Bios482/552

X-ray crystallography

Homework #1

Handed out on January 26, 2006, due on Feb 1, 2006

1.  (5 points)

To form crystal nuclei, it is essential to bring protein solutions to a supersaturated state.

(a)  Describe three approaches that protein crystallographers frequently use to bring their protein solution to supersaturation.

(b)  Let’s assume that Marie is lucky enough to obtain some small crystals from her initial crystallization screen. List four parameters that Marie should vary in order to get large diffracting crystals. Provide a brief rationale.

2.  (5 points)

(a) Identify a unit cell in the lattice in Figure 1 by labeling 4 equivalent lattice points that define it with open circles. Do this using a separate sheet of translucent paper. Also indicate all the symmetry elements within one unit cell. Label the lattice points that are equivalent by translation with the same numbers (i.e. the symmetry at the lattice points are all 1)

(b) Construct the (2,1) lattice plane and the (4,3) plane in the unit cell outlined on the paper and clearly label each.

(c) Assuming that the lattice constants are a=b=10Å in the figure, compute the spacing for the (12,9) plane.

3.  (5 points)

Given the plane projection of symmetry equivalent points below:

(a)  provide the point group name

(b)  fill in the symmetry elements

(c)  indicate the coordinates of 6 equivalent positions.

4. (5 points, 1 points each)

Briefly explain why the following statements are true:

(a)  Small molecule ligands can be easily soaked into protein crystals, but not crystals of inorganic molecules.

(b)  A protein crystallographic data set that can be collected in less than one day or even one hour today, took many weeks to collect in 1975.

(c)  There are only 65 space groups allowed for protein molecules.

(d)  Rotating anode X-ray generator can produce more intense X-rays than sealed X-ray tubes.

(e)  A thin layer of Ni can effectively filter the Cu characteristic X-ray spectrum to produce a monochromatic X-ray beam.

5 (5 points)

The unit cell dimensions of a protein crystal are: a= 122.1, b=135.1, c=195.2Å, a=b=g=90.000. We know that the symmetry is C2221 (see attached space group diagram on page 7 and 8). The molecular mass of one polypeptide is 55,000 daltons.

(1)  How many asymmetric units are there in each unit cell?

(2)  Based on Matthew’s coefficient, how many molecule(s) could be packaged in each asymmetric unit?

(3)  What is the corresponding Matthew’s coefficient?


Figure 1.


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