dielectric volume, is central in the evaluation of these energy terms with a continuum model. The solute-solvent dielectric boundary is described by the molecular surface (MS) of the solute [38]. A grid covering the receptor is set up. In a first step the volume occupied by the isolated receptor is defined on the grid. Subsequently for every position of a docked fragment the volume enclosed by the MS of the fragment-receptor complex is identified.

The screened fragment-receptor interaction and the fragment desolvation are evaluated with a grid-based implementation [ 13,14] of the generalized Born (GB) approximation [31-35]. The GB approach would be too time con suming for the evaluation of the desolvation of the receptor which is calculated by the procedure described in the Methods section of the hydrophobicity maps.

Receptor desolvation It is evaluated using Equation 8 where the index k runs over the grid points in the volume occupied by the fragment. The volume occupied by a docked fragment is the part of the volume enclosed by the MS of the complex that was not occupied by the isolated receptor. It consists of the actual volume of the fragment and the interstitial volume enclosed by the reentrant surface between fragment and receptor,

Screened fragment-receptor interaction The fragment-receptor interaction in solution is calculated via the GB approximation [31]. In a solvent of dielectric constant ew, the interaction energy between two charges embedded in a solute of dielectric constant e„ is

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