The following set of structure factors were collected for a one dimensional protein molecule and two derivatives by Inkibj4H

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									Bios482
X-ray crystallography
Homework #3
Handed out on Feb 24, 2006, due on Mar 3, 2006

1. The following set of structure factors were collected for a one-dimensional protein
molecule and two derivatives. (15 points)

h     Native   Derivative Derivative             h       Native     Derivative Derivative
               #1         #2                                        #1         #2
1         36           56         51             14           48            56         65
2        108         126          84             15          151          147        149
3        158         162        163              16           73            95         65
4         31           36         20             17           16             8         29
5        217         195        219              18          114            94         94
6         65           68         69             19           86            76         78
7         24           48         21             20           87            88       103
8         56           53         88             21          149          168        168
9         71           76         76             22          183          178        169
10        34           49         11             23          137          133        127
11        52           30         64             24          157          158        160
12       111           88         89             25          147          141        164
13        30           35         17             26          230          227        220

The lattice constant for this protein is 51.2. Both derivatives were prepared by using the
same heavy atoms. The scattering factor curve of this atom is given below.

        1/d             f                             1/d          f
        0.00            28                            0.27         24.1
        0.02            27.8                          0.29         23.7
        0.04            27.74                         0.31         23.3
        0.06            27.6                          0.33         22..9
        0.08            27.5                          0.35         22.5
        0.10            27.3                          0.37         22.1
        0.12            27.0                          0.39         21.7
        0.14            26.7                          0.41         21.3
        0.16            26.4                          0.43         20.9
        0.18            26.1                          0.45         20.5
        0.20            25.7                          0.47         20.1
        0.21            25.3                          0.49         19.7
        0.23            24.9                          0.51         19.3
        0.25            24.5




                                             1
Using a difference Patterson function, it was possible to establish the position of the two
derivative atoms at x=0.0 for derivative #1 and x=0.332 for derivative #2. With this
information, carry out the following calculations:

   A. Calculate the resolution of the data provided.
   B. Calculate the R-factor for each derivative compared to the native.
   C. Starting with reflection 1 and every five reflection thereafter, calculate the most
      probable phase angle using the graphical construction for solving the intersection
      of the phase circles (hint: draw Harker constructions with three circles).
   D. Select two reflections from those you have determined, one of which has a well
      defined most probable phase and one that is ambiguous. For these two
      reflections, calculate the probability curve for the combined derivatives and the
      figure of merit. Let’s assume the mean square error E = 25. It is often sufficient
      to sample the protein phase angle once every 10 degrees.

       (Hint: we know that mei
                                   best
                                           m(cos best  i sin  best ) 
                                                                              P( )e  , so
                                                                                      i


                                                                               P( )
        m cos best 
                         P( ) cos , and m sin        best
                                                                
                                                                     P( ) sin  )
                          P( )                                      P( )


2. Explain: (5 points)
       (a) MAD phasing requires data collection at different wavelengths.
       (b) MAD requires at least two data sets collected at two different wavelengths.


3. (a) What are the three major methods for density modification?
   (b) Describe how these three methods are performed on electron density map in the
       real space. (5 points)




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