Protein structure prediction Computer-aided pharmaceutical design: Modeling receptor flexibility

1. a) 1 2 3 4 b) Analysis of Biomolecular Interactions Using a Robotics-Inspired Approach with Applications to Tissue Engineering David Schwarz1 dschwarz@rice.edu Allison Heath1 aheath@rice.edu Cecilia Clementi2 cecilia@rice.edu Lydia E. Kavraki3 kavraki@rice.edu Mark Moll1 mmoll@rice.edu 1 Dept. of Computer Science, Rice University, 2 Dept. of Chemistry, Rice University, 3 Dept. of Computer Science and Dept. of Bioengineering, Rice University Why model protein flexibility? Geometric Space Search: Molecular Expansive Spaces • Protein structure prediction • Computer-aided pharmaceutical design: Modeling receptor flexibility • Applications to molecular simulation • Loosely based on Expansive Spaces Tree (EST) path planning algorithm from robotics • Designed for rapid coverage of space • Here we adapt an EST-like method for coverage molecular conformation spaces • Algorithm: • Existing point chosen randomly for expansion based on: • Energy of explored points • Average distance to nearest • neighbors • Number of times point has • already been used for expansion • New point generated within set radius of chosen point • Two candidate methods to get new point: • Simple (Gaussian neighbor generation) • More complex (Random bounce walk) HIV-1 protease Inhibitors (drug candidates) Two known structures of HIV-1 protease, a protein vital to the life cycle of the human immunodeficiency virus, bound to inhibitors. A pharmaceutical company screening the bulky inhibitor on the right, but only testing it on the closed protein structure on the left, would fail to identify it as a potential inhibitor, and therefore a potential drug. • Illustration of space-covering properties of expansive spaces search. Each point represents a conformation of the receptor. • Expansive search • Random walk Our approach • Dimensional reduction: Collective coordinates • Powerful search algorithm: Expansive spaces search Results Dimensional reduction: Collective Coordinates • Results are for conformational searches of HIV-1 protease starting from PDB structures 1AID and 4HVP and FK506-binding protein (FKBP) starting from PDB structures 1A7X-A and 1FKR-17. • RMSD = Root Mean Squared Distance • Explicitly modeling receptor flexibility is computationally impossible • Collective coordinates = reduced basis for motion of the receptor (dimensionality reduction) • Example: HIV-1 protease • 3120 atoms, each with three Cartesian degrees of freedom (x,y,z), for a total of 9360 dimensions—computationally intractable • use first five principal components as a reduced basis—five dimensional space likely to be tractable • Distinct structures: At least 1 Å RMSD apart • Monte Carlo Simulation is a standard but slow conformational search method • Expansive search generates more distinct structures than Monte Carlo, and complex neighbor generation scheme works best Average distance to known structures (all atom RMSD) Average pairwise distance of generated structures Å RMSD Å RMSD Standard deviation Standard deviation Search set diameter (expansiveness) Average distance to known structures (binding site RMSD) • Set diameter: Maximum distance between any two structures in result set • Expansive search consistently generates broader search sets than random walk or Monte Carlo simulation • Indicates better coverage of conformation space • 1) Generation of molecular dynamics simulation trajectory • Start with known protein structure (from RCSB Protein Data Bank) • b) Run 2 nanosecond simulation (1,000,000 steps) Å RMSD Å RMSD HIV-1 protease structures generated by molecular dynamics Standard deviation Standard deviation FKBP Work in Progress and Future Work • Experiments to determine effectiveness of search algorithm independent of physical model • Molecular docking experiments on results of search to determine usefulness as drug-design target structures • Experiments with alternative parameterizations (such as dihedral coordinates) 2) Determination of collective coordinates by principal component analysis (PCA) of trajectory First principal component of HIV-1 protease from simulation of structure 4HVP • a) Singular value decomposition on representative conformations from trajectory • b) Output: • Set of vectors representing coordinated motions of receptor, in order of decreasing contribution to overall variation of structure Acknowledgements Work on this paper by the authors has been supported in part by NSF 0205671, EIA-0216467, a Texas ATP grant, a Whitaker Biomedical Engineering Grant and a Sloan Fellowship to Lydia Kavraki. David Schwarz has been partially supported by a National Defense Science and Engineering Graduate Fellowship from the Office of Naval Research and a President’s Graduate Fellowship from Rice University.