For Biological Macromolecules:

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For Biological Macromolecules
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• For Biological Macromolecules
• Motion is an integral part of function

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

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• 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

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Conformational changes in Calmodulin
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G-protein transducin
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Mechanosensitive channel, MscL
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Mechanosensitive channel, MscL
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F1-ATP Synthase, molecular motor
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Challenges
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• Challenges
• Motions occur over a wide range of
• length scale,

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

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

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Simulating, Refining Modeling Supermolecular
Complexes at Multi-resolution and Multi-length
Scales Jianpeng Ma Baylor College of
Medicine Rice University
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I. Simulation and Refinement at Multi-resolution
Scales Quantized Elastic Deformational Model
(QEDM) Proc. Natl. Acad. Sci. USA 998620-5
(2002) modeling structural motions without
atomic coordinates and amino-acid sequence
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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.

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B-factors
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Atomic Displacement of Low-frequency mode
Standard NMA
QEDM at 5 Å
QEDM at 7 Å
QEDM at 15 Å
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Pyruvate Dehydrogenase Complexes (25Å)
Truncated E2 core
Zhou et al, J. Biol. Chem. 276, 21704-21713
(2001).
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PDC is an extraordinarily flexible system
Conformational distribution of PDC complex from
cryo-EM
Zhou et al, J. Biol. Chem. 276, 21704-21713
(2001).
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20 size variation
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20 size variation
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Human Fatty Acid Synthase (FAS) at 19 Å Resolution
Proc. Natl. Acad. Sci. USA 99138-43 (2002)
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Experimental Verification QEDM-assisted cryo-EM
Refinement
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• 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.

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II. Simulation and Refinement at Multi-length
Scales Substructure Synthesis Method (SSM) Proc.
Natl. Acad. Sci. USA 100104-9 (2003) modeling
structural motions of filamentous systems from
angstroms to microns
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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.

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G-actin monomer
A 13-subunit repeat of F-actin filament
37.5 Å
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Selected boundary points across the interface
filament
filament
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Lowest-frequency modes in the synthesized system
Bending
Twisting
Stretching
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Bending Modes for F-actin Filament of 4.6 Microns
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• Refining Fibre Diffraction Data by
• Long-range Normal Modes

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Rosalind Franklin, 1951
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• 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.

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Challenge How do we find proper structural
parameters to model the filamentous deformations
without overfitting the data?
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We chose long-range normal modes of the
filaments as refinement parameters.
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G-actin monomer
A 13-subunit repeat of F-actin filament
37.5 Å
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Lowest-frequency modes in the synthesized system
Bending
Twisting
Stretching
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Refinement based on long-range normal modes
Helical selection rule ltnum t6, u13
(conventional method) t6 (or 12, ), u1 (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
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Refinement by single low-frequency vibrational
normal mode (13-subunit repeat normal modes)
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Bending Modes for F-actin Filament
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Refinement by multiple modes and different length
of repeat
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• 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.

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III. Refinement of Anisotropic Temperature
Factors for Supermolecular Complexes in x-ray
Crystallography
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Molecular Chaperonin GroEL
GroES
GroEL
3
175,000 A
3
85,000 A
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Closed
Open
I
H
H
Apical
I
M
Intermediate
M
Equatorial
ATP
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En bloc rigid-body movements
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Isotropic Thermal B-factors
Proteasome
Chaperonin GroEL
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Isotropic Thermal B-factors
Proteasome
Chaperonin GroEL
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Atomic anisotropic B-factors refined using 100
normal modes, Note GroEL has more than 50,000
heavy atoms.
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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.
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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
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Motion is bad news for experimentalists!
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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
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Thank You Very Much