Macromolecular
crystallography
Pavel Plevka
• Importance of crystallography
• Development of crystallography
• Waves, radiation, and diffraction
• Phase problem
• Macromolecular structures
X-ray crystallography
• First method to determine structure of
molecules with atomic resolution
• As of September 17, 2013 there were more
than 70,000 structures determined by protein
crystallography in Protein Data Bank
• Macromolecular structures are crucial for our
understanding of life at the molecular level
• 28 Nobel prizes
WILHELM CONRAD RÖNTGEN
(1845-1923)
• 1901 Nobel Laureate in Physics
in recognition of the extraordinary services he has
rendered by the 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 Xrays
by crystals
Wavelength and diffraction
Wavelength comparison of X-rays and visible light
38
SIR WILLIAM HENRY BRAGG (1862-1942)
SIR WILLIAM LAWRENCE BRAGG (1890-1971)
• 1915 Nobel Laureates in Physics
for their services in the analysis of crystal
structure by means of X-rays.
n = 2d sin
James Batcheller Sumner
(1879-1960)
• 1946 Nobel Laureate in Chemistry
for his discovery that enzymes can be
crystallized
FRANCIS HARRY COMPTON CRICK (1916~2004)
JAMES DEWEY WATSON (1928~)
MAURICE HUGH FREDERICK WILKINS (1916~2004)
• 1962 Nobel Laureates in Physiology and Medicine
for their discoveries concerning the molecular structure
of nuclear acids and its significance for information
transfer in living material.
Rosalind FranklinMaurice Wilkins
James Watson
and Francis Crick
Max Ferdinand Perutz (1914 – 2002)
John Cowdery Kendrew (1917 – 1997)
• 1962 Nobel Laureate in Physics
for their studies of the structures of
globular proteins
Information from X-ray diffraction
experiment
Representative electron density for amino
acid side chains
Electron density maps calculated at 1.5 Angstrom resolution.
Johann Deisenhofer (1943)
Robert Huber (1937)
Hartmut Michel (1948)
• 1988 Nobel Laureates in Chemistry
for the determination of the three-dimensional structure
of a photosynthetic reaction centre
Venkatraman Ramakrishnan (1952)
Thomas A. Steitz (1940)
Ada E. Yonath (1939)
• 2009 Nobel Laureates in Chemistry
or studies of the structure and function of the ribosome
Comparison of microscope and
diffraction
Waves and Radiation
Description of lectromagnetic
waves
• E- electric field strength
• A- amplitude
- wavelenght
A
E
z
A
E
Z
z
E = A cos 2 z/ E = A cos ( + z/ )
• z - position along beam path
- phase
Coherent beam
Addition of waves
Wave as a vector
F=Acos +iAsin
F=exp(i )
A
Real axis
Imaginaryaxis
A- wave amplitude
- wave phase
A
E
Z
z
F
A
X-rays scatter from electrons in
all directions
Primary beam
Secondary beams
X-ray scattering from several
electrons
Primary beam
A
E
Z
z
When do electrons scatter
“in phase” – waves add
constructively?
• Scattering from a single molecule is weak
• If molecules are all oriented in the same
way, the scattering from individual
molecules will add in certain directions
–Which directions?
There is no path and PHASE
DIFFERENCE when rays reflect
from a plane
A
E
Z
z
n = 2d sin
Bragg’s law:
There is NO PHASE DIFFERENCE if the path
differences are equal to prime number multiplies of
wavelength ( )
w
sin w/d
2w = n
n = 2d sin
Bragg’s law:
sin w/d
2w = n
There is NO PHASE DIFFERENCE if the path
differences are equal to prime number multiplies of
wavelength ( )
w
14 Bravais Lattices
(h, k, l)
Diffraction pattern from a protein crystal
Diffraction pattern from a protein crystal
n = 2d sin
Electron density equation
• only the intensities of reflections can be
measured
• phase information is lost
• we must obtain phase information in some
other way
Phase problem
αα
α
Molecular replacement
• source of initial phases is structure of similar molecule
(model)
• the model is repositioned (replaced) to obtain the best
agreement with the x-ray data
• phases are calculated from the model (using the
structure factor equation)
• calculated phases are combined with the experimental
data
Solving the phase problem
Multiple/Single Isomorphous
Replacement (MIR/SIR)
• source of phases – intensity differences between
data from native and derivative (heavy atom
containing) crystals
• Positions of heavy atoms identified from
isomorphous difference Patterson maps
Solving the phase problem 2
Observed amplitudes Unknown structure
Known structure Calculated amplitudes
and phases
Phases
unknown!
Fourier cat Cat
Manx cat Fourier Manx cat
FFT
FFT
Observed amplitudes (tailed cat),
calculated phases (Manx cat)
The tail becomes visible!
FFT
Duck amplitudes + cat
phases
Duck Fourier duck
Looks like a cat!!
Model Bias
Model building
• Fitting of protein sequence in the electron density
• Easy in molecular replacement
• More difficult if no initial model is available
• Unambiquous if resolution is high enough (better
than 3.0 Å)
• Can be automated, if resolution is close to 2Å or
better
What does resolution mean in practice?
6.0 Å
4.5 Å
3.0 Å
1.6 Å
Refinement
• Automated improvement of the model, so
it explains the observed data better
• The phases get improved as well, so the
electron density maps get better
Validation
• Assesment of the final(?) model quality
• How the geometry of amino acids look like?
(Ramachandran plot)
• Are non-covalently atoms far enough from each
other? (no atom bumps)
• Are residues “happy” in their environment?
(hydrophobic in core, polar on surface)
• Are the hydrogen donors/acceptors satisfied?
Depositing
• Depositing structure and diffraction data in PDB is
required for the paper to be accepted in most journals
Summary:
1. Our goal is to obtain three dimensional electron density
distribution, because it shows the shape of a molecule
2. X-rays have suitable wavelength for study of molecular
structures
3. Crystals allow measurement of diffraction data because they
diffract strongly in certain directions
4. Diffraction experiments provide only amplitudes of structure
factors => Phase problem
5. Solution of the phase problem:
Molecular replacement
Isomorphous replacement
6. Model building, refinement, deposition
1. Virus
purification
2. Crystallization
3. Diffraction data 4. Solve structure
1. Virus
purification
3. cryo-EM 4. Reconstruction
2. Grid preparation
Rhinoviruses
– 40% of common cold cases
– economic losses $16bn/year in USA
McMinn et al. Clin Infect Dis 2001. Image by Heng Soy, KI Media 2012.
Structural studies of human
picornaviruses
Enteroviruses (EV71)
– hand-foot-and-mouth-
disease
– encephalitis
Picornavirus replication cycle
Honeybee viruses
cutaneous leishmaniasis
metastasis to
nasopharyngeal
tissues
Ives et al. Science, 2011
Olivier. Nature, 2011
Free Dictionary
Leishmania RNA virus 1