| Cerius²·Ludi |
1. It calculates interaction sites within the protein's active site or from the active analogs.
2. It searches libraries for fragments and fits them onto the interaction sites.
3. It proposes an alignment or linking for the fragments.
To generate the interaction sites, Ludi uses a set of rules that are intended to cover the complete range of energetically favorable orientations for hydrogen bonds and hydrophobic contacts. These rules are based on a statistical analysis of nonbonded contacts found in the literature (Murray-Rust and Glusker 1984, Taylor and Kennard 1984, Vedani and Dunitz 1985, Görbitz 1989, Klebe 1991, Görbitz and Etter 1992, Baker and Hubbard 1984, Kroon et al. 1975) and are described below.
The fitting of fragments to the interaction sites and the alignment (i.e., linking) of fragments to a partially built ligand is modified by several user-defined parameters that are described below. After fitting and aligning, Ludi writes the coordinates of the suggested fragments in PDB or MDL MOL format, depending on the library format.
Interactions between a protein and ligand are usually formed through favorable nonbonded contacts such as hydrogen bonds or hydrophobic interactions. For each nonbonded contact, an atom or functional group of the protein interacts with an atom or functional group of the ligand. Ludi models protein-ligand interaction through the use of interaction sites. For each atom or functional group of the protein that is capable of participating in a nonbonded contact, a set of interaction sites is generated. This set of interaction sites encompasses the range of suitable positions for a ligand atom or functional group involved in the putative interaction. The density of interaction sites within the set is user-specified.
Interaction site generation
The aromatic and aliphatic interaction sites are suitable sites for hydrophobic interactions. The H-donor and H-acceptor interaction sites are suitable sites for hydrogen bond formation.
A statistical analysis of hydrogen bond geometries in crystal packings of small molecules (see references given above) reveals a rather broad distribution. As described earlier, Ludi takes this distribution into account by generating an ensemble of interaction sites distributed over the region of acceptable geometries. This approach has the advantage that it is purely geometrical and therefore avoids costly calculations of potential energy functions.
The next step is to fit fragments onto the interaction sites. Ludi searches the list of interaction sites by distance criteria for suitable sets of two to six sites to match the fragments. The distance criterion used for selecting suitable interaction sites is based upon the square of the distances between the interaction sites i and j, R2ij. If these values fall within a specified range, then a fit of the fragment is performed.
Fragment fitting
Eq. 1
and
Eq. 2
The typical value of (
R)max is 0.2Å - 0.6Å.
Fragments are treated as rigid if the Bond Rotation parameter on the Ludi Design control panel is set to None. If Bond Rotation is set to One at a Time or Two at a Time, rotatable bonds within the fragment are rotated in singles or pairs to generate new conformations.
Ludi is capable of fitting fragments onto the interaction sites and simultaneously aligning (i.e., linking) them to an existing ligand. For this purpose, link sites are defined on the ligand. A link site is a hydrogen atom that can be replaced by a suggested fragment. You can either specify these link sites, or allow Ludi to assume that all the hydrogen atoms of the positioned ligand (within a user-specified cutoff radius) are link sites.
Link sites: aligning fragments with partially built ligands
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The Ludi fragment library is divided into two parts. The standard library is used when Ludi is run in de novo mode. The link library is used when Ludi is run in link mode. The standard library and the link library each consist of two files, a file that specifies the fragment topologies and a file that specifies the interaction types of fragment functional groups. For a detailed description of the format of these files, refer to the File Formats chapter.
Ludi fragment libraries
If the Bond Rotation parameter on a Ludi Design control panel is set to None, fragments are treated as rigid bodies. If Bond Rotation is set to One at a Time or Two at a Time, bonds are rotated in singles or pairs to generate new fragment conformations.
Standard library
For each of the fragments in the standard library, between three and eight atoms are defined to be fitted onto the interaction sites. The standard library contains structures of 5 - 30 atoms. There are approximately 1000 entries in the standard library. The topologies of fragments in the standard library are stored in the MDL Mol format described in File Formats.
Link library
The link library is very similar to the standard library. The topologies of fragments in the link library are stored in the MDL Mol format described in File Formats. The primary difference between the standard library and the link library is that the link library contains definitions of link sites for the fragments. These are hydrogen atoms that can be removed to bond the fragment to the growing ligand.
The link library contains approximately 1100 entries (900 one-link entries, 150 two-link entries, and 50 three-link entries). The number of entries in the link library is larger than the number of entries in the standard library because multiple sets of link sites may be specified for a given fragment in the link library.
Ludi/ACD
Ludi/ACD3 is a Ludi library prepared from the MDL Available Chemical Directory (ACD, a database of 2D structures). It contains all structures in the ACD that are suitable for use with Ludi and that could be converted to 3D by Converter4. This library is suitable for use when running Ludi in standard (no-link) mode (Böhm, 1994b).
The selection criteria for the Ludi/ACD library are:
The structures from Converter were then checked for any necessary changes in protonation state and the Ludi target atom data was generated. The target atom data is stored in $BIOSYM/data/ludi/frag_lib/acd_subset.inp.
Ludi uses rules to generate interaction sites. The position of an interaction site is described by the distance R, angle
Rules governing the generation of interaction sites
, and dihedral angle 
as defined in Figure 2.
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, and . The region in space defined by the values is then populated by discrete interaction sites. The error introduced into the subsequent fitting of fragments by this description of the binding region is of the order of the distance between the interaction sites. However, since the accuracy of the atomic positions in a crystallographic protein structure is within about 0.2 Å - 0.5 Å, this simplification appears to be justified. The rules are summarized in Table 2 and described in more detail in the following sections.
H-donor and H-acceptor rules
The hydrogen bond geometry of carbonyl groups in the solid state has been investigated extensively (Murray-Rust and Glusker 1984, Taylor and Kennard 1984, Klebe 1991). The available data show a distribution in from 100° to 180° with a preference for the lone pair direction ( = 120°, = 180°). However, as this preference is not particularly pronounced, and the other regions are also significantly populated, an even distribution of interaction sites was chosen with:
= 110° - 180° = 0 - 360°
The distribution of H-acceptor atoms around a N-H group is tighter than that around a carbonyl group. The statistical analyses that have been published (Taylor and Kennard 1984, Görbitz 1989, Klebe 1991) all show a strong preference for a linear hydrogen bond with <N-H..O/N = 150° - 180°. A very similar distribution was also found around N-H groups in aromatic rings (Vedani and Dunitz 1985, Klebe 1991). The available data indicate very similar distributions for N-H and O-H. Therefore, identical rules were chosen for both groups and interaction sites are generated with:
= 150° - 180° = 0 - 360°
A problem arises with the generation of the position of the second atom Y adjacent to the H-acceptor position A. The optimal position of this second atom is difficult to obtain from the available experimental data. The position of the site Y was generated assuming <N-H..A-Y = 0°, <H..A-Y = 120°, and RA-Y = 1.23Å, although the particular choice of the angle and the dihedral is admittedly somewhat arbitrary.
= 100° - 140° = -50° - 50°, 130° - 230°
= 150° - 180° = 0 - 360°
= 90° - 130° = -70° - 70°
= 100° - 140° = -50° - 50°
When considering aliphatic and aromatic interaction sites, the following rules apply. If the ligand atom is an aliphatic carbon, then aliphatic interaction sites Lali are generated with RC..L = 4Å. A user-defined number of interaction sites are positioned roughly equally spaced on a sphere around each aliphatic carbon atom.
electron systems (Reid et al. 1985, Stoddard et al. 1990).
Summary of rules
As most of the publications of the statistical analysis do not present a quantitative analysis of the data, there is a certain amount of ambiguity involved in the choice of the rules given above. A very narrow definition of the allowed hydrogen bond geometries would strongly reduce the number of hits obtained in the subsequent fragment fitting and would leave one with the danger of missing the most promising hits. On the other hand, a very broad definition would result in a very large number of hits with the difficulty of selecting the most interesting ones. This choice of rules represents a compromise.
An important problem for every method based on searching through large numbers of structures is the prioritization of the hits. Ludi approaches the problem as follows:
Prioritization of the fitted fragments
2. In link mode, the fragment overlaps the ligand except at the link site atoms.
3. You have specified that electrostatic repulsion be checked and the fragment does not pass the check6.
Second, the hits are prioritized using an empirical scoring function. Whenever a fragment can be fit in multiple orientations only the highest scoring fit is retained.
Receptor mode scoring functions
For receptor mode runs (i.e., runs in which the receptor structure is known), Ludi offers three empirical scoring functions. The original receptor mode scoring function7 (Eq. 3) is a two-term scoring function in which the first term measures the number and quality of receptor-fragment hydrogen bonds, and the second term measures the receptor-fragment hydrophobic contact area. The second term is weighted such that 60Å2 of hydrophobic contact surface is equivalent to an unperturbed hydrogen bond8.
Eq. 3
In Eq. 3 the summation is over fragment-receptor hydrogen bonds; R is the deviation of the H · · O/N hydrogen bond length from the ideal value (1.9Å); is the deviation of the hydrogen bond angle 
from its ideal value (180 °); and Alipo is the area (Å2) of hydrophobic contact between the receptor and fragment.
Eq. 4 |  | for  |
Eq. 5 |  | for 
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Eq. 6 |  | for 
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Eq. 7 |  | for 
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Eq. 8 |  | for 
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Eq. 9 |  | for 
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The second scoring function9 (Eq. 10) gives a score that is correlated with the dissociation constant, Ki, for the ligand-receptor complex (Böhm, 1994a):
| Score | Ki |
|---|---|
| 100 | 100 mM |
| 200 | 10 mM |
| 300 | 1 mM |
| 600 | 1 µM |
| 900 | 1 nM |
The relationship between the dissociation constant and the free energy of binding, G, at equilibrium is expressed in Eq. 11:
Eq. 11
in which R is the gas constant and T is the absolute temperature. By substituting Eq. 11 into Eq. 10 the score is shown to be proportional to the free energy of binding at 25°C:
Eq. 12
The Ludi score is calculated from Eq. 12, with G expressed by an empirical function (Eq. 3-Eq. 13) (Böhm, 1994).
Eq. 13
The values of the adjustable parameters, listed in Table 4, were obtained by fitting experimental binding constants of 45 protein-ligand complexes.
| parameter | value (kcal/mol) |
|---|---|
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G0
| 1.3 |
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Ghb
| -1.1 |
|
Gion
| -2.0 |
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Glipo
| -0.040 |
|
Grot
| 0.33 |
In Eq. 13 G0 represents the contribution to the binding energy that does not directly depend on any specific interactions with the receptor (e.g., the contribution to binding energy due to loss of translational and rotational entropy of the fragment). Ghb and Gion represent the contributions from an ideal hydrogen bond and an unperturbed ionic interaction, respectively. The Glipo term represents the contribution from lipophilic interactions. The lipophilic contribution is assumed to be proportional to the lipophilic contact surface, Alipo, between the receptor and the fragment. The Grot term represents the contribution due to the freezing of internal degrees of freedom in the fragment. NR is the number of acyclic sp3-sp3 and sp3-sp2 bonds. Rotations of terminal CH3 or NH3 groups and flexibility of cyclic portions of the fragment are not taken into account. 
and 
are given in Eqs. 4 through 9.
The third scoring function10 (Eq. 14) (Bohm, 1998) adds a term to Eq. 13 that takes aromatic-aromatic interactions into account:
Eq. 14
In the new term, the angular dependence of aromatic-aromatic interactions is ignored and a simple distance cutoff is used:
Eq. 15 |
 | for 
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Eq. 16 |
 | for 
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| parameter |
value kcal/mol |
|---|---|
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Go
| -0.24 |
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Ghb
| -0.76 |
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Gion
| -1.45 |
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Glipo
| -0.03 |
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Grot
| -0.22 |
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Garo
| -0.75 |
Active analog mode scoring function
The scoring function in active analog mode (i.e., runs in which the receptor structure is not known) is given in Eq. 17.
Eq. 17
Where HB is the number of hydrogen bonds the fragment can make; Alipo is the accessible hydrophobic area (Å2) of the fragment; and occ is the percentage occupancy of the hypothetical active site by the fragment.
Link scoring function
In link mode, a score is given for the link. The link score is not included in the overall score for the fragment but is reported separately. The link score is given by:
Eq. 18
where l1 and l2 are the two ligand link atoms; f1 and f2 are the fragment link atoms being fitted onto the ligand link atoms; rx-y is the distance between the atoms x and y; and 
x-y-z is the angle formed by atoms x, y and z. These distances and angles are illustrated in Figure 3.
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The fields of the Ludi score table are described in Table 6.
Score table fields
1
These vector lengths were chosen to simplify the subsequent fitting of fragments containing N-H or O-H groups (which are fitted onto the donor interaction site D-X) or carbonyl groups C=O (which are fitted onto the acceptor interaction site A-Y):
9
The second scoring function is used when the Scoring Function parameter on the Ludi Recepter Based Design control panel is set to Energy_Estimate_1 and is also the function used when you press the Score button on the Ludi Score control panel.
-naphthol (2 conformers)
and 
are defined as follows: