Good-quality electrostatic potentials on a molecule can be computed based on an advanced representation of its underlying charge structure. The next step is being able to compare two conformations in terms of their electrostatic similarity. You can do this just by comparing the field points of the two molecules, which leads to a pharmacophore-like technique. However, a better solution is to take account of the full electrostatic potential.
Similarity needs to be computed in terms of the underlying potentials, not just in terms of the field points. Although computationally difficult, Cresset’s solution is both elegant and effective. The fields of the two molecules are compared, but only at the places where one of the conformations has a field point; keeping the number of field computations limited, but ensuring the field is computed only at places where at least one of the conformations suggested that the field was important (i.e., at a field point). The full algorithm has been published (Cheeseright et al JCIM 2006).
A score for conformation A into conformation B is computed by determining the field potential for B at the places where the field points for A lie. The overall score can be made symmetric by also computing the converse B-into-A score and averaging the two. However, it is not enough to score a particular alignment: you need to be able to locate the optimal alignment. This is a difficult global optimisation problem. Cresset’s solution is to generate a set of initial alignments by computing colored clique matches between the sets of field points on the two conformations: a clique match is a set of field points on each conformation that match in terms of field point type and in terms of all of the inter-field-point distances (to within a distance tolerance). Each clique match determines an alignment (by least-squares fitting of the matching field points in 3D), and the alignments are then scored according to the field similarity algorithm described above. The top-scoring alignment is then taken as the ‘correct’ alignment for those two conformations.
In many cases, of course, it is not known which conformation the molecules should be in. If comparing two known bioactive conformations, for example from protein crystal structures, then the field similarity algorithm can be applied directly. It is more often the case that one of the molecules has an unknown conformation: the best example is virtual screening – searching with a defined 3D conformation of the query molecule, but not knowing a priori if the conformation of the molecules being searched is going to be relevant. In this case a conformation search is performed, generating a set of conformers that represent the available conformational space of the molecule. Each of these are aligned to the query and the best-scoring alignment is taken as the overall score of the molecule.
In some circumstances it is necessary to compare molecules without knowing the bioactive conformation of any of them. In this situation conformer populations are computed of both molecules and compare each conformation of the first to each conformation of the second. This is the procedure that is used in our FieldTemplater technology for pharmacophore elucidation.
The field similarity algorithm is fast. Comparing a query conformation to a set of 100 conformers of a molecule takes 1-2 seconds on a single CPU core. It has proved very effective for virtual screening. Assessment of the performance of Cresset’s similarity algorithm as embodied in our Blaze virtual screening software shows that it performs significantly better than docking (Cheeseright et al JCIM 2008). The algorithm can be enhanced by combining it with a shape similarity calculation (Grant et al): the overall similarity is a weighted combination of the field similarity and the shape similarity. In most cases an equal weight is used (50% shape, 50% fields), but this is customizable by the user for particular circumstances.
Further enhancements of the field similarity calculation include the ability to add field constraints, pharmacophore constraints and excluded volumes. Field constraints are used to mark a particular region of field as being of higher importance than the rest, pharmacophore constraints require particular types of atoms to be close to each other, while excluded volumes enable the use of protein structure information to constrain alignments to lie within the available space. All of these can significantly improve the accuracy of alignment and scoring.