For Biological Macromolecules:
For Biological Macromolecules:
• Motion is an integral part of function
For Biological Macromolecules:
• Motion is an integral part of function
• Motion is good for theoreticians like me
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
Conformational changes in Calmodulin
G-protein transducin
Mechanosensitive channel, MscL
Mechanosensitive channel, MscL
F1-ATP Synthase, molecular motor
Challenges:
Challenges: • Motions occur over a wide range of length scale,
Challenges: • Motions occur over a wide range of length scale,
• Structural data are available at varying resolutions,
Challenges: • Motions occur over a wide range of length scale,
• Structural data are available at varying resolutions,
• How do we simulate, refine & model structures?
Simulating, Refining & Modeling Supermolecular Complexes
at Multi-resolution and Multi-length Scales
Jianpeng MaBaylor College of Medicine
Rice University
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
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.
Procedures of QEDM
5 Å 7 Å 15 Å
B-factors
Standard NMA
QEDM at 5 Å
QEDM at 7 Å
QEDM at 15 Å
Atomic Displacement of Low-frequency mode
Pyruvate Dehydrogenase Complexes (25Å)
Truncated E2 core
Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).
Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).
Conformational distribution of PDC complex from cryo-EM
PDC is an extraordinarily flexible system
20 % size variation
20 % size variation
Human Fatty Acid Synthase (FAS) at 19 Å Resolution
Proc. Natl. Acad. Sci. USA 99:138-43 (2002)
Experimental Verification&
QEDM-assisted cryo-EM Refinement
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.
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
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.
G-actin monomer
A 13-subunit repeat of F-actin filament
37.5 Å
Selected boundary points across the interface
filamentfilament
Bending
Twisting
Stretching
Lowest-frequency modes in the synthesized system
Bending Modes for F-actin Filament of 4.6 Microns
Refining Fibre Diffraction Data by
Long-range Normal Modes
Rosalind Franklin, 1951
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.
Challenge:
How do we find proper structural parameters to model the filamentous deformations without overfitting the data?
We chose long-range normal modes of the filaments as refinement parameters.
G-actin monomer
A 13-subunit repeat of F-actin filament
37.5 Å
Bending
Twisting
Stretching
Lowest-frequency modes in the synthesized system
Refinement based on long-range normal modes
Helical selection rule: l=tn+umt=6, u=13 (conventional method)t=6 (or 12, …), u=1 (our method)
l: layerline indexn: order of Bessel functionsm: any integert: number of helical turnsu: number of asymmetric unit in one crossover
Refinement by single low-frequency vibrational normal mode(13-subunit repeat normal modes)
Bending Modes for F-actin Filament
Refinement by multiple modes and different length of repeat
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.
III. Refinement of Anisotropic
Temperature Factors for Supermolecular
Complexes in x-ray Crystallography
175,000 A85,000 A
33
GroES
GroEL
Molecular Chaperonin GroEL
I
H
HI
M M
Apical
Equatorial
Intermediate
ATP
Closed Open
E
I
A
25
90 60
Lower hinge
Upper hinge
En bloc rigid-body movements
Chaperonin GroELProteasome
Isotropic Thermal B-factors
Chaperonin GroELProteasome
Isotropic Thermal B-factors
Atomic anisotropic B-factors refined using 100 normal modes,Note: GroEL has more than 50,000 heavy atoms.
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.
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
Motion is bad news for experimentalists!
AcknowledgementsYifei 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 AssociationWelch Foundation
Thank You Very Much