Modeling and Refinement of Structural Motions in Biological Macromolecules

2. For Biological Macromolecules:

3. For Biological Macromolecules: • Motion is an integral part of function

4. For Biological Macromolecules: • Motion is an integral part of function • Motion is good for theoreticians like me

5. For Biological Macromolecules: • Motion is an integral part of function • Motion is good for theoreticians like me • Motion is always bad for experimental • structural biologists

6. Conformational changes in Calmodulin

7. G-protein transducin

8. Mechanosensitive channel, MscL

9. Mechanosensitive channel, MscL

10. F1-ATP Synthase, molecular motor

11. Challenges:

12. Challenges: • Motions occur over a wide range of length scale,

13. Challenges: • Motions occur over a wide range of length scale, • Structural data are available at varying resolutions,

14. Challenges: • Motions occur over a wide range of length scale, • Structural data are available at varying resolutions, • How do we simulate, refine & model structures?

15. Simulating, Refining & Modeling Supermolecular Complexes at Multi-resolution and Multi-length Scales Jianpeng Ma Baylor College of Medicine Rice University

16. I. Simulation and Refinement at Multi-resolution Scales Quantized Elastic Deformational Model (QEDM) Proc. Natl. Acad. Sci. USA 99:8620-5 (2002) modeling structural motions without atomic coordinates and amino-acid sequence

17. Procedures of QEDM • Discretize low-resolution density maps by • Vector Quantization or • Cubic grid points of cryo-EM density maps Apply elastic normal mode analysis to the discretized density maps. For very low-frequency deformational modes, the number of points can be significantly smaller than the number of amino-acids.

18. 5 Å 7 Å 15 Å B-factors

19. Atomic Displacement of Low-frequency mode Standard NMA QEDM at 5 Å QEDM at 7 Å QEDM at 15 Å

20. Pyruvate Dehydrogenase Complexes (25Å) Truncated E2 core Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).

21. PDC is an extraordinarily flexible system Conformational distribution of PDC complex from cryo-EM Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).

22. 20 % size variation

23. 20 % size variation

25. Human Fatty Acid Synthase (FAS) at 19 Å Resolution Proc. Natl. Acad. Sci. USA 99:138-43 (2002)

28. Experimental Verification & QEDM-assisted cryo-EM Refinement

30. Conclusions of QEDM: • Capable of simulating low-frequency deformational motions of proteins based on low-resolution density maps. • Provide useful insights into protein functions in the absence of detailed atomic model. • Provide a means to aid structural refinement in cryo-EM measurements.

31. II. Simulation and Refinement at Multi-length Scales Substructure Synthesis Method (SSM) Proc. Natl. Acad. Sci. USA 100:104-9 (2003) modeling structural motions of filamentous systems from angstroms to microns

32. Modal Synthesis Procedure in SSM • Compute substructure modes by standard normal mode analysis. • Substructures are assembled by imposing geometric boundary conditions. • Calculate the modes for assembled structure by Rayleigh-Ritz principle. • Focus on a set of low-frequency modes. • Does not need to compute Hessian matrix for the assembled structure.

33. G-actin monomer A 13-subunit repeat of F-actin filament 37.5 Å

34. Selected boundary points across the interface filament filament

35. Lowest-frequency modes in the synthesized system Bending Twisting Stretching

36. Bending Modes for F-actin Filament of 4.6 Microns

37. Refining Fibre Diffraction Data by Long-range Normal Modes

38. Rosalind Franklin, 1951

39. In Traditional Fibre Diffraction Refinement: • The filaments are assumed to be a straight helix. • But the filaments like F-actin or DNA molecules deform due to their high flexibility.

40. Challenge: How do we find proper structural parameters to model the filamentous deformations without overfitting the data?

41. We chose long-range normal modes of the filaments as refinement parameters.

42. G-actin monomer A 13-subunit repeat of F-actin filament 37.5 Å

43. Lowest-frequency modes in the synthesized system Bending Twisting Stretching

44. Refinement based on long-range normal modes Helical selection rule: l=tn+um t=6, u=13 (conventional method) t=6 (or 12, …), u=1 (our method) l: layerline index n: order of Bessel functions m: any integer t: number of helical turns u: number of asymmetric unit in one crossover

45. Refinement by single low-frequency vibrational normal mode (13-subunit repeat normal modes)

46. Bending Modes for F-actin Filament

47. Refinement by multiple modes and different length of repeat

48. Conclusion: • Normal modes are good collective variables as structural parameters for refinement. No overfitting of data!!! • Bending motions dominate the contributions, i.e. the filament wiggling motions must be included in the refinement and errors from them can not be compensated from adjusting other local structural parameters.

49. III. Refinement of Anisotropic Temperature Factors for Supermolecular Complexes in x-ray Crystallography

50. Molecular Chaperonin GroEL GroES GroEL 3 175,000 A 3 85,000 A