Sampling Biomolecular Conformations with Spatial and Energetic Constraints

1. Sampling Biomolecular Conformations with Spatial and Energetic Constraints Amarda Shehu1, Cecilia Clementi2,4, Lydia E. Kavraki1,3,4 SAMPLING THE NATIVE STATE ENSEMBLE APPLICATIONS ANALYSIS OF NATIVE STATE ENSEMBLE Sampling Conformations with Spatial and Energetic Constraints Local Fluctuations Results Native state is ensemble of accessible structures at equilibrium Geometry Energy 80% correlation 94% correlation Spatial Constraints Energetic Constraints • Mobility for loop (51-76) of -Lac [3] (in blue) correlates well with results derived from experimental data [1]. • We want to retain part of the structure fixed • Collective motion of atoms • Conformations must be energetically feasible • Minimized PDB structure is reference conformation CI2 fragment mobility Our approach for sampling the native state ensemble: Combining Local Fluctuations Over the Whole Protein • Satisfy spatial constraints: • Molecule in initial reference conformation • 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: • Reference conformation with energy E0 • 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 1 (EC – E0)/RT • 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 e Q shown: [1] in red vs. this work’s results in blue shown: [9] in red vs. this work’s results in blue • 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 96% correlation Cyclic Coordinate Descent Boltzmann fluctuations 3JCC in red - 3JNC in blue 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 Experimental J couplings obtained from Chou J. J., Case D. A., and Bax A. JACS 125, 2003 Obtaining Residue Fluctuations Over the Whole Protein Conclusions Gaussian Confidence • 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 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 • 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 -0.5(x/)2 VlsE subunit 20-aa loop closed Schematic of the CCD algorithm e RMSD(x, R) Sampling Feasible Closure Conformations References -Lac ensemble • 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 M. Vendruscolo et al. JACS, 125, 2003 C. Eicken et al. JBC, 277, 2002 J. Ren et al. JBC, 268, 1993 S. E. Jackson et al. Biochemistry, 32, 1993 D. G. Luenberger. Linear and Non-linear Programming. Addison-Wesley, 1984 L. T. Wang and C. C. Chen. IEEE, 7, 1991 A. A. Canutescu and R. L. Dunbrack. Protein Science, 12, 2003 J. Yakey et al., IEEE, 17, 2001 K. 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, 2003 M. Karplus and J.A. McCammon. Nature Struct. Biol. 9, 2002  x = x – xc xc Residue fluctuations over ensemble of conformations for each region overlapped For questions, comments, and preprint requests: Amarda Shehu shehua@rice.edu Ubiquitin ensemble