Algorithms for Comparing Molecule Conformations David Sehnal.
Sampling Biomolecular Conformations with Spatial and Energetic Constraints
-
Upload
lyle-holman -
Category
Documents
-
view
39 -
download
0
description
Transcript of Sampling Biomolecular Conformations with Spatial and Energetic Constraints
Sampling Biomolecular Conformations with Spatial and Energetic Constraints
Amarda Shehu1, Cecilia Clementi2,4, Lydia E. Kavraki1,3,4
SAMPLING THE NATIVE STATE ENSEMBLE
Cyclic Coordinate Descent
M – current end-of-chain position
F – target end-of-chain position
– axis of rotation (current bond)
d = |F – M| (current error)
– optimal torsional parameter that minimizes d:
= f ( , M, F )
Repeat for any bond in path to M
Steer mobile aminoacid to stationary
counterpart for loop closureSchematic of the CCD algorithmVlsE subunit 20-aa loop closed
Sampling Feasible Closure Conformations
Search conformational space through Robotics
algorithm for set of closure conformations:
M = { q | q = CCD () }
M - self-motion manifold [8]
q – conformation (set of torsional angles)
- seed conformation in dihedral space
S S … S = [-, ]n
Sampling Conformations with Spatial and Energetic Constraints
Native state is ensemble of accessible structures at equilibrium
Spatial Constraints Energetic Constraints
Geometry Energy
We want to retain part of
the structure fixed
Collective motion of atoms
Conformations must be
energetically feasible
Minimized PDB structure is
reference conformation
Satisfy spatial constraints:
i. Molecule in initial reference conformation
ii. Target atom spatial positions (p1, …, pn)
Plan dihedral rotations so that atoms
reach their target positions
Use Robotics-inspired Cyclic Coordinate
Descent [5-7] to satisfy spatial constraints
Satisfy energetic constraints:
i. Reference conformation with energy E0
ii. P(conformation C) =
Conformation C accepted if EC < E0 + 15 RT
where T is room temperature
Use all-atom CHARMM to compute potential
energy of a conformation
1Q
e(EC – E0)/RT
Our approach for sampling the native state ensemble:
Conclusions
Acknowledgements 1Dept. of Computer Science, Rice University
2Dept. of Chemistry, Rice University
3Dept. of Bioengineering, Rice University
4Graduate Program in Structural and Computational
Biology and Molecular Biophysics,
Baylor College of Medicine
Supported by a training fellowship from the Keck Center Nanobiology Training Program of the Gulf Coast Consortia (NIH Grant No. 1 R90 DK071504-01)
NSF ITR 0205671, NSF EIA-0216467, CAREER award CHE-0349303
Welch Foundation: Norman Hackerman Young Investigator award,
and C-1570
Texas Advanced Technology Program 003604-0010-2003
Whitaker, Sloan, Welch foundations
M. Vendruscolo and K. Lindorff-Larsen for kindly providing us
with data for direct comparisons
Hernan Stamati for his help at the initial stages of this work
Giovanni Fossati and Erion Plaku for their help with
computer-related problems
Our method provides a way to validate and predict fluctuations of the native state with no a priori bias Our method is independent of specific energy models and thus can be readily integrated into various conformational search packages
1. M. Vendruscolo et al. JACS, 125, 20032. C. Eicken et al. JBC, 277, 20023. J. Ren et al. JBC, 268, 19934. S. E. Jackson et al. Biochemistry, 32, 19935. D. G. Luenberger. Linear and Non-linear Programming. Addison-Wesley, 19846. L. T. Wang and C. C. Chen. IEEE, 7, 19917. A. A. Canutescu and R. L. Dunbrack. Protein Science, 12, 20038. J. Yakey et al., IEEE, 17, 20019. K. Lindorff-Larsen, R. B. Best, DePristo M.A., C.M. Dobson, and M. Vendruscolo, Nature 433, 125, 2005.10. J.J. Chou, D.A. Case, and A. Bax, JACS 125, 200311. M. Karplus and J.A. McCammon. Nature Struct. Biol. 9, 2002
For questions, comments, and preprint requests:
Amarda Shehu [email protected]
References
ANALYSIS OF NATIVE STATE ENSEMBLE
Results
Our results show that the characterization we obtain for the native state ensemble is fully consistent with experimental data
The native state ensemble generated by our method does not incorporate any apriori experimental data
Our method is promising for characterizing fluctuations of the native state ensemble
shown: [1] in red vs. this work’s results in blue shown: [9] in red vs. this work’s results in blue
80% correlation 94% correlation
96% correlation
Experimental J couplings obtained from Chou J. J., Case D. A., and Bax A. JACS 125, 2003
3JCC in red - 3JNC in blue
Obtaining Residue Fluctuations Over the Whole Protein
RMSD(x, R) e-0.5(x/)2
x = x – xc
xc
Gaussian Confidence Each region anchored at ends
in our method
Regions agree on middle
residue fluctuations
More confidence in fluctuations
close to the middle
Gaussian distribution provides
one confidence measure
Residue fluctuations over ensemble of conformations for each region overlappedUbiquitin ensemble
-Lac ensemble
Combining Local Fluctuations Over the Whole Protein
Boltzmann fluctuations
Explore flexibility of one region at
a time by sliding windows
Each window is 30 aas long to
capture important fluctuations
Windows overlap in 25 aas to
check consistency of results from
different regions
APPLICATIONS
Local Fluctuations
Mobility for loop (51-76) of -Lac [3] (in blue) correlates well with results derived from experimental data [1].CI2 fragment mobility