Sampling Biomolecular Conformations with Spatial and Energetic Constraints

Amarda Shehu1, Cecilia Clementi2,4, Lydia E. Kavraki1,3,4

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 closure

Schematic of the CCD algorithm

VlsE subunit 20-aa loop closed

1

Q

e

(EC E0)/RT

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:Molecule in initial reference conformationTarget 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:Reference conformation with energy E0P(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

Our approach for sampling the native state ensemble:

SAMPLING THE NATIVE STATE ENSEMBLE

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 = [-p, p]n

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

M. Vendruscolo et al. JACS, 125, 2003C. Eicken et al. JBC, 277, 2002J. Ren et al. JBC, 268, 1993S. E. Jackson et al. Biochemistry, 32, 1993D. G. Luenberger. Linear and Non-linear Programming. Addison-Wesley, 1984L. T. Wang and C. C. Chen. IEEE, 7, 1991A. A. Canutescu and R. L. Dunbrack. Protein Science, 12, 2003J. Yakey et al., IEEE, 17, 2001K. Lindorff-Larsen, R. B. Best, DePristo M.A., C.M. Dobson, and

M. Vendruscolo, Nature 433, 125, 2005.

J.J. Chou, D.A. Case, and A. Bax, JACS 125, 2003M. 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 works results in blue

shown: [9] in red vs. this works 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 overlapped

Ubiquitin ensemble

-Lac ensemble

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

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