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Protein CrystallographyPart I — Technical Aspects of and Introduction to X–ray diffraction
Tim GrüneDept. of Structural Chemistry
Head of Dept.: Prof. G. SheldrickUniversity of Göttingen
November/December 2005http://shelx.uni-ac.gwdg.de
Overview
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Density
Molecular Biology Course 2005 1 Protein Crystallography I
Crystals and Protein Crystals
Examples of Crystals
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Ice Crystals Salt Crystals Artificial Monocrystal fora kJ Laser
Crystals from inorganic and especiallyionic compounds (like NaCl) tend to berather stable. They can be kept at roomtemperature, for a long time and in a dryenvironment.
Quartz Crystal
Molecular Biology Course 2005 2 Protein Crystallography I
Crystals and Protein Crystals
Protein Crystals
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Protein Crystals are generally more sensitive then minerals. They are usuallygrown from solution and must be kept in a humid environment throughout theexperiment.
Protein Crystals grown in solution.
If proteins are not handled with care, they quickly degenerate/aggregate
Molecular Biology Course 2005 3 Protein Crystallography I
Crystals and Protein Crystals
Protein Crystals
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Proteins are generally more sensitive then minerals. They are usually grown fromsolution and must be kept in a humid environment throughout the experiment.
Protein Crystals grown in solution.
If proteins are not handled with care, they quickly degenerate/aggregate
Molecular Biology Course 2005 4 Protein Crystallography I
Growing Protein Crystals
Growing Protein Crystals — Vapour Diffusion
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
In order to grow crystals from a protein solution, the protein must be very pure(≥ 90–95%) and very concentrated ( ≈ 15 − 25mg
ml , ranges go from 5mgml to
> 100mgml ). The probably most common method is called the vapour diffusion
method.
equilibration
reservoirsolution
before equilibration
protein/reservoir
after equilibration
The reservoir contains a buffer, a precipitant ( salts, PEG’s with M∅r = 400–
20,000 Da, organic solvents) and additives (small molecules/salts that help pack-ing, e.g. MgCl2).The drop is a (1:1)–mixture of protein and reservoir solution (mother liquor).Volatile components are exchanged until equilibrium is reached. Since at thebeginning the precipitant is diluted in the drop, the drop is being concentratedduring equilibration.
Molecular Biology Course 2005 5 Protein Crystallography I
Growing Protein Crystals
Growing Protein Crystals — Other Techniques
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Batch method: Protein and reservoir are mixeddirectly and covered with a layer of oil⇒ no or little equilibration.
oil seal
Diffusion through Dialysis Membrane: Proteinsolution and reservoir separated by a highmolecular weight cut-off membrane⇒ also non–volatile components are ex-changed.
membrane
Diffusion through Agarose: Reservoir and Pro-tein separated through a layer of agarose⇒ concentration gradient
agarose
Molecular Biology Course 2005 6 Protein Crystallography I
Growing Protein Crystals
Growing Protein Crystals — Comparison
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Vapour Diffusion BatchPRO:• Fast setup — robots can do up
to 100 drops in 30 min• Small amount ( 1nl / drop with
robot)
PRO:• Fast setup• water permeable oil allows con-
centration above initial proteinconcentration
CONTRA: Sudden mixing may cause protein to aggregate
Dialysis Agarose
PRO:• exchange of non–volatile com-
ponents• high degree of control about fi-
nal conditions and diffusion rate
PRO:• exchange of non–volatile com-
ponents• gradient of both protein and
reservoir: infinite number ofconditions in one setup
CONTRA: Slow setup; requires large amounts of protein
Molecular Biology Course 2005 7 Protein Crystallography I
X–rays
What are X–rays?
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
• (Visible) light is composed of electromagnetic waves: every colour has awavelength/energy
• X–rays are the same, but with higher energy, i.e. shorter wavelength
The spectrum of electromagnetic waves
Radio Microvisible
UV X-rays γ-raysInfra-redwavelength λ
10km1013Å
energy
125 keV1.25 keV1.25 eV4.1µeV1.6–3.1eV
30cm3 · 109Å
1mm107Å
800-400nm8− 4 · 103Å
1nm10Å
10pm0.1Å
Typical X-ray experiment:≈1Å
X–rays are generated by accelerating or decelerating electrons. This happenseither in rotating anodes or at synchrotrons.
Molecular Biology Course 2005 8 Protein Crystallography I
X–rays
X–ray Diffraction — Principle of an experiment
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
X-ray beam
λ ≈ 1Å(0.1nm)
crystal ≈ (0.2mm)3
Diffraction pattern on CCDor image plate
≈ 1013 unit cells
T. Schneider
The crystals diffracts in all directions. Since the detector cannot cover the fullsphere around the crystal, the crystal is rotated during an experiment.One typical data set consists of tens to hundreds of images covering 90◦ – 360◦.
Molecular Biology Course 2005 9 Protein Crystallography I
X–rays
X–ray sources — Rotating anode
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
The SMART 6000
Focussing unit
Crystal hold
Detector
(goniometer head)
Rotating Anode
Cryostream(100K)
Beam stop
G. Sheldrick
Electrons are accelerated and hit a (rotating) Cu–plate. This induces a transitionof the inner shell electrons which in turn produces characteristic CuKα radiation(1.54 Å)
Molecular Biology Course 2005 10 Protein Crystallography I
X–rays
X–ray sources — Synchrotron
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
The ESRF (European Synchrotron Radiation Facility) Grenoble
G. Sheldrick
Bunches of electrons are circulating at high velocity and bent by strong magnets.This generates X–rays at range wavelengths, depending on the degree of thebent. Some set-ups allow to tune the wavelength (important for MAD– and SAD–phasing, see later in the lecture).
Molecular Biology Course 2005 11 Protein Crystallography I
X–rays
X–rays: Diffraction pattern
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity ��������������������������������������������������
��������������������������������������������������
���������������������������������
���������������������������������
���������������������������������
���������������������������������
Screen
object (focussing) lense image
visible light
Light is scattered from an objects in all directions. A lense (e.g., eye, a camera,a microscope, or telescope) collects some of the scattered light and focusses iton a screen (and eventually the retina). This creates an image of the object.
Molecular Biology Course 2005 12 Protein Crystallography I
X–rays
X–rays: Diffraction pattern
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Screen
object
X-rays
no image - "blur"no lenses for X-rays
For X-rays, lenses do not exist, therefore one cannot create and X-ray image.With a “normal” object, no information would be collected on the screen.
What is special about crystals so that one can retrieve information through X-raysfrom them?
Molecular Biology Course 2005 13 Protein Crystallography I
Inside Crystals
The Secret of Crystals — Regularity
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
A crystal consists of a unit cell which is “piled up” like bricks (but in three direc-tions) to compose the whole crystal.
The unit cell is characterised by the three side lengths, a, b, c and angles α, β, γ.
c
ab
γ
αβ
α: angle between b and c
β: angle between c and a
γ: angle between a and b
Irrespective of the lengths and angles a unit cell can always be “piled” withoutgaps.
Molecular Biology Course 2005 14 Protein Crystallography I
Inside Crystals
How does the crystal lattice help?
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
In order to understand why crystals produce more than just a blur under X-raydiffraction, one introduces the concept of crystal planes. The corner points ofall unit cells create the crystal lattice. Three non–linear lattice points (corners ofdifferent unit cells) define a plane.
ba
(2 5)
(1 1)
One set of planes is described by the number of section it divides each side ofthe unit cell into (in the figure, side a is divided into two parts by the green set,and b into five parts). These numbers are called the Miller-Indices (hkl) (threein three dimensions).I.e., the green set of planes has the Miller Indices (250), the purple one theIndices (110).
Molecular Biology Course 2005 15 Protein Crystallography I
Bragg’s Law and Resolution
(Bragg) Reflection
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
X-rays are reflected at the lattice planes. Since a set of planes consists of ahuge number of planes, constructive interference occurs at certain angles θ. Atall other angles the waves extinct each other. Therefore one observes the spottypattern.
One set of planesinside the crystal
dX-rays θ
The angle θ, the plane separa-tion d and the wavelength of theincident X-rays are connectedby Bragg’s law or the Bragg con-ditiona:
λ = 2d sin θ
aRemark: Bragg’s law can easily be derived from the above pictur by using the fact that the pathdifference between rays reflected from two adjacent planes must be an integer multiple of thewavelength. This leads to the actual law nλ = 2d sin θ, but higher order reflections (n > 1) aregenerally too weak to be detected.
Molecular Biology Course 2005 16 Protein Crystallography I
Bragg’s Law and Resolution
Indexing of Reflections
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Given a setup of crystal orientation, detector, and beam, each set of planesleads to one reflection. Therefore the reflection that belongs to one plane islabelled with the same Miller Indices (hkl). Assigning these three numbers toeach recorded reflection is called indexing.
beam 2θmax
crystal
recordedimage
(hkl)
The distance d which can be calculated via θ from Bragg’s law is called the reso-lution of that reflection. The resolution of the reflection with maximal θ determinesthe resolution of the data set.
Molecular Biology Course 2005 17 Protein Crystallography I
Bragg’s Law and Resolution
The Meaning of Resolution
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
The resolution of data collected by X-ray diffraction is a measure for how muchdetail can be seen. It is related with the plane distance d via Bragg’s law by
d =λ
2 sin θmax
θmax is the maximum angle to which data (i.e. a reasonable number of reflec-tions) could be collected.The final goal of data collection is to calculate an electron density map for thecrystallised molecule. The resolution corresponds quite well to the minimum dis-tance between two atoms that can still be resolved in the electron density map.
high resolution density map
dd’
low resolution density map
Molecular Biology Course 2005 18 Protein Crystallography I
Bragg’s Law and Resolution
Examples for the Resolution of Electron Density Maps
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
Low Resolution Medium Resolution
High Resolution
G. Sheldrick
The images show three times the same region of a protein map at different res-olutions.N.B.: Crystallographers usually speak of “high resolution” when the number issmall (e.g. 1.2Å) and of “low resolution” when the number is large (e.g. 3Å).
Molecular Biology Course 2005 19 Protein Crystallography I
From X-rays to Electron Density
How to calculate an Electron Density from Diffraction Data
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
An X-ray experiment measures intensities of many reflections. The intensity of areflection (hkl) is proportional to the square modulus of the structure factors:
I(hkl) ∝ |F (hkl)|2
Structure factors are complex quantities introduced in order to facilitate the cal-culation of the electron density, i.e.
F (hkl) = |F (hkl)| eiφ(hkl)
|F (hkl)| is called the amplitude and φ(hkl) the phase of the reflection.The electron density within the unit cell of the crystal is related to the structurefactors via a Fourier transformation:
ρ(x, y, z) =1
Vunit cell
h,k,l=∞∑h,k,l=−∞
|F (hkl)| eiφ(hkl)e−2πi(hx+ky+lz)
The Fourier transform can also be inverted:
F (h, k, l) =∫
Vunit cell
d3x ρ(x, y, z)e2πi(hx+ky+lz)
Molecular Biology Course 2005 20 Protein Crystallography I
From X-rays to Electron Density
Limits of Crystallographic Data Collection
Crystals and Protein Crystals
Growing Protein Crystals
X–ray diffraction
Inside Crystals
Bragg’s Law and Resolution
From X-rays to Electron Den-
sity
If we knew all structure factors, we could calculate a perfect electron density andbuild a perfect model.Obviously it is not possible to collect data from an infinite number of reflectionsat infinite accuracy. This leads to truncation errors of the Fourier transformation,which basically means noise in the electron density map. Even with the bestof equipment there are physical limits why we cannot collect data to arbitraryresolution:
1. Bragg’s Law limits the resolution to λ/2, because |sin θ| ≤ 1
2. Crystal imperfections, mostly mosaicity. Mosaicity describes that the unitcells do not pack without gaps. This leads to a broadening of the signalwhich at high resolution vanishes in the background.
3. Detectors also contribute to a broadening of the signal.
4. Every crystal has a limited size. This means that there is only a limitednumber of sets of planes that can cause reflections. While this is usually nota limiting factor, it becomes an issue for very small crystals ( < 50µm sidelengths)
Molecular Biology Course 2005 21 Protein Crystallography I