Characterizing Cavities in Model Inclusion Fullerenes: A Comparative Study

Point scattering: A new geometric invariant with applications from (Nano)clusters to biomolecules

A new geometric invariant is defined from "first principles" for a point ensemble, which can represent clusters, molecules, crystals, and biomolecules. The scattering of a point ensemble is defined in terms of the Euclidean distance matrix and a vector measuring the weighted departure of the points from the cluster centre. Using the Rayleigh-Ritz theorem this function is maximized obtaining the point scattering of the ensemble. The point scattering shows several properties which are useful for studying clusters, molecules, crystals, and biomolecules. We examined different natural clusters of hard spheres such as colloidal particles and fullerenes, as well as protein-peptide complexes and the effect of temperature on protein structure. In all cases point scattering differentiates point ensembles with different structures, which are not distinguished by other geometric invariants, such as the second moment of mass distribution, surface areas, and volumes. Point scattering also shows better correlation with thermodynamic parameters of binding and describes the interior cavities of hollowed ensembles better than the other geometric measures.

Targacept Active Conformation Search: A New Method for Predicting the Conformation of a Ligand Bound to Its Protein Target

Targacept active conformation search (TACS) is a novel variation of well-established three-dimensional quantitative structure--activity relationship methodologies that seeks to determine probable conformation(s) of ligands bound to their protein targets. A combination of affinity or activity data and energetically accessible conformational ensembles, each conformer described by three-dimensional (3-D) sensitive descriptors, forms the basis of the TACS data model. Recursive pruning is used to reduce the size of both the conformational ensemble and the descriptor space until the TACS data model contains just enough information to determine probable conformation(s) of ligands bound to their protein targets. The TACS algorithm is comprised of five components: (1) conformational ensemble generation, (2) 3-D sensitive descriptor calculation, (3) ensemble descriptor preprocessing, (4) model generation, and (5) prediction of bound conformation(s). Significantly, this method precludes the need for subjective or objective molecular alignment. We report the application of this technique to five benchmark protein-ligand couples where the conformation of a bound ligand has been previously established using X-ray crystallography: 9-cis-retinoic (1) and 9-trans-retinoic acid (2), both agonists for the retinoic acid receptor gamma, compounds KH1060 (3) and MC1288 (4), which bind to the vitamin D3 receptor, and R04 (5), an inhibitor bound to human rhinovirus 14 thermolysin. The binding conformations predicted by TACS were compared to the crystallographic structures extracted from their respective binding sites using root-mean-squared deviation (rmsd) criteria. Three of the conformations found using TACS were within crystallographic error. 9-cis-Retinoic acid, 9-trans-retinoic acid, and MC1288, when superimposed on their crystallographic structures, gave rmsd values of 0.22, 0.17, and 0.34 A, respectively. The rmsd values for KH1060 (1.54 A) and R04 (1.01 A) were larger but still reasonable.