Book of Abstracts: Albany 2007
June 19-23 2007
What is the Statistical-thermodynamic Cost of Binding Entropy in Protein-ligand Docking and Virtual Screening? Analysis Based on the Use of 11 Scoring Functions
The accurate determination of absolute binding free energy (binding affinity) is a key element of computer-aided drug design and of statistical thermodynamic description of protein-ligand association. We present a novel method to estimate the entropy contributions of overall and relative translational and rotational motions to protein-ligand binding affinity (1-3). The method is based on the Monte-Carlo integration of the configurational integral over clusters obtained from multiple docked positions. Then we suggest a method to consider the entropy of torsional motions. We validate the suggested methods on a set of 100 PDB protein-ligand complexes (4) by comparing the averaged root-mean square deviations of the top-scored ligand docked positions, accounting and not accounting for entropy contributions, relative to the experimentally determined positions. We demonstrate that the method increases docking accuracy by 10-21% when used in conjunction with the AutoDock scoring function, by 2-25% with G-Score, by 7-41% with D-Score, by 0-8% with LigScore, by 1-6% with PLP, by 0-12% with LUDI, by 2-8% with F-Score, by 7-29% with ChemScore, by 0-9% with X-Score, by 2-19% with PMF, and by 1-7% with DrugScore. We also compare the performance of the suggested method with the method based on ranking by cluster occupancy only.
Then we focus on the correlation test of the method and on the characterization of protein-ligand energy landscapes described by the 11 scoring functions. Correlation analysis shows no influence of the entropy on the Pearson's correlation coefficient between the experimental and calculated values of binding affinities. Confronting the success of the method achieved in predicting native ligand positions (1, 2), these results draw attention to the free energy approximation of unbound solutes within methods of scoring functions. We demonstrate that neglect or account for unbound free energy have no effect on docking accuracy and the calculations of entropy of overall and relative molecular motions, but it may have a dramatic effect on estimates of binding affinity and correlation coefficients. The calculated values of binding entropy vary from -9.1 to -6.2kcal/mol, showing good agreement with the literature. We calculate positional sizes and the angular volume of the native energy well in energy landscapes of protein-ligand interactions described by each of 11 scoring functions. The averaged geometric mean of positional sizes in principal directions varies from 0.8 to 1.4A. The calculated range of angular volumes is 3.3-11.8rad2.
Key words: Protein-ligand docking; Binding affinity; Entropy; Scoring function; Clustering.
References and Footnotes
Anatoly M. Ruvinsky
Center for Bioinformatics