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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.