C7270
Biological X-Ray Crystallography and
Cryo-Electron Microscopy
Fall 2024
Pavel Plevka, Tibor Füzik, Jiří Nováček
cryo-EM
1. Expression & purification 2. Crystallization
3. Diffraction data 4. Solve structure
3. cryo-EM data 4. Reconstruction
2. Grid preparation1. Expression & purification
5
• Diffraction of light
Aims of the course
• Approaches to resolve phase problem in crystallography
• Use of electrons to display objects with high
magnification and fine detail
• Calculation of three-dimensional reconstruction from
two-dimensional projections
6
What is asked of you:
• Be present and awake
• Participate in discussions
• I am here to help, learning is up to you!
• Ask questions - it will help to clarify the issue not only for you
but for your peers as well!
• In class discussions, be respectful of other students' opinions.
Not part of this course:
• Basic math – mental overload by dealing with simple equations.
(Observed before.)
• Reserve time for thinking.
8
Course textbooks:
Course plan
No lecture
next week!
10
Biological X-Ray Crystallography
Johannes Kepler (1571-1630)
Why do single snowflakes, before they become entangled with other
snowflakes, always fall with six corners? Why do snowflakes not fall with five
corners or with seven?
Niels Stensen (1638-1686)
Although crystals of quartz and hematite appear in a great variety of shapes
and sizes, the same interfacial angles persisted in every specimen. “Law of
Constancy of Angles”
René Just Haüy (1743-1822)
“Law of Constancy of Angles”
“Law of Constancy of Angles”
René Just Haüy (1743-1822)
17
History of fundamental discoveries
WILHELM CONRAD RÖNTGEN (1845-1923)
• 1901 Nobel Laureate in Physics
discovery of the remarkable rays subsequently
named after him
MAX VON LAUE (1879-1960)
• 1914 Nobel Laureate in Physics
for his discovery of the diffraction of X-rays by
crystals
Friedrich and Knipping
Wavelength and diffraction
Waves
Coherent beam
Addition of waves
Particles & waves
Diffraction of light
Diffraction of light
Wavelength and diffraction
Wavelength comparison of X-rays and visible light
38l
Crystallizing a Protein
Protein expression and purification
Vapor-diffusion
Batch and microbatch
Microdialysis
Protein crystallization phase diagram
Preparing crystals for diffraction
experiment
Diffractometer with goniometer
Diffractometer with goniometer
X-ray sources
- sealed X-ray tube
Spectrum of
copper anode
Synchrotron
- Bending magnet
- Wavelength shifter
- Wiggler
- Undulator
X-ray detectors
Single photon counter
Film
Image plates
Area detectors:
- CCDs
- Direct X-rays detectors - Pilatus
Crystals
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• • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • •
A 2D lattice
a
!
b
!
Translationally periodic arrangement
of motifs
Crystal
Translationally periodic arrangement of
points
Lattice
Lattice Ø the underlying periodicity of the crystal
Motif Ø atom or group of atoms associated with each lattice point
Crystal = Lattice + Motif
+ À
Lattice
Motif
À À À À À À À
À À À À À À À
À À À À À À À
À À À À À À À
À À À À À À À
À À À À À À À
À À À À À À À
À À À À À À À
Crystal
=
Courtesy Dr. Rajesh Prasad
§ A cell is a finite representation of the infinite lattice
§ A cell is a parallelogram (2D) or a parallelopiped (3D) with lattice
points at their corners.
§ If the lattice points are only at the corners, the cell is primitive.
§ If there are lattice points in the cell other than the corners, the cell
is nonprimitive.
Unit cells
Instead of drawing the whole structure I can draw a representative part
and specify the repetition pattern
Arrangement of lattice points in the unit cell
No. of Lattice points / cell
Position of lattice points
Effective number of Lattice
points / cell
1 P 8 Corners = 8 x (1/8) = 1
2 I
8 Corners
+
1 body centre
= 1 (for corners) + 1 (BC)
3 F
8 Corners
+
6 face centres
= 1 (for corners) + 6 x (1/2)
= 4
4
A/
B/
C
8 corners
+
2 centres of opposite faces
= 1 (for corners) + 2x(1/2)
= 2
If an object is brought into self-coincidence after some operation
it said to possess symmetry with respect to that operation.
SYMMETRY
Bravais Lattice
A lattice is a set of points constructed by translating a single point in
discrete steps by a set of basis vectors. In three dimensions, there
are 14 unique Bravais lattices (distinct from one another in that they
have different space groups) in three dimensions. All crystalline
materials recognized till now fit in one of these arrangements.
Unit cell selection
Alternative unit cell
selection (also correct)
Positions of twofold
symmetry axes
Positions of mirror planes
Unit cell selection
Positions of glide planes
End of lecture #1 in 2022
SIR WILLIAM HENRY BRAGG (1862-1942)
SIR WILLIAM LAWRENCE BRAGG (1890-1971)
• 1915 Nobel Laureates in Physics
for the analysis of crystal structure by means
of X-rays
nl = 2d sinq
nl = 2d sinq
Bragg’s law:
There is NO PHASE DIFFERENCE if the path
differences are equal to whole number multiplies of
wavelength (l)
w
sinq = w/d
2w = nl
nl = 2d sinq
Bragg’s law:
sinq = w/d
2w = nl
There is NO PHASE DIFFERENCE if the path
differences are equal to prime number multiplies of
wavelength (l)
w