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Crystallography past, present and future
Jenny P. Glusker Philadelphia, PA, U. S. A.
International Year of Crystallography UNESCO, Paris, France 20 January 2014
Quartz crystals found growing naturally. Note the crystal faces that are formed and the angles between two pairs of these faces.
142° 134°
QUARTZ CRYSTALS
LARGE CRYSTALS CAN BE GROWN Potassium dihydrogen phosphate. Large size.
ISOMORPHISM Colorless potash alum grown on a crystal of violet chrome Alum, KCr(SO4)2.12H2O, embedded in colorless KAl(SO4) 2.12H2O.
1665, THE INTERNAL STRUCTURE OF CRYSTALS Left: Robert Hooke in 1665 in his book, “Micrographia,” represented the internal structure of flint crystals by a close-packing of spheres.
Spheres (pink) added to his diagram (top left).
X RAYS FOR VIEWING THE BODY
X rays have enabled one to see bones in the human body. Röntgen reportedly photographed his wife’s hand for 15 minutes, December 1895.
Foot in a high-button shoe. Radiograph, 1896.
DIFFRACTION BY A SIEVE, SPACING, d n λ = 2 d sinθ
λ= wavelength of light, d = sieve wire spacing, θ = angle at which diffracted light beam hits the detector. Note that the diffraction for blue light is closer in than for red light (shorter wavelength for blue light).
Fine sieve. Wires closer together.
Coarse sieve. Wires further apart.
DIFFRACTION PHOTOGRAPH OF ZINCBLENDE (ZnS) Laue, Friedrich and Knipping, 1912
Diffraction of X rays by crystalline zincblende. This photograph led to its crystal structure which contains a four-fold axis of symmetry.
X-RAY DIFFRACTION MYOGLOBIN
From John Kendrew
X-RAY DIFFRACTION
KCl
Positions of spots measured to give the unit-cell dimensions. Intensities of spots measured to give positions of atoms in each unit cell.
DNA photograph courtesy Robert Langridge. Polynucleotide photographs courtesy Dick Dickerson.
DNA DIFFRACTION PATTERN
A
Pulled fibers of DNA
Crystals of polynucleotides (portions of DNA)
DNA helix
DNA structure
SODIUM CHLORIDE CRYSTAL STRUCTURE
Each sodium ion is surrounded by six chloride ions. Each chloride ion is surrounded by six sodium ions. No individual NaCl molecules are seen.
BRAGG’S LAW incident X rays
crystal
diffracted X rays
The crystal has a periodic structure, repeating vertically at a distance d. The electrons around each atom scatter incident X rays. If the path difference of the two waves, 1 and 2, is an integral number of wavelengths, the intensity of the diffracted (scattered) beam will be increased (Young Bragg).
nλ = 2d sinθ 1
2
spacing
1
2
DIFFRACTION
phase problem
electron-density map Aim to get observed and calculated intensities to agree in magnitude.
detection system
crystal
source of X rays
EXPERIMENTAL SETUP This arrangement has not changed much in 100 years but each of the components are now greatly improved in capability and efficiency.
STEROIDS (J. D. BERNAL, 1932)
Wieland and Windaus formulae
Wieland, Dane formula (also crystal structure)
Bernal, Rosenheim King formula
Will not fit into measured unit cell
Fits into unit cell
POTASSIUM DIHYDROGEN PHOSPHATE
Crystal structure
Two orientations of the phosphate groups
Patterson map
Vectors at: 0,0 1/2-2x,-2y 1/2,1/2-2y -2x,1/2 Atoms at: x,y 1/2-x,-y 1/2+x,1/2-y -x,1/2+y
PATTERSON MAPS: HEAVY ATOMS
Patterson map
Electron- density map
ANOMALOUS SCATTERING
No anomalous scattering I (h k l ) = I (-h -k –l )
Anomalous scattering I (h k l ) ≠ I (-h -k –l ) Different path lengths as if the heavy atom had gulped
Absolute configuration of deuterated Li glycolate (action of lactate isomerase).
6Li is an anomalous scatterer for neutrons
H
D
BIOCHEMICAL REACTIONS
6Li
Differences between intensities I (hkl) and I (-h –k –l)
Element neutron X rays (fm) (electrons)
H - 3.8 1 D 6.5 1 C 6.6 6 N 9.4 7 O 5.8 8 Mg2+ 5.3 12 Ca2+ 4.6 20 Mn2+ - 3.6 25 Fe2+ 9.5 26 Co2+ 2.5 27 Ni2+ 10.0 28 Zn2+ 5.6 30
INTERPRETING NEUTRON MAPS
1.8 Å neutron map, blue positive, red negative.
H on N exchanged for D
H on C not exchangeable
O
C C
H
“CATALYTIC” WATER MOLECULE
Metal ion-carboxylate-water motif in D-xylose isomerase. The “catalytic” water is shown with heavy black bonds. Both protons are found to be present on that water W1018.
Heptenitol plus phosphate gives heptulose-2-phosphate
GLYCOGEN PHOSPHORYLASE b
Note how the phosphate group becomes bound to the sugar as time progresses.
Hadju, Machin, Campbell, Greenhough, Clifton, Zurek, Gover, Johnson, Elder. Nature 329, 178 (1987).
THE FUTURE OF CRYSTALLOGRAPHY
Better methods for growing diffraction-quality crystals. Continuing the trend of solving structures of large biochemically relevant crystals and determining details of the reactions they undergo. Membrane proteins. Learning much more about electron density in molecules. Following the courses of chemical and biochemical reactions. More details of chemical bonding. Molecular motion and reactivity in crystals. Time-resolved X-ray diffraction. Studies of metals, alloys, polymers and ceramics and the relationship of their structure to their properties. Aperiodic and partially periodic structures. Shape memory alloys. New materials. Other new radiations for diffraction. Less than crystalline material. However, most scientific advances in the study of crystals in the next 100 years cannot be predicted at this time. The same was true in 1914.
Crystal Discovery of X rays 1895
Diffraction of X rays by crystals 1912 (periodicity)
X-ray diffraction pattern can be interpreted in terms of the atomic arrangement in the crystal, 1914
Crystal structure determinations, scientific journals, databases
Discovery of neutron diffraction 1945
Anomalous dispersion and absolute configuration 1949
Solving the phase problem Patterson map 1934 Isomorphism Direct methods Direct phasing
SYNOPSIS