1. Dissertation Defense Thu Zar W. Lwin Departments of Chemistry and Molecular Biology and Biochemistry University of California at Irvine February 22, 2005 Application of Replica Exchange Method in Protein Folding Simulation

2. 20 natural amino acids - polar and non polar Hydrophobic core Ordered Secondary structures -  helix and  sheet - 33% in  helix, 33% in  sheet, - 33% in loops and turns How are the above structures formed? Basics of Protein Structure O O’ -

3. Structure of Beta Hairpin G E W T Y D D A T K T F T V T E - B1 Domain of Protein G in Streptococcal bacteria - Binds to mammalian IgG - NMR and X-ray ( , ,  - No disulfide bridges => Folding study - Fragmentation study - Stability in aqueous water - Initiation site for folding - Computational studies N C 16 residues

4. How does a protein spontaneously fold into its native structure? How do we predict a protein ’ s native structure from its sequence? Questions about Protein Folding How can we design a protein with a specified function?

5. Replica Exchange Method old new Hansmann, UHE (1997) Chem. Phys. Lett., 281:140-150 Efficient sampling of conformational space Can quickly reach to states available at specified temperature 18 replicas: 270K……………690K

6. Amber Force Field Model Amber CHARMM Cedar Gromos OPLS An all atom energy model

7. Outline Influences of solvent models - Explicit solvent vs. implicit solvent - PB vs. GB Influences of force field on secondary structure propensity Sampling algorithm - Test on model energy function - Ab initio folding

8. Motivation to Analyze Solvation Models Most populated structures Zhou,R. (2003) Proteins, 53:148-161 - These 2 degrees of freedom describe folding landscape - Rg(core) consists of residues that form hydrophobic core F, W, T, V => describes compactness of hydrophobic core - No. of H-bonds represent the secondary structure. (Explicit) (Implicit)

9. Explicit vs. Implicit Solvent Model Every atom of solvent molecule is represented No explicit representation a continuum medium ExplicitImplicit

10. Implicit Solvent: How do we do it? Solvation free energy

11. Components of the Solvation Energy Polar Solvation Models Solvent Accessible (SA) Model 1 PB/PBSA 2 GB/GBSA 1 Lu, Q. and Luo, R. (2003) J. Chem. Phys. 119:11035-11047 2 Onufriev, A. et al. (2004) Proteins 55:383-394 Amber99ci

12. Poisson-Boltzmann Model pp + + - - + + - -  Attempts to solve the Poisson-Boltzmann equation numerically ss Dielectric constant Electrostatic potential Charge density Charge of salt ion in solution

13. Generalized Born Model => It is an approximation to the PB equation. Electrostatic screening effect of salt Effective Born radius Solvent dielectric constant

14. Backbone RMSD (A) At 282K Are the conformations similar to crystal structure?

15. Misfolded Salt Bridges D46 E42 D47 E56 K50 SA appears to generate more mis-folded salt bridges.

16. Calculated NOE Distances 34: 5.52  6.21 A 35: 4.9  6.3 A Blanco, FJ. et al., (1994) Struct. Biol. 1:584-590 NOE pair #Type of proton coupling 1 – 10Intra-residue: H N ….. H CA 11 – 35 11 – 22 23 – 29 30 – 31 32 33, 34 35 Inter-residue: H N, H CA, H CB (i) H CA ….. (i+1) H N (i) H N ….. (i+1) H N H CA ….. H CA ( Y  F, W  V ) H CA ….. H E2 ( K  Y) H CA, H CB ….. H D2, H E1 ( Y  F ) H H2 ….. H CB ( W  F ) PB models agree NMR data. In NMR, the distance information for macromolecules can be obtained from Nuclear Overhauser Effect (NOE), transfer of spin polarization between nuclei. Rate of increase in NOE peak intensity Ç

17. Free Energy Landscape The problem is specific to GB model.

18. Native Contacts and Melting Temperatures of  -Hairpin Solvents%Native Contacts (273K) Melting temperature (K) PB81.6370 PBSA78.3400 GB66.5320 GBSA63.0350 Experiment80.0~300 Muñoz, V., et al. (1997) Nature, 390:196-199

19. Summary Performance of polar solvation based on PB is reasonably good. The nonpolar interaction needs to be better defined.

20. Outline Influences of solvent models - Explicit solvent vs. implicit solvent - PB vs. GB Influences of secondary structure propensity - Force fields Sampling algorithm - Test on model function - Ab initio folding

21. Why is Force Field Analysis Necessary? A Helical peptide can be erroneously folded into a beta-hairpin with Amber96. Ace – A 5 ( AAARA ) 3 A -- NME García, AE and Sanbonmatsu, KY (2002) Proc. Natl. Acad. Sci. USA, 99:2782-2787 Folded short (Fs) peptide

22. AMBER96 vs. QM RMSD 1.794kcal/mol kcal/mol Cond. Phase 300K AMBER96*Cond. Phase 300K QM/MM Amber96QM/MM Beta0.860.61 Pass0.020.16 Alpha R0.110.26 Alpha L0.000.07 Lu, Q. and Luo, R. ( In preparation) *H. Hu, et al., (2003) Proteins, 50: 451-463  

23. Amber94 Favors Helical Structures García, AE and Sanbonmatsu, KY (2001) Proteins, 42:345-354 Hairpin peptide can be erroneously folded into helix with Amber94.

24. AMBER94 vs. QM *Cond. Phase 300K QM/MMCond. Phase 300K AMBER94 RMSD 1.985 kcal/mol Lu, Q. and Luo, R. ( In preparation) kcal/mol Amber94QM/MM Beta0.170.61 Pass0.010.16 Alpha R0.820.26 Alpha L0.000.07 *H. Hu, et al., (2003) Proteins, 50: 451-463

25. Spline Fitting vs. QM Cond. Phase 300K Spline*Cond. Phase 300K QM/MM RMSD=0.0056kcal/mol kcal/mol Amber Spline QM/MM Beta0.660.61 Pass0.010.16 Alpha R0.210.26 Alpha L0.100.07 Lu, Q. and Luo, R. ( In preparation) *H. Hu, et al., (2003) Proteins, 50: 451-463

26. AMBER Force Fields 1.Amber03 Duan, Y. et al. (2003) J. Comput. Chem. 24:1999-2012. 2. Amber99ci Lu, Q. and Luo, R. (in preparation). 3. Amber99m2 Wang, J. and Luo, R. (in preparation). 4. Amber99m1 Simmerling, C. et al. (2002) J. A. Chem. Soc. 124:11258-11259. 5. Amber99off García, AE and Sanbonmatsu, KY (2002) Proc. Natl. Acad. Sci. USA 99:2782-2787. 6. Amber94 Cornell, WD, et al. (1995) J. Am. Chem. Soc. 117:5179-5197.

27. Comparing PME and PB using  -Hairpin Peptide RegionPMEPB Beta0.46 (0.10)0.53 (0.10) Pass0.02 (0.004)0.01 (0.008) Helix-R0.38 (0.09)0.26 (0.07) Helix-L0.09 (0.02)0.19 (0.02) State 40.01 (0.007)0.01 (0.005) RegionPMEPB Beta0.46 (0.10)0.53 (0.10) Pass0.02 (0.004)0.01 (0.008) Helix-R0.38 (0.09)0.26 (0.07) Helix-L0.09 (0.02)0.19 (0.02) State 40.01 (0.007)0.01 (0.005) Distribution of  /  angles from 10 residues in  sheet (450K) 6 force fields => 14  s Is PB good enough?

28. Comparisons Structure - Crystal structure => Native contact => Backbone RMSD - Experimental NOE - Secondary structure propensity Thermodynamics - Population => Fluorescence => NMR - Transition temperature Mechanism - Free energy landscape - Order of hydrogen bonding

29. Native Contact Fraction C  – C  distance of non-neighboring residue pairs => 6.5 A cut off distance => 21 pairs in crystal structure => Fractional number of pairs found in a conformation

30. Backbone RMSD The smaller the RMSD value, the better.

31. Distribution of Salt Bridges E42 E56 K50 D47 D46

32. NOE ff99ci in agreement with all NOE structural data.

33. Secondary Structure Propensity Gray: Helix Olive green: Beta-sheet Is there a balance between secondary structures?

34. Comparisons Structure - Crystal structure => Native contact => Backbone RMSD - Experimental NOE - Secondary structure propensity Thermodynamics - Native population => Fluorescence => NMR - Transition temperature Mechanism - Free energy landscape - Order of hydrogen bonding

35. Research group Type of Exp. Temperature (Kelvin) Hairpin population % Blanco (1994) NMR (direct) 27842 Fesinmeyer (2004) NMR (mutation) 27842  43 Fesinmeyer (2004) NMR (mutation) 29830 Comparison of  Hairpin Populations to NMR Force fieldAvg. % Population at 282 K ff0328 % ff99ci31 % ff99m24.6 % ff99m18.0 % ff99off1.5 % ff940.5 % Experimental data in aqueous water Simulations in PB solvent with dielectric 80.0

36. Comparison of Native Contact Populations to Fluorescence Data Population % (270 K) ff0374.4 ff99ci81.5 ff99m259.5 ff99m150.8 ff99off44.5 ff9443.4 Fluorescence Study (273 K)80.0 Muñoz, V., et al. (1997) Nature, 390:196-199

37. Transition Temperature (K) Muñoz, V., et al. (1997) Nature, 390:196-199 50% of  sheet population exits at transition temperature. T F (K) ff03385 ff99ci368 ff99m2368 ff99m1368 Fluorescence Study~300

38. Comparisons Structure - Crystal structure => Native contact => Backbone RMSD - Experimental NOE - Secondary structure propensity Thermodynamics - Population => Fluorescence => NMR - Transition temperature Mechanism - Free energy landscape - Order of hydrogen bonding

39. Free Energy Landscape Temperature 282K

40. Hydrogen Bonding Probability 3 > 5 > 4 > 24 > 5 > 3 > 27 > 4 > 5 > 3 5 > 4 > 3 > 67 > 5 > 4 > 67 > 6 3 > 5 > 4 > 24 > 5 > 3 > 2

41. Summary Out of 6 force fields, only the most recent 2 force fields (ff03 and ff99ci) treat the backbone torsion right Structure => can produce native like conformaitons. => mis-folded salt bridges can form in imperfect force fields. Thermodynamics => balance between  helical and  sheet structures Mechanism => L shaped landscape => Existence of intermediates and their locations depend on force fields.

42. Outline Influences of solvent models - Explicit solvent vs. implicit solvent - PB vs. GB Influences of secondary structure propensity - Force fields Sampling algorithm - Test on model function - Ab initio folding

43. Dill, K. A. and Chan, H. S., (1997) Nature Struct. Biol., 1:10-19. Residue Model All atom model Why New Method Necessary?

44. Dual REM

45. Model Energy: Global Optimization Thermodynamic Simulation Testing Dual REM  -Hairpin Peptide: Ab Initio Folding 16 residues G E W T Y D D A T K T F T V T E

46. 3004390 Instantaneous Energy to Global minimum Energy Model Efficiency 3d_2d14 5d_4d1 5d_3d43 5d_2d49

47. Distribution of Energy

48. Ergodicity

49. Comparing Imperfectness across Different Resolution Combinations _

50. Simulations PB REM 18 temps (18 nodes) 1 ps MD b/f rep. xch 5 replica xch b/f resol. xch *Lattice REM 9 temps one node 100 MC b/f rep. xch 10 replica xch. b/f resol. xch Simulated Annealing (2.5, 10 anneal step, 200 MC/step) Const. temp lattice run (200 MC) Reconstruction Gas/Min: 500 steps Heating: 100 steps Interface (400 trial exchanges) 270 K 0.90 295 K 0.98 Single PB REMs: Extended structure (5ns) Crystal structure (2ns) Dual REM (2 ns) Interface *MMTSB

51. Ab Initio Folding (RMSD) Dual REM can fold into native structure (1 to 2 Angstrom) Analysis on last 0.5 ns of simulation Dual REM0.2 ns Single REM> 5.0 ns

52. Summary Dual REM is faster than single REM in both testing scenarios. Limitations of this method are: => The imperfectness between the two resolutions must be small. => We have to use fairly efficient low resolution model. => The cost of computation for interface must be low. In our folding simulation, cost of computation for interface is very insignificant.

53. Future Directions Better treatment to the non polar solvation. Similar testing on helical peptide in force field analysis. Improvement on ff99ci with condensed phase QM calculations. Testing of Ab Initio folding on a protein that contains both kind of secondary structures, such as domain B1 of protein G.

54. Acknowledgements Mengjuei Hsieh Morris Chen Dr. Qiang Lu Dr. Chuck Tan Dr. Yu-Hong Tan Dr. Lijiang Yang Department of Chemistry Chemical and Material Physics Program UC Regents Dissertation Fellowship Committee Members: Professor Ray Luo Professor Douglas J. Tobias Professor David A. Brant