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

BIREFRINGENCE (double refraction) Calcite crystal. Notice the two images (birefringence).

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).

CRYSTAL = LATTICE AND MOTIF

crystal lattice

structural motif

crystal structure

TOBACCO NECROSIS VIRUS CRYSTALS Photograph from R. W. G. Wyckoff

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.

SEEING MOLECULES

Electron microscopy X-ray analysis of crystals

No X-ray lens currently available.

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.

OLD-TIME COMPUTING

HEXAMETHYLBENZENE (KATHLEEN LONSDALE, 1928)

Benzene planar All C-C equal

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

COPPER SULFATE PENTAHYDRATE

Patterson map

Cu-Cu and Cu-S vectors

Crystal structure

β-lactam oxazolone

BENZYLPENICILLIN (HODGKIN, 1949)

Two possible formulae

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

FINDING ATOMS IN THE HEXAACID DERIVED FROM VITAMIN B12

Cobalt only input 26 atoms input

ELECTRON-DENSITY MAPS AND RELATIVE PHASES

Summing waves Effects of different relative phases

DIRECT METHODS: RELATIVE PHASES

Choose the least negative background

HEXAMETHYLBENZENE

Kathleen Lonsdale, 1928

7-30

4-70

340

7 -3 0 4 -7 0 3 4 0

5.5 Å

1.5 Å

2.5 Å

0.8 Å

“RESOLUTION”: WHAT WE CAN SEE

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: ISOCITRATE

Asymmetric carbon atom

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.

H-BONDING NETWORK BETWEEN SUBSTRATE AND ENZYME

Oxygen red Nitrogen blue Hydrogen yellow

THE MANDELATE RACEMASE REACTION

INTERMOLECULAR INTERACTIONS

Rosenfield JACS 99 4860 (1977)

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