Chapter 12: Molecular Structure By Diffraction Experiments Flashcards
Describe the structure of a protein crystal
- Contain 10^13 - 10^15 individual molecules
- Weak hydrogen bonds maintain the structure (hence are fragile)
- Formation is a random process as each protein behaves differently
What does successful crystal formation depend on?
- The precipitant used
- The pH
- The concentration of ions
- The temperature
Outline the general process of crystal formation
Crystals are formed by placing the protein in a solution and slowly adding precipitant to reduce the mobile water concentration. Precipitants are generally salts, polymers, or organic solvents.
Define vapour diffusion
A common technique used in protein crystal formation.
Outline the process of vapour diffusion for crystal formation
A drop containing the protein in solution is placed inside a container alongside a larger reservoir of water with polymers. The concentration of polymers in the reservoir is increased so the vapour pressure inside the container is reduced and water is slowly extracted from the drop via controlled evaporation. Eventually, enough water is extracted from the drop for crystallisation to take place.
The vapour diffusion technique is ______ driven and occurs between the macromolecules in the container (the proteins).
Entropy
What are the requirements for a successful diffraction experiment?
• Similar or smaller wavelength to the structural scale
• Absorption shouldn’t be too strong (to prevent radiation damage)
• Appropriate properties of interaction with matter
What are the two main types of diffraction?
Neutron diffraction
X-ray diffraction
Compare the energy of neutron and X-ray diffraction
Neutron: 0.005eV
Electron: 3keV
Compare the scatterers in neutron and X-ray diffraction
Neutron: atomic nuclei (point scatters)
X-ray: electrons (not point scatters)
Compare the scattered wave in neutron and X-ray diffraction
Neutron: wave is isotropical (uniform in all orientations)
X-ray: scattering decreases with increasing angle
Compare the dominant elements in neutron and X-ray diffraction
Neutron: there are no dominant elements
X-ray: heavier elements dominate the diffraction process as scattering power increases with more electrons
What is the spin of a neutron?
1/2
What does scattering power depend on for neutron diffraction?
Relative orientation of neutron spin
Compare the visibility of hydrogen atoms in neutron and X-ray diffraction
Neutron: hydrogen atoms can be seen readily
X-ray: hydrogen atoms are difficult to see
Compare the absorption in neutron and X-ray diffraction
Neutron: low neutron absorption
X-ray: absorption increases with wavelength (but so does radiation damage)
Compare the sources of neutron and X-ray diffraction
Neutron: deuterium or tritium fusion
X-ray: synchotron radiation
Define crystal unit cells
The basic element on the structure of a crystal, due to its periodic structure. They are characterised by three vectors, a, b, c, and three angles, α, β, γ.
Describe a simple model for a unit cell (cubic and orthorhombic)
a = b = c (cubic)
a ≠ b ≠ c (orthorhombic)
Orthogonal axis: α = β = γ = π/2
Define Bragg’s law
A specific case of diffraction that gives the angles for coherent scattering waves from a crystal lattice.
Derive Bragg’s law
d = distance between two electrons
Give the equation for Bragg’s law
d = distance between two electrons
Give the scattering vector for x-ray diffraction
S = scattering vector
k = wave vector
u_0 = incident wave direction
u_1 = scattered wave direction
How is the scattering vector related to the distance between two electrons? (EXTRA: how is this concluded?)
S = scattering vector
d = distance between two electrons
EXTRA: the equations for the scattering vector and
Bragg’s law are combined.
What are the two ways that the distance between two electrons can be changed in X-ray diffraction?
- Decreasing the wavelength (smaller distance)
- Changing the angle of incident waves
Why does the atom an x-ray hits impact the scattering amplitude? (EXTRA: what factor describes this dependence?)
Because each atom have a unique number of electrons and electron distribution.
EXTRA: the scattering factor
Give the equation for the structure factor of a unit cell by considering the equation for a scattered wave
F(S) = structure factor
g_j = scattered wave
f_j = scattering factor
r_j = position
n = number of atoms
How can scattering event calculations in a unit cell be adapted for a whole crystal?
-The calculations are expanded for n unit cells in the a, b and c directions and are defined by t, u and v steps in each direction.
-The structure factor for all unit cells, K(S), is found where r = ta, ub, or vc and the product of three separate exponential is taken for all values of n.
Give the equation for the structure factor for all unit cells for X-ray diffraction
K(S) = structure factor for all unit cells
n = number of unit cells
What are the Laue conditions for scattering?
h, k, l = integers
How are K(S) and F(S) related?
The amplitude of K(S) is proportional to F(S) x n where n = n1 x n2 x n3 (the total number of unit cells)
Define the Miller indices
The three parameters, h, k, l, which represent the sets of planes in which the scatterers must be located so that the scattered waves all have the same phase (so generate constructive interference pattern known as reflections in X-ray diffraction terminology). They indicate how many times each axis should be divided into equal section, which is how these planes are drawn.
What does the intensity of X-ray diffraction reflections depend on?
- How many atoms there are (greater number means higher intensity)
- The location of the respective electrons of each atom in the set of planes.
- The intensity of reflection is proportional to the square of the structure factor.
The intensity of reflections from a unit cell is impacted by the _________ _________ of the atoms in the cell.
Geometric arrangement
Give the equation for the structure factor when the Laue conditions are met
h, k, l = Laue conditions
Describe a primitive unit cell
8 atoms, one in each corner. As these atoms are all shared by 8 other unit cells, primitive unit cells are considered to have one atom each.
Describe a body centred unit cell
8 atoms, one in each corner and one atom at the centre of the cell giving a total of 2 cells following the same logic as or a primitive unit cell.
Describe a face centred unit cell
8 atoms, one in each corner (resulting in 1 overall atom per unit cell). There are also 6 additional atoms, one at the centre of each face which are all shared with the adjacent face so are considered to be 3 per unit cell. This leaves a total of 4 atoms per unit cell.
How can the electron density of a crystal be derived?
The structure factor is a Fourier Transform of the electron density when it is written in integral form.
What is the equation for the electron density?
What is the equation for the electron density in one dimension?
What are the uses of finding the electron density of a unit cell?
The molecular structure of the crystal molecule can be found.
