Challenges in generation of conformational ensembles for peptides and small proteins

Transcription

1 Challenges in generation of conformational ensembles for peptides and small proteins Carlos Simmerling Stony Brook University What could (and does) go wrong? 1. Sampling: difficult to obtain converged ensembles, long-timescale dynamics 2. Force field errors 4 Functional form 4 Inaccurate parameters 4 Treatment of solvent 3. Validation against experimental data 4 Usually need to overcome (1) to improve (2) 1

2 Force field problems >1 million decoys AMBER ff94, ff99 Native not lowest energy = refit prehistoric using decoys? Okur, Strockbine, Hornak, Simmerling, J. Comp. Chem Trpzip2 indole stacking Our model 1HRX 1LE1 4us: the stacking of the outer Trp side chains differs from the published structures 41LE1: updated coordinates differ from the previous ones in the side chain orientations of Trp4 and Trp11 2

3 Model system: trpzip2 β-hairpin 1 Reference data: 150 ns standard REMD (GB, ffga) Thermal profiles independent of initial structure Good model: expt. T m = 345K 1 1 Cochran, Skelton & Starovasnik, PNAS 2001 Trp-cage tc5b mini-protein 4Small, stable and folds quickly 420 residues 498% folded at 280K 4Folding time of 4µsec 4Blind prediction using MD simulations and energy hydrophobic core N α helix i:i 5 C 3 10 helix PP ΙΙ i:i+10 NMR-based structure: Neidigh, Fesinmeyer, Andersen, NSB 2002 Folding rate: Qiu, Pabit, Roitberg, Hagen JACS 2002r Structure prediction: Simmerling, Strockbine, Roitberg, JACS 2002 MD low energy 1L2Y model 1 3

4 Comparison of Amber parameter sets 4 Gly bb is treated differently than others in Amber 4 Study capped Ala 3 and Gly 3 4 TIP3P explicit water 4 MD, REMD converged ensembles at 300K 4 Multiple existing Amber parameter sets 4 Compare to our new ff99sb based on backbone refitting with QM data (LMP2/cc-pVTZ(-f)) for multiple conformations of Ala 3 and Gly 3 Hornak, Abel, Okur, Strockbine, Roitberg and Simmerling, Proteins 2006 Gly 3 Ensembles in explicit water Ala 3, Gly 3 in explicit water Ala 3 Gly often very unreasonable Ala basins quite sensitive Hornak, Abel, Okur, Strockbine, Roitberg and Simmerling, Proteins

5 Gly: chemical shifts for simulation ensemble (SHIFTS, D. Case) Experiment: Random coil ~4ppm Folded state stereospecific HA2 ~ 0.96 HA3 ~ 3.43 Dynamics: agreement with NMR improved Hornak, Abel, Okur, Strockbine, Roitberg and Simmerling, Proteins qualitatively better than previous force fields 4 yields NMR spin relaxation parameters in near quantitative agreement with experimental values 4RDC accuracy that is comparable to or better than the best static structural models and the NMR ensemble Showalter and Brüschweiler, JCTC 2007, JACS

6 HP36: a model system for protein folding. Folded/unfolded state? 4 NMR and X-ray structure differ: 4 core packing, hydrogen bonds, length of the helices 4 Sequence (HP35 N68H vs HP36) 4 ph, temperature X-ray = Yellow NMR = Blue McKnight, Matsudaira,Kim Nat. Struct. Biol, 1996 Chiu, Kubelka, Herbst-Irmer, Eaton, Hofrichter, Davies, PNAS 2005 MD results (explicit water) 4Simulations compared to both experimental coordinate sets Xray ref NMR ref 4MD always moves closer to X-ray 4Validated using expt. double mutant cycles Blue = NMR Yellow = X-ray Green = Simulation WIckstrom, Bi, Hornak, Raleigh and Simmerling, Biochemistry

7 Is there local structure in HP36 unfolded state? HP-3 HP-2 HP-1 REMD in TIP3P Independent initial coordinates Modest native HP-1 population No helix in polyala of same length Trends match experiment Tang, Rigotti, Fairman,. & Raleigh, Biochemistry (2004) Wickstrom, Okur, Song, Hornak, Raleigh & Simmerling, JMB 2006 HP21 : see Lauren Wickstrom s poster 7

8 Decoy-based (GB) parameters ffga, 2002 Ala tetrapeptide QM parameters ff99mod2, 2002 Ala and Gly tetrapeptide QM + tetrapeptide REMD in TIP3P + decoy screening: ff99sb, 2005 All retain ff94 RESP charge model (unlike ff03) Does GB give good results? 8

9 Influence of GB on secondary structure Capped Ala 10 (no salt bridges, etc) REMD: TIP3P, GB HCT, GB OBC, GB neck G solv : PB, GB HCT, GB OBC, GB neck, TIP3P (TI) Roe and Simmerling, J. Phys. Chem. B, 2006 Ala 10 ensembles: GB vs. TIP3P Error bars reflect the difference between 2 REMD Simulations of Ala10 from different initial conformations. Different solvent models give different secondary structure populations. Roe and Simmerling, J. Phys. Chem. B,

10 Comparing Differences in G Pol, G Pol PP2 Collapsed GPol RMSD from TIP3P PE GBHCT Collapsed GBOBC GBNeck Overall PP2 Collapsed Collapsed Analogous to folding GB is qualitative (at least ones in Amber) Ion pairing, secondary structure peptides are particularly sensitive Explicit water is costly Viscosity Dependence of # REMD replicas on system size Partial REMD 1 Hybrid solvent REMD 2 1 Cheng, Cui, Hornak & Simmerling, J. Phys. Chem. B, Okur, Wickstrom, Layten, Geney, Song, Hornak & Simmerling, J. Chem. Theory Comp.,

11 Temperature Replica Exchange 4MD runs over range of T 4Periodically swap structures 4Faster convergence 4Populations as a function of T 4Drawback: E must be small small T for large systems REMD Hansmann, U., CPL 1997 Sugita & Okamoto, CPL 1999 W 300K 325K 350K 375K 4 Impose reversibility/detailed balance I ( X ) w( X X ) = W( X ') w( X ' X ) 4Impose limiting distribution on exchange calculation W = P exch ( X ) = e( β ) E X ( β β )( E E ) n m ( ( ) ) = min 1,exp i j REMD is more efficient than MD REMD MD 4Levy: systems where temperature helps folding rate! 11

12 MD vs. REMD for β-sheet, GB solvent MD N Replica exchange Roe, Hornak and Simmerling, J. Mol. Biol Improving REMD in explicit water Replica requirement Convergence rate 12

13 Better scaling using a hybrid solvent model Perform simulations in full periodic box of explicit solvent Retain only first shell of water + reaction field in exchange calculation Smaller perceived system size permits fewer replicas Avoids problems associated with hybrid solvent MD Approximate since Hamiltonian during exchange not same as during MD Okur, Wickstrom, Layten, Geney, Song, Hornak & Simmerling, J. Chem. Theory Comp., 2006 Hybrid solvent REMD: polyala Ala 10 Explicit Solvent GB OBC Hybrid GB OBC + 1 st shell α 24.9 ± ± ± 1.6 β 19.5 ± ± ± 1.6 P II 39.5 ± ± ± 0.5 α L 8.4 ± ± ± 0.3 SASA ± ± ± 2.5 Alanine dipeptide insensitive to solvent model Alanine tetrapeptide and Ala 10 reveal GB weaknesses Hybrid explicit+gb is in agreement with TIP3P: PPII Okur, Wickstrom, Layten, Geney, Song, Hornak & Simmerling, J. Chem. Theory Comp.,

14 Salt bridges: Ace-Arg-Ala-Ala-Glu-NH 2 TIP3P standard REMD : 46 replicas, 296K to 584K (15%) GB standard REMD: 6 replicas, 300K to 636K Hybrid solvent REMD: 8 replicas, 280K to 570K, 75 water molecules in hybrid shell Okur, Wickstrom & Simmerling, JCTC in press GB Salt bridge PMFs TIP3P, hybrid GB Poor correlation between backbone conformation in GB/TIP3P Improved correlation with hybrid GB salt bridge 2-3 kcal too strong Improved PMF with hybrid Restrained backbone Hybrid reproduces solvent separated mimimum Geney, Layten, Gomperts, Hornak and Simmerling, JCTC 2006 Okur, Wickstrom & Simmerling, JCTC in press 14

15 HP-1 with hybrid solvent REMD MLSDEDFKAVFGM Helical content Hybrid solvent model again significantly improves agreement with standard REMD in explicit solvent Some residual GB-like behavior in hybrid model at low T Use PB, include dispersion term Okur, Wickstrom & Simmerling, JCTC in press Hybrid solvent allows explicit water at nearly the same # replicas as GB. What can we do about REMD convergence rates? 15

16 300K REMD with a structure reservoir 325K 350K 375K 400K J-walk into reservoir Frantz, Freeman & Doll, JCP steps: (1) generate reservoir, (2) run REMD 4uncouple slow, high T sampling from many-replica reweighting Zuckerman PRL 2006, Yang JCP 2006, Simmerling, JCTC 2007 R-REMD results: trpzip2 in GB R-REMD: 10,000 structures and velocities from 400K MD Resulting data are in good agreement with standard REMD 350K ensembles Okur, Wickstrom, Simmerling, JCTC 2007 R 2 > 0.99 R 2 = 0.96 without largest cluster 16

17 Accuracy good, what about efficiency? dpdp 3-stranded β-sheet 1 6 replicas up to 400K, 50ns (300ns) 260ns MD for reservoir Melting profile matches std REMD 2 R-REMD converges much faster even when we include reservoir generation 1 Schenck & Gellman, JACS Roe, Hornak & Simmerling, JMB 2005 (ps) 17

18 R-REMD in explicit water Ala 10 HP-1 R-REMD vs. standard REMD Wickstrom and Simmerling, in prep Reservoir must be Boltzmann weighted (detailed balance) Very difficult to generate, especially in explicit water Reservoir is at high T: faster equilibration, best aspect of REMD Is this ensemble really a requirement? 18

19 W REMD with non-boltzmann reservoir W 300K 325K 350K 375K reservoir 4Impose reversibility/detailed balance I ( X ) w( X X ) = W( X ') w( X ' X ) ( X ) = e( β ) E X = β ( E ) i E j W ( X ) 1 ' = N 4Exchange with reservoir employs new equation 4All other pairs use standard exchange criterion ( β) Roitberg, Okur and Simmerling, JPC B, 2007 Trpzip2 REMD with non-boltzmann reservoir 669 structures in flat cluster reservoir (only 1 native) Correct thermal profile is obtained only with new exchange equation Roitberg, Okur and Simmerling, JPC B,

20 P Using a non-boltzmann reservoir with user-specified probabilities exchange j β ( E ) ( ) i E q, T; q, R q, T; q, R e j i Desirable to expand reservoir (or even build it during the REMD run) j j i N N i ( ) Requires assignment of reservoir weight to replica MD structures Use dihedral angle grid-based weights D. Zuckerman, black box reweighting probability density in dihedral space cluster volume is better defined than RMSD-based approach Roe and Simmerling, in prep Trpzip2/GB with weighted non-boltzmann reservoir Standard REMD Grid-weighted reservoir Standard REMD Grid-weighted reservoir Use of reservoir speeds convergence Populations in reservoir can be arbitrary and dynamic 20

21 Convergence comparison at 300K trpzip2 grid N-B R-REMD in TIP3P 60ns 360ns Standard REMD nearly impossible to converge 4 Needs >30 folding events ~10ns grid-weighted non- Boltzmann R-REMD J-walk into REMD history, in addition to high T sampling 21

22 Goal: thermodynamic ensembles in explicit solvent at relevant temperatures 1. Standard REMD: converge large # of T 2. Hybrid solvent REMD: converge smaller # of T 3. REMD with converge at 1 high T, Boltzmann reservoir get data for lower T 4. REMD with no need to sample non-boltzmann reservoir converged ensemble in MD? 5. REMD using variables other than temperature Applying what we have learned to larger systems - Which protein parameters are best? - How well do various water models perform? - And so on 22

23 HIV-1 protease and peptide substrate Model for dynamic behavior of HIV PR closed bound enzyme semi-open unbound enzyme Hornak, Okur, Rizzo and Simmerling, PNAS 2006 Layten, Hornak and Simmerling, JACS 2006 Hornak, Okur, Rizzo and Simmerling JACS 2006 Hornak and Simmerling, Drug Discovery Today,

24 Summary Force fields and solvent models continue to evolve. Both can introduce biases. Some should be retired. Sampling and accuracy are coupled, especially solvent Standard REMD converges slowly, requires many replicas Replica requirement can be reduced Sampling problem can be decoupled from REMD Structure diversity from other methods can speed convergence of MD-based sampling 4Asim Okur, Dan Roe, Lauren Wickstrom, Ding Fangyu 4Melinda Layten, Salma Rafi, Kun Song, Catherine Kelso, AJ Campbell, Christina Bergonzo Acknowledgements 4NIH, NCSA 4Adrian Roitberg (U Florida) Postdoc positions available! 24

25 Table 4. GB Effective Radii Average RMSD from Perfect (PE) Radii (Ǻ) A) All GBHCT GBOBC GBNeck F) C GBHCT GBOBC GBNeck alpha 0.25 ± ± ± 0.02 alpha 0.16 ± ± ± 0.03 hairpin 0.18 ± ± ± 0.01 hairpin 0.08 ± ± ± 0.02 left 0.20 ± ± ± 0.03 left 0.12 ± ± ± 0.04 pp ± ± ± 0.00 pp ± ± ± 0.01 B) BB GBHCT GBOBC GBNeck G) CA GBHCT GBOBC GBNeck alpha 0.35 ± ± ± 0.03 alpha 0.05 ± ± ± 0.02 hairpin 0.20 ± ± ± 0.01 hairpin 0.09 ± ± ± 0.01 left 0.27 ± ± ± 0.04 left 0.07 ± ± ± 0.03 pp ± ± ± 0.00 pp ± ± ± 0.01 C) H GBHCT GBOBC GBNeck H) CB GBHCT GBOBC GBNeck alpha 0.71 ± ± ± 0.06 alpha 0.03 ± ± ± 0.01 hairpin 0.39 ± ± ± 0.03 hairpin 0.04 ± ± ± 0.00 left 0.50 ± ± ± 0.06 left 0.01 ± ± ± 0.00 pp ± ± ± 0.00 pp ± ± ± 0.00 D) O GBHCT GBOBC GBNeck I) HA GBHCT GBOBC GBNeck alpha 0.16 ± ± ± 0.02 alpha 0.07 ± ± ± 0.01 hairpin 0.16 ± ± ± 0.02 hairpin 0.34 ± ± ± 0.03 left 0.18 ± ± ± 0.02 left 0.10 ± ± ± 0.02 pp ± ± ± 0.00 pp ± ± ± 0.00 E) N GBHCT GBOBC GBNeck alpha 0.26 ± ± ± 0.04 hairpin 0.16 ± ± ± 0.02 left 0.27 ± ± ± 0.05 pp ± ± ± 0.01 J) Overall Averages GBHCT GBOBC GBNeck GBHCT GBOBC GBNeck All C BB CA H CB O HA N for Peter 25