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 shehua@rice.edu

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