How to obtain diffraction data from crystals and electron density maps

Question 1

How are crystals picked

Answer 1

1. Crystals are picked using a nylon loop
2. Then the crystal is in the middle of the loop in a vitrified solution
3. Crystals are usually frozen to protect from radiation damage

Question 2

What are the different x-ray sources

Answer 2

1. Laboratory source, rotating anode
   - Electron beam hitting copper
   - (Cu) target
   - Fixed wavelength 1.5418Å
2. Synchrotron
   - Circular accelerator + Undulator
   - Much more intense
   - Narrow beam
   - Wavelength tunable
3. Free Electron Laser
   - Linear accelerator + Undulator
   - Even more intense
   - Femtosecond pulses

Question 3

What are different detectors

Answer 3

1. Detector, to produce digital image
2. Image plate (phosphorimager)
3. CCD (photon coupled)
4. solid state (direct)- Directly capture the diffractions

Question 4

Describe High energy synchrotron radiation (SR) – X-rays

Answer 4

1. SR- Electromagnetic radiation when charged particles (electrons) are radially accelerated (moved in a circular path under vacuum) – high brilliance

Question 5

What is needed for a synchrotron

Answer 5

1. Automated sample loading needed for screening many crystals at Diamond synchrotron

Question 6

Describe CCD X-ray Detector

Answer 6

1. High sensitivity state-of-the-art detector

Question 7

Describe diffraction of x-rays

Answer 7

1. X-rays are deflected by electrons as they pass through the protein crystal
2. X-rays are absorbed as a pattern of dots (diffraction pattern) by a photon detector

Question 8

What are features of diffraction images

Answer 8

1. Discrete spots
2. Intensities are different from spot to spot
3. In general, intensities decrease from the center to the edge
4. Every black spot represents a reflection
5. The position and intensity of the spots are related to the electrons of each individual protein atom
6. Low resolution inner portion of image- 3-4 A
7. High resolution corresponds to outer portion- 1-2.5 a

Question 9

How do you collect the data

Answer 9

1. Many frames at different crystal angles
2. Slowly rotate the crystal and record one image per rotation
3. ~100 images with ~100- 1000 reflections each = 10^4– 10^5 reflections. Need to collect a full set of several 100 images
4. If a protein is diffracted from all angles, analysis of the diffraction patterns will provide a template of the electron densities within the protein

Question 10

What information can you get from diffraction image

Answer 10

1. The spacing between the spots contains information about the geometry of the crystal (i.e. dimensions of the unit cell)
2. The intensity of the spots contains information about the contents of the unit cell (i.e. protein)
3. The distribution of contents of the unit cell (i.e. atomic positions and properties)

Question 11

What does increasing the number of reflections imply

Answer 11

1. Increasing the Number of Reflections Implies Increasing Resolution

Question 12

How do you scale the data

Answer 12

1. Scale all intensities relative to the background.
2. Match each spot intensity to a set of planes
3. Determine average intensity for equivalent reflections from the same set of planes
4. Replace all equivalent reflections with average

Question 13

How can you tell how good the data is

Answer 13

1. Reflections =spots
2. We will measure some reflections more than once so we have two ways of describing our numbers of reflections
3. Number of reflections = total number of spots recorded on the detector
4. Unique reflections = total number of sets of planes we observe diffraction from.
5. the more reflections the higher the resolution
6. The space group (shape of the lattice) also influences the number of unique reflections.
7. For the same resolution, different space groups will have different numbers of sets of planes available to them.
8. The higher the symmetry of the space group, the fewer unique sets of planes it has (you still get the same resolution but each set of planes contains more information as there are fewer)

Question 14

What happens when reflections hit the detector

Answer 14

1. When reflections hit the detector they arrive at the detector at slightly different times and we cannot detect the difference
2. All we have is the intensity (amplitude^2) of these reflections

Question 15

What is the phase problem of crystallography

Answer 15

1. We can’t measure the phases!
2. X-ray detectors (film, photomultiplier tubes, CCDs, etc) can measure only the intensity of the X-rays (which is the amplitude squared)
3. but we need the full wave equations Ae^(iα) for each reflection to compute the reverse Fourier transform.

Question 16

What do fourier summations do

Answer 16

1. Fourier summations sums waves
2. Diffraction amplitudes are recovered from the measured intensity of the spots
3. In order to reconstruct an image, we need to know the amplitudes and phases of the diffracted waves
4. X-ray detectors are sensitive to the amplitude only
5. Recovering the lost phases is the “phase problem” of X-ray crystallography

Question 17

What are 3 methods to solve the phase problem

Answer 17

1. Multiple Isomorphous Replacement (MIR)
2. Multi-Wavelength Anomalous Dispersion (MAD)
3. Molecular Replacement (MR)

Question 18

What is an electron density map

Answer 18

1. A three-dimensional description of the electron density in a crystal structure, determined from X-ray diffraction experiments.
2. X-rays scatter from the electron clouds of atoms in the crystal lattice; the diffracted waves from scattering planes (h,k,l) are described by structure factors Fhkl.
3. The electron density map describes the contents of the unit cells averaged over the whole crystal and not the contents of a single unit cell.

Question 19

Give example of how to solve phase problem

Answer 19

1. Similarly, we can take the structure of a different protein (imagined in the same crystal type) and take a Fourier transform of it.
2. We can then combine the phases produced by this Fourier transform, with the amplitudes from our diffraction to do the Fourier summation to produce an image of the crystal.
3. This image will not be exactly like our crystal, but will have features in it that the original phase model did not.
4. From this, we can create a better picture of what our protein crystal looks like, Fourier transform that to give us phases and repeat. It is an iterative process.