power of crystals, from scattering to diffraction

a crystal

finite, translationally periodic arrangement of identical repeating units in 3 dimensions

protein crystals are made up of

unit cells, defined by unit cell vectors (a,b,c) and angles (alpha, beta, gamma)

at corners of each unit cell are

lattice points

the environment of any lattice point is identical to

environment of any other lattice point

why do we need to grow crystals

crystals amplify weak x-ray scattering from many individual molecules so that it is measurable

radiation damage is distributed evenly between all molecules in crystal rather than concentrated on one

primary radiation damage

direct effect of x-ray on protein, dependent on x-ray dose

secondary radiation damage

chemical damage to protein via reaction with mobile OH- ions or OH radicals, generated by radiolysis of water and diffuse through solvent channels in crystal

how is damage limited

collect data at 100K

what chemical effects does damage cause

reduction of metal ions, disulphide bonds and decarboxylation of aspartic acid and glutamic acid residues

diffraction can be thought of as

analogues to reflection from planes in a lattice

diffraction occurs when

distance between 2 planes is compatible with angle (θ) such that the extra distance travelled by the bottom wave is an integer number of wavelengths

if the extra distance travelled by a wavelength to reach the other plane is an integer number of wavelengths

reflected waves are in phase and massive constructive interference occurs throughout the entire crystal, leading to a measurable diffraction vector

conditions can be expressed as nλ = 2d sinθ (Braggs law)

sets of bragg planes are defined by

Miller indices (h, k, l), refer to how many times a set of planes cross unit cell axes

distance in angstrom between Bragg planes is

the resolution of the diffraction vector arising from those planes

each spot in a diffraction pattern arises from

a reflection from one set of Bragg planes

position of each spot depends on

geometry of crystal lattice

intensity of each spot is related to

amplitude of diffraction vector from each set of planes, depending on how many electrons there are between planes

phases of diffraction vector tell us

how those electrons are distributed

resolution limit of diffraction pattern is

the smallest interplane distance for which reflections are still measurable

rotational symmetry allows

regular arrangement of irregular molecules in a way that is compatible with both shape of molecule and geometry of crystal lattice

why are other types of symmetry not possible in protein crystals

proteins are homochiral polymers, every amino acid is the L-enantiomer

how many chiral space groups are there in protein crystallography

65