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 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 5 Å 7 Å 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: layerline index n: order of Bessel functions m: any integer t: number of helical turns u: 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: 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.

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

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

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

En bloc rigid-body movements

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 (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

Thank You Very Much