Solving the Phases

1. To solve the structure of a protein by MIR, one must collect the structure factor amplitudes from a native protein crystal |FP(h k l)|, along with those of at least two isomorphous heavy atom derivatives |FP+H1(h k l)| and |FP+H2(h k l)|. One must then take differences to estimate |FH1(h k l)| and FH2(h k l)|, then solve the Patterson's of the heavy atoms to obtain their x y z coordinates, and the phases phiH1(h k l) and phiH2(h k l) of the heavy atom structure factors. With this information, one can estimate the phases of the native protein phiP(h k l). Do the final step of this process for a single structure factor with arbitrary hkl of 1 2 3, by completing the following table. Show your work with an Argand Diagram (where waves are treated as vectors, waves of unknown phase and known amplitude are represented as circles).

type of data Index amplitude phase
protein (native) 1 2 3 10
protein+heavy #1 1 2 3 12
protein+heavy #2 1 2 3 10.8
heavy #1 1 2 3 5 139
heavy #2 1 2 3 8 164

2. From van Holde: Problems 6.1b, 6.3

3. Consider the x-ray diffraction data set contained in this excel file. These data were obtained from a crystal with unit cell:
a = 24.809 b = 41.960 c = 66.779 alpha=90.00 beta=90.00 gamma=90.00 space group=P 21 21 21

a) What is the resolution of the 0 0 40 reflection? (This can be obtained from a very simple calculation.)

b) What are the indices (h k l) of the most intense reflection? (Use the sort function in excel.)

c) Estimate the resolution of this reflection (assume the two small indices are zero).

d) If you knew this crystal contained B-DNA, what would this strong reflection tell you about the orientation of the helical axis.

4. van Holde problem 6.5.