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
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: (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. B-factors
5 Å
7 Å
15 Å

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, (2001).

21. PDC is an extraordinarily flexible system
Conformational distribution of PDC complex from cryo-EM
Zhou et al, J. Biol. Chem. 276, (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: (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: parameters for refinement. No overfitting of data!!!
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
The overall architecture of GroEL contains 14 identical subunits that forms a two-stacked 7-fold ring with a large central cavity. It works with ATP and a co-chaperonin GroES which can bind at both ends of the rings.
Structures shown here are the ligand free form and ligand bound asymmetric
Complex. 3
175,000 A 3
85,000 A

51. Closed Open I H H I M M ATP Apical Intermediate Equatorial
…. Structures
The GroEL subunit undergoes dramatic conformational transition upon the binding of ligand. As ATP binds, the intermediate domain, especially this M helix comes down to close up the nucleotide binding pocket, and the apical domain vertically opens up so that the central cavity is drmatically enlarged.
Equatorial
ATP

52. En bloc rigid-body movements

55. Isotropic Thermal B-factors
Proteasome
Chaperonin GroEL

56. Isotropic Thermal B-factors
Proteasome
Chaperonin GroEL

58. Atomic anisotropic B-factors refined using 100 normal modes,
Note: GroEL has more than 50,000 heavy atoms.

59. Conclusion:
It is finally possible to use collective variables such as low-frequency normal modes to refine the anisotropic thermal parameters for large molecular complexes.

60. Under harmonic modal analysis, we have
unified the schemes in structural refinement
for three seemly remote experimental
techniques:
X-ray crystallography
Electron cryomicroscopy (cryo-EM)
Fibre diffraction

61. Motion is bad news for experimentalists!

62. Acknowledgements Yifei Kong (Baylor, SCBMB) Yinhao Wu (Rice, RQI)
Peng Ge (Rice, RQI)
Zhao Ge (Rice, RQI)
Jun Shen (Rice, RQI)
Billy Poon (Rice, Bioengineering)
Terence C. Flynn (Rice, Bioengineering)
William H. Noon (Rice, Bioengineering)
Dr. Dengming Ming
National Science Foundation (Early Career Award)
National Institutes of Health (R01-GM067801)
American Heart Association
Welch Foundation

63. Thank You Very Much