Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 4.1, pp. 111-113   | 1 | 2 |

Section 4.1.5. From the macromolecule to perfect crystals: the physics view

C. Sauter,a B. Lorber,b A. McPhersonc and R. Giegéd*

aInstitut de Biologie Moléculaire et Cellulaire (IBMC), Centre National pour la Recherche Scientifique (CNRS), 15 rue René Descartes, Strasbourg, F-67084, France,bUPR 9002, IBMC–CNRS, 15 rue René Descartes Cedex, Strasbourg, 67084, France,cDepartment of Molecular Biology and Biochemistry, University of California, 560 Steinhaus, Irvine, CA 92697–3900, USA, and dMachineries Traductionnelles, ARN, UPR 9002, IBMC du CNRS, 15 rue René Descartes, Strasbourg, 67084, France
Correspondence e-mail:

4.1.5. From the macromolecule to perfect crystals: the physics view

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Each of the four stages in crystallization (prenucleation, nucleation, growth and cessation of growth) can be monitored by specific physical techniques. Although systematic characterization of crystallization is usually not carried out in practice, characterization of individual steps and measurement of the physical properties of crystals obtained under various conditions may help in the design of appropriate experimental conditions to reproducibly obtain crystals of a desired quality (e.g. of larger size, improved morphology, increased resolution or greater perfection). Prenucleation and nucleation

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DLS relies on the scattering of monochromatic light by aggregates or particles moving in solution. Since diffusivity of the particles is related to their size by the Stokes–Einstein equation, measurement of diffusion coefficients can be translated into hydrodynamic radii. By making measurements as a function of scattering angle, information regarding aggregate shape can also be obtained. For single-component systems, the method for determining the size of macromolecules, viruses and larger particles up to a few µm is straightforward. For polydisperse and concentrated systems, the problem is more complex, but with the use of auto-correlation functions and advances in signal detection, DLS provides good estimates of aggregate size distribution and supplies a diagnostic tool for quality control of proteins and optimization of crystallization conditions. Experimental necessity encouraged the design of dedicated instruments for protein crystallization, combining e.g. imaging of crystals and DLS analysis within crystallization droplets (Dierks et al., 2008[link]).

In biocrystallogenesis, investigations based on light scattering have been useful in detecting nucleation prior to the appearance of crystals observable under the light microscope, that is, in understanding prenucleation and nucleation. Many studies have been carried out with lysozyme as the model (Kam et al., 1978[link]; Durbin & Feher, 1996[link]), though not exclusively, and they have been developed with two objectives. One is to analyse the kinetics and the distribution of molecular aggregate sizes as a function of supersaturation. The idea is to understand the nature of prenuclear clusters that form in solution and how they transform into crystal nuclei (Kam et al., 1978[link]; Georgalis et al., 1993[link]; Malkin & McPherson, 1994[link]). Such a quantitative approach has sought to define the underlying kinetic and thermodynamic parameters that govern the nucleation process.

A more practical objective is to use light-scattering methods to predict which combinations of crystallants, additives and physical parameters are most likely to lead to the nucleation and growth of crystals (Mikol, Hirsch & Giegé, 1990[link]; Ferré-D'Amaré & Burley, 1997[link]; Borgstahl, 2007[link]; Wilson, 2003[link]; Niesen et al., 2008[link]). 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[link]). Aggregates leading to nuclei, on the other hand, tend to be more globular and three dimensional in form. Thus, mother liquors that indicate 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[link]).

A more quantitative approach is based on measurement of the second virial coefficient B2, which serves as a predictor of the type of interaction between macromolecules occurring in solution. Using static light scattering, it was found that mother liquors that invariably yield crystals have second virial coefficients that fall within a narrow range of small negative values. Correlations between the associative properties of proteins in solution, their solubility and the B2 coefficient were highlighted (e.g. George et al., 1997[link]; Wilson, 2003[link]), and seem to be a general feature. This is a powerful diagnostic of crystallization conditions.

Related methods, such as fluorescence spectroscopy (Crosio & Jullien, 1992[link]; Forsythe et al., 2006[link]), osmotic pressure (Bonneté et al., 1997[link]; Neal et al., 1999[link]), small-angle X-ray scattering (Finet et al., 1998[link]) and small-angle neutron scattering (Ebel et al., 1999[link]; Gripon et al., 1997[link]; Minezaki et al., 1996[link]; Vidal et al., 1998[link]), were used to investigate specific aspects of protein interactions under precrystallization conditions and produced, in several instances, complementary answers to those from light-scattering studies. Growth and cessation of growth

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A number of microscopies and other optical methods can be used for studying the crystal growth of proteins (Van Driessche, Otalora, Sazaki et al., 2008[link]). 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), atomic force microscopy (AFM) and laser confocal microscopy with differential interference contrast microscopy. Each of these methods provides complementary data which, in combination, have yielded answers to many relevant questions.

Time-lapse video microscopy has been used to measure growth rates (Koszelak & McPherson, 1988[link]; Lorber & Giegé, 1992[link]; Zhu et al., 2001[link]). 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[link]). Optical microscopy and interferometric methods gave information on concentration gradients that appear as a consequence of incorporation of molecules into the solid state. These methods, however, suffer from rather shallow response dependence with respect to protein concentration. This can be overcome by the introduction of phase-shift methods, as has been successfully achieved in the case of Mach–Zehnder interferometry. With this technique, gradients of protein concentration 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[link]) or in counter-diffusion crystal growth cells (Garcia-Ruiz et al., 1999[link]). Using laser confocal microscopy combined with differential interference contrast microscopy it was possible to visualize dislocations in protein crystals during growth (Sazaki et al., 2005[link]). Single-molecule visualization techniques gave access to direct observation of the diffusion of individual fluorescence-labelled protein molecules at an interface between a solution and a protein crystal (Sazaki et al., 2008[link]).

Michelson interferometry can be used for direct growth measurements on crystal surfaces (Komatsu et al., 1993[link]). It depends on the interference of light waves from the bottom surface of a crystal growing from a reflective substrate and 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., 1993[link]; Kuznetsov et al., 1995[link]; Kurihara et al., 1996[link]). From these data, one can determine the surface free energy and the kinetic coefficients that underlie the crystallization process.

EM (Durbin & Feher, 1990[link]) and especially AFM (McPherson et al., 2004[link]) 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 directly visualize, over time, the growth and change of a crystal face at near-nanometre resolution. The method is particularly useful in delineating the growth mechanisms involved, identifying dislocations, recording the kinetics of the changes and directly revealing impurity effects on the growth of protein crystals (Konnert et al., 1994[link]; Malkin et al., 1996[link]; Nakada et al., 1999[link]) (Fig.[link]). AFM was also applied for the visualization of growth characteristics of crystals made of viruses (Malkin et al., 1995[link]) and RNA (Ng, Kuznetsov et al., 1997[link]). A noteworthy outcome of such studies was the sensitivity of growth to minor temperature changes. A variation of 2–3 °C was sufficient to transform the growth mechanism of yeast tRNAPhe from spiral screw dislocation growth at low supersaturation to two-dimensional island formation at high supersaturation (Ng, Kuznetsov et al., 1997[link]).


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Growth mechanisms and visualization of protein crystal surfaces by AFM. In (a) and (b) are images of screw dislocations on the surfaces of crystals of the proteins canavalin and trypsin, respectively. The scan areas are 10 µm2 in (a) and 30 µm2 in (b). Screw dislocation growth predominates at low supersaturation. In (c) and (d) are examples of crystal growth by the formation of two-dimensional islands on the surfaces of crystals of the proteins thaumatin and glucose isomerase, respectively. The scan areas are 20 µm2 in (c) and 11 µm2 in (d). Growth by two-dimensional island formation and spread dominates at higher supersaturation. Uncoupling nucleation and growth, and the constant-growth regime

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The preparation of high-quality protein crystals should preferentially occur at lowest supersaturation and under a constant-growth regime. Achieving this aim with conventional crystallization methods is a priori not easy since growth of crystals is accompanied by a decrease of supersaturation in the crystallization medium (see the trajectory of crystal/solution equilibration in a phase diagram, Figs.[link] and[link]). The implication is that it is possible to change the growth regime during the course of the crystallization process, as could be seen by AFM (Ng, Kuznetsov et al., 1997[link]). Such a change will perturb crystal formation and probably accounts for the frequently observed non-reproducibility in diffraction properties of protein crystals. Using flow cells with a constant supply of fresh protein may help to overcome this difficulty. Separating the nucleation and growth phases is another alternative (Chayen, 2005[link]). This can be straightforwardly done by seeding procedures (see Section[link]). Crystal perfection

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The ultimate objective of structural biologists is to analyse crystals of high perfection, in other words, with a minimum of defects, disorder, impurity incorporation and internal stress. Such imperfections can be visualized using laser confocal microscopy combined with differential interference contrast microscopy (Iimura et al., 2005[link]; Sazaki et al., 2005[link]). They can also be evaluated by the resolution limit of diffraction, which expresses the average disorder of the molecules in the crystal lattice. Wilson plots provide good illustrations of diffraction quality for protein crystals. Other sources of disorder, such 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.

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 were 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 the microgravity-grown crystals (Snell et al., 1995[link]; Ng, Lorber et al., 1997[link]; Lorber, Sauter, Robert et al., 1999[link]).

An illustration of mosaic block character in a lysozyme crystal was provided by X-ray topography (Fourme et al., 1995[link]). Comparison of earth- and microgravity-grown lysozyme crystals showed a high density of defects in the earth control crystals, while in the microgravity case, several discrete regions were visible (Stojanoff et al., 1996[link]). X-ray topographs have also been used to compare crystal polymorphs (Izumi et al., 1996[link]), to monitor temperature-controlled growth of tetragonal lysozyme crystals (Stojanoff et al., 1997[link]), to study the effects of solution variations during growth on crystal perfection (Dobrianov et al., 1998[link]; Otálora et al., 1999[link]), to compare crystals grown in solution and in agarose gel (Lorber, Sauter, Ng et al., 1999[link]), and to map defects in the bulk of protein crystals (Hu et al., 2001[link]).


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