X-Ray Crystallography Flashcards
What is X-ray crystallography?
X-ray crystallography is a way of taking ‘photographs’ of a molecule using X-rays.
Electrons from the atoms scatter the X-rays, so we see the electron cloud around the molecule, and we can use this data to build a model of the atom positions and interpret the image.
Why are X-rays of ~ 0.5 to 1.5 Å used?
In order to see a detail x meters in extent, you have to use a radiation no more than double that size
Steps in solving protein structure:
- Purify protein (10mg or more)
- Grow a crystal
- Collect and process diffraction data
- Phase the diffraction data
- Calculate and electron density map
- Build and refine the structure
What is a good protein sample?
Defined buffer
Defined concentration
No aggregation
A crystal acts as an _
Amplifier
They arrange molecules in same orientation, summative effect on waves
A crystal unit cell is defined by its cell constants which are…
Edges: a, b, c
Angles: α, β, γ
What is point group?
Symmetry of a finite object
Combining point group (symmetry of a finite object) and Bravais lattice symmetries generates _ symmetry
Space group
What is the space group?
Complete description of the symmetry of an (ideal) crystal.
Knowing the space group, and the contents of the asymmetric unit, defines the positions of all atoms in the crystal.
How is the space group described?
Described by letter for shape of lattice and number of molecules per rotation (i.e. P2).
When X-rays interact with crystals _ diffraction occurs from planes in the crystal
Coherent
Are darker spots more or less reliable?
More
The set of planes will give rise to what?
A diffraction spot
Containing diffraction from all parts of the protein
What is the asymmetric unit?
The unit cell is divided into a number of identical ASUs
ASUs combine through space group-specific symmetry operations to generate the unit cell
In protein crystallography we determine the structure of the _
ASU
What does Mathews Coefficient tell us?
About the crystal volume per unit of protein
Low vs high solvent crystals
Low solvent content crystals tend to be highly ordered and diffract well.
High solvent content crystals tend to be less ordered – fewer crystal contacts – leading to weaker diffraction
Typical crystalising agents
Salts
Long chain organic polymers
Organic solvents
Why does high salt precipitate protein?
The salt ions order water molecules around them, leaving less unstructured water to solubilize the protein
Why do organic solvents precipitate protein?
They effectively dilute water with a less polar, less H- bond capable solvent with lower dielectric etc.
Why do long chain organic polymers precipitate protein?
PEG prefers to writhe over a large volume of space
Taking the protein out of solution frees up more space for PEG and is energetically favoured
Other factors that can effect crystallisation
Concentration of protein
Changing pH
Temperature
Ligands (conformational locks)
Why does pH effect crystallisation?
Because it changes the number of protons, which can effect salt bridges and H-bonds
How to improve size and diffraction?
Systematic variation of all concentrations and pH.
What to do if you don’t get crystals?
- Check purity and stability
- Remove cysteins and other trouble makers
- Remove flexible parts
- Try single domains
- Try physiologically relevant complexes
What is an X-ray photon?
An elementary particle that has zero rest mass and always moves at the speed of light, a bundle of electromagnetic energy packet
Why do we use X-rays?
Because they have a wavelength similar to inter-atomic distances
What happens when a coherent monochromatic beam of X-rays is fired at a crystal?
It diffracts from the electrons in all directions
What happens to waves that are out of phase?
They cancel each other out
What happens when waves are in phases?
Diffraction/reflection spots can be detected
What is Braggs law?
For the upper and lower beans to be in phase at the detector: 2d sin(θ) = n λ
Reflections only occur at specific values of _
q (whole number values of n)
True or false:
For every angle of incidence, all planes meet the Bragg law conditions
False, only a subset do
Means that a crystal must be rotated to vary the angle of incidence of the beam
The goal of diffraction experiments is to enable what?
Constructive diffraction
What is resolution?
d
How fine and how much detail we can see in the determined structure.
Smallest spacing that will be resolved.
Measured in Å
Although d is a variable in Bragg’s equation in reality is is dictated by _
The crystal
True or false: If we see ‘reflections/spots’ resulting from sets of planes, then this sums the scattering of many bits of the protein.
True
What does the size of the diffraction spot tell us?
The amount of matter on that set of planes
Why are crystals usually frozen?
To protect them from radiation damage
What is synchrotron radiation?
Electromagnetic radiation when charged particles (electrons) are radially accelerated (moved in a circular path under vacuum)
In general intensities of spots decrease from the _ to the _
Centre to the edge
What does a dark ring on a diffraction image represent?
Probably the solvent
What do black spots on diffraction patterns represent?
A reflection
The position and intensity of the spots are related to the electrons of each individual protein atom
The spacing between the spot contains information about _
The geometry of the crystal
For example the dimensions of the unit cell
The intensity of the spots contains information about the _
Contents of the unit cells
For example the distribution of the contents of the unit cell - atomic positions and properties
Each spot intensity needs to be matched to _
A set of planes
Must replace all _ reflections with the average
Equivalent
Determine average intensity for equivalent reflections from the same set of planes
True or false:
More symmetrical data is easier to analyse
True
What does the number of reflections tell us?
The total number of spots measured
What does the number of unique reflections tell us?
The number of sets of planes.
The more _ the higher the resolution
Reflections
The higher the symmetry of the space group the fewer the number of _
unique sets of planes
But each set contains more information
True or false:
Each electron will contribute to many spots on one set of planes
False
Each electron will contribute to the intensity of many spots on many sets of planes.
What kind of analysis is used to correlate the information about how much matter there is along different parts of the unit cell?
Fourier Analysis
What three characteristics describe scattered waves?
Phase, wavelength, amplitude
In Fourier mathematics what does the strength of a diffraction spot tell us?
The waviness of the electron density
What is the phase problem
We cannot measure the phase of a wave, only amplitude and intensity.
But we need the full wave equations to compute the molecular image by Fourier transform
What are the three commonly used methods for solving the phase problem?
Multiple Replacement (MR)
Multi-Wavelength Anomalous Dispersion (MAD)
Molecular Isomorphous Replacement (MIR)
When to use Multiple Replacement (MR)?
When there is an existing closely related structure
When to use Multi-Wavelength Anomalous Dispersion (MAD)
o If there is not a closely related structure
o If there is enough methionines and suitable expression with selenomethionine as methionine source?
o Or Sulphur, Zinc atoms in the protein
When to use Molecular Isomorphous Replacement (MIR)?
If you can soak heavy atoms into your protein crystals
What is the symbol for phase value?
µ
What is Fourier analysis?
A reversible process that can swap between the wave describing our electron density and the intensity of spots diffracted from planes
What is molecular replacement doing?
Taking the structure of a different protein (imagined in the same crystal type) and taking a Fourier transform of it.
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.
Why is molecular replacement an iterative process?
Because the image produced will not be exactly like our crystal but will have features in it that the original phase model did not.
From this, we can create a better picture of what our protein crystal looks like.
We Fourier transform that to give us phases and repeat.
What is an electron density map?
A three-dimensional description of the electron density in a crystal structure, determined from X-ray diffraction experiments.
What are Structure factors?
They describe the diffracted waves from scattering planes (h,k,l)
True or false:
The electron density map describes the contents of a single unit cell
False
Describes the contents of the unit cells averaged over the whole crystal
How to improve phases in electron density map?
Solvent flattening or averaging
How to improve electron density map/model?
Refinement and rebuilding
This is an iterative process.
