Chapter 3.1. Preparation, selection, and investigation of specimens

The preparation of single crystals probably constitutes the most important step in a crystal structure analysis, since without high-quality diffraction data many analyses will prove problematical, if not completely intractable; time and effort invested in crystallization procedures are rarely wasted. There is a wealth of literature available on the subject of growing crystals and this includes the Journal of Crystal Growth (Amsterdam: Elsevier). This section does not intend to be a comprehensive review of the subject, but rather to provide some key lines of approach with appropriate references. The field of crystallizing biological macromolecules is itself a growth area and, in consequence, has been given a special emphasis.

Useful general references for growing crystals for structure analysis include Bunn (1961), Stout & Jensen (1968), Blundell & Johnson (1976), McPherson (1976, 1982, 1990), Ducruix & Giegé (1992) and Helliwell (1992). Volume D50 (Part 4) of Acta Crystallographica (1994) reports the Proceedings of the Fifth International Conference on Crystallization of Biological Macromolecules (San Diego, California, 1993) and is essential reading for crystallization experiments in this area. A biological macromolecular database for crystallization conditions has also been initiated (Gilliland, Tung, Blakeslee & Ladner, 1994).

Crystallization has long been used as a method of purification by chemists and biochemists, although lack of purity can severely hamper the growth of single crystals, particularly if the impurities have some structural resemblance to the molecule being crystallized (Giegé, Theobald-Dietrich & Lorber, 1993; Thatcher, 1993). The process of crystallization involves the ordering of ions, atoms, and molecules in the gas, liquid, or solution phases to take up regular positions in the solid state. The initial stage is nucleation, followed by deposition on the crystallite faces. The latter can be considered as a dynamic equilibrium between the fluid and the crystal, with growth occurring when the forward rate predominates. Factors that affect the equilibrium include the chemical nature of the crystal surface, the concentration of the material being crystallized, and the nature of the medium in and around the crystal. Relatively little research has been done concerning the process of nucleation, but crystal formation appears to be conditional on the appearance of nuclei of a critical size. Too small aggregates will have either a positive or an unfavourable free energy of formation, so that there is a tendency to dissolution, whilst above the critical size the intermolecular interactions will, on average, lead to an overall negative free energy of formation. The rate of nucleation will increase considerably with the degree of supersaturation, and, in order to limit the number of nuclei (and therefore number of crystals growing), the degree of supersaturation must be as low as possible. Supersaturation must be approached slowly, and, when a low degree has been achieved, it must be carefully controlled. Many factors can influence crystallization, but a conceptually simple explanation of crystal growth has been described in detail by Tipson (1956) and elaborated, for example, by Ries-Kautt & Ducruix (1992). These latter authors provide a useful schematic description of the two-dimensional solubility diagram relating the concentration of the molecule being crystallized to the concentration of the crystallizing agent. The presence of foreign bodies, such as dust particles, makes the nucleation process thermodynamically more favourable, and these should be removed by centrifugation and/or filtration. The addition of seed crystals can often be used to control the nucleation process (Thaller, Eichelle, Weaver, Wilson, Karlsson & Jansonius, 1985). In the case of the formation of crystals of macromolecules in solution, Ferré-D'Amaré & Burley (1994) have described the use of dynamic light scattering to screen crystallization conditions for monodispersity. Empirical observations suggest that macromolecules that have the same size under normal solvent conditions tend to form crystals, whereas those systems that are polydisperse, or where random aggregation occurs, rarely give rise to ordered crystals.

General strategies for crystallizing low-molecular-weight organic compounds have been reported by van der Sluis, Hezemans & Kroon (1989) and are listed in Table 3.1.1.1. Many of these strategies are also applicable to inorganic compounds. In the case of biological macromolecules, the main methods utilize one or more of the factors described in Subsection 3.1.1.5 and include batch crystallization, the hot-box technique, equilibrium dialysis, and vapour diffusion (see, for example, Blundell & Johnson, 1976; Helliwell, 1992). The growth of macromolecular crystals in silica hydrogels minimizes convection currents, turbidity, and any strain effects due to the presence of the crystallization vessel. Heterogeneous and secondary nucleation are also reduced (Robert, Provost & Lefaucheux, 1992; Cudney, Patel & McPherson, 1994; García-Ruiz & Moreno, 1994; Thiessen, 1994; Robert, Bernard & Lefaucheux, 1994; Bernard, Degoy, Lefaucheux & Robert, 1994; Sica et al., 1994). Various apparata have been described for use with the vapour diffusion technique (see also Subsection 3.1.1.6) and include a simple capillary vapour diffusion device for preliminary screening of crystallization conditions (Luft & Cody, 1989), a double-cell device that decouples the crystal nucleation from the crystal growth, facilitating the control of nucleation and growth (Przybylska, 1989), microbridges for use with sitting drops in the 35–45 µl range (Harlos, 1992), and diffusion cells with varying depths, in order to control the time course of the equilibration between the macromolecule and the reservoir solution (Luft et al., 1994).

There are many factors that influence the crystallization of macromolecules (McPherson, 1985a; Giegé & Ducruix, 1992; Schick & Jurnak, 1994; Tissen, Fraaije, Drenth & Berendsen, 1994; Carter & Yin, 1994; Spangfort, Surin, Dixon & Svensson, 1994; Axelrod et al., 1994; Konnert, D'Antonio & Ward, 1994; Forsythe, Ewing & Pusey, 1994; Diller, Shaw, Stura, Vacquier & Stout, 1994; Hennig & Schlesier, 1994), but the following are particularly important with respect to solubility (Blundell & Johnson, 1976).

Ionic strength. The solubility of macromolecules in aqueous solution depends on the ionic strength, since the presence of ions modifies the interactions of the macromolecule with the solvent. At low ion concentrations, the solubility of the macromolecule is increased, a phenomenon termed `salting-in'. As the ionic strength is increased, the ions added compete with one another and the macromolecules for the surrounding water. The resulting removal of water molecules from the solute leads to a decrease in the solubility, a phenomenon termed `salting-out'. Different ions will affect the solubility of the protein in different ways. Small highly charged ions will be more effective in the salting-out process than large low-charged ions. Commonly used ionic precipitants are listed in Table 3.1.1.2, column (a) (McPherson, 1985a).

Table 3.1.1.2| top | pdf | Commonly used ionic and organic precipitants, adapted from McPherson (1985a) (a) Ionic compounds (b) Organic solvents† Ammonium‡ or sodium sulfate Ethanol Sodium or ammonium citrate Isopropanol Sodium, potassium or ammonium chloride 2-Methyl-2,4-pentanediol (MPD) Sodium or ammonium acetate Dioxane Magnesium sulfate Acetone Cetyltrimethylammonium salts Butanol Calcium chloride Dimethyl sulfoxide Ammonium nitrate 2,5-Hexanediol Sodium formate Methanol Lithium chloride 1,3-Propanediol   1,3-Butyrolactone   Poly(ethylene glycol) 600–20000 (PEG) †The volatility of solvents such as ethanol and acetone may cause handling problems. ‡Ammonium sulfate can cause problems when used as a precipitant, since pH changes occur owing to ammonium transfer following ammonium/ammonia equilibrium; this effect has been studied in detail by Mikol, Rodeau & Giegé (1989). Monaco (1994) has suggested that ammonium succinate is a useful substitute for ammonium sulfate.

pH and counterions. The net charge on a macromolecule in solution can be modified either by changing the pH (adding or removing protons) or by binding ions (counterions). In general terms, the protein solubility will increase with the overall net charge and will be least soluble when the net charge is zero (isoelectric point). In the latter case, the molecules can pack in the crystalline form without an overall, destabilizing accumulation of charge.

Temperature . Temperature has a marked affect on many of the factors that govern the solubility of a macromolecule. The dielectric constant decreases with increase in temperature, and the entropy terms in the free energy tend to dominate the enthalpy terms (Blundell & Johnson, 1976). The temperature coefficient of solubility varies with ionic strength and the presence of organic solvents. McPherson (1985b) gives a useful account of protein crystallization by variation of pH and temperature.

Organic solvents. Addition of organic solvents can produce a marked change in the solubility of a macromolecule in aqueous solution (care should be taken to avoid denaturation). This is partly due to a lowering of the dielectric constant, but may also involve specific solvation and displacement of water at the surface of the macromolecule. Generally, the solubility decreases with decrease of temperature when substantial amounts of organic solvent are present. Commonly used organic precipitants are listed in Table 3.1.1.2, column (b) (McPherson, 1985a).

Optimal conditions for crystal growth are often very difficult to predict a priori, although many proteins crystallize close to their pI. In order to surmount the problem of testing a very large range of conditions, Carter & Carter (1979) devised the incomplete factorial method, in which a very coarse matrix of crystallization conditions is explored initially. Finer grids are then investigated around the most promising sets of coarse conditions. This technique has been further refined to yield the sparse-matrix sampling technique described by Jancarik & Kim (1991). Table 3.1.1.3 lists the crystallization parameters used by these authors. The 50 conditions constituting the sparse matrix are given in Table 3.1.1.4. A recent update of this matrix and a set of stock solutions in the form of a crystal screen kit can be obtained commercially from Hampton Research (1994). Further developments in screening methods are described in Volume D50 (Part 4) of Acta Crystallographica (1994).

Several liquid-handling systems have been described that can automatically set up, reproducibly, a range of crystallization conditions (different protein concentrations, ionic strengths, amounts of organic precipitant, etc.) for the hanging-drop, sitting-drop, and microbatch methods. A useful introduction describing a system for mixing both buffered protein solutions and the corresponding reservoirs is given by Cox & Weber (1987). Chayen, Shaw Stewart, Maeder & Blow (1990) describe an automatic dispenser involving a bank of Hamilton syringes driven by stepper motors under computer control that can be used to set up small samples (2 µl or less) for microbatch crystallization (or hanging drops). Further systems have been described by Oldfield, Ceska & Brady (1991), Eiselé (1993), Soriano & Fontecilla-Camps (1993), Sadaoui, Janin & Lewit-Bentley (1994), and Chayen, Shaw Stewart & Baldock (1994).

Integral membrane proteins can be considered as those whose polypeptide chains span the lipid bilayer at least once. The external membrane segments exposed to an aqueous environment are hydrophilic, but it is the tight interaction of the hydrophobic segments of the chain with the quasisolid lipid bilayer that constitutes the major problem in their crystallization. Crystallization trials require disruption of the membrane, isolation of the protein, and solubilization of the resultant hydrophobic region (McDermott, 1993). Organic solvents, chaotropic agents, and amphipathic detergents can be used to disrupt the membrane, but detergents such as β-octyl glucoside are most commonly used, since they minimize the loss of protein integrity. The several classes of detergent employed tend to be non-ionic or zwitterionic at the pH used, have a maximum hydrocarbon chain length of 12 carbon atoms, and possess a critical micelle concentration. The key to crystallizing membrane protein–detergent complexes appears to be the attainment of conditions in which the protein surfaces are moderately supersaturated and, in addition, the detergent micellar collar is at, or near, its solubility limit (Scarborough, 1994). Most successful integral membrane protein crystallizations are near the micellar aggregation point of the detergent (Garavito & Picot, 1990).

The final results of a structure analysis cannot be better than the imperfections of the crystal allow, and effort invested in producing crystals giving a clearly defined, high-resolution diffraction pattern is rarely wasted. The selection of twinned crystals, aggregates, or those with highly irregular shapes can lead to poor diffraction data and may prohibit a structure solution. There are many properties of crystals that can be examined prior, or in addition, to an X-ray or neutron diffraction study. These are summarized in Table 3.1.2.1. Many of these properties can yield useful information about the crystal packing and the overall molecular shape. For example, the shape and orientation of the optical indicatrix may be used to find the orientation of large atomic groups that possess shapes such as flat discs or rods and therefore also have strong anisotropic polarizability. A morphological examination can reveal information not only about the crystal quality but also in many cases about the crystal system, whilst identification of extinction directions can assist in crystal mounting. It is regrettable that many modern practitioners of the science of crystallography give little more than a cursory optical examination to their specimens before commencing data collection and a structure analysis.

Table 3.1.2.1| top | pdf | Use of crystal properties for selection and preliminary study of crystals, adapted from MacGillavry & Henry (1962); morphological, optical, and mechanical properties Crystal property Uses and comments Relation with structure Morphological properties Crystal habit Setting crystal parallel to edge, or to symmetry axis, derived from goniometric measurement Habit can be influenced by solvent, crystallization conditions, trace impurities Well formed crystals can be accurately measured for analytical corrections for absorption Morphological determination of crystal class may narrow down choice of space group Best-developed faces correspond to net planes with large density of lattice or pseudo-lattice nodes (Bravais' law, extended by Donnay & Harker) Prominent faces tend to be parallel to important bond systems Face development correlates inversely with surface free energy Twinning Twins may be hard to detect by morphological or diffraction methods. Investigate under the polarizing microscope: optical anomalies strongly indicate mimetic twinning, stacking faults, etc. Mechanical twinning may occur when a single crystal is cut or ground. In such cases, the crystal should be shaped by use of a solvent May indicate hemimorphy or pseudo-hemimorphy of the cell or supercell; see Chapter 1.3 Pseudo-symmetrical stacking Etch figures; epitaxy See IT A (2002), Section 10.2.3 (pp. 805–806), and chemical properties below   Optical properties Refractive index; birefringence (see IT A, Section 10.5.4 , p. 790) Checking quality of crystal: homogeneous extinction, interference figures Extinction direction is used for setting badly formed or ground crystals Magnitude of refractive index may be used for identification of crystal orientation High refractive index may indicate close packing Shape and orientation of indicatrix may be useful for finding orientation of large atomic or ionic groups with strongly anisotropic polarizability (e.g. flat or rod-shaped groups) Optical activity Distinguishes between optical antipodes in studies of absolute configuration Difficult to measure, or even detect, in optically biaxial crystals. No obvious relation with structure Pleochroism Identification of crystal orientation through dependence of colour on direction of light vibration Extended conjugated-bond systems have strong absorption of light vibrating parallel to system; weak absorption perpendicular to system String-like arrangement of some atoms [e.g. iodine in poly(vinyl alcohol)] produces strong absorption parallel to string In inorganic compounds, absorption is greatest for light vibrating along directions in which ions are distorted Reflection of light   Opaque substances contain loosely bound electrons Raman effect   May give information on the orientation and symmetry of scattering groups Mechanical properties Cleavage Useful for obtaining good surfaces for crystal setting Useful for improving crystal shape Correlates with bond-strength anisotropy Hardness Anisotropy of hardness may produce ellipsoids instead of spheres when an abrasion chamber is used Hardness gives an indication of bond strength and bond density Hardness may be very sensitive to impurities, changes in texture through ageing or heat treatment, etc. Plasticity Single crystals: avoid cutting or grinding Polycrystalline material: plastic deformation is often strongly anisotropic, and may then be used to produce single or double orientation Non-directive bonding between large strongly bonded units (long-chain paraffins, layer structures) Plastic flow may also be associated with mechanical twinning or lattice imperfections Crystal property Relation with structure Magnetic properties Paramagnetism; diamagnetism In an isomorphous series of paramagnetic salts, the values of the average susceptibility and of magnetic anisotropy are dependent on the nature of the paramagnetic ion. The shape of the coordination polyhedron may be found from the crystal anisotropies In aliphatic non-conjugated organic crystals, the numerically largest diamagnetic susceptibility is along the direction in which lie the largest molecular directions In crystals containing aromatic compounds or molecules with coplanar conjugated bonds, the numerically largest molecular diamagnetic susceptibility is normal to the plane of the molecular orbitals, and may thus indicate the molecular orientations Ferromagnetism; antiferromagnetism; ferrimagnetism Neutron diffraction by magnetic compounds may give information about the directions of the resultant spin and orbital moments. X-ray diffraction effects are usually unimportant In magnetic materials, the interatomic distances, and, in antiferromagnetic oxides, the valency angles at the oxygen ions are related to the diameter of the electron shell Nuclear magnetic resonance The line width in NMR spectra is related to the distances between the nuclei with magnetic moments Electrical properties Ferroelectricity; pyroelectricity See IT A (2002), Section 10.2.5 , p. 807. Ferroelectricity indicates (i) a structure of polar symmetry, and (ii) the probability of another high-symmetry structure of nearly equal energy, derivable from the ferroelectric by a displacive transition. Often there are several related structures, some ferroelectric and some antiferroelectric Pyroelectricity indicates noncentrosymmetry. Second-harmonic generation is ordinarily a more sensitive test Piezoelectricity Piezoelectricity gives information on symmetry; it occurs only in ten crystal classes. See IT A, Section 10.2.6 Thermodynamic properties Heat capacity (`specific heat') Anomalies indicate polymorphic transitions, disorder, approach to melting point, and temperature variation gives Einstein and/or Debye characteristic temperatures Melting point Atoms in crystals with a low melting point often have large thermal movements; diffraction experiments should preferably be carried out at low temperatures Anomalies in the variation of melting point in a series of homologues indicate a change in packing or bond type Density For measurement, see Chapter 3.2 . Necessary for determination of number of formula weights per cell. May indicate liquid of crystallization, isomorphous replacement, degree of approach to close packing, first-order transitions with change of temperature or pressure Thermal expansion Thermal expansion is usually greatest in directions normal to layers or chains. Abrupt variation with change of temperature or pressure indicates a second-order transition Chemical properties Chemical analysis Gives kinds of atoms in the structure and (in conjunction with the density) the number of each kind in the unit cell Attack of surface May be used to shape crystals Etch figures are sensitive indicators of point-group symmetry (see IT A, Section 10.2.3 ). Change of orientation of etch figures on a face may reveal twinning. Rows of etch pits may reveal grain or sub-grain boundaries Oriented growth on parent crystal Epitaxy often reveals similarity of lattice parameters and even of atomic arrangement in the interface Grain boundaries and twinning orientations may be marked by epitaxic growth, or by oriented growth of crystals or reaction products on the mother crystal (`topotaxy')

A frequently occurring question involves the size and shape of single crystals required for successful diffraction studies. Among other factors, the intensity of diffraction is dependent on the volume of the crystal specimen bathed by the X-ray or neutron beam and is inversely proportional to the square of the unit-cell volume (see Chapter 6.4 ). Hence, small crystals with large unit cells will tend to give rise to weak diffraction patterns. This can be compensated for by increasing the incident intensity, e.g. using a synchrotron-radiation source in the case of X-rays. How large should a crystal be, and what is the smallest crystal size that can be accommodated? X-ray collimators, or slit systems, with diameters in the range 0.1 to 0.8 mm are commonly employed for single-crystal diffraction studies. For many diffractometers, the primary beam is arranged to have a plateau of uniform intensity with dimensions 0.5 × 0.5 mm. For most small inorganic and organic compounds, crystals with dimensions slightly smaller than this will suffice, depending on the strength of diffraction, although successful structure determinations have been reported on very small crystals (0.1 mm and less) with both conventional and synchrotron X-ray sources (Helliwell et al., 1993). Microfocus beam lines at the third generation of synchrotron sources such as ESRF are designed to examine crystals routinely in the 10 µm range (Riekel, 1993). In the case of a biological macromolecule of molecular weight 50 kDa and using a conventional X-ray source (a rotating-anode generator), a crystal of 0.1 mm in all dimensions will probably give diffraction patterns from which the basic crystal system and unit-cell parameters can be deduced, but a crystal of 0.3 mm in each dimension, i.e. roughly 30 times the volume, would be required for the collection of high-resolution data (Blundell & Johnson, 1976). The higher intensity and smaller beam divergence inherent in a synchrotron X-ray source mean that high-resolution data of good quality could be obtained with the smaller crystal. Indeed, useful intensity data have been obtained with crystals with a maximum dimension of 50 µm (Subsection 3.4.1.5 ). At cryogenic temperatures, radiation damage is greatly reduced, and increased exposure times can be utilized (at the expense of increased background) to compensate for a small crystal volume. In the case of neutrons, the sample size is generally larger than for X-rays, owing to lower neutron flux and higher beam divergence. For a steady-state high-flux reactor such as that at the Institut Laue–Langevin (France), a crystal volume of 6 mm³ or larger is recommended for biological samples. Unfortunately, crystals of this size are not readily obtainable in most cases.

The shape or habit of a single crystal is normally determined by the internal crystal structure and the growth conditions. For diffractometry purposes, it is customary to bathe the crystal in the X-ray beam, so that elongated crystals may require cutting with a razor blade in order to trim them to an appropriate size. Large crystals of hard materials can be ground into spheres or cylinders (Jeffery, 1977), so that corrections can be readily made to the observed intensities for systematic errors in absorption (see Chapter 6.3 ). Crystals that have elongated prismatic or needle shapes are often useful if data are collected using oscillation geometry, since the crystal can be translated in the X-ray beam at intervals during data collection to minimize radiation damage (Subsection 3.4.1.5 ). In general, all shapes can be accommodated, but those that are grossly asymmetric (e.g. very thin plates) may give elongated or distorted reflections, leading to poor data quality in certain regions of the diffraction pattern.

The ultimate test of the quality of a crystal and its suitability for a structure analysis is the quality of the diffraction pattern. Ideally, the reflections should appear in the case of monochromatic radiation as single spots without satellites, tails, or streaks between the spots. The diffraction pattern should be indexable in terms of a single lattice.

Optical examination of a crystal under a polarizing microscope should be a prerequisite before mounting the specimen for a diffraction experiment. The presence of satellite crystals, inclusions, and other crystal imperfections will degrade the data quality, indicating the selection of a better specimen. The external morphology can often give a strong indication regarding the nature of the crystal system. A preliminary examination under crossed polars will often show whether the crystal is isotropic, uniaxial or biaxial (see, for example, Hartshorne & Stuart, 1960; Bunn, 1961; Ladd & Palmer, 1985). Crystals that comprise two or more fragments will often be revealed by displaying both dark and light regions simultaneously. For uniaxial crystals, a birefringent orientation is always presented to the incident light beam if the unique axis is perpendicular to the microscope axis, and extinction will occur whenever the unique axis is parallel to the crosswires (assuming that the crosswires are parallel to the planes of polarization of the polarizer and analyser). If the unique axis is parallel to the microscope axis, a uniaxial crystal presents an isotropic cross section and will remain extinguished for all rotations of the crystal. Biaxial crystals have three principal refractive indices associated with light vibrating parallel to the three mutually perpendicular directions in the crystal. The two optic axes and their correspondingly isotropic cross sections that derive from this property are not directly related to the crystallographic axes. In the orthorhombic system, the three vibration directions are parallel to the crystallographic axes, often enabling identification of this crystal system. A monoclinic crystal lying with its unique axis parallel to the crosswires will always show straight extinction. If the crystal is oriented so that the unique axis lies along the microscope axis then, in general, the extinction directions will be oblique. In the triclinic case, the three mutually perpendicular vibration directions are arbitrarily related to the crystal axes. Even if it is not possible to discover the nature of the crystal system unequivocally, the extinction directions should at least enable the principal symmetry directions to be identified and therefore suggest how the crystals should be mounted for optimum data collection (see Chapter 3.4 ).

If at all possible, twinned crystals should not be used for structure analysis studies, but the recognition of twinning is critical, since unnoticed or misinterpreted twinning can prevent structure determination or lead to errors in the final structure solution. A distinction should be made between multiple crystal growth, whereby single crystals grow on or from the faces of a given single crystal, or from a common nucleation point, in non-specific orientations, and crystallographic twinning (see, for example, Phillips, 1971; Bishop, 1972). In the latter case, the relationship between the lattices of twinned crystals is normally that of rotation of 180° about a central lattice line, or reflection across a lattice plane. If the lattice is not geometrically symmetrical about the line or plane, two lattices with differing orientations will be produced, and the corresponding reciprocal lattices will be visible in the diffraction patterns. In ideal circumstances, the two patterns can be deconvoluted. If the lattice is geometrically symmetrical about the twin axis or plane, then the two reciprocal lattices will coincide and there may be no obvious signs of twinning in the diffraction pattern (merohedry). If the twins are present in almost equal amounts, the result will be an apparent mirror plane and perpendicular twofold axis in the Laue symmetry. It is therefore very important to examine carefully the Laue symmetry, preferably from a number of different crystals, if twinning is suspected. In some of these crystals, one twin component may be predominant, causing a breakdown in the pseudosymmetry.

Morphological evidence (a concave shape indicating an intersection between the two twin components) and optical examination under a polarizing microscope should also be employed to test for twinning. For lattices that are twinned in a geometrically nonsymmetrical manner, the different twin components will show extinction at different orientations. However, perfect optical extinction is not positive evidence of lack of twinning, since the geometrical symmetry plane (or axis) on which twinning takes place may be parallel to a symmetry plane (or axis) in the optical properties of the crystal.

Intensity statistics can also be used to detect twinning, particularly in the case of crystals twinned by merohedry (e.g. Britton, 1972; Fisher & Sweet, 1980). If crystallization conditions cannot be found that eliminate twinning, it is still possible, although difficult, to undertake structure analysis. Recent examples include Sr₃CuPtO₆ (Hodeau et al., 1992), RbLiCrO₄ (Makarova, Verin & Aleksandrov, 1993), a serine protease from rat mast cells (Reynolds et al., 1985) and plastocyanin from the green alga Chlamydomonas reinhardtii (Redinbo & Yeates, 1993).