Section 4.1.5. Techniques for physical characterization of crystallization

Dynamic light scattering (DLS) relies on the scattering of monochromatic light by aggregates or particles moving in solution. Because the diffusivity of the particles is a function of their size, measurement of diffusion coefficients can be translated into hydrodynamic radii using the Stokes–Einstein equation. By making measurements as a function of scattering angle, information regarding aggregate shape can also be obtained. For single-component systems, the method is straightforward for determining the size of macromolecules, viruses and larger particles up to a few µm. For polydisperse and concentrated systems, the problem is more complex, but with the use of autocorrelation functions and advances in signal detection (Peters et al., 1998), DLS provides good estimates of aggregate-size distribution.

In bio-crystallogenesis, investigations based on light scattering have been informative in delineating events prior to the appearance of crystals subsequently observable under the light microscope, that is, the understanding of prenucleation and nucleation processes. Many studies have been carried out with lysozyme as the model (Kam et al., 1978; Durbin & Feher, 1996), though not exclusively, and they have developed with two objectives. One is to analyse the kinetics and the distribution of molecular-aggregate sizes as a function of supersaturation. The aim is to understand the nature of the prenuclear clusters that form in solution and how they transform into crystal nuclei (Kam et al., 1978; Georgalis et al., 1993; Malkin & McPherson, 1993, 1994; Malkin et al., 1993). Such a quantitative approach has sought to define the underlying kinetic and thermodynamic parameters that govern the nucleation process. The second objective is to use light-scattering methods to predict which combinations of precipitants, additives and physical parameters are most likely to lead to the nucleation and growth of crystals (Baldwin et al., 1986; Mikol, Hirsch & Giegé, 1990; Thibault et al., 1992; Ferré D'Amaré & Burley, 1997). A major goal here is to reduce the number of empirical trials. The analyses depend on the likelihood that precipitates are usually linear, branched and extended in shape, since they represent a kind of random polymerization process (Kam et al., 1978). Aggregates leading to nuclei, on the other hand, tend to be more globular and three-dimensional in form. Thus, a mother liquor that indicates a nascent precipitate can be identified as a failure, while those that have the character of globular aggregates hold promise for further exploration and refinement. Other analyses have been based on discrimination between polydisperse and monodisperse protein solutions, which suggests that polydispersity hampers crystallization, while monodispersity favours it (Mikol, Hirsch & Giegé, 1990).

A more quantitative approach is based on measurement of the second virial coefficient B2, which serves as a predictor of the interaction between macromolecules in solution. Using static light scattering, it was found that mother liquors that yield crystals invariably have second viral coefficients that fall within a narrow range of small negative values. Recently, a correlation between the associative properties of proteins in solution, their solubility and B2 coefficient was highlighted (George et al., 1997). If this proves to be a general property, then it could serve as a powerful diagnostic for crystallization conditions.

Related methods, such as fluorescence spectroscopy (Crossio & Jullien, 1992), osmotic pressure (Bonneté et al., 1997; Neal et al., 1999), small-angle X-ray scattering (Ducruix et al., 1996; Finet et al., 1998) and small-angle neutron scattering (Minezaki et al., 1996; Gripon et al., 1997; Ebel et al., 1999) have been used to investigate specific aspects of protein interactions under precrystallization conditions and have produced, in several instances, complementary answers to those from light-scattering studies. Of particular interest are the neutron-scattering studies that provided evidence for two opposite effects of agarose and silica gels on lysozyme nucleation, the agarose gel being a promoter and the silica gel an inhibitor of nucleation (Vidal et al., 1998a,b).

A number of microscopies and other optical methods can be used for studying the crystal growth of macromolecules. These are time-lapse video microscopy with polarized light, schlieren and phase-contrast microscopy, Mach–Zehnder and phase-shift Mach–Zehnder interferometry, Michelson interferometry, electron microscopy (EM), and atomic force microscopy (AFM). Each of these methods provides a unique kind of data that are complementary and, in combination, have yielded answers to many relevant questions.

Time-lapse video microscopy has been used to measure growth rates (e.g. Koszelak & McPherson, 1988; Lorber & Giegé, 1992; Pusey, 1993). It was valuable in revealing unexpected phenomena, such as capture and incorporation of microcrystals by larger crystals, contact effects, consequences of sedimentation, flexibility of thin crystals, fluctuations in growth rates and initiation of twinning (Koszelak et al., 1991).

Several optical-microscopy and interferometric methods are suited to monitoring crystallization (Shlichta, 1986) and have been employed in bio-crystallogenesis (Pusey et al., 1988; Robert & Lefaucheux, 1988). Information concerning concentration gradients that appear as a consequence of incorporation of molecules into the solid state can be obtained by schlieren microscopy, Zierneke phase-contrast microscopy, or Mach–Zehnder interferometry. These methods, however, suffer from a rather shallow response dependence with respect to macromolecule concentration (Cole et al., 1995). This can be overcome by introduction of phase-shift methods and has been successfully achieved in the case of Mach–Zehnder interferometry. With this technique, gradients of macromolecular concentration, to precisions of a fraction of a mg per ml, have been mapped in the mother liquor and around growing crystals. Classical Mach–Zehnder interferometry has been used to monitor diffusion kinetics and supersaturation levels during crystallization, as was done in dialysis setups (Snell et al., 1996) or in counter-diffusion crystal-growth cells (García-Ruiz et al., 1999).

Michelson interferometry can be used for direct growth measurements on crystal surfaces (Komatsu et al., 1993). It depends on the interference of light waves from the bottom surface of a crystal growing on a reflective substrate and from the top surface, which is developing and, therefore, changes as a function of time with regard to its topological features. Because growth of a crystal surface is generally dominated by unique growth centres produced by dislocations or two-dimensional nuclei, the surfaces and the resultant interferograms change in a regular and periodic manner. Changes in the interferometric fringes with time provide accurate measures of the tangential and normal growth rates of a crystal (Vekilov et al., 1992; Kuznetsov et al., 1995; Kurihara et al., 1996). From these, physical parameters such as the surface free energy and the kinetic coefficients which underlie the crystallization process can be determined.

EM (Durbin & Feher, 1990) and especially AFM are powerful techniques for the investigation of crystallization mechanisms and their associated kinetics. The power of AFM lies in its ability to investigate crystal surfaces in situ, while they are still developing, thus permitting one to visualize directly, over time, the growth and change of a crystal face at near nanometre resolution. The method is particularly useful for delineating the growth mechanisms involved, identifying dislocations, quantifying the kinetics of the changes and directly revealing the effects of impurities on the growth of protein crystals (Durbin & Carlson, 1992; Konnert et al., 1994; Malkin et al., 1996; Nakada et al., 1999). AFM has also been applied to the visualization of growth characteristics of crystals made of RNA (Ng, Kuznetsov et al., 1997) and viruses (Malkin et al., 1995). A typical example, Fig. 4.1.5.1, shows two images of the surface of a RNA crystal with spiral growth at low supersaturation and growth by two-dimensional nucleation at higher supersaturation. A noteworthy outcome of the study was the sensitivity of growth to minor temperature changes. A variation of 2–3 °C was observed to be sufficient to transform the growth mechanism from one regime (spiral growth) to another (by dislocation).

Figure 4.1.5.1 | top | pdf | Visualization of the surface of yeast tRNAPhe crystals by AFM. (a) Spiral growth with screw dislocations occurring at lower supersaturation and (b) growth by two-dimensional nucleation occurring at higher supersaturation, showing growth and coalescence of islands and expansions of stacks. Notice that supersaturation and type of growth mechanisms are very temperature-sensitive and are modulated by temperature variation, since in (a), crystals grew at 15 °C and in (b), at 13 °C. Reproduced with permission from Ng, Kuznetsov et al. (1997). Copyright (1997) Oxford University Press.

The ultimate objective of structural biologists is to analyse crystals of high perfection, in other words, with a minimum of disorder and internal stress. The average disorder of the molecules in the lattice is expressed in the resolution limit of diffraction. Wilson plots provide good illustrations of the diffraction quality for protein crystals. Other sources of disorders, such as dislocations and related defects, as well as the mosaic structure of the crystal, may strongly influence the quality of the diffraction data. They are responsible for increases in the diffuse background scatter and a broadening of diffraction intensities. These defects are difficult to monitor with precision, and dedicated techniques and instruments are required for accurate analysis (reviewed by Chayen et al., 1996).

Mosaicity can be defined experimentally by X-ray rocking-width measurements. An overall diagnostic of crystal quality can be obtained by X-ray diffraction topography. Both techniques have been refined with lysozyme as a test case and are being used for comparative analysis of crystals grown under different conditions, both on earth and in microgravity. For lysozyme and thaumatin, improvement of the mosaicity, as revealed by decreased rocking widths measured with synchrotron radiation, was observed for microgravity-grown crystals (Snell et al., 1995; Ng, Lorber et al., 1997).

Illustration of mosaic-block character in a lysozyme crystal was provided by X-ray topography (Fourme et al., 1995). Comparison of earth and microgravity-grown lysozyme crystals showed a high density of defects in the earth-grown control crystals, while in the microgravity-grown crystals several discrete regions were visible (Stojanoff et al., 1996). X-ray topographs have also been used to compare the orthorhombic and tetragonal forms of lysozyme crystals (Izumi et al., 1996), to monitor temperature-controlled growth of tetragonal lysozyme crystals (Stojanoff et al., 1997), to study the effects of solution variations during growth on the perfection of lysozyme crystals (Dobrianov et al., 1998), and to quantify local misalignments in lysozyme crystal lattices (Otalora et al., 1999).