crystallography Flashcards
what is the storage form of DNA in chromatin
a long piece of DNA wrapped around a histone octamer
a beta 1 - 42
peptide that form fibres and is deposited in plaques in the brains of those with Alzheimers disease
- structure was determined via solid state NMR
optical microscope vs impossible xray microscope
optical microscope
lens recombine scattered visible light to reconstruct image
x rays shone onto a crystal
refracted beams
but can only measure intensity of waves = amplitude
phase info about relative time of arrival at the detector is lost
there cannot form an image
no lenses capable of focusing x ray
analytical procedures
comp calculations = phase info
then can construct electron sensitive maps
can put electron models = structure
cannot measure phases
can amplitude
phases contain bulk of structural info in image formation in X-ray crystallography
but all we can do is collect amplitudes
amplitude is hight of wave above mean
x rays
why do e use ansgstroms in crystallography
high frequency
energetic
good penetrating power
electromagnetic radiation w short wavelength
1A = 10 to the minus 8 cm
0.1nm
close to the distances between bonded atoms C-C = 1.5A
x ray diffraction
- must produce crystals of the protein or fibres = difficult - protein crystals made by repetition of a unique block many times into a strict lattice
unit cell hs to be repeated by translation in all dimensions
alll unit cells oriented in same way = 3d block
proteins highly solvated in the crystal
texture of cheesee crumble under manipulation
a static image is produced which is the average of all the molecules which we presume are all the same in the crystal to determine atomic positions
the phase problem associates with the way that we measure the diffraction data
any size protein
as small as sodium chloride and as big as 12 kDa
drug discover - can produce imaged of binding sites for ligands
bimolecular techniques to look at what?
DNA and replicate enzymes and catalysis virus organisation nucleosomes and DNA storage Ribosomes and protein synthesis Receptors and signalling Antibodies ion channels photo reaction centre chaperones transcription factors
b dna
hydrated form of DNA
calculate how much solvent is likely to be in a crystal
crystal solvent content
V = 1 / ( 1.23M / (V/Z) )
v = solvent content
M = molecular weight of protein V = vol of unit cell = x x y x z Z = no of protein molecules in unit cell
10% 90 %
early stage check check its sensible
how do the spots on diffraction patterns arise?
x rays interact w atoms scattered by cloud electrons waves shoot of in all directions most goes str8 through due to diffraction by electron cloud disperses rays over a significant anlgle scattered waves interfere w each other constructive and destructive
depending on symmetry of the atom
constructive interference
amplitude doube
phase is same
and destructive
annihilate each other - no signal
braggs law
n lambda = 2d sin theta
where theta = angle of incidence
d = distance
tells us when u get a diffraction spot occurring
stops considered existing as planes in a crystal
diffracted waves from planes of atoms one produce constructive interference when their path difference is an integral number of wavelengths
Ewald sphere
constructive interference only occurs as reciprocal lattice points pass through the sphere
after diffraction occurs
diffraction spots exist on an inverse lattice
edge a in real unit cell = length of reciprocal lattice = 1/a
Fourier transformations
enables dissection or construction of complex wave forms from simple constituents
the diffraction pattern of an object is its Fourier transform
enables domain inversions
from real space to diffraction space
=1/distance
time to frequency 1/time in NMA
optical diffraction patterns stimulate Fourier transforms
lattice sampling of the molecular transform
small spacings between molecules give wide spacings in the diffraction pattern
big spacings put spots close together
in the diffraction pattern
in a salt crystal - very spread not many of the
compete data set captured in shorter time
measuring intensity of acc spot bit easier
why do we need phases
use Fourier transform to generate electron density
as long as we have
phase info needed to supplement intensity information
diffraction pattern comes from interference
couple waves which are out of phase with each other which would be interrfering
electron density 1/v = volume of unit cell
h+K+L = reciprocal lattice co ordinates each diffraction that we measure will have a h k l value hitch will tell u which plan in the crystal gave rise to that
f h k l intensity of black spots by takin square root
each spot
take square root
exponential component of equation
sampling function
tells u what layer in the unit cell this summation is relevant to
imainary component
the phases for each measure h k l
fhkl
allows to move from diffraction space to real space
x ray diffraction procedure
- purify protein
- grew crystals
- measure interference pattern of diffracted waves
= get highest resolution - determine the lost phases
methods: - isomorphous replacement - soak heavy metal ion into crystal of protein and use that to regain phase info - used for myoglobin lysosyme
- anomalous dispersion to solve phase problem
- molecular replacement - use one structure to solve a new structure
- calculate electron density map from Fourier sum of measured wave amplitudes and phases from above -fit model to electron density chicken wire model
- refine model - alter model to give best fit of electron density
- validation
high purity needed
exploit feutre o protein t purify
solubitly -
adding ammonium sulphate to protein sol to fractionally precipitate out
charge - ion exchange choromotogaph
size - gel filtration ch
size exclusion chromatography to remove aggregates before crystallisation trial
hydrophobicity - hydrophobic interaction chromatography green fluorescent protein
attach affinity tags during exp
sds or native electrophoresis to examine purity
assay for specific activity to confirm identity
crystallisation procedure
prepare a supersaturated sol (more dissolved solute than thermodynamically stable) sol of protein by adding precipitants adjusting pH and controlling temp which will effect solubility
then enable nucleation which can be homogenoeoou - aggregation process to produce protein parcels or a particular size - crystal growth = spontaneous or hetero something dropped into crystallisation while setting it up or components that form templates for crystal growth
so that excess supersaturation can be translated into a crystal
catch 2 situation
the eel of spuersutration requires for homogenous nucleation higher than that required for sustained growth (metastable growth)
problem is showers of little crystals as metastable zone isn’t the optimum for growing homogenous
solution
1. slow approach to interface
2. take bad crystals and crush them up centrifuge add small quanitited of seed solution
add seeds into metastable zone without reaching metastable zone = large crystals
protein crystallisation via hanging drop
ammonium sulphate = precipitating agent
native to hanging drop
sitting drop
how to find the right conditions
dunno what temp to use
screen w an array of experimental conditions
known to be effective
commercially available precipitating solution
use robotic nanoliter dispensers to fill plastic trays to speed up process
96 well plae
oblong part of container
solvent resolver
protein in well
tray stored in
crystal hotels with photgraphic review
lare image of drops as their stored
mosquito crystallisation robotic peptte - 96 50 nanoliter drops in a minute
membrane proteins crystallisation s
in order to crystalise need to be taken out of the membrane using detergents
have an apolar end and a polar ed
lipids
but
can interact with membrane proteins to make
have to be careful with conc
at high conc hydrophobic tails collapse together
the unit cell
basic repeating uni of the crystal
can only be moved by translation not rotation
7 crystal systems
w centring = 14 bravais lattices = allowed symmetry operators have 32
2 3 6fold symmetry
cat have 5 fold symmetry
230 space groups that all crystal must fit into
only 65 allowed for chiral molecules like crystals due to the L amino acids
data collection
determination of space group is the first step
can predict orientation of crystal in machine
hkl reciprocal lattice co ordinates
box around whee spot is predicted
estimate backgeound locally in that region
experimental mesurent of intensity
crystal formed by unit cells stacked up in 3d like bricks
only allowed to have translation between 1 brick n next
bricks can have diff shapes
diff organisation of internal content
many diff types of bricks
7 rbravais latticies
general shape of the these bricks
work comes form classic studies of minerals from 20th century
lattices have internal symmetry that defines space group
diffraction process causes certain type of diffracted rays to be annihilated some stronger than other
symmetry in crystal revealed in that diffraction pattern
crystallography magnifies atoms so that we can see atomic structure
has parralelels with microscopy
X-rays only get half way through image formation
measure all scattered waves but cannot refocus them like in a light microscope focuses by lenses onto a plane where u see the waves recombined in an appropriate manner
can only measure the energy of the interference pattern
measure intensity of black spots
regaining lost phases from diffraction
10 to the power 20
molecule v weak
amplify it = duplicates of the same brick throughout lattice same
Gail Rhodes crystallography made crystal clear
electron density eq
summation of all the waves scattered by unique scattered waves
f
structure factor amplitude
comes from the square root of the intensity of the black spots measured in the diffraction pattern
sampling function
tells u which plane in the crystal has generated that particular F
because we’ve collected data from thousands of planes each black spot is a plane
Fourier transform of a spot is a set of interference finger
2d array of dots on a card = diffraction pattern
what is the product of the diffraction exp
electron density map
the X-ray structure that you determine is actually an average of 10 to the 20 proteins scattering simultaneously
if u assume the diffraction pattern of an object is a Fourier transform off the object the inverse transform is the object itself
isomorphous replacement
grow protein crystal
measure a day set for the native protein
then soak heavy metal complexes into the crystal and then remeasure the data to calculate the difference in the intensities for each hkl which are followed soaking in heavy metal
calculate the foriour transform with intensity differences squared and phases set to 0 - in a tube of fouriour map known as a paterson map
calculation gives rise to a map of interatomic vectors the size of which are dependent on the number of electrons in the atoms involved
Patterson showed the this calculation gives rise to a map of interatomic vectors
the size of the interatomic vectors is dependent on the number of electron in atoms involved
when using heavy metal complexes we get dominant peaks in this delta f squared synthesis
we use Patterson maps to find the positions of heavy atoms by inspection of the nap
by hand
>4 sites = tricky
modern software packages employed to sort through combinations of heavy atom species
can see vectors between atoms distributed on paterson map. huge peak at origin corresponding to
vector between each atom and itself
you can determine x y z positions of heavy atoms in real unit cell
for small molecules powerful for getting structure solutions
but hopeless on big proteins would be hopeless because there are n squared minus n peaks where n is the number of atoms involved
if u have 2 atoms you can see you’ve got 3 peaks you’ve got to find in the map
1000 atoms gets v complex
not suitable for big proteins
platinum tetra chloride widely used reacts w methionine residues well
heavy metal it is soaked in = mercury
once u know the poistion of the heavy atom in the crystal - can use those positions to calculate heavy atom structure factor
argand diagram
structure factors are vectors w amplitude and phase plotted w real and imaginary axes
amplitude = real
phase - imaginary
- vector for a particular h k l for the native protein called f p
- another vector for protein heavy atoms derivative complex fpH
- fH
measured fp and fph and know the size of fh
and we know phase angle for fh
info for determining the phase of fp by some trigonometry
phase ambiguity solved
draw axis
draw circle w set radius from origin equal to the value of fp
then minus fh going from the origin = centre of a circle whoms radius is equal to fph
where it intersects with fp circle in 2 places
therefore phase is ambiguous
in order to get an unambiguous estimation of what we have to so is do another heavy atom to go through to procedure again
if we now plot -fh
the second heavy derivative and make the circle origin from this oo ordinate
this circle should intersects at one of the intersections causing the prior ambiguity enabling you to set the phase for fp at this particular angle known as alpha p
harker construction
anomalous scattering to solve the wave problem
near the edge of an x ray absorption edge the normal rules od diffraction break down
pairs of religions roared by centre of symmetry in the diffraction pattern has the same intensity
hkl and bar h bar k bar l
