Transcript Document
Modeling Protein Flexibility with Spatial and Energetic Constraints
Yi-Chieh
1
Wu ,
Amarda
2
Shehu ,
Lydia
2,3
Kavraki
Problem Definition
Method
Results
Protein Flexibility
Model System
Discussion
Motivation
Most current methods
consider proteins as rigid
structures
Models incorporating protein
flexibility provide better
representations
Applications
Protein native state
behavior
Molecular interactions
Drug design and discovery
Problem Statement
Generate a set of conformations that capture the most
important motions
Follow along collective modes of motion starting from an initial
structure
Limited by local search – analysis fails far from the native
HIV-1 protease
A virus protein that assists in HIV replication
Target of drug design – single point of failure
Native structure: fully minimized structure of
4HVP from the Protein Databank
Figure 4. Backbone representation of
HIV-1 protease bound to an inhibitor
(orange).
Rigid geometry model
Dihedrals are the only
degrees of freedom
Reduce problem
dimensionality
(The highest RMSD as measured against the native structure is given. RMSD is measured in angstroms.)
Algorithm
INPUT
PROGRAM
PCA Vector,
Step Size
Move Features
by PCA
Energy
Cutoff
Use CCD to
Satisfy Features
Randomization,
CCD, and
Minimization
Parameters
Minimize
Energy
Check Energy
Step
Flap AllSize Atom RMSD
OUTPUT
Close
Initialize Protein
and Features
Features
Robotic Representation
Atoms ≡ joints
Bonds ≡ links
Apply robotic techniques
Figure 6: Backbone representation of flap
movement along the first PCA. Features
used are shown as gray spheres.
RMSDs of Recovered Conformations along the First PCA
Protein
(Native)
Proteins as Robotic Manipulators
Principle component analysis (PCA)
Identifies major modes of motion
Direct physical interpretations
HIV-1 protease: First eigenvector corresponds
to opening and closing of the flaps
surrounding the binding site
Conformations
Rewind to
Previous
Conformation
Closure
Satisfaction,
Energies, RMSD
Open
Time Analysis
outside cutoff
within cutoff
Figure 2: A protein modeled as an
articulated mechanism.
Cyclic Coordinate Descent (CCD)
Iterative, heuristic approach to solving inverse kinematics
Adjusts one dihedral at a time to move an atom to its
constrained position
Computationally fast and analytically simple
Features: residues with constrained positions
Choose atoms with the largest displacements
(Figure 5)
Internal features moved along the PCA –
capture flap movement
End features unmoved – keep rest of protein
native-like to maintain low-energy
†Figures
adapted from: I. Lotan. (2004). Algorithms exploiting the
chain structure of proteins. PhD Thesis, Stanford University.
2.125
2.235
2.097
2.289
2.159
4.668
3.421
0.5
1.0
2.5
3.340
2.351
1.643
3.171
2.030
1.434
Rest AllAtom RMSD
Total AllAtom RMSD
0.483
0.359
0.337
0.298
0.312
0.517
0.356
1.117
0.804
0.7552
0.798
0.764
1.599
1.166
3.454
2.424
1.691
0.375
0.247
0.240
1.164
0.802
0.582
Provided an approach to generating
physical conformations of a protein
Modeled flexibility of the binding site
Future work
• Investigate other modes of motion
• Incorporate multiple motion vectors
Spatial and Energetic Constraints
Spatial Constraints
Inverse kinematics – CCD
Features defined along backbone, so sidechains kept rigid
Displacement only valid in a small neighborhood
References
•
Energetic Constraints
Full conjugate gradient minimization of CHARMM energy
Energy cutoff of 600 kcal/mol
“Rewind” to previous conformation if high-energy barrier encountered
Flap
Sidechain
RMSD
3.188
2.266
2.113
2.319
2.198
4.814
3.494
Conclusions
Figure 5: Atom displacements along the first PCA.
Red circles mark the indices of our chosen features.
3†:
Figure
Using
CCD to satisfy
spatial constraints.
One joint (circled
in green) is rotated
at a time to bring
the end-effector
(blue) closer to the
target position
(red).
0.1
0.25
0.5
1.0
2.5
0.1
0.25
Flap
Backbone
RMSD
2.856
2.104
2.032
2.166
1.993
4.027
3.111
Energy landscape
Funnel-shaped →
thermodynamically stable
native structure
Varying energetic
constraints → nonsymmetric for open- and
close-flap conformations
More conformations around
the native
Feature Definition
Figure 1†: Rigid geometry model.
Only dihedral angles are used as
degrees of freedom. Backbone
dihedrals (phi and psi) are depicted.
Modeled flap movement of
HIV-1 protease using first
PCA
Opened and closed flaps
but kept protein stable
Movement concentrated in
flaps
Open-flap conformations
are less constrained –
recovered conformations
with higher RMSDs
•
A.A. Canutescu and R. L. Dunbrack. Cyclic coordinate descent: A
robotics algorithm for protein loop closure. Protein Science, 12: 963972, 2003.
A. Shehu. (2004). Sampling Biomolecular Conformations with
Spatial and Energetic Constraints. MS Thesis, Rice University.
For questions, comments, and preprint requests:
Yi-Chieh Wu
[email protected]
Acknowledgements
1Dept. of Electrical and
Computer Engineering, Rice
University
2Dept. of Computer Science,
Rice University
3Dept. of Bioengineering, Rice
University
Computer Research
Association’s Committee on the
Status of Women in Computing
Research Distributed Mentor
Project
W. M. Keck Center
Undergraduate Research
Training Program
Physical and Biological
Computing Group, Rice
University