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Transcript
Analysis of Biomolecular Interactions Using a Robotics-Inspired Approach with Applications to Tissue Engineering David 1 Schwarz [email protected] 1 Mark Moll1 Allison [email protected] [email protected] Dept. of Computer Science, Rice University, 2 Dept. 1 Heath Cecilia 2 Clementi Lydia E. [email protected] 3 Kavraki [email protected] of Chemistry, Rice University, 3 Dept. of Computer Science and Dept. of Bioengineering, Rice University Why model protein flexibility? • Protein structure prediction • Computer-aided pharmaceutical design: Modeling receptor flexibility Geometric Space Search: Molecular Expansive Spaces • Loosely based on Expansive Spaces Tree (EST) path planning algorithm from robotics a) • Designed for rapid coverage of space • Here we adapt an EST-like method for coverage molecular conformation spaces • Applications to molecular simulation HIV-1 protease Inhibitors (drug candidates) 1 2 • Algorithm: • Existing point chosen randomly for expansion based on: 3 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. Our approach • 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) 4 b) Illustration of space-covering properties of expansive spaces search. Each point represents a conformation of the receptor. a) Expansive search b) Random walk • 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 • 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 • 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 1) Generation of molecular dynamics simulation trajectory a) Start with known protein structure (from RCSB Protein Data Bank) b) Run 2 nanosecond simulation (1,000,000 steps) HIV-1 protease structures generated by molecular dynamics • 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 FKBP Work in Progress and Future Work First principal component of HIV-1 protease from simulation of structure 4HVP 2) Determination of collective coordinates by principal component analysis (PCA) of trajectory 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 • 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) 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.