16.2.1 Basics of Crystallisation

Protein crystallisation was first developed in the late nineteenth century as a method to demonstrate protein purity, and crystallisation is still used during the chemical purification of organic compounds. However, most proteins do not tolerate the extremes of temperature, pH and solvents used for crystallising small molecules and predicting how any protein will crystallise is effectively impossible.

A crystal is an ordered repetition of a building block called the asymmetric unit, which is the smallest packing arrangement of the protein before crystallographic symmetry operators are applied to generate the effectively infinite crystal lattice. The packing of protein to build a three‐dimensional crystal is achieved by a series of specific salt bridges, hydrogen bonds and van der Waals' contacts between protein molecules. It is generally accepted that proteins destined for crystallisation should be as chemically pure as possible, which is trivial to assess by SDS polyacrylamide gel electrophoresis and mass spectrometry. The chances of growing crystals are improved by reducing conformational heterogeneity, though this is harder to monitor and achieve. Occasionally the presence of serendipitous impurities in the preparation or deliberately included ligands will aid crystal lattice formation but, on the whole, impurities decrease crystal quality by intercalating between asymmetric units, which may hinder crystal growth completely. It is important to have a monodisperse (a particle of uniform size), stable sample as crystallisation can take up to a few months. Proteins that fold poorly, have low thermal stability or are prone to degradation are less likely to crystallise. Time invested in protein quality control (e.g. circular dichroism for protein folding, thermal melts for protein stability) can save time overall. Protein flexibility, instability, denaturation and polydispersity are most likely to hinder crystallisation.

16.2.1.1 Crystallisation

Crystallisation is a two‐step process. First, a supersaturated solution of the molecule must form and be induced to form critical nuclei, microscopic clusters of the molecule in solution. Second, the nuclei must grow into a three‐dimensional crystal by the deposition of additional molecules on to the growing surface. The formation of nuclei is a thermodynamic process [1] that occurs once the protein reaches supersaturation, but exceeding the supersaturation limit results in protein precipitation. Supersaturation can be achieved by mixing a highly concentrated solution of the protein with crystallisation solutions, usually at a 1 : 1 ratio, and this mixture is left to equilibrate. In the case of vapour diffusion, the most popular protein crystallisation technique, the concentration of the components of the crystallisation drop reach equilibrium with those in the crystallisation well solution. Water is drawn from the drop to the well solution and eventually the protein reaches supersaturation (Figure 16.2).

There are three variants of vapour diffusion, hanging, sitting and sandwich, where water equilibrates between the drop and reservoir (Figure 16.3). Crystals can be obtained by dialysis where water and small molecule components of the crystallisation solution equilibrate between two compartments separated by a semi‐permeable membrane. In the batch method, the crystallisation reagent and protein mixture is covered by oil and water molecules evaporate slowly through the oil. Proteins can also be crystallised in capillaries where the protein and crystallisation solution are not mixed but are just in contact and the two solutions counterdiffuse; somewhere in this dynamic arrangement a supersaturated zone may form. For a review of other common methods, see McPherson and Gavira [2]. Finally, crystallisation of membrane proteins forms a distinct challenge as substantial parts of these protein surfaces are highly hydrophobic as they would ordinarily be embedded in a lipid membrane. Membrane proteins therefore need to be solubilised and crystallised in the presence of detergents, or lipidic cubic phases, introducing further important variables to crystallisation. Membrane protein crystallisation has been reviewed recently by Parker and Newstead [3].

16.2.2 Basics of X‐Ray Crystallography

A single protein molecule in solution will diffract X‐rays but will generate a scattering signal below the detection capabilities of any detector; even if a suitably sensitive detector did exist, the protein would likely be destroyed by absorbing the applied radiation before a useful signal was recorded. Protein crystals thus amplify the scattering signal and mitigate the damaging effects of the radiation. Whilst crystals of small molecules (M_r ∼ < 500 Da) typically do not contain solvent, proteins are highly solvated molecules and consequently macromolecular crystals have solvent contents in the 20–80% range, which can be exploited in soaking experiments of inhibitors, effectors and other ligands, or compounds for experimental phasing. High solvent content is advantageous in phase improvement strategies but creates problems in cryocrystallography because of potential ice formation.

In order to interpret the X‐ray data, we must first understand the principles by which molecules assemble into crystalline three‐dimensional repeating arrays. The unit cell (Figure 16.4), the smallest volume to describe a crystal lattice, repeats identically in three dimensions to form the crystal and is characterised by three distances (measured in Å) a, b, c and three angles α, β, γ (measured in °). There are 230 unique ways that molecules can be arranged symmetrically within a unit cell and still obey the translational symmetry in all three directions. Hence there are 230 possible individual space groups that describe the symmetry within the unit cell. If the space group of the crystal cannot be determined correctly, the crystal structure cannot be solved. Each space group is formed by a unique combination of 7 lattice systems, 14 Bravais lattices and 32 crystallographic point groups. Each of these terms is described briefly in the next two paragraphs, but for a comprehensive description the reader should consult the International Tables for Crystallography [4].

Symmetry rules define the building block of each unit cell, called the asymmetric unit, though the asymmetric unit may contain more than one copy of the molecule. The seven lattice systems impose symmetry rules on the crystal in defining its space group. These lattice systems include triclinic, which imposes no symmetry restraints on the unit cell parameters, and tetragonal, with one fourfold rotation axis, requiring that unit cell dimensions a = b and all three angles are 90°. The most complex lattice system is cubic, in which a = b = c and all three angles are 90°. The 14 Bravais lattices are formed by combining a lattice system with fixed lattice points, or origins, found at the corners of each unit cell only, called primitive (or P for short). Additional lattice points can be accommodated at the centre of each face of the unit cell, called face‐centred (F), at the centre of the unit cell, called body‐centred (I) or on one parallel face, called C‐centred (C). Crystallographic point groups are a set of symmetry operators applied to the asymmetric unit to generate the unit cell and leave a lattice point fixed while moving other parts of the crystal to symmetry‐equivalent positions. Other than in the triclinic space group P1, each unit cell comprises more than one asymmetric unit. In the tetragonal space group P422 there are 8 asymmetric units and in one of the most extreme cases, the cubic space group F432, there are 96.

Four symmetry operators define point groups: rotation and screw axes, mirror and glide planes. However, because amino acids (except glycine) contain chiral centres, mirror and glide planes are incompatible with chiral protein crystals and consequently there are just 65 macromolecular space groups. Rotation axes are n‐fold where n is 2, 3, 4 or 6, because only these rotations can be applied to generate infinite repeats with no gaps, called the crystallographic restriction. Crystallographic and macromolecular symmetry axes can coincide: OmpF crystallises with one molecule in the asymmetric unit of the trigonal space group P321 (PDBid 2OMF) and the biological, trimeric structure of OmpF is reassembled by application of the crystallographic threefold axis (Figure 16.5). Macromolecules with symmetries distinct from two‐, three‐, four‐, and sixfold can still crystallise: GroEL contains sevenfold symmetry [5] and the RNA‐binding protein TRAP has 11‐fold symmetry [6]. The incompatibility of these symmetries with the crystallographic restriction means that entire assemblies are present within crystallographic asymmetric units. Screw axes combine n‐fold/360° rotations with translations along the crystallographic axis and are demarked with a subscript number related to the fraction of the unit cell dimension of the translation. For instance, the space group P2₁ means that there is one twofold axis of rotation combined with a translation of half a unit cell length along the same crystallographic axis.

16.2.2.1 Bragg's Law

Father and son, William Henry and William Lawrence Bragg, are generally viewed as the Godfathers of crystallography and shared the Nobel Prize for Physics in 1915 – when Lawrence was just 25 years old. The Braggs observed that crystalline materials diffracted X‐rays in an ordered manner and William Lawrence proposed that crystals could be viewed as a set of parallel planes separated by the distance d. The electrons interfering with incident X‐rays would produce constructive interference only if the phase shift of waves reflected by different planes was a multiple of 2π. William Henry built a diffractometer to record each reflection on a photographic plate enabling atomic distances in simple salt crystals, such as NaCl, to be determined. Bragg's law is normally expressed as

where d is the interplanar distance, θ is the incident or scattering angle, n is a positive integer and λ is the wavelength of the incident beam (Figure 16.6). Note that Bragg's law also applies to electron and neutron diffraction, such is its applicability to the fundamentals of diffraction.

Waves that traverse larger interplanar spacings are diffracted by smaller θ angles and are usually observed towards the centre of the detector. These waves convey low resolution information on larger features such as the overall solvent distribution and the protein envelope. These low resolution reflections are essential for the structure solution process and have higher than average intensities. Reflections with high θ angles are observed towards the perimeter of the detector due to the small interplanar spacing d (Figure 16.7). These reflections carry information about spatially close features and are the high resolution data essential for building an atomic model of the protein. However, the high resolution reflections can be difficult to measure accurately over background and are lost first if the crystal suffers from radiation damage.

The pattern of reflections recorded is derived from the diffraction of X‐rays from points in the reciprocal lattice, a coordinate system related to real space by the following operations:

We record the intensity of each reflection on the detector in real terms (i.e. a detector coordinate in x and y, and an intensity for each pixel) from which their coordinates in reciprocal space (h, k, l), called Miller indices, can be determined during the indexing and initial processing of the diffraction data. In short, low resolution reflections have low Miller indices and higher resolution reflections have one or more high Miller indices.

The Ewald sphere (Figure 16.8) is a geometrical construction that helps to explain diffraction. The crystal is located at the centre of the Ewald sphere, which has a radius of 1/λ, where λ is the radiation wavelength. Diffraction can only be recorded when reciprocal lattice points coincide with the sphere surface, but only a small number of points fulfil this condition at any given time. To record the data required to calculate the structure of the crystallised molecule it is necessary to rotate the crystal around a rotation axis whilst it is illuminated by the X‐ray beam.

The symmetry relationships within the unit cell dictate that symmetry‐related reflections exhibit the same intensities. Therefore, symmetry within the crystal reduces the quantity of data needed to solve the structure. Some special relationships require further explanation. Friedel pairs are reflections that are related by a transformation through the origin such that the intensity of any reflection, I _h,k,l , is normally equal to the intensity of its Friedel pair I _{−h,−k,−l} . Friedel's law breaks down in the presence of heavier atoms (S, Se or any transition metal) that are anomalous scatterers when the energy of the incident radiation is at or above an atomic absorption edge of the heavy atom. Other reflections may be related to one of the Friedel pairs, for example in the presence of a twofold symmetry axis, and such reflections are called Bijovet pairs and can be used to strategically orient the crystal for data collection.

Finally, all X‐ray detectors are capable of recording the intensity of the diffracted X‐rays, which can be considered as wave forms. A simple wave is a sinusoidal function (Figure 16.9) and though diffracted X‐rays are complex waves, they are repetitive. The mathematical function that relates the electron density of the crystallised molecule to the diffracted waves is the Fourier transform, named after the eighteenth century French mathematician Joseph Fourier, and the operation from reciprocal space to real space is an inverse Fourier transform. In brief, two parameters are needed for the Fourier transform. The first is the amplitude of the wave, which is proportional to the root mean square of the intensity, and the second is the phase, which is the angle at which the wave peaks.

16.2.3 Scaling

Symmetry‐equivalent reflections may not experience the same environment – for instance, variations in crystal quality, shape and size, and the path of the X‐ray beam through the loop and cryoprotectant can affect the signal‐to‐noise ratio of the recorded reflections. The crystal may have been centred poorly, and the X‐ray dose received may vary during the experiment. Many modern detectors are mosaic assemblies and each tile in the detector can have slight variations in sensitivity. The beam flux may also reduce during the time of the data collection. Therefore, each reflection should be recorded multiple times before merging, averaging and outputting a single mean intensity, a process called scaling. Data for multidataset techniques also need to be on the same relative scale and cross‐dataset scaling must be done after internal scaling has been completed. The amplitude of each reflection needs to be calculated, which is proportional to the root mean square of its intensity, for calculating the structure factors necessary for Fourier syntheses. Typically, 5% of the measured data are randomly marked at the end of scaling for cross‐validation, the R _free, which are used to provide an unbiased metric of a quality model.

16.2.4 Radiation Damage

All biological materials suffer from radiation damage when exposed to ionising radiation and radiation damage in protein crystallography is a significant challenge, especially considering third generation synchrotron beamlines where fluxes of 10¹² photons per second and beam cross‐sections of 20–50 μm are not uncommon. One of the first properties of the crystal that is lost during radiation damage is diffraction strength. The higher resolution reflections fade quickly and disappear, a phenomenon first described in the 1960s [7]. The diffraction lifetime is related to the X‐ray dose and Henderson has proposed a generalised limit for protein crystallography of 2 × 10⁷ Gy (J/kg), the X‐ray dose that can be absorbed by a cryocooled protein crystal before the mean reflection intensity is halved [8]. The dose constraint has been refined subsequently to 3–4 × 10⁷ Gy [9]. The radiation absorbed by the sample leads to crystal decay, increasing disorder within the sample, and a consequent reduction in reflection intensity through two phenomena. Primary damage is the ionisation of an atom due to photoelectric absorption or Compton scattering and only a reduction in the total applied dose can reduce the effects of primary damage. Secondary damage occurs from the formation of secondary electrons that diffuse and induce further damage [10] but its accrual rate can be reduced by maintaining the sample at cryogenic temperatures. A constant stream of dry nitrogen gas at 100 K is directed over the crystal during data collection to slow secondary radiation damage. Covalent bonds break on absorbing sufficient energy, resulting in the destruction of the protein. The overall loss of diffraction intensity affects the whole experiment but localised specific damage can also occur, such as disulphide bond destruction, leading to artefacts in the crystallographic analysis. Radiation damage should be avoided as much as possible as even mild damage can complicate structure solution and analysis unnecessarily.

16.2.5 Matthews' Coefficient

Matthews' coefficient (V _M) is a measure of the solvent content of protein crystals and typically ranges between 27 and 65%, corresponding to V _Ms of 1.62 and 3.53 ų/Da, respectively [11]. Crystals with low V _Ms tend to diffract well and those with high V _Ms tend to diffract modestly. The most likely number of copies of the crystallised molecule in the crystallographic asymmetric unit can be calculated in several ways (e.g. http://csb.wfu.edu/tools/vmcalc/vm.html, http://www.ruppweb.org/mattprob/default.html and the CCP4 suite), knowledge of which is imperative for molecular replacement and density modification routines.

16.2.6 Non‐crystallographic Symmetry

Proteins, especially symmetric ones, can pack with multiple copies within the asymmetric unit. The spatial relationships between each molecule do not obey crystallographic symmetry rules; instead they follow non‐crystallographic symmetry (NCS) operators. Detecting and defining NCS operators can be critical to successful structure solution and in the special case of icosahedral virus crystallography, NCS can be exploited to solve new structures without recourse to experimental phasing [12].

There are two forms of NCS. First, protein molecules orientated in the same way within the asymmetric unit can be separated by a simple translation, and the translational symmetry is detected by a native Patterson function. Alternatively, and more commonly, molecules within the asymmetric unit are related by set of rotations alone, as first detected for haemoglobin [13] in a calculation called a self‐rotation function. Both types of NCS are detected by different applications of the Patterson function, which is calculated directly from the intensities of the diffraction data and is thus independent of phase information. The resultant Patterson map containing peaks corresponding to the vector between every atom in the asymmetric unit and every other atom. A simple structure containing three atoms will yield a Patterson map containing just six peaks, but a protein of 43 kDa will yield an uninterpretable Patterson map containing 9 million peaks. Subsets of these peaks will superimpose by correctly applying NCS to determine the spatial relationships between molecules in the asymmetric unit.

16.2.7 Structure Factors

While the amplitude of each reflection is calculated from its measured intensity, this information is insufficient to calculate an electron density map. The Fourier synthesis to calculate the electron density map depends upon the structure factor, F _h,k,l , of each measured reflection. Structure factors encompass both amplitude and phase information of each reflection and each F _h,k,l is thus related to the corresponding reflection intensity, I _h,k,l . Once phase information has been obtained, each F _h,k,l , can be derived and an electron density map calculated.

16.2.8 Phase Problem

It is impossible to measure reflection phases directly and therefore structure factors cannot be calculated for the Fourier transform to generate an electron density map. This is the crystallographic phase problem that can be solved either by molecular replacement, and modern software pipelines perform initial searches automatically, or by experimental phasing (see [14,15)). We introduce both in the next sections but do not discuss direct methods that are used mostly to solve small molecule structures and sometimes to solve atomic resolution structures of small proteins.

16.2.8.2 Experimental Phasing: SAD

The current method of choice for experimental phasing is single‐wavelength anomalous dispersion (SAD). It relies upon collecting data on an anomalous scattering‐containing sample from incident radiation at or above the scatterer's atomic absorption energy. Selenomethionine is most commonly used for anomalous scattering measurements, with data collected above the Se K edge, 12 657 eV (0.9795 Å). Reflections no longer scatter in phase with the incident beam with radiation at or above the electron transition energy, the diffracted X‐rays no longer scatter in phase with the incident beam, I _h,k,l no longer equals I _{−h,−k,−l} and Friedel's law breaks down. Phase information can be obtained by careful measurement of the intensity differences between Friedel pairs, called anomalous differences (Figure 16.10).

The heavy atom positions are found by calculating a Patterson function from the anomalous differences. The Patterson peaks represent vectors between anomalous scatterers within and between asymmetric units. As anomalous differences are miniscule in comparison to normal intensities, the corresponding intensities of I _h,k,l and I _{−h,−k,−l} must be measured accurately; highly redundant data collection is one solution to this problem. The Patterson map is complicated by the presence of multiple heavy atom positions (there are N ²–N peaks in the Patterson function, where N is the number of heavy atoms) and partial occupancy and/or mobile atoms reduce Patterson map peak heights. If the position(s) of the heavy atom(s) can be deduced, phase estimates can be calculated. The phase problem is represented geometrically with the elegant Harker diagram (Figure 16.10): here the structure factor F_PH+ and its Bijvoet pair F_PH− result from the real contributions of the protein (F_P) and heavy atom (F_H) and imaginary contributions F_H+ and F_H−, which are oriented 90° away from the normal contribution F_H but in opposite directions. Two circles of radius F_PH+ and F_PH− can be drawn with the enantiomer shifted from the origin by the enantiomer imaginary contribution (Figure 16.10).

SAD is very effective at finding heavy atom positions when data are collected carefully but initial phases are dependent solely upon the anomalous differences and tend to be poorer than phases from MAD experiments. Single and multiple isomorphous replacement can be combined with anomalous scattering (SIRAS and MIRAS, see section 16.3.5.4), but unlike SAD and MAD these experiments rely upon having multiple isomorphous crystals available and the hit‐and‐miss approach of heavy atom derivatisation.

16.2.8.3 Experimental Phasing: MAD

The normal and anomalous scattering changes, which depend on the wavelength of the incident beam, can also be used to determine phases. This method is called multiple‐wavelength anomalous dispersion (MAD) and unlike SAD addresses phase ambiguity directly [17]. However, multiple datasets are required from ideally a single crystal and only heavy atoms with a transition edge in the range of a tunable synchrotron beamline can be used. Three datasets are typically collected: (i) the peak, where the anomalous scattering is at its highest; (ii) the high energy remote, where the normal scattering is close to its native value; (iii) the inflexion, where the normal scattering is at its lowest (Figure 16.11). Two‐wavelength experiments can mitigate radiation damage when collecting multiple datasets from a single crystal [18]. Heavy atom positions are found as in SAD and the third dataset resolves phase ambiguity because three circles in a Harker can only intersect at one point.

16.2.9 Model Building and Refinement

Atomic models can be built after successful molecular replacement or the calculation of initial experimental phases. The protein model is manipulated using a computer graphics programme (e.g. FRODO and O [19], but nowadays Coot [20]) by reference to the electron density map, followed by rounds of model refinement. The changes to the model are restrained to known stereochemical parameters, such as the covalent bond lengths and angles, and non‐covalent interactions such as van der Waals' contacts. A restraint is an ideal target value to which a function may converge. Refinement is an iterative process with the ambition of interpreting correctly every feature in the electron density map including protein atoms, bound ligands, ions and solvent. During refinement the observed data will be compared to calculated data from the model (atomic coordinates in x, y and z, atomic occupancies and a model for the positional error of each atom [or group of atoms] called the B factor). The two most important reliability factors, R _work and R _free, are calculated; the R _work is calculated using 95% of the data used in refinement and R _free is calculated on the residual 5% that are set aside for cross‐validation [21].

Some side chains or loops in the model may occupy multiple conformations because they are in different orientations in the asymmetric units through which the X‐ray beam passes during the experiment. At low resolution these differences may be invisible, but at resolutions better than 1.8 Å each conformation and the relative occupancy of each can be modelled. Ligands may bind only partially and the occupancy can be adjusted to reflect the electron density.

The atom positional error is represented by the B factor (Ų) as a spherical distribution and is normally modelled isotropically for each atom. Residue groups or overall B factor models may be more appropriate at very low resolution. Anisotropic B factor models can be modelled with ultrahigh resolution datasets. An additional thermal description of the model can be achieved with the TLS (translation libration screw) method (reviewed in [22]) with isotropic B factors.

16.3.1 Construct Design

Potential disordered regions, especially at the N‐ and C‐termini, should be removed from the recombinant construct and XtalPred [23] and PONDR [24] used to predict disorder at the amino acid level. Secondary structure predictions from JPred [25] can check that terminal helices are not cut in half when designing constructs. The crystallisation of thermostable orthologues or engineered variants [26] when the mesophilic equivalent protein has poor solution and/or thermostable characteristics should be attempted rather than focusing on just one family member. Alternate expression systems should be considered and the Oxford Protein Production Facility (OPPF at https://www.oppf.rc‐harwell.ac.uk/OPPF/public/services) offers high throughput cloning and expression services.

16.3.2 Crystallisation Screening

Successful chemical conditions to crystallise groups of proteins have been identified and made commercially available as crystallisation kits for soluble proteins (e.g. PACT, JCSG+), monoclonal antibodies (e.g. GRAS), nucleic acids (e.g. HELIX) and their binding proteins (e.g. Natrix), protein complexes (e.g. Wizard), kinases (e.g. Kinase) and membrane proteins (e.g. MembFac, MemGold, Lipidic‐Sponge Phase). The screens are biased towards what has worked previously, but new screens have emerged (MORPHEUS II and MIDAS) that explore different chemical space. Screens based on one fixed chemical family are also available (MORPHEUS, MPD and ammonium sulphate). Since optimisation may still be necessary to convert poor crystals into well‐diffracting ones, additive screens that contain low concentrations of ions, detergents and solvents may improve crystal quality. The websites of screen suppliers (www.moleculardimensions.com, www.jenabioscience.com, www.qiagen.com and www.hamptonresearch.com) are useful resources.

Most screens will work with protein concentrations of 5–50 mg/ml. The protein should be kept in a simple buffer, and metal ions and phosphates should be avoided to stop salt crystal formation during screening. Small proteins (<30 kDa) might need higher concentrations to crystallise: 190 mg/ml was required for the 15 kDa CBM62 [27]. Larger or less soluble proteins can be crystallised at concentrations as low as 1 mg/ml. Crystallisation should start with a sparse matrix screen and the experiment inspected immediately with a stereo microscope; many heavy precipitates suggest that the protein concentration is too high. If the drops are mostly clear the protein concentration is likely to be too low.

Crystallisation robots are commonplace and permit screening hundreds of conditions using small amounts of protein, 50–300 nl, per drop, and 70–100 μl of crystallisation screen per condition. Most crystallisation robots use almost exclusively multiwell plate format labware. There are many manufacturers and distributors of multiwell plates that can be used, with variations in reservoir volumes, number of wells and shapes (flat bottom or round bottom wells) for the experiment. Initial screening is usually performed in 96‐well format plates with small drops. Subsequently, initial hits are optimised on a larger scale. Anaerobic chambers can be used to store crystallisation experiments if the protein is redox sensitive.

When crystallising protein–ligand complexes, the ligand will generally need to be at a concentration of ∼20‐fold higher than K _d for the protein in order to saturate the binding site. Fundamental biochemistry thus ought to be performed before commencing potentially lengthy crystallisation screenings. Protein–protein complexes ought to be co‐expressed and only those fractions that contain both (or all) proteins purified. Alternatively, pre‐purified proteins should be mixed and the complex purified away from uncomplexed components by size exclusion chromatography.

Sitting drop vapour diffusion is the most common crystallisation technique because it matches best the experimental setups of crystallisation robots. Protein and crystallisation conditions are dispensed on to a plastic shelf. This is a simple and rapid procedure with most robots. For instance, it takes five minutes to dispense screen solutions from a deep well block into a 96‐well plate using a hand‐held multichannel pipette and two minutes for a TTP Labtech Mosquito to dispense protein and crystallisation solution for the entire plate at two drop ratios. Therefore, 192 experiments take less than 10 minutes to set up using only 28.8 μl of protein. Once the tray is finished the user seals all the drops using a clear plastic adhesive sheet and the tray is left at the chosen temperature for the precipitant concentration in the drop to equilibrate with that in the well.

Hanging drop experiments can also be established using robotics but this technique is normally favoured for manual crystallisation optimisation experiments. Here the optimisation reagents are pipetted directly into a 24‐well tissue culture tray and high vacuum grease around the rim of each well is used to provide an airtight seal. The protein and mother liquor are mixed on plastic or silanised glass coverslips, which are inverted over the greased well rim and an airtight seal made by gentle pressing.

In sandwich drop experiments, the protein is mixed with the crystallisation solution and ‘sandwiched’ between two flat glass or plastic surfaces. The sandwich is placed on to a support above the well solution in a tissue culture plate and sealed with vacuum grease and coverslips. Though less trivial to set up, the sandwich method can be advantageous because the sandwiched drop surface area is greatly reduced, which slows the equilibration rate substantially. Slowing the crystallisation process can lead to fewer, larger, better quality crystals, but the sandwich process does not lend itself easily to the economies of scale and throughput of sitting drop crystallisation. In capillary dialysis crystallisation a narrow bore capillary is filled with protein by capillary action and sealed at one end with low melting point wax. The open end of the capillary is placed into a plug of agarose gel into which the crystallisation reagent has been impregnated. Protein and crystallisation reagent diffuse to set up a range of unique crystallisation conditions within one capillary. The batch method has also been miniaturised; here small volumes of protein and crystallisation screen are mixed in a multiwell batch plate and maintained under a layer of paraffin oil to prevent the drop from drying out.

In the absence of crystals or poorly diffracting ones, the construct could be modified, or limited proteolysis in situ could be used to remove disordered regions [28]. Lysines can be methylated [29] and lysines and other residues mutated to alanine [30] to reduce surface entropy. Cysteines can be modified [31] to reduce redox sensitivity. Differential scanning fluorimetry and other biophysical techniques [32] may be used to improve the protein stability as a function of buffer composition (i.e. buffer type, pH, salt).

16.3.3 Cryoprotection

The natural form of crystalline ice on earth is sometimes referred to as hexagonal ice. It was predicted by Hass and Rossmann ∼50 years ago that crystalline ice formation in the solvent channels of protein crystals will disrupt or break the crystal lattice [35]. Cryoprotectants are small molecules such as organic solvents, salts or small organic compounds that inhibit the formation of hexagonal ice in protein crystals [36]. Alcohols have low melting points but are sometimes incompatible with proteins. Salts are widely used on the roads in winter to prevent ice formation and saturated salts can also be used to cryoprotect protein crystals [37]. Polyethylene glycols (PEGs) are widely used as precipitants in protein crystallography, and hence PEG 400 is a very popular cryoprotectant. Other than undiluted, saturated salts, most cryoprotectants are used in the 20–30% range. Ideally the cryoprotectant replaces water and maintains the reservoir composition, assuming that stock solution concentrations can be made high enough to supplement the crystallisation condition with an appropriate cryoprotectant. It is tedious and time consuming to make each mother liquor and cryoprotectant combination from scratch for a large number of crystallisation conditions and often it is possible to simply dilute the reservoir directly with the cryoprotectant (e.g. 8 μl of reservoir and 2 μl of PEG 400 to achieve a 20% PEG 400 cryoprotectant). Some cryoprotectants are immiscible with the reservoir (for instance ammonium sulphate and ethylene glycol) and inspection of the cryoprotectant under the microscope will identify unwanted phase separation.

If the sample diffracts badly, its diffraction at room temperature should be tested to determine if the cryoregime is the root cause of the poor diffraction. The crystal should be mounted in a loop with a viscous oil, such as paratone N, which will protect it from dehydration at room temperature for long enough to establish the sample's base diffraction properties. Some crystallisation conditions are already cryoprotected because of their composition (e.g. the entire MORPHEUS screen) and no additional cryoprotection steps are required.

Glycerol has been used extensively as a cryoprotectant and the concentration required to cryoprotect common crystallisation conditions has been published [38]. Glycerol increases protein solubility and can dissolve protein crystals [39]. Glycerol can also be found in the binding pockets of carbohydrate binding and processing proteins instead of the native ligand when glycerol is used as a cryoprotectant because 20% glycerol, 2.1 M, outcompetes the binding of the desired ligand that is normally often present at mM levels (e.g. [40]).

There are many methods and cryoprotectants available and we direct the reader to Ciccone et al. [39] and Parkin et al. [41].

16.3.3.1 Mounting

Increased automation, especially at synchrotrons, has necessitated mount type and length standardisation. Several crystal mounts, pins and loops are available from commercial suppliers (e.g. www.mitegen.com, www.hamptonresearch.com and www.moleculardimensions.com). The mounts come in a variety of shapes, sizes and materials, including nylon, polyimide and other polymers (Figure 16.12). To reduce background on the diffraction image and to aid sample visualisation, the size of the loop should be matched to that of the crystal.

If no crystal manipulation is necessary, samples can be harvested and cryocooled directly. Otherwise 0.5–1 μl of the cryoprotectant should be placed next to the sample‐containing drop, ideally in the same focal plane (Figure 16.13). The crystal is picked up with the loop and transferred to the adjacent cryoprotectant drop. The loop is rinsed in the cryoprotectant, away from the crystal, before the crystal is removed from the cryoprotectant and cryocooled. This procedure should be completed within a few seconds to avoid dehydrating the sample, so all necessary tools should be to hand. If longer times (minutes to overnight) are required for ligand soaking and/or cryoprotection, the drop must be kept sealed within the experimental chamber.

Acupuncture needles to remove skin (made of unfolded proteins) from the surface of the drop are useful and can also be used to break crystals free from the well or separate multiple, intergrown crystals. A cat's whisker glued to the end of a laboratory pipette tip, mounted on a pencil for handling, is useful as it is just stiff enough to gently push a crystal around without damaging it.

16.3.3.2 Cryocooling

The sample must be cryocooled rapidly once cryoprotected. Since speed is essential to vitrify water without crystalline ice formation, cryocooling by plunging the sample directly into a liquid nitrogen bath is best. Slow cryocooling can result in hexagonal ice formation, even if the sample is cryoprotected adequately. Hexagonal ice has a translucent, white appearance and should be avoided. The cryocooled samples are placed into a pre‐labelled cryovial while being retained under liquid nitrogen by careful juxtaposition of the mount and cryovial (Figure 16.14); such samples can be stored indefinitely in liquid nitrogen dewars.

When liquid nitrogen is exposed to ambient air, moisture condenses on the cold nitrogen gas forming flocculent ice, which should not build up in the liquid nitrogen dewar. Flocculent ice can be removed from liquid nitrogen by filtering through ‘blue roll’ in a metal funnel. The cryomount components can build up static and attract flocculent ice, and this should be avoided. Filling the liquid nitrogen bath and dewars used in cryocooling (Figure 16.15) completely will dilute the potential effect of condensing moisture. Replacing liquid nitrogen frequently or recycling liquid nitrogen by filtering through blue roll into a clean dry dewar every five samples will reduce the risk of flocculent ice. A tall dewar should be used because flocculent ice tends to sink in liquid nitrogen.

16.3.4 Data Collection Strategies

Data collection strategies depend on the type of available X‐ray source and goniometry [43–45]. Many laboratories have stopped investing in in‐house X‐ray facilities, because of the current excellent access to synchrotrons and the high recurrent cost of maintaining in‐house facilities; therefore, much of the following concerns synchrotron data collection strategies. The primary goal is normally to obtain a complete diffraction dataset to the highest resolution possible while avoiding data corruption through radiation damage. The more brilliant the incident X‐ray beam, the stronger is the signal. A bigger crystal increases the signal but may have more internal defects, such as higher mosaic spreads, and a better sample may be required. Each crystal has an inherent diffraction limit and increasing the X‐ray dose will not result in higher resolution; instead poorer quality data will be collected because of radiation damage.

The following discussion focuses on ‘normal’ crystallographic problems. The challenges posed by very large unit cells and crystals exquisitely sensitive to radiation damage (e.g. membrane proteins, viruses and the ribosome) are not covered here, and the reader should consult an excellent recent review that addresses these problems and how they can be overcome [46].

16.3.4.3 Sacrificial Sample

If more than one similar sample is available, one crystal can be ‘sacrificed’ by assessing its radiation sensitivity on the synchrotron beamline so that the user can use exposure and transmission settings that are close to what the next sample is likely to tolerate. In addition to the potential loss of a sample through mishandling, a sacrificial crystal means that several samples of the same crystal should be sent to each synchrotron trip. Fortunately, the universal puck system can hold up to 112 samples in a dry shipper (Figure 16.16) and higher density systems are becoming available.

16.3.5 Native Data Collection, Molecular Replacement and Ligand Soaks

The simplest structures to solve have the simplest data collection requirements. The data collection requirements are low when the structure is already known and the experimental question is ‘How does this small molecule bind to my protein?’ or ‘How does this mutation affect the protein structure?’ The aim is to collect complete, as high resolution data as possible without compromising data quality. The signal‐to‐noise ratio is set by the exposure time and transmission per image and the overall dose should be pushed close to the Henderson limit. The resolution should be below 2 Å to observe most of the ordered water molecules that play important roles in mediating protein–ligand complexes. The data completeness ought to exceed 90–95% and the data redundancy, the number of times single reflections have been recorded, can be as low as 2–3. In molecular replacement, the data should be complete and well‐recorded and it would be better to double the redundancy and ensure 100% completeness for the loss of 0.2 Å in resolution. These important parameters are all defined in the data collection strategy.

16.3.6 Data Processing

After the data have been collected the intensities of all reflections measured are averaged. Friedel pairs for anomalous scattering have to be separated. The occasional rogue reflection, which might have impinged upon the detector at the same place as an ice ring or at the junction between panels in a mosaic detector, has to be recognised and discarded. Synchrotron beamlines usually have semi‐automatic, background‐running routines for data processing. It is probably unnecessary to repeat the data processing manually for simple structure solutions unless data need to be trimmed because of radiation damage, for instance. However, for more difficult structure solutions, indexing, integration and scaling routines should be re‐run and optimised. At this juncture, the structure will be solved by difference Fourier methods, molecular replacement, experimental phasing or potentially by direct methods (which is deliberately not discussed further as it is a procedure beyond the scope of this chapter) and each of the other methods is described briefly in sections 16.3.6.1 to 16.3.6.3.

16.3.7 Model Building and Refinement

The model is subjected to alternating cycles of refinement (e.g. Refmac [90], Phenix.refine [53], Buster [91], SHELXL [92]) and rebuilding (e.g. Coot [20]) no matter how the structure was solved. Automated routines found in ArpWarp [93], Phenix autobuild [53] and Buccaneer [94] can expedite refinement by autobuilding the protein chain, thus removing the subjectivity of the human eye, and can add ordered solvent molecules. Though these routines are robust and reliable for building the protein chain, nothing beats an experienced eye when solving sporadic crystallographic molecular puzzles. Unexpected electron density ‘blobs’ that correlate to molecules from the crystallisation solution, cryoprotectant, or purification conditions that have serendipitously co‐crystallised with the protein often inform on the biochemistry of the target [e.g. 95]. There are substantial differences in the level of detail provided by the model dependent upon the resolution and the quality of the data from which it is built and many refinement protocols can be followed, but there is insufficient space here to go into details. Briefly, a model refined with low resolution data (>3 Å) will benefit from conservative protocols such as rigid body refinement and NCS restraints if possible. Less conservative approaches can be used at high resolution (<1.5 Å), including approaches more typical of chemical crystallography [92]. B factors can be modelled anisotropically for which there should be at least six times the number of non‐H atoms in the asymmetric unit as there are unique reflections in the dataset. For multidomain proteins the TLS protocol can be advantageous and there are on‐line resources (http://skuld.bmsc.washington.edu/∼tlsmd) to generate TLS groups. Ordered water molecules and bound ligands should be built as late on in the refinement process as possible in order to avoid biasing the model.

Broad consensus on how best to model disorder has yet to be reached. Alternative conformations can generally be modelled at high resolution and limited information on the position of long side chains such as lysines and arginines is common because of their disorder. The disordered atoms can be removed from the model, but users of the PDB who are not crystallographers may not notice and may even mistake affected residues for alanine. Alternatively, the occupancy of disordered atoms can be set to zero and so will be ignored during refinement, but the naïve PDB user will not easily notice this. Finally, the B factor of the disordered atoms can be allowed to rise to meaningless values (e.g. above 100 Ų); the PDB user must display B factors while viewing the protein to identify disordered regions that have been treated in this way, which is trivial for the popular graphics programmes PyMol (https://pymol.org) and CCP4MG [96].

Refinement is completed when every feature in the electron density map is accounted for rather than fixating on a target final R _work/R _free. These values report on the global fit of the model to the data and the ambition is to lower them throughout refinement. If the data are being interpreted correctly, both R _work and R _free will diminish. If the R _free rises, the model is probably being overfitted or fitted incorrectly to the data. However, it is impossible to account for everything in every structure and those parts of the electron density that cannot be explained rationally should not be modelled. Towards the end of the refinement, strong peaks in the difference map should have been accounted for and the electron density contour level displayed should be adjusted to avoid looking only at noise. Throughout refinement a variety of geometrical parameters are reported, including the root mean square deviation for bond angles and bond length, and it is generally accepted that these should be no more than 2° and 0.02 Å, respectively. Weighting schemes within refinement packages may be adjusted to ensure that these values remain close to the accepted target. Model building is completed when the electron density is interpreted to the best of the user's knowledge. The deviance of the geometry and other reliability indicators of the structure from well‐refined models in the PDB of the same resolution should give rise to concern, a comparison that can be achieved with the polygon tool in Phenix [97].

16.4.1 Molecular Replacement, the Latest Automated Software Approaches and Drug Discovery

A drug discovery project, either at the fragment screening stage or during medicinal chemistry compound optimisation, requires a steady source of good quality crystals that diffract better than 2 Å to infer useful information about the binding mode of the ligand, the involvement of ordered water molecules and to track conformational changes in the protein. The crystal's solvent channels must allow molecules to access the ligand‐binding site if soaking experiments are used instead of co‐crystallisation. The crystal form should be robust to withstand organic solvents, such as DMSO, which may be required to solubilise the ligand. Whether co‐crystallisation or soaking approaches are used will depend upon the project and the equipment available. For example, ligands can be dispensed using ultrasound with the Labcyte Echo instruments, which dispense very small volumes of potentially rare or expensive ligands in a high‐throughput, highly automated fashion [98]. Hundreds of diffraction datasets might be collected over the course of a typical drug discovery project and to support such projects in academia the Structural Genomics Consortium and Diamond Light Source have developed the LabXChem pipeline, which allows hundreds of samples to be mounted in a day using robotics. The crystal mounts can be handled on any synchrotron beamline and the dedicated XChem beamline, I04‐1, has been designed specifically to handle high throughput projects. More details can be found on the beamline's home page (www.diamond.ac.uk/Beamlines/Mx/I04‐1.html). With automated sample centring, the whole experiment, from crystal mounting to structure solution, can be performed with little user intervention. Over the past decade many synchrotron sites have developed software pipelines to process data automatically. Space limitations do not permit a complete description of these pipelines, but the user uploads essential information (protein sequence, PDB search model, cell dimensions, space group) for each project to the IspyB database [99]. Xia2 [51] and Dimple [100] routines can be invoked for an automatic structure solution. The presence of bound ligands can be detected automatically using PanDDa [101], obviating the need to inspect manually hundreds of solutions that, in the case of fragment‐based screening, contain no bound molecule.

16.4.2 Use of Sulphur as an Anomalous Scatterer for Solving the Phase Problem

The first protein structure solved by SAD measurements was crambin [62], but the methodology has moved on considerably in the intervening 30 years, so to be current we summarise here the recent structure determination by sulphur‐SAD of a biofilm‐degrading endonuclease, NucB [59]. NucB is a 12 kDa protein with four sulphur atoms from two cysteines in a disulphide and two methionines. The crystals used for phasing and high resolution refinement were obtained from different conditions, but both were used directly from initial robotic screens without subsequent optimisation. Both conditions contained PEGs, so reservoir solutions were supplemented with 20% PEG 400 for cryoprotection. The anomalous scattering data for phasing were collected on the Diamond microfocus beamline, I24. The X‐ray energy was set to 6500 eV (1.907 Å), which represents a compromise between a low energy for maximising the anomalous differences and the absorption of the crystal's scattering by air. With improvements in both hardware and software since these data were collected, 7500 eV should now be used. Though the data were collected on a microfocus beamline, the beam dimensions were 50 μm × 50 μm and the microfocus capabilities of the beamline were not used. The photon flux of I24 is one order of magnitude above the standard macromolecular beamlines at Diamond and a 9% beam transmission, 0.1° oscillations with 100 ms exposure times were used. The beamline did not have a multiaxis goniometer at the time of data collection so 999° of data were collected to increase data redundancy to 32‐fold for accurate measurement of weak anomalous differences. The crystals diffract much further than the 2.26 Å limit imposed in this phasing experiment in which data quality was the primary driver and a useful anomalous signal was maintained to the resolution cut‐off. The positions of the four sulphur atoms were found using ShelXD [102] from which initial phases were obtained. High resolution data, to 1.35 Å, were subsequently collected on the same P4₁2₁2 crystal form, but from a crystal grown under different crystallisation conditions. The experimental phases were extended to the high resolution and the model was built automatically with ArpWarp [93]. The data collection and refinement statistics for the NucB structure solution can be found in Basle et al. [59] and we have plotted some of the validation results from this structure as an example of the tools that are available to assess PDB model quality (Figure 16.17).

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Further Reading

1. Blow, D. (2002). Outline of Crystallography for Biologists. Oxford University Press.
2. Chayen, N., Helliwell, J., and Snell, E. (2010). Macromolecular Crystallization and Crystal Perfection. Oxford University Press.
3. Methods in Enzymology Volume 276. Carter, C. Jr. and Sweet, R. (eds.) (1997). Macromolecular Crystallography, Part A. Academic Press.
4. Methods in Enzymology Volume 277. Carter, C. Jr. and Sweet, R. (eds.) (1997). Macromolecular Crystallography, Part B. Academic Press.
5. Methods in Enzymology Volume 358. Carter, C. Jr. and Sweet, R. (eds.) (2003). Macromolecular Crystallography, Part C. Academic Press.
6. Doublie, S. (2007). Macromolecular Crystallography Protocols, Volume 2: Structure Determination. Humana Press.
7. Rupp, B. (2010). Biomolecular Crystallography: Principles, Practice and Application to Structural Biology. Garland Science.
8. Sherwood, D. and Cooper, J. (2010). Crystals, X‐rays and Proteins. Oxford University Press.