• Protein structure prediction

• Computer-aided pharmaceutical design: Modeling receptor flexibility

• Applications to molecular simulation

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.

1) Generation of molecular dynamics simulation trajectorya) Start with known protein

structure (from RCSB Protein Data Bank)

b) Run 2 nanosecond simulation (1,000,000 steps)

1 Dept. of Computer Science, Rice University, 2 Dept. of Chemistry, Rice University, 3 Dept. of Computer Science and Dept. of Bioengineering, Rice University

David Schwarz1

dschwarz@rice.eduMark Moll1

mmoll@rice.eduLydia E. Kavraki3kavraki@rice.edu

Allison Heath1

aheath@rice.edu

Analysis of Biomolecular Interactions Using a Robotics-Inspired Approach with Applications to Tissue Engineering

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.

HIV-1 protease structures generated

by molecular dynamics

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

Geometric Space Search: Molecular Expansive Spaces

• 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)

1 2

3 4

a)

b)

Illustration of space-covering properties of expansive spaces search. Each point represents a conformation of the receptor.

a) Expansive searchb) Random walk

Results

Acknowledgements

• 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)

Work in Progress and Future Work

• 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

HIV-1 protease Inhibitors (drug candidates)

• 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

Cecilia Clementi2cecilia@rice.edu

• Dimensional reduction: Collective coordinates• Powerful search algorithm: Expansive spaces search

Dimensional reduction: Collective Coordinates

Why model protein flexibility?

Our approach

FKBP

• 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

• 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