MCB 111/211 2006

1/3

Problem set 1. Protein structure and X-ray crystallography 1. Local structure. 1a. Ramachandran explored the hard sphere contacts that limit protein main chain conformations. How would you recognize a helix on a Ramachandran diagram? 1b. What is the significance of residues that fall into the “disallowed” region of a Ramachandran diagram. 1c. In the 1980s, several groups realized that side chains adopt common structures that they called rotamers. What is a rotamer and why are rotamers important? 2. Structure classification. 2a. What distinguishes proteins in the α, β and α/β classes? What is the significance of the distinctions between these classes? 2b. What is meant by the topology of a protein? 3. Structure quality. The structure of the 129-amino-acid cytokine, IL-4, was determined

independently by two different NMR groups and two different x-ray crystallography groups (Smith et al. (1994) Nature Structural Biology 1, 301-310). All the groups used essentially the same protein, and all the structures had the same fold in which a short, two-stranded antiparallel β-sheet is packed against a four-helix bundle .

The two crystallography groups analyzed identical crystals. To obtain phases, group 1 used

five heavy atom derivatives and group 2 used two different heavy atom derivatives. Both groups refined their structures (Table 1), and both models agreed well with ideal geometry of the amino acids. The root-mean-square deviation (rmsd) of the Cα atoms 4 - 127 in the two crystal structures was 0.5 Å.

Table 1. Refinement statistics for IL-4 X-ray crystal structures Resolution # of Reflections Data completeness R factor Group 1 10-2.25 8085 93% 0.218 Group 2 6-2.35 7470 83% 0.232 3a. Briefly describe the steps in the process of crystallographic refinement, and list three reasons

for refining a crystal structure (i.e. what new information is obtained from the refined structure that is not obtained from the starting model?).

3b. What is the crystallographic R value and why does the deviation of the model from ideal geometry influence the R value? 3c. Which IL-4 crystal structure do you judge to be more reliable? List two reasons for your answer. 3d. Three loops had high crystallographic B values in both refined crystal structures. List three possible reasons for the high B's.

MCB 111/211 2006

2/3

3e. Propose two experiments to investigate the possible reasons for the high B values of the loops.

4. The structure of T. aquaticus mutS, a 780-residue, DNA-mismatch-repair protein, was

determined in the presence and absence of a DNA duplex containing a single mismatch (Nature 407, 703 (2000)). The DNA complex was solved by MAD phasing of a selenomethionine derivative, and the apoprotein structure was determined by molecular replacement using the protein model from the DNA complex. The refinement statistics are shown in Table 1.

Table 1. Crystal (space group) MutS-DNA (p212121) MutS (p3121) Unit cell (a,b,c) (Å) 103.2, 114.2, 160.8 96.7, 96.7, 427.1 Non-hydrogen atoms 13728 7594 Resolution range 26.6 – 2.2 Å 20.0 – 3.2 Å Rmerge 0.075 (0.309) 0.067 (0.443) Unique reflections 97368 30381 Completeness (%) 97.3 (90.9) 88.6 (85.3)

R-value (Rfree) 0.227 (0.259) 0.331 (0.361) r.m.s.d. bond length (Å) 0.006 0.010 r.m.s.d. bond angle (°) 1.3 1.4 The DNA complex revealed that each subunit of the mutS dimer contains five distinct

domains. Electron density for two of these domains, corresponding to ~270 amino acids, was totally absent in the apoprotein structure.

4a. Why was it necessary to prepare the selenomethionine derivative of MutS (instead of using

normal met) for MAD phasing? 4b. Which structure, the DNA complex or the apoprotein, is more accurate? Give three reasons

that support your answer. 4c. What do you conclude from the R/Rfree values of 0.33/0.36 for the apoprotein structure? 4d. List two experimental approaches to determine if the 270 disordered residues in the

apoprotein are unfolded (as opposed to folded and packed in different positions) in the absence of DNA.

5. Assuming you are using 1.0 Å wavelength X-rays, what is the scattering angle for reflections

at 3.0 Å resolution? 2.0 Å resolution? and 1.5 Å resolution. Recall that the scattering angle is 2x the angle θ in Bragg’s Law.

6. The crystal structure of aquaporin, a transmembrane water channel from E. coli (Tajkhorshid,

E., et al. (2002). Science 296, 525-30) revealed the average positions of water molecules in the channel (Fig. 1). Tajkhorshid and coworkers suggested that the protein orients the water molecules to avoid forming a “proton wire” that would depolarize the cell.

MCB 111/211 2006

3/3

6a. Did the authors directly observe the hydrogen atom positions on the water molecules in the 2.7 Å (wt) and 2.1 Å (mutant) resolution electron density maps?

6b. If not, how were the hydrogen bond partners and orientations determined? Fig. 1. Electron density in the GlpF channel at 2.7 Å resolution (left) and in the selectivity filter at 2.1 Å resolution (right).

7. Find the letter below that best matches the following statements. Each letter may be used

only once. A. <3.5 Å J. multiple isomorphous replacement B. < 6 Å K. β-barrel C. molecular replacement L. B value D. omega loop M. R value E. offset of a FT term from the unit cell origin N. β-turn F. unit cell O. scattered X-ray intensity G. resolution P. exposed in many structures H. usually contains > 4 strands Q. asymmetric unit I. image of a single, isolated molecule R. time and space average i) ______ used to determine the crystal structure of an unknown fold ii) ______ phase iii) ______ capable of spanning a membrane iv) ______ reverses polypeptide chain direction in four amino acids v) ______ nature of crystal structures vi) ______ antiparallel β-sheet vii) ______ parallel β-sheet viii) ______ resolution required to trace a protein chain using the sequence ix) ______ minimum repeat related to the rest of the crystal by translations only x) ______ crystallographic measure of disorder