Transcript Document

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 Ma
Baylor 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
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.
B-factors
5Å
7Å
15 Å
Atomic Displacement of Low-frequency mode
Standard NMA
QEDM at 5 Å
QEDM at 7 Å
QEDM at 15 Å
Pyruvate Dehydrogenase Complexes (25Å)
Truncated E2 core
Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).
PDC is an extraordinarily flexible system
Conformational distribution of PDC complex from cryo-EM
Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).
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
filament
filament
Lowest-frequency modes in the synthesized system
Bending
Twisting
Stretching
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
Lowest-frequency modes in the synthesized system
Bending
Twisting
Stretching
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:
n:
m:
t:
u:
layerline index
order of Bessel functions
any integer
number of helical turns
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
Molecular Chaperonin GroEL
GroES
GroEL
3
3
85,000 A
175,000 A
Closed
Open
H
H
I
Apical
I
M
Intermediate
M
Equatorial
ATP
En bloc rigid-body movements
90
A
Upper hinge
I
Lower hinge
25
E
60
Isotropic Thermal B-factors
Proteasome
Chaperonin GroEL
Isotropic Thermal B-factors
Proteasome
Chaperonin GroEL
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!
Acknowledgements
Yifei Kong
Yinhao Wu
Peng Ge
Zhao Ge
Jun Shen
Billy Poon
Terence C. Flynn
William H. Noon
(Baylor, SCBMB)
(Rice, RQI)
(Rice, RQI)
(Rice, RQI)
(Rice, RQI)
(Rice, Bioengineering)
(Rice, Bioengineering)
(Rice, Bioengineering)
Dr. Dengming Ming
National Science Foundation (Early Career Award)
National Institutes of Health (R01-GM067801)
American Heart Association
Welch Foundation
Thank You Very Much