CS2: 3D Fourier transforms and electron crystallography: Tubulin and FtsZ

1. CS2: 3D Fourier transforms and electron crystallography: Tubulin and FtsZ Biochemistry 655 14/1/11

2. Goals: • The phase problem; MODEL BIAS • Experimental phases from electron crystallography • Richard Henderson and Nigel Unwin • Introduce protein tertiary structure • “Rossmann fold” proteins (by far the largest class in the biome) • Structural homologies; eg. Tubulin, Ftsz • Nucleotide binding • Assembly • Modularity in tertiary structure: • Approximate internal symmetry • Binding sites (a-helices and phosphate binding)

3. The Fourier transform works in both directions • “Real space” and “Reciprocal space” • The two functional representations are “equivalent” • They are simply in different coordinate systems • With continuous, multidimensional objects, the Fourier coefficients become “complex-valued” • This means only that they are 2-valued vectors • Amplitude and phase • Most experiments measure only the amplitude • The phases contain nearly all of the structural information

4. Fourier transforms in structure determination Last time, you learned about amplitudes (REAL-valued coefficients). Actually, the coefficients of Fourier transforms (for crystal structures) are COMPLEX-valued. In addition to an amplitude, they also require a PHASE ANGLE. This gives rise to what is called the PHASE PROBLEM: Phases carry nearly all of the information about the structure. Phases are not generally measured experimentally.

5. A, B determine Phases, extending applications 0.7*sin(x)+0.714*cos(x) sine cosine Asin(x)+Bcos(x) 0.45*sin(x)+0.89*cos(x) sine cosine Asin(x)+Bcos(x)

6. Model Bias A. B. S(|Fh,A|eifB)e2pih•x S(|Fh,B|eifA)e2pih•x Read, R. J. (1997). Methods in Enzymology 277, 112-128.

7. 2D crystals of bacteriorhodopsin

8. Both Real and Reciprocal spaces are accessible with electrons! Real space Reciprocal space

9. The filtering power of averaging Object Filtered averages Image FT of image

10. Tomographic reconstruction (A. Klug)

11. Tubulin a-b dimer Kinesin binding site

12. Tubulin GTP-binding site GTP

13. N-terminal b-a-b crossover – possibly the most important subdomain in the proteome! Cammer & Carter 2010 Bioinformatics, 26:709-714

14. Kinemages • “Kinetic Images” - creation of David Richardson, Duke • Mage - public domain graphics program • http://kinemage.biochem.duke.edu • Also KING ==> better graphics, more memory • Rapid switching, animation • Good for authoring • Good for teaching • Much of the material in this course is enhanced by kinemages. • This case study has 2: • 1ftz.kin • Tubulin.kin