Efficient computational techniques provide advantageous solutions for complex problems in molecular modeling and related fields. These computational algorithms can come at hand where “wet biology” cannot be, or is too expensive to be carried out; they also help in solving computational bottlenecks caused when using the direct calculation. Here we illustrate these ideas by presenting two computational methods. The first algorithm provides a linear-complexity multiscale computation of the many-body problem of calculating long-range electrostatics in charge and dipolar systems [1,2]. The second method brings a Computer Vision approach to a biomolecular structural recognition problem, namely, an automated method for molecular docking [3, 4, 5, 6, 7, 8]. We conclude by demonstrating a possible implementation of electrostatic docking, i.e., combining the use of our multiscale fast electrostatics method in molecular docking.

Here we present a linear order multiscale method for the fast summation of long range forces in a system consisting of a large number of charge and dipolar particles. For a N ‐body system, our algorithm requires an order of work that is proportional to O ( N ), in comparison to order O ( N 2 ) of the direct pairwise computation. Our method is demonstrated on two‐dimensional homogeneous point‐charge and dipolar systems, and a combined heterogeneous particle system, for the calculation of the induced electrostatic potential and energy. The electrostatic interaction is decomposed into a local part and a smooth part. The method thus, has several potential advantages over other O ( N log N ) or O ( N ) techniques, especially for calculation with moving particles or implicit charges locations. This approach is beneficial to large‐scale problems such as molecular statics, molecular dynamics, equilibrium statistics (Monte‐Carlo simulations), molecular docking, and in areas such as magnetism and astrophysics. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 717–731, 2001

Here we dock a ligand onto a receptor surface allowing hinge-bending domain/substructural movements. Our approach mimics and manifests induced fit in molecular recognition. All angular rotations are allowed on the one hand, while a conformational space search is avoided on the other. Rather than dock each of the molecular parts separately with subsequent reconstruction of the consistently docked molecules, all parts are docked simultaneously while still utilizing the position of the hinge from the start. Like pliers closing on a screw, the receptor automatically closes on its ligand in the best surface-matching way. Movements are allowed either in the ligand or in the larger receptor, hence reproducing induced molecular fit. Hinge bending movements are frequently observed when molecules associate. There are numerous examples of open versus closed conformations taking place upon binding. Such movements are observed when the substrate binds to its respective enzyme. In particular, such movements are of interest in allosteric enzymes. The movements can involve entire domains, subdomains, loops, (other) secondary structure elements, or between any groups of atoms connected by flexible joints. We have implemented the hinges at points and at bonds. By allowing 3-dimensional (3-D) rotation at the hinge, several rotations about (consecutive or nearby) bonds are implicitly taken into account. Alternatively, if required, the point rotation can be restricted to bond rotation. Here we illustrate this hinge-bending docking approach and the insight into flexibility it provides on a complex of the calmodulin with its M13 ligand, positioning the hinges either in the ligand or in the larger receptor. This automated and efficient method is adapted from computer vision and robotics. It enables utilizing entire molecular surfaces rather than focusing a priori on active sites. Hence, allows attaining the overall optimally matching surfaces, the extent and type of motions which are involved. Here we do not treat the conformational flexibility of side-chains or of very small pieces of the molecules. Therefore, currently available methods addressing these issues and the method presented here, are complementary to each other, expanding the repertoire of computational docking tools foreseen to aid in studies of recognition, conformational flexibility and drug design. Proteins 32:159–174, 1998. © 1998 Wiley-Liss, Inc.

In this work, we present an algorithm developed to handle biomolecular structural recognition problems, as part of an interdisciplinary research endeavor of the Computer Vision and Molecular Biology fields. A key problem in rational drug design and in biomolecular structural recognition is the generation of binding modes between two molecules, also known as molecular docking. Geometrical fitness is a necessary condition for molecular interaction. Hence, docking a ligand (e.g., a drug molecule or a protein molecule), to a protein receptor (e.g., enzyme), involves recognition of molecular surfaces. Conformational transitions by "hinge-bending" involves rotational movements of relatively rigid parts with respect to each other. The generation of docked binding modes between two associating molecules depends on their three dimensional structures (3-D) and their conformational flexibility. In comparison to the particular case of rigid-body docking, the computational difficulty grows considerably when taking into account the additional degrees of freedom intrinsic to the flexible molecular docking problem. Previous docking techniques have enabled hinge movements only within small ligands. Partial flexibility in the receptor molecule is enabled by a few techniques. Hinge-bending motions of protein receptors domains are not addressed by these methods, although these types of transitions are significant, e.g., in enzymes activity. Our approach allows hinge induced motions to exist in either the receptor or the ligand molecules of diverse sizes. We allow domains/subdomains/group of atoms movements in either of the associating molecules. We achieve this by adapting a technique developed in Computer Vision and Robotics for the efficient recognition of partially occluded articulated objects. These types of objects consist of rigid parts which are connected by rotary joints (hinges). Our method is based on an extension and generalization of the Hough transform and the Geometric Hashing paradigms for rigid object recognition. We show experimental results obtained by the successful application of the algorithm to cases of bound and unbound molecular complexes, yielding fast matching times. While the "correct" molecular conformations of the known complexes are obtained with small RMS distances, additional, predictive good-fitting binding modes are generated as well. We conclude by discussing the algorithm's implications and extensions, as well as its application to investigations of protein structures in Molecular Biology and recognition problems in Computer Vision.

The generation of binding modes between two molecules, also known as molecular docking, is a key problem in rational drug design and biomolecular recognition. Docking a ligand, e.g., a drug molecule or a protein molecule, to a protein receptor, involves recognition of molecular surfaces as molecules interact at their surface. Recent studies report that the activity of many molecules induces conformational transitions by 'hinge-bending', which involves movements of relatively rigid parts with respect to each other. In ligand-receptor binding, relative rotational movements of molecular substructures about their common hinges have been observed. For automatically predicting flexible molecular interactions, we adapt a new technique developed in Computer Vision and Robotics for the efficient recognition of partially occluded articulated objects. These type of objects consist of rigid parts which are connected by rotary joints (hinges). Our approach is based on an extension and generalization of the Geometric Hashing and Generalized Hough Transform paradigm for rigid object recognition. Unlike other techniques which match each part individually, our approach exploits forcefully and efficiently enough the fact that the different rigid parts do belong to the same flexible molecule. We show experimental results obtained by an implementation of the algorithm for rigid and flexible docking. While the 'correct', crystal-bound complex is obtained with a small RMSD, additional, predictive 'high scoring' binding modes are generated as well. The diverse applications and implications of this general, powerful tool are discussed.